He4adsorbed in cylindrical silica nanopores: Effect of size on the single-atom mean kinetic energy

Abstract

This paper reports a study of the short-time dynamics of helium confined in silica nanopores (xerogel powder), with average pore diameters of 24 and $160\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. The longitudinal momentum distribution of helium adsorbed in xerogels has been determined via deep inelastic neutron scattering (DINS) measurements performed on the VESUVIO spectrometer at the ISIS spallation source. DINS measurements, in the attosecond time scale, (i.e., ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$), were performed at a temperature of $T=2.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and saturated vapor pressure conditions, with 95% pore volume filling. The average wave-vector transfer $q$ was about $130\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$. For confined helium, significant changes in the values of the single-particle mean kinetic energies $⟨{E}_{K}⟩$ are found in the bulk phase. These are $32.6\ifmmode\pm\else\textpm\fi{}8.7\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for the $24\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ and $24.4\ifmmode\pm\else\textpm\fi{}5.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for the $160\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ pore diameters, remarkably higher than $⟨{E}_{K}⟩=16.2\ifmmode\pm\else\textpm\fi{}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the value of normal liquid $^{4}\mathrm{He}$ at $T=2.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and saturated vapor pressure conditions. The results are interpreted in terms of a model where $^{4}\mathrm{He}$ atoms are arranged in concentric annuli along the cylindrical pore axis, with $⟨{E}_{K}⟩$ mainly dependent on the ratio between the atomic ``effective'' diameter and the pore diameter. The number of solid layers close to pore surface is found to be strongly pore-size dependent with one single solid layer for $24\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ diameter pore and three solid layers for $160\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ diameter pore.