Phase behavior of a two-dimensional quenched–annealed lattice gas with nearest-neighbor attraction. Grand canonical Monte Carlo simulation

Rżysko, W.; Malo, Beatriz Millan; Sokołowski, S.; Pizio, Orest

doi:10.1016/s0378-4371(99)00225-3

Cited by 3 publications

(4 citation statements)

References 32 publications

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“…1 of Ref. 19. Our simulations of Lennard-Jones fluids in quenched networks have also highlighted the sensitivity of the thermodynamic behavior to the particular structure of a replica.…”

Section: Introductionmentioning

confidence: 51%

“…14 The replica method for quenched-annealed systems is also well suited for computer simulations; several Monte Carlo simulations of phase equilibria in quenched-annealed systems have been reported in the literature. [15][16][17][18][19] However, to the best of our knowledge, all simulations to date have been carried out using a small number of replicas. Furthermore, none of these simulation studies has provided a systematic analysis of the fluctuations that arise when one goes from one replica to another.…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of simple fluids confined by microporous materials

Rżysko¹,

Pablo

Sokołowski³

2000

The Journal of Chemical Physics

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We have performed Monte Carlo simulations of a three-dimensional quenched-annealed system on a cubic lattice with nearest-neighbor interactions. A small fraction of the lattices sites are blocked, thereby creating a quenched matrix. Histogram reweighting techniques are applied to investigate the critical behavior of the system. We have studied lattice sizes ranging from Lϭ10 to Lϭ18. For each size, we have evaluated the number of matrix replicas necessary to obtain statistically meaningful results. This number, determined by analyzing the convergence of the histograms, ranged from 50 for the smallest system sizes to 200 for the largest sizes. We have evaluated the critical temperature, the fourth cumulant of Binder et al. ͓K. K. Kaski, K. Binder, and J. D. Gunton, Phys. Rev. B 29, 3996 ͑1984͔͒, and the critical exponents 1/ and ␤/. The estimated critical temperature is only slightly lower than that of the three-dimensional Ising model. The simulated critical exponents, however, differ significantly from those for Ising-class three-and two-dimensional systems.

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“…1 of Ref. 19. Our simulations of Lennard-Jones fluids in quenched networks have also highlighted the sensitivity of the thermodynamic behavior to the particular structure of a replica.…”

Section: Introductionmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 99%

Critical behavior of simple fluids confined by microporous materials

Rżysko¹,

Pablo

Sokołowski³

2000

The Journal of Chemical Physics

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“…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%

“…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%

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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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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Phase behavior of a two-dimensional quenched–annealed lattice gas with nearest-neighbor attraction. Grand canonical Monte Carlo simulation

Cited by 3 publications

References 32 publications

Critical behavior of simple fluids confined by microporous materials

Critical behavior of simple fluids confined by microporous materials

Fluids Confined in Porous Media: A Soft-Sponge Model

Fluids in porous media. I. A hard sponge model

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