Correlation between glass transition temperature and thermal expansion coefficients of polymers: Its interpretation and implication

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Abstract
A new approach pertaining to the hole and lattice theories of polymeric systems is developed to interpret the universal inverse relationship between the glass transition temperature (Tg) and the difference in thermal expansion coefficients for liquid and glassy polymers (δ α). The success of this particular theoretical consideration rests upon the familiar hypothesis of the iso-free volume state at Tg and the entropy contribution to the hole-polymer segment interaction energy. Based on the experimental data available, we have established the free volume fraction at Tg, vg = 0.025, which is identical with the assessment of the empirical Williams-Landel-Ferry (WLF) equation for the temperature-dependence shift factor aT. However, appreciably higher values of vg are reported by other contemporary models. The present findings justify an alternative form of the WLF equation with the product Tg, δ α playing the role of δ α. The universality of this novel expression is demonstrated, by means of statistical analysis, to be remarkably more warrantable than its original version.