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Fytas NG, Martín-Mayor V, Parisi G, Picco M, Sourlas N. Finite-size scaling of the random-field Ising model above the upper critical dimension. Phys Rev E 2023; 108:044146. [PMID: 37978671 DOI: 10.1103/physreve.108.044146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 10/05/2023] [Indexed: 11/19/2023]
Abstract
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of statistical physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension D=7, i.e., above its upper critical dimension D_{u}=6, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions D>D_{u}, linear length scale L should be replaced in finite-size scaling expressions by the effective scale L_{eff}=L^{D/D_{u}}. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.
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Affiliation(s)
- Nikolaos G Fytas
- Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185 Rome, Italy and INFN, Sezione di Roma I, IPCF-CNR, P.le A. Moro 2, 00185 Rome, Italy
| | - Marco Picco
- Laboratoire de Physique Théorique et Hautes Energies, UMR7589, Sorbonne Université et CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Nicolas Sourlas
- Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, PARIS VI) 24 rue Lhomond, 75231 Paris Cedex 05, France
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Duan Y, Mahault B, Ma YQ, Shi XQ, Chaté H. Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder. PHYSICAL REVIEW LETTERS 2021; 126:178001. [PMID: 33988412 DOI: 10.1103/physrevlett.126.178001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Revised: 01/10/2021] [Accepted: 02/26/2021] [Indexed: 06/12/2023]
Abstract
We show that spatial quenched disorder affects polar active matter in ways more complex and far reaching than heretofore believed. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.
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Affiliation(s)
- Yu Duan
- National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Benoît Mahault
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Yu-Qiang Ma
- National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100193, China
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Monfared S, Zhou T, Andrade JE, Ioannidou K, Radjaï F, Ulm FJ, Pellenq RJM. Effect of Confinement on Capillary Phase Transition in Granular Aggregates. PHYSICAL REVIEW LETTERS 2020; 125:255501. [PMID: 33416387 DOI: 10.1103/physrevlett.125.255501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Accepted: 11/16/2020] [Indexed: 06/12/2023]
Abstract
Using a 3D mean-field lattice-gas model, we analyze the effect of confinement on the nature of capillary phase transition in granular aggregates with varying disorder and their inverse porous structures obtained by interchanging particles and pores. Surprisingly, the confinement effects are found to be much less pronounced in granular aggregates as opposed to porous structures. We show that this discrepancy can be understood in terms of the surface-surface correlation length with a connected path through the fluid domain, suggesting that this length captures the true degree of confinement. We also find that the liquid-gas phase transition in these porous materials is of second order nature near capillary critical temperature, which is shown to represent a true critical temperature, i.e., independent of the degree of disorder and the nature of the solid matrix, discrete or continuous. The critical exponents estimated here from finite-size scaling analysis suggest that this transition belongs to the 3D random field Ising model universality class as hypothesized by F. Brochard and P.G. de Gennes, with the underlying random fields induced by local disorder in fluid-solid interactions.
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Affiliation(s)
- Siavash Monfared
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Tingtao Zhou
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - José E Andrade
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Katerina Ioannidou
- CNRS, University of Montpellier, LMGC, 163 rue Auguste Broussonnet F-34090 Montpellier, France
- MultiScale Material Science for Energy and Environment UMI 3466 CNRS-MIT-Aix-Marseille Université Joint Laboratory, Cambridge, Massachusetts 02139, USA
| | - Farhang Radjaï
- CNRS, University of Montpellier, LMGC, 163 rue Auguste Broussonnet F-34090 Montpellier, France
| | - Franz-Josef Ulm
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Roland J-M Pellenq
- MultiScale Material Science for Energy and Environment UMI 3466 CNRS-MIT-Aix-Marseille Université Joint Laboratory, Cambridge, Massachusetts 02139, USA
- Department of Physics, Georgetown University, Washington, D.C. 20057, USA
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Kumar M, Banerjee V, Puri S. Random field Ising model in a uniform magnetic field: Ground states, pinned clusters and scaling laws. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:96. [PMID: 29110112 DOI: 10.1140/epje/i2017-11584-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Accepted: 10/23/2017] [Indexed: 06/07/2023]
Abstract
In this paper, we study the random field Ising model (RFIM) in an external magnetic field h . A computationally efficient graph-cut method is used to study ground state (GS) morphologies in this system for three different disorder types: Gaussian, uniform and bimodal. We obtain the critical properties of this system and find that they are independent of the disorder type. We also study GS morphologies via pinned-cluster distributions, which are scale-free at criticality. The spin-spin correlation functions (and structure factors) are characterized by a roughness exponent [Formula: see text]. The corresponding scaling function is universal for all disorder types and independent of h.
