Simulation of Diffusion in Lattice Gases and Related Kinetic Phenomena

Kehr, K. W.; Binder, Kurt

doi:10.1007/978-3-642-51703-7_6

Cited by 47 publications

(26 citation statements)

References 150 publications

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“…D K,K decreases with increasing coverages of species coadsorbed with K, due to their increased interference on the diffusion of K. For the same reason, D K,K decreases with decreasing hop rates of the species coadsorbed with K ͑for fixed coverages of these adspecies͒. For vanishingly small coverage of adspecies K, D K,K corresponds to the ''generalized'' tracer diffusion coefficient 11 for a tracer particle K in a ''bath'' of other coadsorbed species, which generally have different hop rates.…”

Section: Chemical Diffusion In Mixed Adlayers For the No؉co Reactionmentioning

confidence: 98%

“…Here, is the angle between successive jumps of the tracer induced by repeated exchange with a single vacancy on the lattice, 11,26 and one assumes that the angle, n , between jumps n steps apart satisfies ͗cos n ͘ϭ͗cos ͘ n . This formula is not expected to generalize to yield exactly f O (1), when O Ͼ0, since the correlations in the tracer's walk are more complicated, being accounted for partly by the term D perc , and partly by f O (1).…”

Section: Appendix C: Tracer Diffusion In Disordered Systemsmentioning

confidence: 99%

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Reactive removal of unstable mixed NO+CO adlayers: Chemical diffusion and reaction front propagation

Tammaro

Evans

1998

The Journal of Chemical Physics

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A lattice-gas model is developed to describe the reactive removal of a preadsorbed, mixed NO+COadlayer covering a Pt(100) surface, via reduction of NO with CO, and behavior of the model is analyzed. Since NO dissociation requires an adjacent empty site, the NO+CO covered surface constitutes an unstable steady state. The creation of vacancies leads NO dissociation, the reaction of CO with the O formed by dissociation, the subsequent creation of more vacancies, and thus the autocatalytic removal of the adlayer. The high mobility of most adspecies leads to an initial "disperse stage" of adlayer removal, characterized by an exponential increase in the number of highly dispersed vacancies. Thereafter follows a transition to a "reaction front propagation" stage of adlayer removal, where a chemical wave develops that propagates into the NO+CO covered region of the surface with roughly constant velocity, and leaves in its wake a surface populated only by excess reactant. We provide a suitable rate equation formulation for the initial disperse stage, but focus on a reaction-diffusion equation analysis of reaction front propagation, examining, in detail, behavior for long times where the front is nearly planar. We emphasize that it is necessary to incorporate the coverage-dependent and tensorial nature of chemical diffusion in the mixed adlayer. Both these features reflect the interference on the surfacediffusion of each adspecies by coadsorbed species. Thus, a key component of this work is the development of an appropriate treatment of chemical diffusion in mixed layers of several adspecies. Disciplines Biological and Chemical Physics | Mathematics CommentsThe following article appeared in Journal of Chemical Physics 108, 18 (1998) A lattice-gas model is developed to describe the reactive removal of a preadsorbed, mixed NOϩCO adlayer covering a Pt͑100͒ surface, via reduction of NO with CO, and behavior of the model is analyzed. Since NO dissociation requires an adjacent empty site, the NOϩCO covered surface constitutes an unstable steady state. The creation of vacancies leads NO dissociation, the reaction of CO with the O formed by dissociation, the subsequent creation of more vacancies, and thus the autocatalytic removal of the adlayer. The high mobility of most adspecies leads to an initial ''disperse stage'' of adlayer removal, characterized by an exponential increase in the number of highly dispersed vacancies. Thereafter follows a transition to a ''reaction front propagation'' stage of adlayer removal, where a chemical wave develops that propagates into the NOϩCO covered region of the surface with roughly constant velocity, and leaves in its wake a surface populated only by excess reactant. We provide a suitable rate equation formulation for the initial disperse stage, but focus on a reaction-diffusion equation analysis of reaction front propagation, examining, in detail, behavior for long times where the front is nearly planar. We emphasize that it is necessary to incorporate the coverage-dependent and ten...

