A Matrix Operator Formalism for Investigating Spatially Bounded Multicomponent Liquid Systems

Vasiliev, Aleksei Nikolaevich

doi:10.1023/b:tamp.0000026187.39100.82

Cited by 2 publications

(3 citation statements)

References 2 publications

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“…Relation (2) can be reduced to a differential equation by expanding the pair correlation functions in Taylor series. The OZ differential equation is written in matrix form [4] as where the matrices G(r) andf (r) are formed of pair and direct correlation functions, I is the N ×N identity matrix, and the matrices for the spatial moments of direct correlation functions are given by the relation…”

Section: Pair Correlationsmentioning

confidence: 99%

Pair correlations in a multicomponent fluid placed in a porous medium

Vasilev

2006

Theor Math Phys

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We consider a multicomponent fluid placed in a porous medium. The Ornstein-Zernike approximation is used to calculate the pair correlation functions for density fluctuations in the mixture components. We show that light scattering in the neighborhood of the critical state of the system is determined (in the single-scattering approximation) by the commonly known Ornstein-Zernike formula. We investigate the shift in the critical parameters due to the porous medium.

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Section: Pair Correlationsmentioning

confidence: 99%

Pair correlations in a multicomponent fluid placed in a porous medium

Vasilev

2006

Theor Math Phys

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“…As an example, we calculate correlation functions for fluctuations of the director orientation and of the order parameter, which characterizes an isotropic subsystem.We previously proposed a formal method for analyzing the correlation behavior of liquid systems containing a large number of components [1]. Such a method can be extended with minimal changes to the case where the liquid is characterized by a vector order parameter.…”

mentioning

confidence: 99%

“…We previously proposed a formal method for analyzing the correlation behavior of liquid systems containing a large number of components [1]. Such a method can be extended with minimal changes to the case where the liquid is characterized by a vector order parameter.…”

mentioning

confidence: 99%

Studying liquid-crystal systems with impurities using matrix-formalism methods

Vasiliev

2006

Theor Math Phys

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We use the matrix formalism to investigate a liquid-crystal system containing impurities. As an example, we calculate correlation functions for fluctuations of the director orientation and of the order parameter, which characterizes an isotropic subsystem.We previously proposed a formal method for analyzing the correlation behavior of liquid systems containing a large number of components [1]. Such a method can be extended with minimal changes to the case where the liquid is characterized by a vector order parameter. The most instructive example of such a system is a liquid-crystal system. It is known that a liquid crystal in the nematic phase is characterized by a unit vector-director that indicates the direction of the preferred orientation of the long axes of the liquid crystal molecules. Although the nematic liquid-crystal order parameter is a tensor quantity, when investigating small deviations of the director from the equilibrium homogeneous distribution, we can take the vector of small fluctuations of the director as the order parameter, and the system can therefore be described by a vector order parameter. We consider such a system, liquid in the isotropic phase, in the presence of impurities. We assume that the liquid crystal and isotropic impurities constitute two interacting subsystems respectively characterized by the director and by the deviation of the density from the mean.The energy of deformation due to inhomogeneities in the director distribution in the nematic liquid crystal is known to be [2]where K ii , i = 1, 2, 3, are the Franck moduli and n( r ) is the unit vector-director.If a system is placed in an external field (we assume that it is a magnetic field for definiteness), we must also take the interaction with this field into account. The energy of interaction of a liquid-crystal system with the magnetic field H iswhere χ a is the anisotropy of magnetic susceptibility. For the isotropic subsystem, the free energy depends on the profile of the scalar order parameter φ( r ), which we choose to be a local density of the isotropic phase. The free energy of the isotropic subsystem is then [3]

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A Matrix Operator Formalism for Investigating Spatially Bounded Multicomponent Liquid Systems

Cited by 2 publications

References 2 publications

Pair correlations in a multicomponent fluid placed in a porous medium

Pair correlations in a multicomponent fluid placed in a porous medium

Studying liquid-crystal systems with impurities using matrix-formalism methods

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