Influence of inertial and memory friction effects on the rotational Brownian motion of noninteracting particles : application to the dielectric relaxation response and comparison with previous theories

Abstract

Abstract A theoretical approach of free rotational Brownian motion of noninteracting particles compelled to rotate in two dimensions (disk model) and experiencing exponentially varying memory friction is presented both in time and frequency domains. This leads to obtain exact analytic expressions for the orientational correlation functions appropriate to dielectric relaxation. It is found that three regimes are possible for the angular velocity depending on the ratio β / γ, where β is the reciprocal of the frictional time and γ is the reciprocal of the charateristic time of the heat bath. The results so obtained are discussed with the help of plots giving the time evolution of the correlation function and allowing one to show only small differences with the small collision model of Sack [Proc.Phys Soc.B70, 402 (1957)]. These differences appear to be much more pronounced when the problem is analyzed in frequency as illustrated in Cole-Cole plots for the dynamic susceptibility. A formal connection with Madden and Kivelson's model is also proposed.