Inertial effects in the theory of dielectric and Kerr effect relaxation of an assembly of non-interacting polar molecules in strong alternating fields. II. The effect of higher-order terms in the distribution function

Abstract

Formulae for the dielectric and Kerr effect responses for any size of the n × n matrix in the perturbation solution of the Kramers equation described in paper I of this series are given. The solution is carried out explicitly for n = 2 and n = 3 for the linear dielectric response and for n = 2, 3 and 4 for the Kerr effect response of an assembly of dipoles having permanent moments only. This is a non-linear response. It is found that for small inertial effects the linear dielectric response and also the Kerr effect response for induced dipoles only (which is a linear response as far as solving the Kramers equation is concerned) is adequately described by the truncation n = 2. This corresponds to the use of a modified Smoluchowski equation. For the Kerr effect response for permanent dipoles it is shown from the n = 3 and n = 4 results that the n = 2 result - corresponding to the use of a modified Smoluchowski equation - does not provide an adequate description of the behaviour of the system. An explanation for this is sought in the work of Wilemski, Titulaer, Stratonovitch, Skinner and Wolynes.