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Basic Principles of Thermoanalytical Techniques and Their Applications in Preparative Chemistry.

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Basic Principles of Thermoanalytical Techniques and Their Applications in
Preparathe Chemistry
Heiko Karl Cammenga" and Matthias Epple*
The investigation of thermodynamic
properties and reactivity yields interesting insights into the chemistry of newly
synthesized substances. With thermal
analysis extensive information can be
gained from small samples (often only a
few milligrams). In addition, the data
obtained by thermal analysis can be
used to plan and optimize a synthesis.
Among the most important applications
are identification and purity analysis,
and the determination of characteristic
temperatures and enthalpies of phase
transitions (melting, vaporization), phase
transformations, and reactions. Investigations into the kinetics of consecutive
reactions and decomposition reactions
are also possible. With the instruments
available today such analyses can usually
be performed quickly and easily. In this
1. Introduction
In general, thermal analysis describes the examination of temperature-dependent properties of materials. In this respect a
feature of thermoanalytical methods is the large variety of possibilities. Common fields of application range from the generation of thermodynamic and kinetic parameters in basic research,
through the characterization of materials, to routine quality
control and maintenance in industrial practice.
As thermally induced processes (phase changes, phase transitions, reactions, decompositions) and temperature-dependent
material properties (heat capacity, thermal stability, mechanical
properties) are very important in chemistry, the potential
amount of information is substantial. For this reason increasing
numbers of chemists are using thermal analysis. The extensive
range of commercially available instruments and their easy operation are further reasons for the growing popularity of thermal analysis. Unfortunately the potential from the information
extracted from the recorded graphs is often not fully exploited.
Thermal analysis has had only a minor impact on preparative
chemistry so far. This is probably because scientists active in the
field of synthesis are not familiar with the many and diverse
possibilities of these methods. In this article, therefore, the basic
principles and potential applications will be expounded. The
Prof. Dr H . K . Cammenga
lnstitut fur Physikalische und Theoretische Chemie der Technische Universitlt
Hans-Sommer-Strasse 10, D-38106 Braunschweig (Germany)
TeleFdx: I n t . code + (531)391-5832
Dr. M. Epple
Insritut fur Anorganische und Angewandte Chemie der Universitlt
Martin-Luther-King-Platz 6, D-20146 (Germany)
Telefax: I n t . code + (4014123-6348
A t i g c ~Chiw 1/11.
Ed. EngL 1995. 34, 1171 - 1 187
review the fundamentals of thermoanalytical methods are described and illustrated with selected examples of applications to low and high molecular weight
Keywords: analytical methods . phase
transformations . kinetics . thermal
user should also know the limits of the methodology, because
the computer-assisted data processing commonly used today
often leads to wrong conclusions and thus to incorrect results,
which could have been avoided had the basic principles behind
the program for evaluation been known.
An important aid that thermal analysis can offer preparative
chemists is, for instance, the rapid determination of purity,
phase state, and stability of newly synthesized substances as well
as of adduct formation with the solvent. Such information can
often be obtained easily from a single measurement. Different
polymorphous forms of solids can be identified. Table 1 collates
Table 1. Some of the variables obtalnabk from thermoanalytical measurements.
Variable or Process
melting point
enthalpy of fusion
mixed melting point
boiling point
enthalpy of vaporization
decomposition temperature
enthalpy of decomposition
enantiomeric purity
heat capacity
expansion coefficient
phase transition temperature
phase transition enthalpy
glass transition
enthalpy of reaction
reaction kinetics
Symbol [a]
Method [b]
TMA. thermal X-ray
TOA. thermal X-ray
[a] The physical quantity determined directly or indirectly. [b] The abbreviations
are explained in the text. [c] From these variables deductions on the mechanism can
be made.
~ r l u g . ~ g r s ~ l l n7bH.
s ~ h u 0-69451
Wrinhcim, 1995
S /f).OO+ .?5/0
H. K. Cammenga and M. Epple
a number of variables that can be obtained from thermodynamic measurements.
Apart from thermodynamic parameters (heat capacities,
phase transition temperatures, enthalpies), kinetic data (rates of
transition, reaction, and decomposition) can often also be obtained from the quantitative evaluation of the data. The precise
evaluation of the shape of a melting peak can enable the determination of the total concentration of impurities even in a range
below 1 mol %, a concentration range in which the usual analytical methods (for example spectrometric methods) reach their
limits. The examination of the enantiomeric purity of newly
synthesized pharmaceuticals is an important application.
Applications in the extensive field of the chemistry of high
molecular weight substances (polymers) include, for instance,
the determination of thermal and mechanical properties in addition to the measurement of the degree of crystallinity and of the
kinetics of polymerization, crystallization, and decomposition.
An interesting branch of thermal analysis is biocalorimetry. In
this field the thermal behavior of living beings (from protozoa
to large mammals, even humans) is examined. The change in the
rate of heat generation of living cultures can be employed, for
instance, in screening procedures to test the effectiveness of
2. Basic Principles of Methods of Thermal analysis
In this section the basic principles of thermal analysis will be
introduced briefly. Detailed information can be found in a series
of more recent
The German Industrial Standard (DIN) 51005 defines thermal analysis as follows:
Thermal analysis (TA): Generic term for methods in which
the physical and chemical properties of a substance, a mixture
of substances, and/or reaction mixtures are measured as a
function of temperature or time, for which the sample is subjected to a controlled temperature program.[’*]
This definition also includes isothermal temperature programs (that is, measurements at constant temperature) and the
observation of free (that is, unregulated) heating and cooling
processes. In almost all cases, however, measurements are carried out at a constant heating rate p = dT/dt (scanning mode),
which strictly speaking also includes isothermal measurements
( p = 0).[141
For a given sample property a potentially large number of
variables may be considered. The most common methods follow
the mass m (thermogravimetry TG), the temperature difference
AT (differential thermal analysis DTA), the change in enthalpy
dH/dt (differential scanning calorimetry DSC),”’] and the linear expansion of a sample l (dilatometry and thermomechanical
analysis TMA).
These four most important methods are illustrated in Figure I. In the case of thermogravimetry (TG, Fig. l a ) the change
in the weight of a sample is measured as a function of time
and/or temperature (example : monitoring the thermal decomposition of a hydrated salt). The sample masses lie in the mg to
g range depending on the particular instrument and problem.
Typically 10 to 20 mg of a substance is sufficient. As a rule it is
Heiko K. Cammenga, born 1938 in Bremen, studied chemistry in Brauiischweig and Helsinki. Following his doctorate on precision measurements oflow vaporpressures at the Technische Hochschule Braunschweig
in 1967, he first became assistant, then senior assistant there at the
“lnstitutf u r Physikalische Chemie”. From 1970 to 1971 he visited the
University of Rochester, N I : U S A , as assistant professor on the invitation of Professor K. C. D. Hickman. There he worked on aproject ofthe
U. S. Office of Saline Water on the basic principles of sea water desalination processes. In 1973 he habilitated in physical chemistry with studies
on the kinetics of vaporization and sublimation. Since 1977 he has been
professor and director ofthe Department ofApplied Physical Chemistry
M. Epple
H, K, Cammenga
at Braunschweig. Since itsfoundation in 1985 he has also been a member
in the collaborative project SFB 179 “Water and Matter Dynamics in
Agro-Ecosystems”. His areas of research are many and diverse. Main focuses are the kinetics and mechanisms of reactions of
(above all organic) solids, kinetics of phase transition processes, chemistry of and damaging processes in building materials,
development and improvement of analytical methods, and ecological-chemical processes. He is author or coauthor of several
books and more than 120 contributions to journals. In 1988 he received the prize of the “Schweizer Gesellschaft f u r Thermoanalytik und Kalorimetrie”.
Matthias Epple, born 1966 in Reutlingen, studied chemistry from 1984 to 1989 at the Technische Universitat Braunschweig. In
1992 he completed his doctorate under the supervision ojProfessor H . K. Cammenga on the investigation ofthe kinetics ofthe
solid-state reactions and of solid-solid phase transitions by time- and temperature-resolved X-ray diffraction. During 1993 he
was postdoctorate fellow with Professor J. C. Berg at the Department of Chemical Engineering at the University of Washington
in Seattle, U S A , and worked in the area of recycledpaper,fiberrecovery by flotation processes. Since January 1994 he has been
working on his habilitation (chemistry of organic solids) at the “lnstitut f u r Anorganische und Angewandte Chemie der
Universitat Hamburg” with Professor A. Reller.
