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Becker M, Loche P, Rezaei M, Wolde-Kidan A, Uematsu Y, Netz RR, Bonthuis DJ. Multiscale Modeling of Aqueous Electric Double Layers. Chem Rev 2024; 124:1-26. [PMID: 38118062 PMCID: PMC10785765 DOI: 10.1021/acs.chemrev.3c00307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2023] [Revised: 11/17/2023] [Accepted: 11/30/2023] [Indexed: 12/22/2023]
Abstract
From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.
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Affiliation(s)
| | - Philip Loche
- Fachbereich
Physik, Freie Universität Berlin, 14195 Berlin, Germany
- Laboratory
of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Majid Rezaei
- Fachbereich
Physik, Freie Universität Berlin, 14195 Berlin, Germany
- Institute
of Theoretical Chemistry, Ulm University, 89081 Ulm, Germany
| | | | - Yuki Uematsu
- Department
of Physics and Information Technology, Kyushu
Institute of Technology, 820-8502 Iizuka, Japan
- PRESTO,
Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Roland R. Netz
- Fachbereich
Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Douwe Jan Bonthuis
- Institute
of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
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2
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Pivnic K, de Souza JP, Kornyshev AA, Urbakh M, Bazant MZ. Orientational Ordering in Nano-confined Polar Liquids. NANO LETTERS 2023. [PMID: 37285463 DOI: 10.1021/acs.nanolett.3c00927] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Water and other polar liquids exhibit nanoscale structuring near charged interfaces. When a polar liquid is confined between two charged surfaces, the interfacial solvent layers begin to overlap, resulting in solvation forces. Here, we perform molecular dynamics simulations of polar liquids with different dielectric constants and molecular shapes and sizes confined between charged surfaces, demonstrating strong orientational ordering in the nanoconfined liquids. To rationalize the observed structures, we apply a coarse-grained continuum theory that captures the orientational ordering and solvation forces of those liquids. Our findings reveal the subtle behavior of different nanoconfined polar liquids and establish a simple law for the decay length of the interfacial orientations of the solvents, which depends on their molecular size and polarity. These insights shed light on the nature of solvation forces, which are important in colloid and membrane science, scanning probe microscopy, and nano-electrochemistry.
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Affiliation(s)
- Karina Pivnic
- School of Chemistry, The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - J Pedro de Souza
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Alexei A Kornyshev
- Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, W12 0BZ 2AZ London, United Kingdom
- Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Michael Urbakh
- School of Chemistry, The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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3
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de Souza JP, Kornyshev AA, Bazant MZ. Polar liquids at charged interfaces: A dipolar shell theory. J Chem Phys 2022; 156:244705. [PMID: 35778078 DOI: 10.1063/5.0096439] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.
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Affiliation(s)
- J Pedro de Souza
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
| | - Alexei A Kornyshev
- Department of Chemistry and Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, Molecular Sciences Research Hub, White City Campus, London W12 0BZ, United Kingdom
| | - Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
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4
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Sokoloff JB. Effects of electrical image potentials and solvation energy on salt ions near a metallic or dielectric wall. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:122. [PMID: 34613538 DOI: 10.1140/epje/s10189-021-00127-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 09/16/2021] [Indexed: 06/13/2023]
Abstract
Electrical image potentials near a metallic or a dielectric wall of higher dielectric constant than that of the solution are attractive, and therefore, could concentrate salt ions near the wall. In fact, ions in room temperature ionic liquids have been observed to precipitate near a metallic surface (but not near a nonmetallic surface). It will be argued that a likely reason for why precipitation of ions in salt water due to electrical image forces has not as yet been observed is that the solvation of the ions is reduced near the wall. This results in an energy barrier. This reduction occurs because of the large decrease near the wall of the dielectric constant of water normal to the wall. The conditions under which ions are able to get past the resulting energy barrier and concentrate at a solid wall, either as a result of a reduction in this barrier due to screening at high ion concentration or as a result of thermal activation over the barrier will be explored.
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Affiliation(s)
- J B Sokoloff
- Physics Department, Florida Atlantic University, Boca Raton, FL, 33431, USA.
