Diffusion in channeled structures. III. Quantum corrections induced by lattice vibrations.
For large energy barrier systems the lattice vibrations can play an important role in the diffusion of a guest component inside channeled structures. Here, quantum corrections to the guest diffusion are studied within a semiclassical framework in which the guest behaves classically and the lattice quantum mechanically. The permeability is expressed in terms of correlation functions that are calculated using path integrals. Forward-backward path integrals for propagators are combined, and, using the Martin-Siggia-Rose formalism [Phys. Rev. A. 8, 423 (1973)], are transformed into a set of generalized Langevin equations that reduce to the classical equation of motion at high temperatures. The random initial conditions to these equations are specified by the density matrix from which an approximate expression for the quantum mechanical potential of mean force is derived. The quantum potential of mean force and activation energy obtained for the guest inside the lattice is slightly higher than the one for the fully classical system, and the diffusion of the guest in the quantum lattice is slower compared to its fully classical counterpart. The macroscopic intrinsic permeability of alpha -quartz towards neon is reported, P'qtm(300K)=9.91x10(8) s/(mkg) within the semiclassical approximation and is lower than P'class (300K)=1.26x10(9) s/(mkg) obtained in the classical case at 300K for the same potential model.
Department of Chemistry, McGill University, 801 Sherbrooke Ouest, Montréal, Québec, Canada H3A 2K6.
Benoit
B
Palmieri
David
D
Ronis