Underlying Heating Rate Research Articles

Critical study concerning the use of sinusoidal modulated thermogravimetric data for evaluation of activation energy of heterogeneous processes

A critical analysis of relationships has been carried out concerning the modulated thermogravimetric methods (MTGA methods) for evaluation of activation energy of heterogeneous processes, which exhibit the advantage of using a single thermogravimetric curve recorded under sinusoidal modulated temperature program. Results reported in the literature have shown that for some heterogeneous processes there are large differences between the value of activation energy determined by a MTGA method and that determined by the an isoconversional method which use thermogravimetric data recorded at several heating rates, as well as the fact that the value of the activation energy determined by an MTGA method depends on the parameters of the sinusoidal modulated temperature program (period, amplitude, underlying heating rate). To find the causes of these findings, MTGA methods were applied for simulated data performed for five different modulated sinusoidal temperature programs, which, unlike the experimental data, are not affected by inherent experimental errors. These data have been also used to evaluate activation energy by three multi-heating isoconversional methods that are applicable for arbitrary temperature programs. It has been obtained that also for the simulated data there are large differences between activation energy values obtained by all considered MTGA methods and that obtained by isoconversional methods, which deliver the correct values of the activation energy. Also, some dependencies of activation energy values obtained by MTGA methods on the parameters of modulated temperature programs are put in evidence. The analysis of the obtained results shows that these findings are due to the assumption made in derivation of relationship underlying each MTGA method, according to which the ratio between two values of the differential conversion function corresponding to two close values of conversion degree which are specific for each MTGA method can be approximated by 1. This approximation is necessary because the differential conversion function cannot be determined using a single MTGA curve. In conclusion, these all show that MTGA methods are not a viable alternative to multi-heating isoconversional methods.

Fast-scan and temperature-modulated calorimetry of recrystallization of poly(ethylene terephthalate)

The recrystallization behavior of poly(ethylene terephthalate), PET, in the melting region was examined by Fast-Scan and Temperature-Modulated Calorimetry. In addition to the prior results of Fast-Scan Calorimetry, FSC, evidence that recrystallization caused double PET melting peaks was obtained. An exothermic recrystallization peak was directly observed in the second heating run of FSC after the lower-temperature melting peak was eliminated through rapid heating and cooling. FSC was then performed with a temperature protocol of a periodic step-wise jump in temperature, a mode of temperature modulated FSC, T-M FSC. A broad and large peak of the effective dynamic heat capacity of complex quantity was observed in the melting region during T-M FSC analysis, which proved that melting occurred in the temperature range between the double melting peaks. A broad negative peak in the phase angle of the dynamic heat capacity was observed in the melting region at a low underlying heating rate with long modulation periods, which indicated that recrystallization and melting occurred simultaneously.

Parametric study of temperature-modulated differential scanning calorimetry for high-temperature oxide glasses with varying fragility

Differential scanning calorimetry (DSC) has proven to be a highly versatile technique for understanding the glass transition, relaxation, and crystallization behavior of inorganic glasses. However, the approach is challenging when probing glass samples that exhibit overlapping transitions or low sensitivity. To overcome these problems, temperature-modulated DSC (TM-DSC) can be utilized, in which a sinusoidal heating rate is superimposed on the linear heating rate known from standard linear DSC. Until recently, it has only been possible to perform TM-DSC measurements on commercial instruments at temperatures below 973 K, which is insufficient for many oxide glasses of industrial interest, particularly silicate glasses. However, recent commercially available software now enables TM-DSC measurements to be performed at temperatures far exceeding 973 K. To investigate the suitability of using TM-DSC to study glass transition and relaxation behavior in high-temperature silicate systems, we have performed systematic TM-DSC measurements on three different oxide glass systems with varying glass transition temperature and liquid fragility. We find that relatively large underlying heating rates (2–5 K/min) and modulation amplitudes (4–5 K) are needed in order to obtain data with high signal-to-noise ratios. For these combinations of experimental parameters, we also observe a linear response as found using Lissajous curves. Overall, this study suggests that TM-DSC is a promising technique for investigating the dynamics of high-temperature oxide glass systems with a wide range of liquid fragilities.

