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Quantum transport in porous media: Inelastic scattering of atoms and its temperature dependence
Phys. Rev. E 49, 3050 – Published 1 April, 1994
DOI: https://doi.org/10.1103/PhysRevE.49.3050
Abstract
In porous media characterized by pore sizes in the range 5–20 Å, fluid transport characteristics at low temperatures may deviate significantly from the classical behavior, due to the interference effect arising from the quantum wave nature of the fluid atoms. An important consideration in this regard is the size and temperature dependence of the inelastic scattering length for the fluid atom, which directly governs the magnitude of the quantum deviation. For a sample of size smaller than the transport of the fluid atoms should be described by the Schrödinger equation confined in the pores. We intend to address this problem in two separate papers. In this paper we present the results of calculations for the inelastic scattering length in the case of a atom confined in a cylindrical pore. Inside the pore, a monolayer of physisorbed atoms is assumed to line the pore wall. Outside the pore, the solid material is assumed to be elastic. The thermal excitation of elastic waves results in the distortion of the cylindrical pore surface, which in turn causes transitions between the quantum eigenstates of inside the pore. By choosing some reasonable parameters of a porous medium, we have obtained the inelastic scattering rate (length) as a function of temperature for two pore radii. Our results show that the inelastic scattering length is on the order of 1 μm even at 50 K. This suggests that the quantum interference effect could be important at low temperatures, and that a deviation from Knudsen flow may be expected. The explicit calculation of quantum transport in this regime is planned to be the subject of a second paper.
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