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Inhomogeneous integral equation theory

Inhomogeneous Integral Equation Theory of a Liquid/Vapour Interface... [Pg.116]

D. Henderson. Integral equation theories for inhomogeneous fluids. In D. Henderson, ed. Fundamentals of Inhomogeneous Fluids. New York Marcel Dekker, 1992. [Pg.240]

An alternative to integral equation theories of the nonprimitive inhomogeneous electric double layer is a mean electrostatic field analysis of an ion-solvent dipole mixture against a charged wall [83-90]. Although this approach has been successful with the primitive model and avoids the difficult problem with the bridge function, it is still in the early stages of development with the nonprimitive electric double layer model. [Pg.629]

It should be noted that Eq. (39) is derived from DFT, and it presents the local expression similar to RHNC in Eq. (35). By noting that at bulk (r) = p r)/p recovers to g i) and the external potential recovers to the inter-molecular interaction (in that case the solute is virtually a solvent particle, and the system is locally inhomogeneous but represents a homogeneous system), both equations are essentially equivalent. This suggests that DFT and integral equation theory are closely related and moreover the closure relation for the integral equation can be derived from DFT. [Pg.28]

A third class of new polymer integral equation theories have been proposed by Kierlik and Rosinberg. Their work is an extension of a density functional theory of inhomogeneous polyatomic fluids to treat the homogeneous phase. The Wertheim thermodynamic pertubation theory of polymerization is employed in an essential manner. Applications to calculate the intermolecular structure of rather short homopolymer solutions and melts have been made. Good results are found for short chains at high densities, but the authors comment that their earlier theory appears to be unsuited for long chains at low to moderate (semidilute) densities. ... [Pg.130]

Screening of electronic interactions can be qualitatively understood, but hardly subject to numerical estimates. The difficulty arises from the inhomogeneous nature of the medium, since the reduced interaction must be described at distances comparable to chemical bonds. Neither is it sufficient to consider only local effects of screening, nor to screen independently the various wavelengths in the Fourier transform of the coulomb interaction. Hubbard formulated an integral equation for the screened interaction, but only very approximate solutions seems to be feasible. We will demonstrate that some numerical evidence supports the determination of interaction integrals based on screening theory. [Pg.176]

Over the p t several years we and our collaborators have pursued a continuous space liquid state approach to developing a computationally convenient microscopic theory of the equilibrium properties of polymeric systems. Integral equations method [5-7], now widely employed to understand structure, thermodynamics and phase transitions in atomic, colloidal, and small molecule fluids, have been generalized to treat macromolecular materials. The purpose of this paper is to provide the first comprehensive review of this work referred to collectively as Polymer Reference Interaction Site Model (PRISM) theory. A few new results on polymer alloys are also presented. Besides providing a unified description of the equilibrium properties of the polymer liquid phase, the integral equation approach can be combined with density functional and/or other methods to treat a variety of inhomogeneous fluid and solid problems. [Pg.321]

The combination of polymeric density functional methods and PRISM theory for the liquid correlations allow a wide range of closure and inhomogeneous material problems to be studied [109]. Present research involves using this approach to treat at an atomistic level the crystallization of the entire alkane series, and the structure of hydrocarbon fluids near surfaces and interfaces [109]. An alternative, purely integral equation approach to the latter problem is to employ the wall-PRISM theory of Yethiraj and Hall [37]. [Pg.373]

The classical models of adsorption processes like Langmuir, BET, DR or Kelvin treatments and their numerous variations and extensions, contain several uncontrolled approximations. However, the classical theories are convenient and their usage is very widespread. On the other hand, the aforementioned classical theories do not start from a well - defined molecular model, and the result is that the link between the molecular behaviour and the macroscopic properties of the systems studied are blurred. The more developed and notable descriptions of the condensed systems include lattice models [408] which are solved by means of the mean - field or other non-classical techniques [409]. The virial formalism of low -pressure adsorption discussed above, integral equation method and perturbation theory are also useful approaches. However, the state of the art technique is the density functional theory (DFT) introduced by Evans [410] and Tarazona [411]. The DFT method enables calculating the equilibrium density profile, p (r), of the fluid which is in contact with the solid phase. The main idea of the DFT approach is that the free energy of inhomogeneous fluid which is a function of p (r), can be... [Pg.38]

J.L. Volakis, Alternative field representations and integral equations for modeling inhomogeneous dielectrics, IEEE Trans. Microwave Theory Tech. 40, 604 (1992)... [Pg.314]


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See also in sourсe #XX -- [ Pg.118 , Pg.119 , Pg.120 , Pg.121 ]

See also in sourсe #XX -- [ Pg.118 , Pg.119 , Pg.120 , Pg.121 ]




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Inhomogeneity

Inhomogenities

Integral equation theories

Integral equations

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