Lattice-Gas Models of Electrochemical Adsorption: Static and Dynamic Aspects

1996 ◽  
Vol 451 ◽  
Author(s):  
Per Arne Rikvold ◽  
Andrzej Wieckowski ◽  
Raphael A. Ramos
Keyword(s):  
Lattice Gas ◽  
Time Dependent ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Lateral Interactions ◽  
Model Formulation ◽  
Lattice Gas Models ◽  
Statistical Mechanical ◽  
Far From Equilibrium ◽  
Electrochemical Adsorption

ABSTRACTWe discuss applications of statistical-mechanical lattice-gas models to electrochemical adsorption. Our strategy to describe specific systems includes microscopic model formulation, calculation of zero-temperature phase diagrams, numerical simulation of thermody-namic and structural quantities at nonzero temperatures, and estimation of effective, lateral interactions. We report applications to adsorption on single-crystal electrodes, presenting simulated and experimental coverages and voltammetric currents for urea on Pt(100) and the underpotential deposition of Cu on Au(111) in sulfuric acid. We also discuss an extension of the method to study time-dependent phenomena far from equilibrium.

scholarly journals Phase Transitions in Lattice-Gas Models Far from Equilibrium

1984 ◽  
Vol 53 (8) ◽  
pp. 806-809 ◽  
Author(s):  
Henk van Beijeren ◽  
Lawrence S. Schulman
Keyword(s):  
Phase Transitions ◽  
Lattice Gas ◽  
Lattice Gas Models ◽  
Far From Equilibrium

scholarly journals Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

2019 ◽  
Vol 21 (11) ◽  
pp. 6216-6223 ◽  
Author(s):  
Daniel Silva ◽  
Per Arne Rikvold
Keyword(s):  
Phase Diagrams ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Dimensional Parameter ◽  
State Diagrams ◽  
Solid Foundation

The fifteen topologically different zero-temperature phase diagrams in the model's full, five-dimensional parameter space provide a solid foundation for studies at finite temperatures.

scholarly journals CASIMIR FRICTION FORCE FOR MOVING HARMONIC OSCILLATORS

2012 ◽  
Vol 14 ◽  
pp. 141-154 ◽  
Author(s):  
JOHAN S. HØYE ◽  
IVER BREVIK
Keyword(s):  
Friction Force ◽  
Constant Velocity ◽  
Order Effect ◽  
Order Theory ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Zero Temperature ◽  
Dielectric Particles ◽  
First Order Theory ◽  
Statistical Mechanical

Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, an earlier theory of ours back in 1992. The energy change ΔE turns out to be finite in general, corresponding to a finite friction force. In the limit of zero temperature the formalism yields, however, ΔE → 0, this being due to our assumption about constant velocity, meaning slowly varying coupling. For couplings varying more rapidly, there will also be a finite friction force at T = 0. As second part of our work, we consider the friction problem using time-dependent perturbation theory. The dissipation, basically a second order effect, is obtainable with the use of first order theory, the reason being the absence of cross terms due to uncorrelated phases of eigenstates. The third part of the present paper is to demonstrate explicitly the equivalence of our results with those recently obtained by Barton (2010); this being not a trivial task since the formal results are seemingly quite different from each other.

scholarly journals Conversion Reactions in Surface-Functionalized Mesoporous Materials: Effect of Restricted Transport and Catalytic Site Distribution

2012 ◽  
Vol 1423 ◽  
Author(s):  
Jing Wang ◽  
David M. Ackerman ◽  
Kapil Kandel ◽  
Igor I. Slowing ◽  
Marek Pruski ◽  
...  
Keyword(s):  
Mesoporous Materials ◽  
Lattice Gas ◽  
Site Distribution ◽  
Functionalized Mesoporous Silica ◽  
Single File ◽  
Catalytic Sites ◽  
Lattice Gas Models ◽  
Statistical Mechanical ◽  
Product Species ◽  
Synthesis Approach

ABSTRACTWe analyze the interplay between anomalous transport and conversion reaction kinetics in mesoporous materials functionalized with catalytic groups. Of primary interest is functionalized mesoporous silica containing an array of linear pores with diameters tunable from 2-10 nm, although functionalization can produce smaller effective diameters, d. For d < 2 nm, transport and specifically passing of reactant and product species within the pores can be strongly inhibited (single-file diffusion). The distribution of catalytic groups can also vary depending on the synthesis approach. We apply statistical mechanical modeling (utilizing spatially discrete stochastic lattice-gas models) to explore the dependence of reactivity on the extent of inhibition of passing of species within the pore, as well as on the distribution of catalytic sites.

