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Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions. Polymers (Basel) 2022; 14:polym14204421. [PMID: 36297998 PMCID: PMC9612006 DOI: 10.3390/polym14204421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Revised: 10/03/2022] [Accepted: 10/04/2022] [Indexed: 11/17/2022] Open
Abstract
The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters.
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Polyelectrolyte Gels: A Unique Class of Soft Materials. Gels 2021; 7:gels7030102. [PMID: 34449600 PMCID: PMC8395725 DOI: 10.3390/gels7030102] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Revised: 07/06/2021] [Accepted: 07/21/2021] [Indexed: 11/17/2022] Open
Abstract
The objective of this article is to introduce the readers to the field of polyelectrolyte gels. These materials are common in living systems and have great importance in many biomedical and industrial applications. In the first part of this paper, we briefly review some characteristic properties of polymer gels with an emphasis on the unique features of this type of soft material. Unsolved problems and possible future research directions are highlighted. In the second part, we focus on the typical behavior of polyelectrolyte gels. Many biological materials (e.g., tissues) are charged (mainly anionic) polyelectrolyte gels. Examples are shown to illustrate the effect of counter-ions on the osmotic swelling behavior and the kinetics of the swelling of model polyelectrolyte gels. These systems exhibit a volume transition as the concentration of higher valence counter-ions is gradually increased in the equilibrium bath. A hierarchy is established in the interaction strength between the cations and charged polymer molecules according to the chemical group to which the ions belong. The swelling kinetics of sodium polyacrylate hydrogels is investigated in NaCl solutions and in solutions containing both NaCl and CaCl2. In the presence of higher valence counter-ions, the swelling/shrinking behavior of these gels is governed by the diffusion of free ions in the swollen network, the ion exchange process and the coexistence of swollen and collapsed states.
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Das S, Lin YH, Vernon RM, Forman-Kay JD, Chan HS. Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins. Proc Natl Acad Sci U S A 2020; 117:28795-28805. [PMID: 33139563 PMCID: PMC7682375 DOI: 10.1073/pnas.2008122117] [Citation(s) in RCA: 131] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.
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Affiliation(s)
- Suman Das
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada
| | - Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada
- Molecular Medicine, Hospital for Sick Children, Toronto, ON M5G 0A4, Canada
| | - Robert M Vernon
- Molecular Medicine, Hospital for Sick Children, Toronto, ON M5G 0A4, Canada
| | - Julie D Forman-Kay
- Molecular Medicine, Hospital for Sick Children, Toronto, ON M5G 0A4, Canada
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada;
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Guzmán E, Fernández-Peña L, Ortega F, Rubio RG. Equilibrium and kinetically trapped aggregates in polyelectrolyte–oppositely charged surfactant mixtures. Curr Opin Colloid Interface Sci 2020. [DOI: 10.1016/j.cocis.2020.04.002] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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6
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Xu X, Shi H, Wang F. Near-Critical Phase Behavior in Polyelectrolyte Solutions: Effect of Charge Fluctuations. J Phys Chem B 2020; 124:4203-4210. [PMID: 32340454 DOI: 10.1021/acs.jpcb.0c01511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
The critical behaviors in polyelectrolyte (PE) solutions are studied by a renormalized Gaussian fluctuation theory. PEs are fully charged linear wormlike chains. The electrostatic interactions are considered in a continuum solvent while ignoring other interactions. The effects of temperature on the criticality are explored in a salt-free polyanion solution, and the effects of salt are explored in a symmetric mixed solution of polycation and polyanion. An unphysical phase coexistence (UPPC), in which a metastable dense phase coexists with an unstable dilute phase, always exists in the phase diagram. In the near-critical region, the UPPC could interfere with the real phase coexistence. The classical critical point is replaced by a "critical line", giving a flat top for the phase diagram. These behaviors are due to the effect of charge fluctuation in the near-critical region. Our results explain why the mean field approach overestimates the critical salt density by about 10% to experimental data in the study of coacervation between oppositely charged PEs.