Angeiv. Clrem. In;. Ed. EngI. 1995, 34, 1171-1187
Thermal Analysis
;" Rl
temper;ture p r r a m
regulation k = TR
power measurement A P- P -P
signal A P
Fig. 1 . The four most commonly used methods of thermal analysis presented schematically. a) Thermogrdvimetry (TG). b) Differential thermal analysis (DTA): S
sample. R reference sample. 0 oven, ATtemperatnre difference between sample and
reference sample. c ) Differential scanning calorimetry (DSC): S sample. R reference
sample. E envii-onment,T, sample temperature, T, reference sample temperature. Ps
electriciil healing power supplied to sample, PRelectrical heating power supplied to
reference sample, A P difference in power. d) Thermomechanical analysis (TMA):
Sa wnplc. 0 o w n . Sr steering rod, Su support. PR displacement recorder (from
refs. [ l . 19J).
possible to detect changes in relative weight in the order of parts
per thousand without difficulty. The purge gas in the sample
chamber can usually be varied, and measurements in inert or
reactive gases and even measurements in a vacuum are possible.
Temperatures of approximately 1500 "C are attained, and in
specially designed equipment more than 2000 "C are possible.
With cooling systems low-temperature measurements to
- I50 .C can be conducted.
Differential thermal analysis (DTA. Fig. lb) is based on the
measurement of the temperature difference between the test
sample S a n d an inert sample (reference R ) during a temperature
program. Both samples are placed as symmetrically as possible
in an oven 0.The temperatures of the test and reference samples
can be measured either directly inside the samples or near the
samples. At thermal equilibrium, the oven and the test and
reference samples should have the same temperature. If the
oven is heated at a constant rate, a constant temperature difference AT, which is smaller the more symmetric
the experimental setup, is established following an initial
transition period caused by the thermal lag within the system. In
general, ideal thermal symmetry is not possible because of different heat capacities of the test and reference samples and
the asymmetries caused by instrument design. As a result the
temperature difference does not reach zero but is constant (stationary state). This results in a constant signal from the
calorimeter (giving rise to the base line, see Section 3.1 and
ref. [XI).
To reach the stationary state the system requires a certain
amount of time during which the signal approaches the base line
asymptotically. Such transient processes also always occur on
changing the heating rate during the course of a measurement program and at the beginning of a measurement in
every case (see for example, Figs. 10 and 12). Under no circumstances may they be confused with thermal events or even
integrated !
If a thermal event (change in heat capacity, melting, boiling,
phase transformation, reaction) now occurs in the test sample,
the stationary state will be disturbed. The temperature of the
test sample is then higher than (exothermic reaction) or lower
than (endothermic reaction) the temperature of the reference
sample; in other words, the signal recorded deviates from the
base line. The temperature difference is plotted against time or
temperature. Depending on the design of the calorimeter the
recorded signal AT can be evaluated qualitatively or quantitatively. For DTA the feasible temperature range is approximately
- 190 to 3000°C.
Differential scanning calorimetry (DSC, Fig. lc) is based on
a related principle for measurement. In this case the temperature
difference arising from thermal activity is balanced by two independent compensatory heaters, which are positioned underneath the test sample and the reference sample. The heater
power required to compensate for the temperature difference
is recorded. In this arrangement the heat used or released ( 4 ) is
obtained directly. Differential scanning calorimetry conducted
with this type of setup is therefore described as "power-compensated DSC" (temperature range approximately between - 180
and 800 "C) .Iz3]
For DSC measurements the samples are tilled into small containers ("crucibles"; made for example from aluminum, highgrade steel, gold, or glass). so that the measurements are not
dependent on the different sample forms (heat radiation and
dissipation varies depending on sample surface and form)
and also to prevent a reaction between the sample and calorimeter (corrosion!). Attention must, however, be paid to possible reactions between the sample and crucible material, such
as, for instance, an attack by acids and bases on the frequently
used aluminum crucibles. A compilation of the compatibility of
important calibration substances (see below) with crucible materials has been published.[241Special high-pressure crucibles are
also available for several instruments. In general the required
sample quantity is only a few mg.
In dilatometry and thermomechanical analysis (TMA,
Fig. Id) the sample length is the property examined. The simplest procedure consists of heating the sample in an oven and
measuring only the change in length. Expansion coefficients can
be determined and transformations detected (for example, the
glass transition in polymers). Whilst in dilatometry as little pressure as possible is applied to the sample, a constant force is
applied in thermomechanical analysis (usually one of pressure,
more rarely one of tension).
In an extension of the method, namely dynamic mechanical
analysis (DMA), the applied force is changed with time, for
instance sinusoidally. The mechanical response of the sample to
the change is observed. Important viscoelastic sample characteristics (storage modulus E , loss modulus E", tan 6 = tan (FIE"))
can be calculated from the penetration depth of the test plunger
and the time delay. D M A plays a particularly important role in
the characterization of polymers.
Besides these four classical techniques a large number of procedures are based on monitoring the temperature dependence of
other variables. Some of these are listed here as examples:
Thermooptical analysis (TOA)[’- 251 is based on following the
optical properties of a sample (absorption, emission of
radiation). Thermomicroscopy is a special case, which
can be used to gain important supplementary information.[26-311Changes in grain size (structural alterations),
phase changes, phase transitions, nucleation processes,
precipitation processes in solids, recrystallizations and
solid-state reactions are often investigated with thermomicroscopy. In thermophotometry, the temperature dependence of optical properties (for example, IR, VIS, UV, index
of refraction, polarization, luminescence) is measured.[’. 321
In evolved gas analysis (EGA) the gases released by a sample
are detected and, if applicable, analyzed quantitatively, for
example by gas chromatography/mass spectrometry or
331 Evolved gas analysis is often applied simultaneously with thermogravimetry.
Emanation thermal analysis (ETA)[34,3 5 1 concerns the detection of the release of radioactive radon from samples that
have been appropriately pre-treated. With this method, for
instance, structural changes of a sample (microscopic cracking, phase transformations, sintering, melting) can be detected with high sensitivity.
Thermoconductometry~71involves the measurement of the
temperature-dependence of electrical conductivity. It is particularly suitable for the detection of phase transformations
in the solid state.
Thermal X-ray m e t h o d ~ [ ’ ~involve
- ~ ~ ] the study of the X-ray
diffraction pattern of a sample. This method enables numerous conclusions to be drawn about solid- solid phase transitions and solid-state reactions. This method can be applied to
powders as well as single crystals (with synchrotron radiation)
Expansion coefficients can also be determined!’]
Thermoanalytical methods are often combined. Such procedures are described as simultaneous methods. For example, the
widespread, simultaneous analysis of a sample by TG and DTA
enables a specific change in mass to be attributed to a thermal
event. In contrast, comparative measurements are often limited
when two different methods are used in succession because of
the different conditions under which they are performed (sample
container, oven type, temperature sensor allocation, atmosphere, etc.) . Sample-to-sample variations that generally occur
in solids can be avoided. A disadvantage of simultaneous methods is that the sensitivity of the measurement system is frequently reduced relative to (optimized) single methods. All other procedures which may contribute towards the characterization of a
sample are described as supplementary methods. This term covers, in particular, the more rarely applied thermoanalytical
methods listed above.
Finally, a brief comment on the calibration of thermoanalytical
instruments is necessary. As in virtually all procedures the temperature is not directly measured at the sample site, a certain doubt
arises over the “true” temperatures that should be attributed to
the processes observed. These can be determined by examining
well-known reference materials (with known melting temperatures, phase transition temperatures, heat capacities, expansion
H. K. Cammenga and M. Epple
coefficients, heats of melting etc.; see for example, reference
[44]) by the method concerned and correlating the temperatures
measured with the thermodynamic equilibrium temperatures. A
calibration function calculated from the observed deviations[45]
can be used to correct the measured temperatures.