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Section: Chemical Diffusion In Mixed Adlayers For the No؉co Reactionmentioning

confidence: 98%

Section: Appendix C: Tracer Diffusion In Disordered Systemsmentioning

confidence: 99%

Reactive removal of unstable mixed NO+CO adlayers: Chemical diffusion and reaction front propagation

Tammaro

Evans

1998

The Journal of Chemical Physics

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“…This function is very difficult to calculate analytically for an interacting system, and thus numerical simulations have usually been employed. 20,[42][43][44][45] However, in the special case of the Langmuir gas model, 12 in which the only interaction between diffusing particles is the exclusion of double occupancy of lattice sites, the corresponding correlation factor f T L ( ) can be analytically estimated in various lattice geometries. [46][47][48][49][50][51][52] For the Langmuir gas, ⌫( )ϭ (1Ϫ ), where is the bare single-particle jump rate and (1Ϫ ) represents the blocking effect of occupied sites.…”

Section: B Coverage Dependence Of F Tmentioning

confidence: 99%

Memory effects and coverage dependence of surface diffusion in a model adsorption system

et al. 1999

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We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W͑110͒ via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors in tracer and collective diffusion. We show that memory effects can be very pronounced deep inside the ordered phases and in regions close to first and second order phase transition boundaries. Particular attention is paid to the details of the time dependence of memory effects. The memory effect in tracer diffusion is found to decay following a power law after an initial transient period. This behavior persists until the hydrodynamic regime is reached, after which the memory effect decays exponentially. The time required to reach the hydrodynamical regime and the related exponential decay is strongly influenced by both the critical effects related to long-wavelength fluctuations and the local order in the overlayer. We also analyze the influence of the memory effects on the effective diffusion barriers extracted from the Arrhenius analysis. For tracer diffusion, we find that the contribution from memory effects can be as large as 50% to the total barrier. For collective diffusion, the role of memory effects is in general less pronounced. ͓S0163-1829͑99͒03011-8͔

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“…Despite some simplifications (interactions are a mere hardcore, no momentum transfer and etc), this type of modeling captures quite well many qualitative features and reproduces a cooperative, essentially many-particle behavior present in realistic physical systems [16,17]. It is also often amenable to analytical analysis.…”

mentioning

confidence: 96%

Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium

2013

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We present exact results on the dynamics of a biased, by an external force F, intruder (BI) in a two-dimensional lattice gas of unbiased, randomly moving hard-core particles. Going beyond the usual analysis of the force-velocity relation, we study the probability distribution P (Rn) of the BI displacement Rn at time n. We show that despite the fact that the BI drives the gas to a non-equilibrium steady-state, P (Rn) converges to a Gaussian distribution as n → ∞. We find that the variance σ 2 x of P (Rn) along F exhibits a weakly superdiffusive growth σ 2 x ∼ ν1 n ln(n), and a usual diffusive growth, σ 2 y ∼ ν2 n, in the perpendicular direction. We determine ν1 and ν2 exactly for arbitrary bias, in the lowest order in the density of vacancies, and show that ν1 ∼ |F| 2 for small bias, which signifies that superdiffusive behaviour emerges beyond the linear-response approximation. Monte Carlo simulations confirm our analytical results, and reveal a striking fieldinduced superdiffusive behavior σ 2 x ∼ n 3/2 for infinitely long 2D stripes and 3D capillaries. A biased intruder (BI) traveling through a quiescent medium, composed of bath particles which move randomly without any preferential direction, drives the medium to a non-equilibrium steady-state with an inhomogeneous particles' spatial distribution: the latter jam in front of and are depleted behind the BI. The BI can be a charge carrier biased by an electric field or a colloid moved with an optical tweezer. The bath particles may be colloids in a solvent or adatoms on a solid surface.Such microstructural changes of the medium (MCM) were experimentally observed, e.g., in microrheological studies of the drag force on a colloid driven through a λ-DNA solution [1] or for a BI in a monolayer of vibrated grains [2]. Brownian Dynamics simulations have revealed the MCM for a driven colloid in a λ-DNA solution [1,3], or for BIs in colloidal crystals [4]. Remarkably, the MCM not only enhance the drag force exerted on the BI, but also induce effective interactions between the BIs, when more than one BI is present [5][6][7][8].The MCM produced by a BI were studied analytically for quiescent baths modeled as hard-core lattice gases with symmetric simple exclusion dynamics [9][10][11][12][13][14][15]. Despite some simplifications (interactions are a mere hardcore, no momentum transfer and etc), this type of modeling captures quite well many qualitative features and reproduces a cooperative, essentially many-particle behavior present in realistic physical systems [16,17]. It is also often amenable to analytical analysis.It was found that in 1D the size of the inhomogeneity grows in proportion to the traveled distance, so that the jamming-induced contribution to the frictional drag force exhibits an unbounded growth with time n. In consequence, the BI velocity v n ∝ n −1/2 [9-11], ensuring the validity of the Einstein relation for anomalous tracer diffusion in 1D hard-core lattice gases [10][11][12]18]. In higher dimensions, the BI velocity approaches a terminal value v and th...

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Simulation of Diffusion in Lattice Gases and Related Kinetic Phenomena

Cited by 47 publications

References 150 publications

Reactive removal of unstable mixed NO+CO adlayers: Chemical diffusion and reaction front propagation

Reactive removal of unstable mixed NO+CO adlayers: Chemical diffusion and reaction front propagation

Memory effects and coverage dependence of surface diffusion in a model adsorption system

Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium

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