The rotational Brownian motion of a linear molecule and its application to the theory of Kerr effect relaxation

Abstract

Exact expressions in the low-field limit for the Laplace transform of the Kerr effect response (KER), including inertial effects, of an assembly of needlelike dipolar anisotropically polarizable molecules are obtained using the Fokker–Planck–Kramers equation for the probability density function in configuration-angular velocity space. The spatial part of the solution of this equation is expanded as a series of associated Legendre functions. The coefficients of Legendre functions of the first and second order may be solved separately, using an expansion in Laguerre polynomials. The coefficients of the Legendre polynomials of order 1 and 2 are evaluated to yield the dielectric and KER after-effect solutions. The dielectric response is in full agreement with the result of Sack. The investigation shows clearly that the KER cannot be obtained by any simple transformation of the dielectric response unlike rotation in two dimensions.