Shape and temperature expansion of free volume holes in some cured polybutadiene-polyisoprene rubber blends

The free volume fraction of a macromolecular structure can be assessed theoretically by using a suitable model; however, it can also be evaluated from experimental data obtained from dilatometry and positron annihilation lifetime spectra. In this second case, a regular geometry of the sub-nanometric cavities forming the free volume has to be assumed, although in fact they are irregularly shaped. The most popular approach is to guess spherical holes, which implies an isotropic growth of these last with temperature. In this work, we compared the free volume fraction, as obtained from experiments in a set of polybutadiene and polyisoprene cured rubbers and their blends, with the analogous quantity expected by using the lattice-hole model. The results allowed us to obtain insights on the approximate shape of the holes. Indeed, a cylindrical flattened geometry of the cavities produced a better agreement with the theory than the spherical shape. Furthermore, the best fit was obtained for holes that expanded preferentially in the radial direction, with a consequent decrease of the aspect ratio with temperature.