Nonequilibrium rate processes

Demirel, Y., 2002, Nonequilibrium Thermodynamics Transport and Rate Processes in Physical and Biological Systems, Elsevier, Amsterdam, pp. 186-205. 

Yeganeh S, Ratner MA, Mujica V (2007) Dynamics of charge transfer rate processes formulated with nonequilibrium Green s function. J Chem Phys 126 161103... 

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. 

States away from global equilibrium are called the thermodynamic branch (Figure 2.2). Systems not far from global equilibrium may be extrapolated around equilibrium state. For systems near equilibrium, linear phenomenological equations may represent the transport and rate processes. The linear nonequilibrium thermodynamics theory determines the dissipation function or the rate of entropy production to describe such systems in the vicinity of equilibrium. This theory is particularly useful to describe coupled phenomena, and quantify the level of coupling in physical, chemical, and biological systems without detailed process mechanisms. 

Extended nonequilibrium thermodynamics is not based on the local equilibrium hypothesis, and uses the conserved variables and nonconserved dissipative fluxes as the independent variables to establish evolution equations for the dissipative fluxes satisfying the second law of thermodynamics. For conservation laws in hydrodynamic systems, the independent variables are the mass density, p, velocity, v, and specific internal energy, u, while the nonconserved variables are the heat flux, shear and bulk viscous pressure, diffusion flux, and electrical flux. For the generalized entropy with the properties of additivity and convex function considered, extended nonequilibrium thermodynamics formulations provide a more complete formulation of transport and rate processes beyond local equilibrium. The formulations can relate microscopic phenomena to a macroscopic thermodynamic interpretation by deriving the generalized transport laws expressed in terms of the generalized frequency and wave-vector-dependent transport coefficients. 

Nonequilibrium thermodynamics transport and rate processes in physical, chemical and biological systems. -2nd ed. 

The theory treating near-equilibrium phenomena is called the linear nonequilibrium thermodynamics. It is based on the local equilibrium assumption in the system and phenomenological equations that linearly relate forces and flows of the processes of interest. Application of classical thermodynamics to nonequilibrium systems is valid for systems not too far from equilibrium. This condition does not prove excessively restrictive as many systems and phenomena can be found within the vicinity of equilibrium. Therefore equations for property changes between equilibrium states, such as the Gibbs relationship, can be utilized to express the entropy generation in nonequilibrium systems in terms of variables that are used in the transport and rate processes. The second law analysis determines the thermodynamic optimality of a physical process by determining the rate of entropy generation due to the irreversible process in the system for a required task. 

This book introduces the theory of nonequilibrium thermodynamics and its use in transport and rate processes of physical and biological systems. The first chapter briefly presents the equilibrium thermodynamics. In the second chapter, the transport and rate processes have been summarized. The rest of the book covers the theory of nonequilibrium thermodynamics, dissipation function, and various applications based on linear nonequilibrium thermodynamics. Extended nonequilibrium thermodynamics is briefly covered. All the parts of the book can be used for senior- and graduate-level teaching in engineering and science. 

Increased attention has been focused on vibrational, rotational, and translational nonequilibria in reacting systems as well. To account for these nonequilibrium effects, it is becoming increasingly traditional to express specific reaction-rate constants in terms of sums or integrals of reaction cross-sections over states or energy levels of the reactants involved [3], [11]. This approach helps to relate the microscopic and macroscopic aspects of rate processes and facilitates the use of fundamental experimental information, such as that obtained from molecular-beam studies [57], in calculation of macroscopic rate constants. Proceeding from measurements at the molecular level to obtain the rate constant defined in equation (4) remains a large and ambitious task. 

The Kramers theory and its extensions have found many applications since the original work by Kramers. Recent application of the non-Markovian theory in the low-friction limit to thermal desorption was described by Nitzan and Carmeli. Another novel application of the Markovian theory is to transition from a nonequilibrium state of a Josephson junction. In what follows we shall briefly review the recent application of the generalized Kramers theory to chemical rate processes. More detailed reviews of the exjjerimental and theoretical status of this field may be found in Hynes. ... 

Disequilibrium due to chemical kinetic limitations on heterogeneous soil surfaces have been modeled by Selim et al. (1976a) and Cameron and Klute (1977). These transport models are commonly known as two-site nonequilibrium models, which assume solute adsorption on the two types of sites occur at different rates. Generally, empirical first-order and second-order expressions are utilized to dc.scribe the nonequilibrium adsorption process. 

We have also seen that new experimental work on the hydrogen-deuterium exchange reaction has eliminated some previous discrepancies and has further confirmed the applicability of the activated state method. In the meantime, many theoretical attempts have been made to evaluate the influence of the nonequilibrium hypothesis on which that method is based. It is encouraging to see the generally optimistic results of these efforts, and we may conclude that we can now use with more confidence the familiar expressions of the rate processes. 

There are three basic concepts that explain membrane phenomena the Nemst-Planck flux equation, the theory of absolute reaction rate processes, and the principle of irreversible thermodynamics. Explanations based on the theory of absolute reaction rate processes provide similar equations to those of the Nemst-Planck flux equation. The Nemst-Planck flux equation is based on the hypothesis that cations and anions independently migrate in the solution and membrane matrix. However, interaction among different ions and solvent is considered in irreversible thermodynamics. Consequently, an explanation of membrane phenomena based on irreversible thermodynamics is thought to be more reasonable. Nonequilibrium thermodynamics in membrane systems is covered in excellent books1 and reviews,2 to which the reader is referred. The present book aims to explain not theory but practical aspects, such as preparation, modification and application, of ion exchange membranes. In this chapter, a theoretical explanation of only the basic properties of ion exchange membranes is given.3,4... 

The normal explanation for specific heat deviation above Tg as effect of crystallization or melting can not be used here. A possible explanation of the observed data could Involve cluster formation. The reported specific heat and volume data Indicate structural changes in the glassy state with different mobilities nonequilibrium vitrification process and altered by the following thermal treatment of the samples. This process, an alteration of cooperative motions due to cluster formation, leads to a decrease in mobility of the chains and prevents equilibrium enthalpies above Tg to be directly attained at the selected scanning rate. 

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