Anal. Chem. 2002, 74, 2749-2762
Thermal Analysis Sergey Vyazovkin
Department of Chemistry, University of Alabama at Birmingham, 901 South 14th Street, Birmingham, Alabama 35294 Review Contents Method Development and Calibrations Thermodynamics Kinetics Inorganics Polymers Energetics and Fuels Pharmaceutical, Biochemical, and Biological Applications Literature Cited
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Since 1988, the field of thermal analysis had been reviewed by Professor David Dollimore, who passed away on August 4, 2000. This tragic event has been memorialized by dedicating the special edition (1) of Thermochimica Acta that collects the papers presented at the 27th NATAS Conference. David was a person of truly encyclopedic knowledge and a great enthusiast of thermal analysis. It is a great honor and responsibility to continue reviewing the present topic in place of him. The present review covers the years 2000 and 2001 and is limited to 200 references. Thermal analysis is concerned with a very wide area of applications described in a huge number of publications. Suffice it to say that according to ISI Web of Science, the most common thermal analysis technique “Differential scanning calorimetry” was mentioned in around 4000 publications in 2000-2001! In this circumstance, an attempt to select 200 papers that comprehensively cover the whole field would be futile. Instead, the review covers the most popular applications of thermal analysis as well as the recent developments of the method. Over the past 2 years, one of the major events in the field of thermal analysis was the 12th International Congress on Thermal Analysis and Calorimetry that was held in Copenhagen, August 14-18, 2000. Over 300 presentations were made at the Congress. The Congress proceedings have been issued as a separate volume of the Journal of Thermal Analysis and Calorimetry (2) that provides a representative collection of papers dealing with the modern problems of the field. The break of the 21st century was marked by a special issue (3) of Thermochimica Acta that summarized the past progress and projected future developments in the field of thermal analysis. Brown (4) published the second edition of Introduction to Thermal Analysis, which makes an excellent text for thermal analysis courses. Wunderlich stresses (5) that thermal analysis courses are extremely important for material sciences education and should be taught more widely; that can, in part, be accomplished by creating and offering Internet courses. Tanaka (6) emphasized the role of thermal analysis in environmental chemistry education in the 21st century. As an important source of emergency information on thermal analysis, we should mention the list server “Thermal” (http:// 10.1021/ac020219r CCC: $22.00 Published on Web 04/19/2002
© 2002 American Chemical Society
www.egr.msu.edu/mailman/listinfo/thermal) ran by Michael Rich at Composite Materials and Structures Center of Michigan State University. The list has a free access and includes dozens of thermal analysis experts who readily answer questions related to thermal analysis. METHOD DEVELOPMENT AND CALIBRATIONS Parkes et al. (7) report the design and operation of a new thermal analysis instrument that uses microwaves to simultaneously heat and detect thermally induced transformations in samples. Physical or chemical alterations in a material cause variations in its dielectric properties that can be revealed by a variety of means including changes in the sample temperature, the differential temperature, or the shape of the power profile during linear heating experiments. The decomposition of basic copper carbonate is used to illustrate the sensitivity of the instrument that shows a large temperature increase on the formation of the strongly coupling oxide. Smith and Shirazi (8) developed a sensitive method for determining the enthalpy of gas-surface interactions. The method combines a quartz microbalance with a microcalorimeter. The calorimeter accommodates both sample and reference holders, which are attached to a quartz crystal microbalance and are in intimate thermal contact with a heat flow sensor. The sample is coated with a thin polymer film capable of adsorbing or desorbing vapors. The technique permits simultaneously measuring the resulting change in the mass per unit area (to (0.25 ng cm-2) and the heat flows (to (50 nW). A microcalorimetric method is proposed by Gomez et al. (9) to determine the contact angle of a nonwetting liquid within a mesoporous solid. It is based on the simultaneous measurement of the heat and work of wetting, as the pressure is raised. The method simply requires a previous determination of the surface area to be wetted. Its utility is illustrated for water in porous hydrophobic silicas. Allen et al. (10) introduced a scanning calorimeter for use with a single solid or liquid sample having a volume of a few nanoliters. Its use is demonstrated with the melting of 52 nL of indium, using heating rates from 100 to 1000 K s-1. The heat of fusion has been determined to be within 5% of the bulk value, and the sensitivity of the measurement is (7 µW. The heat of vaporization has also been measured for individual water droplets from 2 to 100 nL in volume. The measured value, 2250 ( 500 J g-1, is within 23% of the bulk value for water. The use of high heating or cooling rates (faster than 100 °C min-1) has been made in the method of highperformance DSC (11). In addition to higher sensitivity and the possibility of using submicrogram samples, the use of high heating rates also allows one to practically eliminate slow phenomena such as recrystallization of PE on melting or cold crystallization of PET that simplifies interpretation of complex DSC signals. Analytical Chemistry, Vol. 74, No. 12, June 15, 2002 2749
Benoist and Le Parlouer (12) describe a new integrated circuit detector that consists of a thermopile integrated in a silicon epitaxy layer of a silicon wafer. This miniature detector is reported to have a very short response time and about 10 times greater sensitivity as compared to regular DSC instruments. The detector has been employed in a portable single-pan DSC instrument. Dong and Hunt (13) describe another new signle-pan DSC that is demonstrated to have significant advantages over conventional heat flux DSC. Tozaki et al. (14) developed a new method for simultaneously measuring heat flow and thermal expansion at a temperature resolution of millikelvins. The method has been applied to study the thermal behavior of a single crystal of BaTiO3 that is known to undergo a first-order tetragonal-to-cubic transition at around 404 K. This single transition has been detected on heating. On cooling, both heat flow and thermal expansion have shown six thermal events in the narrow region between 402 and 403 K. The multiple events are explained by stepwise nucleation of the tetragonal phase. Nakamura et al. (15) describe a newly designed sample cell attached to TMA that enables swelling of polymer hydrogels to be measured as a function of time. The application of the cell is illustrated by studies of swelling of calcium alginate dry film. Riesen et al. (16) discuss a method of obtaining DSC information from the measurements performed on a simultaneous TGADTA instrument. A calibration enables the measured DTA signal to be converted into a heat flow curve (DSC signal). Unlike regular DSC, the method allows one to detect mass changes during a process and, therefore, to account for heat losses associated with sublimation and vaporization. The method has been validated by correctly determining the melting enthalpy of anthracene and the heat of phenol formaldehyde polymerization. The use of modulated temperature programs has become an integral part of various thermal analysis methods, including DSC, TGA, and TMA. Among these, temperature-modulated DSC (TM-DSC) attracts most attention. As compared to regular DSC, the technique has a higher sensitivity and is capable of separating some complex thermal phenomena by separating the DSC signal into reversing and nonreversing components, which respectively vary in-phase and out-of-phase with the temperature modulations. The separation of the DSC signal is accomplished by using the Fourier transform. However, Hu and Wunderlich (17) suggest that similar information can also be obtained without the Fourier transform from the imbalance in heat capacity, which is measured by using sawtooth temperature modulations in regular DSC. Although TM-DSC opens up exciting opportunities, it also raises numerous concerns associated with the basic assumption of the method that the response of the whole system (i.e., calorimeter and sample) to the temperature modulations is linear. However, the response of kinetic phenomena such as glass transition is clearly nonlinear. The violation of the linearity condition results in measurement errors. Simon and McKenna (18) presented quantitative analysis of such errors for the TMDSC measurements carried out in the glass transition region. Simon (19) recently reviewed the theory of TM-DSC and its applications to measuring heat capacity, the glass transitions, and processes of crystallization and melting. Ozawa (20) recommends that sound application of TM-DSC should at present be limited to heat capacity measurements. Note that the reliability of these 2750
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measurements is strongly dependent on the heat-transfer conditions. The effect is explored in terms of mathematical models (2123). Merzlyakov and Schick (24) discuss the issue of optimizing experimental parameters for TM-DSC measurements and suggest numerical criteria for testing whether the DSC response is linear and stationary. Calibration of TM-DSC presents numerous challenges including that of finding suitable standards. A proper calibration standard should demonstrate a well-defined transition that does not disturb the temperature profile within the sample during modulation (i.e., heat-cool cycle). As mentioned earlier, the response of the whole system must be linear during modulation (25). This requirement can be met when low-energy liquid crystal transitions are used. It has been in particular demonstrated that the nematic-to-smectic transition in a cyanobiphenyl liquid crystal (80CB) can be used for temperature calibration of TM-DSC. Harkvoort et al. (26) tested a number of compounds and reported that adamantane and Zn have fast reversible transitions and can be applied both for temperature and for heat calibrations. Because of its well-defined liquid crystal-to-isotropic transition at 409 K, 4,4′-azoxyanisole can be used for temperature calibrations. However, this substance has a small heat effect that makes it not practically suitable for heat calibrations. Other compounds such as NaNO3, In, Hg, and Pb demonstrate noticeable supercooling and, therefore, are suitable only for heat calibration. The problems of calibration in the cooling mode have been examined by the working group “Calibation” of the German Society for Thermal Analysis (GEFTA) (27). Because of the general occurrence of supercooling for first-order phase transitions, liquid crystals and substances with higher-order phase transitions have been recommended for temperature calibration. For heat calibration, they recommend using substances that show a small degree of supercooling, and substances that have a known temperature dependence of the transformation enthalpy. Wunderlich et al. (28) studied the effects of the heatconducting paths from the temperature sensor to the sample and from the sample-temperature to the reference-temperature sensors on the determination of heat capacity by TM-DSC. The effects were found significant and the relevant calibration procedures were proposed. Using simulations, they (28) demonstrate that the phase angle difference between the sample temperature and the heat flow should be taken into account when determining heat capacity. The results were experimentally verified for aluminum samples of different masses in quasi-isothermal experiments at a wide range of modulation frequencies. A great number of other issues associated with calibration of various calorimeters are discussed in a special issue of Thermochimica Acta (29). There are no kinetic standards based on reactions of solid substances. Sbirrazzuoli et al. (30) proposed an electronic solution to the problem of kinetic standard for calibration of DSC. They used a thermal resistor to generate the heat flow in accord with a desired kinetic equation and a set of Arrhenius parameters. Analysis of the obtained data suggests that for kinetic purposes heat flow calibration should be preferred over the simple peak area calibration. The use of a modulated temperature program in TMA (TMTMA) allows for separation of the temperature-dependent (reversible) expansion from the time-dependent (irreversible) stress relaxation (31). By using TM-TMA, Riesen and Schawe (32) were
able to simultaneously determine the coefficients of thermal expansion and shrinkage a drawn PET fiber. Kociba (33) presented a new idea of calibrating temperature in TMA in the temperature-modulated mode by using magnetic substances with known Curie temperatures. THERMODYNAMICS Thermal analysis provides efficient tools for measuring fundamental thermodynamic properties such as enthalpies, heat capacities, and temperatures of phase transitions. For instance, a theory based on the Laplace equation of the surface and the Gibbs-Duhem equation predicts a size-dependent melting temperature depression. The phenomenon was studied by Allen et al. (34), who applied the technique of thin-film differential scanning nanocalorimetery to investigate the melting behavior of indium films, consisting of ensembles of nanostructures. It was found that the melting point of the investigated indium nanostructures decreases as much as 110 K for particles with a radius of 2 nm. Another size effect is reported by Toda et al. (35) for crystallization and melting of ice crystallites confined in porous silica gel. According to TM-DSC measurements, the processes occur at temperatures 10-20 °C lower as compared to bulk crystals and are explained by the effect of surface tension. While widely used for detecting glass transitions, the method of TMA finds very few applications in studies of first-order solidsolid transitions (36, 37). However the method appears to be quite advantageous in detecting phase transitions in decomposing solids. For instance, heating of KH2PO4 results in the intensive dehydration that starts around 180 °C and causes anomalies in various physical properties (e.g., heat absorption in DSC) that are frequently mistaken for the tetragonal-to-monoclinic transition (37). In this region, TMA demonstrates only the trivial thermal contraction associated with decomposition. The transition occurs in the temperature region 200-220 °C and clearly shows up as an anomalous thermal expansion (37). Price (38) discusses the use of TGA for determining the vapor pressures and enthalpies of vaporization and sublimation. The approach is based on the Langmuir equation for the rate of free evaporation
dm ) PR dt
-
M x2πRT
(1)
where m is the mass, t is the time, P is the vapor pressure, R is the vaporization coefficient, M is the molecular weight of the vapor substance, R is the gas constant, and T is the absolute temperature. Equation 1 is rearranged as
P ) kν -dm/dt(T/M)1/2.