scholarly journals CASIMIR FRICTION FORCE FOR MOVING HARMONIC OSCILLATORS

2012 ◽  
Vol 27 (15) ◽  
pp. 1260011 ◽  
Author(s):  
JOHAN S. HØYE ◽  
IVER BREVIK
Keyword(s):  
Friction Force ◽  
Constant Velocity ◽  
Order Effect ◽  
Order Theory ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Zero Temperature ◽  
Dielectric Particles ◽  
First Order Theory ◽  
Statistical Mechanical

Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving nonrelativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, an earlier theory of ours back in 1992. The energy change ΔE turns out to be finite in general, corresponding to a finite friction force. In the limit of zero temperature the formalism yields, however, ΔE → 0, this being due to our assumption about constant velocity, meaning slowly varying coupling. For couplings varying more rapidly, there will also be a finite friction force at T = 0. As second part of our work, we consider the friction problem using time-dependent perturbation theory. The dissipation, basically a second order effect, is obtainable with the use of first order theory, the reason being the absence of cross terms due to uncorrelated phases of eigenstates. The third part of the present paper is to demonstrate explicitly the equivalence of our results with those recently obtained by Barton (2010); this being not a trivial task since the formal results are seemingly quite different from each other.

STOCHASTIC AND HYDRODYNAMIC LATTICE GAS MODELS: MEAN-FIELD KINETIC APPROACHES

2002 ◽  
Vol 12 (02) ◽  
pp. 227-259 ◽  
Author(s):  
JEAN-FRANÇOIS GOUYET ◽  
CÉCILE APPERT
Keyword(s):  
Phase Transitions ◽  
Lattice Gas ◽  
Kinetic Equations ◽  
Mean Field ◽  
Lattice Gases ◽  
Practical Applications ◽  
Lattice Gas Models ◽  
Far From Equilibrium ◽  
Thermodynamic Phase ◽  
Field Approaches

Fascinating tools to understand the link between microscopic and macroscopic dynamics in many systems, lattice gases have been developed into two important directions: thermodynamic phase transitions and hydrodynamics. Here we present how mean-field approaches allow a more thorough analysis of these systems. The kinetic equations are nonlinear and allow to consider far from equilibrium systems. Another important advantage is to gain more flexibility for practical applications.

Description of far-from-equilibrium processes by mean-field lattice gas models

2003 ◽  
Vol 52 (6) ◽  
pp. 523-638 ◽  
Author(s):  
J.-F. Gouyet ◽  
M. Plapp ◽  
W. Dieterich ◽  
P. Maass
Keyword(s):  
Lattice Gas ◽  
Mean Field ◽  
Equilibrium Processes ◽  
Lattice Gas Models ◽  
Far From Equilibrium

Conventional and Unconventional Numerical Transfer-Matrix Methods

1992 ◽  
Vol 278 ◽  
Author(s):  
M. A. Novotny ◽  
P. A. Rikvold
Keyword(s):  
Surface Tension ◽  
Transfer Matrix ◽  
High Temperature Superconductor ◽  
Lattice Gas ◽  
Materials Science ◽  
Matrix Methods ◽  
Oxygen Ordering ◽  
Lattice Gas Models ◽  
Mechanical Models ◽  
Statistical Mechanical

AbstractWe briefly review the numerical transfer-matrix (TM) method and its application to materials science. We report on the conventional use of TM methods to calculate phase diagrams and critical exponents of classical statistical mechanical models in d=2. Examples presented here are spin-1/2 and spin-1 models (two- and three-state lattice-gas models). Discussed are a model for oxygen -ordering in the high temperature superconductor YBa2Cu3O6+x and a model for the electrosorption of an organic substance on a metal. Some results for the spin-1/2 model in d=3 are also presented. Three unconventional applications of the TM method will also be reported. These include a study of the surface tension of spin-1/2 models, a TM formalism for metastability, and a study of a translationally invariant (non-fractal) spin-1/2 model in non-integer dimensions.

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