- Physics Department and Center for Interdisciplinary Research in Complex Systems, Northeastern University, Boston, MA, 02115, USA.
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5
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Berthoumieux H, Monet G, Blossey R. Dipolar Poisson models in a dual view. J Chem Phys 2021; 155:024112. [PMID: 34266284 DOI: 10.1063/5.0056430] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this work, we study the continuum theories of dipolar-Poisson models. Both the standard dipolar-Poisson model and the dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential ϕ. Applying the Legendre transform approach introduced by Maggs [Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement D and the polarization field P. We compare the convex functionals in P-space to the non-convex functionals in electric field E-space and apply them to the classic problem of the solvation of point-like ions. Since the dipolar-Poisson model does not properly describe polarization saturation, we argue that only the dipolar-Poisson-Langevin functional can be used to provide a nonlinear generalization of the harmonic polarization functional used in the theory of Marcus for the electron transfer rate to nonlinear regimes. We show that the model can be quantitatively parameterized by molecular dynamics simulations.
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Affiliation(s)
- Hélène Berthoumieux
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France
| | - Geoffrey Monet
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France
| | - Ralf Blossey
- University of Lille, Unité de Glycobiologie Structurale et Fonctionnelle (UGSF) CNRS UMR8576, 59000 Lille, France
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6
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Shen X, Sun T, Yang L, Krasnoslobodtsev A, Sabirianov R, Sealy M, Mei WN, Wu Z, Tan L. Ultra-fast charging in aluminum-ion batteries: electric double layers on active anode. Nat Commun 2021; 12:820. [PMID: 33547316 PMCID: PMC7864900 DOI: 10.1038/s41467-021-21108-4] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 01/07/2021] [Indexed: 11/08/2022] Open
Abstract
With the rapid iteration of portable electronics and electric vehicles, developing high-capacity batteries with ultra-fast charging capability has become a holy grail. Here we report rechargeable aluminum-ion batteries capable of reaching a high specific capacity of 200 mAh g-1. When liquid metal is further used to lower the energy barrier from the anode, fastest charging rate of 104 C (duration of 0.35 s to reach a full capacity) and 500% more specific capacity under high-rate conditions are achieved. Phase boundaries from the active anode are believed to encourage a high-flux charge transfer through the electric double layers. As a result, cationic layers inside the electric double layers responded with a swift change in molecular conformation, but anionic layers adopted a polymer-like configuration to facilitate the change in composition.
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Affiliation(s)
- Xuejing Shen
- School of Aerospace, Dalian University of Technology, Dalian, 116024, China
- Department of Mechanical & Materials Engineering, University of Nebraska, Lincoln, NE, 68588, USA
| | - Tao Sun
- School of Aerospace, Dalian University of Technology, Dalian, 116024, China
- Department of Mechanical & Materials Engineering, University of Nebraska, Lincoln, NE, 68588, USA
| | - Lei Yang
- School of Aerospace, Dalian University of Technology, Dalian, 116024, China
- Department of Physics, University of Nebraska, Omaha, NE, 68182, USA
| | - Alexey Krasnoslobodtsev
- Department of Physics, University of Nebraska, Omaha, NE, 68182, USA
- Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, NE, 68588, USA
| | - Renat Sabirianov
- Department of Physics, University of Nebraska, Omaha, NE, 68182, USA
- Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, NE, 68588, USA
| | - Michael Sealy
- Department of Mechanical & Materials Engineering, University of Nebraska, Lincoln, NE, 68588, USA
- Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, NE, 68588, USA
| | - Wai-Ning Mei
- Department of Physics, University of Nebraska, Omaha, NE, 68182, USA
- Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, NE, 68588, USA
| | - Zhanjun Wu
- School of Aerospace, Dalian University of Technology, Dalian, 116024, China.
| | - Li Tan
- Department of Mechanical & Materials Engineering, University of Nebraska, Lincoln, NE, 68588, USA.
- Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, NE, 68588, USA.
