Manifestation of Onsager’s off-diagonal fluxes in diffusion of coadsorbed particles

Vladimir P Zhdanov

doi:10.1016/j.susc.2020.121740

Abstract

According to Onsager’s phenomenological theory, the diffusion fluxes of coadsorbed particles are expressed via the gradients of their chemical potentials and can contain the off-diagonal terms. In the conventional two-dimensional lattice-gas models with jumps of monomers to nearest-neighbour vacant sites, such terms are absent at the mean-field (MF) level or in the framework including the statistical correlations related to lateral interaction between particles but neglecting the dynamical correlations. The role of the off-diagonal terms in these models with dynamical correlations and in other unconventional models is still not clear. Herein, the situation in this area is clarified from two perspectives by using Monte Carlo simulations and analytically, respectively. First, the scale of the related effects is shown for conventional diffusion with emphasis on the concentration profiles under steady-state conditions and diffusion-limited associative desorption under transient conditions. In these cases, the role of the off-diagonal terms is well manifested at the level above the MF approximation provided the coverages are appreciable and the difference between the jump rates of different particles is appreciable as well. Second, the off-diagonal terms are demonstrated to be available and important already at the MF level in unconventional diffusion occurring via concerted exchange and pair jumps.

Highlights

Diffusion of particles adsorbed on a solid surface is of considerable intrinsic interest and important in the context of various applications
For Langmuir particles, this aspect was scrutinized by Quastel [28], and the outcome of his heuristic analysis is that the off-diagonal terms are related to the specifics of the self-diffusion coefficients, DA*and DB*
I show analytically that Onsager’s off-diagonal terms are not necessarily related to the dynamic factors which are beyond the MF approximation or, in other words, that these terms can be obtained in this approximation, but this is possible for various unconventional mechanisms of diffusion (Section 4)

Summary

Introduction

Diffusion of particles (atoms and molecules) adsorbed on a solid surface is of considerable intrinsic interest and important in the context of various applications. In the case of bistable and oscillatory spatio-temporal kinetics in rapid reactions such, e.g., as CO oxidation on the (100) and (110) faces of Pt [12,13], diffusion of coadsorbed species can play a more explicit and important role In these classical and other examples of complex behaviour of heterogeneous catalytic reactions, the underlying mechanisms include usually the steps (e.g., surface restructuring or oxide formation) which can hardly be accurately described by the conventional mass-action law. For Langmuir particles, this aspect was scrutinized by Quastel [28] (reviewed by Liu et al [7]), and the outcome of his heuristic analysis is that the off-diagonal terms are related to the specifics of the self-diffusion coefficients, DA*and DB* Using his equations, one can verify that in the case of A and B coadsorption the off-diagonal terms are negligible provided these coefficients are represented in the MF form, DA* = (1 A B)DAand DB* = (1 A B)DB. I show analytically that Onsager’s off-diagonal terms are not necessarily related to the dynamic factors which are beyond the MF approximation or, in other words, that these terms can be obtained in this approximation, but this is possible for various unconventional mechanisms of diffusion (Section 4)

Conventional diffusion under steady-state conditions

Associative desorption under transient conditions

Diffusion including exchange and pair jumps

Diffusion including exchange of particles

Diffusion including pair jumps

Conclusion