1
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Pineda S, Staňo R, Murmiliuk A, Blanco PM, Montes P, Tošner Z, Groborz O, Pánek J, Hrubý M, Štěpánek M, Košovan P. Charge Regulation Triggers Condensation of Short Oligopeptides to Polyelectrolytes. JACS AU 2024; 4:1775-1785. [PMID: 38818083 PMCID: PMC11134362 DOI: 10.1021/jacsau.3c00668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 02/24/2024] [Accepted: 02/26/2024] [Indexed: 06/01/2024]
Abstract
Electrostatic interactions between charged macromolecules are ubiquitous in biological systems, and they are important also in materials design. Attraction between oppositely charged molecules is often interpreted as if the molecules had a fixed charge, which is not affected by their interaction. Less commonly, charge regulation is invoked to interpret such interactions, i.e., a change of the charge state in response to a change of the local environment. Although some theoretical and simulation studies suggest that charge regulation plays an important role in intermolecular interactions, experimental evidence supporting such a view is very scarce. In the current study, we used a model system, composed of a long polyanion interacting with cationic oligolysines, containing up to 8 lysine residues. We showed using both simulations and experiments that while these lysines are only weakly charged in the absence of the polyanion, they charge up and condense on the polycations if the pH is close to the pKa of the lysine side chains. We show that the lysines coexist in two distinct populations within the same solution: (1) practically nonionized and free in solution; (2) highly ionized and condensed on the polyanion. Using this model system, we demonstrate under what conditions charge regulation plays a significant role in the interactions of oppositely charged macromolecules and generalize our findings beyond the specific system used here.
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Affiliation(s)
- Sebastian
P. Pineda
- Department
of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, Prague 2 128 40, Czech Republic
| | - Roman Staňo
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, Vienna 1090, Austria
- Vienna
Doctoral School in Physics, University of
Vienna, Boltzmanngasse 5, Vienna 1090, Austria
| | - Anastasiia Murmiliuk
- Jülich
Centre for Neutron Science JCNS at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich GmbH, Lichtenbergstraße 1, Garching 85748, Germany
| | - Pablo M. Blanco
- Department
of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, Prague 2 128 40, Czech Republic
- Department
of Material Science and Physical Chemistry, Research Institute of
Theoretical and Computational Chemistry (IQTCUB), University of Barcelona, C/Martí i Franquès 1, Barcelona 08028, Spain
- Department of Physics, NTNU - Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Patricia Montes
- Department
of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, Prague 2 128 40, Czech Republic
| | - Zdeněk Tošner
- Department
of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, Prague 2 128 40, Czech Republic
| | - Ondřej Groborz
- Institute
of Macromolecular Chemistry AS CR, Heyrovský square 2, 162 06 Prague 6, Czech Republic
| | - Jiří Pánek
- Institute
of Macromolecular Chemistry AS CR, Heyrovský square 2, 162 06 Prague 6, Czech Republic
| | - Martin Hrubý
- Institute
of Macromolecular Chemistry AS CR, Heyrovský square 2, 162 06 Prague 6, Czech Republic
| | - Miroslav Štěpánek
- Department
of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, Prague 2 128 40, Czech Republic
| | - Peter Košovan
- Department
of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, Prague 2 128 40, Czech Republic
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2
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Staňo R, Smrek J, Likos CN. Cluster Formation in Solutions of Polyelectrolyte Rings. ACS NANO 2023; 17:21369-21382. [PMID: 37729077 PMCID: PMC10655244 DOI: 10.1021/acsnano.3c06083] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Accepted: 09/13/2023] [Indexed: 09/22/2023]
Abstract
We use molecular dynamics simulations to explore concentrated solutions of semiflexible polyelectrolyte ring polymers, akin to the DNA mini-circles, with counterions of different valences. We find that the assembly of rings into nanoscopic cylindrical stacks is a generic feature of the systems, but the morphology and dynamics of such a cluster can be steered by the counterion conditions. In general, a small addition of trivalent ions can stabilize the emergence of clusters due to the counterion condensation, which mitigates the repulsion between the like-charged rings. Stoichiometric addition of trivalent ions can even lead to phase separation of the polyelectrolyte ring phase due to the ion-bridging effects promoting otherwise entropically driven clustering. On the other hand, monovalent counterions cause the formation of stacks to be re-entrant with density. The clusters are stable within a certain window of concentration, while above the window the polyelectrolytes undergo an osmotic collapse, disfavoring ordering. The cluster phase exhibits characteristic cluster glass dynamics with arrest of collective degrees of freedom but not the self-ones. On the other hand, the collapsed phase shows arrest on both the collective and single level, suggesting an incipient glass-to-glass transition, from a cluster glass of ring clusters to a simple glass of rings.
