Correlation Functions Of Fluids Research Articles

Nonlinear density-functional approach to the crystallization of the classical one-component plasma.

The density-functional approach to freezing of the classical one-component plasma into a bcc crystal is developed on the basis of the improved hypernetted-chain approximation to the fluid correlation functions. The role of the three-body or angular correlations is elucidated through microscopic calculations. A simplified density-wave theory of freezing is thereby obtained.

Molecular theory of solvent-induced self-interactions in a polymer

A theory based on a density-functional formalism is developed to obtain the solvent-induced potential between different sites on a polymer. The expression found for the potential surface is not pair decomposable. The theory brings to light a new approach for deriving solute-solvent correlation functions and computation of multipoint correlation functions in fluids.

Critical Behavior of the Correlation Function of Fluids Composed of Polar Diatomic Molecules

Abstract A critical behavior of fluids composed of polar diatomic molecules is studied by the use of the Ornstein–Zernike (OZ) theory of critical phenomena extended to the interaction site model. Firstly, the asymptotic forms of the atom–atom direct correlation functions cαγ(r) for the polar fluids at large separation are obtained, which are valid off the critical point. Then, the OZ hypothesis that the asymptotic forms of cαγ(r) do not change near and at the critical point is examined, and the critical behavior of the total correlation function is investigated. It is found to be completely analogous to the case of simple fluids. The relation between the OZ hypothesis and some integral equation theories is also discussed.

Excess electrons in simple fluids. I. General equilibrium theory for classical hard sphere solvents

In this paper we develop a theory for an excess electron in simple fluids. It is based upon the path integral formulation of quantum theory which maps the behavior of the electron on to that of a classical isomorphic polymer. The influence functional, i.e., the solvent induced potential between different sites on the polymer, is estimated from the RISM integral equation. The functional is not pair decomposable and the resulting polymer problem is not trivial to solve. The evaluation of the electron partition function and correlation functions is pursued with two approximations: (i) a mean field approximation which neglects the role of polymer fluctuations on the solvent induced interactions: (ii) a polaron approximation which is a linear approximation in the sense that it neglects large fluctuations in the polymer structure itself. The theory brings to light a new approach to the computation of multiparticle correlation functions in fluids, and the theory provides what appears to be a practical scheme for attacking a number of other problems including the analysis of polymer conformations in liquid environments. While this paper focuses on the role of packing forces in these systems, the theory can be generalized to include polarization and charge interactions as well.

Information theory applied to time correlation functions in fluids

Information theory is used to predict the reorientational time correlation functions for a linear molecule in a fluid given only the moment of inertia and the mean squared torque. Comparison with ‘exact’ computer simulation results for a variety of fluids show that the method is remarkably successful—even when the torque is small. It is just as successful, for instance, as a much more elaborate memory-function perturbation theory which uses the same information. The method is quite general and can be usefully applied to any time correlation function.

Time correlation functions in fluids by information theory

Information theory is used for the evaluation of the angular velocity time autocorrelation function for a fluid. The results for the particular case of a linear molecule, where the exact result is known, are as good as those obtained with a more elaborate theory. The method is quite general.

Hypervertex approximations for fluids. I. General formalism and the linear hypervertex approximation for symmetric fluids

A method for generating Dyson equations for two-particle fluid correlation functions is applied to the case of ionic and polar fluids to systematically yield a sequence of approximations that go beyond the lowest-order gamma-ordered approximation. The first two such approximations are given here. For the simplest class of such fluid models—those having hard-core potentials and a high degree of symmetry (e.g., the restricted primitive model, dipolar spheres)—the first of these approximations, the linear hypervertex approximation, is used to derive explicit expressions for thermodynamic quantities and the dielectric constant in terms of the hypervertex function, the hard-sphere reference correlation function, the perturbing pair potential, and the state of the fluid (e.g., the temperature and density of species).

Mode coupling theory of hydrodynamics and steady state systems

Abstract We construct a formal mode coupling theory for hydrodynamic systems which includes contributions from all powers of the hydrodynamic variables. This theory is applied to nonequilibrium steady state systems. A generalization of the local equilibrium distribution is used to describe the nonequilibrium state. This distribution independently constrains all moments of the hydrodynamic variables. The infinite hierarchy of equations for the moments of the hydrodynamic variables is truncated using an inverse system size expansion. Explicit results are obtained for the time correlation functions of fluids with a linear temperature gradient or a linear shear. These results agree with previous studies of these steady states.

Calculation of the Pair Correlation Functions for Fluids Composed of Diatomic Polar Molecules Based on the Interaction Site Model

Abstract A reference hypernetted chain (RHNC) like approximation of the interaction site model is proposed, which is the extension of Lado’s RHNC equation of simple fluids to the case of molecular fluids. By using the proposed RHNC like integral equation, pair correlation functions, structure factors and some thermodynamic quantities for fluids composed of diatomic polar molecules are calculated, where the molecules consist of two fused hardspheres with each center located at a distance l, and at each center charges +q and −q are sited. Calculated pair correlation functions are successful in showing well-marked characteristics of the fluid, such as cusps, not observed for simple fluids like argon. The isothermal compressibility at a constant reduced density and dipole moment has a weak l-dependence in sharp contrast to the total internal energy showing a strong l-dependence.

