The theory of dielectric relaxation of an assembly of molecules containing rotating polar groups, originally developed by Budo, is extended to include inertial effects. It is shown that the inclusion of these effects gives rise to a resonance absorption in the far infrared band of frequencies. To obtain analytical formulae for the polarizability and the absorption coefficient the system is first treated in the harmonic approximation. Nonlinear effects are then taken account of by using the averaging method of Krylov and Bogoliubov. Inclusion of these effects indicates that the frequency of maximum far-infrared power absorption should decrease as the temperature increases in qualitative agreement with experimental findings. Also the nonlinear effects cause the angularvelocity correlation functions to become less oscillatory as temperature is increased. The present treatment gives rise to equations that in the harmonic approximation are formally similar to those of the itinerant oscillator model.

On the Role of Inertial Effects and Dipole-Dipole Coupling in the Theory of the Debye and Far-Infrared Absorption of Polar Fluids

The Effective Eigenvalue Method and Its Application to Stochastic Problems in Conjunction with the Nonlinear Langevin Equation

Dielectric relaxation and molecular motion in polar fluids: Dynamic and kinetic approaches

Birefringence and dielectric relaxation in strong electric fields

The relaxational dynamics of a planar rotator in anM-fold cosine potential subject to a random torque is investigated in detail. For the case of a periodic potential with large barrier height, the numerical results of the relaxation dynamics are in complete agreement with an approximate analytical solution. The latter, is derived on assuming a harmonic potential at the bottom of the potential minima and a large time-scale separation between the short-time libration inside each potential minima and a long-time hopping phenomenon over the potential barriers. ForM≧2, the hopping phenomenon is found to be the dominant feature of the orientational autocorrelation function. The average hopping time is explained satisfactorily in terms of the Kramers activation rate theory. In particular a complete agreement is found between the numerical results of the escape rate and those obtained from the modified Kramers' predictions valid for low friction coefficient. The cosine model is applied to the study of dielectric spectroscopy. The particle mobility and the complex permitivity, of a dielectric material are calculated by numerical solutions for rotational velocity and orientational auto-correlation functions, respectively. The main features of the experimental observables are determined analytically and compared to the corresponding numerical results. The applicability of the plane rotator model to dielectric spectroscopy is also discussed.

Brownian motion in a periodic potential: Application to dielectric relaxation

The Kramers equation for one dimensional motion of brownian particles in a multiwell cosine potential is solved by a series expansion method followed by numerical solution of the resulting set of linear differential equations to obtain angular velocity and orientational autocorrelation functions (a.c.f.s) in the Laplace domain. The former, inverted by analytic function fitting, take the correct forms at zero and large (harmonic limit) potentials and intermediate behaviours compare well with those found using other numerical techniques. Solutions evaluated using delta function initial conditions are of interest in the study of pendula or of chemical dissociation, while solutions evaluated under equilibrium initial conditions and with imaginary Laplace variable iw are important in dielectric spectroscopy. Application of the theory both to superionic conductivity and dielectric-far-I.R. absorption of rotator phases and liquids is demonstrated.

C.J. Reid

Papers

Numerical solutions for brownian motion of particles in a periodic potential