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Affiliation(s)
- Roman Staňo
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Vienna
Doctoral School in Physics, University of
Vienna, Boltzmanngasse
5, 1090 Vienna, Austria
| | - Jan Smrek
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christos N. Likos
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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3
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Beyer D, Košovan P, Holm C. Simulations Explain the Swelling Behavior of Hydrogels with Alternating Neutral and Weakly Acidic Blocks. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Affiliation(s)
- David Beyer
- Institute for Computational Physics, University of Stuttgart, D-70569Stuttgart, Germany
| | - Peter Košovan
- Department of Physical and Macromolecular Chemistry, Charles University, 116 36Prague, Czechia
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, D-70569Stuttgart, Germany
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4
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Yang X, Scacchi A, Vahid H, Sammalkorpi M, Ala-Nissila T. Interaction between two polyelectrolytes in monovalent aqueous salt solutions. Phys Chem Chem Phys 2022; 24:21112-21121. [PMID: 36018307 DOI: 10.1039/d2cp02066a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We use the recently developed soft-potential-enhanced Poisson-Boltzmann (SPB) theory to study the interaction between two parallel polyelectrolytes (PEs) in monovalent ionic solutions in the weak-coupling regime. The SPB theory is fitted to ion distributions from coarse-grained molecular dynamics (MD) simulations and benchmarked against all-atom MD modelling for poly(diallyldimethylammonium) (PDADMA). We show that the SPB theory is able to accurately capture the interactions between two PEs at distances beyond the PE radius. For PDADMA positional correlations between the charged groups lead to locally asymmetric PE charge and ion distributions. This gives rise to small deviations from the SPB prediction that appear as short-range oscillations in the potential of mean force. Our results suggest that the SPB theory can be an efficient way to model interactions in chemically specific complex PE systems.
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Affiliation(s)
- Xiang Yang
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland.
| | - Alberto Scacchi
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland. .,Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Hossein Vahid
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland. .,Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Maria Sammalkorpi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Department of Bioproducts and Biosystems, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Tapio Ala-Nissila
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland. .,QTF Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland.,Interdisciplinary Center for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
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5
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Bertolotto JA, Umazano JP. Counterion condensation theory for finite polyelectrolyte and salt concentrations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:354003. [PMID: 35705074 DOI: 10.1088/1361-648x/ac792e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Accepted: 06/15/2022] [Indexed: 06/15/2023]
Abstract
In the present work we analyze the physical fundamentals of Manning's counterion condensation using his charged line model in a simple salt solution. We extend the theory for the cases of finite saline concentration and polymeric concentration tending to zero and the case of both finite concentrations. To find the equilibrium between the phases of free and condensed counterions, besides minimizing the free energy, we deduce an auxiliary equation to determine the two characteristic parameters of the theory, the fraction of condensed counterions and the volume of condensation. We compare the obtained results in the present work for only one infinite charged line with the ones of counterion condensation theory by Schurr and Fujimoto. We find that the linear density of critical charge depends on the concentration of added salt and takes values higher than one, instead of the unitary value predicted by Manning. We obtain the equations by the activity and osmotic coefficients in function of the critical charge density. We compare them with the corresponding equations by Manning for these parameters. We extend the counterion condensation theory to solutions of linear polyelectrolytes for finite saline and polymeric concentrations using a cell model. We modify the electrostatic contribution to the Gibbs energy adding, to the traditional one calculated by Manning, the energy excess due to the macroion present in a cylindrical cell. We apply the theory to obtain the osmotic coefficient and we compare our results with experimental data of DNA osmotic coefficient and with theoretical adjustment using the Poisson-Boltzmann equation.
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Affiliation(s)
- J A Bertolotto
- Department of Physics, Faculty of Natural Sciences, National University of La Pampa, Santa Rosa, La Pampa, Argentina
| | - J P Umazano
- Department of Physics, Faculty of Natural Sciences, National University of La Pampa, Santa Rosa, La Pampa, Argentina
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6
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Vahid H, Scacchi A, Yang X, Ala-Nissila T, Sammalkorpi M. Modified Poisson–Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions. J Chem Phys 2022; 156:214906. [DOI: 10.1063/5.0092273] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a soft-potential-enhanced Poisson–Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulation with the explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1M and ion sizes ranging from small ions, such as Na+ or Cl−, to softer and larger ions with a size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.
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Affiliation(s)
- Hossein Vahid
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Alberto Scacchi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Xiang Yang
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
- Quantum Technology Finland Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Tapio Ala-Nissila
- Quantum Technology Finland Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
| | - Maria Sammalkorpi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Bioproducts and Biosystems, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
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7
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Radhakrishnan K, Singh SP. Explicit characterization of counterion dynamics around a flexible polyelectrolyte. Phys Rev E 2022; 105:044501. [PMID: 35590562 DOI: 10.1103/physreve.105.044501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 03/04/2022] [Indexed: 06/15/2023]
Abstract
The article presents a comprehensive study of counterion dynamics around a generic linear polyelectrolyte chain with the help of coarse-grained computer simulations. The ion-chain coupling is discussed in the form of binding time, mean-square displacement (MSD) relative to the chain, local ion transport coefficient, and spatiotemporal correlations in the effective charge. We have shown that a counterion exhibits subdiffusive behavior 〈δR^{2}〉∼t^{δ}, δ≈0.9 w.r.t. chain's center of mass. The MSD of ions perpendicularly outward from the chain segment exhibits a smaller subdiffusive exponent compared to the one along the chain backbone. The effective diffusivity of ion is the lowest in chain's close proximity, extending up to the length-scale of radius of gyration R_{g}. Beyond R_{g} at larger distances, they attain diffusivity of free ion with a smooth cross-over from the adsorbed regime to the free ion regime. We have shown that the effective diffusivity drastically decreases for the multivalent ions, while the crossover length scale remains the same. Conversely, with increasing salt concentration the coupling-length scale reduces, while the diffusivity remains unaltered. The effective diffusivity of adsorbed-ion reveals an exponential reduction with electrostatic interaction strength. We further corroborate this from the binding time of ions on the chain, which also grows exponentially with the coupling strength of the ion-polymer duo. Moreover, the binding time of ions exhibits a weak dependence with salt concentration for the monovalent salt, while for multivalent salts the binding time decreases dramatically with concentration. Our work also elucidates fluctuations in the effective charge per site, where it exhibits strong negative correlations at short length-scales.
