Cryogenic Helium Adsorbed in Zeolite Rho: Inside Localization Controlled Self-Diffusion of Confined Quantum Particles

Abstract

Applying Feynman’s treatment of quantum mechanics at finite temperatures via path integrals and the numerical analytic continuation method developed recently (Kowalczyk, P.; Gauden, P. A.; Terzyk, A. P.; Furmaniak, Sylwester, J. Chem. Theory Comput.2009, 5, 1990–1996), we study the mobility of 4He atoms adsorbed in zeolite rho at 40 K. At studied temperature, the self-diffusive motion of 4He atoms in zeolite rho is strongly concentration-dependent. At low pore concentrations, 4He atoms are adsorbed in high-energetic adsorption centers of the zeolite. Due to strong localization in the solid–fluid potential well, an average kinetic energy of 4He atoms at infinite dilution reaches 120 K (i.e., twice of the classical kinetic energy at 40 K, Eclass = 60 K), whereas the self-diffusion constant drops up to 0.001 Å2 ps–1. Increasing pore concentration of 4He leads to the rapid increase in mobility of adsorbed 4He atoms. We show that 8 mmol cm–3, self-diffusive motion of confined 4He atoms increases up to 1 Å2 ps–1. Variation of the kinetic energy, potential energy, and enthalpy of 4He adsorption with pore concentration indicates that high-energetic adsorption sites in studied zeolite sample are saturated at low pore densities. The remaining adsorption sites are characterized by weaker solid–fluid potential, which allows higher delocalization of adsorbed 4He atoms. The reported novel phenomenon of localization controlled self-diffusion of confined 4He seems to be promising for smart designing of nanoporous quantum molecular sieves and storage nanovessels. Understanding of 4He cryogenic adsorption in the smallest pores enriches our knowledge that is crucial for precise analysis of ultramicropore sizes.