Possible Experimental Equivalence of the Gibbs—DiMarzio and Free-Volume Theories of the Glass Transition

Abstract

The observation is made that a straight line with a slope of 1 is obtained when the two parameters of the Gibbs—DiMarzio theory are plotted against each other. The two parameters are Δε/k, the energy difference between the trans and gauche conformations of a hydrocarbon‐type polymer chain, and 2α/k, the ``hole formation energy.'' The identity (practically within experimental error) of these two parameters implies that the free volume V<sub>0</sub> at T<sub>g</sub> is apparently constant since both 2α/k and Δε/k are functions of V<sub>0</sub> alone. Furthermore, the product T<sub>g</sub>Δα (where Δα is the difference in the cubic expansion coefficients above and below T<sub>g</sub>) is also a constant, since that, too, is a function only of V<sub>0</sub>. The ``universal'' value of V₀ is 0.037, and that of T_gΔα is 0.116, extremely close to the value found by Simha and Boyer. Thus, it seems that, within experimental error, the Gibbs—DiMarzio theory and the classical free‐volume theory are practically equivalent, at least for the homopolymers examined here.