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7
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Rubashkin AA, Iserovich P, Vorotyntsev MA. A Theory of Charge Selectivity Reversal in Cation- or Anion-Selective Tight Junctions between Epithelial Cells: A Nonlocal Electrostatic Approach. Biophysics (Nagoya-shi) 2021. [DOI: 10.1134/s0006350921010127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
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8
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Physical origin of Na+/Cl− selectivity of tight junctions between epithelial cells. Nonlocal electrostatic approach. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113884] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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9
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Vatin M, Porro A, Sator N, Dufrêche JF, Berthoumieux H. Electrostatic interactions in water: a nonlocal electrostatic approach. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1825849] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- M. Vatin
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
- ICSM/LMCT Site de Marcoule, Bagnols sur Céze Cedex, France
| | - A. Porro
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
| | - N. Sator
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
| | - J.-F. Dufrêche
- ICSM/LMCT Site de Marcoule, Bagnols sur Céze Cedex, France
| | - H. Berthoumieux
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Sorbonne Université, CNRS, Paris, France
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10
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11
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Gabovich AM, Voitenko AI. Electrostatic interaction near the interface between dielectric media taking into account the nonlocality of the Coulomb field screening. J Mol Liq 2018. [DOI: 10.1016/j.molliq.2017.09.044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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12
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Berthoumieux H. Gaussian field model for polar fluids as a function of density and polarization: Toward a model for water. J Chem Phys 2018; 148:104504. [DOI: 10.1063/1.5012828] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- H. Berthoumieux
- CNRS, UMR 7600, LPTMC, F-75005 Paris, France and Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France
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13
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Molavi Tabrizi A, Goossens S, Mehdizadeh Rahimi A, Knepley M, Bardhan JP. Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvation-layer interface condition. J Chem Phys 2017. [DOI: 10.1063/1.4977037] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amirhossein Molavi Tabrizi
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Spencer Goossens
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Ali Mehdizadeh Rahimi
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Matthew Knepley
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, USA
| | - Jaydeep P. Bardhan
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
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14
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Misin M, Vainikka PA, Fedorov MV, Palmer DS. Salting-out effects by pressure-corrected 3D-RISM. J Chem Phys 2016; 145:194501. [DOI: 10.1063/1.4966973] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Maksim Misin
- Department of Physics, SUPA, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, United Kingdom
| | - Petteri A. Vainikka
- Department of Pure and Applied Chemistry, University of Strathclyde, 295 Cathedral Street, Glasgow G1 1XL, United Kingdom
| | - Maxim V. Fedorov
- Department of Physics, SUPA, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, United Kingdom
- Skolkovo Institute of Science and Technology, 3 Nobel Street, Moscow 143026, Russian Federation
| | - David S. Palmer
- Department of Pure and Applied Chemistry, University of Strathclyde, 295 Cathedral Street, Glasgow G1 1XL, United Kingdom
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15
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Rubinstein AI, Sabirianov RF, Namavar F. Effects of the dielectric properties of the ceramic-solvent interface on the binding of proteins to oxide ceramics: a non-local electrostatic approach. NANOTECHNOLOGY 2016; 27:415703. [PMID: 27585807 DOI: 10.1088/0957-4484/27/41/415703] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The rapid development of nanoscience and nanotechnology has raised many fundamental questions that significantly impede progress in these fields. In particular, understanding the physicochemical processes at the interface in aqueous solvents requires the development and application of efficient and accurate methods. In the present work we evaluate the electrostatic contribution to the energy of model protein-ceramic complex formation in an aqueous solvent. We apply a non-local (NL) electrostatic approach that accounts for the effects of the short-range structure of the solvent on the electrostatic interactions of the interfacial systems. In this approach the aqueous solvent is considered as a non-ionic liquid, with the rigid and strongly correlated dipoles of the water molecules. We have found that an ordered interfacial aqueous solvent layer at the protein- and ceramic-solvent interfaces reduces the charging energy of both the ceramic and the protein in the solvent, and significantly increases the electrostatic contribution to their association into a complex. This contribution in the presented NL approach was found to be significantly shifted with respect to the classical model at any dielectric constant value of the ceramics. This implies a significant increase of the adsorption energy in the protein-ceramic complex formation for any ceramic material. We show that for several biocompatible ceramics (for example HfO2, ZrO2, and Ta2O5) the above effect predicts electrostatically induced protein-ceramic complex formation. However, in the framework of the classical continuum electrostatic model (the aqueous solvent as a uniform dielectric medium with a high dielectric constant ∼80) the above ceramics cannot be considered as suitable for electrostatically induced complex formation. Our results also show that the protein-ceramic electrostatic interactions can be strong enough to compensate for the unfavorable desolvation effect in the process of protein-ceramic complex formation.