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Affiliation(s)
- Keerthi Radhakrishnan
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
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8
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Wang L, Wang S, Tong C. The collapse of polyelectrolyte brushes made of 4-arm stars mediated by trivalent salt counterions. MOLECULAR SIMULATION 2021. [DOI: 10.1080/08927022.2021.1932875] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Lijuan Wang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, People’s Republic of China
| | - Shaoyun Wang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, People’s Republic of China
| | - Chaohui Tong
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, People’s Republic of China
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9
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Fazli Z, Naji A. Active particles with polar alignment in ring-shaped confinement. Phys Rev E 2021; 103:022601. [PMID: 33736018 DOI: 10.1103/physreve.103.022601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 01/13/2021] [Indexed: 12/17/2022]
Abstract
We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.
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Affiliation(s)
- Zahra Fazli
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.,School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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10
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Landsgesell J, Holm C. Cell Model Approaches for Predicting the Swelling and Mechanical Properties of Polyelectrolyte Gels. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01216] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jonas Landsgesell
- Institute for Computational Physics, University of Stuttgart, D-70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, D-70569 Stuttgart, Germany
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11
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Wan L, Tong NH. Poisson-Boltzmann equation with a random field for charged fluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:375101. [PMID: 31174199 DOI: 10.1088/1361-648x/ab27da] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The classical Poisson-Boltzmann equation (CPBE), which is a mean field theory by averaging the ion fluctuation, has been widely used to study ion distributions in charged fluids. In this study, we derive a modified Poisson-Boltzmann equation with a random field from the field theory and recover the ion fluctuation through a multiplicative noise added in the CPBE. The Poisson-Boltzmann equation with a random field (RFPBE) captures the effect of the ion fluctuation and gives different ion distributions in the charged fluids compared to the CPBE. To solve the RFPBE, we propose a Monte Carlo method based on the path integral representation. Numerical results show that the effect of the ion fluctuation strengthens the ion diffusion into the domain and intends to distribute the ions in the fluid uniformly. The final ion distribution in the fluid is determined by the competition between the ion fluctuation and the electrostatic forces exerted by the boundaries. The RFPBE is general and feasible for high dimensional systems by taking the advantage of the Monte Carlo method. We use the RFPBE to study a two dimensional system as an example, in which the effect of ion fluctuation is clearly captured.
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Affiliation(s)
- Li Wan
- Department of Physics, Wenzhou University, Wenzhou 325035, People's Republic of China
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12
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Naji A, Hejazi K, Mahgerefteh E, Podgornik R. Charged nanorods at heterogeneously charged surfaces. J Chem Phys 2018; 149:134702. [PMID: 30292214 DOI: 10.1063/1.5044391] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the spatial and orientational distribution of charged nanorods (rodlike counterions) as well as the effective interaction mediated by them between two plane-parallel surfaces that carry fixed (quenched) heterogeneous charge distributions. The nanorods are assumed to have an internal charge distribution, specified by a multivalent monopolar moment and a finite quadrupolar moment, and the quenched surface charge is assumed to be randomly distributed with equal mean and variance on the two surfaces. While equally charged surfaces are known to repel within the traditional mean-field theories, the presence of multivalent counterions has been shown to cause attractive interactions between uniformly charged surfaces due to the prevalence of strong electrostatic couplings that grow rapidly with the counterion valency. We show that the combined effects due to electrostatic correlations (caused by the coupling between the mean surface field and the multivalent, monopolar, charge valency of counterions) as well as the disorder-induced interactions (caused by the coupling between the surface disorder field and the quadrupolar moment of counterions) lead to much stronger attractive interactions between two randomly charged surfaces. The interaction profile turns out to be a nonmonotonic function of the intersurface separation, displaying an attractive minimum at relatively small separations, where the ensuing attraction can exceed the maximum strong-coupling attraction (produced by multivalent monopolar counterions between uniformly charged surfaces) by more than an order of magnitude.
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Affiliation(s)
- Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Kasra Hejazi
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Elnaz Mahgerefteh
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Rudolf Podgornik
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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13
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Cha M, Ro S, Kim YW. Rodlike Counterions near Charged Cylinders: Counterion Condensation and Intercylinder Interaction. PHYSICAL REVIEW LETTERS 2018; 121:058001. [PMID: 30118289 DOI: 10.1103/physrevlett.121.058001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2018] [Revised: 03/15/2018] [Indexed: 06/08/2023]
Abstract
We study a system composed of like-charged cylinders and dumbbell-like counterions, with the focus laid on the role of the internal structure of counterions, using Monte Carlo simulations. The dumbbell ions are found to exhibit novel counterion condensation behavior governed by their length. Effective electrostatic interactions mediated between charged parallel cylinders also turn out significantly different from the case of pointlike ions, as a result of the complex interplay between the spatially separated charge distribution in the dumbbell counterions, their orientation, and the curvature of the charged cylinder. We show that at a weak-to-moderate electrostatic coupling strength, where effective like-charge interactions are usually found to be repulsive, the intercylinder interaction can become attractive and display a distinctive sensitivity to the cylinder curvature and dumbbell size, proving the significant effect of ion structure.
