1
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Ribar D, Woodward CE, Nordholm S, Forsman J. Cluster Formation Induced by Local Dielectric Saturation in Restricted Primitive Model Electrolytes. J Phys Chem Lett 2024; 15:8326-8333. [PMID: 39109581 PMCID: PMC11331514 DOI: 10.1021/acs.jpclett.4c01829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2024] [Revised: 07/24/2024] [Accepted: 07/31/2024] [Indexed: 08/16/2024]
Abstract
Experiments using the Surface Force Apparatus (SFA) have found anomalously long-ranged charge-charge underscreening in concentrated salt solutions. Meanwhile, theory and simulations have suggested ion clustering to be a possible origin of this behavior. The popular Restricted Primitive Model of electrolyte solutions, in which the solvent is represented by a uniform relative dielectric constant, εr, is unable to resolve the anomalous underscreening seen in experiments. In this work, we modify the Restricted Primitive Model to account for local dielectric saturation within the ion hydration shell. The dielectric "constant" in our model locally decreases from the bulk value to a lower saturated value at the ionic surface. The parameters for the model are deduced so that typical salt solubilities are obtained. Our simulations for both bulk and slit geometries show that our model displays strong cluster formation and these give rise to long-ranged density correlations between charged surfaces, at distances similar to what has been observed in SFA measurements. An electrolyte model wherein the dielectric constant remains uniform does not display similar clusters, even with εr equal to the low saturated value at ion contact. Hence, the observed behaviors are not simply due to an enhanced Coulomb interaction. In the latter case, cluster growth is counteracted by long-ranged repulsions between like-charged ions within clusters; this is an effect that is considerably reduced when the dielectric response drop is local. Our results imply that long-ranged interactions in these systems are mainly due to cluster-cluster correlations, rather than large electrostatic screening lengths.
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Affiliation(s)
- David Ribar
- Computational
Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Clifford E. Woodward
- School
of Physical, Environmental and Mathematical Sciences, University College, University of New South Wales, ADFA Canberra ACT 2600, Australia
| | - Sture Nordholm
- Department
of Chemistry and Molecular Biology, The
University of Gothenburg, 412 96 Gothenburg, Sweden
| | - Jan Forsman
- Computational
Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
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2
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Abstract
Experimental measurements of interactions in ionic liquids and concentrated electrolytes over the past decade or so have revealed simultaneous monotonic and oscillatory decay modes. These observations have been hard to interpret using classical theories, which typically allow for just one electrostatic decay mode in electrolytes. Meanwhile, substantial progress in the theoretical description of dielectric response and ion correlations in electrolytes has illuminated the deep connection between density and charge correlations and the multiplicity of decay modes characterising a liquid electrolyte. The challenge in front of us is to build connections between the theoretical expressions for a pair of correlation functions and the directly measured free energy of interaction between macroscopic surfaces in experiments. Towards this aim, we here present measurements and analysis of the interactions between macroscopic bodies across a fluid mixture of two ionic liquids of widely diverging ionic size. The measured oscillatory interaction forces in the liquid mixtures are significantly more complex than for either of the pure ionic liquids, but can be fitted to a superposition of two oscillatory and one monotonic mode with parameters matching those of the pure liquids. We discuss this empirical finding, which hints at a kind of wave mechanics for interactions in liquid matter.
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Affiliation(s)
- Timothy S Groves
- Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK.
| | - Susan Perkin
- Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK.
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3
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Wang S, Tao H, Yang J, Cheng J, Liu H, Lian C. Structure and Screening in Confined Electrolytes: The Role of Ion Association. J Phys Chem Lett 2024; 15:7147-7153. [PMID: 38959446 DOI: 10.1021/acs.jpclett.4c01698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2024]
Abstract
The effect of ionic association on the structure and property of confined electrolytes is investigated using the classical density functional theory. We find that ionic association strongly affects the ion distribution, surface force, and screening behavior of confined electrolytes. The decay length ξ, which can describe the screening effect of high-concentration electrolytes, satisfies a scaling relationship ξ/λD ∼ (σ/λD)n, with λD being the Debye length and σ representing the ion diameter. We find that n = 1.5 in the nonassociation model, which is contributed by the charge correlation, but n = 3 in the association model, which is contributed by the density correlation. The ion association changes the concentration-dependent characteristics of the screening length by promoting the shift of the decay behavior from the charge-dominated regime to the density-dominated regime. Our result reveals the importance of ion association for electrolyte structure and screening behaviors.
