Isothermal dielectric relaxation of a model system of dipoles

The dielectric relaxation is examined of a set of molecules with dipoles that can be in one of two orientations and which can be at random in one of two states. These states are called slow or fast according to the rate at which the molecules change their orientation, and there is a local interaction between the molecules such that when one rotates it can change the state of its neighboring molecules from slow to fast or vice versa. The system was studied mainly in a mean field approximation, and also by computer simulations. The results show that the non-exponential decay of the system's dielectric response function is due to the fact that initially the decay of the polarization is mainly associated with dipoles on molecules in the fast state, while in the later stages it is associated mainly with those on molecules transferred from slow to fast states. This could be a quite general mechanism for non-exponential dielectric relaxation. A comparison between the relaxation of systems for which the populations of the two types of state was and was not initially in equilibrium shows that a time dependent transition rate is not a very useful concept.