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Affiliation(s)
- Minryeong Cha
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea
| | - Sunghan Ro
- Department of Physics, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea
| | - Yong Woon Kim
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea
- Department of Physics, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea
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14
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Narayanan Krishnamoorthy A, Holm C, Smiatek J. Specific ion effects for polyelectrolytes in aqueous and non-aqueous media: the importance of the ion solvation behavior. SOFT MATTER 2018; 14:6243-6255. [PMID: 30009285 DOI: 10.1039/c8sm00600h] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We present the results of atomistic molecular dynamics simulations with regard to specific ion effects in water, methanol and N,N-dimethylacetamide (DMAc). As a reference system, we introduce rigid and rod-like models of polyanions and polycations in combination with alkali metal cations and halide anions as counterions. Pronounced specific ion effects can be observed in terms of the individual anion and cation condensation behavior. The outcomes of our simulations thus reveal significant deviations from standard electrostatic mean-field theories. A detailed investigation of the individual energy contributions shows that ion-dipole interactions play a pivotal role in rationalizing the findings. The corresponding deviations in terms of the cation and anion distribution can be brought into agreement with the donor and acceptor numbers of the solvents, which thus highlights the importance of solvent-ion interactions in addition to electrostatic attraction.
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15
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Batys P, Luukkonen S, Sammalkorpi M. Ability of the Poisson-Boltzmann equation to capture molecular dynamics predicted ion distribution around polyelectrolytes. Phys Chem Chem Phys 2018; 19:24583-24593. [PMID: 28853454 DOI: 10.1039/c7cp02547e] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Here, we examine polyelectrolyte (PE) and ion chemistry specificity in ion condensation via all-atom molecular dynamics (MD) simulations and assess the ability of the Poisson-Boltzmann (PB) equation to describe the ion distribution predicted by the MD simulations. The PB model enables the extraction of parameters characterizing ion condensation. We find that the modified PB equation which contains the effective PE radius and the energy of the ion-specific interaction as empirical fitting parameters describes ion distribution accurately at large distances but close to the PE, especially when strongly localized charge or specific ion binding sites are present, the mean field description of PB fails. However, the PB model captures the MD predicted ion condensation in terms of the Manning radius and fraction of condensed counterions for all the examined PEs and ion species. We show that the condensed ion layer thickness in our MD simulations collapses on a single master curve for all the examined simple, monovalent ions (Na+, Br+, Cs+, Cl-, and Br-) and PEs when plotted against the Manning parameter (and consequently the PE line charge density). The significance of this finding is that, contrary to the Manning radius extracted from the mean field PB model, the condensed layer thickness in the all atom detail MD modelling does not depend on the PE chemistry or counterion type. Furthermore, the fraction of condensed counterions in the MD simulations exceeds the PB theory prediction. The findings contribute toward understanding and modelling ion distribution around PEs and other charged macromolecules in aqueous solutions, such as DNA, functionalized nanotubes, and viruses.
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Affiliation(s)
- Piotr Batys
- Department of Chemistry and Materials Science, School of Chemical Engineering, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.
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16
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Nová L, Uhlík F, Košovan P. Local pH and effective pK A of weak polyelectrolytes - insights from computer simulations. Phys Chem Chem Phys 2018; 19:14376-14387. [PMID: 28277570 DOI: 10.1039/c7cp00265c] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
In this work we study the titration behavior of weak polyelectrolytes by computer simulations. We analyze the local pH near the chains at various conditions and provide molecular-level insight which complements the recent experimental determination of this quantity. Next, we analyze the non-ideal titration behaviour of weak polyelectrolytes in solution, calculate the effective ionization constant and compare the simulation results with theoretical predictions. In contrast with the universal behaviour with respect to chain length, we find non-universality and deviations from theory with respect to polymer concentration and permittivity of the solvent. The latter we explain in terms of counterion condensation and ion correlation effects, which lead to reversal of the non-ideal titration behaviour at very low permittivities. We discuss the impact of these findings on the interpretation of experimental results.
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Affiliation(s)
- Lucie Nová
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, 128 00 Praha 2, Czech Republic.
| | - Filip Uhlík
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, 128 00 Praha 2, Czech Republic.
| | - Peter Košovan
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 8, 128 00 Praha 2, Czech Republic.
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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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18
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Cha M, Yi J, Kim YW. Hidden Criticality of Counterion Condensation Near a Charged Cylinder. Sci Rep 2017; 7:10551. [PMID: 28874675 PMCID: PMC5585397 DOI: 10.1038/s41598-017-09974-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2017] [Accepted: 08/02/2017] [Indexed: 11/29/2022] Open
Abstract
Counterion condensation onto a charged cylinder, known as the Manning transition, has received a great deal of attention since it is essential to understand the properties of polyelectrolytes in ionic solutions. However, the current understanding is still far from complete and poses a puzzling question: While the strong-coupling theory valid at large ionic correlations suggests a discontinuous nature of the counterion condensation, the mean-field theory always predicts a continuous transition at the same critical point. This naturally leads to a question how one can reconcile the mean-field theory with the strong-coupling prediction. Here, we study the counterion condensation transition on a charged cylinder via Monte Carlo simulations. Varying the cylinder radius systematically in relation to the system size, we find that in addition to the Manning transition, there exists a novel transition where all counterions are bound to the cylinder and the heat capacity shows a drop at a finite Manning parameter. A finite-size scaling analysis is carried out to confirm the criticality of the complete condensation transition, yielding the same critical exponents with the Manning transition. We show that the existence of the complete condensation is essential to explain how the condensation nature alters from continuous to discontinuous transition.
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Affiliation(s)
- Minryeong Cha
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Juyeon Yi
- Department of Physics, Pusan National University, Busan 46241, Korea
| | - Yong Woon Kim
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea.
