Nanoporosity as quantum positron traps

Two-semiempirical positron stationary quantum models are developed for the study of nanoporosity in a wide range of solid porous materials. The cubic and conic well potentials are considered and their geometric parameters are related to the Positron Annihilation LifeTime Spectroscopy measurements (PALS). A new resonance lifetime phenomenon is found, which enables to propose a technique to trap positrons in such sites. The free volume equations of these new models were then compared to the well-known and widely utilized Spherical Free Volume Model (SFVM) and we found remarkable differences. A strong variation of the free volume size-positron lifetime relation with the geometry involved is 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 case are the superposition of Bessel functions of the first kind and trigonometric functions in the cubic case. Generalized free volume diagrams were drawn and a geometrical representation of the diverse cases considered was obtained.