Byung Chan Eu

On the modified moment method and irreversible thermodynamics

The modified moment method for the Boltzmann equation is reexamined and improved. There now is only one consistency condition instead of a set of consistency conditions, and it is a necessary and sufficient condition for the extended Gibbs relation. The condition is seen to be a partial differential equation for the entropy density. A strategy to determine the entropy from the data on transport processes is presented. By this strategy measurements of transport coefficients amount to a measurement of nonequilibrium entropy just as measurements of heat capacity, compressibility, etc., yield an equilibrium entropy. A relative measure of probability for a pair of steady states is given in terms of the entropy productions at the steady states. According to the measure a steady state of lower entropy production is more favorable.

Energy dependence of reaction cross sections at high energy

Abstract The energy dependence of the total reaction cross sections for the reaction A + BC → AB + C is obtained in the sufficiently high energy regime, based on the Born approximation and the stationary phase approximation. The total reaction cross section (σ t ) which is a sum over all final vibrational and rotational states of the integral of the angular distribution over angles, is found to be in the form where Q is the maximum exoergicity and positive. It is shown that, when adjusted to an experimental value, (σ t ) fits remarkably well the cross sections for the reaction K + CH 3 I → Kl + CH 3 , past the maximum of the cross sections reported by Gersch and Bernstein.

The generic van der Waals equation of state and self-diffusion coefficients of liquids

In this paper we use the generic van der Waals equation of state to define the free volume of liquids along the liquid–vapor coexistence line (liquids curve) in the case of liquid argon and along three isotherms in the high-pressure regime in the case of liquid methane. With the free volume computed from the cavity function obtained by means of a Monte Carlo simulation method, we have calculated the self-diffusion coefficients of liquid argon and liquid methane. The Cohen–Turnbull free volume theory is used to calculate them. With the empirical parameter appearing in the Cohen–Turnbull theory suitably adjusted, the theoretical and experimental values of the self-diffusion coefficients agree very well with regard to the density and temperature dependence for the cases of available data compared. A pair of analytic formulas for density dependence of the self-diffusion coefficient is obtained by using the approximate cavity functions for hard spheres and tested against the experimental data on methane. A com...

On the integrability of differential forms related to nonequilibrium entropy and irreversible thermodynamics

The Boltzmann equation has been used in the literature to show that the entropy differential consists of a Pfaffian form in the space of conserved and nonconserved variables (moments) and a term related to the energy dissipation due to the irreversible processes in the system. The said Pfaffian form is called the compensation differential. In this paper, the integrability of the compensation differential is examined by means of the theory of differential forms. The integrability conditions turn out to be generalized forms of the Maxwell relations in equilibrium thermodynamics. It is also shown that the generalized form of the Gibbs–Duhem relation can be seen as an equivalent of the integrability conditions. This conclusion is drawn by using the notion of homotopy operator. The Caratheodory principle is also applied to make the connection with the second law of thermodynamics more intimate than the direct but mathematically more abstract approach using the integrability conditions. The meaning of the integrating factor is clarified by using the notion of contact temperature since the integrating factor, a mathematical function, is endowed with a thermodynamically operational meaning when it is identified with the inverse local absolute temperature through the notion of contact temperature, and the compensation differential is thereby made a thermodynamically meaningful equation governing nonequilibrium processes. Through this study it is shown that in irreversible thermodynamics the compensation differential can play the role parallel to the equilibrium Gibbs relation for the entropy in equilibrium thermodynamics and thus can serve as the foundation on which to formulate a theory of irreversible processes.

Theory of non‐Newtonian viscosity and normal stress coefficients of fluids

The evolution equation for the traceless symmetric part P of the stress tensor derived previously for dense simple fluids is further investigated of its applicability to non‐Newtonian fluid behaviors and normal stress effects. Nonlinear differential equations for three independent components of the stress tensor are obtained in the case of a unidirectional flow in an incompressible fluid. The asymptotic stability of the steady state (equilibrium) is studied with linearized equations and the stability conditions are derived. Approximate steady state solutions are calculated from the evolution equations for the three components and viscometric functions are obtained therefrom. By taking the evolution equations as a set of phenomenological evolution equations, we show that it is possible to apply them even to nonsimple fluids such as polymer solutions, by analyzing experimental data on the shear rate dependencies of the viscometric functions of some polymer solutions. We also show that the approximate visco...

