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Frohoff-Hülsmann T, Wrembel J, Thiele U. Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling. Phys Rev E 2021; 103:042602. [PMID: 34006003 DOI: 10.1103/physreve.103.042602] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 03/04/2021] [Indexed: 12/27/2022]
Abstract
We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well-known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis, we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.
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Affiliation(s)
- Tobias Frohoff-Hülsmann
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - Jana Wrembel
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.,Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany.,Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität, Corrensstr. 40, 48149 Münster, Germany
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2
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Pathania Y, Chakraborty D, Höfling F. Continuous Demixing Transition of Binary Liquids: Finite‐Size Scaling from the Analysis of Sub‐Systems. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000235] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Yogyata Pathania
- Indian Institute of Science Education and Research Mohali Knowledge City, Sector 81, S. A. S. Nagar Manauli 140306 India
| | - Dipanjan Chakraborty
- Indian Institute of Science Education and Research Mohali Knowledge City, Sector 81, S. A. S. Nagar Manauli 140306 India
| | - Felix Höfling
- Freie Universität Berlin, Fachbereich Mathematik und Informatik Arnimallee 6 Berlin 14195 Germany
- Zuse Institute Berlin Takustr. 7 Berlin 14195 Germany
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Smallenburg F, Filion L, Sciortino F. Liquid-Liquid Phase Transitions in Tetrahedrally Coordinated Fluids via Wertheim Theory. J Phys Chem B 2015; 119:9076-83. [PMID: 25384011 DOI: 10.1021/jp508788m] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Network interpenetration has been proposed as a mechanism for generating liquid-liquid phase transitions in one component systems. We introduce a model of four coordinated particles, which explicitly treats the system as a mixture of two interacting interpenetrating networks that can freely exchange particles. This model can be solved within Wertheim's theory for associating fluids and shows liquid-liquid phase separations (in addition to the gas-liquid) for a wide range of model parameters. We find that originating a liquid-liquid transition requires a small degree of interpenetrability and a preference for intranetwork bonding. Physically, these requirements can be seen as controlling the softness of the particle-particle interaction and the bond flexibility, in full agreement with recent findings [Smallenburg, F.; Filion, L.; Sciortino, F. Nat. Phys. 2014, 10, 653].
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Affiliation(s)
- Frank Smallenburg
- †Department of Physics, Sapienza, Universitá di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy
| | - Laura Filion
- ‡Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, Utrecht 3584 CC, The Netherlands
| | - Francesco Sciortino
- †Department of Physics, Sapienza, Universitá di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy
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Edison JR, Belli S, Evans R, van Roij R, Dijkstra M. Phase behaviour of colloids suspended in a near-critical solvent: a mean-field approach. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1031842] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- John R. Edison
- Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University , Utrecht, The Netherlands
| | - Simone Belli
- Institute for Theoretical Physics, Utrecht University , Utrecht, The Netherlands
| | - Robert Evans
- H.H. Wills Physics Laboratory, University of Bristol , Bristol, United Kingdom
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University , Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University , Utrecht, The Netherlands
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5
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Chung S, Malherbe J, Amokrane S. Effect of an external field on the structure and the phase transitions of a confined mixture of neutral and dipolar hard spheres. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1014003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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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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7
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Materniak S, Patrykiejew A. Symmetrical mixtures in external fields. J Chem Phys 2013; 139:014705. [DOI: 10.1063/1.4812370] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
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Materniak S, Patrykiejew A, Rżysko W. Reentrant miscibility in two-dimensional symmetrical mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062306. [PMID: 23848674 DOI: 10.1103/physreve.87.062306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2013] [Indexed: 06/02/2023]
Abstract
The Monte Carlo simulation method in the grand canonical ensemble is used to study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles with negative nonadditivity and the weaker interaction between the pairs of unlike than between the pairs of like particles. We have determined the evolution of the phase diagram topology when the parameters describing the interaction between unlike particles vary. It has been found that such systems may exhibit reentrant miscibility in the liquid and the solid phases.
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Affiliation(s)
- S Materniak
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
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Brunet C, Malherbe J, Amokrane S. Demixing and field-induced population inversion in a mixture of neutral and dipolar-hard spheres confined in a slit pore. Mol Phys 2012. [DOI: 10.1080/00268976.2012.660205] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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10
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Pizio O, Sokołowski S, Sokołowska Z. Phase behavior of binary symmetric mixtures in pillared slit-like pores: A density functional approach. J Chem Phys 2011; 134:214702. [DOI: 10.1063/1.3597773] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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Materniak S, Patrykiejew A, Sokołowski S. The phase behavior of two-dimensional symmetrical mixtures in a weak external field of square symmetry. J Chem Phys 2011; 134:214705. [DOI: 10.1063/1.3583984] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
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12
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Materniak S, Patrykiejew A, Sokołowski S. The phase behavior of two-dimensional symmetrical mixtures. J Chem Phys 2010; 133:244501. [PMID: 21197996 DOI: 10.1063/1.3511711] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles. We discuss the interplay between the demixing transition in a liquid and the freezing in detail. Phase diagrams for several systems characterized by different parameters describing interactions in the system are presented. It is explicitly demonstrated that different scenarios involving demixing and freezing transitions, described in our earlier paper [A. Patrykiejew and S. Sokołowski, Phys. Rev. E, 81, 012501 (2010)], are possible. In one class of systems, the λ-line representing a continuous demixing transition in a liquid phase starts at the liquid side of either the vapor-liquid or liquid-solid coexistence. The second class involves the systems in which the λ-line begins at the liquid side of the vapor-liquid coexistence, in the lower critical end point, and then terminates at the liquid side of the liquid-solid coexistence, in the upper critical end point. It is also shown that in such systems the solid phase may undergo a demixing transition at the temperature above the upper critical end point.
