Statistical thermodynamics of the glass transition and the glassy state of polymers (original) (raw)

1972, The Journal of Physical Chemistry

The hole theory of Simha and Somcynsky is applied to an analysis of the liquid-glass boundary and to the equation of state in the region between the glass transition and the 0-relaxation. Two systems already studied experimentally are considered, namely, polystyrene and poly (o-methylstyrene). The liquid-glass boundary relations are investigated under two sets of conditions corresponding to a low-(LPG) and a high-pressure glass (HPG). The former is formed by cooling the liquid a t atmospheric pressure, whereas the latter is obtained by pressurizing the liquid isothermally. The equation of state is analyzed for LPG only. The link between the conventional thermodynamic relations, experiment, and the statistical theory is formed by identifying the vacancy fraction 1y appearing in the latter with the ordering parameter 2 introduced in the thermodynamic theory. For LPG, ye, the value of y along the boundary, is indeed found to be constant for both polymers. For HPG, 1y, is a decreasing function of pressure, as should be expected. The equation dT,/dP = (bT,/W)z + (bT,/bZ)p X dZ/dP is tested by evaluating the product on the right-hand side by a combination of the statistical theory with experiment. An equation of state for LPG is first computed entirely from theory by assuming that a single constant parameter, y = yg, characterizes not only the liquid-glass boundary line, but the glassy region as well. This results in too low a thermal expansivity, as had been noted earlier by Somcynsky and Simha for several other polymers at atmospheric pressure. Hence, within the frame of the hole theory, y cannot remain constant in the glass but is a function of T and P. It differs, of course, from the function derived by maximization of the configurational partition function of the liquid and is obtained here from experiment. Thus, additional constants enter into the equation of state of the glass, which cannot be obtained solely from the properties of the liquid and the liquid-glass boundary line. On approaching this line, however, the above function reduces to a single constant, viz., yg.