Anisotropy Terms Links

An estimate of the number of monomer units per equivalent random link can be obtained by dividing the value of Aa calculated from the stress-optical coefficient by the anisotropy of the polarisability of the monomer unit calculated from bond polarisabilities. This number can more interestingly be expressed in terms of the number of single bonds in the equivalent random link and is found to be about 5 for natural rubber, about 10 for gutta percha and about 18 for polyethylene. (For the last two the values are extrapolated from measurements at elevated temperature.) The number for polyethylene is considerably higher than the value of 3 suggested by the assumption of totally free rotation around the backbone bonds (see section 3.3.3 and problem 3.7). 

The A, B and C terms are related to flow anisotropy, molecular longitudinal diffusion and mass transfer processes, respectively. The theoretical support for the Knox equation was derived by Horvath [12]. The A term cannot be expressed simply. The theoretical treatment links A to structural parameters of the column packing, porosity, pore volume, pore diameter and tortuosity [12]. A is related to the flow pattern and the general band spreading due to "eddy" diffusion [13]. The B term (longitudinal molecular diffusion) was written as [13] ... 

While the detailed analysis of the Kerr profiles in pure liquids leads to the conclusion that four distinct responses underlie the overall rise and decay of the field-induced polarization anisotropy A n(t), naturally in a real liquid these responses are coupled together. For clarity of discussion we will continue to describe them separately, since the timescale separation assumption in Eq. (3) proved quite valid. Summarized as follows in terms of r (t), which are associated with the instantaneous electronic and noninstantaneous, field-driven nuclear responses linked to intra- and intermolecular motions, the responses are labeled r (electronic) and r2> r, r (nuclear). The underlying assumption of a harmonic potential v j, and a continuum fluid [g(r) = 1] might clearly lead to some over simplifications but if molecules reside at or near the bottom of the potential well, the situation is not unreasonable. The results are very instructive for modeling short-time behavior for molecular solvents at room temperature, which is the next, vastly more complex step (see references on simulations and the next chapter). 

It is shown that the- angular dependence of the scattered light intensity can give information about correlations in density and orientation and at the same time permits conclusions about the type of orientational order present in the system under investigation. Absolute measurements, however, can add to these a quantitative estimation of the mean square of the polarizability fluctuation, which can be connected with phase separation and inhomogeneous cross-linking and the absolute value of the anisotropy which may be interpreted in terms of the kind of order and the relative parallelity of the chains on a microscale. 

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