Theoretical and Simulation Methods

One of the ultimate goals in modeling heterogeneous catalytic reaction systems would be the development of a multiscale approach that could simulate the myriad of atomic scale transformations that occur on the catalyst surface as they unfold as a function of time, processing conditions and catalyst structure and composition. The simulation would establish all of the elementary physicochemical paths available at a specific instant 

This is obviously well beyond what we can currently simulate. Even subsystems of this would be quite difficult to carry out with any meaningful accuracy. This does not mean, however, that theory is of little use and should be abandoned. On the contrary, one of the primary goals of this book is to highlight the impact that theory has made in establishing governing catalytic principles important for the science of catalysis. Many of these ideas could not have been conceptually or quantitatively obtained without the help of state of art computational methods. 

The disparate time and length scales that control heterogeneous catalytic processes make it essentially impossible to arrive at a single method to treat the complex structural behavior, reactivity and dynamics. Instead, a hierarchy of methods have been developed which can can be used to model different time and length scales. Molecular modeling of catalysis covers a broad spectrum of different methods but can be roughly categorized into either quantum-mechanical methods which track the electronic structure or molecular simulations which track the atomic structme (see the Appendix). 

The ability to calculate the intrinsic catalytic reactivity of bond-breaking and bondmaking events requires a full quantum-mechanical description of these events. The simulation of catalyst structure and morphology or reaction kinetics, on the other hand, would be more easily simulated via atomistic scale simulations, provided the appropriate interatomic potentials or intrinsic kinetic data exist. Over the past decade, it has become possible to derive such data from ab initio calculations, thus allowing for a hierarchical 

There are a number of excellent reviews and discussions about the advances that have taken place in quantum-mechanical method development and their ability to calculate a host of different material properties We therefore, do not go into this in detail in this book. Instead, we present a short overview of covering salient features of the different theoretical and computational methods and their application to catalysis. This is presented in the Appendix along with references to more detailed reviews on the different methods. 

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In this chapter we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. The organization of this chapter is as follow. In the first few sections the thermodynamics and statistical mechanics of solvation are introduced. In this regards, Flory s theory of polymer solutions has been compared with the classical solution methods for interpretation of experimental data. Very dilute solution of gases in polymers and the methods of calculation of chemical potentials, and hence calculation of Henry s law constants and sorption isotherms of gases in polymers are discussed in Section 11.6.1. The solution of polymers in solvents, solvent effect on equilibrium and dynamics of polymer-size change in solutions, and the solvation structures are described, with the main emphasis on molecular dynamics simulation method to obtain understanding of solvation of nonpolar polymers in nonpolar solvents and that of polar polymers in polar solvents, in Section 11.6.2. Finally, the dynamics of solvation with a short review of the experimental, theoretical, and simulation methods are explained in Section 11.7. 

While there have been many studies of these two enzymes [43,44] and catalytic reaction pathways have been proposed [45,46], the strategies used by the protein to lower the activation barrier has not been quantitatively understood. Moreover, there have been no studies comparing these strategies. Using theoretical and simulation methods, we were able to provide a quantitative description of the strategy employed by these enzymes to weaken the P-O bond. 

This chapter is concerned with the application of liquid state methods to the behavior of polymers at surfaces. The focus is on computer simulation and liquid state theories for the structure of continuous-space or off-lattice models of polymers near surfaces. The first computer simulations of off-lattice models of polymers at surfaces appeared in the late 1980s, and the first theory was reported in 1991. Since then there have been many theoretical and simulation studies on a number of polymer models using a variety of techniques. This chapter does not address or discuss the considerable body of literature on the adsorption of a single chain to a surface, the scaling behavior of polymers confined to narrow spaces, or self-consistent field theories and simulations of lattice models of polymers. The interested reader is instead guided to review articles [9-11] and books [12-15] that cover these topics. 