ln ν ) B - (∆H/RT) - ln k
KINETICS The methods of thermal analysis make it possible to follow the kinetics of various thermally stimulated processes such as decomposition, oxidation, reduction, crystallization, and polymerization. The kinetics of these processes are most commonly described by the following rate equation
dR/dt ) k(T)f (R) ) A exp(-E/RT)f (R)
(4)
(2)
where k ) and ν ) A plot of P versus ν follows the same trend for different compounds regardless of their chemical structure that allows compounds with known vapor pressure to be used for estimating the calibration constant, k, and thus the vapor pressure of unknown substances to be determined. Combining eq 2 with the Clausius-Clapeyron equation gives (2πR)1/2/R
From the slope of a plot ln ν versus T-1 one determines the enthalpies of vaporization and sublimation, ∆H that can be corrected to a standard state by using empirical equations (38). The method was extensively used by Dollimore and co-workers to determine vapor pressures of various pharmaceutical compounds (39-41). It should be stressed that the method assumes the constancy of R, which is secured when the free surface area does not change during the run. If this condition cannot be met, Price (38) suggests determining the enthalpy by using temperature jumps during which no significant change in the surface may occur. TGA and DSC can be conveniently used to study thermodynamics of the surface processes of adsorption and desorption. High-resolution TGA was employed by Li et al. (42) to measure desorption of water, 1-butanol, and n-heptane from activated carbons treated with oxidizing agents such as hydrogen peroxide, perchloric acid, and nitric acid. Comparison of the themodesorption profiles for molecules of different polarities allows for studying the surface properties of oxidized carbons. Eigenmann et al. (43) demonstrate the potential of the method of pulse thermal analysis for measuring adsorption. Pulse thermal analysis combines TGA with a pulse device that injects a certain amount of a gas into the carrier gas stream flowing through the TGA system. A series of consecutive pulses at a constant temperature and atmospheric pressure gives rise to an increase in the mass that may be irreversible or reversible, being therefore associated with chemisorption and physisorption, respectively. The method has been validated by measuring adsorption of ammonia on zeolites. Highpressure thermogravimetry was applied by Bentzen et al. (44) to characterize a number of hydride-forming alloys in terms of reversible storage capacity, working pressures, and temperatures. The use of simultaneous TGA-DSC allows one to monitor both the heat of adsorption and the mass of adsorbed substance. With the help of this technique, Wang and Yeh (45) studied the mechanism of adsorption of dioxygen and oxidation phenomena on supported platinum metals (Pd, Pt, Rh) over a wide temperature range. Pires et al. (46) found that microporosity of aluminumpillared clays correlated well the heats of adsorption measured by TGA-DSC, which makes possible the use of this technique for controlling the porosity.
(3)
where R is the extent of reaction, k(T) is the Arrhenius rate constant, A is the preexponential factor, E is the activation energy, and f (R) is the reaction model. Equation 4 rests upon the concept of a single-step reaction that was inherited by solid-state kinetics from the kinetics of much simpler reactions in homogeneous media. This concept as well as the two derivative concepts (the concept of constant activation energy and the concept of reaction model as a representative of the mechanism) is inconsistent with the multistep nature of solid-state reactions (47). While contradicAnalytical Chemistry, Vol. 74, No. 12, June 15, 2002
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tory to numerous experimental facts, these concepts are prevalently used in kinetic analyses. This situation is not very surprising as the research area of solid-state decompositions presently lacks an adequate theoretical framework (48). Some compromise between the kinetic complexity of solid-state reactions and the simplicity of their kinetic description is accomplished in the idea that the overall rate of a multistep process can be represented by a combination of single-step rate equations, each of which represents a single step of the overall process. However, it is not practically feasible to identify all single steps and describe their rates by the respective rate equations. In practice, the overall rate of a process is approximated by a combination of a few (usually two to three) rate equations each of which holds for the whole region of temperatures and extents of reaction. This approach is implemented in several software packages (49). Another opportunity is to represent the overall rate by a set of rate equations each of which holds for a given extent of reaction and a temperature region that corresponds to this extent of reaction. This approach is materialized in isoconversional methods and in the closely related method of model-free kinetics (47) that reveal the reaction complexity as a dependence of the effective activation energy on the extent of reaction. This effect has inspired introduction of new kinetic concepts of distributed reactivity (50) and variable activation energy (47). Mention should be made of the parallelism of these concepts with the concept of the timedependent energy barrier that is used in dispersive kinetics (51). In addition to the conceptual issues, a great deal of kinetic concern is associated with computational problems. Most of kinetic data are collected under nonisothermal (usually linear heating rate) conditions, for which eq 4 takes the form
dR/dT ) A/β exp(-E/RT)f (R)
(5)
where β is the heating rate. Because a single nonisothermal run provides information about both the temperature and conversion dependencies (e.g., k(T) and f (R), respectively) of the reaction rate, a large number of methods have been developed for evaluating E, A, and f (R) from a single run. Such evaluation obviously requires separating the temperature and conversion dependencies that, however, cannot be accomplished experimentally in a single run performed at a constant heating rate. The single heating rate methods strive to accomplish the separation computationally, by simultaneously adjusting E, A, and f (R) in order to obtain the best fit of the data. However, the mutual compensation of k(T) and f (R) gives rise to the fact that almost any f (R) can satisfactorily fit data at the cost of drastic variations in the Arrhenius parameters (47). For this reason, the single heating rate methods tend to produce highly uncertain values of Arrhenius parameters that cannot be used to characterize the reaction kinetics (52). The computational problems were largely sorted out in the frameworks of the recent ICTAC Kinetics Project (49), the participants of which were provided with isothermal and nonisothermal data on a hypothetical simulated process as well as on the thermal decompositions of ammonium perchlorate and calcium carbonate. The participants applied a variety of computational methods. While comparing the results, special attention was paid to the ability of the methods to handle multistep reaction 2752
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mechanisms. The model-free isoconversional methods and modelfitting methods that use multiple heating rate data were particularly successful in correctly describing the multistep kinetics in the simulated data. These methods also produced reasonably consistent kinetic results for isothermal and nonisothermal data and were identified as the most prospective techniques currently available for kinetic analyses (49). By analyzing the results of the project, several participants (53-55) concluded that the single heating rate methods should be completely avoided. In any case, the necessary condition for estimating reliable kinetic parameters is the use of multiple heating programs, be they isothermal, nonisothermal, or a mixture of the two (49, 53-55). Unlike a single heating rate run, the use of multiple heating programs allows for separating the temperature and conversion dependencies of the reaction rate. For instance, the isoconversional methods eliminate the conversion dependence (i.e., f (R)) by analyzing the rate data at a constant extent of conversion
d ln(dR/dt)R dT
-1
)-
ER R
(6)
where the subscript R denotes values obtained at a given extent of conversion. Evaluation of ER requires that the rate at a constant extent of conversion should be determined at different temperatures, which is accomplished by using multiple heating programs. This requirement can be satisfied approximately within a single experiment by using a series of heating or cooling steps during which the extent of conversion does not change significantly. Then the change in the reaction rate can be considered roughly as occurring at a constant extent of conversion, and eq 6 can be used for estimating the activation energy. The idea was first implemented by Flynn (56) in his temperature jump method. A modern commercial version of the method, known as modulated thermogravimetric analysis (MTG), imposes a sinusoidal temperature modulation on a linear hating rate program. In reality, the extent of conversion changes even during a quick temperature step that unavoidably introduces some systematic error in the values of the activation energy determined by using MTG. The activation energies obtained by MTG were compared with the values that were obtained by the isoconversional method from a series of linear heating rate runs (57, 58). For the thermal degradation of several EPDM elastomers, Gamlin et al. (58) reported that activation energies calculated from MTG are much lower than those calculated from several runs by using an isoconversional method. Schubnell’s data (57) show that for the thermal decomposition of PTFE the values obtained by MTG are somewhat greater than the values obtained from the isoconversional analysis of multiple runs. However, for the thermal decomposition of MnO2, the MTG values were significantly larger than the values determined by the regular isoconversional method and also demonstrated very strong fluctuations (57). Apart from the possible systematic deviations, the reliability of an activation energy obtained from a single experiment is always questionable because the repeatability of such an experiment remains unknown. Overall, extracting reliable values of the activation energy from a single run is a tempting but rather impractical idea, regardless of the temperature program used.
