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Jung H, Yethiraj A. A simulation method for the phase diagram of complex fluid mixtures. J Chem Phys 2018; 148:244903. [PMID: 29960369 DOI: 10.1063/1.5033958] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The phase behavior of complex fluid mixtures is of continuing interest, but obtaining the phase diagram from computer simulations can be challenging. In the Gibbs ensemble method, for example, each of the coexisting phases is simulated in a different cell, and ensuring the equality of chemical potentials of all components requires the transfer of molecules from one cell to the other. For complex fluids such as polymers, successful insertions are rare. An alternative method is to simulate both coexisting phases in a single simulation cell, with an interface between them. The challenge here is that the interface position moves during the simulation, making it difficult to determine the concentration profile and coexisting concentrations. In this work, we propose a new method for single cell simulations that uses a spatial concentration autocorrelation function to (spatially) align instantaneous concentration profiles from different snapshots. This allows one to obtain average concentration profiles and hence the coexisting concentrations. We test the method by calculating the phase diagrams of two systems: the Widom-Rowlinson model and the symmetric blends of freely jointed polymer molecules for which phase diagrams from conventional methods are available. Excellent agreement is found, except in the neighborhood of the critical point where the interface is broad and finite size effects are important. The method is easy to implement and readily applied to any mixture of complex fluids.
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Affiliation(s)
- Hyuntae Jung
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA
| | - Arun Yethiraj
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA
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2
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Słyk E, Rżysko W, Bryk P. Two-dimensional binary mixtures of patchy particles and spherical colloids. SOFT MATTER 2016; 12:9538-9548. [PMID: 27834426 DOI: 10.1039/c6sm01838f] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using Monte Carlo simulation we study two dimensional mixtures of patchy and spherically symmetric particles. Such mixtures can be synthesized experimentally by covering colloids with appropriate types of DNA strands [L. Feng, et al., Adv. Mater., 2013, 25, 2779]. We focus on finding out the ordered structures that can be formed in such systems. The type of ordered phase strongly depends on the valency, size and binding energy of the patchy particles. If the patch size is small enough, i.e. it allows only one spherically symmetric particle to be bound, the ordered structure follows either a hexagonal or a tetragonal pattern depending on the valency of the patchy particles. Moreover, we find stable quasicrystals of dodecagonal symmetry. Additional structures can be obtained if the patches are larger and the binding energy is higher. Depending on the valency of the patchy particles we find either lanes or branched structures forming polygons of the spherically symmetric particles with few patchy particles inside. For pentavalent patchy particles we find stable quasicrystals of decagonal symmetry.
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Affiliation(s)
- Edyta Słyk
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, 20-031 Lublin, Poland.
| | - Wojciech Rżysko
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, 20-031 Lublin, Poland.
| | - Paweł Bryk
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, 20-031 Lublin, Poland.
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3
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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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4
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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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Rouhiparkouhi T, Weikl TR, Discher DE, Lipowsky R. Adhesion-induced phase behavior of two-component membranes and vesicles. Int J Mol Sci 2013; 14:2203-29. [PMID: 23340655 PMCID: PMC3565373 DOI: 10.3390/ijms14012203] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Revised: 01/17/2013] [Accepted: 01/18/2013] [Indexed: 11/17/2022] Open
Abstract
The interplay of adhesion and phase separation is studied theoretically for two-component membranes that can phase separate into two fluid phases such as liquid-ordered and liquid-disordered phases. Many adhesion geometries provide two different environments for these membranes and then partition the membranes into two segments that differ in their composition. Examples are provided by adhering vesicles, by hole- or pore-spanning membranes, and by membranes supported by chemically patterned surfaces. Generalizing a lattice model for binary mixtures to these adhesion geometries, we show that the phase behavior of the adhering membranes depends, apart from composition and temperature, on two additional parameters, the area fraction of one membrane segment and the affinity contrast between the two segments. For the generic case of non-vanishing affinity contrast, the adhering membranes undergo two distinct phase transitions and the phase diagrams in the composition/temperature plane have a generic topology that consists of two two-phase coexistence regions separated by an intermediate one-phase region. As a consequence, phase separation and domain formation is predicted to occur separately in each of the two membrane segments but not in both segments simultaneously. Furthermore, adhesion is also predicted to suppress the phase separation process for certain regions of the phase diagrams. These generic features of the adhesion-induced phase behavior are accessible to experiment.