Having established that bilayer flexibility and bilayer interaction are the mesoscopic determinants, the next question is whether these determinants can be coupled to molecular parameters. In fact, this has been done to quite some extent. In general, bilayer flexibility can be shown (both experimentally as well as theoretically by simulation methods) to be directly related to bilayer thickness, lateral interaction between heads and tails of the surfactants, type of head group (ethoxylate, sugar, etc.), type of tail (saturated, unsaturated) and specific molecular mixes (e.g. SDS with or without pen-tanol). The bilayer interaction is known to be related to characteristics such as classical electrostatics. Van der Waals, Helfrich undulation forces (stemming from shape fluctuations), steric hindrance, number, density of bilayers, ionic strength, and type of salt. Two examples will be dicussed. 

G. H. Fredrickson, V. Ganesan, and F. Drolet (2002) Field-theoretic computer simulation methods for polymers and complex fluids. Macromolecules 35, pp. 16-39... 

Further improvements in our model potentials and simulation methods will therefore undoubtedly increase the detailed accuracy of molecular crystal structure predictions and will be required for crystal structures that correspond to weakly defined minima. However, for a routine transferable scheme, the addition of a realistic ab initio based electrostatic model clearly improves the range of molecules where a minimum in the lattice energy is close to the observed structure. The use of a theoretically derived, rather than an empirical potential, also increases confidence in the extrapolation of the potential to regions sampled in hypothetical crystal structures. 

The complexity of the equilibrium phases and nonequilibrium phenomena exhibited by multicomponent oil-water-surfactant systems is amply demonstrated in numerous contributions in this volume. Therefore, the need for theoretical (and computational) methods that make the interpretation of experimental observations easier and serve as predictive tools is readily apparent. Excellent treatments of the current status of theoretical advances in dealing with microemulsions are available in recent monographs and compendia (see, e.g., Refs. 1-3 and references therein). These references deal with systems consisting of significant fractions of oil and water and focus on the different phases and intricate microstructures that develop in such systems as the surfactant and salt concentrations are varied. In contrast, the present chapter focuses exclusively on simulations, particularly on a first level introduction to the use of lattice Monte Carlo methods for modeling self-association and phase equilibria in surfactant solutions with and without an oil phase. Although results on phase equilibria are presented, we spend a substantial portion of the review on micellization in surfactant-water mixtures, as this forms the necessary first step in the eventual identification of the most essential parameters needed in computer models of surfactant-water-oil systems. 

The ability to predict catalyst performance as a function of chemical composition, molecular structure and morphology is the formdation for the science and technology of catalysis. We aim to describe the use of currently available theoretical and computational methods for both qualitative and quantitative predictions on the molecular events on which the catalytic reaction is based. This relates to the prediction of catalyst structure and morphology as well as the simulation of dynamic changes that occur on the catalyst surface as the result of reaction. 

Cagin, T, Wang, G., Martin, R., Zamanakos, G., Vaidehi, N., Mainz, D. T, and Goddard III, W. A., Multiscale modeling and simulation methods with applications to dendritic polymers. Computational and Theoretical Polymer Science, 00, 000 000 (2001). 

John C. Tully is Arthnr T. Kemp Professor of Chemistry, Physics, and Applied Physics in the Department of Chemistry at Yale University. Tully is a leading theorist studying the dynamics of gas surface interactions. He develops theoretical and computational methods to address fundamental problems and then works with experimentalists to integrate theory with observation. Energy exchange and redistribution, adsorption and desorption, and dissociation and recombination are among surface phenomena he has elucidated. He uses mixed quantum-classical dynamics, which allow the extension of conventional molecular dynamics simulation methods to processes involving electronic transitions or quantum atomic motion. He is a member of the National Academy of Sciences. 

A method, based on the principles of empirical Bayes, is developed to support prediction of failure rates for a particular asset by using the available observational data for a pool of like assets together with engineering Judgment for the asset degradation rate. We have conducted a preliminary theoretical and simulation evaluation of the performance characteristics of our proposed estimation method. 

Such novel experimental findings have prompted very active theoretical studies of polymer interfaces that encompass both analytical models and simulation methods in order to obtain a fundamental understanding of both the equilibrium and dynamic properties of polymer melts confined by various interfaces. Because of the inherent difficulties encoimtered in analytical approaches, simulations have been the more popular theoretical approach. 

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