3. Measurements on Low Molecular Weight Materials
The preparative chemist is primarily interested in the properties of low molecular weight materials. Thermoanalysis enables
the determination of diverse thermodynamic and kinetic data,
which can, for instance, be used for the identification of synthesized materials and the optimization of syntheses (see Table 1).
This section will highlight and, using representative examples,
demonstrate the different applications.
3.1. Phase Transformations and Phase Transitions
of Pure Substances
Knowledge of phase transition temperatures and enthalpies is
important for the design of syntheses and for industrial manufacture. In particular, phase transition processes are exploited in
purification processes (distillation, sublimation, crystallization).
It is important to avoid the decomposition of a substance in the
process and to achieve as good a separation as possible.
The determination of phase transition temperatures counts
among the oldest applications of thermal analysis (construction
of phase diagrams from cooling curves). The DSC instruments
available today enable a quick and precise analysis when using
temperature programs. Only a little time is required for an
overview. Characteristic temperatures and enthalpies of thermally induced processes count primarily among the information
DSC is generally used for the determination of thermodynamic parameters. Figure 2 shows a typical melting peak. The
change in heat capacity on melting generally gives rise to a
change in the base line, and accordingly, an interpolation must
be carried out.[201From the shape of the peak the five temperatures T, (initial peak temperature), (extrapolated peak-onset
temperature), T, (maximum peak temperature), T, (extrapolated peak-offset temperature) and (final peak temperature) can
TFig. 2. An endothermic peak as obtained by the melting of a pure substance by
DSC. The five characteristic temperatures T., T,, T,. c. and can be determined
from the peak shape; refer to text (from ref. (461).
Angen,. Chem. Inr. Ed. Engl. 1995, 34, 1171-1187
Thermal Analysis
be deduced. For the characterization of melting and phase
transformation temperatures the peak-onset temperature T, is
generally recommended.[461 This temperature is defined as the
intersection of the tangent to the ascending peak slope and the
linearly extrapolated initial base line. The peak-onset temperature is (in contrast to T,) almost independent of the heating rate
and the sample quantity, and is easier to determine than the
initial peak temperature T .
The enthalpies related to the phase changes and transitions
can easily be obtained by integration of the appropriate peak
(the product of heat flow and time gives a quantity of heat). This
procedure naturally presents the problem of the base line construction underneath the peak.["] A linear interpolation is usually undertaken; however, other constructions may also be appropriate.l2'I
In routine operation, melting points of pure materials can
usually be reproduced to within 0.5 K ; enthalpies can be accurately measured to within several percent, depending on the
quality of the instrument and the calibration performed.[221For
the determination of boiling points the normally sealed DSC
crucibles may be pierced with a fine needle in order to enable the
evolved vapor to escape. To limit the extent of vaporization
below the boiling temperature, a small ball may be placed on the
perforation to act as a "valve" which "opens" when the boiling
point is reached, thus giving rise to sharper boiling peaks. The
variation of boiling point with pressure of the environment can
be ascertained by performing DSC at different selected pressures.lso.s'] The enthalpy of vaporization can be calculated
from the vapor pressure curve obtained by this method and the
Clausius -Clapeyron equation.
Liquid crystalline phases are primarily formed by long, asymmetric molecules. Their properties lie between those of crystalline and liquid phases. To investigate transitions between
the different liquid-crystalline phases, DSC, temperature-resolved X-ray diffraction (often with synchrotron radiation),
and polarization microscopy (TOA) may be used to advantage.["R. 491
Solid-solid phase transitions occur quite often.[s, s31 Different orders of transitions are recognized. According to Ehrenfest a phase transition is of the same order as the lowest derivative of Gibbs energy G that exhibits a discontinuity at the
transformation. For example, G is continuous in a first-order
transition, while the derivatives of G with respect to T and p
are discontinuous (for example, S , V , H ) . The enthalpy-temperature curve of a first-order transition therefore exhibits a
discontinuity at the transition temperature (examples: melting,
vaporization). Among other characteristics, higher order transitions have C,(T) curves that often increase long before the
transformation, ending in a maximum at the transition temperature (examples: A transformation, magnetic transformation).
Figure 3 shows a DSC curve of caffeine (1). The low-temperature phase, p-caffeine, is converted into the high-temperature
phase, a-caffeine, at 141 f 2 " C in a
first-order phase transition (A,rsH=
f 0.2 kJmol-'). cr-Caffeine melts
236.0 f0.2 "C
(AfusH= 21.6 f
0.5 k J m o l - ' ) . [ ' ~ s 4 ~ s sThe
1 phase transiCH3
tion peak is not as "sharp" as the melting
Arigcii Ci7rin Ini Ed Enxl 1995. 34. 1171-1187
Fig. 3. DSC curve of caffeine (1. heating rate 5 Kmin-'). At 141 'C the phase
transition fl --t a occurs and at 236 "C the melting process. The temperature is plotted on the right, the heat flow on the left (endothermic peaks point upwards,
exothermic peaks downwards).
peak, as nucleation processes during a phase transition in the
solid state require time. Dilatometric measurements were performed to establish whether this transition was first order. Figure 4 shows the change in length / with temperature of a pressed
pellet of p-caffeine. There is a distinct discontinuity in I at the
transition temperature; in other words, it is a first-order transition.
Fig. 4. Graph showing the linear expansion of a b-caffeine pellet with increase in
temperature. The lower curve shows the change in length 1. the upper curve the
differentiation of the lower curve with time dl/dt. At approximately 140 '-Cthe phase
transition 8 - a begins. The heating rate was I Kmin-' (from ref. 11, 541).
Phenanthrene undergoes a higher order transition between 72
and 74 "C. Figure 5a illustrates a DSC curve, and Figure 5b the
lattice parameters determined by temperature-resolved X-ray
diffraction. In both methods the transformation already begins
to show at low temperatures and comes to an end with a sharp
rise in the transformation rate between 72 and 74 "C. The nature
of this transformation was elucidated by X-ray structure determination on single crystals at elevated temperatures.[561The
transition is one of order-disorder, in which the individual
phenanthrene molecules have two different orientations in the
high-temperature phase (Fig. 6). At room temperature all
phenanthrene molecules lie in the orientation drawn in black. In
the high-temperature phase the positions drawn in white and in
black are taken u p with the same probability; in other words,
H. K. Cammenga and M. Epple
- 70
- 60
- 50
yL0 91"CI
t lmin I
9 [TI
9 [TI
moanalytical procedures can be used as additional methods (see
Section 2). This approach was demonstrated here for the analyses of caffeine (Fig. 4, use of dilatometry) and phenanthrene
(Fig. 5, use of temperature-resolved X-ray methods).
Cases where only small changes in enthalpy, no change in
mass, and little change in length are associated with the events
in progress (for example. some solid-solid phase transitions)
present problems. This situation arises in a solid-solid phase
transition of higher order in anhydrous silver dimesylamide (2), which takes place with
8 . . ,So2CH3
only very small thermal effect, shows no disAge
continuity in its thermal expansion behav2
ior, and is, of course, not associated with a
Thermoconductometry and temperature-resolved X-ray diffraction were therefore the methods chosen for this investigation. In Figure 7 the logarithm of conductivity is plotted against
the reciprocal temperature. The kink at about 142 "C pointing
to a phase transformation is clearly visible. The measurements
carried out by X-ray diffraction enabled the quantitative determination of this higher order transition.[581
1LO 130
Fig. 5. Graph showing the solid-solid phase transition of phenanthrene. a) DSC
curve (heating rate 1 K m i n - ' : according to ref. [l]). b) Crystallographic monitoring of the lattice parameters u, h. c. and 8, and X-ray reflection (102) characteristic
of the transition (temperature program: isothermal steps). The values for the (102)
reflection gathered from examinations of single crystals [56] are plotted as o (from
ref. [41]).
X)OO/T [100a/K1
Fig. 7. Thermoconductometric study of the phase transformation r e p in anhydrous 2 (pressed pellet, 2000 Hz). The quarter hydrate 2.1/4HZO was the starting
material. which was dehydrated by heating. The subsequent cooling curve ( 0 ) and
second heating( x ) were recorded.
Fig. 6. Projection of the arrangement of phenanthrene molecules in a crystal onto
the a/c plane. In the high temperature phase the molecules lie with the same probability either in the black or the white orientation (from ref. [56]).
the structural symmetry of the individual phenanthrene molecule in the crystal increases.
