The behavior of the Debye rotator

When an electric field is created in a liquid containing polar molecules, the resulting buildup of polarization is hindered by the chaotic thermal motion of the molecules of the environment of the dipoles. The dipoles are represented as being embedded in hard spheres, sometimes called Debye rotators, and these spheres are subjected to a frictional torque somewhat analogous to that which would be exerted on a rotating sphere in a viscous liquid, but which is in fact caused by collisions between the rotator and other molecules, and on that account is named 'inner friction'. In addition, the environmental thermal energy greatly reduces the response of the rotators to the applied field, so that only a very slight degree of order is imposed on the random dipole orientation. This effect is often taken into account by the inclusion of a Brownian motion term in the dynamic equation describing the motion of the rotators. The system can be seen as one consisting of orderly processes, namely the field driven and friction retarded motion of the rotators, against a background of the disorderly thermal behavior of the molecules. The relative importance of these factors may vary from system to system, and in principle it is of interest to know what would be the outcome of the operation of the orderly processes alone. That has been examined in what follows, and while it turns out that what is predicted, though as expected is not in accordance with predictions when a Brownian motion term is included, nevertheless has more resemblance to them than might have been anticipated. However, an interesting difference is that the present analysis leads to the expectation of a distribution of relaxation times.