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

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 (T_g) 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 T_g 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 T_g, v_g = 0.025, which is identical with the assessment of the empirical Williams-Landel-Ferry (WLF) equation for the temperature-dependence shift factor a_T. However, appreciably higher values of v_g are reported by other contemporary models. The present findings justify an alternative form of the WLF equation with the product T_g, 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.