Contributions of Tzero™ technology to temperature modulated Differential scanning calorimetry

Differential Scanning Calorimetry (DSC) is the most used of thermal analysis techniques. Temperature Modulated DSC is a technique which has extended a lot the applications of DSC because of new possibilities like improved separation of overlapped transitions, a higher sensitivity and an improved accuracy of heat capacity measurements. Basic principle of Modulated DSC is to apply two heating rates simultaneously and consequently to measure the heat flow obtained by this solicitation. The average underlying heating rate gives the same heat flow than conventional DSC (called total heat flow), while the sinusoidal instantaneous heating rate allows the separation of this total heat flow into two components, one heat flow linearly dependent of the heating rate change, and one heat flow dependent on time and temperature, and not dependent of the heating rate change. This technique allows a direct measurement of heat capacity, and the separation of thermal events due to a heat capacity change (for instance glass transition) from kinetic events (polymerization, dehydration) because of the purely sinusoidal thermal solicitation. Tzero™ technology has been specifically developed to quantify the instrument contribution to the DSC measurement; and offers a much more accurate representation of the absorbed or evolved heat flow by the analyzed material. This technique directly measures the heat transfers through the thermal sensors (thermal resistances and thermal capacitances of the sample and reference platforms) and consequently two independent measurements of sample and reference heat flows. The result is the improved resolution of thermal peaks and a quick return to baseline after a transition. Advanced Tzero™ technology takes in account heat transfers through sample and reference pans in the heat flow measurement. This allows Modulated DSC experiments at average heating rates similar to conventional DSC, typically 10K/min.

Vitrification and devitrification during the non-isothermal cure of a thermoset

The processes of vitrification and devitrification that occur in an epoxy resin when it cures non-isothermally with a hardener are studied in terms of their frequency dependence and as a function of the heating rate. A novel modulated DSC technique, TOPEM, has been used which permits the evaluation of the frequency dependence for a single sample in a scan at constant underlying heating rate, thus avoiding errors arising from the composition of the sample. The effects of both frequency and heating rate on vitrification and devitrification are investigated. Some advantages of this technique are observed and discussed.

Enthalpy Relaxation in the Cooling/Heating Cycles of Polyamide 6/Organoclay Nanocomposites. II. Melting Behavior

Nonisothermally crystallized samples of the neat polyamide 6 homopolymer (PA 6) and of a series of commercial nanocomposites (PNC) containing up to 7.5 wt.% of exfoliated organoclay nanoparticles were characterized at room temperature by wide‐angle and small‐angle X‐ray scattering, while their melting behavior was studied in the temperature‐modulated differential scanning calorimetry (DSC) mode at three underlying heating rates and five modulation frequencies. Both α‐ and γ‐crystal modifications of PA 6 were invariably formed during cooling from the melt, the ratio α‐form/γ‐form tending to decrease the higher the organoclay content and/or the cooling rate. Strongly scattering organoclay platelets within the PNC were spatially organized into two different, mass fractal‐like structures in the ranges of characteristic structural scales of ca. 14–100 nm and ca. 5–14 nm, respectively. The patterns of melting endotherms in both the neat PA 6 and the PNC could be semiquantitatively characterized by a simple Debye model with a single, temperature‐ and underlying heating rate‐dependent characteristic time. The mechanisms of structural rearrangements in the melting intervals of the neat PA 6 sample and the PNC were basically similar; however, the spatial scale of such rearrangements in the latter samples was significantly reduced due to severe steric constraints on the PA 6 chain mobility in the melt state from the infinite cluster of nanoparticles.

