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Direct observation of binding stress-induced crystalline orientation change in
piezoelectric plate sensors
Wei Wu, Wei-Heng Shih, and Wan Y. Shih
Citation: Journal of Applied Physics 119, 124512 (2016);
View online: https://doi.org/10.1063/1.4944890
View Table of Contents: http://aip.scitation.org/toc/jap/119/12
Published by the American Institute of Physics
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JOURNAL OF APPLIED PHYSICS 119, 124512 (2016)
Direct observation of binding stress-induced crystalline orientation change
in piezoelectric plate sensors
Wei Wu,1 Wei-Heng Shih,1 and Wan Y. Shih2,a)
1
Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104,
USA
2
School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia,
Pennsylvania 19104, USA
(Received 22 January 2016; accepted 15 March 2016; published online 31 March 2016)
We have examined the mechanism of the detection resonance frequency shift, Df/f, of a 1370 lm
long and 537 lm wide [Pb(Mg1/3Nb2/3)O3]0.65[PbTiO3]0.35 (PMN-PT) piezoelectric plate sensor
(PEPS) made of a 8-lm thick PMN-PT freestanding film. The Df/f of the PEPS was monitored in a
three-step binding model detections of (1) binding of maleimide-activated biotin to the sulfhydryl
on the PEPS surface followed by (2) binding of streptavidin to the bound biotin and (3) subsequent
binding of biotinylated probe deoxyribonucleic acid to the bound streptavidin. We used a PMN-PT
surrogate made of the same 8-lm thick PMN-PT freestanding film that the PEPS was made of but
was about 1 cm in length and width to carry out crystalline orientation study using X-ray diffraction
(XRD) scan around the (002)/(200) peaks after each of the binding steps. The result of the XRD
studies indicated that each binding step caused the crystalline orientation of the PMN-PT thin layer
to switch from the vertical (002) orientation to the horizontal (200) orientation, and most of the
PEPS detection Df/f was due to the change in the lateral Young?s modulus of the PMN-PT thin
C 2016 AIP Publishing LLC.
layer as a result of the crystalline orientation change. V
[http://dx.doi.org/10.1063/1.4944890]
I. INTRODUCTION
Current biosensing technologies such as enzyme linked immunosorbent assay (ELISA) rely on the use of optical label for
detection and quantification. These methods typically require
multiple bonding and washing steps and are tedious. Over the
last two decades, many label-free detection technologies have
been investigated for biosensing applications including, for
example, quartz crystal microbalance (QCM),1?3 surface acoustic wave (SAW) devices,4,5 surface plasmon resonance (SPR),6
silicon microcantilevers,7?10 electrochemical sensors,11?13 nanotube and nanowire biosensors.14?16 Although these techniques
can carry out relatively rapid detection in liquid, limitations
such as requirement of expensive equipment, insufficient sensitivity, complex signal amplification schemes,8,12,15 and hard to
control detection conditions still render them impractical for
real-world applications.
Piezoelectric microcantilever sensor (PEMS)17?24 consisting of a highly piezoelectric layer such as lead zirconatelead titanate (PZT)20,23,25?28 or lead magnesium niobate-lead
titanate (PMN-PT)17?19,21,22 bonded to a nonpiezoelectric
layer and its successor, piezoelectric plate sensor (PEPS)29
consisting solely of a highly piezoelectric plate are a relatively new type of label-free sensor. With receptors immobilized on a PEMS/PEPS surface, binding of target analyte
shifts the resonance frequency of the PEMS/PEPS. Detection
of a target analyte is achieved by electrically monitoring the
resonance frequency shift of the PEMS/PEPS directly from
the sample in situ and in real time. PEMS and PEPS have
a)
Author to whom correspondence should be addressed. Electronic mail:
shihwy@drexel.edu. Tel.: �215-8952325. Fax: �215-8954983.
