1
|
Aqua JN, Fisher ME. Critical charge and density coupling in ionic spherical models. Phys Rev E 2019; 100:052145. [PMID: 31869903 DOI: 10.1103/physreve.100.052145] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Indexed: 11/07/2022]
Abstract
We investigate ionic criticality on the basis of a specially devised spherical model that accounts both for Coulomb and nonionic forces in binary systems. We show in detail here the consequences of the entanglement of density and charge correlation functions G_{NN} and G_{ZZ} on criticality and screening. We also show on this soluble model how, because of electroneutrality, the long-range Coulomb interactions do not change the universality class of criticality in the model driven primarily by sufficiently attractive nonionic interactions. Near criticality, G_{NN} and G_{ZZ} are fully decoupled in charge symmetric systems. However, in more realistic nonsymmetric models, charge and density fluctuations couple in leading order so that the charge and density correlation lengths diverge asymptotically in a similar way. Similarly, the Stillinger-Lovett sum rule, which characterizes a conducting fluid, is violated at criticality in nonsymmetric models when the critical-point density-decay exponent η vanishes. In addition, if quantum effects are accounted for semiclassically by incorporating algebraically decaying interactions, G_{ZZ} decays only as a power law in the whole phase space, contrary to the usually expected exponential Debye screening. We expect these results on this soluble toy model to be general and to reveal general mechanisms ruling ionic criticality.
Collapse
Affiliation(s)
- Jean-Noël Aqua
- Sorbonne Université, CNRS, Institut des Nanosciences de Paris, INSP, UMR 7588, 4 place Jussieu, 75005 Paris, France
| | - Michael E Fisher
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
2
|
Holovko M, Patsahan T, Patsahan O. Effects of disordered porous media on the vapour-liquid phase equilibrium in ionic fluids: application of the association concept. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.10.045] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
3
|
Patsahan O. Gas-liquid phase coexistence and crossover behavior of binary ionic fluids with screened Coulomb interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062143. [PMID: 25019760 DOI: 10.1103/physreve.89.062143] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Indexed: 06/03/2023]
Abstract
We study the effects of an interaction range on the gas-liquid phase diagram and the crossover behavior of a simple model of ionic fluids: an equimolar binary mixture of equisized hard spheres interacting through screened Coulomb potentials which are repulsive between particles of the same species and attractive between particles of different species. Using the collective variables theory, we find explicit expressions for the relevant coefficients of the effective φ{4} Ginzburg-Landau Hamiltonian in a one-loop approximation. Within the framework of this approximation, we calculate the critical parameters and gas-liquid phase diagrams for varying inverse screening length z. Both the critical temperature scaled by the Yukawa potential contact value and the critical density rapidly decrease with an increase of the interaction range (a decrease of z) and then for z<0.05 they slowly approach the values found for a restricted primitive model (RPM). We find that gas-liquid coexistence region reduces with an increase of z and completely vanishes at z≃2.78. Our results clearly show that an increase in the interaction range leads to a decrease of the crossover temperature. For z≃0.01, the crossover temperature is the same as for the RPM.
Collapse
Affiliation(s)
- O Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Street, 79011 Lviv, Ukraine
| |
Collapse
|
4
|
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]
|
5
|
Bárcenas M, Odriozola G, Orea P. Structure and coexistence properties of shoulder–square well fluids. J Mol Liq 2013. [DOI: 10.1016/j.molliq.2012.10.027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
6
|
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.
Collapse
Affiliation(s)
- O Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine
| |
Collapse
|
7
|
Vale VR, Will S, Schröer W, Rathke B. The General Phase Behavior of Mixtures of 1-Alkyl-3-Methylimidazolium Bis[(trifluoromethyl)sulfonyl]amide Ionic Liquids withn-Alkyl Alcohols. Chemphyschem 2012; 13:1860-7. [DOI: 10.1002/cphc.201100911] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2011] [Indexed: 11/06/2022]
|
8
|
Lockett V, Rukavishnikova IV, Stepanov VP, Tkachev NK. Interfacial tension in immiscible mixtures of alkali halides. Phys Chem Chem Phys 2010; 12:1139-44. [PMID: 20094678 DOI: 10.1039/b917694b] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The interfacial tension of the liquid-phase interface in seven immiscible reciprocal ternary mixtures of lithium fluoride with the following alkali halides: CsCl, KBr, RbBr, CsBr, KI, RbI, and CsI was measured using the cylinder weighing method over a wide temperature range. It was shown that for all mixtures the interfacial tension gradually decreases with growing temperature. The interfacial tension of the reciprocal ternary mixtures at a given temperature increases both with the alkali cation radius (K(+) < Rb(+) < Cs(+)) and with the radius of the halogen anion (Cl(-) < Br(-) < I(-)).