Enthalpy relaxation in the cooling/heating cycles of polypropylene/organosilica nanocomposites: II. Melting behavior

Non-isothermally crystallized samples of the neat isotactic polypropylene homopolymer (PP-0) and of a series of nanocomposites (PNC) containing up to 4.68 vol.% of organosilica were characterized by wide-angle and small-angle X-ray diffraction and by the standard DSC, while their melting behavior was studied in the temperature-modulated DSC mode at three underlying heating rates and five modulation frequencies. It was established that the lamellar morphology of PP remained essentially unchanged, whatever the previous cooling rate and/or the organoclay content. The patterns of melting endotherms in both the neat PP sample and the PNC could be semi-quantitatively characterized by a simple Debye model with a single, temperature- and underlying heating rate-dependent characteristic time. The mechanisms of structural rearrangements in the melting intervals of the neat PP sample and the PNC were basically similar; however, the spatial scale of such rearrangements in the latter samples was significantly reduced due to severe steric constraints on the PP chain mobility in the melt state from the infinite cluster of nanoparticles.

Melting Behavior of the Nonisothermally Crystallized Polypropylene/Organosilica Nanocomposite

Melting behavior of nonisothermally crystallized samples of the neat isotactic polypropylene homopolymer (PP‐0) and the nanocomposite containing 4.68 wt% of organosilica (PP‐4.68) was studied in the temperature‐modulated differential scanning calorimetry (DSC) mode at three underlying heating rates and five modulation frequencies. It was established that the patterns of melting endotherms in both the neat PP sample and the PP–organosilica nanocomposite could be semiquantitatively characterized by a simple Debye model with a single, temperature‐ and underlying heating rate‐dependent characteristic time. The mechanisms of structural rearrangements in the melting intervals of the neat PP sample and the PP–organosilica nanocomposite were basically similar; however, the spatial scale of such rearrangements in the latter sample was significantly reduced due to severe steric constraints on the PP chain mobility in the melt state from the infinite cluster of nanoparticles.

Melting of polymers by non-isothermal, temperature-modulated calorimetry: analysis of various irreversible latent heat contributions to the reversing heat capacity

This paper provides an analysis of contributions to the apparent, reversing heat capacity when measured by temperature-modulated differential scanning analysis (TMDSC) with an underlying heating rate in the temperature range where irreversible transitions with latent heats occur. To deconvolute the data of a TMDSC scan into a total and reversing part, it is common practice to use the sliding averages and the first harmonics of the Fourier series of temperature and heat-flow rate. Under certain conditions, this procedure produces erroneous reversing contributions which are detailed by experiment and simulation. Unless the response to the temperature modulation is linear, the total heat-flow rate is stationary, and the transition is truly reversible and occurs only once during the temperature scan, one cannot expect a true deconvolution of total and reversible effects. In the presence of multiple, irreversible transitions within a modulation period, however, each process involving latent heat can increase the modulation amplitude, as demonstrated by computer-simulation of polymer melting. As a result, the multiple transitions may give erroneously high latent heats when integrating the apparent reversing heat capacity with respect to temperature.

STUDY OF THE CRYSTALLIZATION AND MELTING REGION OF PET AND PEN AND THEIR BLENDS BY TMDSC

The cold crystallization and melting of poly(ethylene therephthalate) (PET), poly(ethylene 2,6-naphthalene dicarboxylate) (PEN) and their blends were studied using temperature modulated differential scanning calorimetry (TMDSC) at underlying heating rates of between 1 and 3 K min-1 and periods ranging from 30 to 90 s. The amplitude of modulation was selected in order to give an instantaneous heating rate β≥0. Heat flow is analyzed by the total heat flow signal o, which is equivalent to the conventional DSC signal, and the reversing heat flow oREV, which only detects the glass transition and the melting processes. The dependence of the melting region in the reversing heat flow on the frequency of modulation is analyzed. The use of the so-called non-reversing heat flow oNREV (=o-oREV)) and the effect of frequency and amplitude on the complex heat capacity are also studied. The results show the complexity of these magnitudes.

