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Extension of the Equation for the Annihilation Lifetime of ortho -Positronium at a Cavity Larger than 1 nm in Radius

1999; American Chemical Society; Volume: 103; Issue: 21 Linguagem: Inglês

10.1021/jp9831841

1520-6106

Kenji Ito, Hiroshi Nakanishi, Yûsuke Ujihira,

Ammonia Synthesis and Nitrogen Reduction

Evaluations of cavity concentrations and their size distributions in industrially important materials by positron annihilation lifetime methods require a well calibrated ortho-positronium (o-Ps) lifetime standard curve as a function of pore size. A semiempirical equation with a fitting parameter obtained by Nakanishi and Jean has been successfully utilized in various porous and polymeric materials to estimate pore sizes up to approximately 1 nm in radius. However, as experimental data accumulate recently, it has become clear that the equation no longer yields a good correlation between o-Ps lifetimes and the pore size for the pore radius larger than 1 or o-Ps lifetime longer than ∼20 ns. Therefore, we assumed for the larger pore that o-Ps behaves more like a quantum particle, bouncing back and forth between the energy barriers as the potential well becomes large. An equation derived from this hypothesis gives excellent fitting with experimental data despite a crude approximation used in our model. More importantly, this approach has produced a simple analytical relationship between the o-Ps lifetime and the pore radius. Agreement between the estimated o-Ps wave packet size at thermal energy (∼1.6 nm) and the fitted parameter RPs (∼1 nm) lends credence to our hypothesis that o-Ps behaves more like a quantum particle as a pore size becomes larger.