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Affiliation(s)
- Xiaofei Xu
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Hao Shi
- School of Physical Science and Technology, Soochow University, Suzhou, Jiangsu Province 215006, China
| | - Fuhan Wang
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou, Jiangsu Province 215006, China
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Lin YH, Brady JP, Chan HS, Ghosh K. A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes. J Chem Phys 2020; 152:045102. [PMID: 32007034 PMCID: PMC7043852 DOI: 10.1063/1.5139661] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 12/23/2019] [Indexed: 12/20/2022] Open
Abstract
The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles. LLPS of neutral homopolymers is quite well described by theory, but it has been a challenge to develop general theories for the LLPS of heteropolymers involving charge-charge interactions. Here, we present a theory that combines a random-phase-approximation treatment of polymer density fluctuations and an account of intrachain conformational heterogeneity based on renormalized Kuhn lengths to provide predictions of LLPS properties as a function of pH, salt, and charge patterning along the chain sequence. Advancing beyond more limited analytical approaches, our LLPS theory is applicable to a wide variety of charged sequences ranging from highly charged polyelectrolytes to neutral or nearly neutral polyampholytes. This theory should be useful in high-throughput screening of protein and other sequences for their LLPS propensities and can serve as a basis for more comprehensive theories that incorporate nonelectrostatic interactions. Experimental ramifications of our theory are discussed.
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Affiliation(s)
- Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Jacob P Brady
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Kingshuk Ghosh
- Department of Physics and Astronomy, University of Denver, Colorado, Colorado 80208, USA
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Kwon HK, Ma B, Olvera de la Cruz M. Determining the Regimes of Dielectric Mismatch and Ionic Correlation Effects in Ionomer Blends. Macromolecules 2019. [DOI: 10.1021/acs.macromol.8b02376] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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9
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Das S, Amin AN, Lin YH, Chan HS. Coarse-grained residue-based models of disordered protein condensates: utility and limitations of simple charge pattern parameters. Phys Chem Chem Phys 2018; 20:28558-28574. [PMID: 30397688 DOI: 10.1039/c8cp05095c] [Citation(s) in RCA: 81] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the "blockiness" measure κ and the "sequence charge decoration" (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature Tcr* increases with increasingly negative SCD for a set of sequences showing a positive correlation between κ and -SCD. Relative to RPA, the simulated sequence-dependent variation in Tcr* is often-though not always-smaller, whereas the simulated critical volume fractions are higher. However, for a set of sequences exhibiting an anti-correlation between κ and -SCD, the simulated Tcr*'s are quite insensitive to either parameter. Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space. These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.
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Affiliation(s)
- Suman Das
- Department of Biochemistry, University of Toronto, Medical Sciences Building - 5th Fl., 1 King's College Circle, Toronto, Ontario M5S 1A8, Canada.
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Abstract
There has been significant interest in the tendency of highly charged particles having the same charge to form dynamic clusters in solution, but an accepted theoretical framework that can account for this ubiquitous phenomenon has been slow to develop. The theoretical difficulties are especially great for flexible polyelectrolytes due to the additional complex coupling between the polyelectrolyte chain configurations and the spatial distribution of the ionic species in solution. For highly charged polyelectrolytes, this leads to the formation of a diffuse "polarizable" cloud of counter-ions around these polymers, an effect having significant implications for the function of proteins and other natural occurring polyelectrolytes, as emphasized long ago by Kirkwood and co-workers. To investigate this phenomenon, we perform molecular dynamics simulations of a minimal model of polyelectrolyte solutions that includes an explicit solvent and counter-ions, where the relative affinity of the counter-ions and the polymer for the solvent is tunable through the variation of the relative strength of the dispersion interactions of the polymer and ions. In particular, we find that these dispersion interactions can greatly influence the nature of the association between the polyelectrolyte chains under salt-free conditions. We calculate static and dynamic correlation functions to quantify the equilibrium structure and dynamics of these complex liquids. Based on our coarse-grained model of polyelectrolyte solutions, we identify conditions in which three distinct types of polyelectrolyte association arise. We rationalize these types of polyelectrolyte association based on the impact of the selective solvent affinity on the charge distribution and polymer solvation in these solutions. Our findings demonstrate the essential role of the solvent in the description of the polyelectrolyte solutions, as well as providing a guideline for the development of a more predictive theory of the properties of the thermodynamic and transport properties of these complex fluids.
