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Cruz C, Ciach A. Phase Transitions and Electrochemical Properties of Ionic Liquids and Ionic Liquid-Solvent Mixtures. Molecules 2021; 26:3668. [PMID: 34208542 PMCID: PMC8234089 DOI: 10.3390/molecules26123668] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2021] [Revised: 06/04/2021] [Accepted: 06/10/2021] [Indexed: 12/20/2022] Open
Abstract
Recent advances in studies of ionic liquids (IL) and ionic liquid-solvent mixtures are reviewed. Selected experimental, simulation, and theoretical results for electrochemical, thermodynamical, and structural properties of IL and IL-solvent mixtures are described. Special attention is paid to phenomena that are not predicted by the classical theories of the electrical double layer or disagree strongly with these theories. We focus on structural properties, especially on distribution of ions near electrodes, on electrical double layer capacitance, on effects of confinement, including decay length of a dissjoining pressure between confinig plates, and on demixing phase transition. In particular, effects of the demixing phase transition on electrochemical properties of ionic liquid-solvent mixtures for different degrees of confinement are presented.
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Affiliation(s)
| | - Alina Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 44/52, 01-224 Warsaw, Poland;
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2
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Yin T, Xu C, Lv H, Liu S, Wang M, Chen Z, Shen W. Asymmetric criticality of binary ionic solutions containing 1-butyl-3-methylimidazolium tetrafluoroborate and alcohol. Phys Chem Chem Phys 2014; 16:17715-23. [DOI: 10.1039/c4cp01344a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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3
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Elshwishin A, Köser J, Schröer W, Qiao B. Liquid–liquid phase separation of ionic liquids in solutions: Ionic liquids with the triflat anion solved in aryl halides. J Mol Liq 2014. [DOI: 10.1016/j.molliq.2013.07.012] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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4
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Patsahan O. Ginzburg criterion for ionic fluids: the effect of Coulomb interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022102. [PMID: 24032770 DOI: 10.1103/physreve.88.022102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Indexed: 06/02/2023]
Abstract
The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.
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Affiliation(s)
- O Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine
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5
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Fantoni R, Pastore G. Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: phase diagram and clustering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052303. [PMID: 23767536 DOI: 10.1103/physreve.87.052303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2012] [Revised: 03/19/2013] [Indexed: 06/02/2023]
Abstract
We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with nonadditive hard-sphere diameters. At high density the positively nonadditive fluid shows more clustering than in the additive model and the negatively nonadditive fluid shows less clustering than in the additive model; at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of the gas-liquid phase transition moves at higher temperatures and higher densities for a negative nonadditivity and at lower temperatures and lower densities for a positive nonadditivity. The law of corresponding states does not seem to hold strictly. Our results can be used to interpret recent experimental works on room temperature ionic liquids.
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Affiliation(s)
- Riccardo Fantoni
- Dipartimento di Scienze dei Materiali e Nanosistemi, Università Ca' Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia, Italy.
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6
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Losada-Pérez P, Glorieux C, Thoen J. The critical behavior of the refractive index near liquid-liquid critical points. J Chem Phys 2012; 136:144502. [PMID: 22502528 DOI: 10.1063/1.3701286] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nature of the critical behavior in the refractive index n is revisited in the framework of the complete scaling formulation. A comparison is made with the critical behavior of n as derived from the Lorentz-Lorenz equation. Analogue anomalies to those predicted for the dielectric constant ε, namely, a leading |t|(2β) singularity in the coexistence-curve diameter in the two-phase region and a |t|(1-α) along the critical isopleth in the one phase region, are expected in both cases. However, significant differences as regards the amplitudes of both singularities are obtained from the two approaches. Analysis of some literature data along coexistence in the two-phase region and along the critical isopleth in the one-phase region provide evidence of an intrinsic effect, independent of the density, in the critical anomalies of n. This effect is governed by the shift of the critical temperature with an electric field, which is supposed to take smaller values at optical frequencies than at low frequencies in the Hz to MHz range.
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Affiliation(s)
- Patricia Losada-Pérez
- Laboratorium voor Akoestiek en Thermische Fysica, Departement Natuurkunde en Sterrenkunde, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.
