Double-quantum light scattering by a system of molecules is discussed in this paper. Expressions have been obtained for the scattered light intensity considering both the coherent and incoherent contributions. In that coherent contributions are also considered in this treatment, it goes beyond the scope of previous studies. It is shown that, for molecules of low symmetry, elliptically polarized light must be used in order to determine five independent quadratic forms in the 18 symmetric components (βijk+βikj). According to the present results, the apparent discrepancy between the observed value of ⅓ for the depolarization ratio for CCl4 and the value to be expected from theory may be due to the fact that the coherent contribution had been neglected in previous theoretical considerations. In general, orientational correlation is essential if there is to be appreciable contribution from coherent scattering. For macromolecules, this constitutes a major difference between single- and double-quantum scattering, and additional information may be expected if the latter is investigated experimentally.
The present work is a continuation of a general study of the effect of pressure on gas and vapor permeation through nonporous polymeric membranes. Permeability coefficients have been measured for 1,1‐difluoroethylene (C2H2F2) and fluoroform (CHF3) in polyethylene at penetrant pressures up to 35 atm and at temperatures between ‐18 and 70°C. The permeability coefficient P̄ for the 1,1‐difluoroethylene—polyethylene system was found to increase with increasing pressure differential Δp across the membrane. Isothermal plots of log ΔP versus Δp are generally linear and can be represented by empirical relations of the form ΔP = P(0)exp{m Δp}, where P(0) and m are constants. The slope m of these isotherms decreases with increasing temperature. Plots of log P̄ versus Δp for the fluoroform—polyethylene system are also linear, but exhibit negative slopes, i.e., P̄ decreases with increasing Δp. An extension of Fujita's “free volume” theory of diffusion in polymers shows that the dependence of P̄ on pressure reflects how the free volume of the polymer is affected by this pressure. An increase in the penetrant pressure may result in two opposing effects: (a) the concentration of the penetrant dissolved in the membrane is increased, thereby increasing the free volume, and (b) the hydrostatic pressure on the membrane is also increased, which causes a decrease in the free volume. If the overall effect is an increase in the free volume of the polymer, then P̄ will also increase, and vice versa.
We report exact results for two and three dimensional directed models of polymer chain adsorption–desorption transition in the presence of attracting substrate. A number of properties of this transition are evaluated explicitly. These include the phase diagram, the adsorption fraction and the monomer-density profile. Our results are obtained by a novel application of the transfer matrix method particularly suitable for studies of polymer chain conformations.
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