Non-isothermal curing of a diepoxide–cycloaliphatic diamine system by temperature modulated differential scanning calorimetry

The non-isothermal curing of an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) with a diamine based on 3,3′-dimethyl-4,4′-diaminodicyclohexylmethane (3DCM) was analysed by temperature modulated differential scanning calorimetry (TMDSC). The TMDSC scans were performed at underlying heating rates, q 0, of between 1 and 0.1 K min −1, and at the following modulation conditions: an amplitude of 0.2 K and a period of 60 s. For values of q 0 equal to or lower than 0.5 K min −1, a vitrification and further devitrification of the system was observed in the modulus of the complex heat capacity, |C p ∗| , and also in the phase angle signal. Both the time and the temperature of vitrification and devitrification are used to construct a continuous heating transformation (CHT) cure diagram. This diagram was completed by the lines that give the evolution of the temperature and the glass transition temperature over time at constant heating rate. The effect of the steric hindrance of the diamine is analysed in the curing kinetics and the maximum glass transition temperature of the resin. The thermal stability of the reacting system was studied by thermogravimetric analysis.

Characterization of amorphous ketoconazole using modulated temperature differential scanning calorimetry

The objective of the present study was to characterize the glassy state of ketoconazole and to calculate its molecular mobility below the glass transition, with a view to further developing the use of modulated temperature differential scanning calorimetry (MTDSC) as a means of studying relaxation behavior. Particular emphasis is placed on identifying the influence of the choice of experimental parameters on the measured values of both the glass transition temperature (Tg) and the relaxation enthalpy magnitude. Amorphous ketoconazole was studied using an amplitude of ±0.212 K, a period of 40 s, and an underlying heating rate of 2 K/min. The correction required for the calculation of the relaxation endotherm magnitude (the ‘Tg shift effect’) was demonstrated and is discussed in terms of the mechanism underpinning this phenomenon. Similarly, the influence of the choice of MTDSC experimental parameters on the measured Tg was studied by varying the amplitude from ±0.011 to ±0.424 K and the period from 25 to 50 s. The influence of the cooling rate from the melt on the magnitude of the relaxation endotherm and position of the glass transition was investigated. It was noted that the magnitude of the relaxation endotherm increased with slower cooling rates, this being ascribed to a combination of annealing during the cooling and heating cycle and a further facet of the Tg shift effect. Annealing experiments were performed at aging temperatures Tg-12–Tg-42 K for periods ranging from 10 min up to 16 h. The relaxation behavior was characterized by fitting the calculated extent of relaxation to the Williams–Watts equation. Overall, the study has highlighted theoretical and experimental issues that need to be considered when using both DSC and MTDSC for the calculation of relaxation times. © 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:996–1003, 2001

Characterization of glassy itraconazole: a comparative study of its molecular mobility below Tg with that of structural analogues using MTDSC

The objective of the present study was to estimate the molecular mobility of glassy itraconazole below the glass transition, in comparison with structural analogues (i.e. miconazole and ketoconazole). Glassy itraconazole and miconazole were prepared by cooling from the melt. The glassy state of the drug was investigated with modulated temperature DSC using the following conditions: amplitude ±0.212 K, period 40 s, underlying heating rate 2 K/min. The glass transition was determined from the reversing heat flow and occurred at 332.4 (±0.5) K and 274.8 (±0.4) K for itraconazole and miconazole, respectively. The jump in heat capacity at the glass transition was 303.42 (±3.43) J/mol K for itraconazole and 179.35 (±0.89) J/mol K for miconazole. The influence of the experimental conditions on the position of the glass transition of itraconazole was investigated by varying the amplitude from ±0.133 to ±0.292 K and the period from 25 to 55 s, while the underlying heating rate was kept constant at 2 K/min. Glass transition temperature, T g, was not significantly influenced by the frequency of the modulation nor by the cooling rate. However, the relaxation enthalpy at the glass transition increased with decreasing cooling rate indicating relaxation during the glass formation process. To estimate the molecular mobility of the glassy materials, annealing experiments were performed from T g−10 to T g−40 K for periods ranging from 15 min to 16 h. Fitting the extent of relaxation of glassy itraconazole to the Williams–Watts decay function and comparing the obtained values with those of amorphous miconazole and ketoconazole indicated that the molecular mobility is influenced by the complexity of the molecular structure. The more complex the structure, the more stable the amorphous state.