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Affiliation(s)
- Tahereh Rouhiparkouhi
- Theory & Bio-Systems, Max Planck Insitute of Colloids and Interfaces, Potsdam 14424, Germany; E-Mails: (T.R.); (T.R.W.)
| | - Thomas R. Weikl
- Theory & Bio-Systems, Max Planck Insitute of Colloids and Interfaces, Potsdam 14424, Germany; E-Mails: (T.R.); (T.R.W.)
| | - Dennis E. Discher
- Biophysical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA; E-Mail:
| | - Reinhard Lipowsky
- Theory & Bio-Systems, Max Planck Insitute of Colloids and Interfaces, Potsdam 14424, Germany; E-Mails: (T.R.); (T.R.W.)
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6
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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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7
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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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9
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Muñoz-Salazar L, Odriozola G. Phase behaviour and separation kinetics of symmetric non-additive hard discs. MOLECULAR SIMULATION 2010. [DOI: 10.1080/08927020903141027] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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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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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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12
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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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13
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Titievsky K, Rutledge GC. Mixtures of interacting particles with well-defined composition field coupling χ parameters. J Chem Phys 2008; 128:124902. [DOI: 10.1063/1.2837651] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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14
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Djikaev Y. The interfacial tension and phase diagram of the Widom-Rowlinson mixture via Monte Carlo simulations. J Chem Phys 2008; 128:014712. [DOI: 10.1063/1.2806279] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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de Miguel E, Almarza NG, Jackson G. Surface tension of the Widom-Rowlinson model. J Chem Phys 2007; 127:034707. [PMID: 17655455 DOI: 10.1063/1.2751153] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.
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Affiliation(s)
- E de Miguel
- Departamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, 21071 Huelva, Spain.
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16
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Kofke DA. Semigrand Canonical Monte Carlo Simulation; Integration Along Coexistence Lines. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141649.ch13] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/09/2023]
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17
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Köfinger J, Wilding NB, Kahl G. Phase behavior of a symmetrical binary fluid mixture. J Chem Phys 2006; 125:234503. [PMID: 17190563 DOI: 10.1063/1.2393241] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have investigated the phase behavior of a symmetrical binary fluid mixture for the situation where the chemical potentials mu(1) and mu(2) of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when mu(1)=mu(2), the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behavior for the case mu(1) not equalmu(2) is investigated via integral-equation theory calculations within the mean spherical approximation and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behavior can occur, these being distinguished by the relationship between the triple lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other is also studied, revealing interesting features.
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Affiliation(s)
- Jürgen Köfinger
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria
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18
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Morrow TI, Maginn EJ. Isomolar-semigrand ensemble molecular dynamics: Application to vapor-liquid equilibrium of the mixture methane/ethane. J Chem Phys 2006; 125:204712. [PMID: 17144728 DOI: 10.1063/1.2363972] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The isomolar-semigrand ensemble molecular dynamics (iSGMD) method is applied to the simulation of the binary system methane/ethane. The vapor-liquid equilibrium properties of this system at a temperature of 192.37 K are computed using the Gibbs-Duhem integration method. The iSGMD method, which resembles conventional hybrid Monte Carlo (MC) but is applicable to phase equilibrium calculations, is designed to overcome the difficulties associated with performing standard Monte Carlo-type particle transformations in liquid systems that are very dense and/or are comprised of complex molecules with many intramolecular degrees of freedom. This work shows that particle transformations using the iSGMD method for the simple system methane/ethane are at least 25 times more successful than standard MC-type transformations. The P-x-y curve for the system methane/ethane at 192.37 K computed using iSGMD simulations agrees very well with the experimental P-x-y curve as well as results of a previous MC study.
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Affiliation(s)
- Timothy I Morrow
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
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19
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Das SK, Horbach J, Binder K, Fisher ME, Sengers JV. Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation. J Chem Phys 2006; 125:24506. [PMID: 16848591 DOI: 10.1063/1.2215613] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.
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Affiliation(s)
- Subir K Das
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
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Vink RLC. Critical behavior of the Widom-Rowlinson mixture: Coexistence diameter and order parameter. J Chem Phys 2006; 124:94502. [PMID: 16526862 DOI: 10.1063/1.2171191] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The critical behavior of the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] is studied in d = 3 dimensions by means of grand canonical Monte Carlo simulations. The finite-size scaling approach of Kim et al. [Phys. Rev. Lett. 91, 065701 (2003)] is used to extract the order parameter and the coexistence diameter. It is demonstrated that the critical behavior of the diameter is dominated by a singular term proportional to t(1-alpha), with t the relative distance from the critical point, and alpha the critical exponent of the specific heat. No sign of a term proportional to t(2beta) could be detected, with beta the critical exponent of the order parameter, indicating that pressure mixing in this model is small. The critical density is measured to be rhosigma3 = 0.7486 +/- 0.0002, with sigma the particle diameter. The critical exponents alpha and beta, as well as the correlation length exponent nu, are also measured and shown to comply with d = 3 Ising criticality.