Excluded volume in the generic van der Waals equation of state and the self-diffusion coefficient of the Lennard-Jones fluid.

In the previous papers applying the generic van der Waals equation of state the mean excluded volume was defined with the contact diameter of particles at which the potential energy is equal to zero-the size parameter in the case of the Lennard-Jones potential. This parameter appears as the upper limit of the integral for the generic van der Waals parameter B (mean excluded volume divided by the density) in the generic van der Waals equation of state. Since the choice is not unique, in this paper we reexamine the manner of defining the upper limit and propose another choice for the upper limit. We also propose an interpretation of the free volume overlap factor alpha appearing in the free volume theory of diffusion and a method of estimating it in terms of the intermolecular potential energy only. It is shown that with the so-estimated free volume overlap factor and the new choice of the upper limit of the integral for B the self-diffusion coefficient in the modified free volume theory of diffusion not only acquires a better accuracy than before, but also becomes calculable in terms of only the intermolecular interaction potential without an adjustable parameter. We also assess some of effective diameters of molecules proposed in the literature for their ability to predict the self-diffusion coefficient within the framework of the modified free volume theory of diffusion.

Integral equations of the correlation functions for polymeric liquids

The integral equations for intramolecular and intermolecular correlation functions are derived for nonrigid polymeric (polyatomic) liquids by the device of the Kirkwood charging parameters. These integral equations are cast into mean‐field‐type equations by using the potential elimination method, reported previously for dense simple fluids. Based on the mean‐field integral equations, we examine the superposition approximations for various levels of correlation. The present theory provides a means to make systematic corrections for superposition approximations for correlation functions of various orders. Upon using the superposition approximations for the triplet correlation functions in the Kirkwood hierarchy and an assumption or another concerning the charging parameter dependence of the cavity functions, we derive a set of generalized Percus–Yevick and hypernetted chain integral equations for the intramolecular and intermolecular pair correlation functions for beads (sites) of polymeric (polyatomic) liquids. This set of integral equations allows the intramolecular and intermolecular correlation functions to be determined self‐consistently. The connection of this set of integral equations to the bead–bead (molecular) Ornstein–Zernike relation is pointed out. The integral equations for the intramolecular correlation functions will be numerically solved for some properties of a single polymer chain in the infinite dilution limit in the sequel to this paper.

Direct observation of a nonequilibrium velocity distribution function in a system with a thermally activated chemical reaction

The velocity distribution functions for the reactant and product of a thermally activated reaction A+A→B+B are calculated from molecular dynamics simulations. The results are compared with a simple phenomenological theory, which assumes that the temperature of the reactant A may be different from the temperature of the system as a whole. Good agreement between the two methods is observed.

Franck-Condon transitions and chemical reactions

By using certain excited electronic states (potentials) of diatomic molecules in the initial and final species channel as distortion potentials in distorted wave theory of scattering, we perform a collision theoretical study of the Franck-Condon transition model for chemical reactions proposed by Herschbach et al. A study with a collinear collision model indicates that to an approximation bimolecular reactions in general may be viewed as two simultaneous Franck-Condon transitions between the ground and excited electronic states of the product and reactant diatomic molecules, if excited electronic states are allowed to participate in the reaction processes. In the one-dimensional model A … X … Y of the reaction geometry for the reaction A + XY → AX + Y the product translational energy distribution P ya , when XY is in the ground vibrational state, is found to be approximately equal to the formula, where u xy is the repulsive excited electronic state of XY evaluated at the equilibrium distance r e of XY in ...

Generalized hydrodynamics, bulk viscosity, and sound wave absorption and dispersion in dilute rigid molecular gases

Generalized hydrodynamic equations are derived from an irreversible kinetic equation for rigid diatomic molecular gases and applied to extract the bulk viscosity by making use of sound wave absorption and dispersion. As a first application of the generalized hydrodynamic equations for molecular gases, the linearized versions of the generalized hydrodynamic equations are applied to study sound wave absorption and dispersion in molecular gases. The results obtained for sound wave absorption and dispersion with the linearized set yield good agreement with experimental data on nitrogen, hydrogen, deuterium, and HD reported in the literature.