Budrugeac and Segal (59) used sets of simulated and experimental data to compare several isoconversional methods. They demonstrate that the integral methods may yield a significant systematic error for a process whose activation energy strongly varies with the extent of reaction. It should be stressed that this error does not invalidate the integral isoconversional methods in general (60). It is unavoidable only in the simpler methods that use integrated kinetic equations such as eq 7 used in the well-
ln (β) ) Const - ER/RTR
(7)
known methods of Ozawa and Flynn and Wall. In this case, the error results from the fact that eq 7 was derived by assuming the constancy of the activation energy. The situation is, however, entirely different for the methods that use integration as a part of the procedure for estimating the activation energy. In particular, Vyazovkin (60) demonstrated that the systematic error can be practically eliminated in the integral isoconversional method that evaluates the activation energy by minimizing the following function n
Φ(ER) )
n
J[ER,Ti(tR)]
∑∑ J[E ,T (t )] i)1 j*i
R
j
(8)
R
where T(t) is the temperature program and J is integral of the Arrhenius exponent with respect to time. The error in ER virtually disappears when the integral is carried out over small time segments, tR-∆R - tR as follows
J[ER,Ti(tR)] ≡
∫
tR
tR-∆R
exp[-ER/RTi(t)] dt
(9)
The application of the Arrhenius equation for describing the temperature dependence of the rate of solid-state decompositions has been criticized by L’vov (61), who explores an approach that is based on the theoretical treatments developed by Hertz and Langmuir for vaporization of metals. The basic assumption of this approach is that the primary step of decomposition of a solid is its congruent dissociative vaporization. Although L’vov fairly mentions that this assumption “might appear at first sight ... very unusual”, he uses his approach to explain numerous experimental values of the activation energies of reversible processes. Note that comparison of theoretical values of the activation energy with the experimental ones may itself present a considerable challenge as the reported values tend to be widely differing (cf. an older paper by Maciejewski (62), who analyzes 168 reported values of E for decomposition of CaCO3). Such a discrepancy is usually explained by the differences in experimental conditions and sample characteristics. However, the method of computation of the activation energy may also contribute to this discrepancy, which in the case of single heating rate methods may be large enough to explain dramatic differences in the reported values. Attempts are also made to develop new reaction models describing the conversion dependence of the reaction rate. The fractal nature of heterogeneous processes involving solids is well known. This stimulates ongoing efforts in applying the mathemati-
cal apparatus of fractal geometry to describing heterogeneous reactions (63-65). The experimental values of ln A and E are frequently found to demonstrate a linear correlation, also known as a kinetic compensation effect or an isokinetic relationship. A search for a physical meaning of the effect remains a matter of inexhaustible interest (66). A comprehensive review on isokinetic relationships has been published by Liu and Guo (67). A compensation effect is usually detected in the form
ln Aξ ) aEξ + b
(10)
where ξ represents a factor that causes a variation in the values of kinetic parameters, although a nonlinear form has also been proposed (52). If ξ is a physical factor that can in principle affect the activation energy barrier, this correlation may represent the so-called “true compensation effect”. However, if ξ is a formal factor associated with a model or a method of computation, the correlation represents a “false” or “artificial compensation effect”. False compensation effects indicate numerical instability of estimating Arrhenius parameters. They are frequently found when fitting single heating rate data to various reaction models. For instance, such effects have recently been reported for thermal decomposition of imido-phenilic-triazine resins and their phenolic precursors (68) and dehydration of lanthanide 2,6-dihydroxybenzoates (69). On the other hand, compensation effects were reported for a reaction of K2CO3 with various oxides (70), for dehydration of formates, acetates, and propionates of various metals (71), and for the thermal depolymerization of polysaccharides at different values of pH (72). Because in the latter cases (70-72) the observed variation in ln Aξ and Eξ may have been caused by physical reasons, the compensation effects have been interpreted in terms of reaction mechanisms. Note that reliable detection of a true compensation effect may be challenging because experimentally estimated Arrhenius parameters tend to be strongly correlated due to mathematical reasons (i.e., false compensation effect). INORGANICS Thermal treatment of inorganic substances has a great synthetic potential as it may turn simple compounds into advanced materials such as ceramics, catalysts, and glasses. The mechanistic and kinetics studies of solid-state reactions are needed in order to take advantage of this potential (73). Unfortunately, the progress in this field has been rather slow (48). The mechanisms are routinely identified in terms of simplistic reaction models that were developed fifty and more years ago, and the concept of a single-step reaction appears to dominate mechanistic and kinetic analyses (47). The popularity of this approach can be explained by the fact that its use affords creating mathematically simple and logically attractive methods such as the well-known method of reduced time plots when the reaction mechanism is identified by visually comparing experimental data against the reaction models in the coordinates of R against t/tR0 (tR0 is the time to reach a given extent of conversion, usually 0.5 or 0.9). This method can be used for analysis of isothermal data. The method was further developed by Gotor et al. (74), who expanded its applicability to virtually any heating program. The method can be used to analyze solid-state reactions whose overall kinetics can be approximated Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
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by a single-step rate equation, or, in other words, whose Arrhenius parameters and reaction model remain unchanged in a certain region of temperatures and conversions. Processes of this type are rather rare and may demonstrate the single-step behavior only under some specific conditions. For instance, these criteria are met for the thermal decomposition of ZnCO3 (smithsonite) under high vacuum and at temperatures above 690 K (74). However, this process demonstrates a complex kinetic behavior at lower temperatures as seen from the application of an isoconversional method that yields a variable activation energy (75). Note that in general the procedures of identifying reaction models (mechanisms) by selecting the best-fit models share one common flaw that the models are selected from an unavoidably incomplete list, which does not necessarily include the correct model. The complex kinetic behavior is observed (47) for many seemingly simple processes such as the thermal decomposition of CaCO3 and dehydration of CaC2O4‚H2O that produce a single gaseous product, and, therefore, often considered as a model or standard single-step processes. It should be remembered that these are reversible processes, and their kinetics are determined not only by the temperature but also by the equilibrium and actual pressure of the gaseous product (76). Maciejewski et al. (77) convincingly demonstrated the complexity of an ostensibly simple decomposition of CoC2O4‚2H2O. By applying a combination of experimental techniques including TGA, DTA, DSC, XRD, TGAMS, and pulse thermal analysis, the process was demonstrated to involve numerous reactions that occur in both solid and gas phases. Similar results were reported by Vanhoyland et al. (78), who applied high-resolution TGA, TGA-FT-IR, and high-temperature DRIFT and XRD to follow decomposition of La2(C2O4)3‚ 10H2O. All these data reflect a typical level of complexity encountered in solid-state decompositions and can be used to illustrate the point that fitting, say, mass-loss data to a single-step reaction model and interpreting it in mechanistic terms may have little value for learning reaction mechanisms. Thermal decomposition of inorganic and metallorganic compounds may provide simpler synthetic routes for many materials. For instance, Diez et al. (79) obtained the metastable β-Bi2O3 by decomposing hydrated bismuth oxalate in a CRTA apparatus under air at ∼270 °C. Aono et al. (80) employ TGA-DTA to follow the thermal decomposition of a heteronuclear La-Mn complex that at relatively low temperatures (600-700 °C) yields singlephase hexagonal LaMnO3 nanoparticles, which could not be obtained by conventional sintering even at 1200 °C. The application of thermal analysis in combination with XRD and FT-IR shows (81) that the thermal decomposition of a mixture of barium carbonate and tin tetrahydroxide results in the formation barium stannate that has a cubic perovskite structure and can be used as a sensor for the detection of liquefied petroleum gas. Tolochko et al. (82) compare citrate and ceramic routes for preparation of La2-xSrxNiO4 conducting oxide. The use of citrate mixtures leads to fine powders and dense ceramics; it also reduces the temperature by 150-200 °C as measured by TGA-DTA. The thermal decomposition of polycarbosilane is a route to Si-C ceramic materials. Simultaneous TG-DTA under argon flow shows a weight gain and an exotherm at approximately 240 °C that results from a reaction with oxygen present in the polymer and suggests its high sensitivity to oxidation (83). The conversion 2754
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of N-methylpolyborosilazane to Si-B-N-C ceramics occurs on heating in three consecutive steps that are conveniently observed and identified by a combination of thermal analysis and spectroscopy as polycondensation (200-350 °C), fragmentation (580-620 °C), and elimination of residual hydrogen (1000-1300 °C) (84). Weinmann et al. (85) used thermally induced hydrosilylation of a mixture of oligovinylsilazane with tris(hydridosilylethyl)boranes to obtain Si-B-C-N ceramics, whose yield and thermal stability were evaluated by high-temperature TGA. Emanation thermal analysis (86) proves to be an effective tool for in situ characterization of microstructure changes that occur during the formation of B-C-N ceramics produced by heating various precursors up to 1100 °C. Thermal analysis is conveniently used for characterizing catalytic properties of inorganic materials. Lashdaf et al. (87) used thermal analysis to test the suitability of volatile β-diketonato complexes of Ru, Pd, and Pt for chemical vapor deposition and atomic layer epitaxy methods of preparation of heterogeneous catalysts. Jan et al. (88) synthesized new RuCl2(p-cymene)(ER2R′) complexes and tested them as catalysts of the ring-opening metathesis polymerization of cyclooctene. They found that for the phosphane (i.e., E)P) complexes the catalytic activity correlates well with the arene lability. The latter is estimated as the temperature at which the p-cymene ligand is liberated as determined by TGA. Maciejewski et al. (89) applied pulse thermal analysis to study the effect of calcination on the activity of TiO2and ZrO2-supported gold catalysts for CO oxidation. Pulse injection of CO into an oxygen stream in TGA shows that the maximum catalytic activity is obtained for the TiO2-supported catalysts calcined at 500 °C and for ZrO2-supported catalysts at 560 °C. Carabineiro et al. (90) use TGA to investigate the kinetics of the reaction of NO, N2O, and CO2 at 450-900 °C with activated carbon without catalyst and impregnated with a precursor salt of vanadium (ammonium monovanadate). The addition of vanadium was found to increase carbon reactivity and adsorption at lower temperatures. Heating the silica samples (15-30 mg) in TGA at a rate of 5 °C min-1 from room temperature to 1250 °C shows two mass-loss steps respectively associated with dehydration (100-130 °C) and dehydroxylation (91). Ek et al. (91) demonstrate that the second mass-loss step can be used to estimate the OH group content, which was found to be in a good agreement with NMR data. Fernandes et al. (92) used TGA to study the kinetics of regeneration of the alumina catalyst deactivated by coke that was formed in the transformation of 1,3-butadiene in a fixed-bed continuousflow reactor. A special issue of Thermochimica Acta was dedicated to the applications of calorimetry in catalysis (93). Sestak (94) discusses history, present state, and prospects of inorganic and polymeric glasses. The kinetics of crystallization of inorganic glasses is widely studied by thermal analysis methods. Malek (95) critically evaluates the limitations of the JohnsonMehl-Avrami nucleation growth model and points out that the actual mechanism is difficult to explore within this model unless some complementary studies are made. Suga (96) analyzes thermodynamic and molecular aspects of transition phenomena in solids, putting a special emphasis on the unique properties of the amorphous (glassy) state. Atake et al. (97) performed heat capacity measurements on the glassy and crystalline GeSe2 and found that the heat capacity of the glassy state is smaller than
that of the crystalline state below ∼60 K, above which the values transpose. The crossing phenomenon is explained by differences in the density-of-states of the lattice vibrations that originate from the different long-range ordering in the layered structures of GeSe2. Heide et al. (98) applied TG-MS to analyze gaseous products that are released from various industrial, laboratory, and natural glasses heated under high vacuum in the temperature region 800-1200 °C. The gaseous products contain several hydrocarbons that appear to form as a result of a reaction between carbon and hydroxide ion. The method has also been used in analysis of antic glasses in order to determine the manufacturing conditions (99). Stoch and co-workers (100) investigate correlations between thermal and biochemical activity of the phosphosilicate glasses used for medical purposes. POLYMERS Polymeric materials are one of the largest application areas of thermal analysis methods. Thermal analysis is used to study the physical processes of melting, crystallization, and glass transition as well as chemical processes of polymerization and degradation. Many of these applications are described in the recent book Characterisation of Polymers by Thermal Analysis by Groenewoud (101). Processes that require large-amplitude cooperative motion of large molecules (e.g., macromolecules) are unavoidably associated with long relaxation times. As a result, nonequilibrium states can be formed and studied in polymers by quickly changing the temperature. For instance, Wundrelich (5) mentions 15 equilibrium and nonequilibrium phases that can be found in a onecomponent polymer system. Because of the slow rates of approaching equilibrium, thermal response of such systems depends on the time scale of an experiment that is determined by the heating rate, the period of temperature modulation, or both. For instance, Mathot (11) demonstrates that heating PET in DSC at 10 °C min-1 shows an exothermic peak followed by an endothermic one, which are respectively associated with cold crystallization and melting. However, the use of the heating rate 100 °C min-1 results in suppressing cold crystallization, which does not have sufficient time to occur in the short-time-scale run. Another example is melting of PE crystals. The process is associated with slow crystal perfection that on slow heating elevates the melting of PE by as much as 10 K (5). The use of fast heating rates makes it possible to outrun the process of crystal perfection and determine the correct value of the melting point (5, 102). In TM-DSC, the period of modulations determines the time scale of experiment that allows one to separate and analyze processes having different relaxation times. Among many interesting phenomena, TM-DSC has helped in the observation of the unusual phenomenon of reversible polymer melting that cannot be explained in terms of classical theories of melting and crystallization of polymers (103, 104). DSC is widely used to study polymer crystallization kinetics under isothermal and nonisothermal conditions. The isothermal data are customarily analyzed in terms of the Avrami equation (105, 106), which is also applied to nonisothermal data in the form of Ozawa’s method (105, 107). The obtained values of the Avrami exponent are routinely interpreted in mechanistic terms (105-107). Because of the simplistic nature of the Avrami model,
