Adsorption processes, Monte Carlo simulations

Grand Canonical Monte Carlo Simulations of Adsorption Processe ... 

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. 

In a few instances, quantum mechanical calculations on the stability and reactivity of adsorbates have been combined with Monte Carlo simulations of dynamic or kinetic processes. In one example, both the ordering of NO on Rh(lll) during adsorption and its TPD under UHV conditions were reproduced using a dynamic Monte Carlo model involving lateral interactions derived from DFT calculations and different adsorption... 

Similarly, our forcefield works equally well for unsaturated halocarbons. For example, calorimetric heats of adsorption for trichloroethylene in the same three faujasite zeolites are in excellent agreement with our (N.V.T) Monte Carlo simulations [16]. Our results at "zero" loading suggest, unlike hydrocarbons, an analogy between the adsorption processes of saturated and unsaturated halocarbons. 

The Monte-Carlo principle uses random numbers in the region 0 < random < 1. The main randomized values in the Monte-Carlo simulation, see Figure 1, of a gas-phase adsorption process for radioactive species are ... 

At a fixed T and for a given value of p, the adsorption process has been simulated by using the grand canonical Monte Carlo method [S]. At any elementary step, a site chosen at random is tested to change its occupancy state according to the Metropolis scheme of probabilities where Hf andtf/ are the hamiltonians... 

It is by now clear that several mechanisms and phases are present in the adsorption process in micropores, due to the interplay between gas-gas and gas-solid interactions, depending on their geometry and size. For this reason all those methods assuming a particular pore-filling mechanism, or adsorption model, should show shortcomings in some regions of the relevant parameters and their predictions should be compared with those based on more fundamental formulations of the adsorption process, like Density Functional Theory (DFT) [13] or Monte Carlo simulation [13,15]. Then, one question that arises is how the adsorption model affects the determination of the MSD ... 

In the present work we attempt a systematic investigation of the influence of these three factors in the determination of the MSD of activated carbons. In Section 2, we present a Monte Carlo simulation method for the adsorption process, which is based on realistic... 

For a given pore of size r/, the adsorption isotherm is obtained by Monte Carlo simulation of the adsorption process in the continuum, following the usual grand canonical ensemble algorithm [15, 17,18],... 

Classical methods, like DS and HK, show shortcomings in the determination of MSD due to the assumptions involved in their formulation of the adsorption process Dubinin equation does not show linearity in the Dubinin plot for single slit pores and Horvath-Kawazoe equation assumes that at a given pressure a pore is either completely filled or completely empty, which is contrary to the behavior observed in computer simulations Resulting MSD are shifted respect to those obtained by Monte Carlo simulations, by amounts that vary with the actual distribution, and too small micropores are predicted... 

In the case of a localized 1/n adsorption, which is observed in many Me UPD systems at relatively high AE or low F (formation of expanded Meads superlattice structures, cf. Section 3.4), the adsorption process can be described by the so-called hard-core lattice gas models using different analytical approximations or Monte Carlo simulations [3.214, 3.262-3.264]. Monte Carlo simulation for 1/2 adsorption on a square lattice is dealt in Section 8.4. Adsorption isotherms become asymmetrical with respect to AE and are affected by the structures of the Meads overlayer and S even in the absence of lateral Meads interactions [3.214, 3.262-3.264]. Furthermore, the critical interaction parameter for a first order phase transition, coc, which is related to the critical temperature, Tc, increases in comparison to the 1/1 adsorption. 

In the Monte Carlo simulations of the chromatographic and related processes we should also account for the new knowledge about the deep heterogeneity of surfaces, about the role of localized adsorption and about the occurrence of surface diffusion. Evidently, now the molecular desorption energy accepted for a concrete simulation is to be understood as the effective value over the spectrum of possible energies in the sense of Eq. 5.71. As such, it is related to a concrete form of the p(E ). The... 

The series of 10 chapters that constitute Part 3 of the book deals mainly with the use of adsorption as a means of characterizing carbons. Thus, the first three chapters in this section complement each other in the use of gas-solid or liquid-solid adsorption to characterize the porous texture and/or the surface chemistry of carbons. Porous texture characterization based on gas adsorption is addressed in Chapter 11 in a very comprehensive manner and includes a description of a number of classical and advanced tools (e.g., density functional theory and Monte Carlo simulations) for the characterization of porosity in carbons. Chapter 12 illustrates the use of adsorption at the liquid-solid interface as a means to characterize both pore texture and surface chemistry. The authon propose these methods (calorimetry, adsorption from solution) to characterize carbons for use in such processes as liquid purification or liquid-solid heterogeneous catalysis, for example. Next, the surface chemical characterization of carbons is comprehensively treated in Chapter 13, which discusses topics such as hydrophilicity and functional groups in carbon as well as the amphoteric characteristics and electrokinetic phenomena on carbon surfaces. 

Kawasaki has rigorously examined the entropic influences of macromo-lecular adsorption throu statistical thermodynamics (48a). Others have used computerized Monte Carlo simulations to investigate the adsorption process of polymer chains (49 52), Under conditions where a macromole-eule s chemical potential changes over time, resorption appears to become an increasingly critical parameter as die number of interacting sites, n, increases. 

Statistical mechanical Monte Carlo as well as classical molecular dynamic methods can be used to simulate structure, sorption, and, in some cases, even diffusion in heterogeneous systems. Kinetic Monte Carlo simulation is characteristically different in that the simulations follow elementary kinetic surface processes which include adsorption, desorption, surface diffusion, and reactivity . The elementary rate constants for each of the elementary steps can be calculated from ab initio methods. Simulations then proceed event by event. The surface structure as well as the time are updated after each event. As such, the simulations map out the temporal changes in the atomic structure that occur over time or with respect to processing conditions. 

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