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Affiliation(s)
- Alexandros Chremos
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
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Andreev M, Prabhu VM, Douglas JF, Tirrell M, de Pablo JJ. Complex Coacervation in Polyelectrolytes from a Coarse-Grained Model. ACS Macro Lett 2018; 51. [PMID: 33299652 DOI: 10.1021/acs.macromol.8b00556] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Complex coacervation refers to the formation of distinct liquid phases that arise when polyelectrolytes are mixed under appropriate polymer and salt concentrations. Molecular-level studies of coacervation have been limited. In this work, a coarse-grained model of the polymers and the corresponding counterions is proposed and used to simulate coacervation as a function of polymer length and overall salt concentration. Several sampling methods are used to determine the phase behavior of the underlying polymers. In particular, the results of simulations in different ensembles are shown to be consistent and to reproduce a number of phenomena observed in experiments, including the disruption of complexation by increasing ionic strength or by decreasing molecular weight. The coacervate concentrations determined from phase behavior calculations are then used to examine the rheology of the corresponding materials. By relying on long dynamic simulations, we are able to generate the dynamic response of the material in the form of dynamic moduli as a function of frequency, which are also found to compare favorably with experimental measurements.
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Affiliation(s)
- Marat Andreev
- Institute of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Vivek M Prabhu
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Jack F Douglas
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Matthew Tirrell
- Institute of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Juan J de Pablo
- Institute of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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12
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Shen K, Wang ZG. Electrostatic correlations and the polyelectrolyte self energy. J Chem Phys 2018; 146:084901. [PMID: 28249457 DOI: 10.1063/1.4975777] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We address the effects of chain connectivity on electrostaticfluctuations in polyelectrolyte solutions using a field-theoretic, renormalizedGaussian fluctuation (RGF) theory. As in simple electrolyte solutions [Z.-G. Wang,Phys. Rev. E 81, 021501 (2010)], the RGF provides a unified theory forelectrostatic fluctuations, accounting for both dielectric and charge correlationeffects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energydepends intimately on the chain conformation, and our theory naturally provides aself-consistent determination of the response of intramolecular chain structure topolyelectrolyte and salt concentrations. The effects of the chain-conformation on theself-energy and thermodynamics are especially pronounced for flexiblepolyelectrolytes at low polymer and salt concentrations, where application of thewrong chain structure can lead to a drastic misestimation of the electrostaticcorrelations. By capturing the expected scaling behavior of chain size from dilute tosemi-dilute regimes, our theory provides improved estimates of the self energy at lowpolymer concentrations and correctly predicts the eventual N-independenceof the critical temperature and concentration of salt-free solutions of flexiblepolyelectrolytes. We show that the self energy can be interpreted in terms of aninfinite-dilution energy μm,0el and a finite concentrationcorrelation correction μcorr which tends to cancel out the formerwith increasing concentration.
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Affiliation(s)
- Kevin Shen
- Division of Chemistry andChemical Engineering, California Institute of TechnologyPasadena, Pasadena, California 91125,USA
| | - Zhen-Gang Wang
- Division of Chemistry andChemical Engineering, California Institute of TechnologyPasadena, Pasadena, California 91125,USA
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Affiliation(s)
- Kevin Shen
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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14
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Das S, Eisen A, Lin YH, Chan HS. A Lattice Model of Charge-Pattern-Dependent Polyampholyte Phase Separation. J Phys Chem B 2018; 122:5418-5431. [DOI: 10.1021/acs.jpcb.7b11723] [Citation(s) in RCA: 66] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Suman Das
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Adam Eisen
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Mathematics & Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Molecular Medicine, Hospital for Sick Children, Toronto, Ontario M5G 0A4, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
- Department of Molecular Genetics, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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15
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Horkay F, Douglas JF. Polymer Gels: Basics, Challenges, and Perspectives. ACS SYMPOSIUM SERIES 2018. [DOI: 10.1021/bk-2018-1296.ch001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Ferenc Horkay
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, United States
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Muthukumar M. 50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions. Macromolecules 2017; 50:9528-9560. [PMID: 29296029 PMCID: PMC5746850 DOI: 10.1021/acs.macromol.7b01929] [Citation(s) in RCA: 265] [Impact Index Per Article: 37.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Revised: 11/27/2017] [Indexed: 12/17/2022]
Abstract
From the beginning of life with the information-containing polymers until the present era of a plethora of water-based materials in health care industry and biotechnology, polyelectrolytes are ubiquitous with a broad range of structural and functional properties. The main attribute of polyelectrolyte solutions is that all molecules are strongly correlated both topologically and electrostatically in their neutralizing background of charged ions in highly polarizable solvent. These strong correlations and the necessary use of numerous variables in experiments on polyelectrolytes have presented immense challenges toward fundamental understanding of the various behaviors of charged polymeric systems. This Perspective presents the author's subjective summary of several conceptual advances and the remaining persistent challenges in the contexts of charge and size of polymers, structures in homogeneous solutions, thermodynamic instability and phase transitions, structural evolution with oppositely charged polymers, dynamics in polyelectrolyte solutions, kinetics of phase separation, mobility of charged macromolecules between compartments, and implications to biological systems.