such interpretations should be done with extreme care. The Avrami exponents often have fractional values (108) and show dependence on temperature and cooling rate (107). Noticeable deviations of experimental data from the Avrami equation are commonly reported (109, 110), and two equations may be needed to fit actual crystallization data (111). The problems of the Avrami analysis appear to become more profound for nonisothermal crystallizations (110, 112). Martins and Pinto (113) attempt to resolve the theoretical limitations associated with the OzawaAvrami analysis of nonisothermal crystallizations. Cheng et al. (114) stress that the two-phase crystallization model does not hold for many polymers because of the presence of a metastable “rigid amorphous fraction”. As was shown by Toda et al. (115), TM-DSC can be used to estimate the crystal growth rate, G, of polymer crystals in the melt under quasi-isothermal conditions. The results are obtained in the form of a dependence d(ln G)/dT on T. The method was recently applied to study crystallization kinetics in poly(-caprolactone)-poly(styrene-co-acrylonitrile) blends (116) and in poly(4,4′-phthaloimidobenzoyldodecamethyoxycarbonyl) (117). Toda et al. (35) employed this method for kinetic analysis of crystallization and melting of ice crystallites confined in porous silica gel. Note that after some rearrangements the aforementioned dependence should afford an estimation of the activation energy as a function of crystallization temperature
E ) RT 2[d(ln G)/dT]
(11)
The resulting value would be a model-free estimate of the activation energy, as it does not require assuming any kinetic model such as that of Avrami. Some polymeric and organic systems may exist in the liquid crystalline (LC) state that is characterized by anisotropy of physical properties in the absence of a three-dimensional crystalline lattice. LC systems may form various mesophases, which are intermediate between the isotropic liquid and ordered crystalline state. Transitions between mesophases can be conveniently followed by DSC as well as other techniques (118, 119). Yoshida et al. (118) demonstrate the potential of the combined DSC-XRD technique as applied to a LC phenanthrene polyester. On cooling from the isotropic liquid state, the polymer shows three exothermic transitions that, based on XRD data, have been associated with successive formation of two mesophases and crystallization. A combination of DSC with polarized light microscopy allows for the study LC transitions and building phase diagrams of complex systems that involve both LC and non-LC components (119). The glass transitions can be detected by several thermal analysis techniques. In DSC, the transition is observed as a change in the heat capacity. Heat capacity is a thermodynamic property directly associated with the intensity of molecular motions. Heating glassy polymers above the glass transition temperature, Tg, initiates long-range motion of polymer main-chain segments that results in increasing the heat capacity as measured by DSC. TM-DSC measures the so-called complex heat capacity, which, unlike its equilibrium value, is time and frequency dependent. This and other closely related topics were addressed in the special issue of Thermochimica Acta (120). The frequency dependence of the complex heat capacity in the glass transition region is treated Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
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theoretically by Hutchinson and Montserrat (121), who propose a model based on the Kohlrausch-Williams-Watts equation. The model helps to optimize the experimental conditions of measurements and understand a correspondence between the Tg values measured in conventional and temperature modulated DSC. Park and McKenna (122) explored the glass transition behavior of polystyrene solutions confined to nanometer-scale pores. DSC shows two glass transitions, one of which is at a lower temperature than the bulk-state Tg and the other is at a higher temperature. The lower value is associated with the confined bulk state, whereas the higher value is assigned to an interacting layer at the pore surface. The glass transition may occur during polymerization if the glass transition temperature of growing polymer rises above the actual temperature of the reaction system. This process is called vitrification. Because of the dramatic decrease in the molecular mobility, the reaction kinetics becomes controlled by slow diffusion of the reaction species in the immobile glassy medium. Vitrification is readily detected when resins are cured in TM-DSC (123-128). Montserrat (123) comprehensively studied the effect of various parameters on the values of Tg, heat capacity, and phase angle determined by TM-DSC for isothermal epoxy cures. Van Assche et al. (124) investigated the frequency dependence of the vitrification phenomenon by using light heating TM-DSC that affords measurements in the frequency range from 0.01 to 1 Hz. TM-DSC and rheology data were compared (125) for cross-linking copolymerization of an unsaturated polyester resin with styrene. Schawe (126) reported that the phase shift signal measured by TM-DSC is very sensitive to changes in the reaction kinetics and can be used for evaluating the diffusion component of the curing rate. Flammersheim and Opfermann (127) propose a diffusioncontrol model of epoxy cure that is based on the WLF equation. For curing of a dicyanate ester resin, Leroy et al. (128) use an isoconversional method to determine a dependence of the activation energy on the extent of cure and then derive a kinetic model that matches this dependence. Note that estimating of such dependencies has been helpful in identifying complex mechanisms of various curing reactions (129-132). Vitrification is not the only reason for diffusion control in curing reactions. The latter becomes operative if, for any reason, the characteristic time of relaxation of the reaction medium exceeds the characteristic time of a chemical reaction. On the basis of kinetic analysis of DSC and rheology data, Vyazovkin and Sbirrazzuoli (133) demonstrate that viscosity may induce diffusion control in the initial cure stages. The phenomenon is described by a kinetic model that predicts that qualitatively different dependencies of the activation energy on the extent of cure should be obtained respectively from the isothermal and nonisothermal DSC data when an isoconversional method is used. The usefulness of polymeric materials is largely determined by their thermal, oxidative, and fire resistance. Crucial information in this area is obtained from kinetic and mechanistic studies of thermal degradation that presents a wide application area for thermal analysis methods. By studying the kinetics and mechanisms of thermal degradation of PMMA, Holland and Hay (134) demonstrated the great potential of thermal analysis-FT-IR spectroscopy as a qualitative and quantitative kinetic tool. They conclude that thermal degradation is initiated at chain ends as 2756
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well as by random scission, which is attributed to preoxidation of the polymer on storage at room temperature. Peterson et al. (135) applied the isoconversional method (eq 8) to obtain reliable values of the activation energy for the thermal and thermoxidative degradation of PS, PE, and PP. The obtained data were compared with numerous previously reported values and interpreted in terms of reaction mechanisms. Note that the variable ER values determined by an isoconversional method correspond to nonlinear Arrhenius plots. Nonlinear Arrhenius plots were reported (136) for the kinetics of oxidative degradation of rubbers. Simon and Kolman (137) propose a method that enables Arrhenius parameters of the oxidation induction period to be estimated from the dependence of the oxidation induction time on the heating rate. The application of the method to oxidation of PP, PE, and oils yields the values of Arrhenius parameters that agree well with the values obtained from isothermal data. According to TGA and DTA, polyurethane decomposes in three well-defined steps (138). The simultaneous use of IR data suggests that the rupture of the weakest bond, C-NH, is the primary degradation step, whose activation energy is about 98 kJ mol-1. Vinylidene chloride-acrylate copolymers are excellent packaging materials that provide an efficient barrier to small molecules such as oxygen. However, at process temperatures, 150-170 °C, these polymers undergo thermally induced degradative dehydrochlorination that can be suppressed in the presence of multifunctional amines (139) and high surface area magnesium hydroxide (140). Howell et al. (139, 140) used TGA to study the effect of these additives on thermal stability of the polymers. The thermal degradation of the polyamides (6, 12, 66, and 612) was studied (141) under air and nitrogen by means of thermal analysis coupled with MS. The data allowed for identifying the degradation products and evaluating the kinetic parameters. Levchik and Weil (142) comprehensively review the combustion and fire-retardant performance of aliphatic nylons. Addition polyimides based on bis(3-aminophenyl)methylphosphine oxide or tris(3-aminophenyl)phosphine oxide have excellent flame-resistance properties (143). Varma (143) investigates the effect of weight percent of phosphorus on thermal behavior and flame resistance of these polyimides. The mechanism of the fire-resistant action of inorganic tin additives on halogenated polyester thermosets was examined by thermal analysis in conjunction with pyrolysisGC and other techniques (144). The residue analysis of sequentially degraded samples suggests that the metal and halogen may volatilize simultaneously, and therefore, both condensed and vapor-phase mechanisms appear to be operating with the branching ratio dependent on both the halogen present and the composition of the polyester. Microthermal analysis combines the visualization power of AFM with the characterization capabilities of thermal analysis that is accomplished by replacing the tip of an AFM probe with a Pt wire that can be controllably heated. Reading et al. (145) reviewed the current state of development of microthermal analysis as applied to polymeric materials. The discussion also involves new techniques such as micropyrolysis-mass spectroscopy and photothermal IR microscopy, which combines microthermal analysis with FT-IR spectroscopy. Hassler and zur Muhlen (146) discussed the details and applications of this technique to the studies of interfaces. The technique was applied (147) to study the role of
carbon and glass fiber reinforcement in an aerospace-grade thermosetting resin. The results show the presence of a soft interphase layer in the glass material and stress the importance of fiber-matrix interactions during the formation of the interphase. Oulevey et al. (148) report a new form of microthermal analysis that enables dynamic mechanical properties to be measured at submicrometer scale. This is accomplished by mounting a sample on a vibrating heating stage and observing the resulting amplitude and phase of the motion of an atomic force microscope cantilever. PS, PMMA, and PTFE respectively show primary relexations at 92, 118, and 138 °C. Secondary relaxations are detected at 60 °C in PMMA and at 80 °C in PTFE. ENERGETICS AND FUELS Ammonium perchlorate remains a key energetic material for rocket technologies. The substance is known to undergo a transition from the orthorhombic to cubic phase at ∼240 °C. Rajic and Suceska (149) used isothermal TGA to determine the kinetics of the thermal decomposition of ammonium perchlorate in the two crystalline phases. In both cases, the mass-loss rate was found to obey the best-fit equation
dR/dt ) k(T)Rn(1-R)m
(12)
The activation energies of the process are very close, being 146.3 and 153.3 kJ mol-1 for orthorhombic and cubic phases, respectively. Note that the use of the single-step eq 12 is likely to disguise the kinetic complexity that was detected (49) when more sophisticated computational techniques were applied to the thermal decomposition of cubic ammonium perchlorate studied under isothermal and nonisothermal conditions. Waesche and Wenograd (150) employed TGA and high-pressure DSC to measure decomposition rates of ammonium perchlorate composite propellants at pressures to 500 psi. The results were extrapolated to give heat evolution rates at the surface temperatures of burning propellants. A semiempirical condensed-phase combustion model was used to calculate propellant burning rates from these heat evolution rates and surface temperatures determined by equilibrium vaporization. Calculated and experimental burning rates are found to agree within an order of magnitude. Singh et al. (151) discuss the mechanistic aspects of thermal decomposition of salts of perchloric and nitric acids and stress that the proton transfer plays a major role in the process of decomposition. Lurie and Chang (152) have shown that in the presence of carbon black the decomposition rate of solid ammonium nitrate may increase by more than 7 orders of magnitude. They carried out kinetic studies in the temperature region 70150 °C and found that at lower temperatures the process proceeds by a two-step mechanism with the first step absent at higher temperatures. They also report that the process rate is proportional to the amount of carbon black and that the activation energy of the process is about 120 kJ mol-1 and does not vary during transformation. Simoes et al. (153) examined the thermal decomposition of phase-stabilized ammonium nitrate in its mixtures with 2-oxy-4,6-dinitramine-s-triazine by using DSC and TGA. The process demonstrates a complex kinetic behavior that the authors were able to describe only by an empirical equation of Sestak and Berggren (eq 12).