If the samples to be examined exhibit a more complex thermal
behavior, or if nothing is known about the samples, the information from DSC is often insufficient, because DSC only yields
the rather unspecific variable "enthalpy change". It is not possible to differentiate clearly between an endothermic phase transition, a melting process, and an endothermic reaction by DSC
alone. Supplementary methods of measurement must be employed in cases that are not clear-cut. In particular the examination of solids could prove to be difficult due to the widespread
appearance of polymorphism : approximately one third of organic solids have two or more polymorphic forms. Other ther1176
3.2. Determination of Phase Diagrams of Mixtures
As already mentioned, a classical application of thermal
analysis is the determination of phase diagrams of mixtures or
alloys from cooling curves (monitoring the temperature while
allowing the sample to cool freely). Knowledge of the phase
state is also important in syntheses, because the materials obtained are often more or less contaminated.
One of the simplest methods for checking the identity and
purity is the determination of the mixed melting point Ti:,
which can easily be obtained from a DSC measurement. The
classical van't Hoff method for the determination of purity provides more extensive information. This method is based on the
lowering of the melting or freezing point, which occurs if a pure
substance is contaminated with an impurity (cryoscopy). A tacit
condition for this procedure is the existence of a eutectic phase
diagram (cf. physical chemistry textbooks), in which the contamination of a pure component always leads to depression of
Angebi. Cheni f n f . E d Engf 1995, 34. 1171-1187
Thermal Analysis
the melting point. If however a solid solution is formed between
the two components (mixed crystals), the melting point of the
mixture always lies between the melting temperatures of the
pure substances; in other words, the method of melting temperature depression cannot be used. This situation is not rare, but
is often not considered.
Such simple, and even more complex, phase diagrams can
easily be determined using thermoanalytical methods. For this
purpose different compositions of mixtures of pure materials are
examined. DSC is the method normally used for these measurements. For more complicated problems, X-ray diffraction (if
necessary temperature-resolved), thermooptical methods, and
temperature-dependent measurements of electrical conductivity
are also often used.
or electrode
The pseudo-binary phase diagram of cis- and truns-azobenzene will be used to demonstrate the procedure. At elevated
temperature cis-azobenzene (3b) is slowly transformed into trunsazobenzene (3a) in the solid state as well as in the melt.[60-631
t [min] +
tlmin] 4
evr. \
20 I
3a, trans
Fig. 8. Melting curves of some mixtares ot C ~ F - and trun.\-azobenzene (3). The
melting temperature of the eutectic (eut.) is 41.4"C. of cis-azohenzene (3b) 71.6 C ,
and of uunns-azobenzene (3a) 68.3 'C.
By repeatedly melting a sample of pure cis-azobenzene, allowing
partial isomerization in the melt, and then cooling, the entire
phase diagram can be established in small stages. In addition of
course, mixtures can also be weighed out and measured.
Melting curves of some cisltrans-azobenzene mixtures with
different compositions are shown in Figure 8. The change in the
melting peaks for the pure substances as well as the eutectic peak
for a mixture containing different portions of the components is
clearly visible. The phase diagram shown in Figure 9 can be
constructed from the melting temperatures of the mixtures. The
eutectic of cis- and trans-azobenzene containing 52 YOof transazobenzene melts at 41.4 "C. When quenching molten mixtures
of cis- and ~r-am-azobenzenepresumably a further modification
of cis-azobenzene occurs, which also forms a eutectic with trunsazobenzene (eutectic temperature 36.7 "C).The melting temperature of the cis-azobenzene is also lowered (broken liquidus
curve).[6'-631The agreement with additional data obtained by
TOA16z1and by the Kofler contact method[30]is good. This
example shows that unexpectedly complex phenomena can also
occur in (seemingly) simple systems.
, V
02 03 O L 0 5 a 6 07 0 8 0 9 10
Fig. 9. The pseudo-binary phase diagram of cis- and rran.\-aLobenrene (3). For
details see text.
A DSC curve of a sample can be recorded quickly. The purity
can already be roughly estimated by visual inspection of the
shape of a melting peak. Figure 10 exhibits melting curves of
naphthalene which was definitely contaminated with transazobenzene. Pure naphthalene has a very sharp melting peak
with a very steeply ascending left slope. The melting peak becomes broader and flatter with increasing concentration of contaminant (the peak area remains approximately constant!). The
extrapolated peak-onset temperature (described here as T,) decreases. This effect is due to the increasing depression in melting
temperature with increasing concentration of contaminant according to the Schroder-van-Laar equation and the van't Hoff
law [Eq. (a)], where T, is the melting point of pure substance A
3.3. Identification and Determination of Purity
The purity of synthesized substances is often of crucial importance for the subsequent synthetic step. While the previous section dealt with larger quantities of foreign substances (impurities). this section outlines the calorimetric determination of
small concentrations of impurities.
(naphthalene in example), T, the melting point of contaminated
substance A, xAthe fraction of main component A in the liquid
phase (melt), xBthe fraction of contaminant B (truns-azoben-
H. K. Cammenga and M. Epple
Fig. 10. The effect of contaminant concentration x3. on the DSC melting curve of
naphthalene. The solid curve represents zone refined (highly pure) naphthalene, the
broken curve naphthalene containing 0.98 mol% 3a, and the dotted curve naphthalene containing 5.01 mol% 3a (from ref. [l]). eut. = eutectic.
zene in example) in the liquid phase, and AfusHA
the enthalpy of
fusion of pure substance A. The basic prerequisite for the use
of this equation is the formation of a eutectic between A and B.
In addition, this equation is only valid under certain conditions
(see ref. [66]),which primarily include an adequately low concentration x, thermal stability of the components even after
melting, and thermodynamic equilibrium (neither temperature
nor concentration gradients). The last of these requirements
results in the use of a low heating rate
(normally 1 to
2 Kmin- ’) and a small sample quantity (a few mg). As a rule of
thumb, a substance is of high purity if the ascending (left) side
of the melting peak is steeper than the descending (right) side.
Quantitative analysis of the melting peak shape provides
more precise values for purity. In this method it is assumed that
the eutectic of A and B initially melts. The pure component A
(in this case naphthalene) then gradually dissolves in the eutectic
with increasing temperature, and as a result the concentration of
B (in this case trans-azobenzene) steadily decreases. Thus one
moves along the solubility curve of B in A, which is approximately given by the van’t Hoff equation. When all of A has
melted, the melt has a contaminant concentration of x,.
By suitable plotting of the melting temperature versus the
corresponding fraction that has melted (Fm),
which can easily be
determined from the ratio of the integral of the curve up to the
particular melting temperature to the integral of the whole
curve, the fraction x: of contamination in the original sample can
be calculated by linearization : the gradient gives the contaminant
concentration x i . The intercept of the extrapolated line with the
temperature axis yields the melting temperature of pure compo6 5 1 The small but measurable total concentration of
contaminants (less than 0.1 mol%), which can often no longer
be quantitatively determined by the usual procedures such as
NMR, UV, IR, and MS, is a particular advantage of this method.
As the reduction in melting temperature, being a colligative
property, depends not on the type of dissolved particles but on
their number only, the concentration of contaminant xB must be
regarded as a summated variable. All foreign substances which
form eutectics with the main component are detected together.
This feature differentiates this method from other sensitive
methods (GC, HPLC, etc.), which can only detect individual
impurities but do not directly yield the purity of the sample. The
requirement that all components behave ideally in the melt limits the safely detectable concentration range to x, z 5 mol% (for
an estimation of the error resulting from approximations associated with the van’t Hoff and Schroder-van Laar equations, see
ref. [66]).
Another method that so far has hardly been used is based on
a mathematical simulation of a measured curve by allocating
suitable thermal resistances and time constants for the calorimeter and calculating the rate of enthalpy change in the
sample.[66,671 In this procedure calculated melting curves are
compared with an experimentally obtained melting curve. The
concentration of contaminant is mathematically varied in the
simulation process until optimal agreement between the calculated and measured curves has been reached.