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Affiliation(s)
- M. Muthukumar
- Department of Polymer Science
and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, United States
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17
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Pryamitsyn VA, Kwon HK, Zwanikken JW, Olvera de la Cruz M. Anomalous Phase Behavior of Ionic Polymer Blends and Ionic Copolymers. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00523] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- Victor A. Pryamitsyn
- Department of Materials
Science and Engineering, Northwestern University, 2220 Campus Drive, Cook 2036, Evanston, Illinois 60208, United States
| | - Ha-Kyung Kwon
- Department of Materials
Science and Engineering, Northwestern University, 2220 Campus Drive, Cook 2036, Evanston, Illinois 60208, United States
| | - Jos W. Zwanikken
- Department
of Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854, United States
| | - Monica Olvera de la Cruz
- Department of Materials
Science and Engineering, Northwestern University, 2220 Campus Drive, Cook 2036, Evanston, Illinois 60208, United States
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18
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Wang L, Wang Z, Jiang R, Yin Y, Li B. Conformation transitions of a single polyelectrolyte chain in a poor solvent: a replica-exchange lattice Monte-Carlo study. SOFT MATTER 2017; 13:2216-2227. [PMID: 28247878 DOI: 10.1039/c6sm02540d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The thermodynamic behaviors of a strongly charged polyelectrolyte chain in a poor solvent are studied using replica-exchange Monte-Carlo simulations on a lattice model, focusing on the effects of finite chain length and the solvent quality on the chain conformation and conformation transitions. The neutralizing counterions and solvent molecules are considered explicitly. The thermodynamic quantities that vary continuously with temperature over a wide range are computed using the multiple histogram reweighting method. Our results suggest that the strength of the short-range hydrophobic interaction, the chain length, and the temperature of the system, characterized by ε, N, and T, respectively, are important parameters that control the conformations of a charged chain. When ε is moderate, the competition between the electrostatic energy and the short-range hydrophobic interaction leads to rich conformations and conformation transitions for a longer chain with a fixed length. Our results have unambiguously demonstrated the stability of the n-pearl-necklace structures, where n has a maximum value and decreases with decreasing temperature. The maximum n value increases with increasing chain length. Our results have also demonstrated the first-order nature of the conformation transitions between the m-pearl and the (m-1)-pearl necklaces. With the increase of ε, the transition temperature increases and the first-order feature becomes more pronounced. It is deduced that at the thermodynamic limit of infinitely long chain length, the conformational transitions between the m-pearl and the (m-1)-pearl necklaces may remain first order when ε > 0 and m = 2 or 3. Pearl-necklace conformations cannot be observed when either ε is too large or N is too small. To observe a pearl-necklace conformation, the T value needs to be carefully chosen for simulations performed at only a single temperature.
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Affiliation(s)
- Lang Wang
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Zheng Wang
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Run Jiang
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Yuhua Yin
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Baohui Li
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
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Lin YH, Song J, Forman-Kay JD, Chan HS. Random-phase-approximation theory for sequence-dependent, biologically functional liquid-liquid phase separation of intrinsically disordered proteins. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.09.090] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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20
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Zhang P, Alsaifi NM, Wu J, Wang ZG. Salting-Out and Salting-In of Polyelectrolyte Solutions: A Liquid-State Theory Study. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b02160] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pengfei Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
- Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
| | - Nayef M. Alsaifi
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
- Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
| | - Jianzhong Wu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
- Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
- Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
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21
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Muthukumar M. Electrostatic Correlations in Polyelectrolyte Solutions. POLYMER SCIENCE SERIES A 2016; 58:852-863. [PMID: 29707042 DOI: 10.1134/s0965545x16060146] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
The major attribute of polyelectrolyte solutions is that all chains are strongly correlated both electrostatically and topologically. Even in very dilute solutions such that the chains are not interpenetrating, the chains are still strongly correlated. These correlations are manifest in the measured scattering intensity when such solutions are subjected to light, X-ray, and neutron radiation. The behavior of scattering intensity from polyelectrolyte solutions is qualitatively different from that of solutions of uncharged polymers. Using the technique introduced by Sir Sam Edwards, and extending the earlier work by the author on the thermodynamics of polyelectrolyte solutions, extrapolation formulas are derived for the scattering intensity from polyelectrolyte solutions. The emergence of the polyelectrolyte peak and its concentration dependence are derived. The derived theory shows that there are five regimes. Published experimental data from many laboratories are also collected into a master figure and a comparison between the present theory and experiments is presented.