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Affiliation(s)
- Alexander I Rubinstein
- Department of Physics, Laboratory of Applied Spectroscopy, Ariel University, Ariel 40700, West Bank. Department of Physics, University of Nebraska at Omaha, Omaha, NE 68182, USA
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16
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Kjellander R. Nonlocal electrostatics in ionic liquids: The key to an understanding of the screening decay length and screened interactions. J Chem Phys 2016; 145:124503. [DOI: 10.1063/1.4962756] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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17
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Tabrizi AM, Knepley MG, Bardhan JP. Generalising the mean spherical approximation as a multiscale, nonlinear boundary condition at the solute–solvent interface. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1198503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | - Matthew G. Knepley
- Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA
| | - Jaydeep P. Bardhan
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA
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18
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Reif MM, Hünenberger PH. Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited. J Phys Chem B 2016; 120:8485-517. [PMID: 27173101 DOI: 10.1021/acs.jpcb.6b02156] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The asymmetric solvation of ions can be defined as the tendency of a solvent to preferentially solvate anions over cations or cations over anions, at identical ionic charge magnitudes and effective sizes. Taking water as a reference, these effects are quantified experimentally for many solvents by the relative acity (A) and basity (B) parameters of the Swain scale. The goal of the present study is to investigate the asymmetric solvation of ions using molecular dynamics simulations, and to connect the results to this empirical scale. To this purpose, the charging free energies of alkali and halide ions, and of their hypothetical oppositely charged counterparts, are calculated in a variety of solvents. In a first set of calculations, artificial solvent models are considered that present either a charge or a shape asymmetry at the molecular level. The solvation asymmetry, probed by the difference in charging free energy between the two oppositely charged ions, is found to encompass a term quadratic in the ion charge, related to the different solvation structures around the anion and cation, and a term linear in the ion charge, related to the solvation structure around the uncharged ion-sized cavity. For these simple solvent models, the two terms are systematically counteracting each other, and it is argued that only the quadratic term should be retained when comparing the results of simulations involving physical solvents to experimental data. In a second set of calculations, 16 physical solvents are considered. The theoretical estimates for the acity A are found to correlate very well with the Swain parameters, whereas the correlation for B is very poor. Based on this observation, the Swain scale is reformulated into a new scale involving an asymmetry parameter Σ, positive for acitic solvents and negative for basitic ones, and a polarity parameter Π. This revised scale has the same predictive power as the original scale, but it characterizes asymmetry in an absolute sense, the atomistic simulations playing the role of an extra-thermodynamic assumption, and is optimally compatible with the simulation results. Considering the 55 solvents in the Swain set, it is observed that a moderate basity (Σ between -0.9 and -0.3, related to electronic polarization) represents the baseline for most solvents, while a highly variable acity (Σ between 0.0 and 3.0, related to hydrogen-bond donor capacity modulated by inductive effects) represents a landmark of protic solvents.
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Affiliation(s)
- Maria M Reif
- Physics Department (T38), Technische Universität München , D-85748 Garching, Germany
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19
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Misin M, Fedorov MV, Palmer DS. Hydration Free Energies of Molecular Ions from Theory and Simulation. J Phys Chem B 2016; 120:975-83. [PMID: 26756333 DOI: 10.1021/acs.jpcb.5b10809] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a theoretical/computational framework for accurate calculation of hydration free energies of ionized molecular species. The method is based on a molecular theory, 3D-RISM, combined with a recently developed pressure correction (PC+). The 3D-RISM/PC+ model can provide ∼3 kcal/mol hydration free energy accuracy for a large variety of ionic compounds, provided that the Galvani potential of water is taken into account. The results are compared with direct atomistic simulations. Several methodological aspects of hydration free energy calculations for charged species are discussed.
