Rice-Allnatt Theory Research Articles

Atomic transport properties and liquid–liquid phase separation of Zn x Bi liquid monotectic alloys

Atomic transport properties specifically the shear viscosity and the diffusion coefficient for Zn x Bi liquid monotectic segregating alloys are theoretically investigated by using the Rice–Allnatt theory. The essential ingredient for the microscopic description of the metals and their alloys is the interionic interaction which in the present work is described by a widely used local pseudopotential. The temperature dependent behaviour of the above mentioned physical properties is also examined. The overall agreement of our calculated results with the available experimental data is found to be good for the full range of concentration. More interestingly, the temperature dependent results for the viscosity and the diffusion coefficient apparently exhibit a signature of liquid–liquid phase separation through a sudden bending in their concentration dependent profiles. Onset of this bending also provides information about the critical temperature and the critical concentration, and also provides a value for the critical exponent of liquid–liquid phase separation.

Rice-Allnatt theory: Comparison of calculated shear-viscosity and thermal-conductivity coefficients with molecular-dynamics results.

For several liquid and fluid states of the Lennard-Jones system, the shear viscosity ${\ensuremath{\eta}}_{s}$ and the thermal conductivity \ensuremath{\lambda} were calculated with the Rice-Allnatt (RA) theory and compared with molecular-dynamics (MD) data. The pair potential was split as Weeks, Chandler, and Andersen proposed [J. Chem. Phys. 54, 5237 (1971)], the pair correlation functions were generated by the perturbation method using the Baxter technique, and the friction coefficient was obtained from MD computations with use of the Green-Kubo relation. Though sufficient agreement with MD results occurred for a certain small region of states, the RA transport coefficients generally deviated largely from the MD data. The failure of the RA theory cannot be ascribed to the uncertainty in the soft part of the friction coefficient, ${\ensuremath{\zeta}}_{s}$, necessary for the kinetic equations. We proved this for states where the product, \ensuremath{\lambda}${\ensuremath{\eta}}_{s}$, is only negligibly dependent on ${\ensuremath{\zeta}}_{s}$.

Analysis of the translational band measured in Ne–Ar mixtures with a new line-shape profile

The translational absorption spectra of Ne–Ar liquid mixtures, arising from the collision induced dipole moment, have been measured at different temperatures along the coexistence curve. The experimental line-shapes have been fitted with a new general profile suitable to reproduce the intercollisional interference effect. In this way we have derived the frequency ω0 that characterizes the rattling component of the motion of the impurity in the liquid. The self diffusion coefficient of Ne in Ar has also been derived from experimental values of ω0 using the Rice–Allnatt theory.

Molecular Dynamics Study on Transport Properties of Fluids

Abstract A molecular dynamics “experiment” has been performed for a system of 216 molecules interacting through a modified Lennard-Jones-type potential. The velocity autocorrelation functions and associated self-diffusion coefficients were computed for varying degrees of the steepness of the repulsive part in the pair potential. The dependence of these quantities upon the hardness of the core, and then the applicability of a perturbation approach to the transport theory, was elucidated. The computed self-diffusion coefficients were compared with the prediction of the Rice-Allnatt theory.

A kinetic theory of dense fluids. Test-particle kinetic equation

Mori’s form of the generalized Langevin equation is applied to a system of particles whose pair interactions are sums of short-ranged, rigid-core repulsions and longer-ranged continuous interactions. It is assumed that the memory function decays exponentially from its initial value at a rate characterized by a single, wave number dependent relaxation time. The test–particle kinetic equation resulting from this one key assumption is strongly reminiscent of that associated with the well-known Rice–Allnatt theory. However, in addition to Fokker–Planck and Enskig operators similar to those of the Rice–Allnatt theory, it also includes coupling between rigid-core scattering events and the diffusive, Brownian motions of the particles as well as contributions associated with three-particle rigid-core collisions. A systematic method of solution is developed and applied to a simplified form of this kinetic equation. Solutions generated by this procedure involve matrix elements of the linearized Enskog operator computed in the basis of generalized Hermite polynomials which are eigenfunctions of the Fokker–Planck operator associated with the long-ranged, continuous portion of the pair potential. The approximate solutions obtained are used to compute the density and velocity autocorrelation functions and the coefficient of self-diffusion as well.

Dense gas transport calculations

The Rice–Allnatt theory of dense gas transport coefficients is examined numerically for several sources of radial distribution functions. The viscosity predictions become physically unacceptable at sufficiently high densities, and all predictions generally show poor agreement with experiment.