0021-8979/2016/119(12)/124512/7/$30.00
been shown to exhibit high detection sensitivity in a variety
of detections including detecting human epidermal growth
factor receptor 2 (Her2),18,19 white spot syndrome virus
(WSSV),17 Bacillus anthracis spores,20 and deoxyribonucleic
acid (DNA).29 Intriguingly, the detection resonance frequency
shift, Df, of these PEMS and PEPS was 100?1000 times
higher than could be accounted for by the effect of mass
change alone.17,18,29?31 The piezoelectric materials used in the
PEMS and PEPS were so-called ?soft piezoelectric,? of which
more than 80% of the piezoelectric response is attributed to
polarization/crystalline orientation switching and the crystalline orientation has been shown to be sensitive to changes in
electric field and stress.32,33 Furthermore, the Young?s modulus of soft piezoelectrics such as PMN-PT is anisotropic,
resulting in the change in Young?s modulus when polarization/crystalline orientation changes.34 The enhancement was
attributed to the polarization/crystalline orientation switchingassociated Young?s modulus change induced by the surface
stress generated by the bound analyte on the sensor surface.21,22,35,36 So far, there has been no experimental study
directly linking the resonance frequency shift of a PEPS to
polarization/crystalline orientation switching in the piezoelectric layer upon binding of an analyte on the sensor surface.
The purpose of this study is to carry out direct X-ray diffraction (XRD) observation of the crystalline orientation
switching in the PMN-PT layer upon binding of the analyte
on the surface of the PMN-PT layer and correlate the observed
crystalline orientation change with the detection Df/f of a
PEPS made of the exactly same PMN-PT layer. The model
detection study was three-step probe DNA (pDNA) immobilization process described in the previous study. The area of a
119, 124512-1
C 2016 AIP Publishing LLC
V
124512-2
Wu, Shih, and Shih
J. Appl. Phys. 119, 124512 (2016)
PEPS is less than 1 mm2 which is insufficient for generating
enough XRD signals within a reasonable time. A larger surrogate PMN-PT strip (strip, hereafter) 10 mm 10 mm of the
same thickness sintered in the same batch as the comparing
PEPS will be used for the XRD study instead. The surrogate
PMN-PT strip had the same gold electrodes and further encapsulated with the same insulation coating to carry out the same
model three-step immobilization of a probe DNA. The larger
area of the strip allowed better XRD signals to clearly differentiate the diffraction patterns before and after analyte binding.
The diffraction-pattern difference will then be used to deduce
the corresponding Young?s modulus change to compare with
the resonance frequency shift of the PEPS made from the same
PMN-PT layer with the same surface treatment.
II. EXPERIMENTAL
A. Fabrication of PMN-PT PEPS and X-ray surrogates
For sintering, a 13 mm 13 mm PMN-PT green tape on
a flat alumina plate and a small crucible containing 0.2 g of a
PbO powder (99.9%, Alfa Aesar) were placed inside a large
covered alumina crucible with the small crucible partially
open to control the PbO atmosphere during sintering. The
temperature was increased at 1 C/min below 400 C and
10 C/min above 400 C and held at 1175 C for 2 h. After
sintering, the PMN-PT freestanding films were coated with
100 nm thick gold electrodes on both sides with a 10 nm chromium bonding layer by thermal evaporator (Thermionics VE
90). For this study, all PMN-PT layers used had a thickness of
8 lm. PMN-PT PEPSs were fabricated by cutting the goldcoated PMN-PT freestanding films into strips 500?600 lm
wide and 2300 lm long by a wire saw (Princeton Scientific
Precision, Princeton, NJ). Two gold wires 10 lm in diameter
were then attached to the top and the bottom electrodes of a
strip using a conductive glue (8331, MG Chemicals). The rear
end of the strip was then glued to a glass slide to form the
final plate geometry. The strips were then poled for 30 min
with an electric field of 15 kV/cm at 80 C on a hotplate. An
optical micrograph and a scanning electron microscopy
(SEM) (FEI XL30, Philips) cross-section micrograph of the
PMN-PT PEPS used in the study which was 1370 lm long
and 537 lm wide are shown in Figs. 1(a) and 1(b). The phase
angle versus frequency resonance spectrum as well as the relative dielectric constant (dielectric constant hereafter) of the
PEPS was measured using an impedance analyzer (Agilent
4294A). The dielectric constant of the PEPS was about 1800
with a loss factor of around 2%?3% as measured at 1 kHz.
