The replica Ornstein-Zernike equations and the structure of partly quenched media

The replica Ornstein-Zernike equations ion-molecular fluid adsorbed in a disordered ion-molecular matrix were applied. The explicit expressions for the potentials screening by the point particles are obtained. The analysis of the screening potentials for ion-dipolar case are presented. It is shown that fluid-fluid interionic potentials include connected and blocked parts. The effects of quenched disorder on the fluid properties have received increased attention in recent years. In theoretical studies the matrix-fluid system is considered as a special binary mixture in which the matrix is treated as a rigid set of obstacles,obtained by quenching an equilibrium configuration of particles (usually noted as species "0") with the fluid molecules (noted as species "1") at equilibrium in the presence of quenched particles. Resulting from the applying of the replica trick the description of the original matrix-fluid system was replaced by a multicomponent equilibrium (s + 1) component mixture for which it was possible to use the standard methods of liquid-state theory (the integral equations, cluster expansions ets.). The specific feature of such (s+1)-component mixture is that a pair of fluid particles from different replicas has no interaction and at the end of calculation it takes the limit s → 0, assuming that there is no problem in performing the analytical continuation for noninteger values of s.In this way Given and Stell [1-2] recently proposed a set of coupled integral equations, the so-called replica Ornstein-Zernike (ROZ) equations, relating the total pair correlation functions h αβ (r) of fluid-matrix mixture to the corresponding direct

mentioning

confidence: 99%

The Screening Potentials of Ion-Dipole System Adsorbed in Ion-Dipolar Disordered Matrices

Holovko¹,

Polishchuk²

1999

“…Accordingly, the derivatives of this free energy expression are taken analytically and give consistent access to the thermodynamics of the sorbed fluid [62][63][64]67]. The analytic continuation of the RISM integral equations for the annealed (s + 1)-component replicated system to the limit of s → 0 in the assumption of replica symmetry persistence leads to the replica RISM integral equations which yield the radial distribution functions g ij αγ (r) dependent on separation r between interaction sites α and γ of molecular species i, j constituting the quenched-annealed system.…”

Section: Replica Drism-kh-mv Integral Equationsmentioning

confidence: 99%

“…Computer simulations show that these so-called blocking direct correlations become particularly essential for quenched-annealed systems including charged species [60]. Employing the so-called replica identity to treat the free energy of the sorbed annealed fluid averaged over the distribution of the quenched matrix, Given and Stell [59,[61][62][63] developed the formalism of the replica OZ equations for fluid and matrix of atomic species. It takes proper account of the blocking correlations in a quenched-annealed system.…”

Section: Introductionmentioning

confidence: 99%

Molecular Description of Electrolyte Solution in a Carbon Aerogel Electrode

Kovalenko¹,

Hirata²

2003

We develop a molecular theory of aqueous electrolyte solution sorbed in a nanoporous carbon aerogel electrode, based on the replica reference interaction site model (replica RISM) for realistic molecular quenched-annealed systems. We also briefly review applications of carbon aerogels for supercapacitor and electrochemical separation devices, as well as theoretical and computer modelling of disordered porous materials. The replica RISM integral equation theory yields the microscopic properties of the electrochemical double layer formed at the surface of carbon aerogel nanopores, with due account of chemical specificities of both sorbed electrolyte and carbon aerogel material. The theory allows for spatial disorder of aerogel pores in the range from micro-to macroscopic size scale. We considered ambient aqueous solution of 1 M sodium chloride sorbed in two model nanoporous carbon aerogels with carbon nanoparticles either arranged into branched chains or randomly distributed. The long-range correlations of the carbon aerogel nanostructure substantially affect the properties of the electrochemical double layer formed by the solution sorbed in nanopores.

“…For the network forming fluids a new type of the cooperative adsorption was discovered which is related to a bridging due to tree-like clusters adsorption. To describe the adsorption of associating fluids in porous media the associative analogues of the replica OZ equations [65] were formulated [21,22]. Since in the presence of porous media the value of liquid-gas critical temperature increases and a coexistence curve is narrower compared to the pure fluids [66] the role of association effects in the presence of porous media increases and it can be very important for different fluids, including simple liquids.…”

Section: Some Applications and Conclusionmentioning

confidence: 99%

The Multi-Density Integral Equation Approach in the Theory of Complex Liquids

Holovko¹

1999

Recent development of the multi-density integral equation approach and its application to the statistical mechanical modelling of a different type of association and clusterization in liquids are reviewed. The effects of pairing, polymerization, solvation, formation of the network bonds and selfassembling are discussed. The numerical and analytical solutions of the integral equations in the multi-density formalism are used for the description of the association phenomena in the electrolyte and polyelectrolyte solutions, water, polymers, microemulsions and other fluids. The application of the multi-density integral equation approach for the treatment of the percolation phenomena, the adsorption of fluids in porous media and the description of electronic structure of associative fluids are illustrated.