Ammonium dintramide is considered as a halogen-free replacement of ammonium perchlorate in solid rocket propellants. Tompa (154) studied the kinetics of the thermal decomposition of ammonium dinitramide by using the methods of TGA, DSC, and high-pressure DSC. He found that under higher pressures (550 psi) the activation energy markedly decreases (from ∼170 to 120 kJ mol-1), indicating acceleration of the process in the presence of decomposition products. Confining samples of explosives in sealed glass capillary tubes allows regular DSC be used to monitor the kinetics of thermal decomposition under elevated pressures. (155, 156) The advantages of this approach are demonstrated by Oxley et al. for decomposition of 3,6-substituted s-tetrazines (155) as well as nitramines and difluoramines (156). The methods of TGA and DSC were applied by Long et al. (157) to study the thermal decomposition of liquid hexahydro1,3,5-trinitro-1,3,5-triazine (RDX) in open, pierced, and closed pans. A comparison of the results suggests that in open pans evaporation is a prevalent process with an activation energy of ∼100 kJ mol-1. Confining the system in either a pierced pan or a closed pan promotes liquid-state decomposition of RDX that occurs with an activation energy of ∼200 kJ mol-1, which is consistent with the energy of an N-N bond scission. Tompa and Bryant (158) studied thermal decomposition of an admixture of RDX with ammonium benzoate by using DSC and microcalorimetry. They report that the presence of ammonium benzoate decreases significantly the temperature and the activation energy (from 197 to 105 kJ mol-1) of RDX decomposition. This is an indication of a reaction between the two components which makes them incompatible in the admixture. RDX-based metallized composite propellants were studied by Divekar et al. (159). Kinetic analysis of DTA data shows that the activation energy for the thermal decomposition of some metallized propellants is similar to that of neat RDX, which suggests that the thermal decomposition is the rate-limiting step of the process. Jones et al. (160) examined the thermal properties of a nanosized Al powder (Alex) by using a variety of thermal analysis methods. They determined the specific heat capacities of nano- and micrometer-size Al powders that are found to be similar between 30 and 400 °C. They also determined the kinetic parameters for the oxidation reaction of Alex, which was detected at an onset temperature of 481 °C. The thermal decomposition of a plastic bonded explosive containing octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), binder, and plasticizer was examined (161) by using DSC and TGA in order to obtain safety information for handling and use. The obtained data allowed for estimating the critical temperature for self-heating at various sample radii and the 500-day cookoff temperature. Thermal conductivity, specific heat, and thermal diffusivity were determined at the critical temperatures in order to calculate the approximate time to explosion at these temperatures. Plastic bonded explosives were also studied by Campbell and co-workers (162) in order to determine the glass transition temperatures. Such measurements are of special importance as the glass transition temperature appears to correlate with the impact sensitivity of plastic bonded explosives. A primer explosive, potassium 4,6-dinitrobenzofuroxan (KDNBF), was studied by Jones et al. (163), who applied the techniques of TGA, DSC, and accelerated rate calorimetry. The compound is found to decompose in the solid state via a multistep Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
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exothermic process. The first step is sufficiently rapid that ignition occurs in large samples. Kinetic analysis was applied to both nonisothermal and isothermal data and a range of activation energies were obtained, depending on the experimental conditions. Hydrazinium nitroformate (HNF) is considered as a very promising ingredient for a new storable composite propellant. The techniques of TGA-DTA, DSC, and microcalorimetry were applied (164) to determine the purity, stability, and compatibility of HNF with other materials. Nazin et al. (165) reviewed the influence of molecular structure on the stability of high-energy compounds. They discuss kinetic and mechanistic data on decomposition of various energy-rich groups in monofunctional compounds as well as in compounds with mixed functional groups. Brown (166) describes the use and limitations of thermal analysis and temperature profile analysis to the study of various binary pyrotechnic systems. He discusses trends in burning behavior and the factors that affect the combustion, such as fuelto-oxidant ratio. To accomplish fast heating rates and high temperatures relevant to the processes of combustion, Brill et al. (167, 168) apply the method of T-jump/FT-IR spectroscopy, in which a small sample (100-200 µg) is spread onto the Pt ribbon filament. The filament is heated in a pressurizable spectroscopy cell at an effective heating rate around 800 °C s-1. The filament temperature is calibrated by using melting point standards. Decomposition products are detected spectroscopically as a function of time and temperature. Thermal decomposition data were collected for the hydrated Li+, Na+, K+, Cu2+, and Pb2+ salts of 3-nitro-1,2,4-triazol-5-one (NTO), the Li+, Na+, K+, Rb+, Cs+, Co2+, and Ni2+ salts of picric acid (167), and the hydrohalide (HCl, HBr, HI) salts of 5-amino-1H-tetrazole (168). Fuels are another energy-related area of application of thermal analysis. TGA is widely used to simulate thermal processes occurring in coal on its combustion. Zajdlik et al. (169) explored the applicability of the shell progressive mechanism to combustion of a single coal particle. They used TGA to monitor time dependences of the particle mass and the temperature in the particle and in the gas phase. The obtained experimental results confirmed that the shell progressive mechanism can be applied for the mathematical description of combustion of a single coal particle. The oxidation of natural graphite particles was investigated by simultaneous TGA-DTA (170). This process provides a model reaction for examining the effect of the particle geometry on process parameters. The reported results suggest that the fraction of edge sites has a strong influence on such parameters as ignition temperature, temperature of the maximum of the DTA curve, and the temperature at which 15% carbon weight loss is attained. Fan and Brown (171) applied TGA to 70 fly ash samples obtained from diverse coals and boilers to determine that loss on ignition (LOI) overestimates the amount of unburned carbon in fly ash by at least 20% in 44% of the tested samples. As an alternative to the LOI tests, they propose to measure unburned carbon by using TGA. The thermal deactivation of solid fuels can be investigated by measuring the reactivity of chars prepared in TGA under welldefined conditions. The obtained data permit estimating kinetic parameters in an annealing model. Zolin et al. (172) report that the annealing model predicts reasonably well the changes in reactivity of chars prepared in different reactor environments at 2758
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much higher heating rates and temperatures, and therefore, TGA experiments can be used to capture the reactivity differences of chars observed in combustion facilities. Burnham (173) demonstrated that the Sestak-Berggren equation in its reduced form, eq 12, is an excellent empirical kinetic law for describing decompositions that have an initial acceleratory period. This equation in particular fits both isothermal and constant heating rate pyrolysis data for cellulose and kerogens. Activation energies derived by nonlinear regression to multiple experiments are consistent with those derived by simple isoconversional methods. Conesa et al. (174) review kinetic models and methods for analysis of TGA data from the standpoint of their application to the pyrolysis of such energy sources as almond shells, olive stones, and tire wastes. The discussion also covers choosing proper conditions for a kinetic run, temperature calibrations, position of the thermocouple, sample mass, and particle size. A combination of TGA with evolved gas analysis techniques such as FT-IR, MS, and GC/MS provides important insights into the mechanism of pyrolysis of coals. For instance, combustion and pyrolysis of the bituminous coals are known to produce polycyclic aromatic hydrocarbons that pose potential health hazards. The mechanisms of formation of these compounds were significantly elucidated with the help of GC/MS (175). The combined TG-MS method was helpful in identifying the alkali or alkali earth chlorides as the sources of deposit formation in the heat exchange tube of the fluidized-bed combustor (176). A newly developed version of pVT-controlled scanning calorimetry, scanning transitiometry, was applied by Stachowiak et al. (177) to investigate the thermodynamic behavior of asphaltenic fluids under in-well pressure and temperature conditions. As the technique permits measurements over extended temperature and pressure ranges, it is capable of detecting phase changes in aliphatic systems during various scans of the three variables p, V, and T. Performing successive compression-decompression cycles shows that both flocculation and solubilization in an asphaltenic fluid are governed by slow kinetic phenomena. PHARMACEUTICAL, BIOCHEMICAL, AND BIOLOGICAL APPLICATIONS Pharmaceutical applications of thermal analysis were addressed in a special issue of Thermochimica Acta (178). An overview of the current pharmaceutical applications of calorimetric measurements has been given by Thompson (179). In the solid state, pharmaceutical compounds may exist in various polymorphic, pseudopolymorphic (solvates), and amorphous forms, whose physical properties such as solubility, bioavailability, processability, and stability may differ significantly. The issue of polymorphic behavior of pharmaceuticals was addressed by Giron (180), who emphasizes the role of thermal analysis techniques in understanding transitions of different polymorphs and solvates as well as glass transitions of amorphous state. The discussion covers both thermodynamic and kinetic aspects of polymorphism and is illustrated by numerous examples. The recent advances in the area of prediction and characterization of polymorphs and solvates were reviewed (181). Gu and Grant (182) suggest using the transition and melting temperatures to derive the thermodynamic stability relationships of the polymorphs (enantiotropes or monotropes). They used the reported values of the heats of solution and solubilities (or dissolution rates)