An important practical application of the calorimetric purity
analysis is the determination of enantiomeric purity of newly
synthesized substances. This type of analysis is particularly important for pharmaceuticals. In these cases calorimetric analysis
can provide valuable results.[68-’11
The example of the selective antimuscarine agent l-cyclohexyl-1-phenyl-4-piperidino-I -butanol (hexahydro-difenidol,
4) will be used to illustrate this application. Figure 11 exhibits
the calorimetrically determined
phase diagram for the enanO
tiomers. In this case a comC
pound with a melting point
maximum at x, = 0.5 is formed
(dystecticsystem). The purity of
the enantiomers was determined to be 99.7 mol % in each case. An estimation of purity by
melting point determination alone would lead to completely
incorrect results here. The course of the curve between the melting temperatures of the pure enantiomers and the eutectics was
calculated with the unsimplified Equation (a) (Schroder-vanLaar equation; middle partial equation). The course of the
curve between the two eutectics arises from the PrigogineDefay equation In4xB(1- x,) = AfusHrc(1/Tmax
- 1/T) Enantiomeric purities are frequently quoted as %ee. The relation to
molar fraction is %ee = IOO(2x - I).[68,701
\ /I
Fig. 11. The calorimetrically determined phase diagram of the two enantiomers of
4. Both components form a dystectic (from ref. [70]).
3.4. Determination of Thermochemical Parameters
Besides the properties of pure, thermally unreactive materials,
the measurement of which was discussed in the previous three
sections, chemical reactions can also easily be examined with
Angew. Chern. Int.
Ed. Engl. 1995, 34. 1111-1187
Thermal Analysis
thermoanalytical methods. These methods enable thermodynamic data (heat capacity change A r c p , enthalpy of reaction
ArH,equilibrium constant K,, and Gibbs energy A r c ) as well as
kinetic data to be determined. The study of reaction kinetics is
discussed extensively in the separate Section 3.5 because of the
large significance of this field of application.
Differential scanning calorimetry (DSC) on small sample
quantities (2-4mg) can provide a general analysis of an unidentified o r newly synthesized material within a few hours. An
analysis by this method provides information on phase transformations and on reactions, among these also decomposition reactions. Although the temperature and enthalpy values obtained are usually still rather inaccurate, valuable conclusions
on the identity, purity, and stability of the sample can still be
drawn.[72 741 Unexpected effects such as phase transitions and
reactions are often found. These easily obtainable results should
be of interest to the preparative chemist in particular. Experience shows that a quantitative determination of the effects taking place requires a larger number of measurements. However,
a quantitative description of the system is not always necessary,
depending on the specific research task.
The determination of different thermochemical parameters is
demonstrated here with the silver dimesylamide quarter-hydrate
(2.1/4H20) as example. Figure 12 shows the DSC curve of a
d t ImW 1
t [min] ---+
Fig. 12. DSC curve o f 2 . 1 / 4 H 2 0 . Thedehydration a begins above 1OO'C andends
with a very rapidly occurring phase transition b at 174-C. At 238°C the now
anhydrous substance melts (c). In the melt, exothermic decomposition d occurs. The
heating rale was 5 K m i n - (from reference [75]).
heating event. Dehydration a appears above 120 "C as a broad,
endothermic peak. At 174 "C the dehydration is concluded by a
rapid phase transition, during which the remainder of the water
of hydration is released (sharp endothermic peak b). The sum of
the enthalpy of dehydration and phase transformation was calculated by integration to be + 18.42 kJmol-1.[751After the dehydration and phase transition the substance is yellow because
the crystals shatter into many small fragments while maintaining the external morphology.[751
From the fusion peak c the melting temperature can be calculated to be 237.7 " C .The calorimetrically determined purity of the
sample is 99.6 mol% (enthalpy of melting 26.48 kJinol-').
Exothermic decomposition d begins only in the melt and is seen
in the falling base line.
At this point it becomes clear how information obtained from
thermal analysis data can be useful in the planning of a synthesis. Silver dimesylamide is used as a starting material for further
Angel% Chem Int Ed EngI 1995. 34. 1171 -1187
syntheses and must be available in an anhydrous form; in other
words, it must be dehydrated.15*]The optimal dehydration temperature lies approximately between 180 and 190 "C, as the entire amount of water of crystallization is released quickly at this
temperature without decomposition. Thermal analysis also shows
that the yellow coloration after dehydration is not due to decomposition. as may have been assumed upon superficial examination. Knowledge of the high purity is of considerable value
for further synthesis planning.
3.5. Kinetic Parameters from ThermoanalyticalMeasurements
The variables measurable by thermoanalytical methods can
often be correlated with the progress of reaction. In the case of
thermogravimetry the quotient from the loss in mass Am(/)at
time t with the total mass loss Am(t = a)equals the proportion
which has reacted so far, the degree of conversion. The degree
of conversion is generally defined by using the extent of reaction
and is described as a [Eq. (b), see physical chemistry textbooks]. For a reaction proceeding to completion the degree of
conversion lies between 0 and 1. The relationship between
the degree of conversion and loss in mass is given by Equation (c), where A m ( [ ) is the mass loss by time t, Am(t = co)
the total mass loss at the end of the reaction, m ( t ) the sample
mass at time f, m(t = 0) the sample mass before reaction, and
m(t = co)the sample mass at the end of the reaction.
This simple equation is, of course, only valid for one-step
reactions proceeding to completion (a(t = co)= 1) in which the
starting material used has not yet undergone decomposition
(a(/ = 0) = 0). An example is the thermal decomposition of
which takes place without the formation of lower
hydrates.[761For the dehydration of CuS0;5 H,O to CuSO,.
which is known to have intermediate steps, this equation must
be applied to the individual steps.
A similar equation applies to DSC for the relationship between the enthalpy of reaction and degree of conversion. In this
case the partial area of the reaction peak up to time t is compared with the total peak area [Eq. (d)], wherc A,H(t) is the
enthalpy of reaction ( = partial peak area) up to time t , ArHthe
total enthalpy of reaction ( = total peak area between t , and tr),
t, the initial peak time (temperature 7;), t, peak-end time (temperature &), and dH/dt enthalpy change ( = heat flow) at time /.
Besides those conditions mentioned for thermogravimetry,
additional conditions apply to DSC. No other thermal event
(phase transition, melting, evaporation) may take place during
w . IC. c ammcnga and M Eppk
the reaction. and furthermore the enthalpy of reaction, which is
dependent on the amount of material, must be independent of
the degree of conversion. This means, for instance, that the
enthalpy changes by the same amount when the degree of con-.-.. <-h:* from = n to ry = 0.1 as it does when the degree
of conversion changes from a = 0.6 to a = 0.7.
Thermogravimetry and DSC are the methods most frequently
used for the determination of kinetic data. Other methods such
as thermooptical analysis, evolved gas analysis, and X-ray diffraction can also be used in kinetic measurements.
A particular feature of thermoanalytical methods is their suitability for the study of the kinetics of nonisothermal reactions.
Conventionally, kinetic measurements are performed isothermally at different temperatures. The calculated rate constants
are plotted according to Arrhenius (In ( k )versus 1/T) to give the
activation energy and collision factor (providing the plot forms
a straight line). This procedure can be time consuming and
requires substantial amounts of material.
Nonisothermal measurements enable, in principle, the activation parameters EA and Ig(k,) to be determined from a single
experiment.[25s7 8 - 8 0 1 This procedure considerably reduces the
measurement time. Although some procedures for evaluation
have been available for over thirty years, this method of analysis
is used comparatively seldom and is therefore unfamiliar to
many chemists. For this reason the most important procedure
for the evaluation of nonisothermally obtained data (the Borchardt and Daniels method) ,IB1]
which i s also frequently included in the commercially marketed TA program packages, will be
introduced briefly here. The rate of reaction is defined by using
the previously introduced degree of conversion M [Eq. (e)] ,
In the most favorable case the order n of the reaction is
known. In this situation k ( T ) can be calculated from the variables dcrldt, co, and a for all temperatures. The value of In (k(T ) )
is plotted versus l / T , and after linear regression the activation
energy EAcan be calculated from the gradient and the collision
factor k, from the intercept, prouiding n has been chosen COr-
rectly. If the order of reaction n i s not known, an optimal fit of
the three parameters E,, k , , and n can be achieved by multiple
linear regression (MLR) or nonlinear regression.[84.851
This procedure is demonstrated in Figure 13. The thermally
induced rearrangement of (diphenylsily1)methyl benzoate (5 a)
- = k(T)Aa)
-10 5
2.26 230
where daldt is the rate of reaction, k( T ) the temperature-dependent rate constant, andf(a) a function characteristic of the reaction mechanism. For a first-order reaction, for instance,
,A@)= 1 - E ; for an nth order reaction Ax)= c:-' x (1 -a)",
where co is the initial concentration.[8z1
For determining the temperature dependence of the rate constant k the Arrhenius equation [Eq. (f)] is applied. k , i s the
collision factor (preexponential factor, often also denoted as k , ,
A , or Z ) and EA the activation energy.
