We analyze a number of structurally diverse systems. A simple interpolation expression represents accurately the implicit form of the theoretical equation of state for the liquid derived previously, and facilitates numerical evaluations. The very good agreement between predicted and measured volumes is in accord with earlier observations. Thermal expansivities, a, are estimated with a maximum error, averaged over all systems investigated, of 3.7%. The theoretical temperature dependence of o is « T1'2. However, the experimental results are better approximated by a linear function or by a proportionality factor which decreases with increasing T. The volume and temperature scaling parameters are compared for different polymers. The characteristic temperature T* shows a parallel trend with Tg. But, not surprisingly, Tg is not strictly a corresponding temperature.Hence the hole fraction 1 -y at Tg is not constant, but increases with increasing reduced, and essentially actual glass temperature. A connection between the liquid and glassy states is provided by the temperature dependence of y, finite also in the glass, as shown earlier, and treated there as an adjustable quantity in the theoretical equation of state. From the difference between the experimental and theoretical y's for the glass and supercooled liquid, respectively, a characteristic frozen fraction can be deduced which increases with decreasing Tg. In accord with well-known macroscopic characteristics, the frozen fractions in the series of n-alkyl methacrylates are comparatively small and exhibit a minimum as a function of side-chain length.We have previously shown the close agreement between master curves constructed from volume-temperature data at atmospheric pressure, encompassing oligomers and polymers,1 and the predictions of our hole theory.1 2 Such comparisons were subsequently extended to detailed data from our laboratory, including elevated pressures for polystyrene and poly(o-methylstyrene).3 Finally, some highpressure results taken from the literature, were also discussed.4 The quantitative success of the theory has enabled us to proceed to the liquid-glass transition region and finally to explore the glassy state in terms of theoretical results, developed originally for the liquid equilibrium state.3•5•6We are now in a position to investigate in detail the volume-temperature relations for series of structurally related as well as widely different polymers. This program is pursued here only at atmospheric pressure. Thus we obtain the specific characteristic volume (V7*) and temperature (T*) scaling factors and define in quantitative detail the performance of the theory. Secondly, we examine the behavior of the hole fraction as a characteristic ordering parameter, in the glassy state of these polymers with their

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The design and calibration of a simple volume dilatometer are described. It overlaps and extends to about 250" the range of our cryogenic dilatometer and thus is suitable for expansivity studies of some polymeric high-temperature glasses, the corresponding liquids, and rubbery polymers. Measurements of specific volume are accurate within f1.3 x cm3/g. The results for three methacrylate polymers are given, namely, cyclohexyl. cyclopentyl, and a highly isotactic methyl. The thermal expansivities and derived free-volume quantities are compared with each other and with previous results for homologous series of poly(alky1 methacrylates) and poly-(vinyl ethers). The typical effects in systems with linear side chains, which are reflected in reduced values of the characteristic product h T g , are not encountered in the present systems. They retain "normal" values, not withstanding the enhanced mobility of the rings.

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Linear thermal expansion coefficients, a', have been determined in the temperature range from liquid N2 to Tg for Nylon 6,6 Nylon 11, and ethylene-co-(28 wt % vinyl acetate), a' shows a twoor possibly threestage discontinuity well above experimental error for the two nylons but a less drastic increase for the copolymer. These events appear to be associated with the well-known mechanical 7 relaxation at ~150°K for these three polymer systems. These increases in a' are much greater than for polystyrene which lacks a strong 7 relaxation in