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.

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.

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.

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

UNIFORM ERGODIC THEOREMS ON APERIODIC LINEARLY REPETITIVE TILINGS AND APPLICATIONS

2008 ◽  
Vol 20 (05) ◽  
pp. 597-623 ◽  
Author(s):  
ADNENE BESBES
Keyword(s):  
Lattice Gas ◽  
Weak Form ◽  
Ergodic Theorems ◽  
Self Similarity ◽  
Lattice Gas Models

The paper is concerned with aperiodic linearly repetitive tilings. For such tilings, we establish a weak form of self-similarity that allows us to prove general (sub)additive ergodic theorems. Finally, we provide applications to the study of lattice gas models.

Lattice gas models for nonideal gas fluids

1991 ◽  
Vol 47 (1-2) ◽  
pp. 97-111 ◽  
Author(s):  
Shiyi Chen ◽  
Hudong Chen ◽  
Gary D. Doolen ◽  
Y.C. Lee ◽  
H. Rose ◽  
...  
Keyword(s):  
Lattice Gas ◽  
Nonideal Gas ◽  
Lattice Gas Models
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