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Affiliation(s)
- Sijie Wang
- State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Haolan Tao
- State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Jie Yang
- State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Jin Cheng
- State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Honglai Liu
- State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Cheng Lian
- State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
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4
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Jäger H, Schlaich A, Yang J, Lian C, Kondrat S, Holm C. A screening of results on the decay length in concentrated electrolytes. Faraday Discuss 2023; 246:520-539. [PMID: 37602784 DOI: 10.1039/d3fd00043e] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/22/2023]
Abstract
Screening of electrostatic interactions in room-temperature ionic liquids and concentrated electrolytes has recently attracted much attention as surface force balance experiments have suggested the emergence of unanticipated anomalously large screening lengths at high ion concentrations. Termed underscreening, this effect was ascribed to the bulk properties of concentrated ionic systems. However, underscreening under experimentally relevant conditions is not predicted by classical theories and challenges our understanding of electrostatic correlations. Despite the enormous effort in performing large-scale simulations and new theoretical investigations, the origin of the anomalously long-range screening length remains elusive. This contribution briefly summarises the experimental, analytical and simulation results on ionic screening and the scaling behaviour of screening lengths. We then present an atomistic simulation approach that accounts for the solvent and ion exchange with a reservoir. We find that classical density functional theory (DFT) for concentrated electrolytes under confinement reproduces ion adsorption at charged interfaces surprisingly well. With DFT, we study confined electrolytes using implicit and explicit solvent models and the dependence on the solvent's dielectric properties. Our results demonstrate how the absence vs. presence of solvent particles and their discrete nature affect the short and long-range screening in concentrated ionic systems.
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Affiliation(s)
- Henrik Jäger
- Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany
| | - Alexander Schlaich
- Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany.
| | - Jie Yang
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany.
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Cheng Lian
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Svyatoslav Kondrat
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany.
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany.
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5
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Hoang Ngoc Minh T, Kim J, Pireddu G, Chubak I, Nair S, Rotenberg B. Electrical noise in electrolytes: a theoretical perspective. Faraday Discuss 2023; 246:198-224. [PMID: 37409620 DOI: 10.1039/d3fd00026e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/13/2023]
Abstract
Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and surface force balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization, the field gradient (for quadrupolar nuclei) and the coupled mass/charge densities. The fluctuations of such various observables arise from the same underlying microscopic dynamics of the ions and solvent molecules. In principle, the relevant length and time scales of these dynamics are encoded in the dynamic structure factors. However, modelling the latter for frequencies and wavevectors spanning many orders of magnitude remains a great challenge to interpret the experiments in terms of physical processes such as solvation dynamics, diffusion, electrostatic and hydrodynamic interactions between ions, interactions with solid surfaces, etc. Here, we highlight the central role of the charge-charge dynamic structure factor in the fluctuations of electrical observables in electrolytes and offer a unifying perspective over a variety of complementary experiments. We further analyze this quantity in the special case of an aqueous NaCl electrolyte, using simulations with explicit ions and an explicit or implicit solvent. We discuss the ability of the standard Poisson-Nernst-Planck theory to capture the simulation results, and how the predictions can be improved. We finally discuss the contributions of ions and water to the total charge fluctuations. This work illustrates an ongoing effort towards a comprehensive understanding of electrical fluctuations in bulk and confined electrolytes, in order to enable experimentalists to decipher the microscopic properties encoded in the measured electrical noise.
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Affiliation(s)
- Thê Hoang Ngoc Minh
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France.
| | - Jeongmin Kim
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France.
| | - Giovanni Pireddu
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France.
| | - Iurii Chubak
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France.
| | - Swetha Nair
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France.
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France.
