J. M. Hutchinson

Characterising the glass transition and relaxation kinetics by conventional and temperature-modulated differential scanning calorimetry

Abstract Over the past 20 years or so, considerable research effort has been directed towards a better understanding of the glass transition in polymers (indeed, of amorphous materials in general), and of the associated relaxation processes, principally by the use of differential scanning calorimetry (DSC). The extent to which phenomenological approaches (e.g. `curve fitting and `peak shift) can describe the response of glasses in DSC is reviewed, and the degree of enlightenment afforded by these models is discussed. More recently, the technique of temperature-modulated DSC (TMDSC), has attracted considerable attention, and its application to the glass transition of polymers is considered here within the framework of the same models as are used for conventional DSC. In particular, the two techniques of DSC and TMDSC are compared in respect of the quantitative analysis of the data and in the light of the problems of heat transfer.

Measurement of the wax appearance temperatures of crude oils by temperature modulated differential scanning calorimetry

Temperature modulated differential scanning calorimetry (TMDSC) is used for the first time to measure the wax appearance temperature (WAT) of crude oil samples. The commercial implementation of TMDSC chosen for this study is alternating differential scanning calorimetry (ADSC) marketed by Mettler-Toledo. We show that changes in the ADSC signals exhibit excellent correlations with WATs measured using conventional differential scanning calorimetry, DSC. For oil samples having low wax contents, ADSC is a more sensitive technique for identifying the onset of wax crystallisation and, specifically, the phase angle between the heating rate and heat flow modulations is extremely sensitive to this process.

The application of temperature-modulated DSC to the glass transition region: II. Effect of a distribution of relaxation times

Abstract An analysis of temperature-modulated differential scanning calorimetry (TMDSC) in the glass transition region is presented. It extends an earlier and simpler model by introducing a distribution of relaxation times, characterised by a Kohlrausch–Williams–Watts (KWW) stretched exponential parameter β, in addition to the usual kinetic parameters of relaxation, namely the Tool–Narayanaswamy–Moynihan (TNM) non-linearity parameter x and the apparent activation energy Δh∗. The present model describes, more realistically than did its predecessor, all the characteristic features of TMDSC in the glass transition region, and it has been used to examine the effects of the important experimental variables, namely the period of modulation and the underlying cooling rate. It is shown that, for typical experimental conditions in practice, it is likely that there well be an interaction between the vitrification process, due to the underlying cooling rate, and the dynamic glass transition whereby the complex heat capacity C p ∗ shows a sigmoidal decrease in a temperature range dependent on the modulation frequency. Accordingly, care must be exercised in the quantitative evaluation of TMDSC data in the glass transition region, and suggestions are made regarding the optimum procedures in this respect. Also, by comparing the cooling rate and modulation period required to define the same transition temperature for conventional DSC and C p ∗ , respectively, a correspondence between them is obtained which allows the magnitude of temperature fluctuations in Donth’s fluctuation dissipation theorem to be evaluated. Finally, it is shown that β and x have similar effects on conventional DSC cooling curves, but have very different effects on C p ∗ , whereby there is little effect of x but a significant broadening of the transition as β decreases. It is argued that the breadth of the C p ∗ transition therefore provides a measurement of β independent of the value of x, thus resolving a problem that has existed for some years.

Enthalpy relaxation in a partially cured epoxy resin

The enthalpy relaxation of a partially cured (70%) epoxy resin, derived from diglycidyl ether of bisphenol-A cured by methyl-tetrahydrophthalic anhydride with accelerator, has been investigated. The key parameters of the structural relaxation (the apparent activation energy Δh*, the nonlinearity parameter x, and the nonexponentiality parameter β) are compared with those of the fully cured epoxy resin. The aging rates, characterized by the dependences of the enthalpy loss and peak temperature on log(annealing time), are greater in the partially cured epoxy than they are in the fully cured resin at an equivalent aging temperature (Ta = Tg − 20°C). There is a significant reduction in Δh*, from 1100 kJ mol−1 for the fully cured system to 615 kJ mol−1, as the degree of cure is reduced. The parameter x determined by the peak-shift method appears essentially independent of the degree of cure (x = 0.41 ± 0.03 for the partially cured resin compared with 0.42 ± 0.03 obtained previously for the fully cured resin), and does not follow the usually observed correlation of increasing x as Δh* decreases. This invariability of the parameter x seems to indicate that it is determined essentially by the local chemical structure of the backbone chain, and rather little by the supramolecular structure. On the other hand, the estimated nonexponentiality parameter β lies between 0.3 and 0.456, which is significantly lower than in the fully cured epoxy (β ≅ 0.5), indicative of a broadening of the distribution of relaxation times as the degree of cross-linking is reduced. Like the parameter x, this also does not follow the usual correlation with Δh*. These results are discussed in the framework of strong and fragile behavior of glass-forming systems, but it is difficult to reconcile these results in any simple way with the concept of strength and fragility.

