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Interactions in microwave adhesive bonding of polymers and composites

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INTERACTIONS IN MICROWAVE ADHESIVE BONDING OF POLYMERS AND
COMPOSITES
By
Shuangjie Zhou
A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemical Engineering and Materials Science
2002
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UMI Number: 3 1 8 9 7 8 9
Copyright 2002 by
Zhou, Shuangjie
All rights reserved.
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ABSTRACT
INTERACTIONS IN MICROWAVE ADHESIVE BONDING OF POLYMERS AND
COMPOSITES
By
Shuangjie Zhou
Microwave processing of advanced materials has been studied as an attractive
alternative to conventional processing. In this dissertation, work was performed in two
sections. The first section was a process study and focused on applying microwave
theories to develop an integrated microwave adhesive bonding system in a single mode
applicator with non-invasive on-line monitoring and precise controlling features. The
second section was a fundamentals study and focused on investigating microwave
heating mechanism to provide explanations for rapid bonding using microwaves.
A single mode microwave heating method was first applied in adhesive bonding
process. The microwave heating mode was chosen based on theoretical computation and
experimental characterization so that the adhesive was placed at the strongest electric
field. Rapid and selective heating of the adhesive was observed. However, only limited
material size could be uniformly heated with single mode microwave method because of
the non-uniform electric field distribution. To solve this problem, a variable frequency
mode switching method (switch between modes with complementary heating patterns)
was used to improve the bonding uniformity of large-size materials. Theoretical heating
modes were applied in this process. A control system was developed to provide rapid,
stable, and uniform bonding by adjusting microwave power and frequency. The control
software was programmed with Lab VIEW. To determine the bonding cycle on-line, a
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new method (with corresponding software) was invented based on microwave theories
and experimental discoveries. Compared with thermal adhesive bonding, the microwave
method reduced the bonding cycle vastly and obtained equal or even higher bonding
strength for the materials used in this research.
The reduction in bonding cycle resulted from faster curing of the epoxy adhesive
with microwaves. The phenomenon of microwave fast curing of epoxy was investigated
with a new method by studying the effect of carbon additive on microwave curing of
epoxy. It was hypothesized that during microwave curing, carbon absorbed most of the
microwaves and weakened the localized superheating of the epoxy functional groups. If
localized superheating were the main mechanism of rate enhancement in microwave
curing of epoxy, then the curing rate should decrease at the presence of carbon.
Microwave curing experiments were carried out at three temperatures with various
carbon concentrations. New correlations for reaction rate constants as functions of carbon
concentration and temperature were proposed. Results showed microwave curing rate
decreased with increasing carbon concentration. Thus, this study suggested reaction rate
enhancement in microwave curing of epoxy result from localized superheating of the
functional groups. However, the carbon particles used in this study were activated and
might adsorb the amine from the epoxy resin because carbon particles might have higher
temperature than the bulk resin in microwave curing. This will result in decrease in
microwave curing rate. Further study is required to elucidate this problem. In addition, at
higher carbon concentration, the required microwave power was lower to maintain the
same bulk temperature. This might also result in decrease in microwave curing rate at
higher carbon concentration.
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Copyright by
Shuangjie Zhou
2002
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ACKNOWLEDGEMENT
I would like to thank my advisor Dr. Martin C. Hawley for his invaluable
guidance during this research. I also acknowledge Dr. Leo Kempel, Dr. Lawrence Drzal,
Dr. Greg Baker, Dr. Christian Lastoskie, and Dr. Jianghua Wei, for their many insightful
suggestions. I am also grateful to Mr. Mike Rich and Mr. Kelby Thayer for their very
helpful training in equipment operation and advice in designing material testing
procedures. Acknowledgement is extended to Dr. Richard Schalek and Dr. Per Askeland
for analyzing the surface of carbon particles and carbon filled epoxy resins. Finally, I
thank my husband Kun for his endless love and support throughout this work.
v
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TABLE OF CONTENTS
LIST OF FIGURES.....................................................................................................................xi
LIST OF TABLES.....................................................................................................................xvi
CHAPTER 1 INTRODUCTION.............................................................................................. 1
1.1
Advantages of Microwave Heating over Thermal Process..........................2
1.2
Literature Survey................................................................................................ 5
1.3
Research T o p ics..................................................................................................8
CHAPTER 2 BACKGROUND FOR MICROWAVE H EA TIN G ................................... 11
2.1
Electromagnetic Fields in a Microwave Enclosure......................................11
2.1.1
M axwell’s Equations...........................................................................................11
2.1.2
Resonant Modes in a Cylindrical Single Mode C avity................................. 14
2.1.3
Electromagnetic Fields in a Cylindrical Single Mode Cavity...................... 17
2.2
Microwaves/Materials Interactions................................................................... 19
2.2.1
Mechanisms of Microwave/Materials Interactions........................................ 19
2.2.2
Dielectric Properties............................................................................................21
2.3
Applications of Microwave E nergy..................................................................25
2.4
Microwave A pplicators.......................................................................................29
2.5
Temperature sensing system ..............................................................................30
CHAPTER 3 SINGLE MODE MICROWAVE ADHESIVE B O N D IN G ....................... 32
3.1
Introduction........................................................................................................... 32
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3.2
Experim ental....................................................................................................... 35
3.2.1
Experimental C ircuit.......................................................................................... 35
3.2.2
M aterials................................................................................................................37
3.2.3
Method of Dielectric Property Measurement.................................................. 37
3.2.4
Sample Setup and Preparation for Adhesive Bonding...................................39
3.3
Results and Discussion....................................................................................... 41
3.3.1
Material Dielectric Properties........................................................................... 41
3.3.2
Characterization of Empty Cavity..................................................................... 42
3.3.3
Characterization of Loaded Cavity and Mode D iagnosis.............................. 44
3.3.4
Single Mode Microwave Adhesive B onding..................................................52
3.3.5
Comparison between single mode microwave and thermal adhesive
bonding in terms of bonding time and strength............................................. 53
3.4
Conclusions.......................................................................................................... 58
CHAPTER 4 VARIABLE FREQUENCY MODE-SWITCHING MICROWAVE
ADHESIVE BO N D IN G ...................................................................................60
4.1
Introduction.......................................................................................................... 60
4.2
Experim ental........................................................................................................ 62
4.2.1
Circuit for Microwave Adhesive Bonding.......................................................62
4.2.2
M aterials................................................................................................................ 62
4.2.3
Sample Setup and Preparation for Adhesive B onding................................... 63
4.3
4.3.1
Results and Discussion........................................................................................ 65
Characterization of Loaded C av ity................................................................... 65
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4.3.2
Mode Diagnosis and Selection of Modes for Mode-switching....................67
4.3.3
Algorithm of Mode-switching........................................................................... 69
4.3.4
Heating Profile of Variable Frequency Mode-switching Adhesive Bonding
and Comparison with Thermal Process.......................................................... 73
4.3.5
Study of Adhesive Curing in Mode-Switching Microwave Process and
Comparison with Thermal Curing................................................................... 78
4.3.6
Comparison of Bond Strength between Mode-Switching Microwave and
Thermal Bonding Processes............................................................................. 82
4.4
Conclusions..........................................................................................................85
CHAPTER 5 IN SITU MONITORING OF VARIABLE FREQUENCY MICROWAVE
PROCESSING IN A SINGLE MODE C A V IT Y .........................................87
5.1
Introduction.......................................................................................................... 87
5.2
Advantages O f This Technique......................................................................... 89
5.3
On-line Monitoring of Microwave Adhesive Bonding of Single-Lap
Bexloy W 502/ Eccobond A 401-37.................................................................90
5.3.1
Experim ental........................................................................................................90
5.3.2
Results and Discussion....................................................................................... 91
5.4
On-line Monitoring of Microwave Adhesive Bonding of Single-Lap
Surlyn SG201U / Eccobond A401-37.............................................................94
5.4.1
Experim ental........................................................................................................ 94
5.4.2
Results and Discussion........................................................................................94
5.5
On-line Monitoring of Microwave Adhesive Bonding of Double-Lap
Bexloy W502/ Eccobond A 401-37.................................................................96
5.5.1
Experi menta 1.........................................................................................................96
5.5.2
Results and Discussion........................................................................................ 98
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5.6
Conclusions........................................................................................................ 101
CHAPTER 6 PROCESS CONTROL SYSTEM FOR MICROWAVE ADHESIVE
B O N D IN G ........................................................................................................ 102
6.1
Introduction........................................................................................................ 102
6.2
Structure of the Process ControlSystem for Microwave Adhesive Bonding
.............................................................................................................................104
6.3
Program for Cavity Characterization..............................................................106
6.4
Program for Process Control............................................................................ 106
6.4.1
Subprograms for Data Acquisition.................................................................. 107
6.4.2
Subprograms for Mode-Switching.................................................................. 107
6.4.3
Subprograms for Microwave Power C ontrol................................................108
6.4.4
Subprogram for On-line M onitoring.............................................................. I l l
6.5
Conclusions........................................................................................................ 112
CHAPTER 7 INVESTIGATION OF MICROWAVE HEATING MECHANISM VIA
STUDY OF MICROWAVE CURING OF EPOXY FILLED WITH
CA RBO N .......................................................................................................... 113
7.1
Introduction........................................................................................................ 113
7.2
Hypothesis of Carbon Effect on Microwave Curing.................................... 115
7.3
Epoxy Curing K inetics......................................................................................116
7.3.1
Kinetics study of thermal curing of neat re s in .............................................. 117
7.3.2
Kinetics study of thermal curing of filler-added resins................................121
7.3.3
Kinetics study of microwave curing of neat resin.........................................124
7.4
Kinetics Model Used in this Study.................................................................. 125
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7.5
Experim ental...................................................................................................... 127
7.5.1
Materials and Sample Preparation................................................................... 127
7.5.2
Experimental Setup for Microwave C uring................................................. 128
7.5.3
Dielectric M easurem ent................................................................................... 129
7.5.4
Cavity Characterization.....................................................................................131
7.5.5
Process Control Strategy and Temperature Profile in Microwave Heating
.............................................................................................................................132
7.6
Results and Discussion...................................................................................... 134
7.6.1
Microwave Power Deposition During Heating and Curing.........................134
7.6.2
Comparison of Reaction Rates between Microwave and Thermal Curing
of Neat and Doped Resins.............................................................................. 137
7.7
Conclusions......................................................................................................... 153
CHAPTER 8 CONCLUSIONS..............................................................................................155
CHAPTER 9 FUTURE W O R K .............................................................................................163
APPENDIX A. MATLAB PROGRAM FOR CALCULATING THE MODE PATTERN
OF TM022 INSIDE THE EMPTY C A V ITY ...............................................178
APPENDIX B. LABVIEW PRO G RA M S........................................................................... 180
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LIST OF FIGURES
Figure 1.1 Temperature Profile in Microwave or Thermal Heating [1]................................3
Figure 1.2 Illustration of Microwave Adhesive Bonding........................................................ 6
Figure 2.1 TE Modes in an Empty Cavity with Diameter of 17.78cm............................... 16
Figure 2.2 TM Modes in an Empty Cavity with Diameter O f 17.78cm .............................16
Figure 2.3 Cylindrical Single-Mode Resonant C avity.......................................................... 30
Figure 3.1 Circuit of Microwave Adhesive B onding.............................................................36
Figure 3.2 Sample Setup and Temperature Measuring Points in Single Mode Microwave
B onding.................................................................................................................................40
Figure 3.3 Characterization of Empty C av ity ........................................................................ 43
Figure 3.4 Reflectance in Cavity Loaded with Samples (Sample Width of 1")................ 45
Figure 3.5 Heating Rate at Different Frequencies..................................................................46
Figure 3.6 Dimension of the Adhesive and Location of Temperature Probes...................48
Figure 3.7 Experimental Temperature D istribution...............................................................48
Figure 3.8 Experimental Configuration for Measurement of Half Wave Number Q
49
Figure 3.9 Measurement of the Half Wave Number Q ......................................................... 50
Figure 3.10 Electric Field Distribution of TM022 Mode at the Cross-Section of the
Cavity (Lighter Region Represents Higher Electric Field Strength).......................... 51
Figure 3.11 Temperature Profile during Single Mode Microwave Adhesive B onding...52
Figure 3.12 Strength of the Assemblies Bonded at Different Conditions.......................... 54
Figure 3.13 Load-Elongation Curves of Assemblies Bonded under Different Conditions
.................................................................................................................................................56
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Figure 4.1 Sample Setup and Temperature Measuring P oints.............................................63
Figure 4.2 Characterization of Loaded Cavity (Sample Size: 93.6 x 76.2 x 6.06mm3)... 66
Figure 4.3 Characterization of Heating Patterns of Modes 1 And 2 ................................... 68
Figure 4.4 Measurement of H alf Wave Number Q ................................................................70
Figure 4.5 Theoretical E Field Patterns in the Empty C av ity ..............................................71
Figure 4.6 Dimension of the Adhesive inside the Cavity......................................................72
Figure 4.7 Power Deposition in Mode-Switching Adhesive Bonding of Bexloy at 110 °C
................................................................................................................................................ 74
Figure 4.8 Power Deposition in Mode-Switching Adhesive Bonding of Bexloy at 120 °C
................................................................................................................................................ 74
Figure 4.9 Temperature Profile in Mode-Switching Bonding of Bexloy at 110 ° C ......... 75
Figure 4.10 Temperature Profile in Mode-Switching Bonding of Bexloy at 120° C ........75
Figure 4.11 Temperature Profile in Thermal Bonding of Bexloy at 120 °C ......................76
Figure 4.12 Temperature Measuring Points for the Eccobond/Surlyn Assembly (Top
V iew )..................................................................................................................................... 77
Figure 4.13 Temperature Profile in Mode-Switching Bonding of Surlyn at 100 ° C
78
Figure 4.14 Adhesive Extent of Cure vs. Time in Microwave Process of 6 Minutes of
Heat up and Then Isothermally at 110°C.........................................................................79
Figure 4.15 Adhesive Extent of Cure vs. Time in Microwave Process of 8 Minutes of
Heat up and Then Isothermally at 120°C.........................................................................80
Figure 4.16 Adhesive Extent of Cure vs. Time in Thermal Heating of 30 Minutes Heat
up and Then Isothermally at 110°C...................................................................................81
Figure 4.17 Adhesive Extent of Cure vs. Time in Thermal Heating of 40 Minutes Heat
up and Then Isothermally at 120°C...................................................................................81
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Figure 5.1 Shifting of Resonant Frequency in Microwave Adhesive Bonding of SingleLap Bexloy Substrates at 110°C .......................................................................................92
Figure 5.2 Shifting of Resonant Frequency in Microwave Adhesive Bonding of SingleLap Bexloy Substrates at 120°C .......................................................................................93
Figure 5.3 Shifting of Resonant Frequency in Microwave Adhesive Bonding of SingleLap Surlyn Substrates at 100°C ........................................................................................95
Figure 5.4 Sample Setup of Double-Lap Shear Assembly..................................................97
Figure 5.5 Temperature Profile in Microwave Adhesive Bonding of Double-Lap Shear
Assembly of Bexloy Substrates.........................................................................................98
Figure 5.6 Shifting of Resonant Frequency in Microwave Adhesive Bonding of DoubleLap Bexloy Substrates at 120°C .....................................................................................100
Figure 6.1 Temperature Oscillation for Determining Ku and T u.......................................110
Figure 7.1 Microwave Interactions with Carbon Black and Epoxy.................................. 116
Figure 7.2 Mode Spectrum o f Loaded Cavity for Microwave Curing..............................132
Figure 7.3 Temperature Profiles during Microwave Heating and Curing at 145, 165 and
185°C................................................................................................................................... 133
Figure 7.4 Power Curves during Microwave Heating and Curing.................................... 136
Figure 7.5 Total Energy Consumed by Each Resin System in the First 60 Minutes of
Microwave H eating........................................................................................................... 137
Figure 7.6 Thermal Curing at 145°C...................................................................................... 139
Figure 7.7 Thermal Curing at 165°C...................................................................................... 140
Figure 7.8 Thermal Curing at 185°C...................................................................................... 141
Figure 7.9 Microwave Curing at 14 5 °C .................................................................................142
Figure 7.10 Microwave Curing at 165°C.............................................................................. 143
Figure 7.11 Microwave Curing at 185°C.............................................................................. 144
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Figure 7.12 Effect of Carbon Concentration on Thermal Curing R ates...........................148
F igure 7.13 Activation Energy in Thermal C uring.............................................................. 149
Figure 7.14 Effect of Carbon Concentration on Microwave Curing Rates...................... 150
Figure 7.15 Activation Energy in Microwave Curing......................................................... 151
Figure B .l Hierarchy of the Labview Program s.................................................................. 181
F igure B.2 Front Panel of the Cavity Characterization Program .......................................182
Figure B.3 Diagram of the Cavity Characterization Program ............................................ 183
Figure B.4 Front Panel for Variable Frequency Mode-Switching Process Control........184
F igure B.5 Diagram for Variable Frequency Mode Switching Process Control (Part 1)
.............................................................................................................................................. 185
Figure B.6 Diagram for Variable Frequency Mode-Switching Process Control (Part 2)
186
Figure B.7 Front Panel for 6t.Vi..............................................................................................187
F igure B.8 Diagram for 6 t.V i.................................................................................................. 188
Figure B.9 Front Panel for Luxtron.Vi...................................................................................189
F igure B.10 Diagram for Luxtron.V i..................................................................................... 189
Figure B .ll Front Panel for Nortech.Vi.................................................................................190
F igure B.12 Diagram for N ortech.V i..................................................................................... 190
Figure B.13 Front Panel for Pow er.V i...................................................................................191
Figure B.14 Diagram for Pow er.V i........................................................................................ 191
Figure B.15 Front Panel for Mode-Switch.Vi.......................................................................192
F igure B.16 Diagram for M ode-Switch.Vi........................................................................... 193
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Figure B.17 Front Panel for Power C ontrol.V i.................................................................... 194
Figure B.18 Diagram for Power Control.Vi..........................................................................195
Figure B.19 Front Panel for Heat Rate.V i............................................................................. 196
Figure B.20 Diagram for Heat R ate.V i................................................................................. 196
Figure B.21 Front Panel for P id .V i........................................................................................ 197
Figure B.22 Diagram for Pid.V i..............................................................................................198
Figure B.23 Front Panel for Pid Parameters.Vi.................................................................... 199
Figure B.24 Diagram for Pid Param eters.Vi........................................................................ 199
Figure B.25 Front Panel for Frequency Diagnosis.Vi.........................................................200
Figure B.26 Diagram for Frequency D iagnosis.V i............................................................. 201
Figure B.27 Front Panel for F-W rite.V i................................................................................202
Figure B.28 Diagram for f-w rite.V i.......................................................................................202
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LIST OF TABLES
Table 1.1 Comparison of Microwave Heating with Thermal M ethod..................................3
Table 3.1 Dielectric Properties of the M aterials..................................................................... 41
Table 3.2 Theoretical and Experimental Values of the Resonant Frequencies of Several
M odes....................................................................................................................................44
Table 3.3 Break Pattern of Microwave Bonded Assemblies................................................ 55
Table 3.4 Break Pattern of Thermally Bonded A ssem blies................................................. 56
Table 4.1 Summary of Mode D iagnosis.................................................................................. 72
Table 4.2 Comparison between Mode-Switching and Thermal Curing at 110°C and
120°C..................................................................................................................................... 82
Table 4.3 Bond Strength of Eccobond/Bexloy Assembly with Microwave or Thermal
M eth o d ..................................................................................................................................84
Table 4.4 Bond Strength of Eccobond/Surlyn Assembly with Microwave or Thermal
M ethod .................................................................................................................................. 84
Table 5.1 Microwave Adhesive Bonding Processes to Be Studied with the on-Line
Monitoring Technique.........................................................................................................89
Table 5.2 Bond Strength of Microwave Bonded Double-Lap Shear Assem blies
100
Table 6.1 PID Controller Parameters for Single Mode Microwave Adhesive Bonding 111
Table 6.2 PI Controller Parameters for Variable Frequency Mode Switching Bonding 111
Table 7.1 Total Heat of Reaction per Gram of Resin of the Fresh S am ples.................... 128
Table 7.2 Dielectric Constants of the M aterials
......................................................... 130
Table 7.3 Dielectric Loss Factors of the M aterials............................................................... 131
Table 7.4 PID Controller Parameters Obtained with Ziegler-Nichols M ethod................133
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Table 7.5 Average Standard Deviations of the Extent of C u re.......................................... 138
Table 7.6 Values of M and N .................................................................................................. 138
Table 7.7 Reaction Rate Constants of Microwave and Thermal Curing of Neat Resin. 145
Table 7.8 Coefficients D's for Thermal C uring.....................................................................147
Table 7.9 Coefficients D's for Microwave C uring............................................................... 152
Table B .l Functions of the Labview Program s.................................................................... 180
x vii
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CHAPTER 1 INTRODUCTION
In this research, work was performed in two sections. The first section was a
process study and focused on applying microwave theories to develop an integrated
microwave adhesive bonding process in a single mode applicator with non-invasive on­
line monitoring and precise controlling features. The second section was a fundamentals
study and focused on the investigation of microwave heating mechanisms to provide
explanations for rapid bonding with microwaves.
Microwave refers to electromagnetic waves in the frequency range from 300MHz
to 300GHz or the characteristic wavelength range from lm to 1mm. Heating is one of the
major non-communication applications of microwave energy. The fundamental
electromagnetic property of nonmagnetic materials for microwave heating and diagnosis
is complex permittivity (e* = e - je ). The real part of the complex permittivity is
permittivity 8 (dielectric constant), which is related to the energy stored in the materials.
The imaginary part of the complex permittivity is loss factor e , which is related to energy
dissipated as heat in the materials. The loss factor of materials is generally due to
contributions by dielectric loss factor (the motion of dipoles) and conductivity (the
motion of charges). Thermoplastic and thermoset polymers, typical dielectric materials,
have polar groups to interact with electromagnetic fields and exhibit dielectric relaxation
at microwave frequencies, ranging from epoxide groups, hydroxyl groups, amino groups,
and so on. These polar groups can directly absorb microwave energy. The localized
heating on the reactive polar sites can initiate or promote reactions that require heat.
1
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1.1 Advantages of Microwave Heating over Thermal Process
Microwave processing of advanced materials has been studied as an attractive
alternative to conventional thermal processing. Thermal heating is a surface-driven, nonselective process. The heating efficiency is controlled by the heat transfer coefficient at
the material surface and the thermal conductivity of the materials. During thermal
heating, heat flows from the surface to the interior of the material. This tends to cause
remarkable temperature gradients in thick materials. Residual thermal stresses resulting
from large temperature gradients will reduce the physical and mechanical properties of
the materials. In addition, the production cycle is long because of the difficulty in heating
poor thermal conductors like polymers.
These problems can be solved with microwave radiation. Microwave heating
offers a number of advantages over thermal heating in a wide range of heating
applications. A comparison between microwave and thermal heating is summarized in
Table 1.1. Microwave heating is selective, instantaneous and volumetric with heat loss at
the boundaries whereas thermal heating is nonselective depending on temperature
gradient. Microwave heating can be easily controlled by very fast changes in the applied
electric field whereas thermal heating is characterized with long lag times and difficulty
for composite cure control. In microwave heating, the heat source can be readily removed
to prevent thermal excursion. Figure 1.1 shows a comparison of heating profiles between
thermal and microwave processes. Microwave heating rate is much higher and materials
can be heated to a higher temperature without causing thermal runaway. Microwave
processing has potential for rapid processing of thick-section and complex-shaped
composites.
2
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Table 1.1 Comparison of Microwave Heating with Thermal Method
Thermal
Microwave
Heating
Low, determined by heat transfer
High, energy directly coupled
Efficiency
coefficients
into materials
Selectivity
No, controlled by Temperature
Yes, determined by material
gradient
loss factor
Low, long-lag
High, microwave power level
Controllability
can be readily adjusted
300
260
O
a
230°C microwave
220
u
L-
180
<u
140
200°C thermal
190°C microwave
Q.
E
100
60
20-
20
30
40
50
60
70
80
eo
Time (m inutes)
Figure 1.1 Temperature Profile in Microwave or Thermal Heating [1]
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The advantages of microwave heating over thermal process can be easily
explained by consideration of the microwave power absorption in the material. The
microwave power absorption rate, P, (W/m3), inside a homogeneous material is shown in
Equation 1.1.
( 1. 1)
P = —ene (o
2 0
where E is the electric field strength inside the material, V/m,
0 ) is
the radian frequency, rad/sec, a»=2nf, f is the frequency in Hz,
e0 is the free space permittivity, e0=l/(367t) x 10'9 F/m,
E
is the effective relative loss factor,
e =Ed ’ +
ct/ ( eo CO),
Ed is the relative loss factor due to dipolar contributions,
o is the material conductivity, S/m.
Specifically, E is responsible for the fast heating and controllability as it can be
easily regulated by the input power;
e
is responsible for the selectivity and conversion of
energy into heat. Microwave heating is volumetric because of the penetration of the
electric field into the material. Equation 1.1 can be used with several other equations in
modeling microwave heating. These equations include M axwell’s equations for solving
the electric field strength, a heat transfer equation for obtaining the temperature
distribution inside the material, and a reaction kinetics equation for calculating extent of
reaction and reaction heat if chemical reaction occurs during the heating. Material
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thermal and dielectric properties have non-linear dependence on both temperature and
extent of reaction. These properties change during the processing, which affects the
electrical field strength and power absorption in the materials. Thus the modeling of
microwave heating is a highly coupled non-linear problem. This problem will be
discussed in more detail in Chapter 9.
1.2 Literature Survey
The application of microwave heating in polymer and composite processing has
been shown to be very promising. In polymer processing, both thermosets and
thermoplastics have been studied. The drying process of various thermoplastics with
microwave energy has been investigated [2]. Microwaves have also been used to cure
thermosetting materials, including polyesters [3][4], polyurethanes [5][6], polyimides
[7,8,9] and epoxies [1,3,10-20]. Both pulsed and continuous microwave curing of
epoxies have been studied [1,15]. In composites processing, both batch [21,22,23] and
continuous processes [15,24-28] have been studied. Demonstrated results in microwave
processing of polymers and composites include increased polymerization rate [7,11-14],
reduced drying time for pelletized polycarbonate and polypropylene [2], increased Tg for
cured epoxy [10], enhanced fiber/matrix adhesion in carbon composites [21], and
increased mechanical strength of graphite/epoxy composite [15].
In addition to the applications mentioned above, microwaves have been recently
applied in several adhesive bonding studies for polymers and composites [29-31], In
adhesive bonding, the adhesive is applied between two thick substrate panels. In
conventional thermal processes, thermal energy has to be transferred through the thick
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substrates to reach the adhesive. If the substrates are polymeric materials, the thermal
bonding cycle will be very long due to the low thermal conductivity of polymers. This
problem is solved with microwave method. Figure 1.2 is the illustration of microwave
adhesive bonding. The polymer or composite parts have low loss factors relative to the
adhesive material at the interface. Microwave energy is then directly transferred into the
interface and cures the adhesive extremely rapidly, even though the substrate materials
are very thick. Therefore, microwaves have the potential to be applied in industrial
adhesive bonding process to shorten the bonding time and thus lower the process cost.