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Affiliation(s)
- M Muthukumar
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts, 01003 USA
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22
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Kwon HK, Zwanikken JW, Shull KR, Olvera de la Cruz M. Theoretical Analysis of Multiple Phase Coexistence in Polyelectrolyte Blends. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00901] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Ha-Kyung Kwon
- Department of Materials
Science and Engineering, ‡Department of Chemistry, and §Department of Chemical and Biological
Engineering and Department of Physics, Northwestern University, 2220 Campus
Drive, Evanston, Illinois 60208, United States
| | - Jos W. Zwanikken
- Department of Materials
Science and Engineering, ‡Department of Chemistry, and §Department of Chemical and Biological
Engineering and Department of Physics, Northwestern University, 2220 Campus
Drive, Evanston, Illinois 60208, United States
| | - Kenneth R. Shull
- Department of Materials
Science and Engineering, ‡Department of Chemistry, and §Department of Chemical and Biological
Engineering and Department of Physics, Northwestern University, 2220 Campus
Drive, Evanston, Illinois 60208, United States
| | - Monica Olvera de la Cruz
- Department of Materials
Science and Engineering, ‡Department of Chemistry, and §Department of Chemical and Biological
Engineering and Department of Physics, Northwestern University, 2220 Campus
Drive, Evanston, Illinois 60208, United States
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23
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Budkov YA, Kolesnikov AL, Georgi N, Nogovitsyn EA, Kiselev MG. A new equation of state of a flexible-chain polyelectrolyte solution: Phase equilibria and osmotic pressure in the salt-free case. J Chem Phys 2015; 142:174901. [DOI: 10.1063/1.4919251] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Yu. A. Budkov
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo, Russia
- National Research University Higher School of Economics, Department of Applied Mathematics, Moscow, Russia
| | - A. L. Kolesnikov
- Ivanovo State University, Ivanovo, Russia
- Institut für Nichtklassische Chemie e.V., Universitat Leipzig, Leipzig, Germany
| | - N. Georgi
- Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
| | | | - M. G. Kiselev
- G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo, Russia
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24
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Budkov YA, Kolesnikov AL, Nogovitsyn EA, Kiselev MG. Electrostatic-interaction-induced phase separation in solutions of flexible-chain polyelectrolytes. POLYMER SCIENCE SERIES A 2014. [DOI: 10.1134/s0965545x14050022] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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25
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Chi P, Wang Z, Yin Y, Li B, Shi AC. Finite-length effects on the coil-globule transition of a strongly charged polyelectrolyte chain in a salt-free solvent. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042608. [PMID: 23679444 DOI: 10.1103/physreve.87.042608] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2012] [Revised: 03/27/2013] [Indexed: 06/02/2023]
Abstract
The nature of coil-globule transition and scaling behavior of a strongly charged polyelectrolyte chain in a solution system with explicit neutralizing counterions and solvent molecules are studied using replica-exchange Monte Carlo simulations, focusing on the effects of finite chain length. The results reveal that at the thermodynamic limit of infinitely long chain length, the coil-globule transition may remain first order. Phase transition temperatures at various ion concentrations are obtained by extrapolating the values obtained at finite chain lengths. Furthermore, it is found that the exponent ν of the radius of gyration, <R(g)(2)> ~ N(2ν), can be slightly larger than 1 under some conditions.