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19
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Cha M, Yi J, Kim YW. Scaling and criticality of the Manning transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:70. [PMID: 28770365 DOI: 10.1140/epje/i2017-11559-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2017] [Accepted: 07/20/2017] [Indexed: 06/07/2023]
Abstract
We consider a system consisting of a charged cylinder in the presence of neutralizing counterions. This system is well known to exhibit the Manning transition of counterion condensation onto the charged cylinder. We study the criticality and the scaling properties of the Manning transition, analyzing involved thermodynamic quantities such as condensed fraction, its fluctuation, and heat capacity. Through the Monte Carlo simulations and finite-size scaling analysis, we find that near the transition point the examined quantities exhibit scale-invariant behaviors with specific exponents, which provides an evidence that the Manning transition is a critical phenomenon having a scale-invariant property, analogous to bulk phase transitions. Furthermore, we numerically confirm that such scaling properties are not affected by the coupling strength.
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Affiliation(s)
- Minryeong Cha
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, 34141, Deajeon, Korea
| | - Juyeon Yi
- Department of Physics, Pusan National University, 46241, Busan, Korea
| | - Yong Woon Kim
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, 34141, Deajeon, Korea.
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20
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Xu X, Kanduč M, Wu J, Dzubiella J. Potential of mean force and transient states in polyelectrolyte pair complexation. J Chem Phys 2017; 145:034901. [PMID: 27448900 DOI: 10.1063/1.4958675] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
The pair association between two polyelectrolytes (PEs) of the same size but opposite charge is systematically studied in terms of the potential of mean force (PMF) along their center-of-mass reaction coordinate via coarse-grained, implicit-solvent, explicit-salt computer simulations. The focus is set on the onset and the intermediate transient stages of complexation. At conditions above the counterion-condensation threshold, the PE association process exhibits a distinct sliding-rod-like behavior where the polymer chains approach each other by first stretching out at a critical distance close to their contour length, then "shaking hand" and sliding along each other in a parallel fashion, before eventually folding into a neutral complex. The essential part of the PMF for highly charged PEs can be very well described by a simple theory based on sliding charged "Debye-Hückel" rods with renormalized charges in addition to an explicit entropy contribution owing to the release of condensed counterions. Interestingly, at the onset of complex formation, the mean force between the PE chains is found to be discontinuous, reflecting a bimodal structural behavior that arises from the coexistence of interconnected-rod and isolated-coil states. These two microstates of the PE complex are balanced by subtle counterion release effects and separated by a free-energy barrier due to unfavorable stretching entropy.
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Affiliation(s)
- Xiao Xu
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
| | - Matej Kanduč
- Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, 14109 Berlin, Germany
| | - Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, USA
| | - Joachim Dzubiella
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
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21
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Landsgesell J, Holm C, Smiatek J. Wang-Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid-Base Reactions. J Chem Theory Comput 2017; 13:852-862. [PMID: 28029786 DOI: 10.1021/acs.jctc.6b00791] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
We present a novel method for the study of weak polyelectrolytes and general acid-base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang-Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang-Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties.
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Affiliation(s)
- Jonas Landsgesell
- Institute for Computational Physics, University of Stuttgart , D-70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart , D-70569 Stuttgart, Germany
| | - Jens Smiatek
- Institute for Computational Physics, University of Stuttgart , D-70569 Stuttgart, Germany
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22
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Šamaj L, Trizac E. Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls. Phys Rev E 2016; 93:012601. [PMID: 26871116 DOI: 10.1103/physreve.93.012601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Indexed: 11/07/2022]
Abstract
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).
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Affiliation(s)
- Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
| | - Emmanuel Trizac
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
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23
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Mallarino JP, Téllez G. Counterion density profile around a charged disk: From the weak to the strong association regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062140. [PMID: 26172694 DOI: 10.1103/physreve.91.062140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Indexed: 06/04/2023]
Abstract
We present a comprehensive study of the two-dimensional one-component plasma in the cell model with charged boundaries. Starting from weak couplings through a convenient approximation of the interacting potential we were able to obtain an analytic formulation to the problem deriving the partition function, density profile, contact densities, and integrated profiles that compared well with the numerical data from Monte Carlo simulations. Additionally, we derived the exact solution for the special cases of Ξ=1,2,3,⋯, finding a correspondence between those from weak couplings and the latter. Furthermore, we investigated the strong-coupling regime taking into consideration the Wigner formulation. Elaborating on this, we obtained the profile to leading order, computed the contact density values as compared to those derived in an earlier work on the contact theorem. We formulated adequately the strong-coupling regime for this system that differed from previous formulations. Ultimately, we calculated the first-order corrections and compared them against numerical results from our simulations with very good agreement; these results compared equally well in the planar limit, whose results are well known.
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Affiliation(s)
- Juan Pablo Mallarino
- Facultad de Ciencias, Laboratorio Computacional HPC, Universidad de los Andes, Bogotá, Colombia
| | - Gabriel Téllez
- Departamento de Física, Universidad de los Andes, Bogotá, Colombia
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24
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Mallarino JP, Téllez G, Trizac E. The contact theorem for charged fluids: from planar to curved geometries. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1008595] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
| | - Gabriel Téllez
- Departamento de Física, Universidad de los Andes , Bogotá, Colombia
| | - Emmanuel Trizac
- Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud , UMR CNRS 8626, Orsay, France
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25
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Deng M, Karniadakis GE. Electrostatic correlations near charged planar surfaces. J Chem Phys 2014; 141:094703. [PMID: 25194382 PMCID: PMC4162522 DOI: 10.1063/1.4894053] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Accepted: 08/15/2014] [Indexed: 11/14/2022] Open
Abstract
Electrostatic correlation effects near charged planar surfaces immersed in a symmetric electrolytes solution are systematically studied by numerically solving the nonlinear six-dimensional electrostatic self-consistent equations. We compare our numerical results with widely accepted mean-field (MF) theory results, and find that the MF theory remains quantitatively accurate only in weakly charged regimes, whereas in strongly charged regimes, the MF predictions deviate drastically due to the electrostatic correlation effects. We also observe a first-order like phase-transition corresponding to the counterion condensation phenomenon in strongly charged regimes, and compute the phase diagram numerically within a wide parameter range. Finally, we investigate the interactions between two likely-charged planar surfaces, which repulse each other as MF theory predicts in weakly charged regimes. However, our results show that they attract each other above a certain distance in strongly charged regimes due to significant electrostatic correlations.