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7
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Freyland W. Liquid Metals, Molten Salts, and Ionic Liquids: Some Basic Properties. SPRINGER SERIES IN SOLID-STATE SCIENCES 2011. [DOI: 10.1007/978-3-642-17779-8_2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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8
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Pérez-Sánchez G, Losada-Pérez P, Cerdeiriña CA, Sengers JV, Anisimov MA. Asymmetric criticality in weakly compressible liquid mixtures. J Chem Phys 2010; 132:154502. [PMID: 20423184 DOI: 10.1063/1.3378626] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The thermodynamics of asymmetric liquid-liquid criticality is updated by incorporating pressure effects into the complete-scaling formulation earlier developed for incompressible liquid mixtures [C. A. Cerdeirina et al., Chem. Phys. Lett. 424, 414 (2006); J. T. Wang et al., Phys. Rev. E 77, 031127 (2008)]. Specifically, we show that pressure mixing enters into weakly compressible liquid mixtures as a consequence of the pressure dependence of the critical parameters. The theory is used to analyze experimental coexistence-curve data in the mole fraction-temperature, density-temperature, and partial density-temperature planes for a large number of binary liquid mixtures. It is shown how the asymmetry coefficients in the scaling fields are related to the difference in molecular volumes of the two liquid components. The work resolves the question of the so-called "best order parameter" discussed in the literature during the past decades.
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Affiliation(s)
- G Pérez-Sánchez
- Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain
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Schröer W, Vale VR. Liquid-liquid phase separation in solutions of ionic liquids: phase diagrams, corresponding state analysis and comparison with simulations of the primitive model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:424119. [PMID: 21715854 DOI: 10.1088/0953-8984/21/42/424119] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Phase diagrams of ionic solutions of the ionic liquid C(18)mim(+)NTF(2)(-) (1-n-octadecyl-3-methyl imidazolium bistrifluormethylsulfonylimide) in decalin, cyclohexane and methylcyclohexane are reported and compared with that of solutions of other imidazolium ionic liquids with the anions NTF(2)(-), Cl(-) and BF4(-) in arenes, CCl(4), alcohols and water. The phase diagrams are analysed presuming Ising criticality and taking into account the asymmetry of the phase diagrams. The resulting parameters are compared with simulation results for equal-sized charged hard spheres in a dielectric continuum, the restricted primitive model (RPM) and the primitive model (PM) that allows for ions of different size. In the RPM temperature scale the critical temperatures vary almost linearly with the dielectric permittivity of the solvent. The RPM critical temperatures of the solutions in non-polar solvents are very similar, somewhat below the RPM value. Correlations with the boiling temperatures of the solvents and a dependence on the length of the side chain of the imidazolium cations show that dispersion interactions modify the phase transition, which is mainly determined by Coulomb forces. Critical concentrations, widths of the phase diagrams and the slopes of the diameter are different for the solutions in protic and aprotic solvents. The phase diagrams of the solutions in alcohols and water get a lower critical solution point when represented in RPM variables.
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Saracsan D, Rybarsch C, Schröer W. Phase Separation in Solutions of Room Temperature Ionic Liquids in Hydrocarbons. ACTA ACUST UNITED AC 2009. [DOI: 10.1524/zpch.2006.220.10.1417] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
The room temperature ionic liquids (RTIL) trihexyl-tetradecyl phosphonium chloride (P666 14Cl) and the bromide (P666 14Br) are soluble in hydrocarbons. The investigated solutions in heptane, octane, nonane and decane show liquid–liquid phase separation with an upper critical solution point at ambient temperatures at molar fractions near 0.03 of the salt. Phase diagrams are reported and analysed presuming Ising criticality. The critical temperatures and the critical densities increase with the chain length of the hydrocarbons, where the figures corresponding to the bromides are above that of the chlorides. Scaled by the critical data the phase diagrams show corresponding state behaviour. In accordance with the prediction of the restricted primitive model (RPM), which is a model fluid of equal sized, charged hard spheres in a dielectric continuum, the critical points are located at low temperature and low concentration, when the corresponding state variables of this model are used. However, the critical temperature T
c
* and the critical density ρc
* are well below the figures of the RPM prediction. Comparison is made with the phase diagrams of alcohol solutions of imidazolium ionic liquids and with simulation results of the RPM.
