The effect of four torques on dielectric behavior

In his notable book 'Polar Molecules' published in 1929, Debye showed that for polar dielectric liquids, dispersion and absorption could be described by the operation of a relaxation mechanism characterized by a frequency-dependent complex permittivity. On the basis of certain assumptions, he developed an expression for that dependence. Among those assumptions was that the polar molecules were taken to have no inertia, and in consequence they can not have any net torque acting on any of them at any time. The polar molecules were taken to be present in a very dilute solution of a polar liquid in a non-polar solvent. Therefore dipole-dipole interactions were ignored, and the driving torque on any dipole was taken to be caused by the applied field alone. That torque was taken to be counterbalanced at all times by a frictional torque proportional to the instantaneous angular velocity of each particular polar molecule. This retarding torque arises from an inner friction, and is not the same as, but is in some way related to, the macroscopic viscosity of the liquid. However, the action of the frictional torque in cancelling the applied torque does not account for energy storage in the liquid. Debye establishes the necessary phase relationships by the postulate that the dipole moment of the polar molecules is complex. While this postulate is quite permissible, it does not give an insight into the physical mechanism involved. In addition to the two torques taken into account by Debye, in a paper published in 2005 Calderwood proposed that there is a third torque acting on the dipoles which is responsible for the electrostatic energy stored when a specimen of a polar dielectric liquid is charged, and which is released on specimen discharge. A detailed account of the behavior of this torque and its significance is given in that paper. One of the features of the third torque is that, in contrast to the friction torque which is dissipative, it is conservative. That is to say, it is spring-like in nature. It is that characteristic which enables the specimen to store and release energy. The presence of spring-like elements in any mechanical or electrical system can also significantly modify its behavior. In this paper a criterion is derived which indicates whether or not significant features of dielectric behavior might be attributed to the third torque. The treatment of Debye did not take the inertial effect of the polar molecules into account. However, these molecules do possess some inertia and so a fourth torque is necessarily associated with any acceleration to which they may be subjected. Account is taken of this in the present analysis by the introduction of the fourth torque. This treatment, like that of Debye, does not take account of dipole-dipole interaction. It is therefore only applicable to dilute solutions of polar molecules in a non-polar solvent.