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Affiliation(s)
- Manoj Kumar
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, 110016, Hauz Khas, New Delhi, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India.
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Fytas NG, Martín-Mayor V. Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions. Phys Rev E 2016; 93:063308. [PMID: 27415388 DOI: 10.1103/physreve.93.063308] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/06/2023]
Abstract
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
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Affiliation(s)
- Nikolaos G Fytas
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Víctor Martín-Mayor
- Departamento de Física Teórica I, Universidad Complutense, E-28040 Madrid, Spain and Instituto de Biocomputación and Física de Sistemas Complejos (BIFI), E-50009 Zaragoza, Spain
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Binder K, Virnau P, Statt A. Perspective: The Asakura Oosawa model: A colloid prototype for bulk and interfacial phase behavior. J Chem Phys 2014; 141:140901. [DOI: 10.1063/1.4896943] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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Pellicane G, Vink RLC, Russo B, Giaquinta PV. Fluids in porous media: the case of neutral walls. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042131. [PMID: 24229139 DOI: 10.1103/physreve.88.042131] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Indexed: 06/02/2023]
Abstract
The bulk phase behavior of a fluid is typically altered when the fluid is brought into confinement by the walls of a random porous medium. Inside the porous medium, phase-transition points are shifted, or may disappear altogether. A crucial determinant is how the walls interact with the fluid particles. In this work, we consider the situation whereby the walls are neutral with respect to the liquid and vapor phases. In order to realize the condition of strict neutrality, we use a symmetric binary mixture inside a porous medium that interacts identically with mixture species. Monte Carlo simulations are then used to obtain the phase behavior. Our main finding is that, in the presence of the porous medium, a liquid-vapor critical point still exists. At the critical point, the distribution of the order parameter remains scale invariant, but self-averaging is violated. These findings provide further evidence that random confinement by neutral walls induces critical behavior of the random Ising model (i.e., Ising models with dilution type disorder, where the disorder couples to the energy).
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Affiliation(s)
- Giuseppe Pellicane
- School of Chemistry and Physics, University of Kwazulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa and National Institute for Theoretical Physics (NITheP), KZN node, Pietermaritzburg, South Africa
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Fytas NG, Martín-Mayor V. Universality in the three-dimensional random-field Ising model. PHYSICAL REVIEW LETTERS 2013; 110:227201. [PMID: 23767743 DOI: 10.1103/physrevlett.110.227201] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2013] [Indexed: 06/02/2023]
Abstract
We solve a long-standing puzzle in statistical mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.
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Affiliation(s)
- Nikolaos G Fytas
- Departamento de Física Teórica I, Universidad Complutense, E-28040 Madrid, Spain
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Annunziata MA, Pelissetto A. Colloids and polymers in random colloidal matrices: demixing under good-solvent conditions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041804. [PMID: 23214607 DOI: 10.1103/physreve.86.041804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2012] [Indexed: 06/01/2023]
Abstract
We consider a simplified coarse-grained model for colloid-polymer mixtures, in which polymers are represented as monoatomic molecules interacting by means of pair potentials. We use it to study polymer-colloid segregation in the presence of a quenched matrix of colloidal hard spheres. We fix the polymer-to-colloid size ratio to 0.8 and consider matrices such that the fraction f of the volume that is not accessible to the colloids due to the matrix is equal to 40%. As in the Asakura-Oosawa-Vrij (AOV) case, we find that binodal curves in the polymer and colloid volume-fraction plane have a small dependence on disorder. As for the position of the critical point, the behavior differs from that observed in the AOV case: While the critical colloid volume fraction is essentially the same in the bulk and in the presence of the matrix, the polymer volume fraction at criticality increases as f increases. At variance with the AOV case, no capillary colloid condensation or evaporation is generically observed.
