Free‐volume and pore size distributions determined by numerical Laplace inversion of positron annihilation lifetime data

Positron annihilation lifetime spectroscopy is a powerful method for characterizing free volumes in a variety of materials. Correlations between positron annihilation rates and the size of free‐volume regions in which o‐Ps localizes are well described. Unfortunately, difficulties in the analysis of positron annihilation lifetime data have limited the approach to the determination of average lifetimes and average free volumes. Recent advances in the development of numerical integral transform methods now make it possible to extract continuous distributions of positron annihilation rates. The application of these methods to the determination of free‐volume distributions is described. The variable transformations required to convert positron annihilation rate probability density functions (PDF) to the corresponding lifetime, radius, and free‐volume PDFs are given and the approach is illustrated by application to positron annihilation lifetime data for amorphous polytetrafluoroethylene.