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Affiliation(s)
- Mingge Deng
- Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912, USA
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912, USA
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26
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Does Electrical Conductivity of Linear Polyelectrolytes in Aqueous Solutions Follow the Dynamic Scaling Laws? A Critical Review and a Summary of the Key Relations. Polymers (Basel) 2014. [DOI: 10.3390/polym6041207] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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27
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Naji A, Kanduč M, Forsman J, Podgornik R. Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond. J Chem Phys 2013; 139:150901. [DOI: 10.1063/1.4824681] [Citation(s) in RCA: 133] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Fischer S, Netz RR. Low-frequency collective exchange mode in the dielectric spectrum of salt-free dilute polyelectrolyte solutions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:117. [PMID: 24154722 DOI: 10.1140/epje/i2013-13117-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2013] [Revised: 09/11/2013] [Accepted: 09/12/2013] [Indexed: 06/02/2023]
Abstract
We study the frequency-dependent dielectric response of flexible polyelectrolyte chains in aqueous salt-free dilute solution as a function of polymer concentration and length by means of Brownian dynamics simulations including hydrodynamic interactions. We show that condensed and uncondensed counter ions are characterized by different dielectric response spectra and thus confirm long-held scaling assumptions used for the interpretation of experimental data. In addition to the well-known relaxation modes of condensed and uncondensed counter ions we observe for a single polyelectrolyte chain, we find in many-chain simulations a novel spectral feature at low frequencies that essentially corresponds to an exchange of counter ions between neighboring polyelectrolytes. Our results suggest that the experimental low-frequency dielectric mode might not be due to condensed counter ions, as is commonly assumed, but rather due to a collective many-chain process. This could resolve a long-standing puzzle in the comparison of experimental results and scaling predictions.
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Affiliation(s)
- Sebastian Fischer
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
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29
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Mallarino JP, Téllez G, Trizac E. Counterion Density Profile around Charged Cylinders: The Strong-Coupling Needle Limit. J Phys Chem B 2013; 117:12702-16. [DOI: 10.1021/jp311873a] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Gabriel Téllez
- Departamento de Física, Universidad de los Andes - Bogotá, Colombia
| | - Emmanuel Trizac
- Laboratoire de Physique Théorique
et Modèles Statistiques (UMR CNRS 8626), Université Paris-Sud, F-91405 Orsay, France
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30
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Miao B, Vilgis TA. Configurational Fluctuation Effects on Counterion Condensation for a Polyelectrolyte Chain. MACROMOL THEOR SIMUL 2012. [DOI: 10.1002/mats.201200033] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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31
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Varghese A, Vemparala S, Rajesh R. Ensemble equivalence for counterion condensation on a two-dimensional charged disk. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011119. [PMID: 22400524 DOI: 10.1103/physreve.85.011119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2011] [Indexed: 05/31/2023]
Abstract
We study the counterion condensation on a two-dimensional charged disk in the limit of infinite dilution, and compare the energy-temperature relation obtained from the canonical free energy and microcanonical entropy. The microcanonical entropy is piecewise linear in energy, and is shown to be concave for all energies. As a result, even though the interactions are long-ranged, the energy-temperature relation and hence the counterion condensation transition points are identical in both the ensembles.
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Affiliation(s)
- Anoop Varghese
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.
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32
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Varghese A, Vemparala S, Rajesh R. Phase transitions of a single polyelectrolyte in a poor solvent with explicit counterions. J Chem Phys 2011; 135:154902. [DOI: 10.1063/1.3653378] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
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33
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Samaj L, Trizac E. Wigner-crystal formulation of strong-coupling theory for counterions near planar charged interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041401. [PMID: 22181140 DOI: 10.1103/physreve.84.041401] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2011] [Indexed: 05/31/2023]
Abstract
We present a new analytical approach to the strong electrostatic coupling regime (SC) that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity, etc. Two geometries are analyzed in detail: one charged wall first, and then two parallel walls at small distances that can be likely or oppositely charged. In all cases, only one type of mobile counterions is present, and ensures electroneutrality (salt-free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counterions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counterion mediated like-charge attraction, and the opposite-charge repulsion.
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Affiliation(s)
- Ladislav Samaj
- Laboratoire de Physique Théorique et Modèles Statistiques, UMR CNRS 8626, Université Paris-Sud, F-91405 Orsay, France
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34
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Moradian A, Miri MF. A submicron device to rectify a square-wave angular velocity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:12. [PMID: 21337018 DOI: 10.1140/epje/i2011-11012-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2010] [Accepted: 01/18/2011] [Indexed: 05/30/2023]
Abstract
We study a system composed of two thick dielectric disks separated by a thin layer of an electrolyte solution. Initially both plates have the same surface charge distribution. The surface charge distribution has no rotational symmetry. We show that the top plate experiences a torque [Formula: see text]([Formula: see text]) if it rotates about its axis by an angle [Formula: see text] . The torque can be controlled by varying the electrolyte concentration, the separation and the surface charge density of the plates. For a specific example of charged rods attached to the plates, we find [Formula: see text]([Formula: see text]) [Formula: see text] sin(4[Formula: see text]) . We also study the dynamics of the system. We consider the case where the angular velocity of the bottom disk is a square-wave signal. We find that the average angular velocity of the top disk is not zero.
