Effects of sinusoidal temperature and pressure modulation on the structural relaxation of amorphous solids

Because molecular diffusivity in liquids and glasses varies as the inverse exponential of the reciprocal of the temperature, T, a sinusoidal change in T would change diffusivity unequally at the extremes of a T-cycle, and this would have a net effect on its diffusion-controlled structural relaxation towards their equilibrium states. A sinusoidal change in pressure P would have a similar effect. To elaborate on the expected effects of the T- and P-modulation on the spontaneous approach of an amorphous solid towards its equilibrium state, formalisms have been developed for two cases: (i) when an amorphous solid's T, or P, is sinusoidally modulated about its fixed values; (ii) when the solid is heated at a constant rate and its T modulated about the increasing value of T. Similar calculations for the two cases have been done for conditions without T-modulation. The structural relaxation features computed for the T-modulated conditions show that the time- and T-dependent relaxation function, fictive temperature and normalized specific heat in the above-given two cases are quite different from those for the unmodulated conditions, and that additional features in the specific heat appear on sinusoidal modulation for different phase conditions. This also affects the features of glass-softening endotherm on modulation. Sinusoidal T- or P-modulation leads to the determination of the second harmonic terms, which in turn may be used for determining the T-dependence of the diffusion process.