Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements

Positron annihilation lifetime measurements are reported for four monodisperse polystyrenes with molar mass M = 4,000, 9,200, 25,000, and 400,000. The temperature dependences of orthopositronium (o-Ps) lifetime (τ₃) and intensity (I₃) were measured from 5°C to T_g + 30°C for each sample. From these data, the free volume hole size, 〈v_f(τ₃)〉, and fractional free volume h_ps=CI₃〈v_f(τ₃)〉 were calculated. The temperature dependences of τ₃, 〈v_f(τ₃)〉 and h_ps show a discrete change in slope at an effective glass transition temperature, T_g,ps, which is measurably below the conventional bulk T_g. This suggests that τ₃ is sensitive to large holes which retain their liquid-like mobility in the glassy state. Good agreement was found for T > h_g,ps between h_ps and the theoretical free volume fraction h_th deduced from experimental P-V-T data for polystyrene using the statistical mechanical theory of Simha and Somcynsky. Below T_g,ps, deviations between h_ps and h_th are observed, h_ps falling increasingly below h_th as temperature decreases. Whereas h_ps and h_th depend strongly on M in the melt, each essentially independent of M in the glass. A free volume quantity, computed from the bulk volume, which is in good numerical agreement with the Simha-Somcynsky h-function in the melt, gives improved agreement with h_ps in the glassy state. © 1994 John Wiley & Sons, Inc.