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Affiliation(s)
| | | | - David S Palmer
- Department of Pure and Applied Chemistry, University of Strathclyde , 295 Cathedral Street, Glasgow, G1 1XL, United Kingdom
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20
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Ivaništšev V, Méndez-Morales T, Lynden-Bell RM, Cabeza O, Gallego LJ, Varela LM, Fedorov MV. Molecular origin of high free energy barriers for alkali metal ion transfer through ionic liquid–graphene electrode interfaces. Phys Chem Chem Phys 2016; 18:1302-10. [DOI: 10.1039/c5cp05973a] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
We study mechanisms of solvent-mediated ion interactions with charged surfaces in ionic liquids by molecular dynamics simulations, in an attempt to reveal the main trends that determine ion–electrode interactions in ionic liquids.
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Affiliation(s)
| | - Trinidad Méndez-Morales
- Departamento de Física da Materia Condensada
- Universidade de Santiago de Compostela
- Santiago de Compostela
- Spain
| | | | - Oscar Cabeza
- Facultade de Ciencias
- Universidade da Coruña
- A Coruña
- Spain
| | - Luis J. Gallego
- Departamento de Física da Materia Condensada
- Universidade de Santiago de Compostela
- Santiago de Compostela
- Spain
| | - Luis M. Varela
- Departamento de Física da Materia Condensada
- Universidade de Santiago de Compostela
- Santiago de Compostela
- Spain
| | - Maxim V. Fedorov
- Department of Physics
- Scottish Universities Physics Alliance (SUPA)
- Strathclyde University
- John Anderson Building
- Glasgow
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21
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Gotovtsev PM, Yuzbasheva EY, Gorin KV, Butylin VV, Badranova GU, Perkovskaya NI, Mostova EB, Namsaraev ZB, Rudneva NI, Komova AV, Vasilov RG, Sineokii SP. Immobilization of microbial cells for biotechnological production: Modern solutions and promising technologies. APPL BIOCHEM MICRO+ 2015. [DOI: 10.1134/s0003683815080025] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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22
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Rubashkin AA, Vorotyntsev MA, Antipov EM, Aldoshin ASM. Nonlocal electrostatic theory of ion solvation: A combination of the overscreening effect in the dielectric response of the medium with a smeared ion charge distribution. DOKLADY PHYSICAL CHEMISTRY 2015. [DOI: 10.1134/s0012501615090031] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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23
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Schaaf C, Gekle S. Dielectric response of the water hydration layer around spherical solutes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032718. [PMID: 26465509 DOI: 10.1103/physreve.92.032718] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 06/05/2023]
Abstract
We calculate the local dielectric function ɛ(r) inside the hydration layer around a spherical solute (i) from molecular dynamics simulations including explicit solutes and (ii) theoretically using the nonlocal dielectric function of bulk water which includes the radial electric field, but not the explicit solute. The observed agreement between the two concepts shows that while ɛ(r) is strongly different from bulk, this difference is not due to restructuring of the hydrogen bond network but is mostly a consequence of the field geometry. The dielectric response differs for anions and cations, yielding a natural explanation for the well-known charge asymmetry of ionic solvation in agreement with experimental data.