Collapse
Affiliation(s)
- Vera Lockett
- Institute of High-Temperature Electrochemistry, Russian Academy of Sciences, 22, S. Kovalevskaya St., 620219 Ekaterinburg, Russian Federation.
| | | | | | | |
Collapse
|
9
|
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.
Collapse
|
10
|
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]
|
11
|
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
| |
Collapse
|
12
|
|
13
|
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]
|
14
|
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]
|
15
|
Weiss VC, Schröer W. Anomalous corresponding-states surface tension of hydrogen fluoride and of the Onsager model. J Chem Phys 2005; 122:84705. [PMID: 15836075 DOI: 10.1063/1.1849152] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
In a corresponding-states analysis of the liquid-vapor surface tension originally suggested by Guggenheim, we study the behavior of different simple (i.e., nonpolar), polar and ionic fluids. The results are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen bonding, one finds deviations from the master curve at low temperatures and, thus, observes the characteristic sigmoid behavior of the reduced surface tension as a function of temperature. The same is obtained for the model ionic fluid, the restricted primitive model. Truly exceptionally low values of the reduced surface tension are found for hydrogen fluoride and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to obtain the square-gradient term in a modified van der Waals theory. Remarkably, in the corresponding-states plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces.
Collapse
Affiliation(s)
- Volker C Weiss
- School of Engineering and Science, International University Bremen, P.O. Box 750561, 28725 Bremen, Germany.
| | | |
Collapse
|
16
|
Kostko AF, Anisimov MA, Sengers JV. Criticality in aqueous solutions of 3-methylpyridine and sodium bromide. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:026118. [PMID: 15447556 DOI: 10.1103/physreve.70.026118] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2004] [Revised: 05/19/2004] [Indexed: 05/24/2023]
Abstract
We address a controversial issue regarding the nature of critical behavior in ternary electrolyte solutions of water, 3-methylpyridine, and sodium bromide. Earlier light-scattering studies showed an anomalous critical behavior in this system that was attributed to the formation of a microheterogeneous phase associated with ion-molecule clustering [M.A. Anisimov, J. Jacob, A. Kumar, V.A. Agayan, and J. V. Sengers, Phys. Rev. Lett. 85, 2336 (2000)]], while some other investigators subsequently found this system to exhibit ordinary Ising-like critical behavior. This contradiction forced us to revisit the problem and perform an accurate and comprehensive study of light scattering in this system paying attention to the achievement of thermodynamic equilibrium, hysteresis effects, aging, and prehistory of the samples, and a possible role of impurities. We show that properly aged, equilibrium samples of aqueous solutions of 3-methylpyridine with NaBr exhibit universal Ising-like critical behavior, typical for other aqueous solutions. No evidence for an equilibrium microheterogeneous phase was found. We have been able to reproduce anomalous behavior (similar to that reported initially) in a fast run on a freshly prepared sample. We attribute the observed anomalies to mesoscopic nonequilibrium aggregates, possibly associated with supramolecular restructuring in aqueous solutions. To support this conclusion we performed a study of aqueous solutions of 3-methylpyridine without NaBr and have found long-living nonequilibrium states in aqueous solutions of 3-methylpyridine.