This will be greatly beneficial for the automotive, marine and aerospace industries, where
adhesive bonding of polymers and composites has been developed as one of the leading
joining techniques. However, industrialization of a new technique requires design of
processes for specific applications, development of control and on-line monitoring
packages, and adequate understanding of process fundamentals.
Adhesives
Microwaves
> Polymer or
composite parts
Figure 1.2 Illustration of Microwave Adhesive Bonding
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Research and development regarding the application of microwaves in adhesive
bonding is still in its early stage. Several investigators have studied microwave adhesive
bonding in multi-mode applicators [29-31]. These studies demonstrated that reduced
bonding cycle was obtained with adequate bonding strength in microwave process
compared with thermal bonding. However, the mechanism of bonding cycle reduction
was not proposed. In addition, these studies did not investigate the relation of microwave
heating characteristics (e.g. uniformity, selectivity, and rapidity) with the electromagnetic
field patterns and material dielectric properties. Moreover, detailed control and on-line
monitoring issues were not considered in these studies.
Process fundamentals can be more conveniently studied in a single mode resonant
applicator compared with a multi-mode applicator. Unlike multi-mode applicator, where
several modes are excited at the same time [32], a single mode applicator supports only
one mode at a time. The electric field patterns inside the single mode applicator are more
controllable and predictable. In addition, single mode applicators are more efficient in
coupling microwave energy into materials compared with multi-mode applicators. This
has been shown in the processing of crossply and thick-section graphite fiber reinforced
composites [22,23]. If adhesive bonding is conducted in a single mode applicator, the
joint area can be placed at the location with the highest electric field strength. This will
further enhance the selective heating of the adhesive.
In a single mode applicator, uniform heating of large size materials can be
achieved with mode-switching method. Adegbite [33] developed a method to obtain
uniform processing in fixed frequency microwave processing. Fellows et al. [34] used
fixed frequency mode switching technique to process V-shaped polyester/glass composite
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parts. However in fixed frequency microwave processing, slow mechanical adjustment of
cavity length for mode switching resulted in instability of temperature and non-uniform
temperature distribution. With the use of a variable frequency microwave power source,
Qiu [35] developed a variable frequency mode switching method for polymer and
composite processing with microwaves. This technology provided more uniform and
stable processing of composite parts compared with fixed frequency mode switching.
However, empirical heating modes were used in the processing. This resulted in
extensive heating characterization and data storage both before and during the processing.
Thus the variable frequency mode switching method needs to be further improved to
solve this problem.
A process control system has been built for microwave variable frequency mode
switching processing in a single-mode cavity [35]. In controlling processing temperature,
both a simple parabolic power controller and a multi-staged PID controller were used for
microwave power control. However, empirical controller parameters were used and
extensive experimental work was needed to find the parameters whenever there was a
change in material setup. In addition, on-line monitoring of the processing was not
considered.
1.3 Research Topics
To summarize the literature survey, research and development in microwave
adhesive bonding is still in its early stage. Several researchers studied this process in
multimode applicators. Results demonstrated that reduced bonding cycle was obtained
with adequate bonding strength in microwave process compared with thermal bonding.
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However, the mechanism of bonding cycle reduction was not proposed. In addition, these
studies did not investigate the fundamental relation of microwave heating characteristics
with the electromagnetic field patterns and material dielectric properties. Moreover,
detailed control and on-line monitoring issues were not considered in these bonding
studies. Some recent studies on microwave processing of composites have developed
methods for controlling the temperature distribution. However, the processing and control
methods were developed with empirical trial and error approaches. These methods are
time-consuming and effort demanding when being generalized to different applications.
Inadequate understanding of process fundamentals and inefficient control and monitoring
methodologies are the major obstacles in industrializing a new technique.
These problems will be addressed in this dissertation. Microwave theories will be
used as a guidance to solve real processing problems. A single mode applicator will be
used to study the microwave adhesive bonding process. There are two major reasons for
using a single mode applicator. First, single mode applicators are more efficient in
coupling microwave energy into materials compared with multi-mode applicators. This
has been shown in the processing of crossply and thick-section graphite fiber reinforced
composites. Second, Process fundamentals can be more conveniently studied in a single
mode applicator compared with a multi-mode applicator. The electromagnetic field
patterns inside the single mode applicator are more predictable and controllable. So
microwave theories can be more conveniently used in the computation of field
distribution and the design of processing, control and on-line monitoring methods.
The first focus of this research is to develop a precisely controlled, rapid and
uniform microwave adhesive bonding system with on-line monitoring feature of the
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bonding process in a single mode applicator. The second focus is to investigate the rapid
curing of the adhesive components to reveal microwave heating mechanisms, thermal or
non-thermal.
The research efforts include the assembly of experimental components,
implementation and development of uniform heating methods, development of process
controller based on control theory, and invention of an on-line monitoring technique to
determine the bonding cycle. Special microwave effects observed in microwave adhesive
bonding are further studied to improve understanding in microwave/material interactions
and in microwave heating mechanisms (thermal or non-thermal).
Specifically the following tasks are proposed to support the objective:
1. Assemble Experimental Setup for Microwave Adhesive Bonding
2. Explore the Application of Microwaves in Single Mode Adhesive Bonding and
Compare the Results with Thermal Process
3. Implement Variable Frequency Mode-switching Method and Apply It in Adhesive
Bonding to Achieve Uniform Heating for Large Materials
4. Invent an On-line M onitoring Technique for Microwave Processing in a Single Mode
Cavity Based on Microwave Theories and Experimental Discoveries
5. Design the Process Control System Incorporating Theoretical Control Algorithms and
On-line Monitoring
6. Investigate Microwave Heating Mechanisms (Thermal or Non-thermal)
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CHAPTER 2 BACKGROUND FOR MICROWAVE HEATING
Electromagnetic field strength and distribution patterns are essential factors that
influence microwave heating efficiency and uniformity. They are determined by
microwave operating conditions, applicator dimensions, and material properties and
dimensions. To understand microwave heating characteristics, the fundamentals in
microwave heating are reviewed in this chapter.
2.1 Electromagnetic Fields in a Microwave Enclosure
2.1.1
M axw ell’s Equations
The basic laws governing electromagnetic wave propagation are Maxwell's
Equations, which describe the relations and variations of the electric and magnetic fields,
charges, and currents associated with electromagnetic waves. Maxwell's Equations can be
written in either differential or integral form. The differential form is most widely used to
solve electromagnetic boundary-value problems and is shown in the following equations.
V x E = ——
(Faraday's law)
V x H = J + ——
at
V •D = p
V •B = 0
(Am pere's law)
(Gauss law)
(Gauss law - magnetic)
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( 2 . 1)
( 2 .2 )
(2.3)
(2.4)
where E is the electric field intensity, H is the magnetic field intensity, D is the electric
displacement density or electric flux density, B is the magnetic flux density, J is the
electric current density, and p is the charge density.
D is defined as:
D = £0E + P
(2.5)
where e0 is the permittivity of free space, P is the volume density of polarization, the
measure of the density of electric dipoles.
B can be expressed as:
B= //0 (H + M)
(2.6)
where juQ is the permeability of free space, H is the magnetic field intensity, and M is the
volume density of magnetization, the measure of the density of magnetic dipoles in the
material.
In a simple isotropic medium, the field quantities are related as follows:
where s is the permittivity and p
D = £E
(2.7)
B = pH
(2.8)
is thepermeability.
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In addition to the Maxwell's Equations, the Equation of Continuity holds due to
the conservation of electric charge:
V - J + |- ^ = 0
at
(2.9)
In the Maxwell's Equations, only two are independent. Usually Equations 2.1 and
2.2 are used with Equation 2.9 to solve for electromagnetic fields.
M axwell’s equations are first-order differential equations with E and B coupled.
They can be converted into uncoupled second-order wave equations through
mathematical manipulations [36]:
( 2 . 10)
where a is the conductivity, and J s is the source current term. In a source free region,
Equations 2.10 become:
( 2 . 11)
Equations 2.1-2.4 are the time-domain representation of Maxwell's Equations. If
the source functions, J(r,t) and p ( r ,t) , oscillate with a constant angular frequency of co
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in the system, then all the fields will oscillate at the same frequency. The Maxwell’s
equations can be written in time-harmonic form:
V x E (r) = -ioM(r)
V x H(r) = j (r) + i'ryD(r)
(2 .1 2 )
V • D(r) = p ( r)
V -B (r) = 0
In time-harmonic case, Equations 2.10 become Helmholtz Equations and Equations 2.11
become Helmholtz equations in source-free region:
(2.13)
where
(2.14)
e is called the complex permittivity.
2.1.2
Resonant Modes in a Cylindrical Single Mode Cavity
In a cylindrical single mode cavity, there are two types of resonant modes,
transverse electric (TE) and transverse magnetic (TM). For TE modes, the electric field
components are transverse and the magnetic field components are parallel to the direction
of wave propagation, which is the axial direction. For TM modes, the electric field
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components are parallel and the magnetic field components are transverse to the direction
of wave propagation. Three subscripts, n, p, and q, are used to represent the physical
appearance of the correponding mode in an empty cavity, i.e. TEnpq and TMnpq. The
subscript n denotes the number of the periodicity in the circumferential direction,
n = 0,l,2 ...; p denotes the number of field zeroes in the radial direction, p = l,2 ,3 ...; q
denotes the number of half wavelengths of the equivalent circular waveguide, q = 0,l,2...
for TM modes and q = l,2 ,3 ... forT E modes.
The relationship between the frequency and cavity diameter and length for a given
resonant mode can be calculated theoretically. The equations forTE and TM modes in an
empty cylindrical single mode cavity are [37]:
(2.15)
(2.16)
where f is frequency, a is cavity diameter, h is cavity height, x np and x 'np are tabulated
zeros of the Bessel’s function and the derivative of the Bessel’s function, respectively.
Resonant frequency f can be plotted as a function of cavity length in a mode chart, as
shown in Figure 2.1 and Figure 2.2.
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TE modes in an empty cavity with diameter of 17.78cm
—e —TE011
—« —TE012
4.5
TE013
—*—TE021
—• —TE111
X
3.5
CD
S'
c
3 -
CD
—I— TE112
myO• x o—
mx cn M
•
TE113
x n5 “ X .U D
□
+
“ O
aAA/A
• xx °D
•
Xxx
anDDa D n n £ l”"—
»•
XxXvY
Da6dl®til9aODDDD^
D
cr
- xx
a> 2.5
u_
2
-
—♦— TE121
—e —TE122
—x—TE211
—
-n-------- >
1.5
8
« » .
10
12
,-------14
16
TE212
—a—TE221
TE311
18
■« TE312
Cavity length (cm)
Figure 2.1 TE Modes in an Empty Cavity with Diameter of 17.78cm
TM modes in an empty c a yty with diameter of 17.78cm
—B—TM012
TM013
4.5
°
4
X
ic
- .
4, 0 .
—6— TM020
■
a *v M $ B S r ------------------------ i
* SP* t*
D **"
A
‘ a“ ■ ...........
* !? * £
xx
■*+++T
N 3.5
CD
X
3
— A —
-TM110
•TM111
O0OOO0O08RQOOOO0
—
S> 2.5
XX x x x x x x x x x x x 5 9 S r
2
—A—■TM022
ooooooSaoooooooo"
no
cr
a>
—♦—TM021
X - -TM112
-------TM120
4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA2
—
TM121
—e - -TM210
1.5 -
-TM211
1
—t—-TM212
8
10
12
14
16
18
-TM310
Length of cavity (cm)
Figure 2.2 TM Modes in an Empty Cavity with Diameter O f 17.78cm
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2.1.3
Electromagnetic Fields in a Cylindrical Single Mode Cavity
In a homogeneous, source-free cylindrical single mode cavity with perfectly
conducting walls, The electromagnetic fields inside the cavity can be derived from
Maxwell's equations and boundary conditions [37].
For TE modes, the EM field components inside an empty cavity are [37]:
_ 1 9 Iffnpq
P
1 9 ^ ,npq
* V = -
A dpdz
_ I 1 d 2 Wnpq
1 9 y/npq
z
dp
d(j)dz
H z - ~ (
d<t>
^Vnpq
—
p
P
2
(2.17)
.
Ez =0
Wnpq)
dz
^
where (/?,^,z)are the cylindrical coordinates, z = ja x p ,k
2
2
= m p Qe , and y/npe] is the
wave potential for TEnpq modes:
¥„pq =■!„(— P) Sm' ^ | s i n ( ^ d
' '
a
Icosh^J
li
where a and h are the diameter and height of the cavity, respectively.
For TM modes, the field components inside an empty cavity are [37]:
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(2.18)
1 t 2Vnpq
p
1 1^
E </>~ A p
1 ,d
Ez=
it
A dpdz
T (
Wnpq
_ 1 ^npq
p ~ ~p~ ^r
=■
dfflz
Wnpq t , 2
+ kWnpq)
dW,npq
dp
(2 .1 9 )
H z =0
d z‘
where y = jure, and yfnpq is the wave potential for TMnpq modes:
Wnpq = J „ ( —
a
/0){sin" ^ l c o s ( ^ 2 )
(cosn^J
h
(2.20)
When the cavity is loaded with materials, Equations 2.17 to 2.20 are no longer
applicable. For simple materials, analytic methods are useful for calculating the EM field
inside the materials and the cavity. For complex situations (e.g. inhomogeneous or
anisotropic materials, irregular shapes, etc.), numerical techniques are usually used to
solve for the EM field. The most widely used numerical techniques include the method of
moments (MOM), the finite-element method (FEM) and the finite difference method
(FDM).
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2.2 Microwaves/Materials Interactions
2.2.1
M echanisms o f Microwave/Materials Interactions
Materials are classified into conductors, semiconductors and dielectrics according
to their electric conductivity. Conductors contain free charges, which are conducted
inside the material under the alternating electric fields so that a conduction current is
induced. Electromagnetic energy is dissipated into the materials while the conduction
current is in phase with the electric field inside the materials. Dissipated energy is
proportional to conductivity and the square of the electric field strength. Conduction
requires long-range transport of charges. In dielectric materials, electric dipoles are
created when an external electric field is applied and they will rotate until they are
aligned in the direction of the field. The polar segments attempt to align up with the
alternating electromagnetic field so that the normal random orientation of the dipoles
becomes ordered. These ordered polar segments tend to relax and oscillate with the field.
The energy used to hold the dipoles in place is dissipated as heat into the material while
the relaxation motion of dipoles is out of phase with the oscillation of the electric field.
Both the conduction and the electric dipole movement cause losses and are responsible
for heat generation in microwave processing. The contribution of each loss mechanism
largely depends on the types of materials and operating frequencies. Conduction loss is
dominant at lower frequencies, while polarization loss is important at higher frequencies.
Most dielectric materials can generate heat via both loss mechanisms. There are mainly
four different kinds of dielectric polarization:
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1. Electron or optical polarization occurs at high frequencies (close to ultraviolet
range of EM spectrum) [38,39]. It refers to the displacement of the electron cloud
center of an atom relative to the center of the nucleus caused by an external
electric field. When no electric field is applied, the center of positive charges
(nucleus) coincides with the center of negative charges (electron cloud). When an
external electric field is present, the electrons are pushed away from their original
orbits and electric dipoles are created.
2. Atomic polarization is also referred to as ionic polarization. It occurs in the
infra-red region of the EM spectrum. This type of polarization is usually observed
in molecules consisting of two different kinds of atoms. When an external electric
field is applied, the positive charges move in the direction of the field and the
negative ones move in the opposite direction. This mainly causes the bending and
twisting motion of molecules. Atomic polarization can occur in both non-ionic
and ionic materials. The magnitudes of atomic polarization in non-ionic materials
are much less than that in ionic or partially ionic materials.
3. Orientation or dipole alignment polarization occurs in the microwave range of
the EM spectrum and is the dominant polarization mechanism in microwave
processing of dielectrics. Orientation polarization is usually observed when
dipolar or polar molecules are placed in an electric field. At the presence of
external electric field, the dipoles will rotate until they are aligned in the direction
of the field. The dipolar rotation of molecules is accompanied by intermolecular
friction, which is responsible for heat generation. Orientation polarization is
fundamentally different from electronic and atomic polarization. The latter is
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because the external field induces dipole moments and exerts displacing force on
the electrons and atoms, while the orientation polarization is because of the torque
action of the field on the pre-existing permanent dipole moments of the
molecules.
4. Interfacial or space charge polarization occurs in low frequency (radio
frequency) range and is a fundamental polarization mode in semiconductors. This
type of polarization is caused by the migration of charges inside and at the
interface of dielectrics under a large scale field.
2.2.2
Dielectric Properties
Most polymers and composites are non-magnetic materials. For non-magnetic
materials, the electromagnetic energy loss in a given material is only dependent on the
electric field. Incident electromagnetic fields can interact with conductive and
nonconductive materials. The fundamental electromagnetic property of nonmagnetic
materials for microwave heating and diagnosis is the complex permittivity:
e =e-je"
(2.21)
The real part of the complex permittivity is permittivity e (dielectric constant), which is
defined as the ratio between the capacitance of a condenser filled with dielectrics and the
capacity of the same condenser when empty. The higher the polarizability of a molecule,
the higher its dielectric constant. The imaginary part of the complex permittivity is loss
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factor e , which is related to energy dissipated as heat in the materials. Usually the
relative values with respect to the permittivity of free space are used:
e - £o(er - j e ef f )
( 2 .2 2 )
where e0 is the permittivity of free space, e r is the relative dielectric constant, and Eej j
is the effective relative dielectric loss factor. The loss factor of materials consists of both
polarization and conduction loss. The polarization loss is further contributed by all four
polarization mechanisms mentioned earlier. The effective relative loss factor is
expressed as [39]:
e'cff (&) = e'd (&) + £ "e(&) + £a + £ "s+ —
(2.23)
where co = 27zf , the subscripts d, e, a, and s refer to dipolar, electronic, atomic and space
charge polarization, respectively. The loss factor is a function of material structures and
compositions, angular frequency, temperature, and pressure.
The ratio of the effective loss factor to the dielectric constant is defined as the loss
tangent, which is also commonly used to describe dielectric losses:
(2.24)
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When introduced into microwave field, the materials will interact with the
oscillating electromagnetic field at the molecular level. Different materials will have
different responses to the microwave irradiation.
For conductive materials such as carbon fibers and acid solutions, microwave
heating is mainly due to the interaction of the motion of ions or electrons with the electric
field. For conductors with high conductivity, the incident microwaves will be largely
reflected and therefore they can not be effectively heated by microwave. The fields
attenuate towards the interior of the material due to skin effect, which involves the
magnetic properties of the material. The conducting electrons are limited in the skin area
to some extent, which is called the skin depth, ds. Defined as the distance into the
sample, at which the electric field strength is reduced to 1/e, the skin depth is given by
[37]:
d ’ ~ 1 -------- L- v T T
|l/ 2 coii0fi cr)
(2'25>
where a) is the frequency of the EM waves in rad/sec, fi() is the permeability of the free
space, 4 n x 10'7 H/m, // is the relative permeability, and a is the conductivity of the
conductor in mhos/m. For graphite, a = 7 x l0 4 mhos/m, and ds = 38.4 // m at 2.45 GHz
in free space. As frequency increases, the skin depth decreases. For a perfect conductor,
the electric field is reflected and no electric field is induced inside a perfect conductor at
any frequency. Therefore, no electromagnetic energy will be dissipated even though the
conductivity of the perfect conductor is infinite.
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Fornonconductive materials such as polymers, glass fibers, and Kevlar fibers,
dielectric heating is mainly due to the interaction of the motion of dipoles with the
alternating electric field. For microwave processing of thermosets, the process is selfadjusting. As the crosslinking occurs, the mobility of dipoles decreases because of the
“trapping” or reaction and the dielectric loss factor decreases. Thus microwave
absorption by crosslinked molecules decreases and microwaves are concentrated in
unreacted molecules. For microwave processing of thermoplastics, the dielectric loss
factor usually increases with temperature and thermal runaway is likely to occur.
Thermal runaway can be prevented by decreasing or even turning off microwave power
at a temperature close to thermal excursion. For microwave processing of polymer
composites, microwave heating selectivity depends on the magnitude of dielectric loss
factor of polymers and fibers. When non-conducting fibers (such as glass) are used,
microwaves will selectively heat the polymer matrix. When conducting fibers (such as
graphite) are used, energy is preferably absorbed by the conductive fibers and heat is
conducted from the fiber to the matrix. In this case, loss factor is mainly due to the fiber
conductivity and can not be used to diagnose the curing process of the low loss matrix
materials.
Dielectric measurement of epoxy has shown that both the dielectric constant and
dielectric loss factor increase with temperature and decrease with extent of reaction [1].
This dependence on temperature and extent of reaction is non-linear. During microwave
processing, the dielectric properties change as a result of heating and reaction. This
affects the electrical field strength and power absorption in the materials. The change in
electric field and power absoiption in turn affects the temperature and extent of reaction
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inside the materials. Thus the modeling of microwave heating is a highly coupled non­
linear problem, which involves Maxwell’s equations for solving the electric field
strength, a heat transfer equation for obtaining the temperature distribution inside the
material, and a reaction kinetics equation for calculating extent of reaction. Reference
data in [1] can be used in the model.
2.3 Applications of Microwave Energy
The use of microwave energy can be classified as either a communication or non­
communication application. Since the discovery of electromagnetic waves, it has been
widely used in communications. The earliest reported non-communication use of
microwaves in polymer processing was in 1940 in an attempt to cure plywood cement
[40]. In the 1960s, microwave processing was successfully applied in the vulcanization of
the rubber in the tire industry [41]. By now, the vulcanization of extruded rubber
weather-stripping for the automotive and construction industries has been one of the most
successful applications of microwave heating in industry [42], Since the mid-1980s, there
has been a resurgence of interest in the microwave processing of polymers and
composites [3,10,16,17,43,44]. Up to now, microwave heating has been used in forest
industry [36], food industry [41,46-51], waste treatment [52-55], organic synthesis
[56,57], material processing [1-28,43,58-33, 81-86], welding [78,79] and adhesive
bonding [29-31,80] applications.
The application of microwave heating in material processing includes the
processing of coal [58], ceramics [59] and polymer and composites [1-28,43,60-33, 8186]. In polymer processing, both thermosets and thermoplastics have been studied. The
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drying process of various thermoplastics with microwave energy has been investigated
[2]. Microwaves have also been used to cure thermosetting materials, including
polyesters [3,4], polyurethanes [5,6], polyimides [7,8,9] and epoxies [1,3,10-20]. Both
pulsed and continuous microwave curing of epoxies have been studied [1,15].
In composite material processing, both conducting fiber (such as graphite) and
non-conducting fiber (such as glass) reinforced composites have been processed with
microwave energy. Lee et. al. [22] processed graphite fiber-epoxy laminates up to 32
plies using a waveguide and a multimode applicator (common microwave oven) and the
attempt by this group to process multi-directional graphite-epoxy composites was not
successful. However, Wei et al. [23] used a cylindrical, tunable single-mode cavity and
successfully processed both cross-ply and unidirectional 24-ply 7.62 X 7.62 cm Hercules
AS4/3501-6 graphite/epoxy prepreg laminates with 2.45 GHz microwaves. The
unpressurized microwave processed composites showed higher modulus with shorter
cure time compared with thermal autoclave process. Part of the reason is that microwave
heating environment can substantially increase the amount of chemical interaction
between the surface of the conducting fiber and the epoxy resin and amine components of
the matrix [21]. As a result, the composite performance can be improved. Thick section
graphite/epoxy composites were successfully processed or heated using single-mode
cylindrical cavity [23,64]. Microwaves have also been used to process non-conducting
fiber reinforced epoxy composites. A 457 mm long, 127 mm OD epoxy/glass filament
wound tube with a wall thickness of 9.5 mm was processed in one minute using a
rectangular multi-mode cavity at a power level of 20 KW [81]. Different applicators
were used to process planar glass fiber/epoxy laminates [22][82][83]. However, there
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was no evidence of improved fiber/matrix bonding by microwaves for glass reinforced
composites [21].
Continuous processing has also been studied and developed for composites with
conducting and non-conducting fibers [24-28, 84]. The control of microwave leakage at
the entrance and exit ports is the critical issue in continuous microwave processing.
Usually an anti-leakage structure called a choke is used at the entries. However, for
conducting fiber-reinforced composites, a specially designed microwave leakage jacket
should be used [85]. In recently developed microwave-assisted pultrusion processes, the
length of the process chamber, the processing time and the pulling forces were reduced
significantly [28, 84 ,86].
Demonstrated results in microwave processing of polymers and composites
include increased polymerization rate [7,11-14], reduced drying time for pelletized
polycarbonate and polypropylene [2], increased glass transition temperature (Tg) for
cured epoxy [10], enhanced fiber/matrix adhesion in carbon composites [21], and
increased mechanical strength of graphite/epoxy composite [15].
Microwave energy has been applied in welding thermoplastics in a multi-mode
oven at a fixed frequency of 2.45GI-Iz [78]. Conductive polyaniline was placed at the
joint interface as microwave absorber. The absorber heats up and conducts heat into the
thermoplastic bulk materials to form molten layers, which are then squeezed by applied
pressure to form the joint. The initial heat generation rate and electric field strength were
estimated. Effect of heating pressure, heating time and welding pressure on weld strength
was investigated. An impedance matching microwave system was developed to increase
the energy transfer efficiency [79]. Two different conductive polyaniline samples were
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studied in the welding. Compared with multi-mode system, the impedance matching
system reduced the input power as well as the welding cycle.
Radio frequency or microwave adhesive bonding has been investigated. Bernard
et al. [80] applied a 50 £2 radio frequency technology in adhesive bonding process in the
automotive industry. An adhesive formulation was determined to adapt to the 50 £2 radio
frequency technology. An applicator was developed to maintain the two parts to be
bonded in position. Compared with the conventional thermal process, the 50 £2, radio
frequency process has shown increased throughput, lower power requirement, less space
occupied by the facilities and reduced cost. Microwave adhesive bonding was studied in a
multi-mode applicators for automotive application [29-31] and bonding of flip-chips (FC)
for electronic packaging application [31]. In automotive application, compared with
thermal bonding, microwave techniques reduced the required curing time of the adhesive
significantly while obtained an equal or slightly higher ultimate tensile strength of the
bonded assemblies. In electronic packaging application, both VFM curing of the
underfill and bonding of the chips were performed. The VFM curing cycle was much
shorter than the thermal curing cycle. In Flip-Chip (FC) bonding experiments, high IC
integrity of the bonded chip was obtained with VFM process. In addition, VFM cured
samples had 50% reduction in stress compared with thermal cured assemblies.