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Affiliation(s)
- Christian Schaaf
- Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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Brodskaya EN, Vanin AA. Effect of water on the local electric potential of simulated ionic micelles. J Chem Phys 2015; 143:044707. [DOI: 10.1063/1.4927089] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Elena N. Brodskaya
- Institute of Chemistry, St. Petersburg State University, Universitetskiy pr. 26, Petrodvoretz, St. Petersburg 198504, Russia
| | - Alexander A. Vanin
- Institute of Chemistry, St. Petersburg State University, Universitetskiy pr. 26, Petrodvoretz, St. Petersburg 198504, Russia
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Ratkova EL, Palmer DS, Fedorov MV. Solvation thermodynamics of organic molecules by the molecular integral equation theory: approaching chemical accuracy. Chem Rev 2015; 115:6312-56. [PMID: 26073187 DOI: 10.1021/cr5000283] [Citation(s) in RCA: 135] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Ekaterina L Ratkova
- †G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya Street 1, Ivanovo 153045, Russia.,‡The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany
| | - David S Palmer
- ‡The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany.,§Department of Chemistry, University of Strathclyde, Thomas Graham Building, 295 Cathedral Street, Glasgow, Scotland G1 1XL, United Kingdom
| | - Maxim V Fedorov
- ‡The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany.,∥Department of Physics, Scottish Universities Physics Alliance (SUPA), University of Strathclyde, John Anderson Building, 107 Rottenrow East, Glasgow G4 0NG, United Kingdom
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26
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Bardhan JP, Knepley MG. Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions. J Chem Phys 2014; 141:131103. [PMID: 25296776 PMCID: PMC4193973 DOI: 10.1063/1.4897324] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2014] [Accepted: 09/25/2014] [Indexed: 01/28/2023] Open
Abstract
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
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Affiliation(s)
- Jaydeep P Bardhan
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Matthew G Knepley
- Computation Institute, The University of Chicago, Chicago, Illinois 60637, USA
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Sergiievskyi VP, Jeanmairet G, Levesque M, Borgis D. Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections. J Phys Chem Lett 2014; 5:1935-1942. [PMID: 26273876 DOI: 10.1021/jz500428s] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.
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Affiliation(s)
- Volodymyr P Sergiievskyi
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Guillaume Jeanmairet
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Maximilien Levesque
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
| | - Daniel Borgis
- †École Normale Supérieure - PSL Research University, Département de Chimie, Sorbonne Universités - UPMC Univ Paris 06, CNRS UMR 8640 PASTEUR, 24 rue Lhomond, 75005 Paris, France
- ‡Maison de la Simulation, CNRS USR 3441, CEA Saclay, 91191 Gif-sur-Yvette, France
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Affiliation(s)
- Maxim V Fedorov
- Department of Physics, Scottish University Physics Alliance (SUPA), University of Strathclyde , John Anderson Bldg, 107 Rottenrow, Glasgow, G4 0NG United Kingdom
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Asmadi A, Kirchner T, Abdallah W, Fedorov MV, Stukan MR. Influence of the Drude charge value on the performance of polarisable water model: A test for microscopic and macroscopic parameters. J Mol Liq 2013. [DOI: 10.1016/j.molliq.2013.09.026] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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31
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Joung IS, Luchko T, Case DA. Simple electrolyte solutions: comparison of DRISM and molecular dynamics results for alkali halide solutions. J Chem Phys 2013; 138:044103. [PMID: 23387564 DOI: 10.1063/1.4775743] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using the dielectrically consistent reference interaction site model (DRISM) of molecular solvation, we have calculated structural and thermodynamic information of alkali-halide salts in aqueous solution, as a function of salt concentration. The impact of varying the closure relation used with DRISM is investigated using the partial series expansion of order-n (PSE-n) family of closures, which includes the commonly used hypernetted-chain equation (HNC) and Kovalenko-Hirata closures. Results are compared to explicit molecular dynamics (MD) simulations, using the same force fields, and to experiment. The mean activity coefficients of ions predicted by DRISM agree well with experimental values at concentrations below 0.5 m, especially when using the HNC closure. As individual ion activities (and the corresponding solvation free energies) are not known from experiment, only DRISM and MD results are directly compared and found to have reasonably good agreement. The activity of water directly estimated from DRISM is nearly consistent with values derived from the DRISM ion activities and the Gibbs-Duhem equation, but the changes in the computed pressure as a function of salt concentration dominate these comparisons. Good agreement with experiment is obtained if these pressure changes are ignored. Radial distribution functions of NaCl solution at three concentrations were compared between DRISM and MD simulations. DRISM shows comparable water distribution around the cation, but water structures around the anion deviate from the MD results; this may also be related to the high pressure of the system. Despite some problems, DRISM-PSE-n is an effective tool for investigating thermodynamic properties of simple electrolytes.