The in-air phase-angle-versus-frequency resonance spectrum
is shown as the solid line in Fig. 1(c). As can be seen from
Fig. 1(c), the PEPS exhibits a strong length-extension-mode
(LEM) resonance peak at around 588 kHz and a strong widthextension-mode (WEM) resonance peak at around 3.04 MHz.
The electromechanical coupling coefficient was deduced from
the WEM peaks as k31 � 0.32 using the method outlined in
the previous publication.24 For the XRD study, surrogates of
1 cm2 were obtained by wire-saw cutting from the same batch
of PMN-PT layers.
The PEPSs and the XRD surrogates were then subject to
the same 3-mercaptopropyltrimethoxysilane (MPS) (Sigma)
FIG. 1. (a) An optical micrograph, (b) a scanning electron microscopy
(SEM) cross-section micrograph, and (c) an in-air (solid) and in-PBS
(dashed-dotted) resonance spectra of a 8-lm thick PMN-PT PEPS.
coating, which serves to electrically insulate the PEPS as well
as to provide the sulfhydryl groups for receptor immobilization, using an improved coating condition as follows. First, a
PEPS (surrogate) was cleaned in a 1-in-40 diluted piranha solution (3 parts of 98% sulfuric acid (Alfa Aesar) and 1 part of
30% hydrogen peroxide (Alfa Aesar)) for 10 min followed by
rinsing with de-ionized (DI) water and ethanol (Fisher). It was
then soaked in a 0.1 mM MPS solution in ethanol with 0.1%
DI water for 30 min followed by soaking in a 0.1% MPS solution in ethanol with 0.5% DI water at pH 9 for 48 h where the
MPS solution was replaced with a fresh one every 12 h.37 For
each MPS solution replacement, the PEPS (surrogate) was
first rinsed with DI water and followed by ethanol before
immersing in a fresh MPS solution. Finally, the PEPS (surrogate) was rinsed with DI water and ethanol before further surface modification for detection. The in-PBS resonance
spectrum of the PEPS after the insulation coating is shown as
the dashed-dotted line in Fig. 1(c). The closeness of the inPBS spectrum to the in-air spectrum indicated that the insulation was good.
B. Model detection
The model detection for the XRD study was the threestep immobilization of a probe DNA as schematically shown
in Fig. 2 for which the relative resonance frequency shift
measured in situ during each step was correlated with the
crystalline orientation change before and after each step as
measured by XRD. The first step was the binding of the
Maleimide-PEG11-Biotin (Pierce) on the MPS by reacting
124512-3
Wu, Shih, and Shih
J. Appl. Phys. 119, 124512 (2016)
FIG. 2. A schematic of model detection steps: step 0 in which the PEPS
surface ready for immobilization, step
1 in which maleimide-PEG-biotin covalently binds to the PEPS surface,
step 2 in which streptavidin binds to
the biotin of the Maleimide-PEG-biotin on the PEPS, and step 3 in which
biotinylated pDNA binds to the streptavidin on the PEPS surface.
the Maleimide of the Maleimide-PEG11-Biotin with the sulfhydryl on the MPS by immersing the PEPS (surrogate) in a
2-lM Maleimide-PEG11-Biotin (Pierce) solution. The second step was the binding of streptavidin to the biotin of the
bound Maleimide-PEG11-Biotin on the MPS surface by
immersing the Maleimide-PEG11-Biotin-coated PEPS (surrogate) in a 10 mg/ml streptavidin (Ray Biotech) solution.
The third step was the binding of the biotinylated pDNA to
the bound streptavidin on the PEPS (surrogate) surface by
immersing the streptavidin-coated PEPS (surrogate) in a
2 mM biotinylated probe pDNA (Complementary DNA)
(Sigma) solution. The pDNA had a sequence of 50 ACAAAGATCATTAACC-30 and was biotinylated at the 50
end. To account for the mass change effect, a 5-MHz QCM
(Stanford Research System) was also subject to the same
MPS coating and the same model detection steps.