Research work throughout the world has shown that microwave techniques have
great potentials in a variety of industrial applications. However, microwave techniques
have not been widely adopted by industry. Part of the reason is because of inadequate
knowledge in microwave/material interactions, design of processes for specific
applications, and intelligent control and automation. Research in this area is expected to
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elucidate microwave fundamentals and enhance the commercialization of microwave
technique [87].
2.4 Microwave Applicators
The most commonly used microwave applicators include waveguide, commercial
multimode microwave ovens, and single mode applicator. Waveguides are hollow metal
tubes, the high-reflecti vity walls of which allow microwaves to propagate. Commercial
multimode microwave ovens have large dimensions compared to the operating
wavelength, allowing the establishment of multi modes at the same time. The EM field
inside multimode ovens is not uniform and shows many peaks and valleys. Turntables are
usually used to rotate the materials to be processed for more uniform heating. Single
mode cavity supports one mode at one time and has well-defined electric field pattern.
The single mode cavity system has higher energy efficiency to transfer microwave power
into the processed materials. A cylindrical single mode cavity will be used in this study.
Since one mode heating is not uniform with high field intensity confined to small regions,
variable frequency techniques can be used to excite several modes with complementary
heating patterns sequentially to obtain more uniform heating. This method will be
discussed in detail in Chapter 4.
A sketch of the cylindrical single-mode cavity used in this study is shown in
Figure 2.3. The cavity is made out of a length of metal circular waveguide with both ends
shorted by the same metal, which is brass in this study. The cavity has an inner diameter
of 17.78cm with cavity length adjustable from 10 cm to 30 cm. Microwave energy is
introduced into the cavity by a coaxial coupling probe. The coupling probe is side
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mounted 3cm above the base of the cavity. The probe is adjustable in the radial direction
so that the coupling probe depth Lp can be changed for locating critical coupling
conditions. The range of the probe depth is from 0 mm to 50 mm. The top short-plate is
adjustable so that the cavity length Lc can be changed. The bottom plate is removable for
sample loading. Both the top and the bottom plates are shorted with the cavity wall by
metallic finger stocks.
Coupling Probe
Shorting Plate
Microwaves
Bottom Plate
Figure 2.3 Cylindrical Single-Mode Resonant Cavity
2.5 Temperature sensing system
Two types of thermometers are used in this study:
1. Multi-channel LUXTRON fluoroptic thermometer: The Luxtron thermometer
uses Decay Time Technology to measure the temperature of the sensor [88].
Luxtron sensors contain a small amount of magnesium fluorogermate. The
sensors are attached at the tip of the optic fiber. The optical system excites the
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sensor with blue light. In turn the sensor fluoresces a red light, the intensity of
which decays exponentially with time. The time constant of the decay is inversely
proportional to the temperature. So by measuring the decay time, the temperature
can be obtained. The temperature probes are electrically nonconductive. So they
will not perturb or be perturbed by the microwave fields.
2. Multi-channel NoEMI-TS fiberoptic thermometer: The working principle of this
type of thermometer is based on the absorption of light by a semi-conducting
crystal bonded to the end of an optical fiber [89]. The crystal is in well contact
with the materials to be processed with microwaves. As the crystal temperature
increases, more low-energy photons are captured and absorbed by the band. The
absorption edge is moved towards the longer wavelengths. Therefore, measuring
the position of the absorption shift gives a measurement of the crystal’s
temperature and thus the temperature of the materials. The sensor is immune to
and does not perturb the electromagnetic field.
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CHAPTER 3 SINGLE MODE MICROWAVE ADHESIVE BONDING
3.1 Introduction
Chapter 1 described the advantages of microwave energy over thermal heating.
Chapter 2 reviewed the fundamentals in microwave heating. This chapter applies single
mode microwave method in adhesive bonding to utilize the advantages of selectivity
(selective heating of adhesive if the adhesive is properly formulated), rapidity and high
efficiency of microwave heating. The feasibility and characteristics of using microwaves
in adhesive bonding in a single mode applicator are studied.
Since microwave heating is strongly dependent upon the magnitude of dielectric
properties of the constituents, microwave energy can be applied in different processes to
perform either volumetric, surface or selective heating. The selective heating feature of
microwaves is utilized in adhesive bonding process. The polymer or composite parts have
low loss factors relative to the adhesive material at the interface. Microwave energy is
then directly transferred into the interface and cures the adhesive extremely rapidly, even
though the substrate materials are very thick.
Research & Development regarding the application of microwaves in adhesive
bonding is still in its early stage. Several investigators have studied microwave adhesive
bonding in multi-mode applicators [29-31]. Paulauskas et al. [29] studied fixed frequency
microwave adhesive bonding in a multi-mode applicator. Glass and glass fiber reinforced
urethane-based composite (SRIM-part) were adhesive bonded with Goodrich 582E
(epoxy based) adhesive. The relationship between input power level and bonding time
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was studied. Additives such as carbon black were added into the adhesives to improve the
lossy characteristics of the adhesive. It was reported that during microwave bonding, the
coupling of microwave energy into the adhesives was highly efficient. The coupling was
further enhanced with the additives. Compared with thermal adhesive bonding, fixed
frequency microwave bonding techniques reduced the required curing time significantly
while obtained an equal or slightly higher ultimate tensile strength of the bonded
assemblies. However, the temperature was not measured or controlled in this study.
Therefore, the comparison between microwave and thermal processes might not be based
on the same heating conditions. In addition, it was unclear whether the reduction of
curing time with carbon black additives was because of increase of heating rate or curing
reaction rate or both.
Paulauskas et al. [30] also applied variable frequency microwave (VFM) in
adhesive bonding in a multi-mode cavity. The frequency was swept over a range to
launch different electric field patterns into the applicator sequentially. An advantage of
VFM bonding over fixed frequency technique was that VFM had a more uniform timeaveraged electric field. Thus VFM did not readily create localized overheating in the
adhesive or the substrates and was not sensitive to sample position. Compared with fixed
frequency microwave bonding, VFM reduced the bonding time slightly.
Wei et al. [31] performed VFM bonding of polymer composites for automotive
application and bonding of flip-chips (FC) for electronic packaging application. A multimode applicator was used. In the automotive application, SRIM (chopped glass fiber
reinforced, urethane-based composite) and Rynite® 5309 (glass fiber/mineral reinforced
thermoplastic polyester composite) panels were studied. A closed-loop feedback control
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was applied to control the temperature. Reduced bonding cycle was achieved with
adequate bonding strength. Uniform bonding was observed.
In electronic packaging
application, both VFM curing of the underfill and bonding of the chips were performed.
The VFM curing cycle was much shorter than the thermal curing cycle. In Flip-Chip (FC)
bonding experiments, high IC integrity of the bonded chip was obtained with VFM
process. In addition, VFM cured samples had 50% reduction in stress compared with
thermal cured assemblies.
These studies on microwave adhesive bonding in multi-mode applicators have
shown the industrial potential of using microwaves in adhesive bonding processes.
However, process fundamentals have not been investigated in these studies. Research
needs to be carried out to relate microwave heating characteristics such as uniformity
with the electromagnetic field patterns. In addition, material dielectric properties largely
determine the heating selectivity in microwave adhesive bonding process. Microwaves
can be selectively coupled into the adhesive if the dielectric properties of the adhesive are
higher than that of the substrates.
In order to study the process fundamentals, a single mode resonant applicator will
be used for microwave adhesive bonding in this research. The electric field patterns
inside the single mode applicator are more controllable and predictable compared with
field patterns inside multimode ovens. In a single mode microwave cavity, two
processing methods can be applied, namely single mode microwave processing and
mode-switching microwave processing. Single mode microwave method refers to the
process that only one mode is used throughout the processing. Only limited material size
can be uniformly heated with single mode microwaves because of the non-uniformity of
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electric field distribution. Mode-switching microwave method refers to the process that
several modes with complementary heating patterns are excited sequentially to obtain
time-averaged uniform heating. The modes can be switched by either mechanically
changing the volume of the cavity [33] or tuning the operating frequency [35]. Modeswitching method is based on knowledge and understanding of single mode heating
characteristics. As the starting point, this chapter studies single mode microwave method
in adhesive bonding. The heating selectivity, rapidity, controllability and mode
characterization will be investigated in this chapter. In Chapter 4, the mode switching
method in [35] will be implemented and applied in adhesive bonding process to improve
heating uniformity.
3.2 Experimental
3.2.1
Experim ental Circuit
The experimental circuit was assembled for microwave adhesive bonding process.
The circuit directs microwaves into the applicator, allows the measurement of
temperature, incident and reflected powers, and reduces the power reflected back to the
power source to prevent damage to the power source. The microwave circuit is illustrated
in Figure 3.1.
Microwave signal generator is a sweep oscillator (HP8350B) connected with a RF
plug-in (HP86235A). A variable frequency amplifier (Lambda LT-1000) is used to
amplify the signal. The amplified power signal is in the range from 0 to 200 Watts.
Microwave frequency can be adjusted from 2 GHz to 4 GHz either manually or
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automatically. A 3-port circulator is used to prevent the reflected power from damaging
the power source. The input and reflected microwave powers are decoupled with 20db
directional couplers (Narda 3043-20) and measured with power meters (HP435B). A
dummy load is used to absorb most of the reflected power. A multi-channel LUXTRON
fluoroptic thermometer and a multi-channel Nortech NoEMI-TS fiberoptic thermometer
are used for sample temperature measurement. The probes are electrically nonconductive.
So they do not perturb or be perturbed by the microwave fields.
Microwave Power
Source
Circulator
Microwave
Applicator
Directional
Coupler
I
[Directional
| Coupler
|~|~1 Thermometry
Pi
Reflected Incident Power
Power Meter
Meter
O
Dummy
Load
- - o
- -
A/D
D
PC
Controller
Figure 3.1 Circuit of Microwave Adhesive Bonding
A cylindrical single mode cavity with a diameter of 17.78cm is used. The
coupling probe is side mounted 3cm above the bottom of the cavity. The cavity length
(Lc) and the probe depth (Lp) are adjusted to be 13.2cm and 2.0cm, respectively. The
sample is loaded at the center of the cavity.
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3.2.2
Materials
Because the major objectives of this chapter are to study the characteristics of
microwave adhesive bonding in a single mode applicator and to study the relation
between electromagnetic field patterns and heating characteristics, commercial substrate
and adhesive materials were used because of the established knowledge of good adhesion
and good mechanical properties. In adhesive bonding, compatibility between the
substrates and the adhesive is required. Epoxy adhesive was selected because of its
compatibility with a wide range of substrate materials. The epoxy adhesive used for this
study was Eccobond A401-37 (epoxy based) from Grace Specialty Polymers. The
substrate was chosen among Zytel® 72G 33L (Glass reinforced Nylon66/6 copolymer),
Hytrel® 5556 (Thermoplastic Polyester) and Bexloy W502 (glass reinforced
ethylene/methacrylic acid copolymer). All three substrate materials were obtained from
DuPont. The selection of substrate was mainly based on material dielectric properties,
because microwaves can selectively heat the adhesive without substantially heating up
the substrates if the adhesive has a higher magnitude of dielectric properties than the
substrates.
3.2.3
M ethod o f Dielectric Property M easurem ent
The dielectric properties of the adhesive and the substrates were measured with
single mode perturbation method developed by Jinder Jow et al [91]. The measurement
was performed at room temperature. The microwave applicator used for the dielectric
measurement was a cylindrical cavity with a diameter of 15.24cm. The mode used was
TM012 at 2.45GHz. Samples were loaded into a cylindrical Teflon holder and placed at
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the center of the cavity. Teflon was selected to be sample holder because of its low
dielectric loss factor (0.0003), temperature independent dielectric properties, high
temperature resistance (up to 260°C) and chemical inertness [92]. The inner diameter and
height of the holder were 10mm and 35mm respectively. Liquid samples were filled into
the holder and degassed in a vacuum chamber to remove trapped air during the filling
process. Solid samples were machined into cylindrical shape and then loaded into the
Teflon holder. Unloaded cavity refers to the cavity with the empty Teflon holder inside.
Loaded cavity refers to the cavity with resin-filled Teflon holder. The empty and loaded
cavities were tuned to critically couple the external circuit by adjusting the cavity length,
probe depth and sample position. The cavity length corresponding to the TM012 mode
was within the range of 15.41cm to 15.45cm at 2.45GHz. In each measurement, the
dimensions of the cavity and the sample, resonant frequency and half-power frequency
bandwidth were measured for both unloaded and loaded cavities. The experimental data
were input into a software to calculate the dielectric properties based on the following
perturbation equations [ 1]:
Zq. ,A =(g'-i)ABG^~
(3.1)
fo
1
1
V
- ------ - = 2 e " A B G ^ -
Qs Qo
Where
vc
(3.2)
A=J 0 (2.405Rs/Rc)2+ J, (2.405Rs/R c) 2
(3.3)
B=1+[L c/(2 teLs)] sin (27tLs/Lc) cos (4ttH/Lc)
(3.4)
G=0.2718(c/fo/Rc)2
(3.5)
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In these equations, e' and
e"
are the dielectric constant and dielectric loss factor.
Vc, Rc and Lc are the volume, radius and length of the unloaded cavity. Vs, Rs and L* are
the volume, radius and length of the loaded cavity. H is the distance from the middle of
the sample to the bottom of the cavity and c is the speed of light, fo and fs are the resonant
frequencies of the unloaded and loaded cavities. Q 0 and Qs are the Q-factors of the
unloaded and loaded cavities, respectively. The Q factor is the ratio of the resonant
frequency to the half-power frequency bandwidth.
3.2.4
Sample Setup and Preparation fo r Adhesive Bonding
The sample setup was based on single-lap shear configuration for the convenience
of testing bond strength. Sample setup and temperature measuring points are shown in
Figure 3.2.
The thickness of the substrate was 3mm. The length of the substrate panels was
5.08cm, smaller than that suggested by single lap-shear Standard Test Method in order to
fit into the cavity. Two substrate panels had an overlap of 0.8cm along the length
direction, where the adhesive was applied. Preliminary experiments indicated that
adhesive wider than 2.54cm could not be uniformly heated with single mode microwaves.
Because the width of the adhesive was the same as that of the substrates, the width of the
substrates was determined to be 2.54cm for single mode microwave adhesive bonding.
Several glass beads (diameter 0.6mm) were embedded in the adhesive to get a uniform
thickness of the adhesive. Since the temperature of the adhesive between the two
substrate panels can not be directly measured, an auxiliary panel was used for
temperature measurement to approximate the real adhesive curing environment. Adhesive
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with the same dimension as the bonding area was applied between the auxiliary panel and
panel 2. Two small holes were drilled through the auxiliary panel, where the temperature
probes were inserted to measure the adhesive temperature. The adhesive dimensions were
1.6cm x 2.54cm with a thickness of 0.6mm. The entire assembly was 9.36cm x 2.54cm
with a height of around 6 .6 mm.
Temperature
Probe Holes
Substrate Panel 1
Auxiliary Panel for
Temperature Measurement
Glass
Beads
Supporting
Panel
Adhesive
Release Films
Substrate Panel 2
(a) Side View
Panel
Temperature
Adhesive
Temperatures
(b) Top View
Figure 3.2 Sample Setup and Temperature Measuring Points in Single Mode Microwave
Bonding
Before bonding, the panels were roughened at the joint areas with abrasion paper
in order to enhance bonding. The joint areas were then degreased with acetone. A Teflon
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mold was used to hold the sample in position. After bonding, the samples were tested
with single lap shear equipment to determine the bonding strength.
3.3 Results and Discussion
3.3.1
Material Dielectric Properties
The results of dielectric measurement are listed in Table 3.1. Three measurements
were made for each sample.
Table 3.1 Dielectric Properties of the Materials
Adhesive
Dielectric
Dielectric Loss
Constant
Factor
E'
e"
Eccobond
Uncured
4.10±0.20
0.307+0.015
A401-37
Fully cured
2.58+0.12
0.02910.001
Substrate
Zytel® 72G 33L
3.09±0.15
0.034+0.002
Substrate
Hytrel® 5556
2.60±0.13
0.09410.005
Substrate
Bexloy W502
2 . 1 1 1 0 .1 0
0.00610.001
Among the three substrates, the dielectric constant and loss factor of Bexloy
W502 (glass reinforced ethylene/methacrylic acid copolymer) were the lowest. In
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addition, the magnitude of the dielectric properties of the Bexloy substrate was lower
than both the uncured and fully cured adhesive. The dielectric property of Zytel® 72G
33L (Glass reinforced Nylon 6 6 /6 copolymer) was lower than the uncured adhesive but
slightly higher than the fully cured adhesive. It can be expected that selective heating of
the adhesive can be obtained at the beginning of curing but will be less significant at the
end of microwave adhesive bonding of the Zytel substrate assembly. The dielectric loss
factor of Hytrel® 5556 (Thermoplastic Polyester) substrate was one third of that of the
uncured adhesive but three times of that of the fully cured adhesive. Therefore after
certain point during the adhesive curing, microwaves will be preferentially absorbed by
the substrates instead of the adhesive. For microwave adhesive bonding of Hytrel
substrate, adhesives with higher dielectric properties should be used to increase the
coupling efficiency of microwave energy into the adhesives.
Because of its low dielectric properties, Bexloy W502 (glass reinforced
ethylene/methacrylic acid copolymer) was selected for the preliminary microwave
adhesive bonding study.
3.3.2
Characterization o f Empty Cavity
Empty cavity characterization was performed in the cylindrical single mode
cavity with the diameter of 17.78cm and cavity length of 13.2cm. The characterization
was performed at room temperature. The frequency was swept from 2.0 to 4.0GHz to
study the mode spectrum. The mode spectrums were obtained with measuring the
incident power (Pi) and the reflected power (Pr) as a function of frequency. The
frequency with minimum reflectance (Pr/Pi) is the resonant frequency of a mode. The
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cavity characterization program was edited with LabVIEW. This program will be
explained in Chapter 6 .
Figure 3.3 illustrates the mode spectrum of the empty cavity. The resonant
frequencies of the modes can be determined with mode diagnosis described in next
section. The experimental resonant frequencies in the empty cavity were close to the
theoretical values shown in the mode chart Figure 2.1 and Figure 2.2.
0 -|----------------1—
2
,----------------------------------------- r J.L_Jll— I—
2.5
3
3.5
4
Frequency (GHz)
Figure 3.3 Characterization of Empty Cavity
As an example, the experimental and theoretical empty cavity resonant
frequencies of TM020, TM022 and TM212 modes are shown in Table 3.2. The relative
deviation from the theoretical value was 0.6% for TM 020,0.5% for TM022 and 0.7% for
TM212.
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Table 3.2 Theoretical and Experimental Values of the Resonant Frequencies of Several
Modes
Resonant Frequency in
Mode
Mode
Mode
TM020
TM212
TM022
2.9830
3.5990
3.756
2.9647
3.5741
3.7356
0 .6 %
0.7%
0.5%
Empty Cavity (F2) (GHz)
Theoretical Resonant
Frequency in Empty Cavity
(Ft) (GHz)
Relative Deviation from
Theoretical Value
((F2-Ft)/Ft* 100%
3.3.3
3.3.3.1
Characterization o f Loaded Cavity and Mode Diagnosis
Characterization of Cavity Loaded with Materials
The mode spectrum of the cavity loaded with materials was also studied in the
cylindrical single mode cavity with the diameter of 17.78cm and cavity length of 13.2cm.
The sample was placed at the center of the cavity. Different material setups should have
different spectrums. Figure 3.4 shows the mode spectrum of the cavity loaded with the
assembly consisting Bexloy W502 substrates (glass reinforced ethylene/methacrylic acidcopolymer from DuPont) and Eccobond A401-37 adhesive (epoxy based from Grace
Specialty Polymers).
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%
Ph
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
Frequency (GHz)
Figure 3.4 Reflectance in Cavity Loaded with Samples (Sample Width of 1")
The mode spectrum of the loaded cavity was different from that of the empty
cavity because of the perturbation of materials. As observed from Figure 3.4, many
resonant modes can be excited within the loaded cavity. In order to locate the modes that
could rapidly heat up the sample, the temperature rise was measured as a function of
frequency and then the heating rate at different frequencies was calculated. Both the
temperature data acquisition and the heating rate calculation were performed with a
LabView program. In this experiment, the step increase of the microwave frequency was
IMHz/second. This small step increase was used to assure that the sample, after being
heated up by a heating mode, could cool down before the next heating mode was excited.
Thus the temperature rise of the adhesive at different frequencies was always relative to
the room temperature. The results of heating rate in the frequency range of 2 - 4GHz are
shown in Figure 3.5.
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2.5
2
-
C /D
u
Pi
4-i
1.5 10.5
0 -I
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
Frequency (GHz)
Figure 3.5 Heating Rate at Different Frequencies
From the results shown in Figure 3.4 and Figure 3.5, it can be observed that the
modes at 2.555, 2.771, 3.256, 3.396, 3.492, 3.715-3.730 and 3.837GHz were
characterized with low reflectance and high heating rate. Thus these modes can be used
in the single mode adhesive bonding study. In addition, the mode at 3.715-3.730GHz had
a wide resonant frequency band and the power reflectance within this frequency range
was always zero. In the adhesive bonding process, the temperature rise and the curing of
the adhesive lead to changes in the dielectric properties, which in turn result in the shifts
of the resonant state. The operating frequency has to be frequently tuned to maintain the
resonant state if the cavity dimensions remain constant. However, if the resonant
frequency band of a mode is wider than the shift of the resonant frequency, then the
operating frequency does not need to be tuned and the heating is continuously at its
highest efficiency. Therefore the mode at 3.715-3.730GHz was chosen for the single
mode microwave adhesive bonding study.
46
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3.3.3.2
Mode Diagnosis
To understand the electric field distribution pattern inside the materials, the mode
at 3.715-3.730GHz was diagnosed in the loaded cavity. The resonant frequency changed
slightly in each experimental run due to the slight change in sample size and position.
The same names (TMnpq or TEnpq) are used for modes in loaded cavity and in empty
cavity, though the field distributions in loaded cavity are slightly different from that in
empty cavity. The diagnosis includes two parts - characterization of the heating pattern
and measurement of the half wave number q. The major assumption used in mode
diagnosis was that after the sample was loaded into the cavity, the change of resonant
frequency was within 10% of the resonant frequency in the empty cavity [90].
3.3.3.2.1
Characterization of Heating Pattern
To characterize the heating pattern of the mode, the distribution of adhesive
temperatures was measured as a function of time. Figure 3.6 shows the adhesive
dimensions and the arrangement of the temperature probes in the adhesive. The adhesive
was 48mm x 48mm. T 5 was the center temperature of the adhesive. T 3 and T 4 measured
the temperatures 1 2 mm away from the center point and along the coupling probe
direction. T ( was the temperature 24mm away from the center point and along the
coupling probe direction, and T 2 was 24mm away from the center point and
perpendicular the coupling probe direction. The temperature distribution is shown in
Figure 3.7. The temperature decreased from the center to the edge, indicating that the
mode at 3.715-3.730GHz preferentially heated the center of the adhesive.
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24mm
T2
1 2 mm
24mm
Coupling Probe
Figure 3.6 Dimension of the Adhesive and Location of Temperature Probes
80 -
C e n te r
T5
70 -
T4
T3
50 40 T2
30 -
20
-
Edge
T im e (m in )
Figure 3.7 Experimental Temperature Distribution
48
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3 .3.3.2.2
Measurement of Half W ave Number q
In the determination of the half wave number q, the relative radial electric field
strength was studied along the axial direction. The experimental configuration is shown
in Figure 3.8. A small metal probe was inserted through the holes in the cavity wall to
measure the power Pb near the cavity wall, which is proportional to the square of the
<2
radial electric field (Pb=Kb|Ep| ) [1]. The diameter of the probe needle was 0.5mm. The
insertion depth was around 1mm. The perturbation of the diagnostic probe to the
microwave field was assumed to be negligible.
Diagnosis
Probe
Figure 3.8 Experimental Configuration for Measurement of Half Wave Number Q
At p=a, (p=7t, The relation between radial electric field strength Ep and q is:
E 0 <x qs\n(cj7r—)
H
h
for TM modes;
49
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(3.6)
£
Ep °= sin(c/;r—)
for TE modes
(3.7)
Where p is the radial position, (p is the angle from the coupling probe, z is the
axial position from the bottom of the cavity, Ep is the radial electric field strength, q is the
half wave number, and h is the cavity height.
With measuring jE^I as a function of z, the number of half waves gave the value
of q. Figure 3.9 shows the result of the half wave number measurement for the mode at
3.715-3.730GHz. There are totally two half waves along the axial direction inside the
cavity, thus q is 2.
Radial Electric Field Along Axial
Direction
E
O
|
10-
m
£
>
8
-
CO
O
-
<
ua
c
(0
0
1
2
3
4
5
R e la tiv e R adial E lectric Field S tre n g th
Figure 3.9 Measurement of the Half Wave Number Q
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Therefore, the mode at 3.715-3.730GHz was center-heating and had a half wave
number of 2. With the assumption that the change of resonant frequency after the sample
being loaded into the cavity was within 10% of the resonant frequency in the empty
cavity, the mode was diagnosed as TM022.
The resonant frequency of TM022 mode in the empty cavity was 3.756GHz as
shown in Table 3.2. The resonant frequency in the loaded cavity was 3.723GHz. Thus the
resonant frequency shifted down slightly (around 0.9%) when the small sized materials
were loaded into the cavity. This is consistent with the theory that an increase in the
dielectric constant leads to a decrease of the resonant frequency [37, Chapter 7]. The
mode pattern inside the empty cavity was computed with a Matlab program and shown in
Figure 3.10.
1
0.8
0.6
0 .4
0.2
0
-
0.2
- 0.4
-
0.6
-
0.8
-1
-1
- 0 .5
0
0 .5
1
F igure 3.10 Electric Field Distribution of TM022 Mode at the Cross-Section of the
Cavity (Lighter Region Represents Higher Electric Field Strength)
51
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The Matlab program is shown in Appendix A. In Figure 3.10, the lighter region
represents higher electric field strength, indicating that TM022 is a center-heating mode.
3.3.4
Single Mode Microwave Adhesive Bonding
The center heating mode TM022. was applied in single mode microwave adhesive
bonding. This mode in the loaded cavity was characterized with a wide band of resonant
frequency with zero reflectance. The center frequency in the resonant frequency band
was used for single mode microwave heating, which was around 3.725GHz.
The assemblies were bonded at I00°C, 110°C and I20°C, respectively. The
temperature profiles during microwave adhesive bonding at all the three temperatures
were similar and the profile at 120°C is shown in Figure 3.11.
140
Adhesive 1
120
-
100
-
Adhesvie 2
80 60 -
Panel
40 -
20
-
Time (min)
F igure 3.11 Temperature Profile during Single Mode Microwave Adhesive Bonding
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The temperature of the adhesive was measured at two points close to the edges of
the bonding assembly. The adhesives were heated from room temperature to 120°C in
around 4 minutes and then kept isothermal. During the heating up process, the adhesive
temperatures at the two measuring points had very slight difference (with 1°C). In the
isothermal bonding phase, the temperature difference between the two measuring points
increased. However, the temperature difference was less than 5 °C. During the whole
heating process, the temperature of the adhesive was much higher than that of the panel.