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Affiliation(s)
- Peng Chi
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China
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26
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Chi P, Li B, Shi AC. Conformation transitions of a polyelectrolyte chain: a replica-exchange Monte-Carlo study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021804. [PMID: 21929012 DOI: 10.1103/physreve.84.021804] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2011] [Revised: 06/03/2011] [Indexed: 05/31/2023]
Abstract
The thermodynamic behavior of a strongly charged polyelectrolyte chain immersed in a salt-free solution is studied using replica-exchange Monte-Carlo simulations. The results reveal that the chain can assume a variety of conformations, and it undergoes two phase transitions upon cooling. The first transition is identified as a continuous counterion condensation transition while the second one as a first-order coil-globule transition. In the globular state, the counterions and the charged chain segments are densely packed forming a three-dimensional Wigner crystal.
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Affiliation(s)
- Peng Chi
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, 300071 Tianjin, China
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27
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Jesudason CG, Lyubartsev AP, Laaksonen A. Conformational characteristics of single flexible polyelectrolyte chain. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2009; 30:341-350. [PMID: 19946724 DOI: 10.1140/epje/i2009-10532-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2009] [Revised: 07/13/2009] [Accepted: 10/08/2009] [Indexed: 05/28/2023]
Abstract
The behaviour of a flexible anionic chain of 150 univalent and negatively charged beads connected by a harmonic-like potential with each other in the presence of an equal number of positive and free counterions, is studied in molecular dynamics simulations with Langevin thermostat in a wide range of temperatures. Simulations were carried out for several values of the bending parameter, corresponding to fully flexible polyion, moderately and strongly stiff polyion as well as for the case when bend conformation is preferable to the straight one. We have found that in all cases three regimes can be distinguished, which can be characterized as "random coil", observed at high temperatures; "extended conformation" observed at moderate temperatures (of the order of 1 in reduced units), and compact "globular conformation" attained at low temperatures. While the transition between high-temperature random and extended conformations is gradual, the transition from the extended coil to the globular state, taking place at a temperature of about 0.2 in reduced units, is of abrupt character resembling a phase transition.
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Affiliation(s)
- C G Jesudason
- Department of Chemistry, University of Malaya, 50603, Kuala Lumpur, West Malaysia, Malaysia.
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28
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Panagiotopoulos AZ. Charge correlation effects on ionization of weak polyelectrolytes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:424113. [PMID: 21715848 DOI: 10.1088/0953-8984/21/42/424113] [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
Ionization curves of weak polyelectrolytes were obtained as a function of the charge coupling strength from Monte Carlo simulations. In contrast to many earlier studies, the present work treats counterions explicitly, thus allowing the investigation of charge correlation effects at strong couplings. For conditions representing typical weak polyelectrolytes in water near room temperature, ionization is suppressed because of interactions between nearby dissociated groups, as also seen in prior work. A novel finding here is that, for stronger couplings, relevant for non-aqueous environments in the absence of added salt, the opposite behavior is observed-ionization is enhanced relative to the behavior of the isolated groups due to ion-counterion correlation effects. The fraction of dissociated groups as a function of position along the chain also behaves non-monotonically. Dissociation is highest near the ends of the chains for aqueous polyelectrolytes and highest at the chain middle segments for non-aqueous environments. At intermediate coupling strengths, dissociable groups appear to behave in a nearly ideal fashion, even though chain dimensions still show strong expansion effects due to ionization. These findings provide physical insights on the impact of competition between acid/base chemical equilibrium and electrostatic attractions in ionizable systems.
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Affiliation(s)
- A Z Panagiotopoulos
- Department of Chemical Engineering and Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ 08544, USA
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29
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Douglas JF, Dudowicz J, Freed KF. Lattice model of equilibrium polymerization. VII. Understanding the role of "cooperativity" in self-assembly. J Chem Phys 2008; 128:224901. [PMID: 18554047 DOI: 10.1063/1.2909195] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Cooperativity is an emergent many-body phenomenon related to the degree to which elementary entities (particles, molecules, organisms) collectively interact to form larger scale structures. From the standpoint of a formal mean field description of chemical reactions, the cooperativity index m, describing the number of elements involved in this structural self-organization, is the order of the reaction. Thus, m for molecular self-assembly is the number of molecules in the final organized structure, e.g., spherical micelles. Although cooperativity is crucial for regulating the thermodynamics and dynamics of self-assembly, there is a limited understanding of this aspect of self-assembly. We analyze the cooperativity by calculating essential thermodynamic properties of the classical mth order reaction model of self-assembly (FAm model), including universal scaling functions describing the temperature and concentration dependence of the order parameter and average cluster size. The competition between self-assembly and phase separation is also described. We demonstrate that a sequential model of thermally activated equilibrium polymerization can quantitatively be related to the FAm model. Our analysis indicates that the essential requirement for "cooperative" self-assembly is the introduction of constraints (often nonlocal) acting on the individual assembly events to regulate the thermodynamic free energy landscape and, thus, the thermodynamic sharpness of the assembly transition. An effective value of m is defined for general self-assembly transitions, and we find a general tendency for self-assembly to become a true phase transition as m-->infinity. Finally, various quantitative measures of self-assembly cooperativity are discussed in order to identify experimental signatures of cooperativity in self-assembling systems and to provide a reliable metric for the degree of transition cooperativity.