2-lM aqueous Maleimide-PEG11-Biotin (biotin hereafter) solution for 30 min, rinsed with DI water, placed in the sample
holder, covered with a thin layer of water, and scanned by X-ray
again for the XRD pattern with bound biotin. Following this, the
surrogate went through two more detection steps one for streptavidin and the other for pDNA, each for 30 min and followed by
the same fine X-ray scan around the (200)/(002) peak.
3. Real-time dielectric constant monitoring
of the PEPS
A separate model detection experiment was carried out
in which the relative dielectric constant of the PEPS instead
of the resonance frequency was monitored in real time using
an Agilent 4294A impedance analyzer. The dielectric constant was measured at 1 kHz in every minute.
III. RESULTS
1. Real-time resonance frequency shift monitoring
of the PEPS
During the detection steps, the LEM resonance frequency
of the PEPS was monitored in real time using an Agilent
4294A impedance analyzer. The model detection steps were
carried out in an open vessel without flow. To avoid the effect
of liquid level change due to drying, the detection was carried
out in a closed chamber with humidity controlled at around
75%. The resonance frequency of the QCM was also monitored using the same Agilent 4294A impedance analyzer in
real time in a closed flow cell during the detection steps.
2. Direct X-ray diffraction characterization
on the surrogate
For XRD characterization of the crystalline orientation
switching due to the binding of molecules to the sensor surface, a 1-cm2 surrogate was used which had the same MPS
coating and model detection steps. The XRD measurements
were carried out using a SmartLab X-Ray Diffractometer
(Rigaku). Because drying could cause unaccountable stress to
the sample, before the first binding step, the surrogate was covered with a thin layer of water and placed in a 4 cm 4 cm
concave glass holder during the X-ray measurements. A rough
scan was carried out to determine the location of the (200)/
(002) peak which we would use to quantify the crystalline orientation switching associated with each detection step. A fine
scan was then carried out in the range 2h � 44 ?47 where
(200)/(002) peak was located with a 0.05 increment in every
4 s for the XRD pattern without bound molecules. The surrogate was then removed from the XRD unit and soaked in a
Figures 3(a), 3(c), and 3(e) show the relative frequency
shift, Df/f, versus time of the PEPS and of the QCM up to the
1st, 2nd, and 3rd detection step, respectively. From Fig. 3(a),
we can see that the PEPS exhibited a much larger Df/f than
QCM for all three detection steps. For better comparison, the
average Df/f over the last 5 min of each detection step of the
PEPS and that of the QCM were compared. Clearly, the Df/f
of the PEPS was about 295 times larger than those of the
QCM of the same detection. The Df/f of a QCM is known to
be due to the mass effect. After adjusting for the size difference between QCM and the current PEPS,29 the enhancement
of Df/f of the current PEPS was estimated to be more than
1000 times larger than could be expected from the mass effect
alone. The reason for this large difference was that the Df/f
of the PEPS was amplified by the crystalline orientation
switching induced by the binding of the molecules on the
PEPS surface, while the Df/f of QCM was known due to
mass fact only.
The PMN-PT had a composition near the so-called morphotropic phase boundary (MPB) where two crystalline phases
coexist, the tetragonal (T) phase in which the ?c? lattice constant is larger than the ?a? lattice constant and the rhombohedral (R) phase where the lattice constant, ?r? is the same in all
three directions. In the tetragonal phase, the polarization is in
the ?c? direction, whereas in the rhombohedral phase, the
polarization is in the body diagonal direction as schematically
shown in Figs. 4(a)?4(c). To see the splitting of the ?c? peak,
?a? peak, and potentially the ?r? peak, we chose to monitor
the ?(002)/(200)? peaks. In Figs. 3(b), 3(d), and 3(f), we show
the X-ray diffraction intensity versus 2h of the surrogate (after
124512-4
Wu, Shih, and Shih
J. Appl. Phys. 119, 124512 (2016)
FIG. 3. Df/f versus time of the model detection in step 1, step 2, and step 3 binding, respectively, (a), (c), and (e), and X-ray diffraction patterns at the
(200)(002) peak of the surrogate PMN-PT strip before and after step 1, before and after step 2, and before and after step 3, respectively, (b), (d), and (f) where
blue is for biotin, red for streptavidin, and green for pDNA.
