Enthalpic relaxation

On heating a polymer which has been annealed into a low enthalpic state a small peak may appear almost like an overshoot, referred to as an enthalpic relaxation event. If heated very slowly this peak may not appear and a true value of Tg is then obtained, but at normal 

Enthalpic relaxation behaviour can be formalised in the TNM (Tool Narayanaswamy and Moynihan) description of ageing [9]. 

Where x and p are the non-linearity and non-exponential parameters respectively, A is the pre-exponential factor, A H is the activation enthalpy, tq is the time constant and 2f is the fictive temperature. The effects of changes in some of these parameters on the overshoot in heat capacity can be seen in Table 1.2. 

Moynihan gives an excellent description of the principles behind the TNM model. While the approach may at first appear complex, the behaviour of these equations is actually 

Effect on trace Position Position and sensitivity Peak development Transition width Compression 

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LeBoeuf, E. J., and Weber, W. J., Jr. (2000a). Macromolecular characteristics of natural organic matter. 1. Insights from glass transition and enthalpic relaxation behavior. Environ. Sci. Technol. 34(17), 3623-3631. 

Fig. 4 (A) DSC scan of the glass transition temperature of a miscible blend of a MK-0591 with 10% PVP, showing the onset, midpoint, and offset glass transition temperatures. (B) DSC scan of the glass transition of sucrose with the enthalpic relaxation endotherm and enthalpy (AHr). (From Ref...

This time-dependent increase in the value of the enthalpic relaxation peak may in itself be used to assess the relaxation time of the system in question this is discussed in more detail in Chapter 3. 

Jenkins and Hay [205] discussed kinetic modeling of the glass transition and of enthalpic relaxation resulting from physical aging, as observed by differential scanning calorimetry. 

Enthalpy relaxation studies have also been used to assess the aging of polyether ether ketone blends with polyetherimide, PEEJC/PEl = 50/50 [Hay, 1992]. The preparation of the blend produced an amorphous system with Tg 215°C, but crystallization of the PEEK occurred after raising the temperature above Tg. Enthalpic relaxation could only be observed in the temperature range Tg to (Tg - 50) and no aging could be detected at temperatures below 150°C (Table 14.15). The system was analyzed using the KWW Eq 14.7 that yielded values of P = 0.4, intermediate between those of the component polymers. 

Figure 11 Contributions (not drawn to scale) to the total measured glass transition and ice-melting endotherm for a frozen aqueous solution crosses represent contribution from the heat of dilution of the supersaturated solution, circles denote the enthalpic relaxation contribution and the broken line is the glass transition. The drawn out curve represents the measured overall heat flow, and the area under that scan corresponds to the total enthalpy change.

FIGURE 12.7 Illustration of thermal history used in enthalpic relaxation experiments via an enthalpy vs. temperature plot. (Adapted from Cowie, J.M.G. and Ferguson, R., Macromolecules, 22, 2307, 1989.)... 

Mohamed, A.A., Finkenstadt, V.L., Palmquist, D.E. and Rayas-Duarte, P. (2009) Thermal properties of extmded injection-molded poly(lactic acid) and milkweed composites Degradation kinetics and enthalpic relaxation. Journal of Applied Polymer Science, 111, 175-184. 

Calorimetry has been one of the most commonly used techniques to follow the enthalpic relaxation during aging. Measurements are readily carried out at temperatures below Tg using a differential scanning calorimeter (DSC), a convenient and widely available instrument. 

A schematic representation of a creep experiment is given in Fig. 13.11. Similar to enthalpic relaxation measurements, in a creep test the sample is quenched from above Tg to the annealing temperature T. A series of short (typically less than 10 % of the aging time ta) load-unload tests are performed. As shown in Fig. 13.11, the applied stress, a, is constant and the time-dependent response, the strain, is measured following both load and unload steps. Because times fe during which creep response is measured are kept deliberately short, the creep response gives a snapshot of the viscoelastic properties of the material at a particular aging time. 

PLA PEG 1000 365 RT 29.4 Tg increase, small enthalpic relaxation peak, phase separation 92... 

PLA-C30B-3% PEG 1000 365 RT 33.5 Tg increase, enthalpic relaxation, phase separation, tactoid clay ... 

In Eq. 2.17, the enthalpic relaxation, AT/reiax, is related to the relaxation function (p and the maximal theoretical enthalpic relaxation. Samples are aged for various lengths of time and is obtained for various time points. 

Amanuel, S., Gaudette, A.N., Stemstein, S.S. Enthalpic relaxation of silica-polyvinyl acetate nanocomposites. J. Polym. Sci. B Polym. Phys. 46, 2733 (2008)... 

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