Depolarization exponent

The two equations demonstrate the key function of the depolarization exponent its dependence on orientation creates the anisotropy. 

Nonspherical inclusions are used for modelling elongated pores or fractures mostly with the basic shape of an ellipsoid. The ellipsoid as shape requires the implementation of depolarization exponents La,Lh,Lc along the principal directions a,b,c of the elhpsoid with the condition La + Lf, + Lc =. ... 

Thus, for application, an estimate of depolarization exponents is necessary. Sen et al. (1981) recommends the following approximation for plate-like... 

In the literature (e.g. Berryman, 1995), references are given for the calculation of the depolarization exponent. There are some extreme values and approximations ... 

The depolarization exponent of an inclusion depends on the aspect ratio and is related to the direction of the field with respect to the axis direction of the ellipsoid. Therefore, different depolarization factors for different directions lead to anisotropy of conductivity and conductivity as a tensor. 

Viscosity measurements of solutions of low-molecular weight PBO in chlorosulfonic acid and other solvents yielded a Mark-Houwink exponent of 1.85, which is very close to the value expected for a rodlike polymer [45]. Depolarized dynamic light scattering of PBT solutions in chlorosulfonic acid resulted in a persistence length of 64 nm, which is one of the highest persistence lengths known when compared with those of other rigid-rod polymers [58]. 

The concentration dependence of x is consistently found to be weak for c < 0.3 w/w(6,7,27). Indeed, Heatley concluded that x from NMR had almost no c-dependence for c below 100-150 g/l(29). At c > 0.3 w/w, x increases much more markedly with c. The most extensive set of measurements, due to Johnson, et a/. (27), shows a temperature-dependent stretched-exponential concentration dependence, the stretching exponent v being markedly larger for a small-molecule model label than for the label at chain center. Viovy and Monnerie, using unlabeled matrix polymers with very different molecular weights found that t(c) does not show a transition near the nominal chain overlap concentration c, i.e., motions leading to fluorescence depolarization are not discontinuously perturbed by an onset of chain overlap(6). 

Here, / is the intensity and n is the Bose-Einstein factor. The values d D = 0.53, d = 1.3, and a = 1 lead to the observed exponent - 0.36.25 That the bending fracton dimension is the proper one to use in (4) is consistent with the fact that it is the bending modes that depolarize the scattered light. 

---