removing gold electrode small peak) before and after the 1st,
2nd, and 3rd detection step around the (002)/(200), respectively, where h was the diffraction angle. Note the peak around
2h � 44.55 was the (002) or ?c? peak corresponding to the
?c? lattice constant (or the polarization) being vertical, while
the peak around 2h � 45.15 was the (200) or ?a? peak corresponding to the ?a? lattice constant being vertical and the ?c?
lattice constant (or polarization) being in horizontal. Note that
the ?r? peak was buried between the ?c? and ?a? peaks and
could only be clearly seen when the peaks were de-convoluted
into three peaks. From Figs. 3(b), 3(d), and 3(f), one can see
that after each detection step, the ?c? peak was decreased
while that the ?a? peak was increased, indicating that more
domains were switched from ?c? to ?a? (or polarization
switched from vertical to horizontal) as a result of binding of
molecules on the PMN-PT surface, clearly illustrating that the
crystalline (or polarization) orientation of the PMN-PT was
switched as a result of the bound molecules on the PMN-PT
FIG. 4. A schematic of (a) the tetragonal ?c? orientation, (b) the orientation
of the rhombohedral phase, and (c) the
tetragonal ?a? orientation.
124512-5
Wu, Shih, and Shih
J. Appl. Phys. 119, 124512 (2016)
surface. Note that the surface stress of an adsorbed streptavidin38,39 layer and that of an adsorbed probe DNA40 layer has
been shown to be compressive that the switching from the ?c?
to ?a? orientation was consistent with the fact the surface
stress in the adsorbed molecular layer was compressive and as
a result the surface stress in the solid layer underneath was tensile. We de-convoluted the (002)/(200) peaks into three peaks,
the ?c? peak, the ?a? peak, and the ?r? peak after baseline removal as illustrated in Fig. 5. To better account for the change
in the height of each peak, the position and width of each of
the ?c,? ?a,? and ?r? peaks were fixed for all detection steps.
The volume fraction, fc, fa, and fr, respectively, of the
de-convoluted ?c,? ?a,? and ?r? peaks at every step are listed
in Table I where the volume fraction of a peak was determined as the area under the de-convoluted peak divided by
the total area under the (002)/(200) peaks. As can be seen, fa
increased from 31.5% at step 0% to 42.2% while fc
decreased from 53.5% to 41.7% after the three reactions.
The change in fr was only 0.5%, much smaller comparing
with the change in fa (�.7%) and that in fc (11.8%), indicating the crystalline orientation switching was mainly from
the vertical ?c? orientation to the horizontal ?a? orientation.
The resonance frequency of a LEM peak could be
related to the velocity of sound, C, and the length, L, of the
PEPS as
f �
C
:
4L
(1)
The factor four in the denominator was due to the fact that
one end of the PEPS was fixed. The sound velocity was
related to the Young?s modulus perpendicular to the poling
direction (thickness direction), Y11, and density, q, as
p????????????
(2)
C � Y11 =q:
Combining Eqs. (1) and (2) and for Df/f 1, Df/f could be
approximated as
Df 1 DY11 1 Dq DL
�
:
f
2 Y11
2 q
L
(3)
When there are three possible crystalline orientations, ?c,?
?a,? and ?r?
TABLE I. Phase fraction of each orientation in each detection step.
Steps
Initial
Biotin
Streptavidin
Probe DNA
fc (%)
fr (%)
fa (%)
53.5
49.5
44.7
41.7
15
16.6
16
16.1
31.5
33.9
39.3
42.2
1
Y11 � fc Y11;c � fa 餣11;a � Y33;a � � fr Y11;r ;
2
(4)
where Y11;c , Y11;a , and Y11;r are the horizontal Young?s modulus of the ?c? orientation, ?a? orientation, and the ?r? phase,
respectively. Conventional Y11 and Y33 are the Young?s modulus along the horizontal and vertical directions, respectively.
