Cone confined rotator model

In the second period, which was ended by review GT after the average perturbation theorem was proved, it became possible to get the Kubo-like expression for the spectral function L(z) (GT, p. 150). This expression is applicable to any axially symmetric potential well. Several collision models were also considered, and the susceptibility was expressed through the same spectral function L(z) (GT, p. 188). The law of motion of the particles should now be determined only by the steady state. So, calculations became much simpler than in the period (1). The best achievements of the period (2) concern the cone-confined rotator model (GT, p. 231), in which the dipoles were assumed to librate in space in an infinitely deep rectangular well, and applications of the theory to nonassociated liquids (GT, p. 329). 

In the third period, which ended in 1999 after the book VIG was published, various fluids had been studied strongly polar nonassociated liquids, liquid water, aqueous solutions of electrolytes, and a solution of a nonelectrolyte (dimethyl sulfoxide). Dielectric behavior of water bound by proteins was also studied. The latter studies concern hemoglobin in aqueous solution and humidified collagen, which could also serve as a model of human skin. In these investigations a simplified but effective approach was used, in which the susceptibility % (m) of a complex system was represented as a superposition of the contributions due to several quasi-independent subensembles of molecules moving in different potential wells (VIG, p. 210). (The same approximation is used also in this chapter.) On the basis of a small-amplitude libration approximation used in terms of the cone-confined rotator model (GT, p. 238), the hybrid model was suggested in Refs. 32-34 and in VIG, p. 305. This model was successfully employed in most of our interpretations of the experimental results. Many citations of our works appeared in the literature. 

Let us consider a small (3 approximation in terms of the cone confined rotator (CCR) model (see VIG, pp. 293-295).16 In this approximation two largest terms (with n = 0 and n 1) are equal. Based on this result, we assume that at small (3 these terms are close at any model potential. Then we set x to be approximately equal to the median frequency ... 

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