The selective heating of the adhesive was because the dielectric loss factor of the
adhesive was much higher than that of the panel and microwaves were concentrated in
the adhesive and the interface.
3.3.5
Comparison between single mode microwave and therm al adhesive bonding in
terms o f bonding time and strength
Thermally bonded assemblies were also prepared under normal pressure for
comparison purposes. Autoclave was not used because only contact pressure was
required to cure the adhesive, as indicated in the adhesive MSDS. Preparation of samples
was the same as that used in microwave process. Samples were bonded at 120°C in a
thermal oven for up to 140 minutes. The oven was preheated to 120°C before samples
were put in.
The mechanical properties of microwave bonded and thermally bonded
assemblies were tested with single-lap shear equipment. The crosshead displacement rate
was 0.05 inch/minute (0.127cm/minute). Three assemblies were tested for each data
point. Results are shown in Figures 3.12 and 3.13 and Tables 3.3 and 3.4. Figure 3.12
53
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shows that microwave energy reduced the bonding time and enhanced the bonding
strength compared with thermal method. In addition, the bonding time was shorter at
higher temperature for microwave process. At 100°C, 110°C and 120 °C, the isothermal
bonding time was about 40, 20 andlO minutes, respectively, in microwave adhesive
bonding. The highest bond strength was close to 6MPa. In thermal heating, the bond
strength increased with time at first and reached the maximum value (around 3MPa) after
100 minutes at 120 °C. The average standard deviation of the bond strength was
0.67MPa and 0.32MPa for microwave and thermal process, respectively.
—
Microwave
at 100 C
—s
Microwave
at 110 C
- A — Microwave
at 120 C
x Thermal at
120 C
0
50
100
150
Time (minute)
F igure 3.12 Strength of the Assemblies Bonded at Different Conditions
The difference in bond strength between microwave and thermal processes is
related to the break pattern in single lap shear test. Table 3.3 summarizes the break
54
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pattern of microwave bonded assemblies. With sufficient bonding time, microwave
bonded assemblies at different temperatures all broke within the substrates. This
phenomenon indicates that the bond was stronger than the substrate material itself in
microwave process. Table 3.4 shows the break pattern of thermally bonded assemblies.
The assemblies broke at the interface, indicating that the adhesion between the substrates
and the adhesive was not strong enough in the thermal process.
Table 3.3 Break Pattern of Microwave Bonded Assemblies
t(min)
T=100°C
T = 110 °C
T=120°C
5
not bonded
mixed (interface
mixed (interface
and panel)
and panel)
mixed (interface
shear in panel
10
interface
and panel)
20
mixed (interface
shear in panel
shear in panel
shear in panel
shear in panel
shear in panel
shear in panel
and panel)
30
mixed (interface
and panel)
40
shear in panel
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Table 3.4 Break Pattern of Thermally Bonded Assemblies
t(min)
T=120°C
Up to 150 min
interface
Figure 3.13 shows the load-elongation curves of the assemblies in the single lapshear test. Microwave bonded assemblies had large elongation before breaking. This was
because the strength of the microwave bonded assemblies was determined by the
substrates. Thermally bonded assemblies had small elongation before breaking, because
the assemblies broke at the interface.
Load-elongation curves
350
a: Microwave
bonding, 40min
at 110 C
300
250
£
200
1
150
b: Thermal
bonding, 150min
at 120 C
100
0.5
Elongation (inch)
Figure 3.13 Load-Elongation Curves of Assemblies Bonded under Different Conditions
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The maximum standard deviation of shear strength was 0.8MPa using the single
lap shear technique in this study. This large experimental error made the design of
bonding cycle uncertain. Further study of extent of cure vs time or on-line monitoring is
necessary to determine the bonding cycle.
In this preliminary microwave adhesive bonding study, observed microwave
effects include reduction of bonding time and enhancement of bonding strength for the
Eccobond A401-37 (epoxy based) / Bexloy W502 (glass reinforced ethylene/methacrylic
acid copolymer) system. The possible reasons causing the reduction of bonding time will
be studied in Chapter 7. The possible reasons causing the enhancement of bond strength
are proposed as follows. First, microwave modification of substrate surface chemistry.
Exposure of materials to microwaves might increase the surface energy for better
adhesion. Second, microwave enhancement of molecular mobility at the interface.
Microwaves were concentrated at the interface and might cause the superheating
phenomenon. The Bexloy substrate was thermoplastics based composite materials. When
thermoplastics are bonded with compatible adhesives at a sufficient temperature (thus
sufficient mobility of materials at interface), diffusion bonding might be one of the
possible bonding mechanisms [93]. The enhancement of molecular mobility of both the
adhesive and the substrate could increase the interdiffusion between the adhesive and the
substrates.
However, adhesion between two polymeric materials with microwaves is a
complex phenomenon that involves multidisciplinary knowledge of microwave
fundamentals, surface chemistry, polymer properties, and so on. Extensive experimental
investigations are needed to improve understanding of microwave adhesive bonding
57
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mechanisms. The study of microwave bonding mechanisms is not included in the
research scope of this dissertation.
3.4 Conclusions
This chapter studies the feasibility and characteristics of using single mode
microwave method in adhesive bonding of polymer composites. Adhesive and substrate
materials were selected based on their compatibility and dielectric properties. An epoxy­
based adhesive was used because of its compatibility with a wide range of substrate
materials. The substrate was chosen from three polymer composites based on dielectric
properties. With the choice of the materials, selective heating of the adhesive was
observed in microwave adhesive bonding process.
To locate the heating modes for adhesive bonding, empty and loaded cavities
were characterized to find the mode spectrum. Among many available modes, a mode
with a wide resonant frequency range (from 3.715 to 3.730GHz) was selected to use in
the bonding process. This mode was diagnosed to be TM022 by characterizing the
heating pattern and measuring the half wave number q.
The bonding results showed that microwave method reduced the bonding time
and enhanced the bonding strength compared with thermal method. In addition, the
bonding time was shorter at higher temperature for microwave process. The difference in
bond strength between microwave and thermal methods is related to the break pattern in
the single lap shear test. With sufficient bonding time, microwave bonded assemblies at
different temperatures all broke within the substrates. This phenomenon indicates that the
bond was stronger than the substrate material itself in microwave process. Thermally
58
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bonded assemblies all broke at the interface, indicating that the adhesion between the
substrates and the adhesive was not strong enough.
59
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CHAPTER 4 VARIABLE FREQUENCY MODE-SWITCHING MICROWAVE
ADHESIVE BONDING
4.1 Introduction
Chapter 3 studied microwave adhesive bonding with one mode throughout the
process. The non-uniform electric field pattern of one mode limited the material size that
could be uniformly heated. This chapter implemented the variable frequency modeswitching method in [35] and applied the method in microwave adhesive bonding of
large-size materials to obtain uniform heating in a single mode applicator.
Uniform adhesive bonding has been achieved in multi-mode applicators with a
frequency-sweeping technique [29-31]. In this technique, the frequency is rapidly swept
over a selected range to launch different electric field patterns into the applicator
sequentially. If the frequency range is well selected and wide enough, then the overall
heating can be uniform. However, this method has poor power efficiency and the
processing frequency range is usually empirically determined because of the difficulty of
characterizing the heating patterns of the modes in a multi-mode applicator. Tremendous
experimental efforts are required and yet heating modes with common hot and cold spots
could be used in the same heating process.
In single mode resonant applicators, only one mode is excited at one time and the
field pattern is more defined than that in multi-mode applicators. Frequency-sweeping in
a single mode applicator is not the best approach to create uniform field patterns, because
microwaves are not efficiently coupled into materials at non-resonant frequencies and the
reflectance can be very high. Instead, several modes with complementary heating
60
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patterns can be excited distinctively and alternatively in the single mode cavity to obtain
time-averaged uniform heating. By switching among the selected resonant modes, the
energy efficiency can be highly improved. In a fixed frequency system, mode switching
could only be achieved by mechanically adjusting the volume (most time the length) of
the cavity [33,34]. This mechanical approach affects the rapidity and controllability of the
process. In a variable frequency system, the frequency can be varied to change the modes
electronically. Qiu et al. [35] used this method in composite processing. The results
showed that the speed and the controllability of the process were improved.
In Qiu et al.'s work [35], the mode selection was based on empirical heating
patterns. A large number of modes were involved in the mode-switching and a complex
mode-switching algorithm was needed. For each new material setup, the heating patterns
need to be re-characterized with extensive experimental measurement. This approach
needs to be implemented to reduce the amount of experimental work in heating pattern
characterization, reduce the number of modes, and simplify the mode-switching
algorithm. In this chapter, the variable frequency mode-switching method was
implemented and applied in microwave adhesive bonding of large-size materials to
obtain uniform heating in a single mode applicator. The electromagnetic modes were
diagnosed to obtain the theoretical electric field patterns. Modes with complementary
heating patterns were then selected according to the dimensions of the materials to be
heated. The mode combination with the least number of modes in it was used.
The main objective of this chapter is to design the variable frequency modeswitching based on theoretical mode patterns, verify the heating uniformity of this
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approach and compare the variable frequency mode-switching with single mode and
thermal adhesive bonding.
4.2 Experimental
4.2.1
Circuit fo r Microwave Adhesive Bonding
The circuit configuration used in this chapter was the same as that used in Chapter
3 (Figure 3.1). The microwave power source had variable frequency ability and the
frequency can be adjusted from 2 GHz to 4 GHz either manually or automatically. A
cylindrical single mode cavity with a diameter of 17.78cm was used. The cavity length
(Lc) and the probe depth (Lp) are adjusted to be 13.2cm and 2.0cm, respectively. The
sample is loaded at the center of the bottom plate of the cavity.
4.2.2
Materials
In the preliminary study of microwave adhesive bonding in Chapter 3, the
materials used were Bexloy W502 (major component: glass reinforced
ethylene/methacrylic acid copolymer) as the substrate and Eccobond A401-37 (epoxy
based) as the adhesive. In this chapter, this material system is also used. In addition, a
nylon 6 and ethylene/methacrylic acid copolymer substrate (Surlyn SG201U) is also used
with the Eccobond adhesive. The complex dielectric constant of Surlyn SG201U is 2.30j0.008.
62
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4.2.3
Sample Setup and Preparation fo r Adhesive Bonding
The sample setup was similar as that used in Chapter 3. All dimensions were the
same except that the width of the assembly was 7.62cm, three times as that used in
Chapter 3. The sample setup and temperature measuring points are shown in Figure 4.1.
Substrate Panel 1
\
Glass
Beads
Supporting Panel
Temperature
Probe HolesV
\
II II
Auxiliary Panel for
Temperature Measurement
^ ______
7
A
Adhesive Release Films
y
Substrate Panel 2
(a) Side View
Adhesive
Temperatures
Panel
Temperature
(b) Top View
Figure 4.1 Sample Setup and Temperature M easuring Points
Several glass beads (diameter 0.6mm) were embedded in the adhesive to get a
uniform thickness of the adhesive. Because of the large dimension of the assembly, the
adhesive temperature was measured at 5 points. Since the temperature of the adhesive
63
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between the two substrate panels can not be directly measured, an auxiliary panel was
used for temperature measurement to approximate the real adhesive curing environment.
Adhesive with the same dimension as the bonding area was applied between the auxiliary
panel and panel 2. Several small holes were drilled through the auxiliary panel, where the
temperature probes were inserted to measure the adhesive temperature. Two pieces of
microwave transparent release film with a thickness of 20pm were put between the
adhesive and the panels in the temperature measuring region. Adhesive between the
release films was tested with Differential Scanning Calorimetry (DSC) to measure the
residual heat. The extent of cure was then calculated with the following equation:
a = ( H t o t - H res) I H tot
(4.1)
Where a is the extent of cure, Hlot is the total heat of reaction, and Hrcs is the residual
heat measured with DSC.
The adhesive dimensions were 1.6cm x 7.62cm with a thickness of 0.6mm. The
entire assembly was 9.36cm x 7.62cm with a height of 6.6mm.
Before bonding, the Bexloy panels were degreased with acetone and dried at
77°C. The panels were roughened at the joint areas with abrasion paper in order to
enhance bonding. For the Surlyn substrates, a different preparation procedure was used
because the Nylon component tends to absorb moisture when exposed to air. The
existence of moisture not only affects adversely the bond quality, but also causes the
formation of hot spots in the substrates in microwave heating because of the high
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dielectric properties of water. The surface of Surlyn substrates was prepared according to
the procedures for adhesive bonding of Nylon 6 [94]:
1) Degrease with acetone.
2) Scrub with household cleaner, rinse, and dry at 150F for 2 days.
3) Roughen the surface to be bonded with 240-grit sandpaper.
4) Bond the substrates as soon as the materials are prepared.
After adhesive bonding, the assemblies were cut into 9.36cm x 2.54cm coupons
for single lap shear test.
4.3 Results and Discussion
4.3.1
Characterization o f Loaded Cavity
The mode spectrum (reflectance vs. frequency) usually changes as the type, size
or position of the material changes in a single mode cavity. Therefore, the cavity loaded
with materials needs to be characterized to locate the resonant frequencies of the modes
whenever there is a change in the factors mentioned above. The mode spectrums were
characterized for the cavity loaded with materials of dimensions shown in Figure 4.1 for
both Bexloy and Surlyn substrates. The frequency was swept from 2.0 to 4.0GHz and the
reflectance was obtained as the ratio of the reflected power (Pr) to the incident power
(Pi). The incident power level was controlled at 15±1W. The frequency with minimum
reflectance (Pr/Pi) is the resonant frequency of a mode. The mode spectrums for Bexloy
65
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and Surlyn substrates were very similar. The reason might be that the dielectric properties
of the two substrates were close and the size and position of the assemblies were the
same. Results of the mode characteristics for the Bexloy substrates are shown in Figure
4.2 and the mode spectrum for the Surlyn substrates is not plotted here because of its
similarity to Figure 4.2. A large number of modes were available in the cavity at
different frequencies. Most of the modes should have different heating patterns, though
some of them could have similar heating patterns. The availability of modes with various
heating patterns made it possible to select modes with complementary heating patterns to
obtain time-averaged uniform heating.
1
0.8
0.6
0.4
0.2
0
2.4
2.9
3.4
3.9
Frequency (GHz)
F igure 4.2 Characterization of Loaded Cavity (Sample Size: 93.6 x 76.2 x 6.06mm3)
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4.3.2
Mode Diagnosis and Selection o f Modes fo r Mode-switching
In order to locate modes with complementary heating patterns and to understand
the electric field distribution pattern inside the cavity, several electromagnetic modes
were diagnosed in the loaded cavity with the approach described in Chapter 3. Among
these diagnosed modes, the modes with resonant frequencies of 2.8450GHz and
3.3830GHz formed one of the possible mode combinations with complementary heating
patterns. Therefore these two modes were selected to use in the variable frequency modeswitching heating. For this reason the diagnosis of these two modes is briefly described
below. The mode at 2.8450GHz is referred to as mode 1 and the one at 3.3830GHz is
referred to as mode 2. The diagnosis includes two parts - characterization of the heating
pattern and measurement of the half wave number q. The major assumption used in
mode diagnosis was that after the sample was loaded into the cavity, the change of
resonant frequency was within 1 0 % of the resonant frequency in the empty cavity.
4.3.2.1
Characterization of Heating Pattern
To characterize the heating pattern of each mode, the temperature distribution in
the adhesive was measured as a function of time. Figure 4.3 (a) and (b) show the heating
profiles of Modes 1 and 2, respectively. The temperature distributions of both modes
were symmetric with respect to the horizontal central axis of the assembly. But the
heating preferences of the two modes were different. In heating with Mode 1, the center
temperature T 3 was the highest and the edge temperatures T 1 and T 5 were the lowest. In
heating with Mode 2, the edge temperatures T 1 and T 5 were the highest and the center
temperature T 3 was the lowest. Therefore Mode 1 preferentially heats the center of the
adhesive and Mode 2 preferentially heats the edges.
67
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120
100
/-“•s
□ □ □ ao o D D o D DD aaQ DD
U
-1°
?
A*
80
3
2D
<
e
£
ft * * 8 8 g t t 8 8
0 T1
A T2
□ A
ft0
□ «
$
s
•
*♦
60
40
□ T3
O T4
+ T5
20
0
0
5
10
15
20
Time (minute)
(a)
Heating Pattern of Mode 1 at 2.8450GHz
120
100
++++++++++*****+**
-«.rtOOO°
° T1
+ o
*T 2
+O
n T3
ft T4
+ T5
11□ D
time (minute)
(b)
Heating Pattern of Mode 2 at 3.3830GHz
Figure 4.3 Characterization of Heating Patterns of Modes 1 And 2
68
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4.3.2.2
Measurement of Half Wave Number Q
In the determination of the half wave number q, the relative radial electric field
strength was studied along the axial direction. Figure 4.4 (a) and (b) show the results of
the measurement of half wave number q, which is 0 for mode 1 and 2 for mode 2.
With the assumption used in the mode diagnosis, modes 1 and 2 were diagnosed
to be TM020 and TM212 respectively. The theoretical electric field patterns of the two
modes in the empty cavity were computed with electromagnetic field equations [37,
Chapter 5] and shown in Figure 4.5. Lighter region represents higher electric field
strength. These two modes provide complementary heating patterns for the adhesive
dimensions shown in Figure 4.6. Though the introduction of materials into the applicator
will distort the field distributions slightly, the mode patterns remain similar. The results
of mode diagnosis are summarized in Table 4.1.
4.3.3
Algorithm o f M ode-switching
Because only two modes were involved in the mode-switching, a simple
algorithm was used: If the center temperature (T3) is 3°C lower than the edge one
(maximum of T1 and T5), then switch the heating to center heating mode TM020. If the
edge temperature is 3°C lower than the center one, then switch the heating to edge
heating mode TM212.
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s
*o->
o
PQ
js
S
2
tfcj
u
o
ccd
w
*->
ca
u
u-.
°
5
0.2
0.4
0.6
0.8
Relative Radial Electric Field
(a) M ode 1 at 2.8450GHz: Half Wave Number q=0
14
S
o
4-*
O
m
U
■s
12
10
>
sO
uo
ea
8
6
4
2
0
0
0.2
0.4
0.6
0.8
Relative Radial Electric Field
(b) Mode 2 at 3.3830GHz: Half Wave Number q =2
Figure 4.4 Measurement of Half Wave Number Q
70
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1
0.8
0.8
0.4
0.2
0
0.2
•
•0.4
•
0.6
•0.8
•1
•1
-0.5
0
0.5
1
(a) Theoretical E field Pattern of Mode 1 (TM020) at the Cross-section of
the cavity at the adhesive plane in the Empty Cavity
1
0.8
0.6
0.4
0.2
o
0.2
•
-0.4
•
0.6
-
0.8
-1
(b) Theoretical E field Pattern of Mode 2 (TM212) at the Cross-section
of the cavity at the adhesive plane in the Empty Cavity
F igure 4.5 Theoretical E Field Patterns in the Empty Cavity
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Adhesive
C rosssection of
Coupling Probe
F igure 4.6 Dimension of the Adhesive inside the Cavity
T able 4.1 Summary of Mode Diagnosis
Resonant Frequency in
Loaded Cavity (F|) (GHz) for
the Bexloy Substrates
Resonant Frequency in
Loaded Cavity (Ft) (GHz) for
the Surlyn Substrates
Heating Preference
Half Wave Number q
Mode Name Diagnosed
Resonant Frequency in
Empty Cavity (F 2) (GHz)
Percentage of Frequency
Shift ((F,-F2)/F2* l0 0 % )fo r
the Bexloy Substrates
Percentage of Frequency
Shift ((F|-F2)/F2*100%) for
the Surlyn Substrates
M ode 1
2.8450
M ode 2
3.3830
2.8454
3.3846
Center of
the adhesive
0
TM020
2.9830
Edge of the
adhesive
2
TM212
3.5990
-4.63%
-6.00%
-4.61%
-5.96%
72
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4.3.4
Heating Profile o f Variable Frequency M ode-switching Adhesive Bonding and
Comparison with Thermal Process
4.3.4.1
Heating Profile of Eccobond/Bexloy Assembly
The TM020/TM212 mode combination was used in the variable frequency mode-
switching adhesive bonding process. For the assembly with Bexloy substrates, two
different heating cycles of the adhesive were used. One was to heat up the adhesive from
room temperature to 110°C in 6 minutes and then maintain at a constant level. The other
was to heat up the adhesive from room temperature to 120°C in 8 minutes and then
maintain constant. The microwave power profiles of these two heating cycles are shown
in Figures 4.7 and 4.8. A higher power level was required in the heating up phase and a
lower power was used in the isothermal phase. The heating profiles of these two heating
cycles are shown in Figure 4.9 (110°C) and Figure 4.10 (120°C), respectively. Adhesive
temperatures were measured at 5 different locations across the adhesive. The maximum
temperature gradient within the adhesive was less than 10°C. Heating uniformity of the
adhesive was greatly improved compared with single mode heating (Figure 4.3 (a) and
(b)). Panel materials were not substantially heated up and microwaves were concentrated
at the adhesive curing and interfacial bonding region.
To compare variable frequency mode-switching adhesive bonding with thermal
bonding, two thermal heating processes were performed in a thermal oven at 110°C and
120°C, respectively. The temperatures were measured with the same methods as that used
in microwave heating. The thermal heating profile at 120°C is shown in Figure 4 .11.
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30
25 ♦ ♦ ♦ ♦
20
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♦
♦
-
♦
♦
♦
§
♦
fc 15 £
5 0 —
0
20
10
30
40
Time (min)
Figure 4.7 Power Deposition in Mode-Switching Adhesive Bonding of Bexloy at 110 °C
20
-
Time (min)
F igure 4.8 Power Deposition in Mode-Switching Adhesive Bonding of Bexloy at 120 °C
74
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o Substrate T
□ Adhesive T1
A Adhesive T2
X Adhesive T3
- Adhesive T4
o Adhesive T5
Time (min)
F igure 4.9 Temperature Profile in Mode-Switching Bonding of Bexloy at 110 °C
140
120
U
60
u
T3
1
2
<u
p.
E
£
-
100 -
Adhesive T
° T1
80 -
,
...............................................................................................
a T2
PanelT
60
□ T3
40 -
x T4
+ T5
20
• T6
0
0
10
15
20
25
Time (minute)
F igure 4.10 Temperature Profile in Mode-Switching Bonding of Bexloy at 120 °C
75
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140
120
100
100
:
:
:
Time (minute)
Range of Adhesive
Average Adhesive Temperature
Panel Temperature
F igure 4.11 Temperature Profile in Thermal Bonding of Bexloy at 120 °C
Because the thermal heating mechanism was from outside to inside, the substrates
were first heated up and then heat was transferred to the adhesive via conduction.
Therefore the temperature of the substrates was always higher than that of the adhesive
and the heating of the adhesive was much slower compared with microwave process. The
maximum temperature gradient within the adhesive was around 2°C. For the thin film
adhesive sample, thermal temperature profile was more uniform than mode-switching
with the mode combination used in this study. However, in heating 3 dimensional
adhesive structures with complex shapes, thermal method will very possibly cause large
temperature gradients within the adhesives due to its non-selectivity and surface heating
nature. Microwave energy, on the other hand, can be tailored to perform uniform heating
with proper mode selections.
76
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4.3.4.2
Heating Profile of Eccobond/Surlyn Assembly
For Eccobond A401-37/Surlyn SG201U, the adhesive temperature could not get
higher than 100°C, otherwise the substrate surface adjacent to the adhesive would
degrade. The adhesive was heated up from room temperature to 100°C in 5.5 minutes and
then maintained at an isothermal temperature of 100°C. The temperature profile during
this process is shown in Figure 4.13. The temperature measuring points for the
Eccobond/Surlyn assembly are illustrated in Figure 4.12. The adhesive temperature was
measured at three points instead of five, because the temperature distribution is
symmetric with respect to the horizontal central axis of the assembly, as shown in Figure
4.3.
Panel
Temperature
o
o
o
o
o
/
Adhesive
Temperatures
T1
T2
T3
1
Figure 4.12 Temperature Measuring Points for the Eccobond/Surlyn Assembly (Top
View)
77
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120
100 ’
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o Adhesive T1
□ Adhesive T2
a Adhesive T3
o Substrate T
20
-
0
0
10
20
30
40
50
60
Time (min)
Figure 4.13 Temperature Profile in Mode-Switching Bonding of Surlyn at 100 °C
4.3.5
Study o f Adhesive C uring in M ode-Switching Microwave Process and
Comparison with Thermal Curing
During mode-switching microwave adhesive bonding, the extent of cure of the
adhesive was tested off-line with DSC as the function of heating time at 110°C and
120°C. Three samples at different locations were measured for each time point. The
average extent of cure and the standard deviation were calculated. Figure 4.14 shows the
average extent of cure vs time during the microwave process of 6 minutes of heat up and
then held isothermally at 110°C. Figure 4.15 represents the average extent of cure vs
time during microwave process with 8 minutes of heat up and then held isothermally at
120°C. The maximum incident power level was 35 Watts. The heating rate can be
78
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further increased with higher incident power. The microwave curing started at around
70°C. A significant degree of cure (70% for 110°C and 88% for 120°C) was obtained
before the isothermal curing stage was reached. The isothermal curing time was 24
minutes and 12 minutes for microwave at 110°C and 120°C, respectively. The ultimate
extent of cure was around 97% for 110°C and 99% for 120°C. The maximum standard
deviation of the extent of cure was 9.0% for both microwave 110°C and 120°C. The
average standard deviation was 3.9% for 110°C and 3.6% for 120°C.
11
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W
▲
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i
i
i
10
20
30
i
40
50
Time (minute)
F igure 4.14 Adhesive Extent of Cure vs. Time in Microwave Process of 6 Minutes of
Heat up and Then Isothermally at 110°C
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♦♦
0.4 -
Time (minute)
F igure 4.15 Adhesive Extent of Cure vs. Time in Microwave Process of 8 Minutes of
Heat up and Then Isothermally at 120°C
Adhesive curing was also studied in thermal adhesive bonding. Adhesives were
heated from room temperature to 110°C in 30minutes and to 120°C in 40 minutes.
Figures 4.16 and 4.17 show the adhesive extent of cure vs. time at 110°C and 120°C in
thermal heating processes. The curing started at around 110°C during thermal heating up.
Before the isothermal curing stage was reached, a low degree of cure (3% for 110°C and
20% for 120°C) was obtained. The required isothermal curing time was 90 minutes at
110°C and 60 minutes at 120°C. The ultimate extent of cure was around 95% for thermal
110°C and 99% for thermal 120°C. Comparison between mode-switching curing and
thermal curing is summarized in Table 4.2. Mode-switching microwave curing started at
a lower temperature and was much faster than thermal curing. At 110°C, the ultimate
extent of cure of microwave samples was slightly higher than that of thermal samples. At
120°C, the ultimate extent of cure for the two methods was about the same.
