Use of the memory function to simulate the Debye and Poley absorptions in liquids

Abstract

A single, simple equation is derived to describe the molecular rotational processes giving rise to the microwave and far infrared absorption bands of dipolar molecules in the liquid phase. The absorption spectrum over 3 decades of frequency is deduced by approximating the associated orientational correlation function with a hierarchy of response functions (or memory functions). These and the correlation function form a set of integro-differential equations called the Mori series. By truncating this at a certain level, with an empirical function such as a single exponential of correlation time 1/γ, a spectrum can be calculated which contains equilibrium averages proportional to the intermolecular mean square torque, 〈o(v)²〉, its derivative 〈o(v)²〉, etc., depending on the level at which the Mori series is truncated. The formalism is tested with the liquids CHF₃, CClF₃, CBrF₃ HCCCH₃ and the nematogen MBBA, a series chosen to cover the extremes of molecular isotropy and anisotropy.