Some exact results and the application of the mean spherical approximation to charged hard spheres near a charged hard wall

An inconsistency within one of the Henderson–Abraham–Barker equations which fails to conserve local charge neutrality when applied to ionic mixtures near charged walls is discussed and is resolved by a careful analysis of the limit in which the wall particle is allowed to grow to infinite radius and zero curvature. This gives rise to a correction term which is needed only for the case of electrostatic interactions. The resulting equation is used to obtain exact asymptotic forms for the wall–fluid correlation functions at large positive and negative distances from the interface. Also, an exact relation for the contact value of the density profile is given. By means of a simple argument, results for both the total and direct wall–fluid correlation functions are given in the mean spherical approximation for charged hard spheres near a charged wall. These results are used to determine the capacitance of the interface in the mean spherical and exponential approximations. A modified form of the exponential approximation agrees closely with the Gouy–Chapman theory whereas the mean spherical approximation does not. On the basis of the exact expression for the contact value of the density profile it is argued that, for large charge on the wall, the Gouy–Chapman theory may give a reasonable capacitance even at high concentration.

Computation of the Correlation Functions for Fluids Composed of Diatomic Molecules by Means of the Method of Integral Equations

Abstract Pair correlation functions and structure factors of molecular fluids were computed, based on the reference interaction site model (RISM) integral equation coupled with the Percus-Yevick (PY) and the hyper-netted chain (HNG) approximations. The system considered is a fluid of diatomic molecules consisting of two identical spheres of diameter a with each center located at a distance L(L<σ). The total potential energy for the molecular fluid is assumed to be the sum of pair potentials of the Lennard-Jones type. It is shown that the pair correlation functions calculated are in agreement with results of molecular dynamics studies. The structure factors calculated by using two kinds of approximations (PY and HNG) are found to deviate from each other for small values of k(wave vector). Discussions are given on the behavior of the structure factors, S(k). The rise of S(k) at small k is ascribed to the effect of attractive forces between molecules.

Two-scale-factor universality near the critical point of fluids

Experimental evidence is presented in support of the validity of the hypothesis of two-scale-factor universality for the correlation function of fluids near the gas-liquid critical point. For Xe, SF 6, and CO 2, the dimensionless quantity R = ξ 0( B 2P c Γk BT c ) 1 3 is universal within the experimental accuracy of 10% and agrees with the value predicted by theory.

New self-consistent approximations for ionic and polar fluids

A general approximation scheme for the pair correlation function of fluids at equilibrium is discussed, and two new specific approximations that come out of it—one for polar fluids and one for ionic fluids—are introduced. The approximation scheme, developed for hard-core particles, is based upon the replacement of the actual structure of the Ornstein–Zernike direct correlation function c (12) outside the core by a form that can be wholly characterized in terms of its poles in Fourier space. The locations and residues of the poles are constrained by thermodynamic self-consistency; the approximate scheme is designated as the self-consistent Ornstein–Zernike approximation (SCOZA) scheme.

Time correlations in classical statistical mechanics

A formal expansion is given for the time evolution of a classical many-body system. It is suggested that this new method is capable of throwing light on some of the ad hoc assumptions which are currently made in the theory of liquids, and on some of the unresolved problems in the understanding of time correlation functions in fluids.

Computer simulation of a diatomic molecule dissolved in a monatomic fluid—Correlation functions, band shapes, and relaxation times

Four N2-Ar ‘solute-solvent’ systems representing different temperatures and densities were simulated on a computer by the molecular dynamics technique. From the data for each system, the dipole, angular velocity, force-on-the-bond, and P 2 correlation functions were calculated. These functions were used to determine rovibrational infra-red and Raman band-shapes, and N.M.R. relaxation times for quadrupolar, magnetic dipole-dipole and spin-rotation relaxation mechanisms. The P 2 and dipole correlation functions were compared with those calculated by Gordon from experimental data. The lack of agreement was examined to determine restrictions on the application of Gordon's method for obtaining these correlation functions. Also, the band shapes were compared with the experimental data to help determine these restrictions. The N.M.R. relaxation times were examined for temperature dependence and for dominant contributions to the total relaxation time. The force-on-the-bond correlation function was found to requir...

A geometrical sum rule for two-dimensional fluid correlation functions

A formal integral relation is derived relating the triplet correlation function g3 to the higher gn for a two-dimensional fluid. The relation is obtained as a power series in the density and is shown to converge absolutely for all realistic fluids. It is also shown that the rule is satisfied to a good approximation by a limited number of the lower gn. The extension to three dimensions is discussed.

Born-Green correlation functions for fluids with van der Waals forces

In recent work on the asymptotic form of correlation functions in `classical' fluids it has been proposed that the direct correlation function f(r) ~ -ϕ(r)/kT at large r, where ϕ(r) is the interatomic potential. It is pointed out here that for the Born-Green theory, and for ϕ(r) which has the van der Waals form -Ar-6 at large r this relation is modified to read f(r) ~ - (ϕ(r)/kT)(1/KT(2P-n0kT)) where n0 is the mean density, P the fluid pressure and KT the isothermal compressibility. The multiplying factor can be significantly different from unity and negative. It is emphasized that small-angle scattering of X rays or neutrons from liquid argon, for example, could in principle decide between the two results.