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11
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Abstract
Abstract
Based on the principle of isomorphic critical behavior of fluid mixtures we derive a simple equation for closed solubility loops in a temperature–concentration diagram at constant pressure. The validity of the simple equation is tested by comparisons with experimental solubility data for liquid mixtures at atmospheric pressure and at elevated pressures. We also elucidate the nature of liquid–liquid phase separation in the vicinity of a double critical point. Specifically, we show how from an expansion around the critical double point one can develop a description of solubility loops as a function of pressure.
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12
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The measurements of coexistence curves and light scattering for 2,6-dimethypyridine+H2O in the critical region. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.05.004] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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13
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Liquid–liquid phase transition in the ionic solutions of tetra-n-butylammonium chloride in o-xylene and ethylbenzene: Phase diagrams and corresponding state analysis. J Mol Liq 2009. [DOI: 10.1016/j.molliq.2008.11.015] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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14
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Dittmar HR, Schröer WH. Lower Critical Solution Temperature in the Metastable Region of an Ionic Solution in a Non-Polar Solvent. J Phys Chem B 2009; 113:1249-52. [DOI: 10.1021/jp8103485] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Harro R. Dittmar
- Department of Biology and Chemistry, University of Bremen, D-28359 Bremen, Germany
| | - Wolffram H. Schröer
- Department of Biology and Chemistry, University of Bremen, D-28359 Bremen, Germany
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15
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Pradeep UK. Critical behavior on approaching a special critical point in a complex fluid. J Chem Phys 2008; 129:204903. [PMID: 19045877 DOI: 10.1063/1.3013540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.
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Affiliation(s)
- U K Pradeep
- Department of Physics, Indian Institute of Science, Bangalore, India.
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16
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Hynninen AP, Panagiotopoulos AZ. Simulations of phase transitions and free energies for ionic systems. Mol Phys 2008. [DOI: 10.1080/00268970802112160] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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17
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18
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Gutkowski KI, Bianchi HL, Japas ML. Nonasymptotic Critical Behavior of a Ternary Ionic System. J Phys Chem B 2007; 111:2554-64. [PMID: 17302450 DOI: 10.1021/jp067069z] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Refractive indices n and salt concentrations ms of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10-3 < t = (T - Tc)/Tc < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10-3 < t < 8.07 x 10-2. From these experimental results, compositions fD (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, ms, fD, and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, ms, and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable fD requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.
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Affiliation(s)
- Karin I Gutkowski
- Unidad de Actividad Química, Comisión Nacional de Energía Atómica, Av. del Libertador 8250, 1429 Buenos Aires, Argentina
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19
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Schröer W, Wagner M, Stanga O. Apparent mean-field criticality of liquid–liquid phase transitions in ionic solutions. J Mol Liq 2006. [DOI: 10.1016/j.molliq.2006.03.002] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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20
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Ciach A, Patsahan O. Field-theoretic description of ionic crystallization in the restricted primitive model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021508. [PMID: 17025438 DOI: 10.1103/physreve.74.021508] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2006] [Indexed: 05/12/2023]
Abstract
Effects of charge-density fluctuations on a phase behavior of the restricted primitive model are studied within a field-theoretic formalism. We focus on a lambda line of continuous transitions between charge-ordered and charge-disordered phases that is observed in several mean-field theories, but is absent in simulation results. In our study the RPM is reduced to a phi(6) theory, and a fluctuation contribution to a grand thermodynamic potential is obtained by generalizing the Brazovskii approach. We find that in a presence of fluctuations the lambda -line disappears. Instead, a fluctuation-induced first-order transition to a charge-ordered phase appears in the same region of a phase diagram, where the liquid-ionic-crystal transition is obtained in simulations. Our results indicate that the charge-ordered phase should be identified with an ionic crystal.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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21