80
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0-6 '
0.5 0 .4 0.3 0.2 0.1 0 <F
0
w
♦
i
l
50
l
100
150
200
Time (minute)
F igure 4.16 Adhesive Extent of Cure vs. Time in Thermal Heating of 30 Minutes Heat
up and Then Isothermally at 110°C
o
U
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w
11
0.9 0.8 0.7 0 .6 0.5 0 .4 0.3 0.2 0.1 nU i'
0
♦
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1
1
50
100
150
Time (minute)
F igure 4.17 Adhesive Extent of Cure vs. Time in Thermal Heating of 40 Minutes Heat
up and Then Isothermally at 120°C
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T able 4.2 Comparison between Mode-Switching and Thermal Curing at 1 L0°C and
120°C
Curing
Conditions
Total
Required
Heating
Time
Ultimate
Extent of
Cure
Maximum
Standard
Deviation
O f Extent of
Cure
Average
Standard
Deviation
Of Extent
I of Cure
4.3.6
Microwave
Process of 6
min heat up and
then
isothermally at
110°C
30 min
Microwave
Process of 8
min heat up and
then
isothermally at
120°C
20 min
Thermal
Process of 30
min heat up and
then
isothermally at
110°C
120 min
Thermal
Process of 40
min heat up
and then
isothermally at
120°C
100 min
97.4%±1.0%
98.5% ±1.0%
95.4%±0.2%
98.8% ±0.4%
9.0%
9.0%
3.1%
3.8%
3.9%
3.6%
1.1%
1.6%
Comparison o f B ond Strength between M ode-Switching Microwave and
Thermal Bonding Processes
4.3.6.1
Bond Strength of Eccobond/Bexloy Assembly
For Eccobond/Bexloy, two assemblies were prepared for each microwave or
thermal process. After bonding, each assembly was cut into 3 coupons and tested with
single-lap shear equipment at a crosshead displacement rate of 0.05 inch/minute
(0.127cm/minute). Results are shown in Table 4.3. For each mode-switching bonded
82
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assembly, the shear strength of the three coupons was close. This result verified the
heating uniformity of the TM020/TM212 mode-switching process. In addition, the
comparison between the results in Table 4.2 and that in Figure 3.12 shows that the shear
strength of mode-switching bonded large size samples was approximately equal to that of
the single mode microwave bonded small size samples. In addition, the shear strength of
mode-switching bonded samples was significantly higher than that of thermally bonded
ones. In the single lap-shear testing, microwave bonded assemblies all broke in the
substrate, indicating that the interface and the adhesive were stronger than the substrate.
On the other hand, thermally bonded samples all broke at the interface, showing that the
bond strength of thermal samples did not reach the maximum possible value even when
the adhesive was almost fully cured.
4.3.6.2
Bond Strength of Eccobond/Surlyn Assembly
For microwave adhesive bonding of the Eccobond/Surlyn assembly, the heating
up time was 5.5 minutes and the isothermal bonding time was approximately 45minutes
at 100°C. To compare with thermal process, some assemblies were also bonded in a
thermal oven at 120°C. The thermal bonding temperature was 120°C instead of 100°C
because thermal bonding at 100°C was too slow. The approximate time for the thermal
bonding at 120°C was 100 minutes determined by trial and error. The strength of the
bonded assemblies was determined with single lap shear test at a crosshead displacement
rate of 0.05 inch/minute. For each bonding process, three samples were tested. Results
are shown in Table 4.4.
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Table 4.3 Bond Strength of Eccobond/Bexloy Assembly with Microwave or Thermal
Method
Bonding Cycles
Shear
Strength
(MPa)
Break
Pattern
Assembly
1
Coupon
1_1
Coupon
1_2
Coupon
1_3
Assembly Coupon
2
2_1
Coupon
2_2
Coupon
2_3
Average Shear Strength (MPa)
Standard Deviation of the
Shear Strength (MPa)
Microwave
6 min heatup, 24 min
isothermal
bonding at
110°C
Shear in
Panel
5.63
Microwave
8 min heatup, 12 min
isothermal
bonding at
120°C
Shear in
Panel
5.95
Thermal
30 min
heat-up,
90 min
isothermal
at 110°C
Shear at
interface
3.69
Thermal
40 min
heat up,
60min
isothermal
at 120°C
Shear at
interface
3.74
6.05
6.12
2.45
3.84
5.60
4.84
2.66
3.12
7.45
5.77
2.65
3.05
5.02
7.06
2.88
2.67
5.46
5.09
2.76
2.94
5.87
0.84
5.80
0.79
2.85
0.43
3.23
0.46
Table 4.4 Bond Strength of Eccobond/Surlyn Assembly with Microwave or Thermal
Method
Bonding Conditions
Break Pattern
Strength of the
Assembly (MPa)
Microwave 5.5 min heat up and 45
Shear in Panel
6.14±1.02
Shear in Panel
6.0610.48
min isothermal bonding at 100°C
Thermal at 120°C for 100 min
Table 4.4 shows that microwave bonded assemblies at 100°C for 45 minutes
obtained the same strength as thermally bonded assemblies at 120°C for 100 minutes.
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Both microwave and thermally bonded assemblies broke in the substrates in single lap
shear test. Since the interface and adhesive were stronger than the substrates for both
microwave and thermally bonded assemblies, it was uncertain whether there was
microwave enhancement of the adhesion between the adhesive and the substrate for the
Eccobond/Surlyn assembly.
4.4 Conclusions
This chapter implemented the variable frequency mode-switching method to
select modes based on theoretical electric field patterns, reduce the number of modes
used in mode-switching and simplify the mode-switching algorithm. The implemented
mode-switching method is applied in microwave adhesive bonding of large-size materials
to obtain uniform heating in a single mode applicator.
Eccobond A401-37 (epoxy based) was used as the adhesive to bond two substrate
materials, Bexloy W502 (major component: glass reinforced ethylene/methacrylic acid
copolymer) and Surlyn SG201U (Nylon 6 and ethylene/methacrylic acid copolymer). In
the mode-switching process, it was observed that microwaves heated the adhesive rapidly
and selectively. Compared with single mode heating, mode-switching greatly improved
the heating uniformity.
The extent of cure of the adhesive was studied off line as a function of time at
different temperatures for both microwave and thermal bonding processes. Results
showed that the adhesive curing with microwaves was much faster than the thermal
process at the same temperature.
85
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For Eccobond A401-37/Bexloy W502, results of microwave adhesive bonding
have shown 75% to 80% reduction in bonding time and at least 2-fold enhancement of
bonding strength compared with thermal process. Microwave bonded assemblies broke in
the substrates, while thermally bonded assemblies broke at the interface even at 99% of
cure of the adhesive.
For Eccobond A401-37/Surlyn SG201U, assemblies bonded with microwaves at
100°C for 45 minutes obtained the same strength as thermally bonded assemblies at
120°C for 100 minutes. Both microwave and thermally bonded assemblies broke in the
substrates in single lap shear test. Since the interface and adhesive were stronger than the
substrates for both microwave and thermally bonded assemblies, it was uncertain whether
there was microwave enhancement of the adhesion between the adhesive and the
substrate.
Therefore, observed microwave effects in adhesive bonding of the two systems
include reduction of bonding time for both systems and enhanced bonding strength for
Bexloy W502 substrates. These results motivate further investigation into microwave
heating and bonding mechanisms.
86
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CHAPTER 5 IN SITU MONITORING OF VARIABLE FREQUENCY
MICROWAVE PROCESSING IN A SINGLE MODE CAVITY
5.1 Introduction
Studies on the single mode and mode-switching microwave adhesive bonding are
presented in Chapters 3 and 4. The bonding cycle was determined by measuring either
the bonding strength (with single-lap shear test) or the extent of cure (with DSC) vs. time.
These measurements were carried out off-line and required tremendous amount of
experimental work. In order to reduce the amount of experiments and to realize
intelligent processing, an on-line monitoring technique needs to be developed.
Among several research efforts of monitoring microwave processing on-line,
Compton, et. al andYoung et al. [95,96] have employed Fourier transform infrared
(FTIR) spectroscopy to directly monitor the cure of composite materials. In this
technique, an exposed optical fiber sensor is embedded in the materials to monitor
material spectroscopic properties associated with the curing process. Marand et al. [12]
have applied cavity perturbation technique to on-line monitor the dielectric properties of
epoxy. At the same time, they used the FTIR technique to monitor the spectroscopic
properties of epoxy. The development of these on-line monitoring techniques has led to
improvements in processing materials and studying reaction mechanisms. Without
debating the significance of these techniques, some inherent disadvantages in these
techniques exist. In on-line monitoring with FTIR, the exposed fiber sensor has lower
signal to noise ratio compared with that in the transmission spectra. Repeated usage leads
to degradation and breakage of the fiber sensor, which results in high cost. In on-line
87
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monitoring material dielectric properties, the cavity perturbation technique is difficult to
be applied in microwave processing of materials with large sizes and complex shapes.
Under these circumstances, a new method needs to be developed to monitor in
situ microwave adhesive bonding of large samples. In variable frequency mode-switching
microwave processing in a single mode cavity, resonant frequencies shift due to changes
in material dielectric properties. Any decrease in the dielectric property leads to an
increase in the resonant frequency [37, Chapter 7]. The operating frequency needs to be
constantly tuned to maintain the resonant state inside the microwave cavity. The resonant
frequency shifting, which reflects the change in dielectric properties, can be used to
monitor in situ the microwave processing. This provides a new method for determining
the microwave/material interactions on-line. This new on-line monitoring technique was
described in detail in [97] (patent application in process). The method can be applied in
the microwave processes that involve changes of material dielectric properties in a single
mode applicator. In this chapter, the application of this on-line monitoring technique in
several microwave adhesive bonding processes is studied. In these processes, different
substrates or assembly setups were used. These processes are presented in Table 5.1. The
substrates were obtained from DuPont and the adhesive was from Grace Specialty
Polymers.
88
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Table 5.1 Microwave Adhesive Bonding Processes to Be Studied with the on-Line
Monitoring Technique
Substrate
Process 1
Process 2
Process 3
Bexloy W502 (major
Surlyn SG201U
Bexloy W502
component: glass
(major components:
(major component:
reinforced
nylon 6 and
glass reinforced
ethylene/methacrylic
ethylene/methacrylic
ethylene/methacrylic
acid copolymer)
acid copolymer)
acid copolymer)
Eccobond A401-37
Eccobond A401-37
Eccobond A401-37
(major component:
(major component:
(major component:
epoxy)
epoxy)
epoxy)
Single-lap
Single-lap
Double-lap
Adhesive
Assembly
Setup
5.2 Advantages Of This Technique
The advantages of this technique over existing approaches are:
-
D ia g n o sis w ith N on-insertion M e th o d
The measurement of resonant frequencies does not use a probe to be embedded
into material samples. Thus this technique eliminates the disadvantages such as
degradation, breakage and high cost, which are associated with the usage of
probes.
89
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A b ility to M o n ito r the M icrow ave P rocessing o f M aterials w ith L arge Sizes a n d
-
C om plex Shapes
This technique monitors the change in resonant frequencies by scanning the
frequency and measuring the microwave reflectance. The diagnosis can always be
performed regardless of material sizes and shapes. Therefore this technique has
wider applications relative to the method of monitoring dielectric properties with
cavity perturbation technique.
-
N o R eq u irem en t o f S ep a ra te D iagnostic C ircuit
In this technique, the diagnosis uses the same circuit as that of variable frequency
microwave processing. No additional facilities are required. The diagnosis is fast
because no circuit switching is involved.
5.3 On-line Monitoring o f Microwave Adhesive Bonding of Single-Lap Bexloy
W502/ Eccobond A401-37
5.3.1
Experimental
The material setup was the same as that used in Chapter 4 in the variable
frequency mode-switching adhesive bonding process. Because the bonding cycle for the
Bexloy/Eccobond system had been determined with off-line measurement of the extent of
cure vs. time in Chapter 4, applying the on-line monitoring method to this system can
provide a check-up for the new method.
90
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The two electromagnetic modes TM020 and TM212 used in Chapter 4 were
applied in this study to obtain uniform heating. The starting resonant frequencies for
modes TM020 and TM212 were 2.8450 GHz and 3.3830 GHz, respectively.
In microwave adhesive bonding of the low loss Bexloy W502 substrates, the
substrates are not substantially heated up. The change of substrate dielectric properties is
not as dramatic as that of the adhesive. In the epoxy adhesive curing process, the
dielectric constant and loss factor decrease as cross-linking reaction proceeds. Any
decrease in the dielectric property leads to an increase in the resonant frequency [37,
Chapter 7]. Thus the shifting of the resonant frequency can be used to monitor in situ the
microwave adhesive bonding process. The resonant frequencies were diagnosed
periodically. The diagnosis took about 2 seconds each time and had nearly no influence
on microwave heating.
5.3.2
Results and Discussion
Figure 5.1 shows the resonant frequency shifting during the microwave process of
6 minutes heat up of the adhesive and then isothermally at 110°C. The low loss Bexloy
W502 substrates were not substantially heated up. The resonant frequency shifting curves
take similar shapes as the adhesive curing curve shown in Figure 4.5. At the very
beginning of sample heating up, the cross-linking did not take place and the rising of
temperature should lead to an increase in adhesive dielectric properties. Consequently it
was expected that the resonant frequency should shift down slightly. However, the
resonant frequency of TM020 did not shift up or down at the beginning in most
experimental runs and shifted down slightly in some experiments. The resonant
frequency of T M 212 shifted up slightly at the beginning in nearly all experiments. The
91
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reason for this phenomenon might be that the increase in the adhesive dielectric
properties at the beginning was too small to be detected because of the small size of the
adhesives in this experimental setup.
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1a
0.5
0
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a
0
10
20
30
40
50
Time (minute)
F igure 5.1 Shifting of Resonant Frequency in Microwave Adhesive Bonding of SingleLap Bexloy Substrates at 110°C
As shown in Figure 5.1, the resonant frequencies shifted up at an increased rate
with the onset of curing, which occurred after 2 or 3 minutes of heating (temperature
around 70°C). The shifting rate remained high for a period of time, corresponding to the
high curing rate of the adhesive. When the curing approached completion, the curing rate
decreased and the shifting of resonant frequencies slowed down as well. After 92% of
cure was obtained, which occurred after the 20th minute, the frequency shifting became
less obvious. This was because the increase in the extent of cure was too small to detect
92
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with the shifting of resonant frequency. After this point it took another 10 minutes to
reach the ultimate extent of cure. The final frequency shifting was about 4.0MHz and
2.9MHz for TM020 and TM212 modes respectively.
Similar frequency shifting results were obtained for the process of 8 minutes heat
up and then isothermally at 120°C, as shown in Figure 5.2. The resonant frequencies of
both modes kept shifting and became less obvious after 94% of cure was reached, which
occurred after the 13th minute. After this point it took another 7 minutes to reach the
ultimate extent of cure. The final frequency shifting was around 3.5MHz for TM020 and
2.5MHz for TM212.
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1.5
Uh
w
1
§
e
oC/J
0.5 -
OS
A A
▲ A A A
A
□
A
Mode TM020
□ Mode TM212
o 9-2-0.5 ->—
10
15
20
25
30
Time (minute)
F igure 5.2 Shifting of Resonant Frequency in Microwave Adhesive Bonding of SingleLap Bexloy Substrates at 120°C
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Therefore, monitoring the resonant frequency shifting provided information about
the curing status of the adhesive during microwave adhesive bonding. When the curing
rate was high, the rate of resonant frequency shifting was high too. When the curing
approached completion, the curing rate decreased and the shifting of resonant frequencies
slowed down as well and finally leveled off.
5.4 On-line Monitoring of Microwave Adhesive Bonding of Single-Lap Surlyn
SG201U / Eccobond A401-37
5.4.1
Experimental
For Surlyn/Eccobond system, the two electromagnetic modes TM020 and TM212
were again applied in this study to obtain uniform heating. The starting resonant
frequencies for modes TM020 and TM212 were 2.8454 GHz and 3.3846 GHz,
respectively.
5.4.2
Results and Discussion
Figure 5.3 shows the resonant frequency shifting during the microwave process of
5.5 minutes heating up of the adhesive and then maintained isothermally at 100°C. At
the very beginning of sample heating up, the cross-linking did not take place and the
rising of temperature led to a small increase in the dielectric properties of the adhesive.
However, the resonant frequency shifted down noticeably at the beginning of microwave
heating. This phenomenon was different from that of Eccobond/Bexloy system. The
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reason might be that the dielectric properties of Surlyn substrates increased noticeably
with temperature because of the Nylon-6 component. After the minimum resonant
frequency was reached, the resonant frequency shifted up at a high rate. This
corresponded to the rapid decrease of material dielectric properties, which resulted from
the high curing rate of the adhesive. Finally the shifting of the resonant frequency slowed
down and became less obvious after a total time of 50 minutes. This indicated that the
curing reaction of the adhesive almost completed.
0.001
N
a
o
■
0.0005
-C
C/3
:
■
i
I
*
0
U
c<u
3 -0.0005
cr
0.001
c3
C
O
oUo -0.0015
-
-
Pi
-
♦ ■
*
♦ Mode 1 (TM020)
■ Mode 2 (TM212)
♦♦
0.002
10
20
30
40
50
60
Time (minutes)
F igure 5.3 Shifting of Resonant Frequency in Microwave Adhesive Bonding of SingleLap Surlyn Substrates at 100°C
With the on-line monitoring method, the microwave bonding cycle was
determined to be 5.5 minutes heating up and 45 minutes isothermal bonding.
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5.5 On-line Monitoring of Microwave Adhesive Bonding of Double-Lap Bexloy
W502/ Eccobond A401-37
5.5.1
Experimental
Variable frequency microwave mode switching method was applied in bonding a
double-lap shear assembly of Bexloy W502 / Eccobond A401-37. The sample setup is
shown in Figure 5.4. The size of the substrate panels 1 and 2 was 45mm x 76.2mm. The
size of substrate panels 3 and 4 was 45mm x 11mm. The length of each overlap was
4mm, where the adhesive was applied. The space between panels 1 and 2 was 3mm. Two
supporting panels were used to prevent deformation of the bonds. Several glass beads
(diameter 0 .6 mm) were embedded in the adhesive to get a uniform thickness of the
adhesive. The length of the entire assembly was 93mm (shorter than that suggested by
double lap shear Standard Test Method to fit into the cavity). The two electromagnetic
modes TM020 and TM212 were again applied in this study to obtain uniform heating.
The starting resonant frequencies for mode TM020 and TM212 were 2.8392GHz and
3.3765GHz, respectively.
Because both the electric field and sample dimensions are symmetric with respect
to the central axis of the sample, the temperature distribution is symmetric too. This
symmetric temperature distribution was observed in previous single lap adhesive bonding
study. In this study the temperatures of the adhesive of the top layer were measured at 3
locations (T) to T 3). Panel temperature was also monitored at 1 point (T4).
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Substrate
Panel 1
Glass_
Beads
Adhesive
Su Dstrate Panel 3
Substrate
Panel 2
i_____
Supporting Panel 1
Substrate Panel 4
Supporting Panel 2
(a) Side View
Y
▲
Adhesive
Temperatures
T3
t4
Substrate
Temperature
(b) Top View
Figure 5.4 Sample Setup of Double-Lap Shear Assembly
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The adhesive was heated up to 120°C in 9 minutes and then maintained
isothermal. The temperature profile during this process is shown in Figure 5.5. The on­
line monitoring method was used to determine the bonding cycle.
140
120
/— ■v
U
60 100
<D
Q
0 80
3c3
60
<U
01
a 40
£
20
. f
t
□f t
*
x x x x x x x x x x x x
~ X X
X
o Adhesive T1
□ Adhesive T2
X
%- X
X
X
10
15
A
Adhesive T3
X
Substrate T
20
25
Time (min)
Figure 5.5 Temperature Profile in Microwave Adhesive Bonding of Double-Lap Shear
Assembly of Bexloy Substrates
5.5.2
Results and Discussion
Figure 5.6 shows the resonant frequency shifting during the microwave process of
9 minutes heating up of the adhesive and then maintained isothermally at 120°C. At the
very beginning of sample heating up, the cross-linking did not take place and the rising of
temperature led to a small increase in the dielectric properties of the adhesive.
Consequently the resonant frequency shifted down at the beginning of microwave
heating. The degree of frequency shifting down of the double-lap assembly was larger
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than that of the single-lap assembly. This was because of the larger material size used in
the double-lap assembly. After the minimum resonant frequency was reached, the
resonant frequency shifted up at a high rate. This corresponded to the rapid decrease of
material dielectric properties, which resulted from the high curing rate of the adhesive.
Finally the shifting of the resonant frequency slowed down and became less obvious after
a total time of 19 minutes. This indicated that the curing reaction of the adhesive almost
completed.
With the on-line monitoring method, the microwave bonding cycle was
determined to. be 9 minutes heating up and 10 minutes isothermal bonding.
The strength of the bonded assemblies was determined with double lap shear test
at a crosshead displacement rate of 0.05 inch/minute. For each bonding cycle, three
samples were tested. Results are shown in Table 5.2. The assemblies did not break even
after the strain reached 100%. During the testing, the cross-section of the substrate
became narrower and narrower and the testing load dropped slightly after the peak was
reached. Obviously if further tested, the assembly would break within the substrate in a
tensile manner because of the narrowing cross-section of the substrate. The break pattern
in double-lap shear test was different than that in the single-lap shear test. This was
because single-lap shear setup caused deformation of the assemblies during testing and
finally tore the assembly up in a shear manner. The double-lap shear setup, however, did
not result in deformation of the tested assemblies.
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3.50
3.00
2.50
c
o
C /3
<D
Pi
♦♦
2.00
x:
in
u
e<u
a
cr
£Uh
ccd
♦
1.50
-
1.00
a
□
♦ Mode 1 (TM020)
o
°
□
♦
-1.50
-
n
□ □□
1.00
0.50
0.00
-0.50 I) 9
♦
♦ ♦♦♦
□ □ □□
dD
5'
□ Mode 2 (TM212)
l
'1
10
15
20
2
♦
2.00
Time (min)
Figure 5.6 Shifting of Resonant Frequency in Microwave Adhesive Bonding of DoubleLap Bexloy Substrates at 120°C
Table 5.2 Bond Strength of Microwave Bonded Double-Lap Shear Assemblies
Bonding Cycles
Break Pattern
Shear Strength (Peak Value)
Microwave 9 min heat-
Did not break even at
5.93MPa ± 0.39MPa
up, 10 min isothermal
100% strain
bonding at 120°C
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5.6 Conclusions
A method has been developed to on-line monitor microwave processing in a
single mode applicator. This method is not intrusive, able to monitor microwave
processing of materials with large sizes and complex shapes, and do not require separate
diagnostic circuit. The new on-line monitoring method was applied in several microwave
adhesive bonding processes, including bonding of single-lap Bexloy /Eccobond, single­
lap Surlyn /Eccobond, and double-lap Bexloy /Eccobond assemblies. During the bonding
process, the curing of the adhesive led to decreases in the dielectric constant and loss
factor. Resonant frequencies of the modes, which reflected changes in material dielectric
properties, were monitored during microwave adhesive bonding. When the curing rate
was high, the rate of resonant frequency shifting was high too. When the curing
approached completion, the curing rate decreased and the shifting of resonant frequencies
slowed down as well and finally leveled off. Thus when the resonant frequencies stopped
shifting, the bonding was considered completed. Bonding cycles were determined with
the on-line monitoring method.
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CHAPTER 6 PROCESS CONTROL SYSTEM FOR MICROWAVE ADHESIVE
BONDING
6.1 Introduction
In Chapters 3 and 4, single mode and mode-switching microwave adhesive
bonding in a single mode cavity are discussed. A new on-line monitoring technique for
microwave processing in a single mode cavity is presented in Chapter 5. In all the work,
data acquisition and process control was essential to eliminate the extensive recording of
experimental data by hand, reduce the continuous adjustment of the instruments, tailor
microwave energy to perform uniform and stable heating, and enhance the repeatability
of the experiments. The process control system was developed at the beginning of this
research and implemented throughout the dissertation. In this chapter, the functions,
structures and algorithms of the process control system are discussed.
Research has been conducted to build process control systems for microwave
processing in a single-mode cavity [33, 35, 34]. Adegbite et al. [33] developed a process
control system to obtain uniform processing in fixed frequency microwave processing.
Using a fixed frequency microwave power source, the mode switching was realized by
adjusting cavity length and coupling probe depth. To ease the operation of the microwave
processing system, work was done to automate the control of the fixed frequency
microwave power source and the adjustment of the resonant cavity. Relatively uniform
processing was achieved for 3-inch 24-ply square graphite/epoxy composite parts.
However, the mechanical tuning of the cavity affected the rapidity and stability of the
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temperature control. Large temperature fluctuations and gradients were observed
throughout the heating process.
Fellows et al. [34] used fixed frequency mode switching technique to process Vshaped polyester/glass composite parts. Slow mechanical adjustment of cavity length for
mode switching resulted in instability of temperature control and non-uniform
temperature distribution.
With the use of a variable frequency microwave power source, Qiu et al. [35]
developed a process control system for variable frequency microwave processing of
polymer and composite materials. This technology provided more uniform and stable
processing of composite parts compared with fixed frequency mode switching. The
variable frequency power source was automated to realize computer control of
microwave power and frequency. Control hardware was implemented based on the fixed
frequency control system. Two processing techniques were studied, including mode
sweeping and intelligent mode switching. The temperature distribution was more uniform
with intelligent mode switching than mode sweeping heating. In mode switching
processing, empirical heating modes were used. The empirical heating characteristics of
each mode, including heating rate and heating pattern, were measured before the
processing and stored in a database. These data were then used for mode selection during
processing to achieve uniform heating. In controlling processing temperature, both a
simple parabolic power controller and a multi-staged PID controller were used for
microwave power control. However, empirical controller parameters were used and
extensive experimental work was needed to find the parameters when there was a change
in material setup.
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The variable frequency microwave power source and control hardware used in
this chapter are those implemented by Qiu et al. [35]. This chapter is focused on
developing software to perform data acquisition and process control to achieve rapid,
uniform and stable heating.
6.2 Structure of the Process Control System for Microwave Adhesive Bonding
Two bonding processes were studied in this dissertation: single mode microwave
adhesive bonding for small size materials and mode switching microwave adhesive
bonding for large materials. The process control system was first developed for single
mode microwave adhesive bonding and then implemented for mode switching process to
obtain uniform heating for large size materials. The process control system for the
variable frequency mode switching adhesive bonding process will be described as
follows.