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France
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6
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Yang J, Kondrat S, Lian C, Liu H, Schlaich A, Holm C. Solvent Effects on Structure and Screening in Confined Electrolytes. PHYSICAL REVIEW LETTERS 2023; 131:118201. [PMID: 37774307 DOI: 10.1103/physrevlett.131.118201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 07/04/2023] [Accepted: 08/15/2023] [Indexed: 10/01/2023]
Abstract
Using classical density functional theory, we investigate the influence of solvent on the structure and ionic screening of electrolytes under slit confinement and in contact with a reservoir. We consider a symmetric electrolyte with implicit and explicit solvent models and find that spatially resolving solvent molecules is essential for the ion structure at confining walls, excess ion adsorption, and the pressure exerted on the walls. Despite this, we observe only moderate differences in the period of oscillations of the pressure with the slit width and virtually coinciding decay lengths as functions of the scaling variable σ_{ion}/λ_{D}, where σ_{ion} is the ion diameter and λ_{D} the Debye length. Moreover, in the electrostatic-dominated regime, this scaling behavior is practically independent of the relative permittivity and its dependence on the ion concentration. In contrast, the crossover to the hard-core-dominated regime depends sensitively on all three factors.
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Affiliation(s)
- Jie Yang
- Institute for Computational Physics, University of Stuttgart, 70569 Stuttgart, Germany
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Svyatoslav Kondrat
- Institute for Computational Physics, University of Stuttgart, 70569 Stuttgart, Germany
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| | - Cheng Lian
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Honglai Liu
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
| | - Alexander Schlaich
- Institute for Computational Physics, University of Stuttgart, 70569 Stuttgart, Germany
- Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, 70569 Stuttgart, Germany
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7
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Härtel A, Bültmann M, Coupette F. Anomalous Underscreening in the Restricted Primitive Model. PHYSICAL REVIEW LETTERS 2023; 130:108202. [PMID: 36962045 DOI: 10.1103/physrevlett.130.108202] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 12/19/2022] [Accepted: 02/08/2023] [Indexed: 06/18/2023]
Abstract
Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.
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Affiliation(s)
- Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Moritz Bültmann
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Fabian Coupette
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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8
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Zeidler A, Salmon PS, Usuki T, Kohara S, Fischer HE, Wilson M. Structure of molten NaCl and the decay of the pair-correlations. J Chem Phys 2022; 157:094504. [PMID: 36075708 DOI: 10.1063/5.0107620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The structure of molten NaCl is investigated by combining neutron and x-ray diffraction with molecular dynamics simulations that employed interaction potentials with either rigid or polarizable ions. Special attention is paid to the asymptotic decay of the pair-correlation functions, which is related to the small-k behavior of the partial structure factors, where k denotes the magnitude of the scattering vector. The rigid-ion approach gives access to an effective restricted primitive model in which the anion and cation have equal but opposite charges and are otherwise identical. For this model, the decay of the pair-correlation functions is in qualitative agreement with simple theory. The polarizable ion approach gives a good account of the diffraction results and yields thermodynamic parameters (density, isothermal compressibility, Debye screening length, and heat capacity) in accord with experiment. The longest decay length for the partial pair-distribution functions is a factor of ≃2.5 times greater than the nearest-neighbor distance. The results are commensurate with the decay lengths found for the effective restricted primitive model, which are much shorter than those found in experiments on concentrated electrolytes or ionic liquids using surface force apparatus.
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Affiliation(s)
- Anita Zeidler
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Philip S Salmon
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Takeshi Usuki
- Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, 1-4-12 Koshirakawa, Yamagata 990-8560, Japan
| | - Shinji Kohara
- Research Center for Advanced Measurement and Characterization, National Institute for Materials Science (NIMS), Ibaraki 305-0047, Japan
| | - Henry E Fischer
- Institut Laue Langevin, 71 Avenue des Martyrs, 38042 Grenoble Cedex 9, France
| | - Mark Wilson
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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9
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Frusawa H. Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis. SOFT MATTER 2022; 18:4280-4304. [PMID: 35615919 DOI: 10.1039/d1sm01811f] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.
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Affiliation(s)
- Hiroshi Frusawa
- Laboratory of Statistical Physics, Kochi University of Technology, Tosa-Yamada, Kochi 782-8502, Japan.