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.

Square-Well Potential. III. Transport Properties of Liquids

The Davis-Rice-Sengers square-well theory of transport for simple dense gases and liquids is tested with Yvon-Born-Green theoretical pair correlation functions for σ2/σ1=1.85. Comparison with experiment shows that the theory correctly predicts the qualitative features of liquid argon transport properties and quantitatively is very good at high temperatures and densities in the liquid region. An adjustment of intermolecular potential parameters is shown to improve the predictions of the theory uniformly. Some comments are made concerning the success of this theory in light of recent studies of the Rice-Allnatt theory.

Generalized Rice-Allnatt theory for transport in liquids

The Rice-Allnatt theory is generalized to take into account the effects of spatial displacements during collisions. The new term appearing in the singlet equation modifies the kinetic part of the transport coefficients. The most important consequence of the extension is that the Smoluchowski equation is no longer needed to describe the distortion of the non-equilibrium pair correlation function, which accounts for the potential parts of the transport coefficients. This function is evaluated in the same approximation as the generalized collision operator. Explicit expressions are given for the potential parts of the thermal conductivity and shear and bulk viscosities, for a 6–12 Lennard-Jones potential modified by a hard core. Comparison is made with the corresponding results of the Prigogine-Nicolis-Misguich theory.

A Comparative Analysis of the Rice-Allnatt and Square-Well Liquid Transport Theories

Abstract The Yvon-Born-Green pair correlation function theory is discussed from the viewpoint of its role as theoretical data input for the Rice-Allnatt liquid transport theory. The general behavior of the Rice-Allnatt theory is shown to compare favorably with that of the square-well transport theory of Davis, Rice, and Sengers, although the former is not as quantitative. The predictive ability of the Rice-Allnatt theory is improved by a systematic adjustment of the Lennard-Jones parameters used in the YBG pair correlation functions, based on the critical point locus.

Recalculation of the friction constant and transport coefficients of liquid argon from the Rice-Allnatt theory

The linear trajectory approximation of the ?soft? friction constant in the Rice-Allnatt theory of transport has been computed with specific attention to the lower limit of the integral. The results are significantly different from the Palyvos-Davis values for ζS in the dense gas region but agree within 2% in the liquid region. The Rice- Allnatt expressions for the coefficients of shear viscosity and thermal conductivity have been simplified and a correction of a numerical error in the collisional contributions to momentum and heat transfer is made. The coefficients D, η, and λ have been calculated for the corrected ζS and related expressions. No significant change in D is obtained, but a worsening of agreement with experimental viscosities and thermal conductivities occurs. Conversely, a better prediction of the ratio mλ/kη is obtained. More recent viscosity data for liquid argon indicate the theory is less satisfactory than has previously been considered. These results suggest that any improvement of this class of theory can only come through the use of a better representation of the radial distribution function.

Molecular distributions in a non-uniform liquid

At distances greater than the rigid-core diameter σ, the soft interactions of the Rice-Allnatt theory are handled according to the Fokker-Planck approximation, and in this region the radial distortion u(r) of the equilibrium distribution satisfies the same equation as the radial distortion of the Kirkwood-Eisenschitz theory. In calculations based upon the Rice-Allnatt theory, Lowry, Rice and Gray have applied the boundary condition that r2e -ψ du/dr -> 0 as r -> σ to the equation for u(r). In this paper calculations and arguments are presented which suggest that the radial distortion selected by this condition is identical with that selected by the strong boundary condition of Eisenschitz, r3u(r) -> 0 as r -> infinity.

Rice–Allnatt Theory of Transport for Rough Spheres

The Rice–Allnatt theory for liquids of monoatomic molecules is extended to rotating hard cores surrounded by symmetrical soft potentials. The kinetic equation is solved by the Chapman–Enskog method. Numerical values for the thermal conductivity, the shear viscosity, and the bulk viscosity coefficients are evaluated and tabulated to show the dependence on molecular moment of inertia.

Comments on Friction Constant Formalism

Expressions for the molecular friction constant based on the acoustic continuum and small-step diffusion models have been compared with experimental data. The integral describing ζ was evaluated by assuming an (n, m) potential and by substituting internal energy and pressure for terms involving integrals of the radial distribution function. The experimentally estimated values of the friction constant, from which a hard-core contribution is removed, do not yield consistent or realistic values of the potential parameters n and m. The successful prediction of the coefficient of thermal conductivity and shear viscosity for liquid argon using the Rice—Allnatt theory is based on the extrapolation of experimental data for self-diffusion. Statistical analysis of these data indicates that they do not permit a reliable test of the theory. Predicted values of the bulk viscosity coefficient of liquid argon are 40%—50% lower than recent experimental data, and the pressure dependence of the bulk viscosity coefficient at constant density calculated from the Rice—Allnatt theory is of the wrong sign.