Existing hardware configuration in [35] was used in variable frequency
microwave adhesive bonding process. Software was programmed in LabVIEW for cavity
characterization, data acquisition and process control. The software in this dissertation
was developed in parallel with that for variable frequency microwave processing of
composites [35] and further implemented the program in [35]. There are three major
implementations of this work over that in [35]:
First, the software in [35] required extensive input information because empirical
heating modes were used. The empirical heating characteristics of each mode, including
heating rate and temperature distribution, were measured before the processing and stored
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in a database. These data were then used for mode selection during processing to achieve
uniform heating. Therefore the adaptability of the program to other processes was
affected. If a new material setup is used, then the extensive heating characterization needs
to be performed again before the processing. This problem can be solved with the
theoretical modes, which were used in adhesive bonding process in this research. With
the theoretical modes, the heating rate and temperature distribution were not necessary to
be measured and input into computer before the experiments.
Second, the parameters of the proportional-integral-differential (PID) controller in
[35] were empirical values. The controller parameters in this dissertation were obtained
based on control theory. This implementation eliminated the trial and error procedure of
adjusting controller parameters and also provided sound basis for automatic tuning of the
parameters.
Third, an on-line monitoring technique was developed for microwave adhesive
bonding process in this dissertation. A sub-controller was programmed to perform the on­
line monitoring.
The hierarchy of the software for microwave adhesive bonding process is shown in
Figure B .l in Appendix B. The software includes two main programs. One is cavity
characterization before bonding to obtain the mode spectrum, the other is process control
during bonding to achieve rapid, uniform and stable heating with on-line monitoring
feature. LabVIEW was used to program the software, which includes a number of sub­
programs. These programs are shown in Appendix B. The images in Appendix B of
this dissertation are presented in color.
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6.3 Program for Cavity Characterization
The LabVIEW program for the cavity characterization (cavity characterization.vi)
is shown in Figure B.2 and Figure B.3. Cavity characterization was performed with
measuring the incident power (Pi) and the reflected power (Pr) as a function of frequency
to obtain the mode spectrums. The frequency with minimum reflectance (Pr/Pi) was the
resonant frequency of a mode. The most important caution when editing and using this
program is to make sure that the scale factors for the input power (Pi Scale) and reflected
power (Pr Scale) in the program should be the same as that in the power meters. The
following equations were used to convert the acquired data into power data [98]:
Pi [W] = Pi Scale [W/v] x Acquired Voltage for Input Power [v]
(6.1)
Pr [W] = Pr Scale [W/v] x Acquired Voltage for Reflected Power [v]
(6.2)
Other parts of this program are straightforward and will not be explained in more
detail in this chapter.
6.4 Program for Process Control
The LabVIEW program for the process control (VFMS.vi) is shown in Figure B.4,
Figure B.5 and Figure B.6. The process control program is composed of a number of sub­
programs, including data acquisition, mode-switching, power and on-line monitoring
controllers.
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6.4.1
Subprograms fo r Data Acquisition
In data acquisition, the temperatures of the materials and the incident and reflected
microwave powers are obtained through an A/D board and then fed back to the process
controllers. The subprogram 6T acquires temperature data at six points, three of which
are measured with Luxtron thermometer and the other three are measured with Nortech
thermometer. The following equations are used to convert the acquired voltage data into
temperature [88,89]:
For Luxtron: T [°C] = Acquired voltage [v] x 1000 [mv/v] / 20 [mv/°C]
For Nortech: T [°C] = Acquired voltage [v] x 40 [°C/v] - 100 [°C]
(6.3)
(6.4)
The LabVIEW programs for temperature data acquisition are shown in Figures B.7
to B.12. The microwave power data are obtained with the subprogram power.vi, as
shown in Figures B.13 and B.14.
6.4.2
Subprograms fo r M ode-Switching
A variable frequency mode-switching controller was programmed with LabVIEW
to achieve uniform heating by switching among modes with complementary heating
patterns. The LabVIEW programs are shown in Figures B.15 and B.16. The temperature
distribution was analyzed on-line to obtain the heating characteristics and to decide the
complementary heating pattern. The mode-switching controller minimized the
temperature gradient by determining which mode was to be used next. The resonant
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frequency of the new mode was controlled through a GPIB interface between the sweep
oscillator and the computer.
6.4.3
Subprograms fo r Microwave Power Control
The objective of the power controller is to keep the heating rate below maximum
void free value during the adhesive heating up and maintain the temperature at constant
value during isothermal bonding. The LabVIEW programs for power control are shown
in Figures B .I7 and B.18.
There are two phases during the microwave adhesive bonding process. The first
phase is the heating from room temperature to the isothermal bonding temperature. The
second phase is isothermal microwave bonding. Different algorithms were used in the
two phases to control the heating rate and isothermal bonding temperature, respectively.
6.4.3.1
Control of Heating Rate
During the heating up of the adhesive from room temperature to the bonding
temperature, on-off control was used to keep the heating rate below the maximum void
free value (2°C/s for the Eccobond adhesive). The heating rate was calculated on-line
with the LabVIEW programs shown in Figures B.19 and B.20. If the heating rate was
below the maximum value, then the maximum input power level was used for fast
heating. If the heating rate exceeded the maximum value, then the power was turned off
to prevent bubble formation.
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6.4.3.2
Control of Isothermal Bonding Temperature
During isothermal bonding, traditional proportional-integral-differential (PID)
was used to control the bonding temperature by adjusting the incident power level. The
highest measured temperature was controlled in the isothermal bonding. The velocity
form of the PID algorithm was used:
Pn ~ P n—1 ~ K c [(en - e n —\) + - ^ - e n +
(<?n ~ 2 e n_i + £71- 2 )]
(6.5)
Where Pn and Pn-i are the desired and previous incident powers, Kc is the proportional
control gain,
Tj
and Td are the integral and differential control time constants, At is the
sampling period, en, en.j, and en_2 are the temperature offsets at time n, n-1 and n-2,
respectively. The PID controller was implemented with LabVIEW program, as shown in
Figures B.21 and B.22.
The PID parameters Kc, Ti and Td were obtained with Ziegler-Nichols frequency
response method [99]. The proportional control action was used to find the ultimate gain
Ku and the ultimate period Tu. The gain was slowly increased until the process began to
oscillate. Ku is the gain when this oscillation occurs and Tu is the period of the
oscillation. The parameters of PID control were then calculated with Ziegler-Nichols
method based on Ku and Tu. The typical temperature oscillation for determining Ku and
Tu is shown in Figure 6.1.
The PID parameters for single mode adhesive bonding are listed in Table 6.1. In
variable frequency mode switching bonding with TM020 and TM212 modes, PID control
was not as stable as desired. The temperature fluctuation could be as high as ±3 °C with
respect to the set point temperature. To stabilize the control, differential action was
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disabled and the proportional- integral (PI) actions were used together. The PI parameters
were obtained with Ziegler-Nichols method and listed in Table 6.2. The parameters for
the two modes were close but not the same. Therefore a separate PI controller was used
for each of the two modes. With these control parameters, the temperature oscillation can
be controlled within ±1°C with respect to the set point temperature. To simplify the PED
LabVIEW program, an additional subroutine was used to input the PID parameters, as
shown in Figures B.23 and B.24.
122
120
-
110
200
220
240
260
280
Time (sec)
Figure 6.1 Temperature Oscillation for Determining Ku and Tu
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300
Table 6.1 PID Controller Parameters for Single Mode Microwave Adhesive Bonding
Kc (watt/°C)
Ti (sec)
Td (sec)
9.0
7.1
1.7
(0.6Ku)
(0.5Tu)
(0.12Tu)
Parameters obtained from
Ziegler-Nichols method
* Ku=l 5 watt/°C, Tu=l 4.3 sec.
T able 6.2 PI Controller Parameters for Variable Frequency Mode Switching Bonding
Mode 1
Ku
Tu
(watt/°C)
(sec)
12.0
42.4
(TM020)
Mode 2
11.0
37.4
(TM212)
6.4.4
Kc
Ti
(sec)
4.8
33.9
(0.4Ku)
(0.8Tu)
4.4
29.9
(0.4Ku)
(0.8Tu)
Subprogram fo r On-line M onitoring
The algorithm of on-line monitoring was described in detail in Chapter 5. Material
dielectric properties changed with temperature and extent of reaction during heating and
curing. This led to a shifting of resonant frequencies. The resonant frequencies were
diagnosed (LabVIEW program Figures B.25 and B.26) and updated (LabVIEW program
Figures B.27 and B.28) periodically to maintain the resonant state inside the single mode
applicator. With the on-line monitoring, the bonding cycle can be directly determined.
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6.5 Conclusions
A process control system was developed for single mode and variable frequency
mode switching microwave adhesive bonding processes. Compared with previous work
in microwave process control, the control system developed in this study has several
improvements. First, theoretical modes were used instead of empirical heating modes.
This eliminated extensive heating characterization and data storage. Second, the PID
controller parameters were obtained based on control theory instead of empirical values.
This eliminated the trial and error procedure of adjusting controller parameters and also
provided sound basis for automatic tuning of the parameters. Third, an on-line monitoring
technique was developed to obtain the bonding cycle directly.
The software was programmed with LabVIEW for cavity characterization, data
acquisition and process control. Cavity characterization was performed before the
bonding process to obtain the mode spectrum. In data acquisition, material temperatures
and microwave powers were obtained. Process control included the control of heating
rate, isothermal temperature and on-line monitoring of the resonant frequency. Heating
rate was adjusted with an on-off control algorithm. Isothermal temperature was controlled
with the traditional PID algorithm. The PID parameters were obtained based on control
theory. The resonant frequencies of the modes were monitored with the on-line
monitoring sub-controller to obtain the bonding cycle. This process control system was
successfully used in the microwave adhesive bonding process to provide rapid, uniform
and stable heating with the ability to determine the bonding cycle on-line.
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CHAPTER 7 INVESTIGATION OF MICROWAVE HEATING MECHANISM
VIA STUDY OF MICROW AVE CURING OF EPOXY FILLED WITH CARBON
7.1 Introduction
The experimental results in Chapters 3 and 4 have shown that microwaves
reduced the curing time of the epoxy based adhesive with equal or even higher bonding
strength. These results motivate further investigation into microwave heating
mechanisms to provide explanations for reaction rate enhancement with microwaves. The
enhancement of polymer curing rate with microwaves has been demonstrated in a number
of studies [7,10,12-14, 100]. Some investigators suggested that the reaction rate
enhancement was because of microwave thermal effect, which is localized superheating
[7, 10]. Some other investigators attributed the rate enhancement to specific microwave
non-thermal effects such as accelerated reaction of the secondary amine group [12] and
improved diffusion rate of reactive species [100]. Whether the reaction rate enhancement
was mainly because of microwave thermal or non-thermal effect requires further
investigation.
Fu et al [101] studied the microwave thermal or non-thermal effect by comparing
continuous-power and pulsed-power microwave curing of epoxy resins. In pulse-power
curing, as power is turned on and off, the system is only partially processed with
microwave irradiation. If the microwave enhancement of reaction rates is due to thermal
effect, which is localized superheating, energy will be transferred from those “hot spots”
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to the surrounding area. As a result, the local temperature of those “hot spots” will
decrease when the power is turned off. Therefore, the reaction rates of the system will
decrease. However, since the bulk temperature is kept stable, this decrease is limited. If
the microwave enhancement of reaction rates is due to non-thermal effect, there is no
microwave effect when the incident power is turned off. Therefore, the power-off state
will lead to significant decrease of reaction rates. It is expected that continuous-power
curing will have faster reaction rates than pulsed-power curing if non-thermal effect is the
main reason of microwave enhancement of reaction rates. Results showed that
continuous-power microwave curing had only slightly higher reaction rates and ultimate
extents of cure than pulsed-power processing. The results seemed to support the theory of
thermal effect. But non-thermal effect could not be disproved because the power level in
pulsed-power curing was much higher than that in continuous-power curing.
The problem encountered in previous study [101] was that microwave power has
large influence on both microwave thermal and non-thermal effects. If microwave
thermal effect could be preferentially modified without altering the non-thermal effect,
then the changes in reaction rate could be attributed to microwave thermal effects only
and microwave heating mechanism could be revealed. It has been pointed out that
microwave heating of materials depends largely on dielectric properties [39].
Microwaves can be more efficiently coupled into components with higher dielectric
properties. Fillers with high dielectric properties can be added into resins in microwave
curing to modify microwave thermal effect without significantly affecting the nonthermal alignment of polar groups in the electromagnetic field.
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In this chapter, microwave heating mechanism is investigated via studying
microwave curing of carbon filled epoxy. Carbon black was used as the additive because
of its high dielectric properties. The effect of carbon black concentration on microwave
heating efficiency and curing kinetics of epoxy is studied and the reason of reaction rate
enhancement with microwaves - thermal or non-thermal, is discussed.
7.2 Hypothesis of Carbon Effect on Microwave Curing
The effect of carbon black on microwave absorption by polymer reactants is
illustrated in Figure 7.1. In microwave curing of the neat resin (Figure 7.1(a)),
microwaves are absorbed by the functional groups, dissipated into heat and then the heat
is transferred to the entire molecules. Therefore the localized temperature of the
functional groups should be higher than that of the bulk, though the degree of localized
superheating is uncertain. When carbon black is filled into the resin (Figure 7.1(b)), much
less microwaves are absorbed by the functional groups because most microwaves are
absorbed by carbon owing to its much higher dielectric property. Heat is then transferred
from carbon to the resin molecules and the functional groups of the resin. Thus the
heating mechanism of the functional groups was actually similar to a thermal heating
process when carbon black is present. Carbon black weakens the localized super-heating
effect of the functional groups. Therefore, if localized super-heating was the main reason
of curing rate enhancement with microwaves, then the curing rate should decrease with
increasing carbon concentration.
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Polar group
Microwaves
Heat transfer.
Polymer molecule
(a) Microwave interaction with neat epoxy
Polar group
Carbon
Microwaves
Heat transfer
Polymer molecule
(b)
Microwave interaction with epoxy filled with carbon
Figure 7.1 Microwave Interactions with Carbon Black and Epoxy
7.3 Epoxy Curing Kinetics
Epoxy resins are the most widely used matrix materials for advanced composites.
A large amount of work has been performed in the curing of the general class of epoxy
resins. A variety of models were proposed for thermal curing of neat epoxy resins. These
models have been further applied to thermal curing of doped resins and microwave
curing of neat resins. Research efforts on the curing kinetics of epoxy and other
commonly used resins (such as vinylester and polyester) are reviewed as follows.
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7.3.1
Kinetics study o f therm al curing o f neat resin
There are mainly two categories of kinetics models for the curing process [102].
One is mechanistic model, which is obtained based on reaction mechanisms. The other is
phenomenological model, which is developed without considering the details of cure
reactions. Mechanistic models offer the advantages of better prediction and interpretation
without, conducting cure experiments for each new variable in the cure system. However,
the mechanistic models usually take more complex forms with more kinetic parameters
than the phenomenological models. In addition, the complexity of cure reactions
sometimes makes the derivation of mechanistic models very difficult or even impossible.
On the other hand, phenomenological models have the advantages of relatively simpler
form than the mechanistic models. Therefore phenomenological models have been used
in most studies of cure kinetics. A summary of mechanistic and phenomenological
models for cure reactions is presented as follows.
7.3.1.1
Mechanistic Models
The proposed reaction kinetic mechanism for epoxy-aromatic diamine system is
[103]:
K,
a\ + e —» r*2 + OH
K,'
K2
^2 + c —> #3 + OH
K2'
k3
OH + e —> et + OH
K3’
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(7.1)
Where m, aj,
e, and et are primary amine, secondary amine, tertiary amine, epoxide,
and ether group, respectively. Ki and Ki', i= l ,2,3, are specific reaction rate constants for
the catalytic and non-catalytic reactions, respectively. From the kinetic mechanism,
mechanistic models for the curing process can be derived.
For the simplified case of no etherification, steric hindrance or OH impurity, a
cure kinetics expression for epoxy has been derived as follows [104]:
doc
— = {kl + k 2a ) ( l - a ) ( B - a )
(7.2)
where B is the ratio of the initial hardener equivalents to epoxide equivalents. For a
stoichiometric mixture, B = l.
a is the extent of cure,
k\ and ki are the catalytic and non-catalytic polymerization reaction rate constants,
respectively.
The above equation holds well up to the gelation point. To model the whole
curing reaction, the following kinetics model has been proposed [105], which models the
reaction kinetics before gelation with equation 7.2 and models the reaction kinetics after
gelation with an equivalent first order reaction:
^ - = (ki + k 2 oc){1 - a)(B - a ) , when a < a gd
da
= k 2 {\ — a), when OC>OCgei
dt
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(7.3)
Where k 3 is the first order reaction rate constant with Arrhenius temperature dependency
and oCgd is the extent of cure at the gelation point.
It has been shown that for a stoichiometric mixture of epoxide and amine, the
etherification can be neglected at low curing temperatures [106-111]. However, the
etherification can no longer be ignored at high curing temperatures or with excess
epoxide [110,111]. In addition, the reaction rate constant for primary and secondary
amine is not always the same. For the generalized case of epoxy curing with
etherification, steric hindrance and an OH impurity, the curing kinetics has been derived
for a stoichiometric mixture of epoxide and amine [111]. The kinetics models are shown
in the following equations:
da
—
2(1 -n )d > + n<i>n / 2
= [-----------
2 -/i
dt
r v ^
vr,
,
+ LFt y ) ] ( l - a) [ kl + k 2 F(jp)]
(7.4)
(1 - H ) 0 + 0 " / 2
1
F (</>) = 1 + ----------------------------<?0
(7.5)
2 —n
(1 - </>)(1 - //)(2 - L) + 2(1 -< pn ' 2 )(1 - - ) - (2 - n ) L ( 1 + 1 2 ^ 0 } ln ^
a
n
eQ
-------------------------------------------------------------------------------------- -----------2(2-n )
(7.6)
Where n is the reaction rate constant ratio between the secondary amine-epoxy reaction
and the primary amine-epoxy reaction, n = K 2/K 1 = K 27Ki',
L is the reaction rate constant ratio between the etherification and the primary
amine-epoxy reaction, L= K 3/K 1 = KV/KV,
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[OH]o is the initial concentration of OH impurity,
<t>=ai/e0,
eo is the initial epoxide concentration,
&i=eoK|' and &2= 6 o^Ki.
If L=0 (i.e. no etherification), n=l (i.e. no steric hindrance) and [OH]o=0 (i.e. no
OH impurity), then the above reaction kinetics simplifies into the following equation for
a stoichiometric epoxy-amine mixture:
^ = {ki +k2a){\-aj1
at
( 7 .7 )
This kinetics equation is consistent with equation 7.2, because in equation 7.2 B=1 for a
stoichiometric mixture.
7.3.1.2
Phenomenological Models
The simplest phenomenological model is the nlh order reaction kinetics model
[112,113,114], which assumes that the kinetics can be expressed as:
~j~ = k ( T ) f ( a )
clt
(7.8)
where a is the extent of cure, t is the time, the function/(a) is expressed as ( 1 -a )1’, and
k(T) is the overall reaction rate constant which obeys the Arrhenius relation:
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FI R
k(T) = Aex p ( ~ = y ^ )
(7.9)
The nth order reaction kinetics is computationally simple. According to this
model, the maximum reaction rate should occur at the beginning of the reaction.
However, in real cases, a=0.3 ~ 0.4 at maximum reaction rate, which is better explained
by the autocatalyzed reaction mechanism [115,116]. The reactions between amines and
epoxide are autocatalyzed by the hydroxide group formed in the reactions. The initial rate
should be slow due to lack of catalytic hydroxide groups. The cure kinetics expression of
autocatalyzed reaction for a stoichiometric reactant mixture is given by:
^
= ( k l + k 2a m ) ( l - a ) n
at
where k\ is the non-catalytic polymerization reaction rate constant,
(7 . 1 0 )
is the autocatalytic
polymerization reaction rate constant, m is the autocatalyzed polymerization reaction
order, and n is the non-catalyzed polymerization reaction order. This model has been
widely used to represent adequately the cure kinetics of epoxy and unsaturated polyester
cure systems [115-125].
7.3.2
Kinetics study o f therm al curing o f filler-added resins
In commercial thermosetting polymer systems, fillers are generally used in the
resin formulation to improve the thermal, mechanical and/or electrical properties of the
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cured product. Knowledge of the effects of fillers on the curing kinetics is necessary for
designing cure cycles and optimizing part properties. The kinetic models developed for
neat resin curing have been applied to the curing of filler-added resins. A variety of
filler/resin systems have been investigated, including calcium carbonate filler/styrene and
polyester resins [126] [127], aluminum/polyester [126], glass/polyester [ 126][ 128][ 129],
kaolinite clay/polyester [129], chopped glass fiber/vinylester [130], and carbon black and
silica fillers/epoxy resin [131]. The effects usually depend on specific filler and resin
systems studied.
It was reported that poly(vinyl acetate) (PVAc), when used as low profile
additives in curing unsaturated polyester resin, decreases the rate of cure and ultimate
extent of cure [132] and decreases the total heat of cure [133]. It was indicated that the
major effect of PVAc was the reduction of the radical generation rate, which was
possibly because that PVAc acted as a radical scavenger.
Experimental evidence [134] has shown that both the thermal conductivity and
the viscosity of the resin increased at the presence of a high quantity of filler. These
effects enhanced the curing reactions and the cure started at a lower temperature with
increasing filler content. However, fillers reduced the concentration of functional groups
per unit volume. This effect resulted in a decrease in the total heat of cure with increasing
filler content.
It was observed that the addition of CaCC>3 to the styrene/polyester system led to a
decrease in the induction period without any significant effect on the subsequent curing
rate [127]. The possible reason for this effect was that the filler-rich phase preferentially
adsorbs inhibitors, including dissolved oxygen that acted as a co-inhibitor.
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A model to describe the effect of particulate fillers on the heat transfer and cure
process was developed with the assumption that the presence of filler did not alter the
reaction kinetics and that the thermal characteristics of the composite are adequately
described by the "spherical inclusion model" [126]. A simple nth order model was used to
examine the effect of fillers (glass, calcium carbonate and aluminum) on the timetemperature profiles, peak temperatures, extent of cure, and gel time of a polyester resin
system. It was shown that the filler content significantly affected the progression of the
cure fronts through the thickness of the mold. In addition, the type of filler affect the ratio
of polymerization rate to the rate of heat transfer, which resulted in the dependence of the
minimum gel time on the type of filler.
The influence of kaolinite clay and glass fiber on the curing of a polyester resin
was investigated [129]. It was reported that the fillers did not affect the total heat of
reaction per unit mass of the resin or the peak temperature. In addition, the fillers had
very little effect on the progression of the curing for high temperature peroxide initiation.
However it was observed that for room temperature curing of polyester system, glass
fillers had a severe inhibiting effect on the curing [135].
The effect of chopped glass fiber on the curing of a polyester system was
investigated [128], It was reported that the glass fibers resulted in some changes in the
overall reaction rate of the polyester cure system but had little effect on the reaction
exponents. In addition, the glass fibers did not result in significant changes in the ultimate
heat of cure per unit mass of the resin or final degree of conversion. However, in the
curing of vinylester resin, the glass fibers significantly decreased the ultimate extent of
cure [130]. The reason for this inhibition was partly because of the chemical structure of
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the vinylester resin and the sizing agent of the reinforcement which was formulated for a
polyester resin.
The carbon black filler had a significant effect on the thermal curing reaction rate
of DGEBA/mPDA [122]. It was observed that the sum of the kinetic exponents is
approximately 2, independent of temperature and filler concentration. Carbon black
influenced both the catalytic and non-catalytic reaction rate constants. For all the
temperature studied, the catalytic and non-catalytic reaction rate constants first decreased
to a minimum value at around 2wt% of carbon concentration. As carbon concentration
further increased, the rate constants increased and finally leveled off. The possible reason
for the carbon effect on epoxy curing was attributed to the chemical complexes on the
carbon black surface. These chemical groups, such as phenolics, carboxylics, quinones,
hydroquinones, and lactones, might catalyze the curing of epoxy.
7.3.3
Kinetics study o f microwave curing o f neat resin
Thermal cure kinetics models have been used in modeling the reaction kinetics of
microwave cured epoxy resins [15,111,101]. It was demonstrated that the cure kinetics
ofDGEBA/wPDA and DGEBA/DDS systems could be described by the autocatalytic
kinetic model up to vitrification in microwave curing process [15, 111]. In the
comparative study of continuous-power and pulsed-power microwave curing of epoxy
resins [101], a semi-empirical kinetic model was used:
^
= (&! + k 2a m ){ a H - a ) n
at
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(7.11)
where a is the extent of cure, ki and k 2 are rate constants, m and n are constants, and a„
is the ultimate extent of cure. This model is similar to equation (7.10) except that the
ultimate extent of cure a u is included in the equation. This is because at certain stage of
the reaction, gelation and vitrification take place, and the reaction rates are controlled by
physical deposition. Due to these physical transitions, the ultimate extent of cure is
usually less than 100%.
7.4 Kinetics Model Used in this Study
In this study, neat and carbon-filled epoxy systems are cured with both thermal method
and microwaves. The phenomenological kinetics model with the form of equation 7.10 is
used. The reaction rate constants ki and k 2 obey the Arrhenius relation:
* ,C r) = A , e x p ( - J ^ )
(7.12)
where i = 1 (for non-catalytic polymerization reaction),
2 (for autocatalytic polymerization reaction).
In Equation 7.12, Aj and Ej are the Arrhenius frequency factor and the activation
energy, respectively. Ej and Aj can be obtained from the reaction rate constants at
different temperatures. If plotting Ln(kj) vs. -1/R T and performing linear regression, then
the slope is Ej and the intercept is Ln(Aj).
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When carbon black filler is used in the resin, ki and k 2 are the overall reaction rate
constants of the filled resin. Let k |0 and k2o represent the reaction rate constants of the
neat resin. The relationship between k| and ki0, and k2 and k2o can be described in the
following equations:
ki = k io * fi
(7.13.1)
k2 = k2o * f 2
(7.13.2)
where fi and f2 govern the effect of carbon black on the resin curing. If the effect of
carbon black varies at different temperature, then f| and f2 are functions of both carbon
concentration and temperature:
f i= f i( c ,T )
(7.14.1)
f2 = f2(c,T )
(7.14.2)
where c is carbon concentration and T is temperature.
The reaction rate constants and the kinetic exponents can be obtained with a leastsquare fit of experimental data (extent of cure vs. time) to the kinetic model equation.
Then from the rate constants at different carbon concentration, the expressions for f|(c, T)
and f2(c, T) can be obtained.
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7.5 Experimental
7.5.1
Materials and Sample Preparation
The epoxy resin used in this study was diglycidyl ether of bisphenol A (DGEBA)
/ diaminodiphenyl sulfone (DDS). The DGEBA used was DER332 from Dow Chemical
with an epoxy equivalent weight of 173. The curing agent DDS was from TCI America
with an amine equivalent weight of 62. Conducting additives used were carbon black
powder from Mallinckrodt Baker Inc. The average particle size of the carbon black was
75|im. All of the materials were used as received without further purification. In
preparing the neat epoxy resin, stoichiometric DGEBA/DDS (2.79 DGEBA: 1 DDS by
weight) were mixed at 130°C. The mixture was well stirred at 130°C until DDS was
completely dissolved (in approximately 5 minutes). Doped resins were also prepared with
carbon black concentrations of up tolOwt%. The resins were degassed at 0.02bar and
100°C for 5 minutes. Fresh samples were kept in a -20°C freezer and used within 2
weeks. The fresh samples were analyzed with Differential Scanning Calorimetry (DSC)
to determine the total heat of reaction per gram of resin. Results are shown in Table 7.1.
