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Free volumes in simple and polymeric liquids
Authors:A A Miller
Abstract:Values of ε0ν0 the vaporization energy and volume in the hypothetical liquid state at 0°K., are derived for some simple polar and nonpolar molecules used as models for vinyl polymers. The following empirical relationship between the free volume fraction, f = (v ? v0)/v, and the liquid compressibility coefficient β is demonstrated: ?f2 ∝? This is applied to several vinyl polymer liquids near their glass transition temperatures, Tg, giving. fg ? 0.17, if the “hard-core” volume v* is considered to be independent of pressure and temperature, (i.e., v* = v0); or, fg ?0.12, if the P,T dependence of v* is considered to be the same as that of the glass. These agree with fg values derived by Simha and Boyer from thermal expansion coefficients for the two analogous cases. An empirical viscosity-free volume equation of the Doolittle form: η = ATneb/f is applied to the glass transition, on assuming that this is an isoviscosity state and with the use of reported values for the expansion and compressibility coefficients and dTg/dP for three polymers: polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). Reasonable values of b/n are thus obtained. This viscosity equation is critically examined in the light of molecular theories of liquid viscosity.
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