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Joubaud R, Bernard O, Delville A, Ern A, Rotenberg B, Turq P. Numerical study of density functional theory with mean spherical approximation for ionic condensation in highly charged confined electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062302. [PMID: 25019771 DOI: 10.1103/physreve.89.062302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2013] [Indexed: 06/03/2023]
Abstract
We investigate numerically a density functional theory (DFT) for strongly confined ionic solutions in the canonical ensemble by comparing predictions of ionic concentration profiles and pressure for the double-layer configuration to those obtained with Monte Carlo (MC) simulations and the simpler Poisson-Boltzmann (PB) approach. The DFT consists of a bulk (ion-ion) and an ion-solid part. The bulk part includes nonideal terms accounting for long-range electrostatic and short-range steric correlations between ions and is evaluated with the mean spherical approximation and the local density approximation. The ion-solid part treats the ion-solid interactions at the mean-field level through the solution of a Poisson problem. The main findings are that ionic concentration profiles are generally better described by PB than by DFT, although DFT captures the nonmonotone co-ion profile missed by PB. Instead, DFT yields more accurate pressure predictions than PB, showing in particular that nonideal effects are important to describe highly confined ionic solutions. Finally, we present a numerical methodology capable of handling nonconvex minimization problems so as to explore DFT predictions when the reduced temperature falls below the critical temperature.
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Affiliation(s)
- R Joubaud
- ANDRA, DRD/EAP, Parc de la croix blanche, 1,7 rue Jean Monnet, 92298 Châtenay-Malabry Cedex, France and University Paris-Est, CERMICS (ENPC), 77455 Marne la Vallée cedex 2, France and Department of Mathematics, Imperial College London, SW7 2AZ London, United Kingdom
| | - O Bernard
- Sorbonne Universités, UPMC University Paris 06, UMR 8234 PHENIX, 75005 Paris, France and CNRS, UMR 8234 PHENIX, 75005 Paris, France
| | - A Delville
- CRMD, CNRS-Université d'Orléans, 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - A Ern
- University Paris-Est, CERMICS (ENPC), 77455 Marne la Vallée cedex 2, France
| | - B Rotenberg
- Sorbonne Universités, UPMC University Paris 06, UMR 8234 PHENIX, 75005 Paris, France and CNRS, UMR 8234 PHENIX, 75005 Paris, France
| | - P Turq
- Sorbonne Universités, UPMC University Paris 06, UMR 8234 PHENIX, 75005 Paris, France and CNRS, UMR 8234 PHENIX, 75005 Paris, France
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Masuda N, Konno N. Return times of random walk on generalized random graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:066113. [PMID: 15244673 DOI: 10.1103/physreve.69.066113] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2003] [Indexed: 05/24/2023]
Abstract
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even broader classes of related stochastic models. Abundant results are obtained for random walk on simple graphs such as the regular lattices and the Cayley trees. However, random walks and related processes on more complex networks, which are often more relevant in the real world, are still open issues, possibly yielding different characteristics. In this paper, we investigate the return times of random walks on random graphs with arbitrary vertex degree distributions. We analytically derive the distributions of the return times. The results are applied to some types of networks and compared with numerical data.
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Affiliation(s)
- Naoki Masuda
- Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, 2-1, Hirosawa, Wako, Saitama, 351-0198 Japan
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Jiang J, Blum L, Bernard O, Prausnitz JM, Sandler SI. Criticality and phase behavior in the restricted-primitive model electrolyte: Description of ion association. J Chem Phys 2002. [DOI: 10.1063/1.1468638] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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