Three semi-empirical positron stationary Quantum Models were developed for the study of nanoporosity in a wide range of solid porous materials. The cubic, conic and cylindrical well potentials were considered and their geometric parameters related to the Positron Annihilation LifeTime (PALT) measurements. If a conic or a cubic symmetry is assumed, a resonance lifetime phenomenon was found, which enables proposal of a technique to catch positrons in free volume sites. In the cylindrical case, an alternative method to determine free volume sizes in materials was developed. The free volume equations of these new models were then compared to the well-known and widely utilised Spherical Free Volume Model (SFVM) and remarkable differences were found. A strong variation of the free volume size–positron lifetime relation with the geometry involved was observed and a remarkable dependence of the electron layer thickness parameter ΔR with the hole-shape under study and with the nature of the material considered. The mathematical functions appearing in the conic and cylindrical cases are the superposition of Bessel functions of the first kind and trigonometric functions in the cubic case. Generalised free volume diagrams were constructed and a brief geometrical scheme of the diverse cases considered was obtained.
Keywords: free volume diagrams, positron cages, positron annihilation, Bessel functions of the first kind, nanoporosity, porous materials, superposition, quantum models, free volume models