Diffusion-influenced excited-state reversible transfer reactions, A* + Bright harpoon over left harpoonC* + D, with two different lifetimes: theories and simulations

We report accurate Brownian simulation results for the kinetics of the pseudo-first-order diffusion-influenced excited-state reversible transfer reaction A(*) + Bright harpoon over left harpoonC(*) + D with two different lifetimes using two different propagation algorithms. The results are used to test approximate solutions for this many-particle problem. Available theories fail when one of the two reactions or (decay) rate constants is large. To remedy this situation, we develop two uniform approximations, which are based on introducing a generalized Smoluchowski term into the relaxation-time approximation. The best of these is the extended unified theory of reversible target reactions, which reduces correctly in all limits and exhibits superior agreement with simulations.     

Experimental verification of the Smoluchowski theory for a bimolecular diffusion-controlled reaction in liquid phase

We report experimental verification of the Smoluchowski theory for diffusion-controlled reactions in solution at the steady-state limit. We have determined both the diffusion coefficients and the self-termination reaction rates of the diphenylmethyl radical simultaneously. Smoluchowski theory is insufficient to discuss the reaction rate for the self-termination reaction of the diphenylmethyl radical, so the reaction rate of an encounter complex based on the Collins-Kimball treatment is estimated.     

Analytical theories of transport in concentrated electrolyte solutions from the MSA

Ion transport coefficients in electrolyte solutions (e.g., diffusion coefficients or electric conductivity) have been a subject of extensive studies for a long time. Whereas in the pioneering works of Debye, Hückel, and Onsager the ions were entirely characterized by their charge, recent theories allow specific effects of the ions (such as the ion size dependence or the pair association) to be obtained, both from simulation and from analytical theories. Such an approach, based on a combination of dynamic theories (Smoluchowski equation and mode-coupling theory) and of the mean spherical approximation (MSA) for the equilibrium pair correlation, is presented here. The various predicted equilibrium (osmotic pressure and activity coefficients) and transport coefficients (mutual diffusion, electric conductivity, self-diffusion, and transport numbers) are in good agreement with the experimental values up to high concentrations (1-2 mol L(-1)). Simple analytical expressions are obtained, and for practical use, the formula are given explicitly. We discuss the validity of such an approach which is nothing but a coarse-graining procedure.     

Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker-Planck equation

The problem of the derivation of the diffusion equation exactly following from the Fokker-Planck (or Klein-Kramers) equation for heavy (or large) particles in a fluid in an external force field is solved in the case in which the particles are ions subject to a uniform (but in general time-varying) electric field. It is found that such a diffusion equation maintains memory of the initial ion velocity distribution, unless sufficiently large values of time are considered. In such temporal asymptotic limit, the diffusion equation exactly becomes (i) the Smoluchowski equation when the electric field is constant in time, and (ii) a new equation generalizing the Smoluchowski equation, when the electric field is arbitrarily time varying. Finally, it is shown that the obtained exact (or asymptotic) results make questionable the procedures and the results of approximate theories developed in the past to get a "corrected" Smoluchowski equation when the external force can also be, in general, position dependent.     

Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.     

原子簇离子产生的动力学方程与分布函数

由激光等离子体反应产生的原子簇分子与离子，经历了分子-离子反应的过程．本文尝试将Smoluchowski方程加以扩展，用于描述原子簇离子的生成过程．通过应用解析方法，求解不可逆聚合过程的动力学方程，推导出了原子簇离子统计分布的函数关系式，证实了实验中观察到的原子簇的统计分布规律．     

Recent developments in the kinetic theory of nucleation

A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.     

Variational formula for the relaxation time in the Boltzmann equation

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the Boltzmann equation, which allows us to extend the standard RTA using relaxation times that depend on the initial distribution. Tests of the approach on a calculation of the mobility for a one-dimensional (1D) tight-binding band indicate that our analysis typically provides a better approximation than the standard RTA.     

The effect of bulk motion on coagulation rates of colloidal dispersions

Following the work in 1917 of Smoluchowski, the theory of coagulation of micronsized particles progressed very little until quantitative estimates were possible for induced-dipole attraction and electrostatic double-layer repulsion. A second increase in our understanding of coagulation of colloids has been achieved through application of recent results in fluid mechanics concerning the viscous forces operative between two particles in relative motion.In this survey the essential features of recent theories and experiments of the behavior of spherical of hydrophobic colloids in aqueous suspensions are outlined. Departures from earlier theories are reviewed, and attempts to incorporate simultaneously the effects of bulk flow and of Brownian motion are described.     

Substrate concentration dependence of the diffusion-controlled steady-state rate constant

The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B2*. Comparisons to Brownian dynamics simulations excluding hydrodynamic interactions show excellent agreement up to bulk number densities of B2*rho0 < approximately = 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.     