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Affiliation(s)
- R L C Vink
- Institut für Theoretische Physik II, Heinrich Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany.
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21
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Djikaev Y. Histogram analysis as a method for determining the line tension of a three-phase contact region by Monte Carlo simulations. J Chem Phys 2005; 123:184704. [PMID: 16292918 DOI: 10.1063/1.2056548] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A method is proposed for determining the line tension, which is the main physical characteristic of a three-phase contact region, by Monte Carlo (MC) simulations. The key idea of the proposed method is that if a three-phase equilibrium involves a three-phase contact region, the probability distribution of states of a system as a function of two order parameters depends not only on the surface tension, but also on the line tension. This probability distribution can be obtained as a normalized histogram by appropriate MC simulations, so one can use the combination of histogram analysis and finite-size scaling to study the properties of a three phase contact region. Every histogram and results extracted therefrom will depend on the size of the simulated system. Carrying out MC simulations for a series of system sizes and extrapolating the results, obtained from the corresponding series of histograms, to infinite size, one can determine the line tension of the three phase contact region and the interfacial tensions of all three interfaces (and hence the contact angles) in an infinite system. To illustrate the proposed method, it is applied to the three-dimensional ternary fluid mixture, in which molecular pairs of like species do not interact whereas those of unlike species interact as hard spheres. The simulated results are in agreement with expectations.
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Affiliation(s)
- Yuri Djikaev
- Department of Chemistry, Baker Laboratory, Cornell University, Ithaca, New York 14853-1301, USA.
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Jagannathan K, Yethiraj A. Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture. J Chem Phys 2005; 122:244506. [PMID: 16035781 DOI: 10.1063/1.1940053] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.
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Góźdź WT. Phase separation of the Widom–Rowlinson mixture in confined geometry. J Chem Phys 2005; 122:074505. [PMID: 15743252 DOI: 10.1063/1.1844332] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The behavior of binary Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] mixture in confined geometry is investigated. The influence of confinement on phase separation is examined. Coexistence curves for the mixture in slitlike pores and pores of complex geometry are calculated in Monte Carlo simulations. Finite size scaling analysis is used to determine precisely the location of critical point for the bulk mixture.
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Affiliation(s)
- W T Góźdź
- Institute of Physical Chemistry Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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Abstract
In this paper, we present a cluster algorithm for the numerical simulations of nonadditive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than previous simulations. The phase separation for symmetric binary mixtures is studied for different nonadditivities as well as for the Widom-Rowlinson model [B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] in two and three dimensions. The critical densities are determined from finite size scaling. The critical exponents for all the nonadditivities are consistent with the Ising universality class.
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Affiliation(s)
- Arnaud Buhot
- UMR 5819 (UJF, CNRS, CEA) DRFMC/SI3M, CEA Grenoble, 17 rue des Martyrs, 38054 Grenoble cedex 9, France
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Pedesseau L, Jouanna P. Phases, periphases, and interphases equilibrium by molecular modeling. I. Mass equilibrium by the semianalytical stochastic perturbations method and application to a solution between (120) gypsum faces. J Chem Phys 2004; 121:12511-22. [PMID: 15606272 DOI: 10.1063/1.1821491] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation C(k)<=>mu(k) between the concentrations C(k) and the chemical potentials mu(k) of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation C(k)<=>mu(k) implies in fact two problems: a direct problem C(k)=>mu(k) and an inverse problem mu(k)=>C(k). Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 A thick gypsum interface. The major unexpected observation is the repulsion of SO(4) (2-) ions towards the reference solution and the attraction of Ca(2+) ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime importance for all coupled chemical-mechanical problems dealing with interfaces, and more generally for a wide variety of applications such as phase changes, osmotic equilibrium, surface energy, etc., in complex chemical-physics situations.