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Affiliation(s)
- Mario Alberto Annunziata
- CNR, Istituto dei Sistemi Complessi (Area della Ricerca di Roma Tor Vergata) Via del Fosso del Cavaliere 100, I-00133 Roma, Italy.
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Annunziata MA, Pelissetto A. Fluid–fluid demixing curves for colloid–polymer mixtures in a random colloidal matrix. Mol Phys 2011. [DOI: 10.1080/00268976.2011.622724] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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11
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Tarjus G, Rosinberg ML, Kierlik E, Tissier M. Hierarchical reference theory of critical fluids in disordered porous media. Mol Phys 2011. [DOI: 10.1080/00268976.2011.620024] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Fischer T, Vink RLC. Fluids with quenched disorder: scaling of the free energy barrier near critical points. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:234117. [PMID: 21613708 DOI: 10.1088/0953-8984/23/23/234117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In the context of Monte Carlo simulations, the analysis of the probability distribution P(L)(m) of the order parameter m, as obtained in simulation boxes of finite linear extension L, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, P(L)(m) becomes scale-invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of P(L)(m) at the peaks (P(L, max)) and the value at the minimum in between (P(L, min)) becomes L-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead ΔF(L) := ln(P(L, max)/P(L, min)) proportional to L(θ) should be observed, where θ > 0 is the 'violation of hyperscaling' exponent. Since θ is substantially non-zero, the scaling of ΔF(L) with system size should be easily detectable in simulations. For two fluid models with quenched disorder, ΔF(L) versus L was measured and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random field Ising model.
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Affiliation(s)
- T Fischer
- Institute of Theoretical Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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Vink RLC, Neuhaus T, Löwen H. Fluid phase separation inside a static periodic field: An effectively two-dimensional critical phenomenon. J Chem Phys 2011; 134:204907. [DOI: 10.1063/1.3582903] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Schwanzer DF, Coslovich D, Kurzidim J, Kahl G. Effects of porous confinement on the structural properties of the Gaussian core model. Mol Phys 2010. [DOI: 10.1080/00268970902845321] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Krakoviack V. Statistical mechanics of homogeneous partly pinned fluid systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061501. [PMID: 21230672 DOI: 10.1103/physreve.82.061501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2010] [Indexed: 05/30/2023]
Abstract
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.
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Affiliation(s)
- Vincent Krakoviack
- Laboratoire de Chimie, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
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Vink RLC, Fischer T, Binder K. Finite-size scaling in Ising-like systems with quenched random fields: evidence of hyperscaling violation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051134. [PMID: 21230464 DOI: 10.1103/physreve.82.051134] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2010] [Indexed: 05/30/2023]
Abstract
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.
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Affiliation(s)
- R L C Vink
- Institute of Theoretical Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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De Sanctis Lucentini PG, Pellicane G. Critical behavior of symmetrical fluid mixtures in random pores. PHYSICAL REVIEW LETTERS 2008; 101:246101. [PMID: 19113634 DOI: 10.1103/physrevlett.101.246101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2008] [Indexed: 05/27/2023]
Abstract
We study the liquid-liquid demixing of a binary mixture with a symmetrical coupling to the quenched disorder by means of computer simulation. The critical point in the thermodynamic limit is estimated both by assuming the knowledge of the critical exponents and independently of them. The finite-size scaling analysis of the susceptibilities and the values of the critical amplitudes show that the universality class of the fluid mixture is compatible with the diluted quenched-Ising model. Our findings extend the class of systems exhibiting the same critical behavior of diluted antiferromagnets.
