Kinetics microscopic theories

The kinetic-molecular theory (KMT) represents the properties of gases by modeling the gas particles themselves at the microscopic level. The KMT assumes that ... 

Of special interest in the recent years was the kinetics of defect radiation-induced aggregation in a form of colloids-, in alkali halides MeX irradiated at high temperatures and high doses bubbles filled with X2 gas and metal particles with several nanometers in size were observed [58] more than once. Several theoretical formalisms were developed for describing this phenomenon, which could be classified as three general categories (i) macroscopic theory [59-62], which is based on the rate equations for macroscopic defect concentrations (ii) mesoscopic theory [63-65] operating with space-dependent local concentrations of point defects, and lastly (iii) discussed in Section 7.1 microscopic theory based on the hierarchy of equations for many-particle densities (in principle, it is infinite and contains complete information about all kinds of spatial correlation within different clusters of defects). 

The mechanism by which equilibrium is attained can only be visualized in terms of microscopic theories. In the kinetic sense, equilibrium is reached in a gas when collisions among molecules redistribute the velocilies lor kinetic energies) of each molecule until a Maxwellian distribution is reached for the whole bulk. In the case of the trend toward equilibrium for two solid bodies brought into physical contact, we visualize the transfer of energy by means of free electrons and phonons (lattice vibrations). 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

It should also be emphasised that an initial period of interaction of elementary substances when there is still no compound layer and consequently there is only one common interface at which substances A and B react directly, is outside the scope of the proposed macroscopic consideration. The stage of nucleation of a chemical compound between initial phases is to be the subject of examination within the framework of a microscopic theory which would have to provide, amongst other parameters of the process, a minimal thickness sufficient to specify the interaction product formed at the A-B interface as a layer of the chemical compound ApBq possessing its typical physical and chemical properties. However, it can already now be said with confidence that this value is small in comparison with really measured thicknesses of compound layers and therefore can hardly have any noticeable effect on the shape of the layer thickness-time kinetic dependences observed in practice. 

Here, // is the chemical potential of the electrons in the system at a given temperature T, P is the pressure, and N is the number of electrons. The chemical potential accounts for the kinetic energy of the electrons and the potential energy due to interactions of the electrons with the other electrons and the core ions. (A microscopic theory for electrons in a solid phase is discussed in Section 4.3.) From Eq. 1 it follows that n can be defined as the increase in internal energy of the electron system when one electron is added to the system under conditions of constant volume V and entropy S ... 

Metals form a class of solids with characteristic macroscopic properties. They are ductile, have a silver-white luster, and they conduct electricity and heat remarkably well. An early, but still relevant microscopic model aimed at explaining the electrical conductivity, heat conductivity, and optical properties was proposed by Drude [10]. His model incorporates two important successes of modem science the discovery of the electron in 1887 by J. J. Thomson, and the molecular kinetic gas theory put forward by Boltzmann and Maxwell in the second half of the 19th century. 

The kinetic-molecular theory describes the microscopic behavior of gases. One main point of the theory is that within a sample of gas, the frequency of collisions between individual gas particles and between the particles and the walls of their container increases if the sample is compressed. The gas law that states this relationship in mathematical terms is... 

Kinetic-molecular theory A theory that attempts to explain macroscopic observations on gases in microscopic or molecular terms. 

In 1905, Albert Einstein created a mathematical model of Brownian motion based on the impact of water molecules on suspended particles. Kinetic molecular theory could now be observed under the microscope. Einstein s more famous later work in physics on relativity may be applied to chemistry by correlating the energy change of a chemical reaction with extremely small changes in the total mass of reactants and products. 

Our approach to the study of the departure from equilibrium in chemical reactions and of the "microscopic theory of chemical kinetics is a discrete quantum-mechanical analog of the Kramers-Brownian-motion model. It is most specifically applicable to a study of the energy-level distribution function and of the rate of activation in unimolecular (dissociation Reactions. Our model is an extension of one which we used in a discussion of the relaxation of vibrational nonequilibrium distributions.14 18 20... 

The previous sections dealt with a generalized theory of heterogeneous electron-transfer kinetics based on macroscopic concepts, in which the rate of the reaction was expressed in terms of the phenomenological parameters, and a. While useful in helping to organize the results of experimental studies and in providing information about reaction mechanisms, such an approach cannot be employed to predict how the kinetics are affected by such factors as the nature and structure of the reacting species, the solvent, the electrode material, and adsorbed layers on the electrode. To obtain such information, one needs a microscopic theory that describes how molecular structure and environment affect the electron-transfer process. 

This review is organized to cover the basic features of simple electron transfer reactions. The first three sections develop background material on the thermodynamics, kinetics, and microscopic theory of electron transfer reactions. More general, semiquantitative treatments of these topics are presented, with the objective of introducing the conceptual approaches used to characterize electron transfer processes. The fourth section describes experimental studies on two electron transfer systems, selected from both physiological and nonphysiological... 

This chapter is intended to serve as a framework for the discussion of some of these questions. Thus we construct a kinetic theory that treats both the solute and solvent dynamics. We need to adopt such a detailed point of view if we are to attempt an answer to the questions posed above. Only the beginnings of a theory are presented, but we hope to provide some insight into how condensed-phase reactions might be described by a microscopic theory. 

Here, we consider several specific problems, to illustrate some of the complexities encountered when treating actual systems, and also to point out how the general ideas presented earlier apply to these cases. The examples we pick either correspond to reactions that have been discussed in the course of formulating the kinetic theory, or else show how the theory can be implemented for the treatment of actual systems. We do not attempt to comment on the wide variety of reactions studied in the condensed phase, for which a microscopic theory would be desirable. Discussions of other systems can be found in recent reviews. ... 

A fully microscopic treatment of this problem is a very difficult task. It is usually the motion of some internal coordinate of a complex molecule that is important for the description of the isomerization reaction (cf. Sections III and IV). A microscopic theory at the same level as that for the bimolecular processes described in the previous sections would entail a full description (or model) of the internal structure of the molecule and its interactions with the surrounding solvent. The collision dynamics for such a process are necessarily complex, but a theory at this detailed level is not out of the question for some models of small molecule isomerization reactions. However, it is probably premature to embark on such a program, since the implications of the kinetic theory for the reactions for which it is more easily formulated have not yet been fully explored. 

How is the phenomenon of temperature explained on the basis of the kinetic molecular theory What microscopic property of gas molecules is reflected in the temperature measured ... 

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