As the carbon black concentration increased from 0 to 10wt%, the total reaction heat per
gram of resin had a slightly decreasing trend. This was because an increase in additive
concentration corresponded to a decrease in the concentration of the reacting species
DGEBA/DDS.
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Table 7.1 Total Heat of Reaction per Gram of Resin of the Fresh Samples
Materials
Neat
Resin Doped
Resin
Resin
Resin Doped
DGEBA/
with lwt% of
Doped with
Doped with
with 10wt%
DDS Resin
Carbon
2wt% of
5wt% of
of Carbon
Black
Carbon
Carbon
Black
Black
Black
398.5±9.1
403.1+12.6
Total Heat
of
Reaction
413.9±5.1
403.4± 13.2
381.9±6.3
per Gram
of Resin
(J/g)
7.5.2
Experim ental Setup fo r Microwave Curing
The microwave curing circuit is the same as that used previously in adhesive
bonding experiments, as shown in Figure 3.1. A cylindrical single mode cavity with a
diameter of 17.78cm was used for microwave curing. The coupling probe was side
mounted 3cm above the bottom of the cavity. The cavity length and the probe depth were
adjusted to be 13.2cm and 2.0cm, respectively. The sample was loaded at the center on
the bottom plate of the cavity.
For each microwave curing experiment, 0.1±0.003 grams of resin was loaded into
a cylindrical Teflon holder, the inner diameter of which was 1.25cm. The thickness of the
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resin was around 0.6mm. Because of the small dimensions of the sample, the temperature
within the resin was assumed as uniform. The temperature of the resin was measured
with a Nortech NoEMI-TS fiberoptic thermometer. A LabVIEW program was developed
for data acquisition of temperature, incident power and reflected power and to perform
process control. For thermal curing experiment, 0.1±0.003 grams of resin was applied on
a cylindrical Teflon disk with a diameter of 1.25cm. The samples were put into the oven
after the oven was preheated to the curing temperature.
7.5.3
Dielectric M easurem ent
The dielectric properties of the carbon black, uncured neat and doped resins were
measured with single mode perturbation method at room temperature. The dielectric
measurement method was described in detail in literature [1]. The diagnosis mode used
was TM012 at 2.45GHz. The microwave applicator for the dielectric measurement was a
cylindrical single mode cavity with a diameter of 15.24cm. A cylindrical Teflon holder
was used to contain the resins. The inner diameter and height of the Teflon holder were
1.0cm and 3.5cm respectively. The cavity length corresponding to the TM012 mode was
around 15.43cm at 2.45GHz. Results of the dielectric constant and loss factor are shown
in Tables 7.2 and 7.3, respectively. The dielectric properties increased noticeably with
carbon concentration. Compared with the dielectric properties of the neat resin, the
dielectric constant and loss factor of the resin doped with 10wt% of carbon black
increased by around 100% and 50%, respectively. With the measured values of carbon
black and neat resin, the dielectric constants and loss factors of doped resins are predicted
with mixing rule and also shown in Tables 7.2 and 7.3. For lightly doped resins (e.g. 1%
and 2%), the mixing rule holds with a relative error of less than 10%. But for heavily
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doped resins (e.g. 5% and 10%), the relative error can be as high as 30% and the mixing
rule does not hold any more.
T able 7.2 Dielectric Constants of the Materials
Materials
Dielectric
Constant
e'
Dielectric Constant
e'
Predicted with
Relative
Error
Measured
M ixing Rule
Carbon Black
26.63±0.54
\
\
Neat DGEBA/DDS Resin
4.21±0.25
\
\
Resin Doped with lw t% of
4.76±0.18
4.4342
-6.8%
4.78±0.24
4.6584
-2.5%
6.76±0.31
5.331
-21.1%
8.60±0.27
6.452
-25.0%
Carbon Black
Resin Doped with 2wt% of
Carbon Black
Resin Doped with 5wt% of
Carbon Black
Resin Doped with 10wt%
of Carbon Black
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Table 7.3 Dielectric Loss Factors of the Materials
Materials
1
Dielectric
Dielectric Loss
Relative
Loss Factor e"
Factor e" Predicted
Error
Measured
with Mixing Rule
Carbon Black
2.35±0.05
\
\
Neat DGEBA/DDS Resin
0.21±0.03
\
\
Resin Doped with lwt%
0.21±0.01
0.2314
10.2%
0.24±0.03
0.2528
5.3%
0.26±0.02
0.317
21.9%
0.32±0.03
0.424
32.5%
of Carbon Black
Resin Doped with 2wt%
of Carbon Black
Resin Doped with 5wt%
of Carbon Black
Resin Doped with 10wt%
of Carbon Black
7.5.4
Cavity Characterization
Before microwave curing, the loaded cavity was characterized to locate the
heating modes. The mode spectrum, as shown in Figure 7.2, was obtained with
measuring the incident power (Pi) and the reflected power (Pr) as a function of
frequency. The frequency with minimum reflectance (Pr/Pi) was the resonant frequency
of a mode. Among many available electromagnetic modes, a center heating mode TM020
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was selected because the material sample was loaded at the center of the cavity. For the
experimental setup in this study, the resonant frequency of TM020 was around 2.89 GHz.
2.9
3
Frequency (GHz)
Figure 7.2 M ode Spectrum of Loaded Cavity for Microwave Curing
7.5.5
Process Control Strategy and Temperature Profile in Microwave Heating
In this study, the resins were cured at 145, 165 and 185°C. Traditional
proportional-integral-differential (PID) method was used to control the curing
temperature by adjusting the incident power level. The PID controller was programmed
with labview as a subroutine. The three parameters Kc, Ti and Td were obtained with
Ziegler-Nichols frequency response method. The details of the method are described in
literature [99]. The controller parameters are listed in Table 7.4.
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Table 7.4 PID Controller Parameters Obtained with Ziegler-Nichols Method
Ku
Mode TM020
3.0
Tu
Kc
Ti (0.5Tu)
Ti (0.12Tu)
(second)
(0.6Ku)
(second)
(second)
11.5
1.8
5.75
1.38
The typical temperature profiles during microwave heating and curing of both
neat and filled resins are shown in Figure 7.3. With the PID parameters shown in Table
7.4, the curing temperature was controlled within 1°C of the set point temperature.
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185°C
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7.6 Results and Discussion
7.6.1
Microwave Power Deposition During Heating and Curing
During microwave heating and curing, data acquisition of incident and reflected
powers was performed every second. The power deposition was calculated as the
difference between the incident and reflected powers. The reflected power was close to
zero for the experimental setup in this study.
The power depositions during microwave curing at 145°C are shown in Figure
7.4. The vertical axis was the average power deposition in every 5 minutes. Each curve
was the average of 3 sets of experimental data. The shapes of the power deposition curves
for all the resin systems were similar. At the beginning, high power levels were required
to heat up the materials from room temperature to the isothermal curing temperature. The
heating up of the resins took approximately 1.4 minutes. After the isothermal curing
temperature was reached, the power level dropped at the beginning of curing and then
started increasing after 15 minutes (for neat resin and resin doped with lwt% of carbon)
or 20 minutes (for resins doped with 5wt% and 10wt% of carbon black). This
phenomenon can be explained with the exothermal heat generation and dielectric
property change during the curing process. It has been shown that the curing of
DGEBA/DDS was governed by an autocatalyzed reaction mechanism and the maximum
curing rate usually occurred at the extent of cure of 0.3-0.4. Therefore at the beginning of
curing, the curing rate kept increasing until the maximum rate was reached.
Correspondingly the rate of heat generation from the exothermal curing reaction
increased. This tended to lower the power requirement. However, the decrease in
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dielectric properties in cross-linking process tended to increase the power requirement.
Therefore at the beginning of curing, the trend of power requirement was determined by
the dominating factor of the two causes. As observed from Figure 7.4, the power level
decreased at the beginning of curing, showing that the dominating factor was the
exothermal heat generation. The minimum power might occur at the maximum reaction
rate. After the maximum curing rate was reached, the curing slowed down and the
decrease in the rate of exothermal heat generation caused an increase in the power
requirement. At the same time, the decrease in dielectric properties also required higher
power level. This explained why the microwave power deposition increased at later time
of the curing process.
The shapes of the power deposition curves at 165 and 185°C were similar to that
at 145°C. But the power level was higher at higher temperature.
The total energy consumed during microwave heating of each resin system (0.1
gram of neat or doped resins) was computed with numerical integration of the power
data. Figure 7.5 shows the total energy consumed by each resin system at different
temperatures in the first 60 minutes of microwave heating.
As observed from Figure 7.5, the increase in the carbon concentration led to a
decrease in the energy requirement at all the three curing temperatures. One possible
reason of this phenomenon was the aggregation of carbon particles in the epoxy resin.
The carbon density is higher than the epoxy density, so the carbon particles tend to
aggregate into the bottom of the resin, as shown by Environmental Scanning Electron
Microscope (ESEM) analysis. Though this was not a serious problem because the density
difference was not very large, some carbon particles were surrounded by others and
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might not absorb microwave energy. This might result in decrease in power requirement.
Another possible reason for lower energy consumption at higher carbon concentration
was that the conducting additives improved the dielectric properties of the resin and thus
enhanced the microwave heating efficiency. Consequently lower power level was
required to maintain the same isothermal curing temperature.
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100
Time (min)
Figure 7.4 Power Curves during Microwave Heating and Curing
136
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□ 145 degree C
a
5? 30 ■
0
165 degree C
o 185 degree C
I: Error Bar
2
4
6
8
10
12
Carbon Concentration (wt%)
Figure 7.5 Total Energy Consumed by Each Resin System in the First 60 Minutes of
Microwave Heating
7.6.2
Comparison o f Reaction Rates between Microwave and Thermal Curing o f
Neat and Doped Resins
Microwave and thermal curing of the neat and doped resins were performed at
145, 165 and 185°C. The extent of cure of the resins was tested with DSC as a function
of curing time. Three samples were measured for each time point. The average standard
deviations of the extent of cure for thermal and microwave curing processes are shown in
Table 7.5. The average extent of cure was used in data regression to determine the
kinetic parameters. In the data regression, the kinetic parameters were first assigned
initial values and Equation 7.10 was integrated numerically with the fourth-order RungaKutta method to regenerate the extent of cure as a function of time. The least square
method was then used to minimize the difference between the experimental data and the
calculated values by solving for the reaction kinetic parameters. The experimental and
137
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calculated values of the extent of cure are shown in Figures 7.6-7.8 for thermal curing
and in Figures 7.9-7.11 for microwave curing. Markers and lines represent experimental
and calculated values, respectively. It can be seen that both microwave and thermal
curing curves have the typical shape of autocatalytic reaction. The initial curing rate was
slow due to lack of catalytic hydroxide groups. As the reaction proceeded, hydroxide
groups were generated and the maximum curing rate occurred at the extent of cure of
around 0.3 to 0.4.
In both thermal and microwave curing, no obvious trend was found for the
reaction order constants m and n as function of filler concentration. The average values of
m and n for thermal and microwave curing are shown in Table 7.6.
T able 7.5 Average Standard Deviations of the Extent of Cure
Curing Conditions
Thermal Curing
Microwave Curing
Average Standard Deviation
3.4%
5.5%
of the Extent of Cure
T able 7.6 Values of M and N
Thermal Curing
Microwave Curing
m
0.8310.15
0.9410.11
n
1.2110.10
1.5710.21
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Thermal curing
T=145 degree C
0.9
0.8
0.7
5 0.6
<4-.
o 0.5
c
& 0.4
x
W
0.3
4— i
0.2
0
20
60
40
80
100
Time (min)
o
neat resin-exp
X
0.5wt% carbon-exp
+
lwt% carbon-exp
....... • ■ lwt% carbon-reg
X
2wt% carbon-exp
----- - 2wt% carbon-reg
A
5wt% carbon-exp
---- - 5wt% carbon-reg
O
7wt% carbon-exp
----- ■ 7wt% carbon-reg
P
10wt% carbon-exp
----- - neat resin-reg
■ 0.5wt% carbon-reg
10wt% carbon-reg
exp: experimental data
reg: regression data
F igure 7.6 Thermal Curing at 145°C
139
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Thermal curing, T=165 degree C
3
u
< 4 -.
o
+-»
a<u
4-*
x
0.4 -
W
20
0
o
X
+
X
A
o
□
40
Time (min)
neat resin-exp
0.5wt% carbon-exp
lwt% carbon-exp
2wt% carbon-exp
5wt% carbon-exp
7wt% carbon-exp
10wt% carbon-exp
60
80
------- neat resin-reg
0.5wt% carbon-reg
.........lwt% carbon-reg
2wt% carbon-reg
--------5wt% carbon-reg
--------7wt% carbon-reg
10wt% carbon-reg
exp: experimental data
reg: regression data
Figure 7.7 Thermal Curing at 165°C
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Thermal curing
T=185 degree C
0.9 a 0.7 -
5 0.6 w
I 0.4 x
W 0.3 0.2
-
0
10
30
20
40
50
60
Time (min)
o
neat resin-exp
X
0.5wt% carbon-exp
+
lwt% carbon-exp
..........lwt% carbon-reg
X
2wt% carbon-exp
------- 2wt% carbon-reg
A
5wt% carbon-exp
------- 5wt% carbon-reg
o
7wt% carbon-exp
------- 7wt% carbon-reg
□
10wt% carbon-exp ------- 10wt% carbon-reg
------- neat resin-reg
0.5wt% carbon-reg
exp: experimental data
reg: regression data
F ig u re 7.8 Thermal Curing at 185°C
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Microwave curing
T=145 degree C
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
Time (min)
o
neat resin-exp
------- neat resin- reg
+
lwt% carbon-exp
..........lwt% carbon-reg
X
2wt% carbon-exp
2wt% carbon-reg
A
5wt% carbon-exp
• • ■5wt% carbon-reg
□
10wt% carbon-exp
10wt% carbon-reg
exp: experimental data
reg: regression data
F ig u re 7.9 Microwave Curing at 145°C
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Microwave curing
T=165 degree C
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
Time (min)
o
neat resin-exp
------- neat resin-reg
+
lwt% carbon-exp
..........lwt% carbon-reg
X
2wt% carbon-exp
- ....... 2wt% carbon-reg
A
5wt% carbon-exp
- • • - 5wt% carbon-reg
□
10wt% carbon-exp
10wt% carbon-reg
exp: experimental data
reg: regression data
F igure 7.10 Microwave Curing at 165°C
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Microwave curing
T=185 degree C
0.9
0.8
0.7
U 0.6
O 0.5
e
£
* 0.4
w
0.3
14
4-4
0.2
0
10
20
30
40
50
Time (min)
o
neat resin-exp
------- neat resin-reg
+
*
lwt% carbon-exp
2wt% carbon-exp
..........lwt% carbon-reg
------- 2wt% carbon-reg
a
5wt% carbon-exp
------- 5wt% carbon-reg
10wt% carbon-exp--------------- --------10wt% carbon-reg
°
exp: experimental data
reg: regression data
Figure 7.11 Microwave Curing at 185°C
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60
7.6.2.1
Comparison of Reaction Rates between Microwave and Thermal
Curing of Neat Resin
The calculated rate constants of neat resin curing with microwaves and thermal
method are shown in Table 7.7. For both microwave and thermal curing, the magnitude
of the rate constant k2was higher than that of the reaction rate k|. This verifies that the
epoxy curing is mainly governed by autocatalytic reaction mechanism. Compared with
thermal curing, microwaves enhanced both k| and k2, but preferentially enhanced the
non-catalytic reaction rate k|. This result indicated that microwaves preferentially
enhanced the activity of amine and epoxide groups and accelerated the non-catalyzed
reaction between epoxide and amine.
T able 7.7 Reaction Rate Constants of Microwave and Thermal Curing of Neat Resin
Non-catalytic
Autocatalytic
reaction rate
reaction rate
constant ki
constant k2
Microwave 145°C
0.016
0.084
0.19
Microwave 165°C
0.040
0.16
0.26
Microwave 185°C
0.089
0.24
0.37
Thermal 145°C
0.0024
0.065
0.037
Thermal 165°C
0.0040
0.10
0.040
Thermal 185°C
0.0068
0.18
0.039
'
k ,/ k 2
145
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7 . 6 . 2.2
Effect of Carbon Black Concentration on Thermal Curing Rates
The reaction rate constants k| and k2 at different carbon concentrations were
obtained with the data regression method mentioned earlier. The rate constants for
thermal curing are shown as the markers in Figure 7.12 (a) and (b). The rate constants
increased with increasing carbon concentration. This might be explained with the carbon
surface chemistry. X-ray Photoelectron Spectroscopy (XPS) analysis of carbon surface
has shown the presence of functional groups such as carboxide, hydroxide, carboxyl, and
ester groups. These groups might have catalytic effect on the curing.
From the reaction rate constants at different temperatures, the activation energy E-,
of thermal curing was calculated with linear regression, as shown in Figure 7.13. Since
the activation energy changes with carbon concentration, the effect of carbon black on
resin curing depends on both carbon concentration and temperature. In modeling of
thermal curing, the following expression was used:
f i (c,T) = ^ L = ^ L ex p
ki0 AjQ
(-£'
£(0)
RT
= (1 + d n c + cli2c 2 + d /3c 3)exp(
(7.15)
where i = 1 (for non-catalytic polymerization reaction),
2 (for autocatalytic polymerization reaction).
In this equation, fj(c, T) is the ratio of the rate constant of the doped resin to that
of the neat resin. The rate constants obey the Arrhenius relation. Aj and Ajo are the pre-
146
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exponential factor in the curing of doped and neat resins, respectively. Ej and Ejo are the
activation energy in the curing of doped and neat resins, respectively. For thermal curing,
fj(c, T) had an exponential dependence on the temperature, shown by the Arrhenius
relation. The ratio of the pre-exponential factor Aj/Ajo only depended on the carbon
concentration and a polynomial function was used to correlate the ratio Ai/Aj0. The
coefficients d's in the polynomial were obtained with least-square method and are shown
in Table 7.8. The calculated coefficients were then used to regenerate the reaction rate
constants k\ and k2 as functions of carbon concentration, as shown in Figure 7.12 (a) and
(b) (lines).
T able 7.8 Coefficients D's for Thermal Curing
dn
0.0035
d2i
0.0008
di2
-0.2077
d22
-0.0244
di3
0.0802
d23
0.0092
147
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Thermal Curing
0.012
0.01
185C
0.008
3
165C
0.006
0.004
145C
0.002
0
2
4
6
10
8
carbon concentration (wt%)
(a) Non-catalytic reaction rate kj vs. carbon concentration
Thermal Curing
0.25
185C
0.2
0.15
165C
0.1
145C
0.05
0
0
2
6
8
4
carbon concentration (wt%)
10
(b) Catalytic reaction rate k2 vs. carbon concentration
Markers: reaction rate constants obtained from experimental data regression
Lines: reaction rate constants calculated with kinetic model Equation (7.15)
Figure 7.12 Effect of Carbon Concentration on Thermal Curing Rates
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Carbon concentration
Figure 7.13 Activation Energy in Thermal Curing
7.6.2.3
Effect of Carbon Black Concentration on Microwave Curing Rates
The reaction rate constants ki and k2 for microwave curing at different carbon
concentrations are shown as markers in Figure 7.14 (a) and (b), respectively. Both ki and
k2 decreased with increasing carbon concentration. This effect was more obvious at
higher temperatures.
The activation energy of microwave curing is shown in Figure 7.15 as a function
of carbon concentration. The activation energy changed as a function of carbon
concentration.
149
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Microwave Curing
0.08
0.06
185C
0.04
165C
145C
0.02
0
2
6
4
8
10
Carbon Concentration (wt%)
(a) Non-catalytic reaction rate k t vs. carbon concentration
Microwave Curing
0.25
0.2
185C
0.15
,65C
0.1
145C
0.05
0
0
6
2
4
8
10
Carbon Concentration (wt%)
(b) Catalytic reaction rate k2 vs. carbon concentration
Markers: reaction rate constants obtained from experimental data regression
Lines: reaction rate constants calculated with kinetic model Equation (7.16)
F igure 7.14 Effect of Carbon Concentration on Microwave Curing Rates
150
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>a
►
♦♦
♦
o
—
♦ El
■ E2
■
.
Ui
i
"■
2
Activation Energy E
c
on
I
i
3
5
10
15
Carbon Concentration (wt% )
F ig u re 7.15 Activation Energy in Microwave Curing
In modeling microwave curing, Equation 7.16 is used. The function fj(c, T) had an
exponential dependence on the temperature. This was similar to the thermal curing.
However for the ratio of the pre-exponential factor A JA \0, a polynomial expression alone
could not sufficiently model the data. The trend of the data also showed an exponential
dependence on the carbon concentration.
/ ,. ( c , T ) = i =
^/o
A
. eXp ( - £ i Z i ! £ L )
Ao
RT
= exp(-rf/0c)(l + d n c + d i2c2 )exp(—^ L— — )
Rl
The coefficients d's are shown in Table 7.9.
151
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(7.16)
Table 7.9 Coefficients D's for Microwave Curing
dio
1.05
d20
0.52
dn
-0.55
d2i
-0.59
d|2
0.30
d22
0.12
If localized superheating is the main reason of rate enhancement in microwave
curing of epoxy, then the curing rate should decrease with increasing carbon
concentration. Therefore the microwave curing results suggest that the reaction rate
enhancement in microwave curing of epoxy result from localized superheating of the
polar functional groups. However, there were also other possibilities that have not been
ruled out. The carbon particles used in this study were activated and might adsorb the
amine from the epoxy resin because carbon particles might have higher temperature than
the bulk resin in microwave curing. This will also result in decrease in microwave curing
rate. In addition, the power deposition during the curing process also could affect the
curing rate. The microwave power curves in this study showed that the power level was
lower at higher carbon concentration to maintain the same isothermal curing temperature
of the bulk resin. This might also result in decrease in curing rate with microwaves.
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7.7 Conclusions
The effects of carbon black concentration on microwave curing of DGEBA/DDS
were studied. The magnitude of the dielectric properties increased noticeably with
increasing concentration of carbon black. Compared with the dielectric properties of the
neat resin, the dielectric constant and loss factor of the resin doped with 10wt% of carbon
black increased by around 100% and 50%, respectively. Microwave curing experiments
were earned out at three different temperatures with different carbon black
concentrations. Parallel thermal curing was also performed for comparison. Correlation
for reaction rate constants as functions of carbon concentration and temperature was
proposed. For the neat epoxy resin, the curing rates with microwaves were much higher
than that with thermal method. In microwave curing of the resins with different carbon
concentrations, the reaction rate constants decreased with increasing carbon
concentration. In thermal curing process, the rate constants increased with increasing
carbon concentration. These trends were more obvious at higher temperature. According
to the hypothesis made at the beginning of the paper, the presence of carbon black
weakened the localized super-heating of the functional groups with microwaves because
the conducting carbon absorbed most microwaves during the curing process. If localized
super-heating were the main reason of curing rate enhancement with microwaves, then
the curing rate should decrease with increasing carbon concentration. This study suggests
that reaction rate enhancement in microwave curing of epoxy result from localized
superheating of the polar functional groups. However, there were also other possibilities
153
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that have not been ruled out. The carbon particles used in this study were activated and
might adsorb the amine from the epoxy resin because carbon particles might have higher
temperature than the bulk resin in microwave curing. This will also result in decrease in
microwave curing rate. In addition, the power deposition during the curing process also
could affect the curing rate. The microwave power curves in this study showed that the
power level was lower at higher carbon concentration to maintain the same isothermal
curing temperature of the bulk resin. This might also result in decrease in curing rate with
microwaves.
154
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CHAPTER 8 CONCLUSIONS
In this research, work was conducted in two sections. The first section was the
development of a precisely controlled, rapid and uniform microwave adhesive bonding
system with on-line monitoring features of the bonding process in a single mode
applicator. The second section was the investigation of microwave heating mechanisms
to provide explanations for reaction rate enhancement with microwaves.
A single mode applicator was used throughout this study because of its high
energy efficiency, good controllability, and convenience in studying process
fundamentals. In a single mode microwave cavity, several processing methods can be
applied, including single mode microwave processing and mode switching microwave
processing. Single mode microwave method refers to the process that only one mode is
used throughout the processing. Mode switching microwave method refers to the process
that several modes, with complementary heating patterns, are excited sequentially to
obtain time-averaged uniform heating. The mode switching method is based on
knowledge and understanding of single mode heating characteristics.
The single mode microwave method was first applied in an adhesive bonding
process to explore the characteristics of using microwaves for adhesive bonding in a
single mode applicator. Adhesive and substrate materials were selected based on their
compatibility and dielectric properties. An epoxy-based adhesive (Eccobond A401-37)
was used because of its compatibility with a wide range of substrate materials and its
high dielectric loss properties. A substrate (Bexloy W502, major component: glass
reinforced ethylene/methacrylic acid copolymer) with very low dielectric loss properties
155
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was chosen from three polymer and composite materials. With the choice of the
materials, rapid and selective heating of the adhesive was observed in the microwave
adhesive bonding process. The microwave heating mode with the desired heating pattern
was determined from cavity characterization, theoretical resonant frequency, and
theoretical electric field distributions. The bonding results showed that the bonding time
was reduced at higher temperatures for the microwave process. Compared with the
thermal method, the microwave method reduced the bonding time and at the same time
enhanced the bonding strength for the selected materials. The difference in bond strength
between microwave and thermal methods was related to the break pattern in the single
lap shear test. With sufficient bonding time, microwave bonded assemblies at different
temperatures all broke within the substrates. This phenomenon indicated that the bond
was stronger than the substrate material itself if processed with microwaves. Thermally
bonded assemblies all broke at the interface, indicating that the adhesion between the
substrates and the adhesive was not sufficiently strong. Therefore single mode microwave
method was successfully applied in adhesive bonding to obtain rapid heating with
enhanced bonding strength. However, only limited material size could be uniformly
heated with single mode microwaves because of the non-uniformity of the electric field
distribution.
To solve this non-uniformity problem using single mode heating, a variable
frequency mode switching method was implemented based on existing method and then
applied in microwave adhesive bonding of large-size materials to obtain uniform heating
in a single mode applicator. Implementations were performed with modes selected by
studying theoretical electric field patterns to reduce the number of modes used in mode
156
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switching to simplify the mode switching algorithm. In mode switching microwave
bonding, Eccobond A401-37 (epoxy based) was again used as the adhesive to bond two
substrate materials, Bexloy W502 (major component: glass reinforced
ethylene/methacrylic acid copolymer) and in a separate process, Surlyn SG201U (Nylon
6 and ethylene/methacrylic acid copolymer). Experimental temperature profiles showed
that uniform heating of the large size materials were obtained with the mode switching
method. The bonding cycles were determined with measuring the extent of cure of the
adhesive as a function of time for both microwave and thermal bonding processes. The
bonding strength was determined with single-lap shear test. The results were slightly
different for the two types of substrates. For Eccobond A401-37/Bexloy W502,
microwave process had a 75% to 80% reduction in bonding time and at least 2-fold
enhancement of bonding strength compared with thermal process. Microwave bonded
assemblies broke in the substrates in single lap shear test, while thermally bonded
assemblies broke at the interface even at 99% of cure of the adhesive. For Eccobond
A401-37/Surlyn SG201U, assemblies bonded with microwaves at 100°C for 45 minutes
obtained the same strength as thermally bonded assemblies at 120°C for 100 minutes.