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10
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Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation. ENTROPY 2022; 24:e24040500. [PMID: 35455163 PMCID: PMC9028018 DOI: 10.3390/e24040500] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 03/28/2022] [Accepted: 03/28/2022] [Indexed: 12/04/2022]
Abstract
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction.
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11
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Patsahan O, Ciach A. Mesoscopic Inhomogeneities in Concentrated Electrolytes. ACS OMEGA 2022; 7:6655-6664. [PMID: 35252660 PMCID: PMC8892908 DOI: 10.1021/acsomega.1c06013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
A mesoscopic theory for water-in-salt electrolytes combining density functional and field-theoretic methods is developed in order to explain the unexpectedly large period of the oscillatory decay of the disjoining pressure observed in recent experiments for the lithium bis(trifluoromethylsulfonyl)-imide (LiTFSI) salt [T. S. Groves et al., J. Phys. Chem. Lett. 2021, 12, 1702]. We assumed spherical ions with different diameters and implicit solvent, inducing strong, short-range attraction between ions of the same sign. For this highly simplified model, we calculated correlation functions. Our results indicate that mesoscopic inhomogeneities can occur when the sum of the Coulomb and the water-mediated interactions between like ions is attractive at short and repulsive at large distances. We adjusted the attractive part of the potential to the water-in-LiTFSI electrolyte and obtained both the period and the decay rate of the correlations, in semiquantitative agreement with the experiment. In particular, the decay length of the correlations increases nearly linearly with the volume fraction of ions.
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Affiliation(s)
- Oksana Patsahan
- Institute
for Condensed Matter Physics of the National Academy of Sciences of
Ukraine, Lviv 79011, Ukraine
| | - Alina Ciach
- Institute
of Physical Chemistry, Polish Academy of
Sciences, 01-224 Warszawa, Poland
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12
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de Souza JP, Pivnic K, Bazant MZ, Urbakh M, Kornyshev AA. Structural Forces in Ionic Liquids: The Role of Ionic Size Asymmetry. J Phys Chem B 2022; 126:1242-1253. [PMID: 35134297 PMCID: PMC9007453 DOI: 10.1021/acs.jpcb.1c09441] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Revised: 01/04/2022] [Indexed: 11/29/2022]
Abstract
Ionic liquids (ILs) are charged fluids composed of anions and cations of different size and shape. The ordering of charge and density in ILs confined between charged interfaces underlies numerous applications of IL electrolytes. Here, we analyze the screening behavior and the resulting structural forces of a representative IL confined between two charge-varied plates. Using both molecular dynamics simulations and a continuum theory, we contrast the screening features of a more-realistic asymmetric system and a less-realistic symmetric one. The ionic size asymmetry plays a nontrivial role in charge screening, affecting both the ionic density profiles and the disjoining pressure distance dependence. Ionic systems with size asymmetry are stronger coupled systems, and this manifests itself both in their response to the electrode polarization and spontaneous structure formation at the interface. Analytical expressions for decay lengths of the disjoining pressure are obtained in agreement with the pressure profiles computed from molecular dynamics simulations.
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Affiliation(s)
- J. Pedro de Souza
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - Karina Pivnic
- 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
| | - Michael Urbakh
- School
of Chemistry, The Sackler Center for Computational Molecular and Materials
Science, Tel Aviv University, Tel Aviv, 6997801, Israel
| | - Alexei A. Kornyshev
- Department
of Chemistry, Molecular Sciences Research Hub, Imperial College London, London, W12 0BZ 2AZ, United Kingdom
- Thomas
Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom
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13
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Abstract
Recent experiments have shown that the repulsive force between atomically flat, like-charged surfaces confining room-temperature ionic liquids or concentrated electrolytes exhibits an anomalously large decay length. In our previous publication [J. Zeman, S. Kondrat, and C. Holm, Chem. Commun. 56, 15635 (2020)], we showed by means of extremely large-scale molecular dynamics simulations that this so-called underscreening effect might not be a feature of bulk electrolytes. Herein, we corroborate these findings by providing additional results with more detailed analyses and expand our investigations to ionic liquids under confinement. Unlike in bulk systems, where screening lengths are computed from the decay of interionic potentials of mean force, we extract such data in confined systems from cumulative charge distributions. At high concentrations, our simulations show increasing screening lengths with increasing electrolyte concentration, consistent with classical liquid state theories. However, our analyses demonstrate that-also for confined systems-there is no anomalously large screening length. As expected, the screening lengths determined for ionic liquids under confinement are in good quantitative agreement with the screening lengths of the same ionic systems in bulk. In addition, we show that some theoretical models used in the literature to relate the measured screening lengths to other observables are inapplicable to highly concentrated electrolytes.