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Ciach A. Universality class of the critical point in the restricted primitive model of ionic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066110. [PMID: 16906917 DOI: 10.1103/physreve.73.066110] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2006] [Indexed: 05/11/2023]
Abstract
A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of the individual Feynman diagrams contributing to the number-density correlation functions is cured when all the diagrams are segregated into disjoint sets according to their topological structure. By performing a resummation of all diagrams belonging to each set a regular expression represented by a secondary diagram is obtained. The secondary diagrams are again segregated into disjoint sets, and the series of all the secondary diagrams belonging to a given set is represented by a hyperdiagram. A one-to-one correspondence between the hyperdiagrams contributing to the number-density vertex functions, and diagrams contributing to the order-parameter vertex functions in a certain model system belonging to the Ising universality class is demonstrated. Corrections to scaling associated with irrelevant operators that are present in the model-system Hamiltonian, and other corrections specific to the RPM are also discussed.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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22
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Universality and corresponding state behaviour in the phase diagrams of alcohol solutions of ionic liquids with the BF4− anion. J Mol Liq 2006. [DOI: 10.1016/j.molliq.2005.11.021] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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23
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Kim YC, Fisher ME, Panagiotopoulos AZ. Universality of ionic criticality: size- and charge-asymmetric electrolytes. PHYSICAL REVIEW LETTERS 2005; 95:195703. [PMID: 16383996 DOI: 10.1103/physrevlett.95.195703] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2005] [Indexed: 05/05/2023]
Abstract
Grand-canonical simulations designed to resolve critical universality classes are reported for z:1 hard-core electrolyte models with diameter ratios lambda=a+/a- less than or approximately equal 6. For z=1 Ising-type behavior prevails. Unbiased estimates of Tc(lambda) are within 1% of previous (biased) estimates but the critical densities are approximately 5% lower. Ising character is also established for the 2:1 and 3:1 equisized models, along with critical amplitudes and improved Tc estimates. For z=3, however, strong finite-size effects reduce the confidence level although classical and O (n>or=3) criticality are excluded.
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Affiliation(s)
- Young C Kim
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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24
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Hynninen AP, Dijkstra M, Panagiotopoulos AZ. Critical point of electrolyte mixtures. J Chem Phys 2005; 123:084903. [PMID: 16164326 DOI: 10.1063/1.1979490] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The critical behavior of electrolyte mixtures was studied using grand canonical Monte Carlo simulations. Mixtures consist of large multivalent macroions and small monovalent co- and counterions. The system can be viewed as a binary mixture of macroions (with their counterions) and salt (co- and counterion pair). The primitive model description was used, in which the ions are point charges with a hard core and the solvent is treated as a uniform dielectric continuum. The grand canonical simulations are based on insertions and removals of neutral molecules: macroion with its counterions or coions and a counterion. We propose a distance biasing method that enables direct grand canonical simulations up to charge asymmetry of 10:1. We calculated the critical loci that connect the salt-free state, which consists of only macroions and counterions, with the pure salt state using mixed-field finite-size scaling with no pressure mixing. The critical parameters are determined for macroion to counterion charge asymmetries of 2:1, 3:1, and 10:1. Our results suggest that binary electrolyte mixtures are type-I mixtures, where the two components mix continuously.
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Affiliation(s)
- Antti-Pekka Hynninen
- Soft Condensed Matter Group, Debye Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Abstract
Water is not restricted to moderate temperatures and low pressures, but can exist up to very high temperatures, far above its critical point at 647 K. In this supercritical regime, water can be gradually compressed from gas-like to liquid-like densities. The resulting dense supercritical states have extraordinary properties which can be tuned by temperature and pressure, and form the basis for innovative technologies. This Review covers the current knowledge of the major properties of supercritical water and its solutions with nonpolar, polar, and ionic compounds, and of the underlying molecular processes.