The combination of the two equations gives Equation (g).
Equation (h) is thus valid for an nth order reaction. By taking
logarithms the Equation (i) is obtained.
k ( T ) = __ - k , exp(
k(T) =
c;-1(1 - a)"
k , exp( -
: 0.97
: 110.5kJ rno1.l
: 10 17
'-9 5
-8.5 -1
231 238 2.i2 2.i6 2.50
1/T [ 1 0 3 K - ' ] d
Fig. 13. Determination of the kinetics of the rearrangement of benzoic acid ester 5 a
to 5 b by DSC. a ) DSC curve (heating rate 0.3 Kmin-'). At 39.4'-C the substance
melts (sharp endothermic melting peak). Between 105 and 180°C the exothermic
rearrangement reaction takes place. b) Kinetic plot, obtained by multiple linear
regression (MLR) for an n-th order reaction. The calculated fit parameters are
included. The crosses mark the range used for MLR. The reaction only starts at
elevated temperatures. Even ten cycles of melting and resolidification d o no lead to
any conversion.
was studied. This compound melts at 39.4 "C (enthalpy of fus
= 25.74 kJmol-'). Rearrangement to the silyl ester
5 b takes place in the melt in the temperature region between 105
and 180°C. The enthalpy of reaction calculated as described in
Section 3.4 is A,H = - 169.1 kJmol-'. Kinetic analysis of the
exothermic reaction peak by multiple linear regression resulted
in a first-order reaction (n = 0.97) with an activation energy EA
of 110.5 kJmol-' and a collision factor Ig(k,/s-'mol'-"
l " - l ) ~ l g ( k m / s - l )of 10.17. These results agree well with the
In k( T ) = In (daldt) - (n - 1) . In (c,) - n . In (1
= Ink,
Anpew. Chem. I n f . Ed. Engl. 1995, 34. 1171-1187
Thermal Analysis
results obtained by conventional methods (NMR, isothermal)
and by theoretical calculations.[86. 871
Besides the Borchardt and Daniels method, a series of other
methods for the evaluation of nonisothermal measurements exist.
The following categories of procedures can be differentiated:[" "I
Dirc)c/ wwt/iods employ the degree of conversion
and the
rate of reaction drldt. They are particularly suitable for DTA
and DSC measurements in which the signal recorded is proportional to dz/df. The most important method is that of
Borchardt and Daniels.i811
I n t q r a l nietlzods employ only the degree of conversion
They are particularly suitable for the thermogravimetric and temperature-resolved X-ray diffraction
methods, as in these cases the signal recorded (mass, intensity) is directly related to the degree of conversion.
Difi'iwntid methods involve the derivative of the reaction rate
dz/dt with respect to time or ternperat~re.~"- 9 3 1 These methods naturally react very sensitively to noisy curves and are
therefore not applicable in many cases except after curve
Some methods make use only of specifi'c points on the experimental curve, such as the maximum in the rate of reaction
dcc/d/.["'- l o o ] Usually several measurements with different
heating rates are necessary. These methods are often based on
simplifying assumptions, which are not always justified.
P [Krniri'I-
Fig. 14. Isomerization of civazobenzene 3 b in the melt analyzed by DSC with
different methods of data processing. The calculated isomerization activation energy (first-order reaction) is plotted against the heating rate. /j.The points 0 were
determined by the Borchardt and Daniels method [81], x by the Ellerstein method
[92], + by the Coats and Redfern method [88], A by multiple linear regression [84],
and 0 by the Freeman and Carroll method [91]. In addition. the values determined
by the Kissinger method [96]and by discontinuous (isothermal) spectrophotometric
measurements [60]are also plotted. The mean values from multiple linear regression
and the mean of all non-isothermal measurements are also included (from ref.
[102]). Very recently Flammersheim and Eckert, using samples we provided, obtained EA= 103 k 1 kJ mol-' by multivariate nonlinear regression (heating rate 140 K min-l). The reaction and its data may thus be used as a kinetic reference.
of the activation energies obtained. The differential procedures
As these methods always deal only with different mathematical variants of the same basic kinetic equations (see above), they
of Ellerstein, and also of Freeman and Carroll, react particularly
sensitively to the increasing noise. The selected heating rate can
should. in principle, produce identical activation energies and
therefore have considerable impact on the result.
collision factors for a given reaction. However, the chosen
In summary, the nonisothermal methods deliver results conmethod of evaluation may depend on the heating rate as a
sistent with those from isothermal measurements. In each indiresult of different approximations made when differentiating
vidual case the heating rate must always be varied and the calcuthe equations and of varying signal-to-noise ratios. Nonlinear
lated kinetic data analyzed critically to avoid serious errors in
methods of curve fitting are therefore being increasingly used
conclusions. This is all the more important because programs
(for consecutive, equilibrium, and parallel reactions as well),
for kinetic data processing with a convenient and easy operation
which perform a numerical optimization without approximathat can lead to an all too uncritical handling of the data are
tions.["'] However, caution is advised here if the process invesoffered by instrument manufacturers today.
tigated is not well known. Clearly, the more variables (i.e.,
The examples given so far concern homogenous chemical rekinetic parameters of assumed partial stages of a reaction) that
actions. In general the applicability of kinetic procedures and
are fitted to a curve, the better the mathematical fit will be. This
their agreement with results obtained by "classical isothermal"
should, however, not encourage a noncritical acceptance of the
methods is good in these
7 8 , 8 6 . l o 2 ] The examination of
calculated activation parameters and reaction mechanisms.
Different methods of evaluation were applied to the example
heterogenous reactions (for instance, when at least one participant in the reaction is a solid) proves to be more difficult.
of the thoroughly investigated thermal isomerization of cis- to
Whilst the possible mechanisms for homogenous reactions
trans-azobenzene in the melt (3b -+ 3a; enthalpy of isomerizaby the functions,/(a)is2i) are usually zeroth, first, or
tion according to DSC: AisoHE8= - 48.2 k J m ~ l - ' f . [ ~ ' - ~ (expressed
second order, the circumstances surrounding the reactions of
DSC measurements were performed at six different heating
solids are completely different. Because of the fixed orientation
rates. The results for the activation energy obtained are depicted
of the molecules or atoms, nucleation, diffusion, and thermal
in Figure 14.[''*] Besides the results determined by the methods
conduction phenomena play crucial roles. The resulting rate
of Borchardt and Daniels,["] Eller~tein,[~']Coats and Redlaws are often complicated even though numerous simplificafern.[s8] Freeman and Carroll,['ll and K i ~ s i n g e r , [and
~ ~ ]by multions were involved in their derivation.[821Selection and verifitiple linear regression from the DSC curves, results arising from
cation of the "correct" reaction mechanism is difficult. As yet
isothermally performed spectrophotometric measurements (discontinuous, classical Arrhenius evaluation)[601are also plotted.
no successful unified theory for solid-state reactions has been
developed, despite extensive theoretical and practical efforts.
The "classically" performed optical measurements conform
The basic principles of the kinetics of these reactions as underwell to the mean value from the calorimetric measurements. It is,
stood today can be found in several monograph^.'^. l o 3 however, clear that the methods always produce slightly differing results. At low heating rates the signal-to-noise ratio of the
The significance of the kinetic parameters E, and k , in the
solid-state reactions is controversial.['0g - 31 Increasingly, the
DSC curve increases, which manifests itself in a greater scatter
H. K. Cammenga and M. Epple
view is taken that the calculated variables are artifacts; in other
words, they have no physical
In fact, the concept of an "activation energy" was originally developed for
collision-induced reactions in the gas phase and is already not
valid without reservation in liquid phases.