Self-diffusion in simple fluids

Self-diffusion coefficients of simple liquids as predicted by Rice-Allnatt theory, noting friction coefficient and correlation function

Kinetic Theory of Dense Fluid Mixtures. II. Solution to the Singlet Distribution Functions for the Rice—Allnatt Model

The Rice—Allnatt theory of dense fluids has been extended to binary mixtures. It is shown that the linearized Rice—Allnatt equation for the singlet distribution function is a linear integral equation of the second kind. Moreover, it is shown that a simple modification of the Rice—Allnatt equation, the modification being of the same order of approximation as those utilized in deriving the equation, results in a linear equation admitting mass, momentum, and kinetic energy as homogeneous solutions, thus allowing the local hydrodynamic variables to be completely specified by the zero-order solution to the integral equation. The singlet distribution functions are solved, and the binary diffusivity, thermal diffusion ratio, and kinetic contributions to thermal conductivity and viscosity are obtained.

On the Kinetic Theory of Dense Fluids. XV. Some Comments on the Rice—Allnatt Theory

In this paper it is shown that, within the framework of the Rice—Allnatt theory of transport phenomena in simple dense fluids, the cross-correlation functions of the soft and hard forces are exactly zero. A relation is found between the soft doublet and soft singlet friction coefficients, and an approximate theory is developed for the soft components of the shear viscosity and the thermal conductivity. The main assumption in this approximation is that of small step diffusion. The soft doublet friction coefficient which is derived in the first part of the paper is then used to calculate values for the soft force contribution to the viscosity and thermal conductivity. It is shown that the equilibrium properties of simple liquids are not known with sufficient accuracy to allow a complete test of the R—A theory, but that the expressions in this theory seem to be moderately insensitive to the equilibrium properties used.

On the Kinetic Theory of Dense Fluids. XVI. The Ideal Ionic Melt

In this paper a theory is constructed to describe to first order the properties of a fused salt. The Rice—Allnatt theory of simple dense fluids is used in conjunction with the following assumptions: (1) oppositely charged ions are of nearly equal size and have identical electronic properties, except for the sign of the charge; (2) a negative ion is, on the average, surrounded by positive ions and vice versa; (3) short-range repulsive interactions occur only between pairs of oppositely charged ions; (4) the role of the Coulomb potential is to determine the fluid density and local fluid structure, but the Coulomb potential makes an insignificant contribution to the direct dissipation of energy and momentum. These conditions are taken to define an ideal ionic melt, and integrodifferential equations for the singlet and pair distribution functions of this system are derived. From these there is obtained an expression for the ion mobility in a weak electric field. This expression predicts a deviation from the Nernst—Einstein relation. A recipe for calculating the thermal conductance and shear viscosity is outlined. Some comparisons of theory with experiment are made. In particular, the theory can account for the magnitude of the deviation of the mobility—diffusion relationship from the Nernst—Einstein relation.

On the Kinetic Theory of Dense Fluids. XIV. Experimental and Theoretical Studies of Thermal Conductivity in Liquid Ar, Kr, Xe, and CH4

In this paper we report experimental and theoretical studies of the thermal conductivity of liquid Ar, Kr, Xe, and CH4, in the temperature range 90°—235°K and the pressure range 1–500 atm. It is found that: (a) The magnitude, the temperature dependence, and the pressure dependence of the thermal conductivity all decrease in the following order: CH4, Ar, Kr, Xe. (b) The gross behavior of the coefficient of thermal conductivity is the inverse of the behavior of the self-diffusion coefficient: κ increases (whereas D decreases) as the pressure increases along an isotherm and κ decreases (whereas D increases) as the temperature increases along an isobar. (c) The statistical theory of Rice and Allnatt leads to easily interpreted analytic formulas for the coefficient of thermal conductivity. (d) The theory of Rice and Allnatt leads to predictions in quantitative agreement with experiment. The importance of accurate pair correlation functions, the relative roles of strong repulsive and soft attractive potentials, and implications of the Rice—Allnatt theory are briefly discussed.