Mean field kinetic theory for a lattice gas model of fluids confined in porous materials

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.     

Non-equilibrium thermodynamics and kinetic theory of gas mixtures in the presence of interfaces

A broad range of the boundary value problems of the kinetic theory of gases and gas mixtures is considered based on kinetic theory and non-equilibrium thermodynamics. The interrelation of the kinetic theory and non-equilibrium thermodynamics is discussed. The balance equations at the interface are obtained for the case of the boundary layers with peculiar properties. Procedures for deriving the boundary conditions for slightly rarefied gas mixtures are outlined. The problems of calculating slip coefficients are discussed. The specificity of the kinetic effects in the boundary conditions is shown. A set of general relations related to gas mixture flows in capillaries is deduced. The possibility of non-equilibrium kinetic effects in the form of a paradoxical distribution of non-equilibrium temperature is shown. Methods of non-equilibrium thermodynamics are used to obtain the phenomenological equations describing the thermophoresis and diffusiophoresis of particles and cross phenomena. The growth and evaporation of droplets is considered based on kinetic theory and non-equilibrium thermodynamics.     

Self-consistent field equations in the distribution function theory of polymeric liquids

In the distribution function approach to the conformational and thermodynamic properties of polymeric liquids site-site (pair) distribution functions are essential components of the theory. These site-site pair distribution functions are basically mean fields obeying integral equations. In our recent works, a set of self-consistent field equations has been proposed for site-site pair correlation functions which allow us to study conformational and thermodynamic properties of polymeric liquids. In this article, we present a short review of the theory and its applications to a number of aspects of polymeric liquids we have made until now. We also present a self-consistent version of the polymer reference interaction site model where the integral equations for the intramolecular site-site correlation functions are obtained from the Kirkwood hierarchy on the basis of the present theory. The present theory is shown to predict correctly the scaling properties associated with swollen and collapsed polymers in good and poor solvents, respectively. At finite densities, self-consistent solutions of the intra- and intermolecular equations yield the structures and thermodynamics of polymer melts which are favorably compared with Monte Carlo simulation results. Self-consistent theory results are found to be more accurate than the non-self-consistent approaches that use an ideal Gaussian chain conformation distribution function. © 1995 John Wiley & Sons, Inc.     

Dynamics of Capillary Rise

An overview and detailed analysis of the classical theory of capillarity is presented. A number of known equations of capillary rise dynamics are shown to be different limiting cases of one rather general equation. Some internal inconsistencies of the classical equations are pointed out. The role of nonlinear dissipation and flow pattern effects in the front zone of the liquid column and near the capillary entrance is discussed. Numerical simulations and experimental data demonstrating some characteristic types of dynamic behavior predicted by the theory are reported. Special attention is paid to the capillary rise of surfactant solutions. As applied to this special case, the existing theory is substantially elaborated by setting up a closed system of equations describing the surfactant transport and relaxation processes in the adsorption layer. A simplified relation for the capillary rise dynamics in the case of strong depletion of the interfacial region is obtained, which is in qualitative agreement with the experimental behavior. Copyright 2000 Academic Press.     

Melting point depression and phase behavior of poly(ether-sulfone) and poly(ethylene oxide) blends: Equation-of-state theory approach

Melting-point depression in miscible polymer blends is interpreted with Flory-Prigogine's equation-of-state theory (FP theory) and Sanchez-Lacombe's lattice fluid theory (LF theory). The equations for equilibrium melting point depression in polymer mixtures are proposed from both the FP and LF theories. For miscible poly(ether-sulfone) (PES)/poly(ethylene oxide) (PEO) blends, the proposed equations are tested. The interaction parameters, X₁₂ in FP theory and ζ₁₂ in LF theory, can be determined with these equations. The theoretically predicted equilibrium melting-point depression is subdivided into three terms, namely, the equation-of-state, the entropy and the contact interaction terms. When the estimated interaction parameters are converted to the heat of mixing by use of both theories, the composition dependence of the heat of mixing can be properly predicted. Using the interaction parameters obtained from the melting-point depression in PES/PEO blends, the spinodal curves are simulated from both the FP and LF theories.     

A coupled hartree-fock calculation of the paramagnetic contribution to the cotton-mouton constant of helium

The perturbation equations necessary for the evaluation of the paramagnetic part of the Cotton-Mouton constant of helium are derived as an example of coupled Hartree-Fock theory for a double perturbation and the ensuing integro-differential equations solved numerically. A comment is made on the errors in the numerical solution of such equations.     

