To determine the free volume in polymers, positron annihilation lifetime spectroscopy data are transformed into nanohole volumes by modeling the cavities as spheres or, more generally, using geometries assuming an isotropic thermal expansion. However, this guess could be unrealistic owing to the irregular shape of nanoholes and constrained movements of the macromolecules. In this work, it is shown that a comparison of hole-lattice theory with positron and dilatometric data for a homologous series of perfluoropolyethers supplies information on the anisotropic expansion of nanoholes; the relation between volume and typical unconstrained size of the cavities can be expressed by a power law with noninteger exponents.