Note that Y11,c � Y11,t, Y11,a � Y33,t, and Y33,a � Y11,t, as can
be seen from the schematics shown in Figs. 4(a)?4(c). As a
result, Y11 can be further expressed as
1
Y11 � fc Y11;t � fa 餣33;t � Y11;t � � fr Y11;r :
2
(5)
Thus, the horizontal Young?s modulus, Y11, of the PEPS
before and after each bonding event could be determined
using Eq. (5) with the fa, fc, and fr determined from the XRD
study if Y11,r, Y33,t, and Y11,t were known. For PMN0.65PT0.35 rhombohedral ceramics, Y11,r was known to be
76 GPa.34 However, Y11,t and Y33,t were not known. One
way to obtain Y11,t and Y33,t to compute Y11 for the LEM
resonance frequency shift after each bonding event was to
determine Y11,t and Y33,t, independently from other resonance peaks such as the WEM and the thickness extension
mode (TEM) resonance peaks. Because the current 8-lm
PEPS did not have an observable TEM peak, a 15 lm thick
PMN-PT PEPS 1.3 mm long and 274.3 lm wide with a similar grain size was fabricated such that both the WEM and
TEM peaks were measurable. The WEM resonance frequency, fw, of a PEPS of width, w, can be expressed as
1
fw �
2w
s???????
Y11
;
q
(6)
and the TEM resonance frequency, ft, of a PEPS of thickness, t, can be expressed as
s???????
1 Y33
;
(7)
ft �
q
2t
where the vertical Young?s modulus, Y33, can be expressed as
Y33 � fc Y33;t � fa Y11;t � fr Y33;r ;
FIG. 5. An example of three-peak deconvolution of the (002)/(200) peak following baseline removal.
(8)
according to the schematics shown in Figs. 4(a)?4(c). The
phase angle versus frequency resonance spectrum of the
15-lm thick PEPS is shown in Fig. 6, which showed the fw
and ft of the 15-lm thick PEPS to 5.79 MHz and 101 MHz,
respectively, as indicated by the arrows in Fig. 6. With
q � 7.8 g/cm3, w � 274.3 lm, and t � 15 lm, solving Eqs. (6)
and (7) yielded Y11 � 78.8 GPa and Y11 � 71.6 GPa,
124512-6
Wu, Shih, and Shih
J. Appl. Phys. 119, 124512 (2016)
Dq
1
Dax Daz
?
2
:
�
q
2
ax
az
(12)
Therefore, DL/L and Dq/q could be deduced using Eqs. (11)
and (12), respectively, using the values of the lattice constants listed in Table II. Because the mass of the PMN-PT
layer was conserved and Dax/ax and Daz/az were small, further combining Eqs. (3), (11), and (12), we had
Df 1 DY11
3 Dax 1 Daz
;
(13)
�
�
f
2 Y11
2 ax
2 az
where Y11, ax, and az at each stage could be deduced using
Eqs. (4), (9), and (10), respectively.
3 Dax
1 Daz
11
The 12 DY
Y11 , �ax � 2 az �, and Df/f as estimated from
the changes of XRD pattern are listed in Table III. As can be
seen, these estimated Df/f values denoted as (Df/f)XRD
were increasing with each bonding step and were in good
agreement with actual values of the measured Df/f denoted
as (Df/f)det from all the detection steps. Furthermore, as
can be seen from Table III, the change in length and the
change in density contributed only less than 10% to the
deduced (Df/f)XRD. Clearly, most of the deduced (Df/
f)XRD was due to the change in horizontal Young?s modulus,
Y11 resulting from binding stress induced crystalline orientation switching.
