Forced rotational diffusion of linear molecules. Nonlinear aspects

Abstract

The decay of fluctuations in orientation of a system of linear molecules interacting via electrostatic forces is determined by solution of the forced diffusion equation in its nonlinear form. The results consist of series expansions of the time dependent coefficients of the expansion of the distribution function for orientation in spherical harmonics. Separate expansions in terms of the scale of fluctuations and in terms of the magnitude of the dipole–dipole forces are given. The nonlinearity causes the appearance of terms in the expression for the fluctuation decays which evolve on a time scale shorter than that of the free diffusion.

Magnetic relaxation of a system of superparamagnetic particles weakly coupled by dipole-dipole interactions

“…First, we notice an apparent difference between the recurrence relations derived by Warchol and Vaughan [19] for electric dipoles and ours, Eq. ( 47) concerning the sign of the interaction term.…”

“…Then he took the zero wave-vector limit of the resulting equation in order to obtain the relevant correlation functions for the calculation of the dielectric constant of the dipolar assembly. This model in its nonlinear version has been also considered by Warchol and Vaughan [19].…”

“…now negative, and for identical electric dipoles of magnitude m, Warchol and Vaughan[19], allowing one in particular to reproduce Berne's result for the dipole autocorrelation function pertaining to dielectric relaxation of dipolar molecules. Now, from Eq.…”

Nonlinear response of a dipolar system with rotational diffusion to an oscillating field

“…The distribution function will have cylindrical symmetry. Quite generally it can be assumed to satisfy the equation [27,28] ∂…”