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Donley JP. Closure to the PRISM equation derived from nonlinear response theory. J Chem Phys 2024; 161:124902. [PMID: 39319656 DOI: 10.1063/5.0226882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2024] [Accepted: 09/06/2024] [Indexed: 09/26/2024] Open
Abstract
Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N, both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.
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Affiliation(s)
- James P Donley
- Material Science Institute, University of Oregon, Eugene, Oregon 97403, USA
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Freger V. Ion partitioning and permeation in charged low-T* membranes. Adv Colloid Interface Sci 2020; 277:102107. [PMID: 32000110 DOI: 10.1016/j.cis.2020.102107] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Revised: 01/15/2020] [Accepted: 01/16/2020] [Indexed: 11/25/2022]
Abstract
Understanding ion transport in membrane materials is key to engineering and development of desalination and water purification technologies as well as electro-membrane applications. To date, modeling of ion transport has mainly relied on mean-field approaches, originally intended for weak inter-ionic interactions, i.e., high reduced temperature T*. This condition is violated in many membranes, which could explain disagreement between predicted trends and experiments. The paper highlights observed discrepancies and develops a new approach based on the concept of ion association, more adequate in the low-T⁎ limit. The new model addresses ion binding and mobility consistently within the same physical picture, applied to different types of single and mixed salts. The resulting relations show a significantly weaker connection between ion partitioning and permeability than the standard ones. Estimates using primitive model (PM) of ions in a homogeneous dielectric suggest that non-PM mechanisms, originating from the molecular structure of the ion-solvating environment, might enhance ion association in membranes. PM analysis also predicts that ion solvation and association must be rigidly related, yet non-PM effects may decouple these phenomena and allow a crossover to non-trivial regimes consistent with experiments and simulations. Despite the crude nature of the presented approach and some questions remaining open, it appears to explain most available experimental data and presents a step towards predictive modeling of ion-selective membrane separations in water-, environment- and energy-related applications.
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Freger V. Selectivity and polarization in water channel membranes: lessons learned from polymeric membranes and CNTs. Faraday Discuss 2018; 209:371-388. [DOI: 10.1039/c8fd00054a] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
The aspects of ion exclusion and concentration polarization are highlighted as critical for achieving high selectivity in an artificial water channel.
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Affiliation(s)
- Viatcheslav Freger
- Technion – Israel Institute of Technology
- Wolfson Department of Chemical Engineering
- Haifa
- Israel
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Sing CE. Development of the modern theory of polymeric complex coacervation. Adv Colloid Interface Sci 2017; 239:2-16. [PMID: 27161661 DOI: 10.1016/j.cis.2016.04.004] [Citation(s) in RCA: 181] [Impact Index Per Article: 25.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Revised: 04/10/2016] [Accepted: 04/19/2016] [Indexed: 11/15/2022]
Abstract
Oppositely charged polymers can undergo the process of complex coacervation, which refers to a liquid-liquid phase separation driven by electrostatic attraction. These materials have demonstrated considerable promise as the basis for complex, self-assembled materials. In this review, we provide a broad overview of the theoretical tools used to understand the physical properties of polymeric coacervates. In particular, we discuss historic theories (Voorn-Overbeek, Random Phase Approximation), and then describe recent developments in the field (Field Theoretic, Counterion Release, Molecular Simulation, and Polymer Reference Interaction Site Model methods). We provide context for these methods, and map out the patchwork of theoretical models that are used to describe a diverse array of coacervate systems. We use this review of the literature to clarify a number of important theoretical challenges remaining in our physical understanding of complex coacervation.
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Affiliation(s)
- Charles E Sing
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 S. Mathews Ave. Urbana IL, 61801, United States.