Both microwave and thermally bonded assemblies broke in the substrates. Since the
interface and adhesive were stronger than the substrates for both microwave and
thermally bonded assemblies, it was uncertain whether there was microwave
enhancement of the adhesion between the adhesive and the substrate. Therefore, observed
microwave effects in adhesive bonding of the two systems include reduction of bonding
time for both systems and enhanced bonding strength for Bexloy W502 substrates.
157
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In the previous bonding study, the bonding cycle had been determined by
measuring either the bonding strength (with single-lap shear test) or the extent of cure
(with DSC) vs. time. These measurements had been conducted off-line and required
tremendous amount of experimental work. A successful process calls for the development
of an on-line monitoring technique to determine the bonding cycle on-line. In this study,
a new method (with corresponding software) was developed for on-line monitoring of
variable frequency microwave bonding of large materials. This method used a high
power processing circuit to monitor the resonant frequency shifting, which resulted from
changes in material dielectric properties during microwave processing in a single mode
applicator. This method was not intrusive, able to monitor microwave processing of
materials with large sizes and complex shapes, and did not require separate diagnostic
circuit (thus avoiding hardware switching between circuits). The new on-line monitoring
method was applied in several microwave adhesive bonding processes, including bonding
of single-lap Bexloy /Eccobond, single-lap Surlyn /Eccobond, and double-lap Bexloy
/Eccobond assemblies. During the bonding process, the curing of the adhesive led to
decreases in the dielectric constant and loss factor. Resonant frequencies for the modes,
which reflected changes in material dielectric properties, were monitored during the
bonding process. When the curing rate was high, the rate of resonant frequency shifting
was also high. When the curing approached completion, the curing rate decreased and the
shifting of resonant frequencies slowed down as well and finally leveled off. Thus when
the resonant frequencies stopped shifting, the bonding was considered completed and the
bonding cycles were determined.
158
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Throughout the microwave adhesive bonding study, process control was essential
for realizing uniform and stable heating and repeatable processing. A process control
system was developed in this study for single mode and variable frequency mode
switching microwave adhesive bonding processes. Compared with previous work in
microwave process control performed by other researchers, the control system developed
in this study has several advantages. First, theoretical modes were used instead of
empirical heating modes. This simplified the controller by eliminating extensive heating
characterization and data storage. Second, the PID controller parameters were obtained
based on control theory instead of empirical values. This eliminated the trial and error
procedure of adjusting controller parameters and also provided sound basis for automatic
tuning of the parameters. Third, an on-line monitoring technique was developed to obtain
the bonding cycle directly. The software was programmed with LabVIEW for cavity
characterization (to locate the microwave modes), data acquisition (to obtain material
temperatures and microwave powers) and process control (to control heating rate and
isothermal temperature and implement the on-line monitoring method). This process
control system was successfully used in the microwave adhesive bonding process to
provide rapid, uniform and stable heating with the ability to determine the bonding cycle
on-line.
The obtained results in microwave bonding process study have shown that
microwave processing reduced the curing time of the epoxy based adhesive with equal or
even greater bonding strength. In this study, the mechanism of microwave fast curing of
epoxy was investigated by studying the effect of carbon additive on microwave curing of
epoxy - diglycidyl ether of bisphenol A (DGEBA) / diaminodiphenyl sulfone (DDS).
159
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Carbon was used as the additive because of its high dielectric loss properties, which
modified microwave thermal effect without significantly affecting the non-thermal
alignment of polar groups in the electromagnetic field. During the microwave curing
process, carbon absorbed most microwaves and weakened the localized superheating of
the epoxy functional groups. If localized superheating were the main mechanism of rate
enhancement in microwave curing of epoxy, then the curing rate should decrease at the
presence of carbon. Microwave curing experiments were carried out at three different
temperatures with various carbon black concentrations. Parallel thermal curing was also
performed for comparison. Correlation for reaction rate constants as functions of carbon
concentration and temperature was proposed. In thermal curing of the epoxy with
different carbon concentrations, the rate constants increased with increasing carbon
concentration. The reason might be the functional groups adsorbed on the carbon surface
had catalytic effect on the curing reaction. In microwave curing process, the reaction rate
constants decreased with increasing carbon concentration. These trends were more
obvious at higher temperature. Thus, this study suggested reaction rate enhancement in
microwave curing of epoxy result from localized superheating of the functional groups.
However, the carbon particles used in this study were activated and might adsorb the
amine from the epoxy resin because carbon particles might have higher temperature than
the bulk resin in microwave curing. This will result in decrease in microwave curing rate.
Further study is required to elucidate this problem with the use of passivated carbon
particles or carbon with smaller surface area. In addition, at higher carbon concentration,
the required microwave power was lower to maintain the same bulk temperature. This
might also result in decrease in microwave curing rate at higher carbon concentration.
160
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In summary, this study successfully developed a microwave adhesive bonding
process in a single mode applicator with precise control and on-line monitoring features
and at the same time contributed to better understanding of process fundamentals.
The major accomplishments of this study are itemized as follows:
(1) Assembled experimental setup for microwave adhesive bonding in a single
mode applicator.
(2) Explored for the first time the application of microwaves in adhesive bonding
in a single mode applicator.
(3) Implemented existing variable frequency mode switching method and applied
it in adhesive bonding of large materials.
(4) Invented an on-line monitoring technique for microwave processing of large
materials with complex shapes in a single mode cavity.
(5) Designed the process control system for microwave adhesive bonding
incorporating theoretical control algorithms and on-line monitoring of
bonding cycle.
(6) Proposed new correlations for reaction rate constants as functions of carbon
concentration and temperature in microwave curing of carbon filled epoxy.
(7) Studied for the first time the relation between microwave power levels and
curing process.
(8) Investigated microwave heating mechanisms with new approaches and
suggested that reaction rate enhancement in microwave curing of epoxy result
from localized superheating of the functional groups.
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(9) Quantified advantages of microwave processed bonding for a few
adhesive/substrate systems.
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CHAPTER 9 FUTURE WORK
Throughout this research, several interesting problems have emerged. In this
dissertation, the effect of material dielectric properties on the bonding process was not
quantitatively studied. To achieve selective heating of the adhesives, the dielectric
properties of the adhesives should be higher than that of the substrates. However, one
question remains to be answered - what should be the minimum difference between the
adhesive and substrate dielectric properties to obtain desired selective heating profiles?
This problem can be studied with extensive experiments, but can also be quantitatively
estimated by modeling microwave heating.
The importance of modeling microwave heating is also shown in another process.
In Chapter 7, the power deposition into the cavity was experimentally measured during
microwave curing of the epoxy resin. The shape of the power curve was qualitatively
related with the curing reaction and heat transfer. However, if the power level can be
predicted with a model during microwave curing, then smoother control can be realized.
Development of mathematical models for microwave heating is beneficial for the
process in a number of ways. In addition to setting criteria for material selection and
realizing smooth and precise control, the occurrence of hot spots and thermal runaway
can be predicted with the model and procedures can be taken to avoid these undesired
phenomena.
Microwave heating modeling has been studied by a number of investigators [1 ST­
MS]. In many cases, the problems are simplified by decoupling the M axwell’s equations
with the heat transfer equation to obtain analytical solutions. For example in some
163
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studies, thin materials are considered so that the electric-field can be assumed to be
constant within the material and the heat transfer equation can be solved independently
[137,138]. In some other studies, the electric-field is incorporated but is assumed to decay
exponentially with distance [139,140,141]. But for complex microwave heating systems
such as microwave drying of porous materials, analytical solutions cannot be obtained
and numerical methods have to be used [142, 143]. Jolly and Turner [142] developed a
one-dimensional model for the heating of a dielectric slab and used a finite-difference
scheme to solve the problem numerically. Later Turner and Jolly [143] extended the one­
dimensional model to study microwave drying of porous materials numerically.
The modeling of microwave adhesive bonding is a more comprehensive problem.
The material system consists of two different materials: the adhesive and substrates.
Curing reaction takes place in the adhesive and has to be incorporated in the modeling.
The material thermal and dielectric properties have non-linear dependence on both
temperature (T) and extent of reaction (a). Material properties that affect microwave
heating include specific heat C P(T, a), thermal conductivity k(T, a ), dielectric constant
e'(T, a), dielectric loss factor e"(T, a), and electrical conductivity a(T, a). Because data
in handbook are only for limited temperature range for a few materials, accurate
experimental determination o f these material properties over the heating temperature
range at different extent of cure need to be performed prior to the modeling.
The energy balance within a unit volume of the materials is given by:
Heat
Build-up
Absorbed
Microwave Power
P
+
Heat
Transfer
kV
2T
Heat from
Reaction
+
p — (-A Hr)
dt
164
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(9.1)
Where p is density (kg/m3), C p is heat capacity (J/kg/K), T is temperature (K), t is time
(second), K is thermal conductivity (W/K/m), a is extent of cure, and - A H r is reaction
heat (J/kg).
In Equation (9.1), the heat generation source terms include chemical reaction heat
and microwave power absoiption. The reaction heat can be obtained from the reaction
kinetics. Microwave curing kinetics of neat resin has been extensively studied in
literature and microwave curing kinetics of carbon-doped resin is investigated in Chapter
7 of this dissertation. The obtained results can be used in the heating model. The local
microwave power absorption rate P (W/m3) is:
P = —ene a)
(9.2)
2 0
where E is the electric field strength inside the material (V/m), CO is the radial frequency,
(rad/sec), e0 is the free space permittivity, and e" is the effective relative loss factor. The
electric field can be determined by solving the M axwell’s equations described in Chapter
2.
With a well-designed numerical approach, Equations (9.1), (9.2) and the
M axwell’s equations can be solved together to determine the microwave heating and
curing profiles provided that the material properties are known.
165
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Many experimental results obtained in this research can be used to verify the
heating model, such as the temperature profiles in Chapters 3 and 4 and the power
deposition curves in Chapter 7.
In addition to the work mentioned above, the mechanisms responsible for bond
strength enhancement need to be investigated for the Eccobond A401-37/Bexloy W502
system. Adhesion between two polymeric materials with microwaves is a complex
phenomenon that involves multidisciplinary knowledge of microwave fundamentals,
surface chemistry, polymer properties, etc. More exploratory experiments need to be
canned out to provide explanations for the enhanced adhesion. Microwaves might modify
the substrate surface chemistry. Microwaves might also enhance the molecular mobility
at the interface to result in better adhesion.
Finally, the effect of carbon surface complex on microwave curing of epoxy
needs to be studied. A number of studies have shown microwaves enhanced the curing
rate of epoxy compared with thermal energy. In Chapter 7 of this dissertation, carbon
particles were added into epoxy to study the mechanism of rate enhancement in
microwave curing of epoxy. Carbon absorbs most microwaves and weakens the localized
superheating of the epoxy functional groups. Experimental results showed that the
addition of carbon enhanced thermal curing rate but decreased microwave curing rate of
epoxy. These results suggested reaction rate enhancement in microwave curing of epoxy
result from localized superheating of the functional groups. However, there were also
other possibilities that have not been ruled out. The carbon particles used in this study
were activated and might adsorb the amine from the epoxy resin because carbon particles
might have higher temperature than the bulk resin in microwave curing. This will result
166
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in decrease in microwave curing rate. In future studies, carbon particles can be passivated
to remove the surface complexes. Then the passivated carbon particles can be used as
additives in epoxy curing to eliminate the effect of surface complexes on the curing.
Alternatively, carbon particles with smaller surface area can be used as additives in the
epoxy to reduce the effect of carbon surface complexes on the curing. Experiments can
be performed to study how these carbon particles affect thermal and microwave curing
and the results can be compared with that obtained in this dissertation. The comparison
will contribute in the elucidation of the microwave heating mechanisms and improve
understandings in microwave/materials interactions.
These future studies will generate new methods for process design, improve
understanding in process fundamentals, and enhance the industrialization of microwave
processing techniques.
167
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REFERENCES
168
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Hill, J. M. and Jennings, M.J., A ppl. M ath. M odel. 17, 369 (1993).
138.
Roussy, G., Bennani, A., and Thiebaut, J., J. A ppl. P hys., 62, 1167 (1987).
139.
Smyth, N.F., J. A ust. M ath. Soc. B, 33, 403 (1992).
140.
Coleman, C. J., A ppl. M ath. M odel, 14,439 (1990).
141.
Marchant, T. R., J. Eng. M ath. 28, 379 (1994).
142. Jolly P.G. and Turner, I. W., J. M icrow ave P o w e r E lectrom ag. E nergy, 25, 3
(1990).
143. Turner I.W. and Jolly, P.G., J. M icrow ave P o w er E lectrom ag. E nergy, 25, 211
(1990).
176
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APPENDICES
177
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APPENDIX A. MATLAB PROGRAM FOR CALCULATING THE MODE
PATTERN OF TM022 INSIDE THE EMPTY CAVITY
% --------------------------------------------------------------------------------------------%
% This program computes the electric field pattern of aTM npq mode
% and returns a 2-D view of any specified cross-section of an empty
% cylindrical single mode cavity.
%
% In this example, the electric field pattern of TM022 is computed.
%
% Variables that need to be specified are:
%
n, p, q: parameters associated with the name of themode
%
xnp: solution of Jn(x)=0, where Jn is bessel function of
%
the first kind.
z: axial position in the cylindrical cavity, unit mm
%
%
h:
cavity height, unit mm
%
a:
radius of the cylindrical cavity, unit mm
%
% -------------------------------------------------------------------------------------------%
% Other variables and functions are decribed before each executable
% sentence.
%
% --------------------------------------------------------------------------------------------
n=0;p=2;q=2;xnp=5.520;
z=13;a=88.9;h=132;
% rhogrid: dimensionless radial position, from 0 and 1
% phigrid: dimensionless angular position, from 0 to 2:,!pi
rhogrid=0:0.01:1 ;phigrid=-pi:2*pi/100:pi;
% "meshgrid" transforms the domain specified by vectors phigrid
% and rhogrid into arrays specified by phi and rho
% phi: dimensionless angular position, which specifies the rows
%
of the array.
% rho: dimensionless radial position, which specifies the columns
%
of the array.
[phi, rho]=meshgrid(phigrid, rhogrid);
% "pol2cart" transforms polar to Cartesian coordinates
[x,y]=pol2cart(phi,rho);
178
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% space: spacing between points in both x and y direction
space=xnp*0.01;
% "besselj" is the Bessel function of the first kind
Jn=besselj(n,xnp*rho);
% "gradient" returns the numerical gradient of the matrix Jn
[Fx,Fy]=gradient(Jn,space);
% Jngrad: d(Jn)/dy, gradient of Jn in the y direction
Jngrad=Fy;
% Erho: rho component of electric field strength
Erho=xnp/(a!t!0.001)H'-(-l!,:q*pi/(h*0.001))*Jngrad.*cos(n*phi).*sin(q*pi*z/h);
% Ephi: phi component of electric field strength
Ephi=l./(rho*(a*0.001)+eps).;Hn .* (-ri!q*pi/(h*0.001)).!t!Jn.*cos(n*phi).*sin(q*pi*z/h);
% Ez: z component of electric field strength
Ez=xnpA2/(a*0.001)A2*Jn.:,:cos(n:Hphi):,:cos(q*pi*z/h);
% E: magnitude of electric field strength
E=sqrt(Erho.A2+Ephi.A2+Ez A2);
% "mesh" plots 3-D mesh surface
mesh(x,y,E);
% specify the view point to directly overhead 2-D view
view(0,90);
% set axis scaling and appearance
axis equal;axis tight;
179
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APPENDIX B. LABVIEW PROGRAMS
The functions of each LabVIEW program are listed in Table B .l.
Table B .l Functions of the Labview Programs
Main Program
cavity
characterization .vi
VFMS.vi
Sub-programs
6T.vi
luxtron .vi
nortech .vi
power.vi
mode-switch .vi
power control .vi
pid .vi
PID parameters .vi
heat rate .vi
frequency
diagnosis.vi
f-write .vi
Function
Obtain the mode spectrum before
bonding
Perform data acquisition, process
control, and on-line monitoring during
variable frequency mode switching
bonding
Acquire temperature data at 6 points
Convert voltage to temperature for
LUXTRON thermometer
Convert voltage to temperature for
NORTECH thermometer
Acquire incident and reflected power
data
Achieve uniform heating
Control heating rate and temperature
Control the temperature with PID
algorithm
Input PID parameters
Calculate heating rate
Monitor the variable frequency adhesive
bonding process on-line
Write the operating frequency to
| hardware
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
The hierarchy of the LabVIEW programs is shown in Figure B .l.
Data acquisition and process control software for
microwave adhesive bonding process
Cavity
characterization .vi
6T.vi
luxtron
.vi
Power.
VFMS.vi
modeswitch .vi
power
control .vi
nortech
.vi
frequency
diagnosis .vi
heat
rate .vi
f-write
.vi
PID
parameters .vi
F igure B .l Hierarchy of the Labview Programs
181
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
1cavity characterizations j
pica to
IIUIFIU
l»l«H
lull
Param eter'5 .
-rllb-IIS -rl
'
device]
Pi(W)|
SZI
|0.00
channel
2,3
IE
Pi Scale)
3|300.00
Pr Scale
a 300.00
3
Starting f(GHz)|
0
Increment]
0.0002
Ending f(GHz)|
0.00
sed
Pr/Pi
1.0
F3
©
P ress this
button to
stop the
program,
0.90 .8 0.70 .6 -
0.5-
%.4f
0.2
M
|m l|
|o.oo
Chart of Reflectance
(Pr/Pi)
0.4-
^11000.00
time|
Pr(W)|
jo.oo |
Frequency! reflectance!
0.0000
0.0000
^4.0000
Format
Loop Delay
(milliseconds)
H
Monitoring
0.3-
0.1 H
0.0
0
i
10
I
20
i
30
40
i
50
60
I
Figure B.2 Front Panel o f the Cavity Characterization Program
182
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®0 o
_<r
o
JBk
A
3
3
Lu
w ♦,
U.
O
u. a
Figure B.3 Diagram o f the Cavity Characterization Program
183
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without perm ission.
y
I
CTQ
S
no
CO
^ j# ]
ON-HNE MONITORING]
Heat Ratej T max]
[oo
foo| [oo| [oo
Pj
an i n J i i—
TEMPERATURE
Bondi] Deltl]
CONTROL
PARAMETERS: ^12000 | ^|3J0
-1
<
p
«-l
p*
2
cT
T
►
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CD
-O
cG
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PID Parameters:
Kcl| Til]
Tdlj
Operating frequency
ZOO
0.0000
i
Kc2j
Ti2
f|33.9|
Td2
o
800
2.8390
3 j3.3808
o
^|3.3780
3
V|
T1(Q
/ \
T2( C)
/ \
T3(C)
/\
T4(Q
/ \
T5(C)
600
T6(Q
fl upper|
400
3 2.8450
200
1000
199?
Curing time
0.00
min
0.00
3 3.3840
—
3
C trl
Press this button
to stop program
140J
initial t| diagnosis Interval increment]
®Z8410 | Jj 60
^|0.0002
Mode 2: |nitja| | 2| f2 lower] f2upper|
n
aoooo
1000
^ Z8410
o
0.0000
MODE CONTROLPARAMETERS:
M odel: initial flj fl lower]
o
mode2|
120J
sr
5‘
mode l|
T (C )vs.t Chart
flu
CP
Prj
Tmargin)
POWER CONTROLPARAMETERS:
Max Pj Min Pj Initial v| Pi Scalej Pr Scale
^|O60[
300JO 111300.00
|2 0 J
0
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in
§
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VFMS
▼I *J3 ▼ ! -Oa
device! Al channels
a
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3
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PARAMETER INPUT]
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o
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| II
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Pi S c a le
r ( C) i
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in itia l fl
Figure U.5 Diagram For Variable Frequency Mode S
185
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R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
1 VFMS.vi Diagram *
.......................... ....... —- - ......
....... -...-= = t£l ^
VFMS
□ ^1
*.GP w 1 ■Oh ^
abc (5
HI
CLEAR
axxcaTixiTranr»crrixixrtirriiTii»iii.i:rxrrrnaTJxrixiTt«Tix»xmxixrxrni<niTn
sta tu s
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en t
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T (C) vs. j L m j
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MODE
switch
O perating fr eq u e n c y
1AAA
D eltT [ W ] |
F TZ
i for Variable Frequency Mode Switching Process Control (Part 1)
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
□
iVFMSAri Diagram *
f m
n
g
i a
i g
a
r 1 4 p t Dialog
ta sk ID
Heat Rate
n itia l V
T (n -2 )
M ax T im e (m in )
Loop D elay
(m s )
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Figure B.6 Diagram for Variable Frequency Mode S\
186
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R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
Til
Heat Rate
[Bond Tl
liM d l
F'Sv'R
CTRL
T max
min
Curing time
t
60
|[sec
rmn
TF
1000
am for Variable Frequency Mode Switching Process Control (Part 2)
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
6T.vi
< > l# l £
11
i i
1 2 p t D ialog Font
▼ |
6T
♦
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F igure B.7 Front Panel for 6t.Vi
187
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6T.vi Diagram *
p 3 1
12p t Dialog Font
s is S a n
▼ ! *JCT ^
I
Scanned Data
[o b i ] h
Index 2 : T lux
I n
&
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M i
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DBL
Index 3 : T lux
I n
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iNOR
DBL
Index 7 : T nor
/(NOR;
DBL
Figure B.8 Diagram for 6t.Vi
188
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1
luxtron.vi
PFjl
hLUX‘i
I.'
; • II
e signal]
3 0.00
T<C)j
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Figure B.9 Front Panel for Luxtron.Vi
luxtron.vi Diagram
iiB
'LUX
866pt
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co n v e r t v
to mv
|20 |
scale factor
TiTTT
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£ l ik
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Figure B.10 Diagram for Luxtron.vi
189
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nortech.vi
liSf
I
H 1 12ptMalo Isnor
u it
e signalj
~j 0.00
T ^
0.00
Figure B .ll Front Panel for Nortech.Vi
E r— .—= nortech.vi Diagram
S S H H l S S f f l i
0 El
SISS
xNOi
£
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l= i".l r l ^ i ----- , t- > —*,,i1' 1
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|l0 0 [ ~ ^
TfTTT
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Figure B.12 Diagram for N ortech.vi
190
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□
ms
jpower.vij
12pt D1«log Font
▼! So ▼!
Scanned Data
Pi Scale
IL
300.00
{
0.00
0.00
!S o ”
p
Pi (watt)!
Pr(watt)|
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0.00
l= —
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i
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Figure B.13 Front Panel for Power.Vi
p o w e r .v i D iagram
i
H
i
l
l
Scanned Data
1 Power
a t
l
Pi(watt)|
:|>4
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Pi Scale
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Figure B.14 Diagram for Power.Vi
191
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m o d e-sw itch .vi
12pt Dialog Font
Tdifference
Array data
too"'""
Initial fl|
p l =
0.0000
2.8410
9
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Figure B.15 Front Panel for Mode-Switch.Vi
192
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C3
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O)
J--i
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Figure B.16 Diagram for Mode-Switch.Vi
193
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j
power control.vi i
00
W sv*w'
12pt Dialog Font
Task ID|
1F H
Bond T( C)|
|T 20 .00 I
Pi Scale
Pl(watt)|
jj| 300.00
a p r~ ~ l
t margln|
^|2.00
CTRt-
Heat Rate (C/s)|
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Figure B .l7 Front Panel for Power Control.Vi
194
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Cl
a
yj
u.
u.
cl
Figure B.18 Diagram for Power Control.Vi
195
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1heat rate.vl j
T 4,n-l|
3
12pt Dialog Font
i ii
m
T4,n|
3|o.oo
|o.oo
T5,n|
T5,n-l]
^0.00
|0.00
Heat Rate (C/s)
T6,n|
T6, n-1
=10.00
1
0.00
=|0.00
m u
F ig u re B.19 Front Panel for Heat Rate.Vi
h e a t rate.vi D iagram
1 -------------- ------------------------1
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.
91
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.
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1 4 p t Dialog •Rate:'
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|H eat R ate ( C / s )
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Figure B.20 Diagram for Heat Rate.Vi
196
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p i d .vi
I
ii 11,2p*Diai°9
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||4.00
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F igure B.21 Front Panel for Pid.Vi
197
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RvVtW's'1
i I CL \
Q
o
u.
cn
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Figure B.22 Diagram for Pid.Vi
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
n
--------1PID parameters.vl
93
0 E
12pt Dialog Font
▼ !
3p
Ipararn
Operating frequency!
0.0000
Kclj
f
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ITdlJ
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|0.00
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i
1
1
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|0.00
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F igure B.23 Front Panel for Pid Parameters.Vi
□
pid
:
1
a
z
a
param eters.vi Diagram *
i z
i r
, ............. :
z
n
m
-
H
::
S @
: : : : : : : : : : :
H
S
'' PID1'
1 4 p t Dialog F parcam
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1 lOperating freq u en cy
ijifjji
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,
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Figure B.24 Diagram for Pid Parameters.Vi
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
ms
i Frequency diagnosls.vi!
□
n
a n
n
Task ID|
m
m
^i'rvVW-
r 12pt Dialog Font
counterj
r e f# in 1
diagnosis Interval]
frequency
of mode 1
60
fl lower)
2.8390
fl upper!
12 lower!
f2 upper]
'•3780 |
^3.3840 |
Pi Scale!
2.8450
0.0000
frequency
of mode 2
r e f# out 1
0.0000
Pr Scale
ref#out_2j
jjfcoQ.OQ^ ^|300.00
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ref#in_2j
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0.0002
M im m *
Figure B.25 Front Panel for Frequency Diagnosis.Vi
200
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Figure B.26 Diagram for Frequency Diagnosis.Vi
201
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|\ |
..
S f-w rite.vi.........
1.....................................
12pt Dialog Font
i
L^IL- ■■ ■
=I0 E
T’| n
y A
♦
This program writes frequencies to the
sw eep oscillator via GPIB.
AOUl
Frequency!
*
o
o
o
o
i
illi 1
:
IE
Figure B.27 Front Panel for F-Write.Vi
f-w r ite .v i Diagram
v /x j
1 4 p t D ialog F o n t
F re q u e n c y
fc v H
address
□+
BB+
E3-»
EH
l/W M I
o ®
"1?
Figure B.28 Diagram for f-write.Vi
202
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