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Affiliation(s)
- In Suk Joung
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University, Piscataway, New Jersey 08854, USA
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32
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Odinokov AV, Titov SV, Tikhomirov VA, Basilevsky MV, Alfimov MV. Inclusion complexes of β-cyclodextrine with organic ligands: molecular dynamics simulation of the thermodynamic stability in gas phase and in water solution. MOLECULAR SIMULATION 2013. [DOI: 10.1080/08927022.2012.740636] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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33
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Stukan MR, Asmadi A, Abdallah W. Bulk properties of SWM4-NDP water model at elevated temperature and pressure. J Mol Liq 2013. [DOI: 10.1016/j.molliq.2012.12.023] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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34
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Bardhan JP, Jungwirth P, Makowski L. Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies. J Chem Phys 2013; 137:124101. [PMID: 23020318 DOI: 10.1063/1.4752735] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).
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Affiliation(s)
- Jaydeep P Bardhan
- Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, Illinois 60612, USA
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35
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Sergiievskyi VP, Frolov AI. A universal bridge functional for infinitely diluted solutions: A case study for Lennard-Jones spheres of different diameters. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2012. [DOI: 10.1134/s0036024412080122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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36
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Ratkova EL. A comparative analysis of models for hydration free energy calculations using the RISM theory of integral equations. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2012. [DOI: 10.1134/s0036024412060222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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37
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Bonthuis DJ, Gekle S, Netz RR. Profile of the static permittivity tensor of water at interfaces: consequences for capacitance, hydration interaction and ion adsorption. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2012; 28:7679-7694. [PMID: 22414296 DOI: 10.1021/la2051564] [Citation(s) in RCA: 133] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We derive the theoretical framework to calculate the dielectric response tensor and determine its components for water adjacent to hydrophilic and hydrophobic surfaces using molecular dynamics simulations. For the nonpolarizable water model used, linear response theory is found to be applicable up to an external perpendicular field strength of ∼2 V/nm, which is well beyond the experimental dielectric breakdown threshold. The dipole contribution dominates the dielectric response parallel to the interface, whereas for the perpendicular component it is essential to keep the quadrupole and octupole terms. Including the space-dependent dielectric function in a mean-field description of the ion distribution at a single charged interface, we reproduce experimental values of the interfacial capacitance. At the same time, the dielectric function decreases the electrostatic part of the disjoining pressure between two charged surfaces, unlike previously thought. The difference in interfacial polarizability between hydrophilic and hydrophobic surfaces can be quantized in terms of the dielectric dividing surface. Using the dielectric dividing surface and the Gibbs dividing surface positions to estimate the free energy of a single ion close to an interface, ion-specific adsorption effects are found to be more pronounced at hydrophobic surfaces than at hydrophilic surfaces, in agreement with experimental trends.
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Affiliation(s)
- Douwe Jan Bonthuis
- Physik Department, Technische Universität München, 85748 Garching, Germany
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38
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Sergiievskyi VP, Fedorov MV. 3DRISM Multigrid Algorithm for Fast Solvation Free Energy Calculations. J Chem Theory Comput 2012; 8:2062-70. [DOI: 10.1021/ct200815v] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Maxim V. Fedorov
- Nanoscience
Division, Department
of Physics, Scottish Universities Physics Alliance (SUPA), Strathclyde University, Room JA 6.10, John Anderson
Building 107, Rottenrow East Glasgow, United Kingdom G4 0NG
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39
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Luchko T, Joung IS, Case DA. Integral Equation Theory of Biomolecules and Electrolytes. INNOVATIONS IN BIOMOLECULAR MODELING AND SIMULATIONS 2012. [DOI: 10.1039/9781849735049-00051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
The so-called three-dimensional version (3D-RISM) can be used to describe the interactions of solvent components (here we treat water and ions) with a chemical or biomolecular solute of arbitrary size and shape. Here we give an overview of the current status of such models, describing some aspects of “pure” electrolytes (water plus simple ions) and of ionophores, proteins and nucleic acids in the presence of water and salts. Here we focus primarily on interactions with water and dissolved salts; as a practical matter, the discussion is mostly limited to monovalent ions, since studies of divalent ions present many difficult problems that have not yet been addressed. This is not a comprehensive review, but covers a few recent examples that illustrate current issues.