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Affiliation(s)
- Jack F Douglas
- Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
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30
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Affiliation(s)
- Dmytro Antypov
- Department of Materials Science and Metallurgy, Pembroke St., Cambridge CB2 3QZ, U.K
| | - James A. Elliott
- Department of Materials Science and Metallurgy, Pembroke St., Cambridge CB2 3QZ, U.K
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31
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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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32
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Hehmeyer OJ, Arya G, Panagiotopoulos AZ, Szleifer I. Monte Carlo simulation and molecular theory of tethered polyelectrolytes. J Chem Phys 2007; 126:244902. [PMID: 17614585 DOI: 10.1063/1.2747600] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.
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Affiliation(s)
- Owen J Hehmeyer
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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33
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Konieczny M, Likos CN, Löwen H. Soft effective interactions between weakly charged polyelectrolyte chains. J Chem Phys 2006; 121:4913-24. [PMID: 15332927 DOI: 10.1063/1.1781111] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We apply extensive molecular dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from molecular dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.
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Affiliation(s)
- M Konieczny
- üInstitut fr Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany.
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34
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Li Y, Huang Q, Shi T, An L. How does solvent molecular size affect the microscopic structure in polymer solutions? J Chem Phys 2006; 125:44902. [PMID: 16942187 DOI: 10.1063/1.2213610] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Monte Carlo simulation has been used to investigate the effects of linear solvent molecular size on polymer chain conformation in solutions. Increasing the solvent molecular size leads to shrinkage of the polymer chains and increase of the critical overlap concentrations. The root-mean-square radius of gyration of polymer chains (R(g)) is less sensitive to the variation of polymer concentration in solutions of larger solvent molecules. In addition, the dependency of R(g) on polymer concentration under normal solvent conditions and solvent molecular size is in good agreement with scaling laws. When the solvent molecular size approaches the ideal end-to-end distance of the polymer chain, an extra aggregation of polymer chains occurs, and the solvent becomes the so-called medium-sized solvent. When the size of solvent molecules is smaller than the medium size, the polymer chains are swollen or partially swollen. However, when the size of solvent molecules is larger than the medium size, the polymer coils shrink and segregate, enwrapped by the large solvent molecules.
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Affiliation(s)
- Yunqi Li
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China
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35
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Jiang J, Feng J, Liu H, Hu Y. Phase behavior of polyampholytes from charged hard-sphere chain model. J Chem Phys 2006; 124:144908. [PMID: 16626246 DOI: 10.1063/1.2186316] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A molecular thermodynamic theory is developed for polyampholytes from the coarse-grained charged hard-sphere chain model. The phase behavior of polyampholytes with variations in sequence and chain length is satisfactorily predicted by the theory, consistent with simulation results and experimental observations. At a fixed chain length, the phase envelope expands as the sequence of charge distribution becomes less random. With increasing chain length, the phase envelope expands for diblock and random polyampholytes, but shrinks for zwitterionic polyampholytes. The predicted critical temperature, density, and pressure exhibit scaling relations with chain length for all the three (diblock, random, and zwitterionic) polyampholytes.
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Affiliation(s)
- Jianwen Jiang
- Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore.
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36
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Hynninen AP, Dijkstra M. Melting line of charged colloids from primitive model simulations. J Chem Phys 2005; 123:244902. [PMID: 16396568 DOI: 10.1063/1.2138693] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).