The extensive characterization of solid-state reactions is considerably more difficult (and therefore more laborious) than
that of a homogeneous reaction. Additional analyses by optical,
e l e ~ t r i c a l , [ and
~ ~ l diffraction methods, amongst others, must
usually be performed.
Figure 15 illustrates an example of the application of a supplementary method to a solid-state reaction. Lithium sulphate
yll ; ig;:/: ;
60 70
80 90 100
205 210 215 220 225 230
20 ["I-
Fig. 15. Analysis of the dehydration of lithium sulphate monohydrate by temperalure-resolved X - r a y diffraction (TXRD). On the left the temperature is plotted
against time; on the right the recorded diffractograms (scans 3 to 13) are portrayed.
The heating rate was + 0.5 Kmin-', the angular velocity relative to 0.3"2Hmin-'.
and product P
The reflections from starting material E ( = Li,SO;H,O)
( = Li,SO,) are marked (from ref. (771).
monohydrate was discussed as a potential kinetic standard for
Here we discuss the study of the dehydration of lithium sulphate monohydrate by time- and temperature-resolved X-ray powder
During the heating
process performed at a constant heating rate, powder diffractograms of the sample are recorded continually. During dehydration the reflections of the hydrate (E) become smaller until
they have completely disappeared. The reflections of the anhydride (P) develop concurrently. The reflections could be indexed." "] The quantitative ratio of hydrate to anhydride can be
calculated from the intensities of the reflections, from which the
degree of conversion can be determined.14'] It is then possible to
draw conclusions on the kinetics of the solid-state reaction from
the temperature- and time-dependent degree of conversion data.
The data recorded point to a nucleation mechanism A, according to Avrami -Erofeev.[*'I
However, the X-ray reflections of the hydrate do not decrease
monotonically as would be expected. Instead, for instance, the
intensity of the (101) reflection suddenly increases in scan 9, and
decreases again in the following scan. Such effects can also be
observed with other hydrate reflections. They indicate that during the dehydration, processes are taking place that cannot be
explained by simple kinetic models. Neither DSC nor TG measurements gave any indication of such processes.'771Such observations show that solid-state reactions involve very complicated
processes that can only be explained after analysis by as many
methods as possible (see for example, ref. [116]).
For this reason nonisothermal kinetic measurements should
preferably be performed in a homogeneous (liquid) phase. In
this case DSC is usually the method of choice. In favorable cases
all energetic and kinetic parameters of a reaction can be determined from very few measurements by this method with mg
quantities, as shown in Sections 3.4 and 3.5. Naturally, the nonisothermal procedure can also be applied advantageously to
other techniques (for example, the large variety of spectrometric
methods['17. ''I), an option that unfortunately has only been
used very sporadically as yet.
4. Measurements on High Molecular Weight
Substances (Polymers)
An important field for the application of thermoanalysis is
the examination of high molecular weight substances.'". 1 9 - 1 2 2 1
The main methods used are DSC, thermogravimetry, and thermomechanical procedures. The processes and variables examined include glass transition temperatures (DSC, TMA, DMA),
degrees of crystallinity and melting processes (DSC), rates of
polymerization (DSC), heat capacities (DSC), rates of crystallization (TOA) , softening processes (TMA, DMA), mechanical
variables such as expansion coefficient, elasticity, storage modulus, loss modulus (TMA, DMA), thermal stability (TG, DSC),
and the determination of the composition and compatibility of
multicomponent mixtures (DSC, TG, TMA, DMA). In the following examples will be used to illustrate these applications.
Glass transitions appear as a shift in the base line (in an
endothermal direction, change in heat capacity ACJ during a
DSC measurement. The glass transition in polyethylene terephthalate (PET) is illustrated in Figure 16 (78.7-83.7 "C).
Knowledge of glass transition temperatures is important for the
assessment of elastic properties and estimation of the compatibility of the individual components in polymer mixtures (polymer
The exothermic crystallization of amorphous regions (peak
temperature 157.6 "C) and the melting process (peak-onset temperature 239.6 "C) can also be seen in Figure 16. By comparing
the measured enthalpy of melting with the enthalpy of melting
tabulated for an entirely crystalline polymer, the crystalline fraction of the sample can be estimated (polymers generally contain
crystalline as well as amorphous regions).
Angew. Chem. Ini. Ed. Engf. 1995, 34, 1171-1187
Thermal Analysis
ImW mill 0 2
100 200 300 LOO
703 800 900
5l"clFig. 17. TG curve of the decomposition of a natural rubber!ethylene-propylene
copolymer blend. The solid line illustrates the mass curve (lefthand scale. Am), the
broken line the differential mass signal drn/dt (righthand scale). For details see text
(from ref. [126]).
The ratio of the glass transition temperature T, to the melting
temperature T,,, can provide information on the type of polymer. For highly symmetrical, highly crystalline homopolymers
made from very small monomer components (for example, polyethylene, polyoxymethylene), T,/T,-,,lies below 0.5; for certain
unsymmetrical polymers T,/T,,, lies above 0.76. For the large
majority of polymers the ratio TJT,,, is approximately 2/3.11231
Rates of polymerization can be accurately measured by
DSC.[' 241 Important information on the treatment necessary for
complete curing (length of time, temperature, type and quantity
of catalyst) can be gained from the position and shape of the
normally exothermic reaction peak. In addition, the reaction
peak can be analyzed by the kinetic methods of evaluation introduced in Section 3.5.
TMA and DMA are used to measure the temperature-dependent mechanical
Besides the expansion coefficient, the response of a sample to the application of a force that
is changed with time (for example, a sinusoidal oscillation) can
also be measured. Glass transition temperatures can often be
recorded more clearly by this method than by DSC (the elasticity increases markedly when the polymer is heated beyond the
glass transition temperature).
The thermal stability ofpolymers can be estimated by DSC or
TG measurements. Decomposition manifests itself as an exothermic or endothermic peak during DSC analysis or as mass loss in
thermogravimetric analysis. An important application of this
thermal decomposition of polymeric materials is the determination of the composition of samples containing several components. Thermogravimetry is the selected method of analysis. By
quantitative analysis of the dependence of the mass loss on
temperature and type of purge gas, the mass fractions of the
individual components are determined. This procedure can, for
example, be used for quality control of polymers.
Figure 17 portrays the TG curve of the decomposition of a
mixture of natural rubber and an ethylene-propylene copolymer. The measurement is begun in a stream of nitrogen. Between approximately 150 "C and 300 "C the plasticizer (a lowboiling ester of adipic acid) is given off (22.0 wt %). Pyrolysis of
the rubber (29.6 wt %) and the ethylene-propylene copolymer
(3 3.5 wt %) follows. At 600 "C the purge gas is switched from
nitrogen to air. A sharp peak corresponds to the combustion of
the soot contained in the sample (32.2 wt%). An occasional
residue (here: 2.7 wt'Y0) consists of ash and filler, in this case of
zinc oxide ZnO.
Angel!,. Clieni. In!. Ed. Engl. 1995. 34, 1171 - I187
The individual components can be determined with good accuracy. Naturally the method has its limits if the decomposition
reactions of the individual components overlap strongly. Reducing the heating rate in this instance often gives a better separation of the peaks. If even this measure does not lead to
success, other methods of analysis (for example, simultaneous
TG/DTA, EGA with mass spectrometry or FTIR) must be used.
5. Possible Applications of Thermal Analysis in
The potential applications of thermal analysis in industrial
production and routine analysis are manifold. Possibilities are
quality control of raw materials on delivery, continuous control
of production by analysis of aliquots, and the examination of
products for quality assurance.["l The methods of analysis used
essentially are:
differential scanning calorimetry (DSC) for the determination of melting point, boiling point, vapor pressure, purity,
heat capacity, heat of reaction, thermal stability
thermogravimetry (TG) for the determination of moisture
content, fractions of volatile components, and thermal stability, as well as the released gases and remaining residues after
combustion or pyrolysis (if necessary coupled with gas chromatography, FTIR, or mass spectrometry)
dilatometric methods of analysis (dilatometry, TMA, DMA),
for the determination of mechanical behavior (expansion coefficients, glass transition temperatures, elasticity, plasticity),
especially of polymers (see Section 4).