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Affiliation(s)
- Johannes Zeman
- Institute for Computational Physics, University of Stuttgart, D-70569 Stuttgart, Germany
| | - Svyatoslav Kondrat
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, D-70569 Stuttgart, Germany
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14
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Krucker-Velasquez E, Swan JW. Underscreening and hidden ion structures in large scale simulations of concentrated electrolytes. J Chem Phys 2021; 155:134903. [PMID: 34624965 DOI: 10.1063/5.0061230] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The electrostatic screening length predicted by Debye-Hückel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes. We measure the decay of the charge-charge correlation among ions in the bulk and compare it against scaling trends found experimentally and determined in certain weak coupling theories of ion-ion correlation. Moreover, we find that additional large scale ion structures emerge at high concentrations. In this regime, the frequency of oscillations computed from the charge-charge correlation function is not dominated by electrostatic interactions but rather by excluded volume interactions and with oscillation periods on the order of the ion diameter. We also find the nearest neighbor correlation of ions sharing the same charge transitions from negative at small concentrations to positive at high concentrations, representing the formation of small, like-charge ion clusters. We conclude that the increase in local charge density due to the formation of these clusters and the topological constraints of macroscopic charged surfaces can help explain the degree of underscreening observed experimentally.
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Affiliation(s)
- Emily Krucker-Velasquez
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James W Swan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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15
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Forces between interfaces in concentrated nanoparticle suspensions and polyelectrolyte solutions. Curr Opin Colloid Interface Sci 2021. [DOI: 10.1016/j.cocis.2021.101482] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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16
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Dean JM, Coles SW, Saunders WR, McCluskey AR, Wolf MJ, Walker AB, Morgan BJ. Overscreening and Underscreening in Solid-Electrolyte Grain Boundary Space-Charge Layers. PHYSICAL REVIEW LETTERS 2021; 127:135502. [PMID: 34623837 DOI: 10.1103/physrevlett.127.135502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions adjacent to grain boundaries. The general analytical form of these space-charge regions is known only in the dilute limit, where defect-defect correlations can be neglected. Using kinetic Monte Carlo simulations of a three-dimensional Coulomb lattice gas, we show that grain boundary space-charge regions in nondilute solid electrolytes exhibit overscreening-damped oscillatory space-charge profiles-and underscreening-decay lengths that are longer than the corresponding Debye length and that increase with increasing defect-defect interaction strength. Overscreening and underscreening are known phenomena in concentrated liquid electrolytes, and the observation of functionally analogous behavior in solid electrolyte space-charge regions suggests that the same underlying physics drives behavior in both classes of systems. We therefore expect theoretical approaches developed to study nondilute liquid electrolytes to be equally applicable to future studies of solid electrolytes.