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Affiliation(s)
- S Materniak
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
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Brunet C, Malherbe JG, Amokrane S. Binary mixture adsorbed in a slit pore: Field-induced population inversion near the bulk instability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:021504. [PMID: 20866815 DOI: 10.1103/physreve.82.021504] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2010] [Indexed: 05/29/2023]
Abstract
The recently proposed method for modulating through an external field the composition of a binary fluid mixture adsorbed in a slit pore is discussed. The population inversion near the bulk (demixing) instability is first analyzed in the case of a symmetric mixture of nonadditive hard spheres, without field. It is next investigated for a mixture comprising dipolar particles subject to an external field. The influence of several factors on the adsorption curves including bulk composition, pore width, field direction, polarizability versus permanent dipoles, and temperature on this field induced population inversion is shown by Monte Carlo simulation.
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Affiliation(s)
- C Brunet
- Université Paris Est, Créteil, France
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Dorsaz N, Foffi G. Phase behaviour of the symmetric binary mixture from thermodynamic perturbation theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:104113. [PMID: 21389447 DOI: 10.1088/0953-8984/22/10/104113] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the phase behaviour of symmetric binary mixtures of hard core Yukawa (HCY) particles via thermodynamic perturbation theory (TPT). We show that all the topologies of phase diagram reported for the symmetric binary mixtures are correctly reproduced within the TPT approach. In a second step we use the capability of TPT to be straightforwardly extended to mixtures that are nonsymmetric in size. Starting from mixtures that belong to the different topologies of symmetric binary mixtures we investigate the effect on the phase behaviour when an asymmetry in the diameters of the two components is introduced. Interestingly, when the energy of interaction between unlike particles is weaker than the interaction between like particles, the propensity for the solution to demix is found to increase strongly with size asymmetry.
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Affiliation(s)
- N Dorsaz
- Institute of Theoretical Physics and Institut Romand de Recherche Numérique en Physique des Matériaux, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
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Patrykiejew A, Sokołowski S. Two-Dimensional Symmetrical Mixtures in an External Field of Square Symmetry. J Phys Chem B 2010; 114:396-406. [DOI: 10.1021/jp908710e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- A. Patrykiejew
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
| | - S. Sokołowski
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
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16
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Patrykiejew A, Sokołowski S. Interplay between demixing and freezing in two-dimensional symmetrical mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:012501. [PMID: 20365417 DOI: 10.1103/physreve.81.012501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2009] [Indexed: 05/29/2023]
Abstract
The interplay between demixing and freezing in two-dimensional symmetrical binary mixtures of Lennard-Jones particles is studied using Monte Carlo simulation. It is demonstrated that different scenarios are possible. For example, the line of continuous liquid demixing transition can start at the liquid side of the vapor-liquid coexistence at the lower critical end point and then it can terminate at the liquid side of the liquid-demixed solid coexistence at the upper critical end point. Other situations are also possible. We distinguish four different scenarios depending on the interactions between unlike particles.
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Affiliation(s)
- A Patrykiejew
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland.
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Sałamacha L, Patrykiejew A, Sokołowski S. Ground-State Properties of Two-Dimensional Symmetrical Mixtures in an External Field of Square Symmetry. J Phys Chem B 2009; 113:13687-96. [DOI: 10.1021/jp901383v] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Affiliation(s)
- L. Sałamacha
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
| | - A. Patrykiejew
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
| | - S. Sokołowski
- Department for the Modelling of Physico-Chemical Processes, Faculty of Chemistry, MCS University, 20031 Lublin, Poland
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Allahyarov E, Löwen H. Nonadditivity in the effective interactions of binary charged colloidal suspensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:424117. [PMID: 21715852 DOI: 10.1088/0953-8984/21/42/424117] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Based on primitive model computer simulations with explicit microions, we calculate the effective interactions in a binary mixture of charged colloids with species A and B for different size and charge ratios. An optimal pairwise interaction is obtained by fitting the many-body effective forces. This interaction is close to a Yukawa (or Derjaguin-Landau-Verwey-Overbeek (DLVO)) pair potential but the AB cross-interaction is different from the geometric mean of the two direct AA and BB interactions. As a function of charge asymmetry, the corresponding nonadditivity parameter is first positive, then significantly negative and is then positive again. We finally show that an inclusion of nonadditivity within an optimal effective Yukawa model gives better predictions for the fluid pair structure than DLVO theory.
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Affiliation(s)
- E Allahyarov
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany. Department of Physics, Case Western Reserve University, Cleveland, OH 44106, USA. Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
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19
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Assoud L, Messina R, Löwen H. Binary crystals in two-dimensional two-component Yukawa mixtures. J Chem Phys 2008; 129:164511. [DOI: 10.1063/1.2996515] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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