S. Montserrat

A kinetic analysis of the curing reaction of an epoxy resin

Abstract The kinetics of a curing reaction under non-isothermal conditions using DSC is discussed. A simple, consistent method of kinetic analysis was applied. The method allows the correct determination of the most suitable kinetic model and the calculation of kinetic parameters. This method was used to study the kinetics of an epoxy resin based on diglycidyl ether of bisphenol A, cured by methyl tetrahydrophthalic anhydride with an accelerator. An activation energy of 73kJmol−1 was calculated and the autocatalytic kinetic model (Sestak-Berggren equation) was found to be the most covenient description of the studied curing process. The isothermal curves calculated for the kinetic parameters determined in non-isothermal conditions are in good agreement with experimental curves when the curing temperature Tc is above the maximum glass-transition temperature of the system, Tg∞ = 109°C. The influence of the vitrification phenomenon is discussed when Tc is below Tg∞. The temperature-time-transformation diagram of the studied epoxy system has been constructed and is discussed.

Thermal degradation kinetics of epoxy–anhydride resins: I.: Influence of a silica filler

Abstract Thermal degradation kinetics of epoxy–anhydride resins has been studied by thermogravimetry in both, isothermal and non-isothermal conditions. It was found that the kinetics of thermal degradation can be fairly described by a simple reaction-order model. The calculated kinetic parameters, Ea and n, are considerably lower for pure resin than for resin containing silica filler. Therefore, the addition of silica filler increases thermal degradation rate of the resin. A difference was also observed between the set of kinetic parameters obtained by kinetic analysis of isothermal and non-isothermal data, particularly with respect to the activation energy.

Influence of the accelerator concentration on the curing reaction of an epoxy-anhydride system

The effect of accelerator content on the curing reaction of an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) with methyl-tetrahydrophthalic anhydride was studied by DSC. The uncatalysed curing occurs at high temperature (between 190 and 310°C) with thermal degradation. The addition of accelerator which is a tertiary amine catalyst agent, namely dimethylbenzylamine (DMBA), causes two exothermic peaks. The cure extent and the position of the peaks depend on the accelerator content. The first peak, which is sharp and well defined, appears between 80 and 200°C and may be attributed to the catalysed curing. The second peak, which is broad, only appears for low accelerator content (lower than 1 pbw) in the zone of uncatalysed curing (between 200 and 320°C), and may be attributed to the uncatalysed curing. The activation energy corresponding to the first exothermic peak in the catalysed curing, calculated by the Kissinger method, decreases with the accelerator content. Kinetic analysis performed by Maleks method shows that the autocatalytic model (two-parameter Sestak-Berggren equation) can describe satisfactorily the kinetics of the catalysed and uncatalysed curing. In the catalysed system, the parameters m and n increase slightly with the accelerator content, and the pre-exponential factor, ln A, undergoes a slight decrease. The maximum Tg of the fully cured epoxy obtained by isothermal curing at 110°C in catalysed systems shows no significant changes. These results mean that the differences observed in the kinetics of curing between catalysed systems do not imply significant changes in the structure of the network of the epoxy resin.

Addition of a reactive diluent to a catalyzed epoxy-anhydride system. I. Influence on the cure kinetics

The effect of a reactive diluent (RD) on the kinetics of the curing of an epoxy resin, based on diglycidyl ether of bisphenol A (DGEBA), with a carboxylic anhvdride derived from methyl-tetrahydrophthalic anhydride (MTHPA) catalyzed by a tertiary amine has been studied. The reactive diluent was a low-viscosity aliphatic diglycidyl ether, and the compositions per 100 parts by weight (pbw) of DGEBA were 10, 30, and 50 pbw of RD with the stoichiometric quantity of MTHPA and 1 pbw of catalyst. The curing kinetics was monitored by differential scanning calorimetry (DSC), and the kinetic parameters were determined from the nonisothermal DSC curves by the method described by Malek. The kinetic analysis suggests that the two-parameter autocatalytic model is the more appropriate to describe the kinetics of the curing reaction of this epoxy-anhydride system. The kinetic parameters thus derived satisfactorily simulate both the nonisothermal DSC curves and the isothermal conversion-time plots. Increasing the RD content leads to a small increase in both the nonisothermal and the isothermal heats of curing and has a slight effect on the kinetic parameters E, ln A, m, and n, and, consequently, on the overall reactivity of the system. On the other hand, the increase of the RD content significantly affects the structure of the crosslinked epoxy. It is confirmed that the introduction of aliphatic chains in the structure of the epoxy increases the mobility of the segmental chains in the glass transition region. The consequence of this chemical modification is a decrease of the glass transition temperature, Tg.