Viscosities of liquids, colloidal suspensions, and polymeric systems under zero or non-zero electric field

The viscosities of pure liquids, polymer solutions and melts, and colloidal suspensions under zero or non-zero electric field are surveyed in this paper and the focus is placed on the case that no electric field is applied. The free volume concept and Eyring's rate theory is used for deriving the viscosity equations of pure liquids, polymer solutions and melts, and colloidal suspensions. The derived equations are found to be more universal and could be reduced to many currently used equations under certain simplifications. Qualitatively, those derived equations are in consistent with experimental results, too.     

Statistical mechanics and fluid structure

In the axiomatic approach to the derivation of statistical mechanics the theory is based upon the equations of motions of classical mechanics (Hamilton equations). Since these equations are unstable with respect to initial conditions, in the time τ ≈ 10^?12 s they generate chaos in the system of atoms and molecules. This chaos can be described by only probability theory laws. The laws of this theory are introduced into statistical mechanics as the second postulate. However, for both postulates (i.e., Hamilton equations and probability theory laws) to be compatible with each other, about one and a half ten of additional requirements defining in detail the matter model underlying the theory must be imposed on the system. This report analyzes only the restrictions imposed by probability theory. The main of them are: a transition to the thermodynamic limit, the condition of correlation attenuation, and a short-range character of the interaction potential. The matter model formulated based on these restrictions is a continuous medium in which a correlation sphere with a small radius R ≈ 10^?7 cm (physical point) is submerged. It is submerged in an infinite thermostat, the particles of which behave as the ideal gas relative to the particles forming the correlation sphere. Here all macroscopic parameters of matter in this physical point are determined by the state of the correlation sphere. Thus formulated model determines the macro- and microscopic structure of matter, and finally, results in thermodynamic and hydrodynamic equations.     

Theory of excluded volume equation of state: higher approximations and new generation of equations of state for entire density range

A novel theory of an equation of state based on excluded volume and formulated in two preceding papers for gases and gaseous mixtures is extended to the entire density range by considering higher (beginning from the third) approximations of the theory. The algorithm of constructing higher approximations is elaborated. Equations of state are deduced using the requirement of maximum simplicity and contain a single free parameter to be chosen by reason of convenience or simplicity or to be used as a fitting parameter with respect to the computer simulation database. In this way, precise equations of state are derived for the hard-sphere fluid in the entire density range. On the side, the theory reproduces most known earlier equations of state for hard spheres and determines their place in the hierarchy of approximations. Equations of state for van der Waals fluids are also presented, and their critical parameters are estimated.     

SCF equations for pure spin states with many-particle interactions

SCF equations for any pure spin state are given for a spin-free system with many-particle interactions. The equations are very simple and explicit. Due to the use of different antisymmetric requirement our equations are different from some of the other methods. In our method, the abstract group theory formalism is converted into some explicit and straightforward equations which makes the many-particle interaction problem easier to handle.     

A nondiagonal quasidegenerate fourth-order perturbation theory

A canonical quasidegenerate Rayleigh-Schrödinger perturbation theory, correct through fourth order in the energy, is explored for a block-diagonal unperturbed Hamiltonian. The theory is developed completely within a Lie Algebra in Hilbert space. Explicit equations forn-particle transition elements in terms of solutions of simultaneous linear equations are presented. A two-dimensional anisotropic anharmonic oscillator is used to provide numerical results. The perturbation theory is shown to be stable under small separation of model and complement spaces. An iterative variant of the fourth order perturbation theory is introduced; the iterative variant is related to the non-iterative one in much the same way as nondegenerate coupled cluster theories are related to nondegenerate perturbation theory. The quasidegenerate coupled cluster theory appears to be stable in the presence of multiple intruder states.     

由成核率数据拟合饱和蒸汽压力

Saturated vapor pressure was calculated from the nucleation experimental data using the thermodynamically consistent nucleation theory in which the effect of real gas is considered. The cubic polynomial fit equations of saturation pressure for several substances were obtained based on the calculation. The results of the calculations were compared to those of thermodynamic equilibrium equation and the empirical equation and applied to the predictions of the classical nucleation theory. The results show that the saturation pressures estimated from the nucleation data agree fairly well with those of empirical equations for the substances investigated, and this indicates that the predictions from the classical nucleation theory are close to the experimental data.     