Aging of polycarbonate studied by temperature modulated differential scanning calorimetry

Abstract The enthalpy relaxation behaviour of polycarbonate has been studied by alternating differential scanning calorimetry (ADSC). Samples have been annealed at 125°C, about 20°C below their glass transition temperature, for periods up to 2000xa0h, and then scanned in the ADSC using the modulation conditions: heating rate=1xa0Kxa0min −1 ; temperature amplitude=1xa0K; period=1xa0min. The data have been analysed in terms of total, reversing and non-reversing heat flows, and also in terms of complex, in-phase and out-of-phase specific heat capacities and a phase angle. The effect of aging time on each of these parameters is illustrated and compared with the predictions of an earlier theoretical model. It is shown that there is very good agreement between the experimental results and the theoretical predictions, the most important aspects being the following. The total heat flow closely corresponds to conventional DSC in respect of both peak endotherm temperature and enthalpy loss (derived from the area under the peak). In contrast, the non-reversing heat flow peak area does not provide a good measure of the enthalpy loss because the reversing heat flow (and complex specific heat capacity) depends significantly on aging, the transition region becoming much sharper as the aging time increases. Likewise, the phase angle (when appropriately corrected for the problem of heat transfer) also becomes sharper on aging, and the (negative) peak moves towards higher temperatures. The out-of-phase specific heat capacity is calculated using the corrected phase angle, and it is shown that the area under this peak is essentially independent of aging time, confirming another prediction from the earlier theoretical model that this area provides no information about the enthalpy loss that occurs during the aging process.

Studying the Glass Transition by DSC and TMDSC

First, the principal features of the glass transformation process in polymers are reviewed, and then it is shown how they are manifest in conventional DSC, and the quantitative analysis of typical DSC data is discussed in terms of the Tool-Narayanaswamy-Moynihan (TNM) model. Subsequently, the way in which the glass transition is manifest in Temperature Modulated DSC is presented, and the effects of both experimental and material parameters are discussed. In conclusion, the two techniques are compared in terms of the information they provide about the glass transformation process.

An introduction to temperature modulated differential scanning calorimetry (TMDSC): a relatively non-mathematical approach

Abstract The purpose of this paper is a rather general overview of the principles of temperature modulated differential scanning calorimetry (TMDSC). The technique is compared to conventional DSC, and particular attention is paid to whether or not the heat flow in TMDSC may be separated into so-called thermodynamic and kinetic components. It is shown that in general it is not valid to make such a separation, and that in some cases to do so may lead to confusion. The problem of applying TMDSC in transition regions is considered in the light of the need to maintain a quasi-constant structure within any one modulation period, for which a knowledge of the molecular timescale is required. The view presented here is that either this is not normally known “a priori” or it must be deduced from an appropriate kinetic theory, and hence that the technique of TMDSC will always suffer from this limitation.

Addition of a reactive diluent to a catalyzed epoxy‐anhydride system. II. effect on enthalpy relaxation

Enthalpy relaxation in an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) with a reactive diluent cured with methyl-tetrahydrophthalic anhydride (MTHPA) with an accelerator was investigated by differential scanning calorimetry. The reactive diluent (RD) added was an aliphatic diglycidyl ether which was mixed in a proportion of 50 parts by weight (pbw) per 100 parts of DGEBA, with the stoichiometric quantity of MTHPA. The key parameters of the enthalpy relaxation investigated were the nonlinearity parameter, x, the apparent activation energy,Δh*, and the nonexponentiality parameter, β. The results were compared with other data obtained previously in similar epoxy-anhydride systems without an RD but with different degrees of conversion in order to analyze the effects of (a) the introduction of aliphatic chains of the RD in the epoxy structure and (b) a reduction in the crosslink density of the resin.

Interpretation of glass transition phenomena in the light of the strength–fragility concept

The use of a phenomenological model to describe relaxation in the glassy state is reviewed, and it is shown that many important glass transition phenomena may be interpreted in this way. The key parameters of the model (the non-linearity parameter x, the non-exponentiality parameter β, and the apparent activation energy Δh*) are discussed in terms of their influence on these phenomena and, more particularly, on the relationship between relaxation in the non-equilibrium glassy state and the strength/fragility of the corresponding equilibrium melt behaviour. Good correlations between these parameters are shown, on the basis of which one can associate fragile behaviour with a high degree of non-linearity, a wide distribution of relaxation times and a large apparent activation energy. However, strong behaviour, which may be associated with a relatively linear response, a narrow distribution and a smaller apparent activation energy, can be characterized by continuity between melt and glass as the transition region is traversed on cooling.

Structural relaxation in fully cured epoxy resins

Enthalpy relaxation in a fully cured epoxy resin at 80°C has been investigated in two different laboratories, the Universitat Politecnica de Catalunya and Aberdeen University, and using two different instruments (Mettler and Perkin-Elmer, respectively) for differential scanning calorimetry. The same values of activation energy (1100 kJ mol−1) and ΔCp (0.34 J g−1 K−1) were obtained in each laboratory. However, the peak-shift method for the evaluation of the Narayanaswamy parameter, x, yields different values (0.45 from Catalunya and 0.39 from Aberdeen); similar differences are found for the non-exponentiality parameters β (0.3 < β < 0.456 from Catalunya and 0.456 < β < 0.6 from Aberdeen). These discrepancies are tentatively attributed to differing thermal gradients in the two calorimeters. Nevertheless, the values of x appear high when compared with other glasses with similar activation energies. It is suggested that this results from a ‘strengthening’ due to the cross-linked epoxy network structure.