In Figs. 3(g)?3(i), we show the relative dielectric constant shift, De/e, versus time of the measurement for PEPS
(full symbols) and for the QCM (open symbols) up to the
end of the 1st, 2nd, and 3rd detection step, respectively. As
can be seen, the PEPS exhibited a relative dielectric-constant
change of about 1% in every detection step, while the dielectric constant of the QCM exhibited no discernible change in
this scale over the entire course of the experiment. Again,
the difference in the De/e versus time between the PEPS and
the QCM echoed the difference in the detection Df/f shown
in Figs, 3(a), 3(c), and 3(e) and was consistent with the
switching of the crystalline orientation from the ?c? domain
to the ?a? domain shown in Figs. 3(b), 3(d), and 3(f):?a?
domains are known to have a higher dielectric constant.41
FIG. 6. Phase angle-versus-frequency resonance spectrum of a 15-lm thick
PEPS where WEM stands for the width-extension-mode resonance peak and
the TEM the thickness-extension-mode resonance peak.
TABLE II. Lattice constants and Young?s modulus of 8 lm PMN-PT PEPS.
Lattice constants (A?)
a
3.998
Young?s modulus (GPa)
c
r
Y11,t
Y33,t
Yr
4.043
4.027
82.9
63.8
76
respectively. Assuming the 15 lm PEPS had the same crystalline orientation distributions as initial orientation distribution
(fa � 0.315; fc � 0.535; fr � 0.150) of the 8 lm PEPS before the
model bonding events and using Eqs. (5) and (8) together with
Y11,r � Y33,r � 76 GPa, the two unknowns, Y11,t and Y33,t, in
Eqs. (5) and (8) were solved numerically to be Y11,t � 82.9 GPa
and Y33,t � 63.8 GPa, which were then used to compute the
changes in Y11 after each bonding event as listed in Table III.
Similarly, the average lattice constant in the length
direction, ax, that in the width direction, ay, and that in the
vertical direction, az, can be expressed as
1
ax � ay � afc � 餫 � c辠a � rfr ;
2
(9)
az � cfc � afa � rfr ;
(10)
and
IV. CONCLUSION
We have examined the mechanism of the detection resonance frequency shift, Df/f, of a 1370 lm long and 537 lm
wide [Pb(Mg1/3Nb2/3)O3]0.65[PbTiO3]0.35 (PMN-PT) PEPS
made of a 8-lm thick PMN-PT freestanding film. The Df/f
of the PEPS in model detections of (1) binding of
maleimide-activated biotin to the sulfhydryl on the PEPS
surface followed by (2) binding of streptavidin to the bound
biotin and (3) subsequent binding of biotinylated pDNA to
respectively, where a and c were the lattice constants in the a
and c directions of the tetragonal phase and r the lattice constant of the rhombohedral phase. It followed
DL Dax
�
;
ax
L
(11)
and
TABLE III. Deduced phase fraction and effective average Young?s modulus of 8 lm PMN-PT strip after each step of immobilization.
Steps
0
1
2
3
fa (%)
fc (%)
fr (%)
Y11 (GPa)
31.5
33.9
39.3
42.2
53.5
49.5
44.7
41.7
15
16.6
16
16.1
78.86
78.52
78.04
77.76
1 DY11
2 Y11
�%�
0
0.22
0.53
0.70
3 Dax
2 ax
z
� 12 Da
az �%�
0
0.03
0.05
0.07
(Df/f)XRD (%)
(Df/f)det (%)
0
0.25
0.58
0.77
0
0.36
0.79
1.07
124512-7
Wu, Shih, and Shih
the bound streptavidin was monitored. The results of the
XRD studies indicated that each binding step caused the
crystalline orientation of the PMN-PT thin layer to switch
from the vertical (002) orientation to the horizontal (200)
orientation, as a result, changing the lateral Young?s modulus of the PMN-PT thin layer to result in the PEPS detection
Df/f, which is not due to mass effect. These results were also
consistent with the dielectric-constant increase measured
during the detection.
ACKNOWLEDGMENTS
This work was supported, in part, by the National
Institutes of Health under Grant Nos. 1R41AI112224 and
1R41AI120445, and the Coulter-Drexel Translational
Research Partnership grant, and the Nanotechnology
Institute of Benjamin Franklin Partnership of Southeastern
Pennsylvania.
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