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Kumar AN, Singh JK. The effects of interaction range, porosity and molecular association on the phase equilibrium of a fluid confined in a disordered porous media. Mol Phys 2008. [DOI: 10.1080/00268970802418963] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Binder K, Horbach J, Vink R, De Virgiliis A. Confinement effects on phase behavior of soft matter systems. SOFT MATTER 2008; 4:1555-1568. [PMID: 32907146 DOI: 10.1039/b802207k] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
When systems that can undergo phase separation between two coexisting phases in the bulk are confined in thin film geometry between parallel walls, the phase behavior can be profoundly modified. These phenomena shall be described and exemplified by computer simulations of the Asakura-Oosawa model for colloid-polymer mixtures, but applications to other soft matter systems (e.g. confined polymer blends) will also be mentioned. Typically a wall will prefer one of the phases, and hence the composition of the system in the direction perpendicular to the walls will not be homogeneous. If both walls are of the same kind, this effect leads to a distortion of the phase diagram of the system in thin film geometry, in comparison with the bulk, analogous to the phenomenon of "capillary condensation" of simple fluids in thin capillaries. In the case of "competing walls", where both walls prefer different phases of the two phases coexisting in the bulk, a state with an interface parallel to the walls gets stabilized. The transition from the disordered phase to this "soft mode phase" is rounded by the finite thickness of the film and is not a sharp phase transition. However, a sharp transition can occur where this interface gets localized at (one of) the walls. The relation of this interface localization transition to wetting phenomena is discussed. Finally, an outlook to related phenomena is given, such as the effects of confinement in cylindrical pores on the phase behavior, and more complicated ordering phenomena (lamellar mesophases of block copolymers or nematic phases of liquid crystals under confinement).
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Affiliation(s)
- Kurt Binder
- Institut für Physik, Johannes Gutenberg Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany.
| | - Jürgen Horbach
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.
| | - Richard Vink
- Institut für Theoretische Physik, Georg-August Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
| | - Andres De Virgiliis
- Instituto de Investigaciones Fisicoquimicas, UNLP, CONICET, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina.
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Pellicane G, Vink RLC, Caccamo C, Löwen H. Colloid-polymer mixtures in the presence of quenched disorder: a theoretical and computer simulation study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:115101. [PMID: 21694215 DOI: 10.1088/0953-8984/20/11/115101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We use theory and computer simulation to study the structure and phase behavior of colloid-polymer mixtures in the presence of quenched disorder. The Asakura-Oosawa model (AO) (Asakura and Oosawa 1954 J. Chem. Phys. 22 1255) is used to describe the colloid-colloid, colloid-polymer, and polymer-polymer pair interactions. We then investigate the behavior of this model in the presence of frozen-in (quenched) obstacles. The obstacles will be placed according to two different scenarios, both of which are experimentally feasible. In the first scenario, polymers are distributed at positions drawn from an ideal gas configuration. In the second scenario, colloidal particles are distributed at positions drawn from an equilibrium hard sphere configuration. We investigate how the unmixing transition of the AO model is affected by the type of quenched disorder. The theoretical formalism is based on the replica method of Given and Stell (1994 Physica A 209 495). Our foremost aim is to test the accuracy of three common closures to the replica Ornstein-Zernike equations, namely the hypernetted chain, the Percus-Yevick, and the Martinov-Sarkisov equations. The accuracy is determined by comparison with grand canonical Monte Carlo simulations. We find that, for quenched polymer disorder, all three closures perform remarkably well. However, when quenched colloid disorder is considered, i.e. the second mentioned scenario, the predictions of all three closures worsen dramatically.
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Affiliation(s)
- Giuseppe Pellicane
- Dipartimento di Fisica Contrada Papardo, Università degli Studi di Messina, 98166 Messina, Italy
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