Hole size distributions in cardo-based polymer membranes deduced from the lifetimes of ortho-positronium

To clarify the free volume size distributions of the cardo-based polymer membranes, where ortho-positronium (o-Ps) undergoes pick-off annihilation, the o-Ps lifetime distributions were analyzed by the LT9 programme. It was found that the cardo-based polysulfone membrane has much narrower o-Ps lifetime/hole size distributions than the cardo-based polyimide membranes with the 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane dianhydride (6FDA) moiety. Further, the lifetime/hole size distributions of the cardo-based polymer membranes are appreciably broadened with increasing temperature. This suggests that in these membranes there are holes not only of different sizes but also of different thermal expansion coefficients. It is also shown that in a membrane with a wider hole size distribution the average o-Ps lifetime tends to be longer than would be expected from the correlation between the o-Ps lifetime and the total free volume for common polymers.