In this paper we show that there exists a linear relationship between the size of a cavity where an ortho-positronium (o-Ps) atom annihilates by the ’pick-off mechanism and the total free volume of the molecular liquid or polymer under consideration. This relationship is used to determine the free volume of electron irradiated poly(aryl-ether-ether-ketone) (PEEK) samples and the result is compared with that obtained from gas diffusivity measurements.