Equation For Radial Distribution Function Research Articles

An investigation of metastable states of binary mixtures in the neighborhood of spinodal using the integral equation method

A generating functional is suggested for the purpose of producing a set of integral equations for radial distribution functions of binary mixtures in the neighborhood of stability limit, i.e., spinodal. This set of integral equations is used to derive an equation of state from which it follows that the terms which are non-analytical by the total density of mixture start to play an important part in the region of thermodynamic variables where the third virial coefficient must be included.

Deriving integral equations for radial distribution functions of multicomponent mixtures on the basis of scale transformations in the phase space

It is shown that scale transformations of the coordinate part of the phase space for one of the mixture components correspond to virtual variations in the local density for the same component in a thermodynamic system. The investigation results are used to construct different variants of a generating functional with the goal of deriving a system of integral equations for the radial distribution functions of mixtures. An equation of state, which is a modification of the Tate equation, is obtained. Systems of integral equations that imply, in the limit, the Perkus-Yevick equations and systems of equations for hypernetted chains are derived for radial distribution functions.

Analytical theory of solution of attracting molecules of different size derived from hypernetted-chain equation for radial distribution function

The Flory–Huggins formula of mixing entropy of different size molecules originally proved for polymer solution is generally proved for attracting spherical molecules different in size. The Scatchard formula of the excess energy known for application in the solubility parameter is also proved theoretically. The proof is based on analytical solutions of the radial distribution functions for mixture and does not rely on the lattice model. The hypernetted-chain (HNC) equation is perturbed taking hard-sphere system as reference and the attractive force as perturbation. The obtained equation for the perturbed radial distribution function for mixture is solved analytically under simplifying assumptions, which enabled to give the equation of state in analytical form. In order to give the excess Gibbs free energy in explicit form, the vapor pressure of liquid mixture is obtained by applying a phase equilibrium condition corresponding to the Maxwell’s equal-area rule to mixture. The excess entropy and enthalpy are derived directly.

Integral equations for radial distribution function with effective allowance for long-range interaction

Integral equations for radial distribution function with effective allowance for long-range interaction

Derivation of an integral equation for pair correlation functions in molecular fluids

A new integral equation for equilibrium pair correlation functions in molecular fluids is derived from a systematic functional Taylor expansion. The derivation employs a new Ornstein-Zernike-like equation and a generalization of the functional Taylor expansion techniques frequently employed to derive integral equations for radial distribution functions in simple atomic liquids.

Structure factor and excitation spectrum of the many-body system calculated by the decoupling of green functions

Using the method of retarded Green functions, the system of self-consistent equations for radial distribution functions and the excitation spectrum of a many-body system are found. The simplest approximation is used, in which the elementary excitations are not damped. The Feynman relation for the structure factor, and the Hubbard-Beeby formulae of the self-energy spectrum of collective excitations in liquids is involved in this system. The properties of the classical and quantum liquids are described qualitatively.

Self-consistent equations for the radial distribution function

A procedure for deriving integral equations for approximate radial distribution functions is described. It employs a functional expansion that guarantees that the pressure obtained from such an approximate radial distribution function by means of the virial theorem will be in agreement with the pressure obtained from the same function by means of fluctuation theory. A natural choice of a dependent functional is shown to yield an equation that has been discussed by Rowlinson and by Lado. A second equation that is self-consistent in the same sense as the first is also exhibited. When Verlet's approximation for the three-body term that is found in the equation is used, this equation stands with respect to the first self-consistent equation as Verlet's PY2 and HNC2 equations stand to the PY and HNC equations, respectively. Variants and extensions of the procedure leading to these self-consistent equations are also discussed.