Predicted reaction rates of H(x)N(y)O(z) intermediates in the oxidation of hydroxylamine by aqueous nitric acid

This work reports computed rate coefficients of 90 reactions important in the autocatalytic oxidation of hydroxylamine in aqueous nitric acid. Rate coefficients were calculated using four approaches: Smoluchowski (Stokes-Einstein) diffusion, a solution-phase incarnation of transition state theory based on quantum chemistry calculations, simple Marcus theory for electron-transfer reactions, and a variational TST approach for dissociative isomerization reactions that occur in the solvent cage. Available experimental data were used to test the accuracy of the computations. There were significant discrepancies between the computed and experimental values for some key parameters, indicating a need for improvements in computational methodology. Nonetheless, the 90-reaction mechanism showed the ability to reproduce many of the trends seen in experimental studies of this very complicated kinetic system. This work highlights reactions that may govern the system evolution and branching behavior critical to the stability of the system. We hope that this analysis will guide experimental investigations to reduce the uncertainties in the critical rate coefficients and thermochemistry, allowing an unambiguous determination of the dominant reaction pathways in the system. Advances in efficient and accurate solvation models that effectively separate entropic and enthalpic contributions will most directly benefit solution-phase modeling efforts. Methods for more accurately estimating activity coefficients, including at infinite dilution in multicomponent mixtures, are needed for modeling high ionic strength aqueous systems. A detailed derivation of the solution-phase equilibrium and transition state theory rate expressions in solution is included in the Supporting Information.     

Kinetics on Diffusion-Controlled Reactions in a Fractal Medium

The kinetics are investigated for diffusion-controlled reactions in a fractal medium described by a Smoluchowski equation. A class of model potentials are taken into account so as to solve the time-dependent Smoluchowski equation. Corrections to the standard solution are proposed for the fractal geometry of the medium.     

Collision theory treatment of monomolecular and bimolecular gas reactions

An exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum-mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).     

Time-dependent quantum theory II. Absorption of light by dimers: Quantum theory and classical analogy

The quantum theory of light absorption by a pair of neighboring absorbers is developed in the point dipole approximation for the circumstance where excited states decay only by radiative damping. Comparison with classical local field theories, in which the monomers are represented by constant, frequency-dependent complex polarizabilities, shows that these local field theories are valid for non-harmonic absorbers only in the weak interaction limit, and only when there exist no states with both monomers simultaneously excited (e.g. one excited vibrationally, the other electronically) that are nearly degenerate with the single excitation states and also connected to them by appreciable transition moments. Failure of the local field theories is, thus, shown to be a consequence of the non-harmonic nature of real absorbers. Using a general relation between the level-shift function and complex polarizability, a recipe is formulated for calculating the complex polarizability and spectrum of a dimer.     

Limitations of the photostationary approximation in the photochemistry of provitamin D: The ambiguous role of the irreversible degradation channel

The limitations of the generally accepted photostationary approximation in the photochemistry of provitamin D resulting from the strong spectral dependence of the effectiveness of the irreversible channel were established theoretically by a simplified model. The results show clearly that disregard of the irreversible channel with low quantum yield in a system of reversible photochemical reactions over a wide spectral range is not always justified. As a result the approximation according to which the concentration of the main photoisomers of provitamin D is constant only holds in a specific region of the spectrum, and this must be taken into account during concentration analysis of the photoisomeric mixture. Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 44, No. 5, pp. 279–283, September–October, 2006.     

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5-2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K.     

Conjugate reactions: New potentials of an old idea

Main concepts of the Shilov–Ostwald theory of conjugate chemical reactions are analyzed from the standpoint of complex reaction kinetics, theory of reaction routes, and thermodynamics of irreversible processes. Classification of conjugate reactions and an algorithm of catalytic system design for conducting these processes are proposed.     

Quasi-Steady-State Laws in reversible model of enzyme kinetics

In enzyme kinetics, the Quasi-Steady-State Assumption (QSSA) has been proposed for over 80 years, which plays a very important role in simplifying systems of equations derived from chemical reactions with enzymes. Five years ago, we proved that the QSSA is always true in the simplest model with the second elementary reaction irreversible, and called them as Quasi-Steady-State Laws. Thus, all conclusions based on QSSA have a solid foundation in irreversible case. However, the chemical reactions are not always so simple in many life processes. The second elementary reaction should be reversible in general, and the irreversible case is actually only an approximation. So it is more important and interesting to study the reversible case, and it has already attracted enzymologists for a long time. The basic assumption, i.e. QSSA in this general case has appeared in 1930. We proved this lasting over 80 years assumption in this paper.