Collapse
Affiliation(s)
- A F Kostko
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | | | | |
Collapse
|
17
|
Kudlay A, Ermoshkin AV, de la Cruz MO. Phase diagram of charged dumbbells: a random phase approximation approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:021504. [PMID: 15447493 DOI: 10.1103/physreve.70.021504] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2004] [Indexed: 05/24/2023]
Abstract
The phase diagram of the charged hard dumbbell system (hard spheres of opposite unit charge fixed at contact) is obtained with the use of the random phase approximation (RPA). The effect of the impenetrability of charged spheres on charge-charge fluctuations is described by introduction of a modified electrostatic potential. The correlations of ions in a pair are included via a correlation function in the RPA. The coexistence curve is in good agreement with Monte Carlo simulations. The relevance of the theory to the restricted primitive model is discussed.
Collapse
Affiliation(s)
- Alexander Kudlay
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | | | | |
Collapse
|
18
|
Orea P, Duda Y, Weiss VC, Schröer W, Alejandre J. Liquid–vapor interface of square-well fluids of variable interaction range. J Chem Phys 2004; 120:11754-64. [PMID: 15268210 DOI: 10.1063/1.1740749] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Properties of the liquid-vapor interface of square-well fluids with ranges of interaction lambda=1.5, 2.0, and 3.0 are obtained by Monte Carlo simulations and from square-gradient theories that combine the Carnahan-Starling equation of state for hard spheres with the second and third virial coefficients. The predicted surface tensions show good agreement with the simulation results for lambda=2 and for lambda=3 in a temperature range reasonably close to the critical point, 0.8</=T/T(c)</=0.95. As expected, the surface tension increases with the range of interaction and decreases monotonically with temperature. A comparison between theory and simulation results is also given for the width of the interface and for the coexistence curves for the different interaction ranges.
Collapse
Affiliation(s)
- Pedro Orea
- Ingeniería Molecular, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, 07730 México D.F., México
| | | | | | | | | |
Collapse
|
19
|
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]
|
20
|
Kulinskii VL, Malomuzh NP. Critical behavior of ionic liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:061506. [PMID: 12188731 DOI: 10.1103/physreve.65.061506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2001] [Revised: 04/05/2002] [Indexed: 05/23/2023]
Abstract
The renormalization of the Landau-Ginzburg Hamiltonian for a system with Coulombic interactions caused by spatially inhomogeneous polarizational effects is discussed. It is shown that for ionic liquids with a strong dependence of the degree of dissociation on density, the nonclassical fluctuation region is significantly narrowed. The essential role of the association of ions is noted.
Collapse
Affiliation(s)
- V L Kulinskii
- Department of Theoretical Physics, Odessa National University, 2 Dvoryanskaya Strasse, 270100 Odessa, Ukraine
| | | |
Collapse
|
21
|
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.
Collapse
Affiliation(s)
- S Z Mirzaev
- Heat Physics Department, Uzbekistan Academy of Sciences, Katartal 28, Tashkent, 700135 Uzbekistan
| | | |
Collapse
|
22
|
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]
|
23
|
|
24
|
17 Ionic fluids near critical points and at high temperatures. ACTA ACUST UNITED AC 2000. [DOI: 10.1016/s1874-5644(00)80007-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
25
|
Koulinskii VL, Malomuzh NP, Tolpekin VA. Influence of charge fluctuations on the critical behavior of electrolyte solutions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:6897-905. [PMID: 11970628 DOI: 10.1103/physreve.60.6897] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/1998] [Revised: 06/16/1999] [Indexed: 04/18/2023]
Abstract
The effective Hamiltonian of electrolyte solution near its critical point is constructed. The vapor-liquid critical point is investigated in detail. The strong dependence of the Landau-Ginsburg number on the concentration of electrolyte is demonstrated. It is shown that the charge fluctuations in electrolytes essentially suppress the fluctuation of the order parameter and broaden the region of classical behavior.
Collapse
Affiliation(s)
- V L Koulinskii
- Department of Theoretical Physics, Odessa State University, 2 Petra Velikogo, 270100 Odessa, Ukraine
| | | | | |
Collapse
|
26
|
Kleemeier M, Wiegand S, Schröer W, Weingärtner H. The liquid–liquid phase transition in ionic solutions: Coexistence curves of tetra-n-butylammonium pricrate in alkyl alcohols. J Chem Phys 1999. [DOI: 10.1063/1.477905] [Citation(s) in RCA: 80] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|