Adsorption Monte Carlo

Ramsahye NA, Maurin G, Bourrelly S (2007) On the breathing effect of a metal-organic framework upon CO2 adsorption monte carlo comptu-ed to microcalorimetry experiments. Chem Commun 31 3261-3263... 

MacRitchie " and Dickinson and Stainsby " have reviewed the behavior of proteins at a variety of interfaces. There have also been a number of recent research papers which have taken a theoretical or computational approach examples include the computation of the electrostatic interaction energy between a protein and a charged surface the computation of electrostatic and van der Waals contributions to protein adsorption " Monte Carlo simulation of the conformational behavior of a polypeptide chain near a charged surface " protein structure prediction based on statistical potential development of a model system for the interaction... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Panagiotopoulos A Z 1987 Adsorption and oapillary oondensation of fluids in oylindrioal pores by Monte Carlo simulation in the Gibbs ensemble Mol. Phys. 62 701-19... 

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

Grand Canonical Monte Carlo Simulations of Adsorption Processe ... 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

Siepmann J I and I R McDonald 1993b. Monte Carlo Study of the Properties of Self-assembh Monolayers Formed by Adsorption of CH3(CH2)i5SH on the (111) Surface of Gold. Molecul Physics 79 457-473. 

Molecular mechanics methods have been used particularly for simulating surface-liquid interactions. Molecular mechanics calculations are called effective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force held is parameterized correctly. 

J. E. Lane, T. H. Spurling. Monte Carlo simulation of the effects of adsorption on interparticle forces. Aust J Chem 55 231-239, 1980. 

In Sec. II we briefly review the experimental situation in surface adsorption phenomena with particular emphasis on quantum effects. In Section III models for the computation of interaction potentials and examples are considered. In Section IV we summarize the basic formulae for path integral Monte Carlo and finite size scahng for critical phenomena. In Section V we consider in detail examples for phase transitions and quantum effects in adsorbed layers. In Section VI we summarize. 

In this seetion of our work we present examples of the applieation of eomputer simulation methods to study ehemieally assoeiating fluids. In the first ease we eonsider the adsorption and surfaee phase transitions by means of a eonstant pressure Monte Carlo simulation. The seeond example is foeused on the problem of ehemieal potential evaluation. 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

FIG. 9 Changes of the monolayer film critical temperature with the concentration of impurities obtained from the Monte Carlo simulations (open circles) and resulting from the mean field theory (solid line). (Reprinted from A. Patrykiejew. Monte Carlo studies of adsorption. II Localized monolayers on randomly heterogeneous surfaces. Thin Solid Films, 205 189-196, with permision from Elsevier Science.)... 

FIG. 7 Log-log plots of the interface width (w ) versus the Monte Carlo time t, measured at different adsorption probabihties using channels of width L = 30. Data were obtained during the displacement of an A-poisoned phase by the reactive regime. From top to bottom the probabihties are 0.5192, 0.5202, 0.5211, 0.5215, and 0.5238. 

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

A. Milchev, D. P. Landau. Adsorption of living polymers on a solid surface A Monte Carlo simulation. J Chem Phys 204 9161-9168, 1996. 

E. Eisenriegler, K. Kremer, K. Binder. Adsorption of polymer chains at surfaces Scaling and Monte Carlo analysis. J Chem Phys 77 6296-6320, 1982. 

For adsorption in zeolites, the biased Monte Carlo method as developed by Smit is an excellent method to determine the free energies of molecules adsorbed on zeolites [9bj. This method can be used to compute the concentration of molecules adsorbed on zeolites, as we discuss below. 

Table 1.1 Configurationally biased Monte Carlo simulations of the adsorption enthalpies of hydrocarbons for two zeolites.

We did not extensively discuss the consequences of lateral interactions of surface species adsorbed in adsorption overlayers. They lead to changes in the effective activation energies mainly because of consequences to the interaction energies in coadsorbed pretransition states. At lower temperatures, it can also lead to surface overlayer pattern formation due to phase separation. Such effects cannot be captured by mean-field statistical methods such as the microkinetics approaches but require treatment by dynamic Monte Carlo techniques as discussed in [25]. 

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