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Affiliation(s)
- Hermann Weingärtner
- Physikalische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany, Fax: (+49) 234-321-4293
| | - Ernst Ulrich Franck
- Institut für Physikalische Chemie, Universität Karlsruhe, 76128 Karlsruhe, Germany
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27
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Ciach A. Effect of charge-density fluctuations on the order-disorder transition in the lattice restricted primitive models of electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046103. [PMID: 15600456 DOI: 10.1103/physreve.70.046103] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2004] [Revised: 06/23/2004] [Indexed: 05/24/2023]
Abstract
Lattice restricted primitive models, where equally charged ions of a diameter sigma are located at sites of a simple cubic lattice with a lattice constant a , are studied within the field-theoretic approach. We focus on the transition between charge-disordered and charge-ordered phases for sigma/a=1 and sigma/a=2 . By using renormalization-group methods we show that at high concentrations of ions the transition is continuous for sigma/a=1 , while for sigma/a=2 it is only first order, as found previously in simulations. For sigma/a=1 the effect of charge-density fluctuations on the positions of the continuous transition and the tricritical point (TCP) is determined within a formalism developed in this work. The temperature and the concentration of ions at the TCP agree very well with simulation results.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
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28
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Caballero JB, Puertas AM, Fernández-Barbero A, de las Nieves FJ. Oppositely charged colloidal binary mixtures: A colloidal analog of the restricted primitive model. J Chem Phys 2004; 121:2428-35. [PMID: 15260798 DOI: 10.1063/1.1767995] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The equilibrium phase diagram of a colloidal system composed of 1:1 mixture of positive and negative particles with equal charge is studied by means of Monte Carlo simulations. The system is the colloidal analog of the restricted primitive model (RPM) for ionic fluids. A liquid-gas transition is found in the low-temperature-low-density region, similar to the liquid-gas transition in the RPM. The fluid-crystal transition is also studied, and the liquid phase is shown to be stable in a narrow range of temperatures. In the liquid, the pair distribution function shows alternating layers of particles with opposite sign of charge surrounding every particle. In the vapor phase, clusters of particles are observed, again in agreement with the RPM. However, a decreasing distribution of clusters is obtained, instead of the discrimination between charged and neutral clusters found in the RPM.
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Affiliation(s)
- José B Caballero
- Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, 04120, Spain
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29
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Ciach A, Stell G. Criticality, tricriticality, and crystallization in discretized models of electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:016114. [PMID: 15324136 DOI: 10.1103/physreve.70.016114] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2004] [Indexed: 05/24/2023]
Abstract
The Restricted Primitive Model of ionic systems is studied within a field-theoretic approach in order to provide a theoretic basis for the qualitative difference in the phase diagrams obtained in simulations for sigma/a=1,sigma/a=2, and sigma/a>/=3 ( a is the lattice constant and sigma is the ion diameter). The evolution of the phase diagrams from the case sigma/a=1 to the case sigma/a=square root[2] [nearest-neighbor ( NN ) occupancy excluded] is studied in the model with NN repulsion, 0</=J</= infinity, supplementing Coulomb forces. The boundary of stability of the charge-disordered phase with respect to short-wavelength charge fluctuations and the tricritical point are found in a mean-field ( MF ) approximation. Next, the effect of fluctuations is studied and we find that for J exceeding a particular value J0 a fluctuation-induced first-order phase transition should be expected instead of the continuous transition found in MF. At J= J0 the line of continuous transitions splits into two lines enclosing the two-phase region, whose thickness increases from zero when J>/= J0 increases. We argue that this transition corresponds to formation of a bcc ionic crystal. For high densities the ions form an fcc crystal, for which we find a fluctuation-induced first-order charge-ordered-charge-disordered transition, in agreement with recent simulation studies. Our results also shed light on the simulation results obtained for an off-lattice ionic system, for which a schematic phase diagram is constructed.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences 01-224 Warszawa, Poland
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30
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Kim YC, Fisher ME. Discretization dependence of criticality in model fluids: a hard-core electrolyte. PHYSICAL REVIEW LETTERS 2004; 92:185703. [PMID: 15169507 DOI: 10.1103/physrevlett.92.185703] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2003] [Indexed: 05/24/2023]
Abstract
Grand-canonical simulations at various levels, zeta=5-20, of fine-lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or restricted primitive model (RPM). With the aid of finite-size scaling analyses, it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of zeta (> or approximately 4), thus the continuum (zeta--> infinity ) RPM exhibits Ising-type (as against classical, self-avoiding walk, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the intrinsically erratic zeta dependence, yielding (T*(c),rho*(c)) approximately equal to (0.0493(3),0.075) for the zeta=infinity RPM.
