Statistical physics chemical kinetics

The papers on which the articles in this volume are based, were prepared at the invitation of the organizing committee, for presentation at the Conference on Stochastic Processes in Chemical Physics which was held at the University of California at San Diego, La Jolla, March 18-22, 1968. The purpose of this meeting was to bring together selected experts in the fields of probability theory, applied mathematics, transport processes, statistical mechanics, chemical kinetics, polymer chemistry, and molecular biochemistry for an exchange of ideas and to stimulate interest and activity in the application of the theory of stochastic processes to problems in chemical physics. 

The book is therefore situated at the interface between physical chemistry (classical thermodynamics and statistical mechanics, chemical kinetics, transport phenomena) and the theory of reactors, themselves at the heart of chemical reaction engineering. It therefore possesses a marked pluridisciplinary character. However, in order to keep this book readable by newcomers to the fields both of GPTRs and the kinetic modelling of reactions, basic concepts, theories and laws of the underlying scientific disciplines are given. The main equations are illustrated by simple numerical applications in order to show how the data tables are used. 

Chemistry can be divided (somewhat arbitrarily) into the study of structures, equilibria, and rates. Chemical structure is ultimately described by the methods of quantum mechanics equilibrium phenomena are studied by statistical mechanics and thermodynamics and the study of rates constitutes the subject of kinetics. Kinetics can be subdivided into physical kinetics, dealing with physical phenomena such as diffusion and viscosity, and chemical kinetics, which deals with the rates of chemical reactions (including both covalent and noncovalent bond changes). Students of thermodynamics learn that quantities such as changes in enthalpy and entropy depend only upon the initial and hnal states of a system consequently thermodynamics cannot yield any information about intervening states of the system. It is precisely these intermediate states that constitute the subject matter of chemical kinetics. A thorough study of any chemical reaction must therefore include structural, equilibrium, and kinetic investigations. 

These theories may have been covered (or at least mentioned) in your physical chemistry courses in statistical mechanics or kinetic theory of gases, but (mercifully) we will not go through them here because they involve a rather complex notation and are not necessary to describe chemical reactors. If you need reaction rate data very badly for some process, you will probably want to fmd the assistance of a chemist or physicist in calculating reaction rates of elementary reaction steps in order to formulate an accurate description of processes. 

Next, we review findings of educational research about the main areas of physical chemistry. Most of the work done was in the areas of basic thermodynamics and electrochemistry, and some work on quantum chemistry. Other areas, such as chemical kinetics, statistical thermodynamics, and spectroscopy, have not so far received attention (although the statistical interpretation of entropy is treated in studies on the concepts of thermodynamics). Because many of the basics of physical chemistry are included in first-year general and inorganic courses (and some even in senior high school), many of the investigations have been carried out at these levels. 

Chemical Kinetics of Solids covers a special part of solid state chemistry and physical chemistry. It has been written for graduate students and researchers who want to understand the physical chemistry of solid state processes in fair depth and to be able to apply the basic ideas to new (practical) situations. Chemical Kinetics of Solids requires the standard knowledge of kinetic textbooks and a sufficient chemical thermodynamics background. The fundamental statistical theory underlying the more or less phenomenological approach of this monograph can be found in a recent book by A. R. Allnatt and A.B. Lidiard Atomic Transport in Solids, which complements and deepens the theoretical sections. 

The authors of this book started working on chemical kinetics more than 10 years ago focusing on investigations of particular radiation - induced processes in solids and liquids. Condensed matter physics, however, treats point (radiation) defects as active particles whose individual characteristics define kinetics of possible processes and radiation properties of materials. A study of an ensemble of such particles (defects), especially if they are created in large concentrations under irradiation for a long time, has lead us to many-particle problems, common in statistical physics. However, the standard theory of diffusion-controlled reactions as developed by Smoluchowski... 

Despite the fact that formalism of the standard chemical kinetics (Chapter 2) was widely and successfully used in interpreting actual experimental data [70], it is not well justified theoretically in fact, in its derivation the solution of a pair problem with non-screened potential U (r) = — e2/(er) is used. However, in the statistical physics of a system of charged particles the so-called Coulomb catastrophes [75] have been known for a long time and they have arisen just because of the neglect of the essentially many-particle charge screening effects. An attempt [76] to use the screened Coulomb interaction characterized by the phenomenological parameter - the Debye radius Rd [75] does not solve the problem since K(oo) has been still traditionally calculated in the same pair approximation. 

