Statistical mechanical modeling of chemical

Cummings P T and Stell G 1984 Statistical mechanical models of chemical reactions analytic solution of models of A + S AS in the Percus-Yevick approximation Mol. Phys. 51 253... 

STATISTICAL MECHANICAL MODELING OF CHEMICAL REACTIONS IN CONDENSED PHASE SYSTEMS... 

There have been several other methods proposed for the statistical mechanical modeling of chemical reactions. We review these techniques and explain their relationship to RCMC in this section. These simulation efforts are distinct from the many quantum mechanical studies of chemical reactions. The goal of the statistical mechanical simulations is to find the equilibrium concentration of reactants and products for chemically reactive fluid systems, taking into account temperature, pressure, and solvent effects. The goals of the quantum mechanics computations are typically to find transition states, reaction barrier heights, and reaction pathways within chemical accuracy. The quantum studies are usually performed at absolute zero temperature in the gas phase. Quantum mechanical methods are confined to the study of very small systems, so are inappropriate for the assessment of solvent effects, for example. 

On a modest level of detail, kinetic studies aim at determining overall phenomenological rate laws. These may serve to discriminate between different mechanistic models. However, to it prove a compound reaction mechanism, it is necessary to determine the rate constant of each elementary step individually. Many kinetic experiments are devoted to the investigations of the temperature dependence of reaction rates. In addition to the obvious practical aspects, the temperature dependence of rate constants is also of great theoretical importance. Many statistical theories of chemical reactions are based on thermal equilibrium assumptions. Non-equilibrium effects are not only important for theories going beyond the classical transition-state picture. Eventually they might even be exploited to control chemical reactions [24]. This has led to the increased importance of energy or even quantum-state-resolved kinetic studies, which can be directly compared with detailed quantum-mechanical models of chemical reaction dynamics [25,26]. 

Vaporization equilibria involve a balance of forces. Particles stick together at low temperatures but they vaporize at high temperatures to gain translational entropy. The chemical potential describes the escaping tendency, fjp from the vapor phase, and Pt from the condensed phase. When these escaping tendencies are equal, the system is at equilibrium and no net particle exchange takes place. We used the statistical mechanical model of Chapter 11 for the chemical potential of the gas phase. For the liquid or solid phase, we used a lattice model. Vapor pressure and surface tension equilibria, combined with models, give information about intermolecular interactions. In the next chapter we will go beyond pure phases and consider the equilibria of mixtures. 

Suspension Model of Interaction of Asphaltene and Oil This model is based upon the concept that asphaltenes exist as particles suspended in oil. Their suspension is assisted by resins (heavy and mostly aromatic molecules) adsorbed to the surface of asphaltenes and keeping them afloat because of the repulsive forces between resin molecules in the solution and the adsorbed resins on the asphaltene surface (see Figure 4). Stability of such a suspension is considered to be a function of the concentration of resins in solution, the fraction of asphaltene surface sites occupied by resin molecules, and the equilibrium conditions between the resins in solution and on the asphaltene surface. Utilization of this model requires the following (12) 1. Resin chemical potential calculation based on the statistical mechanical theory of polymer solutions. 2. Studies regarding resin adsorption on asphaltene particle surface and... 

Nearly all theories to date predict that IETS intensities should be proportional to n, the surface density of molecular scatterers. Langan and Hansma (21) used radioactively labeled chemicals to measure a surface concentration vs solution concentration curve ( Fig. 10 ) for benzoic acid on alumina using the liquid doping technique. The dashed line in Fig. 10 is a 2 parameter fit to the data using a simple statistical mechanical model by Cederberg and Kirtley (35). This model matched the free energy of the molecule on the surface with that in solution. The two parameters in this model were the surface density of binding sites ( 10" A )... 

The statistical theories provide a relatively simple model of chemical reactions, as they bypass the complicated problem of detailed single-particle and quantum mechanical dynamics by introducing probabilistic assumptions. Their applicability is, however, connected with the collisional mechanism of the process in question, too. The statistical phase space theories, associated mostly with the work of Light (in Ref. 6) and Nikitin (see Ref. 17), contain the assumption of a long-lived complex formation and are thus best suited for the description of complex-mode processes. On the other hand, direct character of the process is an implicit dynamical assumption of the transition-state theory. 

Yu TK, Yu CC, Orlowski M. A statistical polishing pad model for chemical mechanical polishing. IEEE lEDM Washington DC, Dec 5-8 1993. pp 865-868. Seok J, Sukam CP, Kim AT, Tichy JA, Cale TS. Multiscale material removal modeling of chemical mechanical polishing. Wear 2003 254 307-320. 

This chapter discusses several statistical mechanical theories that are strongly positioned in the historical sweep of the theory of liquids. They are chosen for inclusion here on the basis of their potential for utility in analyzing simulation calculations, and their directness in conneeting to the other fundamental topic discussed in this book, the potential distribution theorem. Therefore tentacles can be understood as tentacles of the potential distribution theorem. From the perspective of the preface discussion, the theories presented here might be useful for discovery of models such as those discussed in Chapter 4. These theories are a significant subset of those referred to in Chapter 1 as ... both difficult and strongly established. .. (Friedman and Dale, 1977), but the present chapter does not exhaust the interesting prior academic development of statistical mechanical theories of solutions. Sections 6.2 and 6.3 discuss alternative views of chemical potentials, namely those of density functional theory and fluctuation theory. 

Simple Models. Simulations are usually used for the direct calculation of properties or as an aid in the understanding of physical or chemical phenomena. However, they are also often carried as an aid in the development of simple models for future studies. This is particularly evident in the study of adsorption and flow in microporous systems, where standard hydrodynamic theories are inadequate but can in some cases be extended to treat the effects due to the confinement. Typically simulations of nanosystems need to be on longer timescales than those in the bulk due to the inhomogeneity of the system. Thus development of efficient models is important, and there has therefore been much activity in this field in recent years. Theories such as density functional theories have been extended and verified using simulation methods and simple statistical mechanical models have also been developed. 

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