Isothermal curing of an epoxy resin by alternating differential scanning calorimetry

Abstract The quasi-isothermal curing of a diepoxide resin with a triamine of polyoxypropylene was studied by alternating differential scanning calorimetry (ADSC), which is a temperature modulated DSC technique. The complex heat capacity measurements allows to analyse the vitrification process at curing temperatures (Tc) below the maximum glass transition of the fully cured epoxy (Tg∞=85.8°C). Initially, the modulus of the complex heat capacity, |C ∗ p | , increases until a maximum (conversion between 0.42 and 0.56) and then decreases. This step is followed by an abrupt decay of |C ∗ p | , due to the vitrification of the system, which allows the determination of the vitrification time. This value agrees well with that determined by the partial curing method. The phase angle and out-of-phase heat capacity show an asymmetric wide peak during the vitrification process. The change in |C ∗ p | at vitrification decreases with the increase of Tc becoming zero at temperature Tg∞. This epoxy-triamine system shows a delay of the vitrification process respect to other model epoxy systems probably due to the presence of polyoxypropylene chains in the network. The decay of |C ∗ p | during vitrification may be normalised between unity and zero by defining a mobility factor. This mobility factor has been used to simulate the reaction rate during the stage where the reaction is controlled by diffusion. The observed reaction rate is simulated by the product of the kinetic reaction rate, determined by the autocatalytic model, and the mobility factor.

The application of modulated differential scanning calorimetry to the glass transition of polymers. I. A single-parameter theoretical model and its predictions

Abstract A single relaxation time model describing the kinetics of enthalpy relaxation has been applied to modulated differential scanning calorimetry (MDSC) in the glass transition region. The model is able to describe semi-quantitatively all the characteristic features of MDSC: the average or total heat capacity which is very similar to the conventional DSC response at the same average heating rate; a phase angle between heating rate and heat flow modulations which passes through a maximum in the transition region; a “loss heat capacity” which shows a similar behaviour to the phase angle; and a “storage heat capacity” which shows a sigmoidal change from glassy to liquid-like C p . The model is used to predict the effects of the experimental and material parameters. Of the experimental parameters, the most important are the average heating rate and the period. The former affects significantly only the total heat capacity, and in the same way as in conventional DSC. The latter affects significantly only the storage heat capacity, causing the sigmoidal transition to shift to higher temperatures as the period is reduced. The amplitude of temperature modulation appears to have no significant effect within a reasonable range. These predictions, and those for the effects of some material parameters, namely the initial enthalpic state and the non-linearity parameter, are discussed in the light of published experimental data.

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.

The application of modulated differential scanning calorimetry to the glass transition

The modulated differential scanning calorimetry (MDSC) technique superimposes upon the conventional DSC heating rate a sinusoidally varying modulation. The result of this modulation of the heating rate is a periodically varying heat flow, which can be analysed in various ways. In particular, MDSC yields two components (‘reversing’ and ‘non reversing’) of the heat flow, and a phase angle. These each show a characteristic behaviour in the glass transition region, but their interpretation has hitherto been unclear. The present work clarifies this situation by a theoretical analysis of the technique of MDSC, which introduces a kinetic response of the glass in the transition region. This analysis is able to describe all the usual features observed by MDSC in the glass transition region. In addition, the model is also able to predict the effects of the modulation variables, and some of these are discussed briefly.

A theoretical model of temperature-modulated differential scanning calorimetry in the glass transition region

Abstract A new analysis of an earlier theoretical model of the enthalpic response of glasses to temperature-modulated differential scanning calorimetry in the glass transition region has been made. This yields quasi-continuous values of the complex specific heat capacity, C∗ p , and its in-phase and out-of-phase components, C′p and C″p, respectively, as well as those of the phase angle,f. This analysis has been used to predict the effects of three parameters: the period, the amount of annealing, and the non-linearity parameter. Increasing the period reduces the mid-point transition temperature for C′p in a quantitatively similar way to the effect of cooling rate on Tg, from which a relationship between period and cooling rate has been derived and compared with a fluctuation model for the glass transition. The amount of annealing is shown to have no effect on the area under the C″p peak, confirming that this out-of-phase component does not provide information about the enthalpic state of the glass. Finally, the non-linearity parameter has opposite effects on the cooling and heating stages of intrinsic thermal cycles, with reducing x causing the C″p peak to broaden on cooling and to sharpen on heating. For these same intrinsic cycles, the area difference under the C″p peaks on heating and cooling may be either positive or negative, depending on the value of x. This last observation may have implications for the interpretation of C″p in terms of entropy changes occurring during the modulation periods.