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Affiliation(s)
- Tyler Luchko
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
| | - In Suk Joung
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
| | - David A. Case
- Department of Chemistry and Chemical Biology and BioMaPS Institute Rutgers University Piscataway NJ 08854, USA
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40
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Enami S, Mishra H, Hoffmann MR, Colussi AJ. Hofmeister effects in micromolar electrolyte solutions. J Chem Phys 2012; 136:154707. [PMID: 22519343 DOI: 10.1063/1.4704752] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Shinichi Enami
- The Hakubi Center, Kyoto University, Kyoto 606-8302, Japan.
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41
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Frolov AI, Arif RN, Kolar M, Romanova AO, Fedorov MV, Rozhin AG. Molecular mechanisms of salt effects on carbon nanotube dispersions in an organic solvent (N-methyl-2-pyrrolidone). Chem Sci 2012. [DOI: 10.1039/c1sc00232e] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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42
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Fedorov DG, Kitaura K. Energy Decomposition Analysis in Solution Based on the Fragment Molecular Orbital Method. J Phys Chem A 2011; 116:704-19. [DOI: 10.1021/jp209579w] [Citation(s) in RCA: 77] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Dmitri G. Fedorov
- NRI, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono 1-1-1, Tsukuba, 305-8568, Japan
| | - Kazuo Kitaura
- NRI, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono 1-1-1, Tsukuba, 305-8568, Japan
- Graduate School of Pharmaceutical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
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43
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Chen Z, Baker NA, Wei GW. Differential geometry based solvation model II: Lagrangian formulation. J Math Biol 2011; 63:1139-200. [PMID: 21279359 PMCID: PMC3113640 DOI: 10.1007/s00285-011-0402-z] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2010] [Revised: 12/24/2010] [Indexed: 10/18/2022]
Abstract
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.
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Affiliation(s)
- Zhan Chen
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Nathan A. Baker
- Pacific Northwest National Laboratory,
902 Battelle Boulevard P.O. Box 999, MSIN K7-28, Richland, WA 99352 USA
| | - G. W. Wei
- Department of Mathematics, Michigan State University, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
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45
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Basilevsky M, Odinokov A, Nikitina E, Petrov N. The dielectric continuum solvent model adapted for treating preferential solvation effects. J Electroanal Chem (Lausanne) 2011. [DOI: 10.1016/j.jelechem.2010.09.022] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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46
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On calculations of the ion hydration free energy within the framework of the RISM approach. Russ Chem Bull 2011. [DOI: 10.1007/s11172-011-0037-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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47
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Kolombet VA. Calculation of the hydration energy of polyvalent metal ions by the RISM method. RUSS J INORG CHEM+ 2011. [DOI: 10.1134/s0036023611080110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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48
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Sergiievskyi VP. Model for calculating the free energy of hydration of bioactive compounds based on integral equation theory of liquids. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2011. [DOI: 10.1134/s1990793111020382] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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49
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Ratkova EL, Fedorov MV. Combination of RISM and Cheminformatics for Efficient Predictions of Hydration Free Energy of Polyfragment Molecules: Application to a Set of Organic Pollutants. J Chem Theory Comput 2011; 7:1450-7. [DOI: 10.1021/ct100654h] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ekaterina L. Ratkova
- The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
| | - Maxim V. Fedorov
- The Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
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50
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Frolov AI, Ratkova EL, Palmer DS, Fedorov MV. Hydration Thermodynamics Using the Reference Interaction Site Model: Speed or Accuracy? J Phys Chem B 2011; 115:6011-22. [DOI: 10.1021/jp111271c] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Andrey I. Frolov
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
| | - Ekaterina L. Ratkova
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
| | - David S. Palmer
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
| | - Maxim V. Fedorov
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
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