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Affiliation(s)
- A Moradian
- Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45195-1159, 45195, Zanjan, Iran
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35
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Samaj L, Trizac E. Counter-ions at charged walls: two-dimensional systems. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:20. [PMID: 21359929 DOI: 10.1140/epje/i2011-11020-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2010] [Accepted: 01/24/2011] [Indexed: 05/30/2023]
Abstract
We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the vicinity of a single uniformly charged line (one single double layer), or between two such lines (interacting double layers). The weak-coupling Poisson-Boltzmann theory, which applies when the coupling constant [Formula: see text] is small, is briefly recapitulated (the coupling constant is defined as [Formula: see text] [Formula: see text] [Formula: see text] e (2) , where [Formula: see text] is the inverse temperature, and e the counter-ion charge). The opposite limit ( [Formula: see text] [Formula: see text] ∞ is treated by using a recent method based on an exact expansion around the ground-state Wigner crystal of counter-ions. These two limiting results are compared at intermediary values of the coupling constant [Formula: see text] = 2[Formula: see text] ([Formula: see text] = 1, 2, 3) , to exact results derived within a 1D lattice representation of 2D Coulomb systems in terms of anti-commuting field variables. The models (density profile, pressure) are solved exactly for any particles numbers N at [Formula: see text] = 2 and up to relatively large finite N at [Formula: see text] = 4 and 6. For the one-line geometry, the decay of the density profile at asymptotic distance from the line undergoes a fundamental change with respect to the mean-field behavior at [Formula: see text] = 6 . The like-charge attraction regime, possible for large [Formula: see text] but precluded at mean-field level, survives for [Formula: see text] = 4 and 6, but disappears at [Formula: see text] = 2 .
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Affiliation(s)
- L Samaj
- Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, UMR CNRS 8626, 91405, Orsay, France.
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36
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Kanduc M, Naji A, Forsman J, Podgornik R. Dressed counterions: strong electrostatic coupling in the presence of salt. J Chem Phys 2010; 132:124701. [PMID: 20370139 DOI: 10.1063/1.3361672] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We reformulate the theory of strong electrostatic coupling in order to describe an asymmetric electrolyte solution of monovalent salt ions and polyvalent counterions using field-theoretical techniques and Monte Carlo simulations. The theory is based on an asymmetric treatment of the different components of the electrolyte solution. The weak coupling Debye-Hückel approach is used in order to describe the monovalent salt ions while a strong coupling approach is used to tackle the polyvalent counterions. This combined weak-strong coupling approach effectively leads to dressed interactions between polyvalent counterions and thus directly affects the correlation attraction mediated by polyvalent counterions between like-charged objects. The general theory is specifically applied to a system composed of two uniformly charged plane-parallel surfaces in the presence of salt and polyvalent counterions. In the strong coupling limit for polyvalent counterions, the comparison with Monte Carlo simulations shows good agreement for large enough values of the electrostatic coupling parameter. We delineate two limiting laws that in fact encompass all the Monte Carlo data.
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Affiliation(s)
- Matej Kanduc
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
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37
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Kanduč M, Naji A, Podgornik R. Counterion-mediated weak and strong coupling electrostatic interaction between like-charged cylindrical dielectrics. J Chem Phys 2010; 132:224703. [DOI: 10.1063/1.3430744] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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38
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Okamoto R, Onuki A. Ion distribution around a charged rod in one and two component solvents: Preferential solvation and first order ionization phase transition. J Chem Phys 2009; 131:094905. [DOI: 10.1063/1.3216518] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chepelianskii A, Mohammad-Rafiee F, Trizac E, Raphaël E. On the Effective Charge of Hydrophobic Polyelectrolytes. J Phys Chem B 2008; 113:3743-9. [DOI: 10.1021/jp8076276] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Chepelianskii
- Laboratoire de Physique des Solides, UMR CNRS 8502, Bat. 510, Université Paris-Sud, 91405 Orsay, France, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195, P.O. Box 45195-1159, Iran, Laboratoire Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France, and Université Paris-Sud, LPTMS, UMR CNRS 8626, 91405 Orsay, France
| | - F. Mohammad-Rafiee
- Laboratoire de Physique des Solides, UMR CNRS 8502, Bat. 510, Université Paris-Sud, 91405 Orsay, France, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195, P.O. Box 45195-1159, Iran, Laboratoire Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France, and Université Paris-Sud, LPTMS, UMR CNRS 8626, 91405 Orsay, France
| | - E. Trizac
- Laboratoire de Physique des Solides, UMR CNRS 8502, Bat. 510, Université Paris-Sud, 91405 Orsay, France, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195, P.O. Box 45195-1159, Iran, Laboratoire Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France, and Université Paris-Sud, LPTMS, UMR CNRS 8626, 91405 Orsay, France
| | - E. Raphaël
- Laboratoire de Physique des Solides, UMR CNRS 8502, Bat. 510, Université Paris-Sud, 91405 Orsay, France, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195, P.O. Box 45195-1159, Iran, Laboratoire Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France, and Université Paris-Sud, LPTMS, UMR CNRS 8626, 91405 Orsay, France
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Fischer S, Naji A, Netz RR. Salt-induced counterion-mobility anomaly in polyelectrolyte electrophoresis. PHYSICAL REVIEW LETTERS 2008; 101:176103. [PMID: 18999768 DOI: 10.1103/physrevlett.101.176103] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2008] [Indexed: 05/27/2023]
Abstract
We study the electrokinetics of a single polyelectrolyte chain in salt solution using hydrodynamic simulations. The salt-dependent chain mobility compares well with experimental DNA data. The mobility of condensed counterions exhibits a salt-dependent change of sign, an anomaly that is also reflected in the counterion excess conductivity. Using Green's function techniques this anomaly is explained by electrostatic screening of the hydrodynamic interactions between the chain and counterions.
