Impulsive stimulated scatttering signal in supercooled liquids with Debye or Havriliak-Negami relaxation of the specific heat capacity and thermal expansion coefficient

A generalized physical model is introduced to describe the impulsive stimulated scattering (ISS) response of relaxing systems to photothermal excitation in a periodical grating geometry. The proposed approach starts from Debye and Havriliak-Negami expressions for both the frequency-dependent heat capacity, C({\omega}), and thermal expansion coefficient, {\gamma}({\omega}). Simulations are carried out on glycerol to test and compare the developed models with the existing semi-empirical model [1]. Debye behavior of the specific heat capacity is shown to be compatible with a two-temperature scenario, in which, in addition to the classical, experimentally observable temperature that characterizes the distribution of the system over vibrational energy states, a second temperature characterizes the state of the configurational energy landscape. The models here developed have been applied for the interpretation of the experimental ISS signals of supercooled glycerol, illustrating simultaneous and separate assessment of C({\omega}) and {\gamma}({\omega}) up to sub-100 MHz from thermoelastic transients.