Partitioning of Polymerizing Fluids in Random Microporous Media: Application of the Replica Ornstein–Zernike Equations

Pizio, Orest; Renugopalakrishnan, V.; Trokhymchuk, Andrij

doi:10.1006/jcis.1998.5999

Cited by 3 publications

(2 citation statements)

References 34 publications

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“…They showed how the statistical−mechanics approaches for liquids, that is, diagrammatic expansions and integral equations, can be extended to describe fluids confined in a random porous matrix. The work of Madden and Glandt has incited much interest in the theoretical study of fluid adsorption in random porous media. − …”

Section: Introductionmentioning

confidence: 99%

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Fluids Confined in Porous Media: A Soft-Sponge Model

2007

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The morphology of many porous materials is sponge-like. For describing fluid adsorption in such materials, we propose here a quite general sponge model which is built by digging spherical cavities in a continuum. In contrast to the hard-sponge model proposed recently by Zhao et al. [Zhao, S. L.; Dong, W.; Liu, Q. H. J. Chem. Phys. 2006, 125, 244703], the continuum in the present soft-sponge model is permeable to fluid particles. Although the general expression of the fluid−matrix interaction potential is not pair additive, we were able to extend some statistical-mechanics formalism of liquid state to deal with this model. We derived the diagrammatic expansions of various correlation functions and Ornstein−Zernike equations. Usually, one would not expect that the thermodynamic quantities (e.g., internal energy) of a system with a nonpair-additive interaction can be completely determined from the structural information at the two-body level. We found a remarkable result that for the soft-sponge model considered here, the internal potential energy can be determined from only two-body correlation functions. In the particular case of a soft-sponge model with nonoverlapping cavities, we show that the fluid−matrix interaction can be also described by a pair-additive potential. In this case, the Madden−Glandt formalism applies. The Ornstein−Zernike equations obtained by using the pair-additive fluid−matrix interaction potential look to be quite different from those obtained by starting with the nonpair-additive potential. We found the relationship between the two descriptions and show how the two sets of Ornstein−Zernike equations can be transformed from each other for a soft-sponge model with nonoverlapping cavities.

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Section: Introductionmentioning

confidence: 99%

“…A judicious choice of template allows for tuning the porosity, pore size, or both in a controlled way for the porous material design. Despite the large number of experimental and theoretical investigations devoted to porous materials, − …”

Section: Introductionmentioning

confidence: 99%

Fluids Confined in Porous Media: A Soft-Sponge Model

2007

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Rose water in random porous media: Associative replica Ornstein-Zernike theory study

Ogrin

Urbič

2022

Journal of Molecular Liquids

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Fluids in porous media. I. A hard sponge model

Zhao

Dong

Liu

2006

The Journal of Chemical Physics

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The morphology of many porous materials is spongelike. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum. We found an analytical expression for describing the interaction potential between fluid particles and the spongelike porous matrix. The diagrammatic expansions of different correlation functions are derived as well as that of grand potential. We derived also the Ornstein-Zernike (OZ) equations for this model. In contrast to Madden-Glandt model of random porous media [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the OZ equations for a fluid confined in our hard sponge model have some similarity to the OZ equations of a three-component fluid mixture. We show also how the replica method can be extended to study our sponge model and that the same OZ equations can be derived also from the extended replica method.

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Partitioning of Polymerizing Fluids in Random Microporous Media: Application of the Replica Ornstein–Zernike Equations

Cited by 3 publications

References 34 publications

Fluids Confined in Porous Media: A Soft-Sponge Model

Fluids Confined in Porous Media: A Soft-Sponge Model

Rose water in random porous media: Associative replica Ornstein-Zernike theory study

Fluids in porous media. I. A hard sponge model

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