A calibration of complex heat capacity obtained by temperature-modulated DSC in the melting region of polymer crystals

Complex heat capacity obtained in melting region of polymer crystals by temperature-modulated differential scanning calorimetry of heat flux type has been calibrated with a method based on a model proposed by Hatta. The calibration method corrects for the effect of thermal conductivity of the DSC apparatus on the magnitude and phase angle of the heat capacity. The validity of the correction has been confirmed by examining the reversible melting and crystallization of indium under quasi-isothermal conditions. For the irreversible melting of polymer crystals analyzed with an additional underlying heating rate, the calibrated heat capacity becomes a complex quantity with a frequency dependence roughly approximated by Debye's type, the characteristic time of which depends on the underlying heating rate. This behavior qualitatively agrees with the previous results obtained by the calibration of baseline-subtraction from the phase angle. The applicability of the “baseline-subtraction” has also been discussed.

Enthalpy relaxation of an epoxy-anhydride resin by temperature-modulated differential scanning calorimetry

The enthalpy relaxation of an epoxy–anhydride resin was studied by physical aging and frequency-dependence experiments with alternating differential scanning calorimetry (ADSC), which is a temperature-modulated differential scanning calorimetry technique. The samples were aged at 80 °C, about 26 K below the glass-transition temperature, for periods up to 3800 h and then scanned under the following modulation conditions: underlying heating rate of 1 K min−1, amplitude of 0.5 K, and period of 1 min. The enthalpy loss was calculated by the total heat-flow signal, and its variation with the log (aging time) gives a relaxation rate (per decade), this value being in good agreement with that calculated by conventional DSC. The enthalpy loss was also analyzed in terms of the nonreversing heat flow, revealing that this property is not suitable for calculating enthalpy loss. The effect of aging on the modulus of the complex heat capacity, |Cp*|, is shown by a sharper variation on the low side of the glass transition and an increase in the inflexional slope of |Cp*|. Likewise, the phase angle also becomes sharper in the low-temperature side of the relaxation. The area under the corrected out-phase heat capacity remains fairly constant with aging. The dependence of the dynamic glass transition, measured at the midpoint of the variation of |Cp*|, on ln(frequency) allows one to determine an apparent activation energy, Δh*, which gives information about the temperature dependence of the relaxation times in equilibrium over a range close to the glass transition. The values of Δh*, determined from ADSC experiments in a range of frequencies between 4.2 and 33 mHz and at an amplitude of 0.5 K, and an underlying heating rate of 1 K min−1, were analyzed and compared with that obtained by conventional DSC from the dependence of the fictive temperature on the cooling rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2272–2284, 2000

Effects of Modulated Differential Scanning Calorimetry (MDSC) Variables on Thermodynamic and Kinetic Characteristics During Gelatinization of Waxy Rice Starch

ABSTRACTThe total, reversing, and nonreversing thermal properties during gelatinization of waxy rice starch (starch‐to‐water ratio = 1:2, w/w) were examined by modulated differential scanning calorimetry (MDSC). The effect of MDSC operating variables (i.e., the amplitude and frequency of temperature modulation and the underlying heating rate) on these thermal properties was determined by response surface methodology (RSM) and statistical analysis. The frequency of temperature modulation and the underlying heating rate significantly influenced the gelatinization temperatures and enthalpy changes in total and nonreversing endotherms. In addition, the combination of 0.025Hz and 4–8°C/min with a properly low degree of oscillation was suitable for characterization of starch gelatinization by MDSC. The enthalpy changes in the reversing (thermodynamic) endotherms increased, but those in the nonreversing (kinetic) endotherms decreased with increasing periods (i.e., decreasing frequencies) and underlying heating rates. However, the total enthalpy changes were only slightly influenced by the MDSC variables studied. In addition, the activation energies for the total and nonreversing events were 281.8–417.3 and 386.3–739.7 kJ/mol, respectively, depending on the MDSC conditions. From the compensation relationship between the activation energy and frequency factor, we concluded that the total and nonreversing endotherms were linked to the same single transition.

