Simulation of a glass transition in a hot-wire experiment using time-dependent heat capacity

The transient hot-wire method is used for simultaneous measurements of the thermal conductivity lambda and the heat capacity per unit volume pc(p) and yields a peak in lambda and a dip in pc(p) near a glass transition. Through simulations, it is shown that these anomalous results arise due to a time dependence in c(p), which is described by a fractional exponential function: c(p)(t) = c(p)(liquid) + [c(p)(glass) - c(p)(liquid)] e(-(t/tau)beta), where tau is the heat capacity relaxation time and beta is a sample dependent parameter (0 < beta less than or equal to 1). By a comparison with experimental data for cyclohexanol and glycerol, it is demonstrated that this model can be used to reproduce the peak and the dip as well as the temperature at which these occur. In addition, it is shown that the maximum in lambda occurs at tau = 0.3 s, whereas tau of the minimum in pc(p) is dependent on beta and moves from 0.4 to 1 s for a change in beta from 1 to 0.5. The difference in tau between the peak and the dip is in agreement with the experimental results. It is concluded that the anomalies reveal glass forming characteristics such as a rough classification in terms of strong and fragile glass formers.