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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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Bernard O, Torres-Arenas J, Simonin JP. Multiply associating electrolytes in the binding mean spherical approximation: thermodynamic properties and speciation. J Chem Phys 2014; 140:034502. [PMID: 25669395 DOI: 10.1063/1.4860435] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ionic solutions exhibiting multiple association are described within the binding mean spherical approximation (BiMSA). This model is based on the Wertheim formalism, in the framework of the primitive model at the McMillan-Mayer level. The cation and the anion form the various complexes according to stepwise complexation-equilibria. Analytic expressions for the Helmholtz energy, the internal energy, the speciation, and for the osmotic and activity coefficients are given considering a binary solution with an arbitrary number of association sites on one type of ion (polyion) and one site on the ions of opposite sign (counterions). As an alternative, mean field expressions, as developed in SAFT-type theories, are also presented. The result obtained from the latter approximate method exhibits a reasonable agreement with those from BiMSA for the speciation, and a remarkable one for the osmotic coefficient.
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Affiliation(s)
- O Bernard
- Laboratoire Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques, PECSA (UMR CNRS 7195), Université P. M. Curie, Case 51, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - J Torres-Arenas
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, León, Guanajuato, CP 37150, Mexico
| | - J-P Simonin
- Laboratoire Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques, PECSA (UMR CNRS 7195), Université P. M. Curie, Case 51, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Daub CD, Åstrand PO, Bresme F. Thermo-molecular orientation effects in fluids of dipolar dumbbells. Phys Chem Chem Phys 2014; 16:22097-106. [DOI: 10.1039/c4cp03511a] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Plots of first-order (left) and novel second-order (right) thermomolecular orientation effects in fluids of dipolar dumbbells.
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Affiliation(s)
- Christopher D. Daub
- Department of Chemistry
- Norwegian University of Science and Technology (NTNU)
- Trondheim, Norway
| | - Per-Olof Åstrand
- Department of Chemistry
- Norwegian University of Science and Technology (NTNU)
- Trondheim, Norway
| | - Fernando Bresme
- Department of Chemistry
- Chemical Physics Section
- Imperial College London
- London, UK
- Department of Chemistry
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Das SK, Kim YC, Fisher ME. Near critical electrolytes: Are the charge-charge sum rules obeyed? J Chem Phys 2012; 137:074902. [DOI: 10.1063/1.4743957] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Alejandre J, Bresme F, González-Melchor M. Interfacial properties of charge asymmetric ionic liquids. Mol Phys 2010. [DOI: 10.1080/00268970902780270] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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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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Kim YC, Fisher ME. Charge fluctuations and correlation lengths in finite electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051502. [PMID: 18643069 DOI: 10.1103/physreve.77.051502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2008] [Indexed: 05/26/2023]
Abstract
Fluctuations of the charge Q_{Lambda} inside a subdomain Lambda embedded in an electrolyte contained in a finite cubical box of dimensions LxLxL with periodic boundary conditions are investigated. When Lambda is an LxL "slab" of width W , asymptotically exact expressions for the mean-square fluctuation Q_{Lambda};{2} are obtained in terms of the Lebowitz length xi_{L}(T,rho) and of the "true" or asymptotic screening/decay length xi_{Z,infinity}(T,rho) together, when the charge correlation decay is oscillatory, with the characteristic wavelength lambda_{Z}(T,rho) . In finite systems, the normalized charge fluctuations exhibit threefold scaling behavior in the ratios xi_{Z,infinity}W , Wlambda_{Z} , and WL . This enables one to estimate all the correlation lengths away from criticality quite precisely from finite-size grand canonical Monte Carlo simulations. The results for xi_{Z,infinity},lambda_{Z} , and xi_{L} are presented for the restricted primitive model or hard-sphere 1:1 electrolyte for densities rho less, similar1.3rho_{c} and T greater, similar4T_{c} . The fitted values compare favorably with the expectations of generalized Debye-Hückel theory [Lee and Fisher, Europhys. Lett. 39, 611 (1997)]; specifically, if xi_{D} proportional, variant(Trho);{12} is the Debye length, we find xi_{Z,infinity}<xi_{D}<xi_{L} , although, since ion-pairing is neglected, the charge oscillations set in only for densities approximately 1.9 times larger than predicted.
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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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Ciach A, Góźdź WT, Stell G. Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051505. [PMID: 17677071 DOI: 10.1103/physreve.75.051505] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2006] [Indexed: 05/16/2023]
Abstract
The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa, Poland
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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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