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 ortho positronium ( o ‐Ps) lifetime (τ 3 ) and intensity ( I 3 ) were measured from 5°C to T g + 30°C for each sample. From these data, the free volume hole size, 〈 v f (τ 3 )〉, and fractional free volume h ps = CI 3 〈 v f (τ 3 )〉 were calculated. The temperature dependences of τ 3 , 〈 v f (τ 3 )〉 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 τ 3 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.