to calculate the transition temperature of polymorphs for auranofin, carbamazepine, chloramphenicol palmitate, cyclopenthiazide, gepirone hydrochloride, lamivudine, MK571, premafloxacin, sulfamerazine, sulfamethoxazole, sulfathiazole, and urapidil. The resulting stability relationships are found to be in good agreement with those reported using other methods, such as DSC. The molecular mobility of amorphous pharmaceutical materials is an important factor that determines their stability. The mobility can be evaluated as relaxation times by using dynamic mechanical analysis. Although relaxation times can be easily described by the empirical Kohlrausch-Williams-Watts equation, Shamblin et al. (183) demonstrated that knowledge of the parameters of the equation is not sufficient for predicting stability of drugs. They stress the importance of knowing the distribution of relaxation times. Craig et al. (184) evaluated the use of TM-DSC as a means of assessing the relaxation behavior of amorphous lactose via measurement of the heat capacity, glass transition, and relaxation endotherm. The use of this technique enabled separation of the glass transition from the relaxation endotherm, thereby facilitating calculation of the relaxation time as a function of temperature. The mechanism and kinetics of thermal decomposition of solid drugs are studied in connection with estimating their thermal stability. Thermal analysis provides valuable tools for these studies. The dehydration of nedocromil magnesium pentahydrate was investigated (185) by TGA and DSC as a function of temperature, particle size, sample weight, water vapor pressure, and dehydration-rehydration cycle. The two-step dehydration kinetics are best described by the Avrami-Erofeyev equations with an activation energy being markedly greater for the second step. The activation energy decreased with increasing sample weight and decreasing particle size. The dehydration rate increased with decreasing water vapor pressure. Thermal analysis information in combination with XRD and solid-state NMR has provided an insight into the dehydration mechanism and the nature of solid-state phase transformation during the dehydration. Rotich et al. (186) studied thermal decomposition of substituted aminobenzoic acids. Most of the substances sublimed well before melting, generally with an increasing rate of mass loss beyond their respective melting points. The processes of sublimation and vaporization were extensively studied by Alexander and co-workers, who used TGA to determine the vapor pressure as well as sublimation and vaporization enthalpies for numerous pharmaceutical compounds including several parabenes (39), derivatives of benzoic acid (40), and allopurinol (41). DSC presents a useful means of studying interaction of excipients as well as of detecting their incompatibilities. Wissing et al. (187) applied high sensitivity DSC to model mixes of aspirin with magnesium stearate and stearic acid. The samples were heated to temperatures between 45 and 70 °C and held for 1 h, during which the heat flow to or from the sample was measured. While no thermal events were detected for the individual components or mixes with stearic acid other than melting of stearic acid, 50% w/w mixes of magnesium stearate showed a marked endothermic response at temperatures above 55 °C. Compacts of magnesium stearate and aspirin were also studied, with considerably more pronounced thermal events taking place compared to the powder mixes. Giordano et al. (188) provide a comprehensive review on the thermal properties of cyclodextrins and their
inclusion compounds. Special attention is paid to thermal analysis studies of the hydrated forms of cyclodextrins and interactions of cyclodextrins with water and drugs. A great number of biochemical and pharmaceutical applications are concerned with microcalorimetry. A review on isothermal microcalorimetry was published by Wadso (189). Hansen (190) reviewed the application of calorimetry to measurement of the kinetics of slow processes, whose rate cannot be readily followed by conventional chemical analyses. He also discusses instrument selection and derivation of rate laws from calorimetric data. As mentioned earlier, for solids there are no standard reactions whose kinetics can be used for validation and calibration of kinetic measurements. The situation appears to be different for liquidphase kinetics. The reaction of triacetin hydrolysis in an imidazole/acetic acid buffer system was analyzed by several microcalorimetric groups (191). Based on the analysis of the interlaboratory data, this second-order reaction, performed at 298 K, occurs with the reaction rate constant, k ) (2.80 ( 0.10) × 10-6 dm3 mol-1 s-1, and the enthalpy change, ∆H ) -91.7 ( 3.0 kJ mol-1. However, notice should be taken of the earlier work by Guan and Kemp (192), who demonstrated that the best fit for the hydrolysis of triacetin is first order rather than the assumed second order. Cuppo et al. (193) applied high-sensitivity differential scanning microcalorimetry to study gelatin transitions in order to determine the dependence of the kinetic and thermodynamic parameters upon changes in composition and in temperature. Fitting data to exponential functions shows that the characteristic time and the fractional exponent of gelation are very sensitive to the concentration of gelatin chains and to the microscopic phase segregation. Isothermal titration microcalorimetry and DSC were applied by Barreleiro et al. (194) to study the interaction of DNA with vesicles of cationic lipids mixed with varying amounts of a zwitterionic lipid in dilute solutions. Analysis of reaction enthalpies as a function of a charge ratio has helped in elucidating the interaction mechanisms. The thermal behavior of triple helices of DNA was examined by using DSC (195), which shows two independent processes: the dissociation of the third strand from the target duplex and the dissociation of tile double helix in two single strands. Grasso et al. (196) conducted a DSC study of the interaction of the human prion peptide with different artificial membranes that helped them to detect a specific affinity of the protein to a certain type of membrane. The heat produced by animal cells in culture can be used as the primary indicator of the kinetics of their metabolism. The validity of the relationship between heat and metabolism is demonstrated by Kemp (197) theoretically through the concept of thermal advancement and in experiments by the use of continuous cultures. This validation permitted the application of heat flux as a probe of the metabolic state of cells in culture. Morgan et al. (198) suggest estimating the efficacy of antimicrobial agents by using flow microcalorimetry instead of applying traditional microbiological techniques, which are invasive and destructive. They used the method to continuously monitor the power output (bioactivity) of Streptococcus mutans in the presence of antimicrobial agents and demonstrated good reproducibility, precision, and accuracy. Another exciting area of biocalorimetry is calorespirometry, which combines measurements of metabolic heat and CO2 Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
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production rates as a function of temperature. This technique shows promise in matching plants to climate to optimize their growth rate (199). Calorimetry is also used to study the behavior of insects. Schmolz and Lamprecht (200) studied the metabolic rates of insects during their different life cycles: larvae, pupae, and adult. Larvae have high metabolic rates after hatching from the egg. Prior to pupation, metabolism is strongly reduced. During metamorphosis, the pupal instars typically exhibit a U-shaped pattern of heat production. Insect adults have low resting metabolic rates, close to the pupal metabolism. Metabolic rates of active insects are up to 50 times higher than resting metabolism. Professor Sergey Vyazovkin received his Ph.D. from the Byelorussian State University in 1989. He then joined the Institute for Physical Chemistry (Minsk) where he worked until 1993. Since 1993 he had held visiting positions at the Technical University of Vienna, the University of Toledo, and the Univerisity of Nice Sophia-Antipolis. Before joining the University of Alabama at Birmingham, he worked in the University of Utah as a research faculty and the deputy director of the Center for Thermal Analysis. His research interests are concerned with the application of thermal analysis methods to study thermally stimulated reactions in polymeric, energetic, and pharmaceutical materials. He has authored over 80 publications, including several invited review papers, and edited a special issue of Thermochimica Acta on kinetics of thermally stimulated reactions. He is a member of the American Chemical Society Analytical Division, the North American Thermal Analysis Society, and the International Confederation for Thermal Analysis and Calorimetry.
LITERATURE CITED (1) Cahoon, J., Riga, A., Eds. Thermochim. Acta 2001, 367, 1-458. (2) Sorensen, O. T., Moller, P. J., Eds. J. Therm. Anal. Calorim. 2001, 64, 1-1339. (3) Hemminger, W., Ed. Thermochim. Acta 2000, 355, 1-276. (4) Brown, M. E. Introduction to Thermal Analysis, 2nd ed.; Kluwer: Dodrecht, 2001. (5) Wunderlich, B. Thermochim. Acta 2000, 355, 43-57. (6) Tanaka, H. J. Indian Chem. Soc. 2000, 77, 531-538. (7) Parkes, G. M. B.; Bond, G.; Barnes, P. A.; Charsley, E. L. Rev. Sci. Instrum. 2000, 71, 168-175. (8) Smith, A. L.; Shirazi, H. M. J. Therm. Anal. Calorim. 2000, 59, 171-186. (9) Gomez, F.; Denoyel, R.; Rouquerol, J. Langmuir 2000, 16, 43744379. (10) Olson, E. A.; Efremov, M. Y.; Kwan, A. T.; Lai, S.; Petrova, V.; Schiettekatte, F.; Warren, J. T.; Zhang, M.; Allen, L. H. Appl. Phys. Lett. 2000, 77, 2671-2673. (11) Mathot, V. B. F. J. Therm. Anal. Calorim. 2001, 64, 15-35. (12) Benoist, L.; Le Parlouer, P. J. Therm. Anal. Calorim. 2000, 59, 351-358. (13) Dong, H. B.; Hunt, J. D. J. Therm. Anal. Calorim. 2001, 64, 341350. (14) Tozaki, K.; Masuda, R.; Matsuda, S.; Tokitomo, C.; Hayashi, H.; Inaba, H,; Yoshimura, Y.; Kimura, T. J. Therm. Anal. Calorim. 2001, 64, 331-339. (15) Nakamura, K., Kinoshita, E., Hatakeyama, T., Hatakeyama, H. Thermochim. Acta 2000, 352-353, 171-176. (16) Riesen, R.; Vogel, K.; Schubnell, M. J. Therm. Anal. Calorim.. 2001, 64, 243-252. (17) Hu, W.; Wunderlich, B. J. Therm. Anal. Calorim. 2001, 66, 677697. (18) Simon, S. L.; McKenna, G. B. Thermochim. Acta 2000, 348, 7789. (19) Simon, S. L. Thermochim. Acta 2001, 374, 55-71. (20) Ozawa, T. Thermochim. Acta 2000, 355, 35-42. (21) Ozawa, T.; Kanari, K. J. Therm. Anal. Calorim. 2000, 59, 257270. (22) Buehler, F.; Seferis, J. C. Thermochim. Acta 2000, 348, 161168. (23) Jiang, Z.; Imrie, C. T.; Hutchinson, J. M. J. Therm. Anal. Calorim. 2001, 64, 85-107. (24) Merzlyakov, M.; Schick, C. J. Therm. Anal. Calorim. 2000, 61, 649-659. (25) Schick, C.; Jonsson, U.; Vassiliev, T.; Minakov, A.; Schawe, J.; Scherrenberg, R.; Lorinczy, D. Thermochim. Acta 2000, 347, 5361. (26) Hakvoort, G.; Hol, C. M.; van Ekeren, P. J. J. Therm. Anal. Calorim. 2001, 64, 367-375. (27) Sarge, S. M.; Hohne, G. W. H.; Cammenga, H. K.; Eysel, W.; Gmelin, E. Thermochim. Acta 2000, 361, 1-20. (28) Moon, I.; Androsch, R.; Wunderlich, B. Thermochim. Acta 2000, 357, 285-291. (29) Della Gatta, G., Beezer, A. E., Richardson, M. J., Schiraldi, A., Eds. Thermochim. Acta 2000, 347, 1-140. 2760
Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
(30) Sbirrazzuoli, N.; Vincent, L.; Vyazovkin, S.Chemom. Intell. Lab. Syst. 2000, 52, 23-32. (31) Price, D. M. J. Therm. Anal. Calorim. 2001, 64, 323-330. (32) Riesen, R.; Schawe, J. E. K. J. Therm. Anal. Calorim. 2000, 59, 337-350. (33) Kociba, K. J. J. Therm. Anal. Calorim. 2000, 60, 779-784. (34) Zhang, M.; Efremov, M. Y.; Schiettekatte, F.; Olson, E. A.; Kwan, A. T.; Lai, S. L.; Wisleder, T.; Greene, J. E.; Allen, L. H., Phys. Rev. B 2000, 62, 10548-10557. (35) Toda, A.; Tomita, C.; Arita, T.; Hikosaka, M. J. Therm. Anal. Calorim. 2001, 64, 775-782. (36) Hashimoto, S.; Iwahara, H. Mater. Res. Bull. 2000, 35, 22532262. (37) Vyazovkin, S.; Ferrin, T. L. Solid State Commun. 2000, 113, 627631. (38) Price, D. M. Thermochim. Acta 2001, 367-368, 253-262. (39) Chatterjee, K.; Dollimore, D.; Alexander, K. Instrum. Sci. Technol. 2001, 29, 133-144. (40) Chatterjee, K.; Dollimore, D.; Alexander, K. Int. J. Pharm. 2001, 213, 31-44. (41) Burnham, L.; Dollimore, D.; Alexander, K. Thermochim. Acta 2001, 367-368, 15-22. (42) Li, Z. J.; Jaroniec, M.; Choma, J. Thermochim. Acta 2000, 345, 165-172. (43) Eigenmann, F.; Maciejewski, M.; Baiker, A. Thermochim. Acta 2000, 359, 131-141. (44) Bentzen, J. J.; Pedersen, A. S.; Kjoller, J. J. Therm. Anal. Calorim. 2001, 64, 859-866. (45) Wang, C. B.; Yeh, C. T. Appl. Catal., A 2001, 209, 1-9. (46) Pires, J.; de Carvalho, M. B.; Carvalho, A. P.; Guil, J. M.; PerdigonMelon, J. A. Clays Clay Miner. 2000, 48, 385-391. (47) Vyazovkin, S. Int. Rev. Phys. Chem. 2000, 19, 45-60. (48) Galwey, A. K.; Brown, M. E. J. Therm. Anal. Calorim. 2000, 60, 863-877. (49) Brown, M. E.; Maciejewski, M.; Vyazovkin, S.; Nomen, R.; Sempere, J.; Burnham, A.; Opfermann, J.; Strey, R.; Anderson, H. L.; Kemmler, A.; Keuleers, R.; Janssens, J.; Desseyn, H. O.; Li, C.-R.; Tang, T. B.; Roduit, B.; Malek, J.; Mitsuhashi, T. Thermochim. Acta 2000, 355, 125-143. (50) Burnham, A. K.; Braun, R. L. Energy Fuels 1999, 13, 1-22. (51) Plonka, A. Prog. React. Kinet. 2000, 25, 109-217. (52) Zsako, J.; Pokol, G.; Novak, C.; Varhelyi, C.; Dobo, A.; Liptay, G. J. Therm. Anal. Calorim. 2001, 64, 843-856. (53) Maciejewski, M. Thermochim. Acta 2000, 355, 145-154. (54) Burnham, A. K. Thermochim. Acta 2000, 355, 165-170. (55) Roduit, B. Thermochim. Acta 2000, 355, 171-180. (56) Flynn, J. H. In Thermal Analysis; Schwenker, R. F., Garn, P. D., Eds.; Academic Press: New York, 1969; Vol. 2, p 1111. (57) Schubnell, M. J. Therm. Anal. Calorim. 2000, 61, 1005-1011. (58) Gamlin, C.; Dutta, N.; Roy-Choudhury, N.; Kehoe, D.; Matisons, J. Thermochim. Acta 2001, 367-368, 185-193. (59) Budrugeac, P.; Segal, E. Int. J. Chem. Kinet. 2001, 33, 564573. (60) Vyazovkin, S. J. Comput. Chem. 2001, 22, 178-183. (61) L′vov, B. V. Thermochim. Acta 2001, 373, 97-124. (62) Maciejewski, M. Thermochim. Acta 1987, 110, 145-152. (63) Korobov, A. Discrete Dyn. Nat. Soc. 2000, 4, 165-179. (64) Segal, E. J. Therm. Anal. Calorim. 2000, 61, 979-984. (65) Goss, B. G. S.; Barry, M. D.; Birtwhistle, D.; George, G. A., Polym. Degrad. Stab. 2001, 74, 271-282. (66) Sestak, J.; Mares, J. J.; Kristofik, J.; Hubik, P. Glass Sci. Technol. 2000, 73, 104-110. (67) Liu, L.; Guo, Q. X. Chem. Rev. 2001, 101, 673-695. (68) Mathew, D.; Nair, C. P.; Ninan, K. N. Eur. Polym. J. 2000, 36, 1195-1208. (69) Sikorska-Iwan, M.; Rzaczynska, Z.; Kula, A.; Jaroniec, M. J. Therm. Anal. Calorim. 2001, 66, 841-849. (70) Milic, S.; Colovic, N.; Antonijevic, M.; Gaal, F. J. Therm. Anal. Calorim. 2000, 61, 229-238. (71) Vlase, T.; Jurca, G.; Doca, N. Thermochim. Acta 2001, 379, 6569. (72) Lai, V. M. F.; Lii, C. Y.; Hung, W. L.; Lu, T. J. Food Chem 2000, 68, 319-325. (73) Logvinenko, V. J. Therm. Anal. Calorim. 2000, 60, 9-15. (74) Gotor, F. J.; Criado, J. M.; Malek, J.; Koga, N. J. Phys. Chem. A 2000, 104, 10777-10782. (75) Budrugeac, P.; Criado, J. M.; Gotor, F. J.; Popescu, C.; Segal, E. J. Therm. Anal. Calorim. 2001, 63, 777-786. (76) Pokol, G. J. Therm. Anal. Calorim. 2000, 60, 879-886. (77) Maciejewski, M.; Ingier-Stocka, E.; Emmerich, W. D.; Baiker, A. J. Therm. Anal. Calorim. 2000, 60, 735-758. (78) Vanhoyland, G.; Nouwen, R.; Van Bael, M. K.; Yperman, J.; Mullens, J.; Van Poucke, L. C. Thermochim. Acta 2000, 354, 145-151. (79) Diez, E.; Monnereau, O.; Tortet, L.; Vacquier, G.; Llewellin, P.; Rouquerol, F. J. Optoelectron. Adv. Mater. 2000, 2, 552-556. (80) Aono, H.; Tsuzaki, M.; Kawaura, A.; Sakamoto, M.; Traversa, E.; Sadaoka, Y. J. Am. Ceram. Soc. 2001, 84, 969-975. (81) Reddy, C. V. G.; Manorama, S. V.; Rao, V. J. J. Mater. Sci.-Mater. El. 2001, 12, 137-142. (82) Tolochko, S. P.; Makhnach, L. V.; Kononyuk, I. F.; Vashuk, V. V.; Lomonosov, V. A.; Hauck, J.; Altenburg, H.; Shelekhina, V. M. Inorg. Mater. 2000, 36, 1137-1140.
(83) Ly, H. Q.; Taylor, R.; Day, R. J.; Heatley, F. J. Mater. Sci. 2001, 36, 4037-4043. (84) Jansen, R.; Kroschel, M. Z. Anorg. Allg. Chem. 2000, 626, 16341638. (85) Weinmann, M.; Kamphowe, T. W.; Schuhmacher, J.; Muller, K.; Aldinger, F. Chem. Mater. 2000, 12, 2112-2122. (86) Sato, T.; Hubacek, M.; Balek, V.; Subrt, J.; Kriz, O.; Mitsuhashi, T. J. Therm. Anal. Calorim. 2000, 60, 661-665. (87) Lashdaf, M.; Hatanpaa, T.; Tiitta, M. J. Therm. Anal. Calorim. 2001, 64, 1171-1182. (88) Jan, D.; Delaude, L.; Simal, F.; Demonceau, A.; Noels, A. F. J. Organomet. Chem. 2000, 606, 55-64. (89) Maciejewski, M.; Fabrizioli, P.; Grunwaldt, J. D.; Beckert, O. S.; Baiker, A. Phys. Chem. Chem. Phys. 2001, 3, 3846-3855. (90) Carabineiro, S. A.; Fernandes, F. B.; Ramos, A. M.; Vital, J.; Silva, I. F. Catal. Today 2000, 57, 305-312. (91) Ek, S.; Root, A.; Peussa, M.; Niinisto, L. Thermochim. Acta 2001, 379, 201-212. (92) Fernandes, V. J.; Araujo, A. S.; Fernandes, G. J. T. J. Therm. Anal. Calorim. 2001, 64, 807-811. (93) Auroux, A., Ed. Thermochim. Acta 2001, 379, 1-290. (94) Sestak, J. J. Therm. Anal. Calorim. 2000, 61, 305-323. (95) Malek, J. Thermochim. Acta 2000, 355, 239-253. (96) Suga, H. J. Therm. Anal. Calorim. 2000, 60, 957-974. (97) Atake, T.; Abe, R.; Honda, K.; Kawaji, H.; Johnsen, H. B.; Stolen, S. J. Phys. Chem. Solids 2000, 61, 1373-1377. (98) Heide, K.; Gerth, K.; Hartmann, E. Thermochim. Acta 2000, 354, 165-172. (99) Heide, K.; Hartmann, E.; Gert, K.; Wiedemann, H. G. Thermochim. Acta 2000, 365, 147-156. (100) Stoch, L.; Waclawska, I.; Ciecinska, M. J. Therm. Anal. Calorim. 2001, 65, 341-350. (101) Groenewoud, W. M. Characterisation of Polymers by Thermal Analysis; Elsevier: Amsterdam, 2001. (102) Kwan, A. T.; Efremov, M. Y.; Olson, E. A.; Schiettekatte, F.; Zhang, M.; Geil, P. H.; Allen, L. H. J. Polym. Sci. B., Polym. Phys. 2001, 39, 1237-1245. (103) Wunderlich, B.; Pyda, M.; Pak, J.; Androsch, R. Thermochim. Acta 2001, 377, 9-33. (104) Wurm, A.; Merzlyakov, M.; Schick, C. J. Therm. Anal. Calorim. 2000, 60, 807-820. (105) Andjelic, S.; Jamiolkowski, D.; McDivitt, J.; Fischer, J.; Zhou, J.; Vetrecin, R. J. Appl. Polym. Sci. 2001, 79, 742-759. (106) Ho, R. M.; Hseih, P. Y.; Yang, C. C.; Lin, J. J. J. Polym. Sci. B, Polym. Phys. 2001, 39, 2469-2480. (107) Lee, S. W.; Lee, B.; Ree, M. Macromol. Chem. Phys. 2000, 201, 453-463. (108) Liu, X. F.; Hay, J. N. Polymer 2001, 42, 9423-9431. (109) Won, J. C.; Fulchiron, R.; Douillard, A.; Chabert, B.; Varlet, J.; Chomier, D. Polym. Eng. Sci. 2000, 40, 2058-2071. (110) Liu, S. L.; Chung, T. S. Polymer 2000, 41, 2781-2793. (111) Lisowski, M. S.; Liu, Q.; Cho, J. D.; Runt, J.; Yeh, F. J.; Hsiao, B. S. Macromolecules 2000, 33, 4842-4849. (112) Sajkiewicz, P.; Carpaneto, L.; Wasiak, A. Polymer 2001, 42, 5365-5370. (113) Martins, J. A.; Pinto, J. J. C. C. Polymer 2000, 41, 6875-6884. (114) Cheng, S. Z. D.; Li, C. Y.; Calhoun, B. H.; Zhu, L.; Zhou, W. W. Thermochim. Acta 2000, 355, 59-68. (115) Toda, A.; Tomita, C.; Hikosaka, M.; Saruyama, Y. Polymer 1997, 38, 2849-2852. (116) Song, M.; Hourston, D. J. Polymer 2000, 41, 8161-8165. (117) Chen, W.; Moon, I. K.; Wunderlich, B. Polymer 2000, 41, 41194125. (118) Yoshida, H.; Houshito, Y.; Mashiko, K.; Masaka, K.; Nakamura, S. J. Therm. Anal. Calorim. 2001, 64, 453-458. (119) Roussel, F.; Buisine, J. M.; Maschke, U.; Coqueret, X. Phys. Rev. E 2000, 62, 2310-2316. (120) Schick, C., Hohne, G. W. H., Eds. Thermochim. Acta 2001, 377, 1-228. (121) Hutchinson, J. M.; Montserrat, S. Thermochim. Acta 2001, 377, 63-84. (122) Park, J. Y.; McKenna, G. B. Phys. Rev. B 2000, 61, 6667-6676. (123) Montserrat, S. J. Therm. Anal. Calorim. 2000, 59, 289-303. (124) Van Assche, G.; Van Mele, B.; Saruyama, Y. Thermochim. Acta 2001, 377, 125-130. (125) Van Assche, G.; Verdonck, E.; Van Mele, B. Polymer 2001, 42, 2959-2968. (126) Schawe, J. E. K. J. Therm. Anal. Calorim. 2001, 64, 599-608. (127) Flammersheim, H. J.; Opfermann, J. R. Macromol. Mater. Eng. 2001, 286, 143-150. (128) Leroy, E.; Dupuy, J.; Maazouz, A. Macromol. Chem. Phys. 2001, 202, 465-474. (129) Pielichowski, K.; Czub, P.; Pielichowski, J. Polymer 2000, 41, 4381-4388. (130) Mas, C.; Serra, A.; Mantecon, A.; Salla, J. M.; Ramis, X. Macromol. Chem. Phys. 2001, 202, 2554-2564. (131) Dunne, R. C.; Sitaraman, S. K.; Luo, S. J.; Rao, Y.; Wong, C. P.; Estes, W. E.; Gonzalez, C. G.; Coburn, J. C.; Periyasamy, M. J. Appl. Polym. Sci. 2000, 78, 430-437. (132) Li, S. Y.; Vuorimaa, E.; Lemmetyinen, H. J. Appl. Polym. Sci. 2001, 81, 1474-1480. (133) Vyazovkin, S.; Sbirrazzuoli, N. Macromol. Chem. Phys. 2000, 201, 199-203.