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Affiliation(s)
- Young C Kim
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
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31
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Wagner M, Stanga O, Schröer W. The liquid–liquid coexistence of binary mixtures of the room temperature ionic liquid 1-methyl-3-hexylimidazolium tetrafluoroborate with alcohols. Phys Chem Chem Phys 2004. [DOI: 10.1039/b404933k] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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32
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Wagner M, Stanga O, Schröer W. Critical viscosity near the liquid–liquid phase transition in the solution of the ionic liquid 1-methyl-3-hexylimidazolium tetrafluoroborate in 1-pentanol. Phys Chem Chem Phys 2004. [DOI: 10.1039/b315616h] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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33
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Cheong DW, Panagiotopoulos AZ. Critical parameters of unrestricted primitive model electrolytes with charge asymmetries up to 10:1. J Chem Phys 2003. [DOI: 10.1063/1.1612473] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Daub CD, Patey GN, Camp PJ. Liquid–vapor criticality in a fluid of charged hard dumbbells. J Chem Phys 2003. [DOI: 10.1063/1.1609192] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Ciach A, Stell G. Effect of space discretization on phase diagrams in ionic systems: a field-theoretic approach. PHYSICAL REVIEW LETTERS 2003; 91:060601. [PMID: 12935060 DOI: 10.1103/physrevlett.91.060601] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2003] [Indexed: 05/24/2023]
Abstract
Using Landau-Ginzburg-Wilson field-theoretic methods we determine for what kind of space discretization the transition between charge-disordered and charge-ordered phases in the restricted primitive model is fluctuation-induced first order. We identify this transition with ionic-crystal formation. We predict four types of generic phase diagrams in ionic systems for various kinds of space discretization for low and intermediate densities of ions. Our results also shed light on the simulation results obtained for an off-lattice ionic system over a wide range of densities, including the fcc crystal.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences 01-224 Warszawa, Poland
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36
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Malik P, Rzoska SJ, Drozd-Rzoska A, Jadżyn J. Critical behavior of dielectric permittivity and electric conductivity in temperature and pressure studies above and below the critical consolute point. J Chem Phys 2003. [DOI: 10.1063/1.1569241] [Citation(s) in RCA: 21] [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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37
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Ciach A, Góźdź WT, Evans R. Effect of a nearby charge-ordered phase on correlation functions in ionic systems. J Chem Phys 2003. [DOI: 10.1063/1.1539046] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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38
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Gutkowski KI, Bianchi HL, Japas ML. Critical behavior of a ternary ionic system: A controversy. J Chem Phys 2003. [DOI: 10.1063/1.1536611] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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39
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Wagner M, Stanga O, Schröer W. Corresponding states analysis of the critical points in binary solutions of room temperature ionic liquids. Phys Chem Chem Phys 2003. [DOI: 10.1039/b305959f] [Citation(s) in RCA: 121] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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40
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Mirzaev SZ, Kaatze U. Critical concentration fluctuations of the ionic binary mixture ethylammonium nitrate-n-octanol: an ultrasonic spectrometry study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:021509. [PMID: 11863532 DOI: 10.1103/physreve.65.021509] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2001] [Indexed: 05/23/2023]
Abstract
Between 200 kHz and 130 MHz, the ultrasonic attenuation spectrum of the ionic ethylammonium nitrate--n-octanol mixture of critical composition has been measured at various reduced temperatures (1.5 x 10(-4)<or= t <or=5.7 x 10(-2)). Using static and dynamic light scattering data as well as viscosity and heat capacity data from the literature, the experimental spectra have been evaluated to yield the scaling function, with the background contribution to the spectra as the only adjustable parameter. Agreement, within the limits of experimental error, of the measured scaling function with that of the nonionic binary system ethanol--dodecane and with the theoretical predictions of the Bhattacharjee-Ferrell dynamic scaling model is found. The amplitude of the fluctuation correlation length xi(o) (=0.47 nm) and the amount of the coupling constant /g/ (=1.3) are rather high as compared to nonionic binary critical mixtures. The amplitude of the relaxation rate of order parameter fluctuations Gamma(o)(=2.6 x 10(8) s(-1)) exhibits an unusual small value, likely to the most part a reflection of the high viscosity and thus small diffusion coefficient of the ionic liquid.
