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Diffusion in channeled structures. III. Quantum corrections induced by lattice vibrations.
1Department of Chemistry, McGill University, 801 Sherbrooke Ouest, Montréal, Québec, Canada H3A 2K6.
Summary
Quantum lattice vibrations slow down guest diffusion in channeled structures. This study quantifies quantum corrections, finding slower diffusion and lower permeability in a semiclassical model compared to classical simulations.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Physical Chemistry
Background:
- Lattice vibrations significantly influence guest diffusion in systems with large energy barriers.
- Understanding quantum effects is crucial for accurately modeling diffusion in channeled structures.
Purpose of the Study:
- To investigate quantum corrections to guest diffusion within a semiclassical framework.
- To develop a method for calculating permeability incorporating quantum mechanical effects.
Main Methods:
- Utilized a semiclassical approach with classical guest and quantum lattice dynamics.
- Employed path integrals to express permeability via correlation functions.
- Applied the Martin-Siggia-Rose formalism to derive generalized Langevin equations.
Main Results:
- Derived an approximate quantum mechanical potential of mean force.
- Observed that quantum effects lead to a slightly higher activation energy.
- Found that quantum lattice diffusion is slower than classical diffusion.
Conclusions:
- The semiclassical model reveals that quantum corrections reduce guest permeability.
- Calculated permeability for neon in alpha-quartz (P'qtm(300K)=9.91x10^8 s/(mkg)) is lower than the classical counterpart (P'class(300K)=1.26x10^9 s/(mkg)).
- Highlights the importance of quantum mechanics in accurately predicting diffusion in materials.
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