We have tried, without being overly formalistic, to develop the subject in a systematic manner with attention to basic concepts and clarity of derivations. The reader is assumed to be familiar with the basic concepts of classical mechanics, quantum mechanics, and chemical kinetics. In addition, some knowledge of statistical mechanics is required and, since not all potential readers may have that, we have included an appendix that summarizes the most important results of relevance. The book is reasonably self-contained such that a standard background in mathematics, physics, and physical chemistry should be sufficient and make it possible for the students to follow and understand the derivations and developments in the book. A few sections may be a little more demanding, in particular some of the sections on quantum dynamics and stochastic dynamics. 

The traditional apparatus of statistical physics employed to construct models of physico-chemical processes is the method of calculating the partition function [17,19,26]. The alternative method of correlation functions or distribution functions [75] is more flexible. It is now the main method in the theory of the condensed state both for solid and liquid phases [76,77]. This method has also found an application for lattice systems [78,79]. A new variant of the method of correlation functions - the cluster approach was treated in the book [80]. The cluster approach provides a procedure for the self-consistent calculation of the complete set of probabilities of particle configurations on a cluster being considered. This makes it possible to take account of the local inhomogeneities of a lattice in the equilibrium and non-equilibrium states of a system of interacting particles. In this section the kinetic equations for wide atomic-molecular processes within the gas-solid systems were constructed. 

Refs. [i] Landau LD, Lifshitz EM (1970) Statistical physics, 2nd edn. Pergamon, Oxford [ii] Kuznetsov AM (1997) Stochastic and dynamic views of chemical reaction kinetics in solutions. Presses polytechniques et universitaire romandes, Lausanne [iii] Kornyshev AA, Leikin S, Sut-mann G (1997) Electrochim Acta 42 849... 

Benson. The Foundations of Chemical Kinetics Djerassi. Optical Rotatory Dispersion Hill. Statistical Mechanics IIiNE. Physical Organic Chemistry Laitinen. Chemical Amilysis... 

Accompanying the development of chemistry in other fields, researches unique to Japanese solution chemistry were grown. Investigations on properties of solutions by thermodynamics and statistical thermodynamics, chemical equilibria and reaction kinetics became to be the main fields of physical and inorganic solution chemistry in Japan. Even after a break of scientific investigations due to the War II we still had difficulties to communicate with scientists outside Japan. Not only solution chemists but also scientists in other fields in Japan had to tread a thorny path for several years in the 1940 s-1950 s. 

The physical chemistry courses taught at UNTVEN comprise chemical thermodynamics at second-year level electrochemistry, chemical kinetics and surface chanistry at third-year level quantum chemistry in the first semester of the first postgraduate level (called B.Sc. Honours ) spectroscopy and statistical thermodynamics in the second semester of the B.Sc. Honours level (an optional course only rarely selected by students). 

The first section of this book covers liquids and. solutions at equilibrium. I he subjects discussed Include the thcrmodvnamics of solutions, the structure of liquids, electrolyte solutions, polar solvents, and the spectroscopy of solvation. The next section deals with non-equilibrium properties of solutions and the kinetics of reactions in solutions. In the final section emphasis is placed on fast reactions in solution and femtochemistry. The final three chapters involve important aspects of solutions at interfaces. Fhese include liquids and solutions at interfaces, electrochemical equilibria, and the electrical double layer. Author W. Ronald Fawcett offers sample problems at the end of every chapter. The book contains introductions to thermodynamics, statistical thermodynamics, and chemical kinetics, and the material is arranged in such a way that It may be presented at different levels. Liquids, Solutions, and Interfaces is suitable for senior undergr.iduates and graduate students and will be of interest to analytical chemists, physical chemists, biochemists, and chemical environmental engineers. 

The physical structure of the polymer is then computed from knowledge of the chemical kinetics, utilizing the statistical methods developed by Macosko and Miller (2A,... 

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