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Affiliation(s)
- Laurent Pedesseau
- UMR 5568 CNRS-UM2, ISTEEM, Université Montpellier II, 34095 Montpellier Cedex 5, France
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Góźdź WT. Critical-point and coexistence curve properties of a symmetric mixture of nonadditive hard spheres: A finite size scaling study. J Chem Phys 2003. [DOI: 10.1063/1.1589746] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Das SK, Horbach J, Binder K. Transport phenomena and microscopic structure in partially miscible binary fluids: A simulation study of the symmetrical Lennard-Jones mixture. J Chem Phys 2003. [DOI: 10.1063/1.1580106] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jagannathan K, Yethiraj A. Monte Carlo simulations for the phase behavior of symmetric nonadditive hard sphere mixtures. J Chem Phys 2003. [DOI: 10.1063/1.1563595] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wilding NB. Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:052503. [PMID: 12786203 DOI: 10.1103/physreve.67.052503] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2003] [Indexed: 05/24/2023]
Abstract
We report a Monte Carlo finite-size scaling study of the demixing transition of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of species, and for a choice of the unlike-to-like interaction ratio delta=0.7, this transition is found to be continuous at liquid-vapor coexistence. The associated critical end point exhibits an Ising-like universality. These findings confirm those of earlier smaller scale simulation studies of the same model, but contradict the findings of recent integral equation and hierarchical reference theory investigations.
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Affiliation(s)
- Nigel B Wilding
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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Pini D, Tau M, Parola A, Reatto L. Phase diagram of symmetric binary mixtures at equimolar and nonequimolar concentrations: a systematic investigation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046116. [PMID: 12786445 DOI: 10.1103/physreve.67.046116] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2002] [Indexed: 05/24/2023]
Abstract
We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths epsilon(ij), i,j=1,2, such that epsilon(11)=epsilon(22)>epsilon(12). The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio delta=epsilon(12)/epsilon(11) by means of the hierarchical reference theory. The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As delta is increased in the interval 0<delta<1, we find first a regime where the phase diagram at equal species concentration displays a tricritical point, then one where both a tricritical and a liquid-vapor critical point are present. We did not find any clear evidence of the critical end point topology predicted by mean-field theory as delta approaches 1, at least up to delta=0.8, which is the largest value of delta investigated here. Particular attention was paid to the description of the critical-plus-tricritical point regime in the whole density-concentration plane. In this situation, the phase diagram shows, in a certain temperature interval, a coexistence region that encloses an island of homogeneous, one-phase fluid.
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Affiliation(s)
- D Pini
- Istituto Nazionale di Fisica della Materia and Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano, Italy
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Kristóf T, Vorholz J, Maurer G. Molecular Simulation of the High-Pressure Phase Equilibrium of the System Carbon Dioxide−Methanol−Water. J Phys Chem B 2002. [DOI: 10.1021/jp020532x] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Tamás Kristóf
- Department of Physical Chemistry, University of Veszprém, H-8201 Veszprém, P.O. Box 158, Hungary, and Lehrstuhl für Technische Thermodynamik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany
| | - Johannes Vorholz
- Department of Physical Chemistry, University of Veszprém, H-8201 Veszprém, P.O. Box 158, Hungary, and Lehrstuhl für Technische Thermodynamik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany
| | - Gerd Maurer
- Department of Physical Chemistry, University of Veszprém, H-8201 Veszprém, P.O. Box 158, Hungary, and Lehrstuhl für Technische Thermodynamik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany
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Almarza NG, Enciso E, García MF, González MA, Bermejo FJ. Reentrant miscibility in fluids with spherical interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:012501. [PMID: 11461308 DOI: 10.1103/physreve.64.012501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2001] [Indexed: 05/23/2023]
Abstract
We have obtained the closed-loop fluid-fluid immiscibility in the phase diagram of a binary mixture with interactions with spherical symmetry. That topology appears when a short-range attractive interaction is considered between unlike pair molecules. We present "exact" results obtained from Monte Carlo simulation on different ensembles and results from the application of a first-order perturbation theory.
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Affiliation(s)
- N G Almarza
- Departamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense, 28040 Madrid, Spain
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Potoff JJ, Panagiotopoulos AZ. Critical point and phase behavior of the pure fluid and a Lennard-Jones mixture. J Chem Phys 1998. [DOI: 10.1063/1.477787] [Citation(s) in RCA: 323] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Caccamo C, Costa D, Pellicane G. A comprehensive study of the phase diagram of symmetrical hard-core Yukawa mixtures. J Chem Phys 1998. [DOI: 10.1063/1.477053] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mackie AD, Onur K, Panagiotopoulos AZ. Phase equilibria of a lattice model for an oil–water–amphiphile mixture. J Chem Phys 1996. [DOI: 10.1063/1.471026] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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