(134) Holland, B. J.; Hay, J. N. Polymer 2001, 42, 4825-4835. (135) Peterson, J. D.; Vyazovkin, S.; Wight, C. A. Macromol. Chem. Phys., 2001, 202, 775-784. (136) Celina, M.; Wise, J.; Ottesen, D. K.; Gillen, K. T.; Clough, R. L. Polym. Degrad. Stab. 2000, 68, 171-184. (137) Simon, P.; Kolman, L. J. Therm. Anal. Calorim. 2001, 64, 813820. (138) Mahajan, R. R.; Makashir, P. S.; Kuran, E. M. J. Polym. Mater. 2000, 17, 47-52. (139) Howell, B. A.; Uhl, F. M. Thermochim. Acta 2000, 357, 113117. (140) Howell, B. A.; Uhl, F. M.; Townsend, D. Thermochim. Acta 2000, 357, 127-131. (141) Herrera, M.; Matuschek, G.; Kettrup, A. Chemosphere 2001, 42, 601-607. (142) Levchik, S. V.; Weil, E. D. Polym. Int. 2000, 49, 1033-1073. (143) Varma, I. K. Mater. Res. Innovations 2001, 4, 306-310. (144) Atkinson, P. A.; Haines, P. J.; Skinner, G. A. Polym. Degrad. Stab. 2001, 71, 351-360. (145) Reading, M.; Price, D. M.; Grandy, D. B.; Smith, R. M.; Bozec, L.; Conroy, M.; Hammiche A.; Pollock, H. M. Macromol. Symp. 2001, 167, 45-62. (146) Hassler, R.; zur Muhlen, E. Thermochim. Acta 2000, 361, 113120. (147) Tillman, M. S.; Hayes, B. S.; Seferis, J. C. J. Appl. Polym. Sci. 2001, 80, 1643-1649. (148) Oulevey, F.; Burnham, N. A.; Gremaud, G.; Kulik, A. J.; Pollock, H. M.; Hammiche, A.; Reading, M.; Song, M.; Hourston, D. J. Polymer 2000, 41, 3087-3092. (149) Rajic, M.; Suceska, M. J. Therm. Anal. Calorim. 2000, 63, 375386. (150) Waesche, R. H. W.; Wenograd, J. Combust. Explos. Shock 2000, 36, 125-134. (151) Singh, G.; Kapoor, I. P. S.; Mannan, S. M.; Kaur, J. J. Hazard. Mater. 2000, 79, 1-18. (152) Lurie, B. A.; Chang, L. S. Combust. Explos. Shock 2000, 36, 607617. (153) Simoes, P. N.; Pedroso, L. M.; Portugal, A. A.; Campos, J. L. Thermochim. Acta 2000, 364, 71-85. (154) Tompa, A. S. Thermochim. Acta 2000, 357, 177-193. (155) Oxley, J. C.; Smith, J. L.; Zhang, J. J. Phys. Chem. A 2000, 104, 6764-6777. (156) Oxley, J. C.; Smith, J. L.; Zhang, J.; Bedford, C. J. Phys. Chem. A 2001, 105, 579-590. (157) Long, G. T.; Vyazovkin. S.; Brems, B. A.; Wight, C. A. J. Phys. Chem. B 2000, 104, 2570-2574. (158) Tompa, A. S.; Bryant, W. F. Thermochim. Acta 2001, 367, 433441. (159) Divekar, C. N.; Asthana, S. N.; Singh, H. J. Propul. Power 2001, 17, 58-64. (160) Jones, D. E. G.; Brousseau, P.; Fouchard, R. C.; Turcotte, A. M.; Kwok, Q. S. M. J. Therm. Anal. Calorim. 2000, 61, 805818. (161) Tompa, A. S.; Boswell, R. F. Thermochim. Acta 2000, 357, 169175. (162) Campbell, M. S.; Garcia, D.; Idar, D. Thermochim. Acta 2000, 357, 89-95. (163) Jones, D. E. G.; Feng, H. T.; Fouchard, R. C. J. Therm. Anal. Calorim. 2000, 60, 917-926. (164) de Klerk, W. P. C.; van der Heijden A. E. D. M.; Veltmans, W. H. M. J. Therm. Anal. Calorim. 2001, 64, 973-985. (165) Nazin, G. M.; Prokudin, V. G.; Manelis, G. B. Russ. Chem. Bull. 2000, 49, 234-237. (166) Brown, M. E. J. Therm. Anal. Calorim. 2001, 65, 323-334. (167) Brill, T. B.; Zhang, T. L.; Tappan, B. C. Combust. Flame 2000, 121, 662-670. (168) Brill, T. B.; Ramanathan, H. Combust. Flame 2000, 122, 165171. (169) Zajdlik, R.; Jelemensky, L.; Remiarova, B.; Markos, J. Chem. Eng. Sci. 2001, 56, 1355-1361. (170) Jiang, W.; Nadeau, G.; Zaghib, K.; Kinoshita, K. Thermochim. Acta 2000, 351, 85-93. (171) Fan, M. H.; Brown, R. C. Energy Fuels 2001, 15, 1414-1417. (172) Zolin, A.; Jensen, A.; Dam-Johansen, K.; Salatino, P.; Hurt, R.; Liu, G. Proc. Combust. Inst. 2000, 28, 2181-2188. (173) Burnham, A. K. J. Therm. Anal. Calorim. 2000, 60, 895-908. (174) Conesa, J. A.; Marcilla, A.; Caballero, J. A.; Font, R. J. Anal. Appl. Pyrolysis 2001, 58, 617-633. (175) Liu, K. L.; Han, W. J.; Pan, W. P.; Riley, J. T. J. Hazard. Mater. 2001, 84, 175-188. (176) Xie, W.; Xie, Y.; Pan, W. P.; Riga, A. Thermochim. Acta 2000, 357, 231-238. (177) Stachowiak, C.; Grolier, J. P. E.; Randzio, S. L. Energy Fuels 2001, 15, 1033-1037. (178) Craig, D. Q. M., Thompson, K., Eds. Thermochim. Acta 2001, 380, 1-202. (179) Thompson, K. C. Thermochim. Acta 2000, 355, 83-87. (180) Giron, D. J. Therm. Anal. Calorim. 2001, 64, 37-60. (181) Vippagunta, S. R.; Brittain, H. G.; Grant, D. J. W. Adv. Drug Delivery Rev. 2001, 48, 3-26. (182) Gu, C. H.; Grant, D. J. W. J. Pharm. Sci. 2001, 90, 1277-1287. (183) Shamblin, S. L.; Hancock, B. C.; Dupuis, Y.; Pikal, M. J. J. Pharm. Sci. 2000, 89, 417-427.
Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
2761
(184) Craig, D. Q. M.; Barsnes, M.; Royall, P. G.; Kett, V. L. Pharm. Res. 2000, 17, 696-700. (185) Zhu, H. J.; Grant, D. J. W. Int. J. Pharm. 2001, 215, 251-262. (186) Rotich, M. K.; Glass, B. D.; Brown, M. E. J. Therm. Anal. Calorim. 2001, 64, 681-688. (187) Wissing, S.; Craig, D. Q. M.; Barker, S. A.; Moore, W. D. Int. J. Pharm. 2000, 199, 141-150. (188) Giordano, F.; Novak, C.; Moyano, J. R. Thermochim. Acta 2001, 380, 123-151. (189) Wadso, I. J. Therm. Anal. Calorim. 2001, 64, 75-84. (190) Hansen, L. D. Ind. Eng. Chem. Res. 2000, 39, 3541-3549. (191) Beezer, A. E.; Hills, A. K.; O’Neill, M. A. A.; Morris, A. C.; Kierstan, K. T. E.; Deal, R. M.; Waters, L. J.; Hadgraft, J.; Mitchell, J. C.; Connor, J. A.; Orchard, J. E.; Willson, R. J.; Hofelich, T. C.; Beaudin, J.; Wolf, G.; Baitalow, F.; Gaisford, S.; Lane, R. A.; Buckton, G.; Phipps, M. A.; Winneke, R. A.; Schmitt, E. A.; Hansen, L. D.; O’Sullivan, D.; Parmar, M. K. Thermochim. Acta 2001, 380, 13-17. (192) Guan, Y. H.; Kemp, R. B. Thermochim. Acta 2000, 349, 163176.
2762
Analytical Chemistry, Vol. 74, No. 12, June 15, 2002
(193) Cuppo, F.; Venuti, M.; Cesaro, A.Int. J. Biol. Macromol. 2001, 28, 331-341. (194) Barreleiro, P. C. A.; Olofsson, G.; Alexandridis, P. J. Phys. Chem. B 2000, 104, 7795-7802. (195) Giancola, C.; Petraccone, L.; Pieri, M.; De Napoli, L.; Montesarchio, D.; Piccialli, G.; Barone, G. Int. J. Biol. Macromol. 2001, 28, 387-394. (196) Grasso, D.; Milardi, D.; La Rosa, C.; Rizzarelli, E. New J. Chem. 2001, 25, 1543-1548. (197) Kemp, R. B. Thermochim. Acta 2001, 380, 229-244. (198) Morgan, T. D.; Beezer, A. E.; Mitchell, J. C.; Bunch, A. W. J. Appl. Microbiol. 2001, 90, 53-58. (199) Criddle, R. S.; Anekonda, T. S.; Tong, S.; Church, J. N.; Ledig, F. T.; Hansen, L. D. Aust. J. Plant Physiol. 2000, 27, 435-443. (200) Schmolz, E.; Lamprecht, I. Thermochim. Acta 2000, 349, 61-68.
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