Description of the irreversible melting of polymers measured by temperature modulated calorimetry

The melting behaviour of polymers is investigated by temperature modulated differential scanning calorimetry (TMDSC). The measurements are performed in both the quasi isothermal and the scanning mode. For the scanning mode measurements the specific complex heat capacity (given by real c′ and imaginary part c″) was determined. The assumption that the crystals melt from their lateral surface only and that the melting rate is caused by superheating yields to a prediction of the frequency and underlying heating rate dependence of c″. These results are verified experimentally. By adaptation of this model a model function for description of | c| (the modulus of the complex specific heat capacity) in quasi isothermal experiments is obtained. The comparison of this function with experimental data from poly(ethylene terephthalate) and syndiotactic polypropylene shows a good correspondence.

Modulated temperature differential scanning calorimetry for examination of tristearin polymorphism: I. Effect of operational parameters

AbstractThe transformations of tristearin were examined by modulated temperature differential scanning calorimetry (MTDSC) in order to study the effect of operational parameters on the nature of information obtained from this technique. Tristearin has been used as a model polymorphic system showing metastable phases and complicated transformation routes occurring at relatively slow rates. The parameters examined were underlying heating/cooling rates and the amplitude of modulation. The first conclusion is that MTDSC enables overlapping α‐melting and β‐crystallization events to be separated, thus increasing the information obtained compared to normal thermal analysis. Other general conclusions are that observation of reversible processes is strongly influenced by the underlying heating rate; low to moderate heating rates are recommended. Amplitude of modulation has a complicated effect on the phenomenon being studied; when studying systems that exhibit metastable or polymorphic transitions, it is recommended that a range of amplitudes be tested to enable confirmation of whether an observed ‘recrystallization’ effect is a new phase or the same phase as the one melting. Cooling with modulation disturbs the crystallization process, possibly leading to smaller or imperfect crystals; however, the phases obtained are not different compared to normal DSC. The usefulness of MTDSC in analyzing these types of complicated systems is primarily qualitative at the moment. Some recommendations have been made as to the combinations of parameters for studying such systems.

Characterisation of the glass transition of HPMC using modulated temperature differential scanning calorimetry

The glass transitional behaviour of HPMC powder and film samples has been studied using modulated temperature differential scanning calorimetry (MTDSC) in order to explore the ability of the technique to detect transitions which involve small changes in heat capacity. HPMC E4M Prem samples were studied in both powder and film form using a TA Instruments MDSC 2920 using a range of pans, modulation amplitudes and underlying heating rates. Moisture contents were measured using a TA Instruments TGA 2950. Studies on HPMC powder demonstrated the greater clarity with which the glass transition, seen at approximately 162°C, may be seen using MTDSC compared to conventional DSC. The practical difficulties associated with casting suitable HPMC films are discussed, with similar results for T g being found for hermetically sealed pans and pin-holed pans. Increasing the modulation amplitude from 0.212 to 0.5°C improved the signal to noise ratio and increased the magnitude of the measured T g. Increasing the underlying heating rate from 2 to 5°C/min also improved the signal. The study has outlined several features which need to be considered in association with the measurement of HPMC glass transitions using MTDSC; these include the method of sample preparation, the choice of pans, the modulation amplitude and the underlying heating rate.

Calorimetric and Dielectric Investigations of Glass Transition in Intermediate Glass-forming Liquid

The calorimetric glass transition and dielectric dynamics of α-relaxation in propylene glycol (PG) and its five oligomers (polypropylene glycol, PPG) have been investigated by the modulated differential scanning calorimetry (MDSC) and the broadband dielectric spectroscopy. From the temperature dependence of heat capacity of PPGs, it is clarified that the glass transition temperature (Tg) and the glass transition region are affected by the heating rate. The kinetic changes of PG and PPGs near Tg strongly depend on the underlying heating rate. With increasing the molecular mass of PPGs, the fragility derived from the relaxation time against temperature also increases. The PG monomer is stronger than its oligomers, PPGs, because of the larger number density of the —OH end group which tends to construct the intermolecular network structure. Adam-Gibbs (AG) theory could still hold for MDSC results due to the fact that the dielectric relaxation time can be related to the configurational entropy.