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Affiliation(s)
- S Z Mirzaev
- Heat Physics Department, Uzbekistan Academy of Sciences, Katartal 28, Tashkent, 700135 Uzbekistan
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Oleinikova A, Bonetti M. Electrical conductivity of highly concentrated electrolytes near the critical consolute point: A study of tetra-n-butylammonium picrate in alcohols of moderate dielectric constant. J Chem Phys 2001. [DOI: 10.1063/1.1415458] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Ohtani N, Tsuchimoto D. Phase Behavior of Benzyltributylphosphonium Salts in Aromatic Hydrocarbons or Aqueous Solutions. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2001. [DOI: 10.1246/bcsj.74.1225] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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43
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Schröer W. Generalization of the Kirkwood - Fröhlich theory of dielectric polarization for ionic fluids. J Mol Liq 2001. [DOI: 10.1016/s0167-7322(01)00178-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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44
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Bianchi HL, Japas ML. Phase equilibria of a near-critical ionic system. Critical exponent of the order parameter. J Chem Phys 2001. [DOI: 10.1063/1.1409362] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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46
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Ciach A, Stell G. Why the Ising and continuous-space models of ionic systems exhibit essentially different critical behavior. J Chem Phys 2001. [DOI: 10.1063/1.1329138] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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47
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Romero-Enrique JM, Orkoulas G, Panagiotopoulos AZ, Fisher ME. Coexistence and criticality in size-asymmetric hard-core electrolytes. PHYSICAL REVIEW LETTERS 2000; 85:4558-4561. [PMID: 11082595 DOI: 10.1103/physrevlett.85.4558] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2000] [Indexed: 05/23/2023]
Abstract
Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma(-)/sigma(+) = 1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma(+/-) = 1 / 2(sigma(+)+sigma(-)), relevant for the low densities in question, both T(*)(c) ( = k(B)T(c)sigma(+/-)/q(2)) and rho(*)(c) ( = rho(c)sigma(3)(+/-)) decrease rapidly (from approximately 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with T(*)(c) lower by approximately 0%-11% and rho(*)(c) greater by 37%-12%).
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Affiliation(s)
- JM Romero-Enrique
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2431, USA
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48
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Ohtani N, Hosoda Y. Phase Behavior of Tetrabutylammonium Salt in Aromatic Hydrocarbons or Aqueous Solutions. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2000. [DOI: 10.1246/bcsj.73.2263] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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49
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Heimburg T, Mirzaev SZ, Kaatze U. Heat capacity behavior in the critical region of the ionic binary mixture ethylammonium nitrate-n-octanol. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:4963-4967. [PMID: 11089044 DOI: 10.1103/physreve.62.4963] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2000] [Indexed: 05/23/2023]
Abstract
At temperatures between 30 degrees C and 58 degrees C we have recorded the heat capacity of the ionic ethylammonium nitrate-n-octanol mixture of critical composition and also of the constituents. Different samples of the binary mixture have been measured with its upper critical demixing temperature T(c) varying between 41.04 degrees C and 46.87 degrees C, depending on small traces of water within the liquid under test. Almost identical heat capacity profiles result if the data are displayed as a function of the temperature distance to the actual T(c) value. In the homogeneous phase the critical contribution exhibits power-law behavior with the critical exponent alpha=0.11 as theoretically predicted for nonionic liquids and in conformity with our understanding of the ionic criticality as being asymptotically Ising like. The noncritical background part of the heat capacity can be related to the heat capacities of the constituents using a simple mixture relation. In the two-phase regime a series of almost perfectly reproducible events is found which may be taken to indicate the existence of nonequilibrium intermediate states in the ethylammonium nitrate-n-octanol system.
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Affiliation(s)
- T Heimburg
- Max-Planck-Institut fur Biophysikalische Chemie, Am Fassberg, 37077, Gottingen, Germany
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50
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Orkoulas G, Panagiotopoulos AZ, Fisher ME. Criticality and crossover in accessible regimes. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5930-5939. [PMID: 11031656 DOI: 10.1103/physreve.61.5930] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/1999] [Indexed: 05/23/2023]
Abstract
The near-critical behavior of (d = 3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neighbor interactions is studied through Monte Carlo simulations using histogram reweighting techniques and comparisons with series expansions. By carefully analyzing numerical data from relatively small finite systems using scaling and extrapolation methods, it is demonstrated that one can reliably estimate critical exponents, critical temperatures, and universal amplitude ratios, thereby distinguishing convincingly between different "nearby" universality classes and revealing systematic crossover effects. This study is preparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc.
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Affiliation(s)
- G Orkoulas
- Institute for Physical Science and Technology, University of Maryland, College Park 20742-2431, USA
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