Characteristics of MTDSC Results for Glass Transitions

From a simple model [31] of the glass transition, it is possible to derive approximate analjdical expressions that model the response to the modulation at the glass transition. (See the discussion in section 4.4). Viz 

The is given by relating the period of oscillation to the time-scale associated with the Arrhenius relationship, viz 

h and n are all fitted parameters that change with the degree of annealing (see Fig. 17). 

Equation (44) is an ad-hoc model that is used here for illustrative purposes because it is often useful to think of the glass transition as a combination of a step change in heat capacity with an additional peak that increases in size with increasing enthalpy loss. This is illustrated in Fig. 17. However, it must be stressed that at higher levels of annealing this model cannot be applied. There is no simple analytical expression that can be used and one is forced to use numerical solutions to models such as that given in equation 94. would normally show an Arrhenius dependence on cooling rate  

These must of course be obtained from two separate experiments as these signals can never give the same Tg in a single experiment. One way of looking at this is to think in terms of the time taken to traverse the transition as (with suitable weighting) a measure of the time-scale of the linear cooling rate measurement. This then is related to the period that gives a measure of the time-scale of the cyclic measurement. Thus, fi and co can be related by 

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