Small-angle light scattering from optically anisotropic spheres and disks. Theory and experimental verification

The small-angle light scattering (SALS) theory for optically anisotropic spheres and disks is examined in depth. An error is found in the existing sphere equations. The correct form of the equations is identified and then experimentally verified for dilute starch suspensions. Increased concentrations and solid films of starch granules are used to identify the effect of concentration on the scattering envelope. Spherulitic films of isotactic polypropylene, isotactic polystyrene, nylon 610, PET, and nylon 66 are then used to examine different aspects of the SALS theory. Experimental observations are found to agree with the predictions of the correct SALS equations. Disk theory is interrogated and correlated with predictions for spheres. It is found that the predicted patterns from spheres and disks are very similar under identical optical conditions, in contradiction to earlier predictions. A method is developed for identifying the optical sign of spherulites too small to be seen in the optical microscope. This study constitutes a comprehensive examination of SALS theory and includes many other aspects of the phenomena. A catalogue of theoretical V_v SALS patterns from spheres and disks is also included.     

Theoretical determination of electronic lifetimes in metals

For a variety of different fields in condensed matter physics it is important to understand the dynamics of excited electrons of bulk and surface states. In this article the results of first-principles computations for the lifetime of excited electrons in various metals are presented. In addition to crystalline systems also calculations of the electronic lifetimes in surface states of these materials are discussed. Preceding is a section in which the general theory is presented needed to calculate the lifetime of excited one-particle states. The method of choice is many-body perturbation theory using the GW approximation for the electronic self-energy. The key equations are summarized and a physical interpretation is given. This part is supplemented by the appendix in which the equations actually used in the calculations are presented in more detail.     

A reduced density-matrix theory of absorption line shape of molecular aggregate

A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (F?rster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.     

Dependence on effective saturation of numbers of singlet peaks in one- and two-dimensional separations

The average numbers of singlet peaks in one-dimensional (1D) and two-dimensional (2D) separations of randomly distributed peaks are predicted by statistical-overlap theory and compared against the effective saturation. The effective saturation is a recently introduced metric of peak crowding that is more practitioner-friendly than the usual metric, the saturation. The effective saturation absorbs the average minimum resolution of statistical-overlap theory, facilitating the comparison of 1D and 2D separations by traditional metrics of resolution and peak capacity. In this paper, singlet peaks are identified with maxima produced by a single mixture constituent. Their effective saturations are calculated from published equations for the average minimum resolution of 1D singlet peaks, and from equations derived here for the average minimum resolution of 2D singlet peaks. The fractions of peaks that are singlets in 1D and 2D separations are predicted by statistical-overlap theory as functions of saturation but are compared as functions of effective saturation. The two fractions differ by no more than 0.033 at any effective saturation between 0 and 6, when the distribution of peak heights is exponential and the edge effect is neglected. This result shows that 1D and 2D separations of randomly distributed peaks are about the same in their ability to separate singlet peaks as maxima, when assessed relative to effective saturation. Empirical equations in effective saturation are reported for the fractions of peaks that are singlets. It is argued that the effective saturation is a good metric for comparing separations having different average minimum resolutions.     

Two types of Kramers rate equations for reactions in condensed media

Two cases of bilinear coupling of a particle to a medium are compared. They differ in that one of the mediums does not modify the particle potential, whereas the other does. Two corresponding kramers-type rate equations for adiabatic reactions are derived directly from a dynamic rate theory and interpreted from the view of the stochastic theory. Both equations become identical in the weak coupling limit. Their relations to transition-state theory are also discussed. Corresponding results for nonadiabatic reactions are considered. © 1994 John Wiley & Sons, Inc.     

Density-functional theory with effective potential expressed as a direct mapping of the external potential: applications to atomization energies and ionization potentials

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Moller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods.     

Viscous flow and non-linear phenomena in non-equilibrium thermodynamics of membrane transport Part 2 — The phenomenological equations

Phenomenological equations are deduced which give the flows of matter, volume, charge and heat for a discontinuous system in which inertial terms in the viscous equations of motion are not negligible. It is found that the equations contain terms in the powers of the first-order affinities, with corresponding phenomenological coefficients. These coefficients can all be derived from first-order coefficients, however, and thus refer to a system which is close to equilibrium. The theory agrees with well-documented specific hydrodynamic calculations, but generalizes these in the framework of now equilibrium thermodynamics.     

Stability in chemical and biological systems: Multistage polyenzymatic reactions

General principles of the theory of stability of solutions to differential equations are considered. The stability of equations describing the dynamics of changes in reagent concentrations in polyenzymatic biochemical chains is analyzed. Various mechanisms of formation of stable and unstable stationary states are considered, and unbalanced regimes and collapse are analyzed. The influence of systems of toxins and drugs on stability is studied. An interpretation of pathological processes based on stability theory is given.