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Affiliation(s)
- Sebastian Fischer
- Physik Department, Technische Universität München, Garching, Germany
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41
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Goel T, Patra CN, Ghosh SK, Mukherjee T. Structure of cylindrical electric double layers: A systematic study by Monte Carlo simulations and density functional theory. J Chem Phys 2008; 129:154906. [DOI: 10.1063/1.2992525] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Kim WK, Sung W. Charge density coordination and dynamics in a rodlike polyelectrolyte. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021904. [PMID: 18850862 DOI: 10.1103/physreve.78.021904] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2008] [Indexed: 05/26/2023]
Abstract
We study static and dynamic correlation functions of segmental charge density fluctuation on a rodlike polymer in ionic solutions. The polymer is described by an effective Hamiltonian which incorporates the Coulomb interaction between fluctuating charges screened by ionic fluid environment. We analytically calculate the correlation functions and discuss how charge distribution and dynamics are affected by counterion valency and concentration in electrolyte. We find that the charge correlation exhibits an underdamped oscillation with a wavelength comparable to the counterion size and with the amplitude increasing with the counterion valency. The dynamic correlation of charge density is shown to decay with a characteristic time varying with the counterion valency and concentration. The multivalency gives rise to faster decay of the correlation than that given by one dimensional diffusion.
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Affiliation(s)
- Won Kyu Kim
- Department of Physics and PCTP, Pohang University of Science and Technology, Pohang 790-784, South Korea.
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Lo TS, Khusid B, Koplik J. Dynamical clustering of counterions on flexible polyelectrolytes. PHYSICAL REVIEW LETTERS 2008; 100:128301. [PMID: 18517915 DOI: 10.1103/physrevlett.100.128301] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2007] [Indexed: 05/26/2023]
Abstract
Molecular dynamics simulations are used to study the spatiotemporal dynamics of charge fluctuations around a polyelectrolyte molecule at charge densities above and below the classic counterion condensation threshold. Surprisingly, the counterions form weakly interacting clusters which exhibit slowly decaying short range orientational order. Local charge fluctuations create energy fluctuations at the order of k_(B)T that is sufficient to affect the polyelectrolyte interaction with an approaching ligand molecule. The predictions of the classical theory appear to be appropriate only over much longer time scales.
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Affiliation(s)
- Tak Shing Lo
- Benjamin Levich Institute, City College of the City University of New York, New York, New York 10031, USA
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Mielke SP, Grønbech-Jensen N, Benham CJ. Brownian dynamics of double-stranded DNA in periodic systems with discrete salt. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031924. [PMID: 18517439 DOI: 10.1103/physreve.77.031924] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2007] [Revised: 12/20/2007] [Indexed: 05/26/2023]
Abstract
Numerical models of mesoscale DNA dynamics relevant to in vivo scenarios require methods that incorporate important features of the intracellular environment, while maintaining computational tractability. Because the explicit inclusion of ions leads to electrostatic calculations that scale as the square of the number of charged particles, such models typically handle these calculations using low-potential, mean-field approaches, rather than by considering the discrete interactions of ions. This allows approximation of the long-range, screened self-repulsion of DNA, but is unable to capture detailed electrostatic phenomena, such as short-range attractions mediated by ion-ion correlations. Here, we develop a dynamical model of explicitly double-stranded, sequence-specific DNA in a bulk environment consisting of other polyions and explicitly represented counterions and coions. DNA is represented as two interwound chains of charged Stokes spheres, and ions as free, monovalently charged Stokes spheres. Brownian dynamics simulations performed at salt concentrations of 0.1, 1, 10, and 100 mM demonstrate this model captures anticipated behaviors of the system, including increasing compaction of the polyion by the ionic atmosphere with increasing ionic strength. The decay of the distance dependence of the ion concentrations as one moves away from the polyion approaches their equilibrium values in quantitative agreement with predictions of Poisson-Boltzmann theory. The simulation results also demonstrate quantitative agreement with experimental measurements of the persistence length of B-DNA, which increases significantly at low ionic strengths. The model also captures behaviors intimating the importance of explicitly representing ionic and polyionic structure. These include penetration of the polyion interior by both coions and counterions, and counterion-mediated accumulation of coions near the surface of the polyion. Such phenomena are likely to play an important role in the formation of alternative DNA secondary structures, suggesting the present methods will prove valuable to dynamic models of superhelical stress-induced DNA structural transitions.
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Affiliation(s)
- Steven P Mielke
- UC Davis Genome Center, University of California, Davis, California 95616, USA
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Manning GS. Electrostatic Free Energies of Spheres, Cylinders, and Planes in Counterion Condensation Theory with Some Applications. Macromolecules 2007. [DOI: 10.1021/ma071457x] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Gerald S. Manning
- Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, New Jersey 08854-8087
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Abstract
We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.
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Affiliation(s)
- Gerald S Manning
- Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, New Jersey 08854-8087, USA.
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