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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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37
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Cheong DW, Panagiotopoulos * AZ. Phase behaviour of polyampholyte chains from grand canonical Monte Carlo simulations. Mol Phys 2005. [DOI: 10.1080/00268970500186045] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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38
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39
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Kłos J, Pakula T. Lattice Monte Carlo simulations of a charged polymer chain: Effect of valence and concentration of the added salt. J Chem Phys 2005; 122:134908. [PMID: 15847503 DOI: 10.1063/1.1871936] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The configurational properties of a single polyelectrolyte chain accompanied by counterions and added salt are simulated using the cooperative motion algorithm on the face-centered cubic lattice. In particular, a greater emphasis is put on the effect of valence z(s) and concentration of the added positive (negative) salt ions n(s) on the polymer behavior. This is achieved by inspecting two families of systems with widely varying numbers n(s) of monovalent (z(s)=1) or multivalent (z(s)=4) salt ions at two fixed reduced temperatures T*=0.5, 1. The calculations indicate that especially at the lower temperature the addition of some amount of multivalent salt has a tremendous impact on chain conformations compared to the situation with monovalent salt. Even for relatively low concentrations of the former, the mean radius of gyration <s2>(1/2) and the mean end-to-end distance <R2>(1/2) decrease sharply, i.e., the polymer exists in strongly collapsed forms. This reduction of polymer size is also accompanied by a drop in the system inner energy e* and the effective mean charge per monomer q*. The analysis of various pair-correlation functions g(ab)(r) indicates that the latter effect-caused by condensation of ions onto the chain-is dominated by the multivalent ones. Furthermore, it is found that for z(s)=4, the uncondensed salt ions tend to group themselves into small clusters.
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Affiliation(s)
- J Kłos
- Max-Planck-Institute for Polymer Research, Postfach 3148, 55021 Mainz, Germany
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40
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Chang R, Yethiraj A. Osmotic Pressure of Salt-Free Polyelectrolyte Solutions: A Monte Carlo Simulation Study. Macromolecules 2004. [DOI: 10.1021/ma0486952] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Rakwoo Chang
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
| | - Arun Yethiraj
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
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41
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Klos J, Pakula T. Lattice Monte Carlo simulations of three-dimensional charged polymer chains. J Chem Phys 2004; 120:2496-501. [PMID: 15268392 DOI: 10.1063/1.1637872] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The configurational properties of strongly charged polyelectrolytes accompanied by neutralizing counterions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The full Coulomb potential and the excluded volume condition between different ions/beads are taken into account and the reduced temperature T* is considered the main, variable parameter. The calculations that have been carried out for solutions of both single and several chains indicate a few regions of their behavior: (1) for T*--> infinity, it corresponds to that of neutral, self-avoiding polymers under good solvent conditions; (2) for T* approximately 1, due to the electrostatic interactions being effectively stronger, the chains are more outstretched compared to their size at other temperatures; (3) for T* well below one, the counterion condensation becomes more and more dominant, which gradually leads to strongly collapsed chains; and (4) at the lowest temperatures the chains and counterions assume low-energy configurations in the form of neutral, compact aggregates.
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Affiliation(s)
- J Klos
- Max-Planck-Institute for Polymer Research, Postfach 3148, 55021 Mainz, Germany.
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42
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Kudlay A, Olvera de la Cruz M. Precipitation of oppositely charged polyelectrolytes in salt solutions. J Chem Phys 2004; 120:404-12. [PMID: 15267302 DOI: 10.1063/1.1629271] [Citation(s) in RCA: 103] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study phase separation in symmetric solutions of weakly charged flexible chains of opposite sign. Precipitation is caused by effective attractions due to charge fluctuations and by short-range attractions between monomers. The contribution from charge fluctuations is computed within the random phase approximation (RPA), which takes into account the connectivity of charges in the polyions. The impenetrability of the ions is accounted for by using a modified Coulomb potential in the RPA. In good solvent conditions the precipitate monotonically swells and eventually dissolves upon addition of salt. However, near the theta-solvent condition, but still in the good solvent, the precipitate can be stable at any salt concentration. Moreover, the density of the precipitate after initial decrease can increase with addition of salt. This effect is a result of redistribution of salt between the precipitate and the supernatant, which is due to an interplay of electrostatic and hardcore interactions. For not too weakly charged polyions the precipitate properties become strongly dependent on temperature even in good solvent conditions.
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Affiliation(s)
- Alexander Kudlay
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
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43
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Ermoshkin AV, Olvera de la Cruz M. A Modified Random Phase Approximation of Polyelectrolyte Solutions. Macromolecules 2003. [DOI: 10.1021/ma034148p] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- A. V. Ermoshkin
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108
| | - M. Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108
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