Besides production control and quality assurance, thermal
analysis can provide important information on the potential
hazards of decomposable material^.['^'-'^^^ The data obtained
by these methods are not only important for large scale production, but also for the preparative chemist, as the prevention of
accidents in pilot plants and even in the laboratory is imperative.
The following text gives a brief summary of the possibilities for
technical safety.
Exothermic decomposition reactions present a considerable
risk. Potentially hazardous organic compounds are, for example,
nitrenes, isocyanates, azo and hydrazo compounds, azides,
amino-halide compounds (for example, halogen-substituted anilines), oximes, epoxides, peroxides, and N-oxides. The danger
H. K. Cammenga and M. Epple
arises from the high exothermic decomposition energy resulting
from the formation of small, very stable molecules (N2. H 2 0 ,
CO,). Most decompositions of this type are also autocatalytic.
The enthalpy of decomposition AdeFH( p = constant) can be
determined by DTA and DSC measurements. It can, in many
cases, also be calculated from the tabulated thermodynamic
enthalpies of formation, which, however, always involves uncertainty about the assumed reaction products and the complete
conversion required. For organic compounds an approximate
calculation by incremental methods is usually possible. In ref.
[I 291 the chemical structure is compared with the decomposition
energy AdecU( V = constant), enabling an approximate estimation. The enthalpy of decomposition is expediently related to the
mass of the chemical substance and is given in J g - ' . Typical
values are. for instance, - 1740 J g - ' for nitrobenzene,
- 1882 J g - ' for 4-nitroaniline, - 800 J g - ' for azobenzene,
- 830 J g- ' for 3,5-dimethoxyaniline, -920 J g- for maleic
anhydride, - 406 J g- for glucose, and - 835 J g- ' for sodium
The adiabatic temperature rise AT,,, which is defined as the
quotient of the enthalpy of decomposition and heat capacity, is
more significant [Eq. (j)]. An adiabatic temperature rise of 50 to
300 350
Fig. 18. DTA curves of the decomposition of 3-nitrobenzoic acid contaminated
with different salts. a) Pure substance, b) 3-nitrobenzoic acid contaminated with
1.6 wt.% NaCI, curve c) 3-nitrobenzoic acid contaminated with 1.3 wt.% FeCi,.
d ) 3-nitrobenroicacid Contaminated with 1.5 wt.% VCI,, and e) 3-nitrobenzoic acid
contaminated with 1.6 wt.% MoCI,. In contrast to the other figures. the exothermic
signal points upwards (from ref. [128]).
6. Biocalorimetry
100 K is generally regarded as
If the heat capacity C,
is not known, the approximation C, x p z 1.7 J cm-3 K - (P is
the density in gcm-3) can be used for organic materials.['27] C,
can also be determined by DSC or approximately calculated by
incremental methods.['0]
Nonexplosive materials can easily be examined by DSC and
TG for the risk of an exothermic decomposition. A quick general analysis scanned at 10 K m i n - ' to approximately 500 "C is
performed. If the DSC analysis reveals no exothermic peak and
the TG analysis no great loss in mass, the substance may be
regarded as
If an exothermic peak appears, the hazard potential must be
further assessed by performing additional investigations (measurements using a low heating rate, adiabatic thermal storage
experiments, estimation of the adiabatic temperature rise and
1281 Conclusions on the longadiabatic induction
term storage behavior of unstable materials can be drawn by
performing adiabatic temperature experiments, in Dewar flasks
for example.
In this context it is interesting that the heat transfer behavior
of a 2 m3 agitated reactor is approximately the same as that of
a 500 cm3 Dewar
A powder exhibiting similar heat
transfer behavior as reactor occupies an even smaller volume of
0.1 m3.[1271This makes it clear how quickly dangers resulting
from difficulties with heat dissipation can arise when scaling up
chemical syntheses from the laboratory to industrial production
(or even only on storage of chemicals).
The decomposition temperature may be considerably lowered
by additives and impurities. Figure 18, which portrays DTA
curves of 3-nitrobenzoic acid in a pure form and with different
additives. makes this point clear. A shift of the decomposition
peak to lower temperatures results, especially following the
addition of heavy metals.
Biocalorimetry involves the use of calorimetric methods for
the study of biological processes. The application of calorimetry
to living organisms is already very old. As far back as 200 years
ago Lavoisier and Laplace examined the heat production of
guinea-pigs with their newly developed ice calorimeter.[31As
heat exchange with the environment belongs to the fundamental
characteristics of living systems, biocalorimetry with its methods of measurement, which meanwhile have become considerably more sensitive, today offers applications for the examination of a wide variety of subjects ranging from microorganisms,
through plants and insects, to man.[134- 1 3 7 1
An example taken from the examination of microorganisms
demonstrates the potential for the application of this method.
Figure 19 illustrates the growth of a strain of Escherichia coli
bacteria without and with the addition of antibacterial agents.
The addition of amoxycillin and clavulinic acid causes strong
bacterial growth inhibition, which manifests itself in a drop in
heat generation. Control experiments showed that the addition
of amoxycillin or clavulinic acid alone had no effect on bacterial
growth." 3 8 s ' 391 Such measurements can produce important contributions towards judging the effectiveness of pharmaceuticals,['38.
7. Summary and Outlook
We hope we have shown that the reputation of thermal analysis
as merely a qualitative method for measurement is unjustified.
Providing investigations are performed carefully and the data
evaluated critically, thermal analysis can provide quantitative
results on material properties, thermodynamics, and kinetics. As
is the case with all analytical methods, a certain basic knowledge
of the operation of instruments, algorithms, and programs for
Angeii CIiem. I n t . Ed. Engl. 1995,34. 11 71 - 1187
Thermal Analysis
t [hl+
Fig. 19. Heat flow -time diagrams of the growth of Escherichiu coli bacteria (solid
line: heat evolution, broken line: growth curve). a) Undisturbed growth. h) Inhibited growth following the addition of antibacterial agents (amoxycillin, clavulinic
acid) (from to ref. [138, 1391).
the data processing is required. Thermal analysis is a method for
the measurement of thermodynamic and kinetic properties of
materials that is easy to operate. The four most frequently applied methods, thermogravimetry, differential thermal analysis,
differential scanning calorimetry, and dilatometry can be used
in many different ways to characterize synthesized materials.
The range of possible applications in technical practice is extensive. Special advantages are the speed and small samples required.
Besides these established methods, an increasing number of
other methods are being developed. As virtually all physical
methods of measurement can also (at least potentially) be performed with temperature programming, this trend will certainly
continue. Investigations into kinetics in particular should profit
from such new developments. Although most procedures of this
type are (still?) not commercially available, we have purposely
included a series of examples to demonstrate the variety of results obtainable. In addition, the intention was to expound the
limits beyond which results obtainable by current methods are
no longer reliable for a definite characterization.
We would like to thank Henning Arnecke, Sigurd Bauerecker,
Dr. Heino Bothe, Dr. N . Eckardt, Dr. Sabine Eligekausen,
PrqJ Dr. Claus Fuhrer, Dr. Peter Gabel, Dietmar Hamann, Erwin Kuisersherger, Dr. Kerstin Martin, Gerlind Ohlschluger, Dr.
Joachiin Reichelr, Dr. Stgfan M . Sarge, Petra 3.Schneider, Axe(
Stcrr, Dr. Ingeborg Steppuhn, Manfred Steppuhn, Prof. Dr. R.
Tacko, Dr. U s e Ulhrich, and Martin W e t e l f o r rheir contributions towurris this study as well as the Fonds der Chemischen
Industrie, the Deutsche Forschungsgenwinschaft, and the Arbeitsgernrinschqfi Industriellev Forschungsvereinigungen ( A I F ) ,for
their ,finunciul support.
Received: January 11, 1993
Revised: February 5. 1994 [A941 IE]
German version: Anpew. Chem. 1995, 107, 1284-1301
Translated by Ms. Sigrid Rohson. London (UK)
Inr. Ed. Enzl. 1995, 34, 1171 -1187
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DIN 51006 (thermogravimetry). DIN 51007 (differential thermal analysis),
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"American Society for Testing and Materials" (ASTM) 1131. Important
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968-83 (cahbration of DSC), E914-83 and El 131-86 (thermogravimetry),
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