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Affiliation(s)
- Jacob M Dean
- Department of Chemistry, University of Bath, Claverton Down BA2 7AY, United Kingdom
- The Faraday Institution, Quad One, Harwell Science and Innovation Campus, Didcot OX11 0RA, United Kingdom
| | - Samuel W Coles
- Department of Chemistry, University of Bath, Claverton Down BA2 7AY, United Kingdom
- The Faraday Institution, Quad One, Harwell Science and Innovation Campus, Didcot OX11 0RA, United Kingdom
| | - William R Saunders
- Department of Physics, University of Bath, Claverton Down BA2 7AY, United Kingdom
| | - Andrew R McCluskey
- Department of Chemistry, University of Bath, Claverton Down BA2 7AY, United Kingdom
- European Spallation Source ERIC, P.O. Box 176, SE-221 00, Lund, Sweden
| | - Matthew J Wolf
- Department of Physics, University of Bath, Claverton Down BA2 7AY, United Kingdom
| | - Alison B Walker
- Department of Physics, University of Bath, Claverton Down BA2 7AY, United Kingdom
| | - Benjamin J Morgan
- Department of Chemistry, University of Bath, Claverton Down BA2 7AY, United Kingdom
- The Faraday Institution, Quad One, Harwell Science and Innovation Campus, Didcot OX11 0RA, United Kingdom
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17
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Ciach A, Patsahan O. Correct scaling of the correlation length from a theory for concentrated electrolytes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:37LT01. [PMID: 34186526 DOI: 10.1088/1361-648x/ac0f9e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 06/29/2021] [Indexed: 06/13/2023]
Abstract
Self-consistent theory for concentrated electrolytes is developed. Oscillatory decay of the charge-charge correlation function with the decay length that shows perfect agreement with the experimentally discovered and so far unexplained scaling is obtained. For the density-density correlations, monotonic asymptotic decay with the decay length comparable with the decay length of the charge correlations is found. We show that the correlation lengths in concentrated electrolytes depend crucially on the local variance of the charge density.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland
| | - O Patsahan
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, Ukraine
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18
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Jones P, Coupette F, Härtel A, Lee AA. Bayesian unsupervised learning reveals hidden structure in concentrated electrolytes. J Chem Phys 2021; 154:134902. [PMID: 33832269 DOI: 10.1063/5.0039617] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Electrolytes play an important role in a plethora of applications ranging from energy storage to biomaterials. Notwithstanding this, the structure of concentrated electrolytes remains enigmatic. Many theoretical approaches attempt to model the concentrated electrolyte by introducing the idea of ion pairs, with ions either being tightly "paired" with a counter-ion or "free" to screen charge. In this study, we reframe the problem into the language of computational statistics and test the null hypothesis that all ions share the same local environment. Applying the framework to molecular dynamics simulations, we find that this null hypothesis is not supported by data. Our statistical technique suggests the presence of two distinct local ionic environments at intermediate concentrations, whose differences surprisingly originate in like charge correlations rather than unlike charge attraction. Through considering the effect of these "aggregated" and "non-aggregated" states on bulk properties including effective ion concentration and dielectric constant, we identify a scaling relation between the effective screening length and theoretical Debye length, which applies across different dielectric constants and ion concentrations.
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Affiliation(s)
- Penelope Jones
- Department of Physics, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - Fabian Coupette
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg im Breisgau, Germany
| | - Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg im Breisgau, Germany
| | - Alpha A Lee
- Department of Physics, University of Cambridge, CB3 0HE Cambridge, United Kingdom
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19
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Cats P, Evans R, Härtel A, van Roij R. Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations. J Chem Phys 2021; 154:124504. [PMID: 33810662 DOI: 10.1063/5.0039619] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inspired by recent experimental observations of anomalously large decay lengths in concentrated electrolytes, we revisit the Restricted Primitive Model (RPM) for an aqueous electrolyte. We investigate the asymptotic decay lengths of the one-body ionic density profiles for the RPM in contact with a planar electrode using classical Density Functional Theory (DFT) and compare these with the decay lengths of the corresponding two-body correlation functions in bulk systems, obtained in previous Integral Equation Theory (IET) studies. Extensive Molecular Dynamics (MD) simulations are employed to complement the DFT and IET predictions. Our DFT calculations incorporate electrostatic interactions between the ions using three different (existing) approaches: one is based on the simplest mean-field treatment of Coulomb interactions (MFC), while the other two employ the Mean Spherical Approximation (MSA). The MSAc invokes only the MSA bulk direct correlation function, whereas the MSAu also incorporates the MSA bulk internal energy. Although MSAu yields profiles that are in excellent agreement with MD simulations in the near field, in the far field, we observe that the decay lengths are consistent between IET, MSAc, and MD simulations, whereas those from MFC and MSAu deviate significantly. Using DFT, we calculated the solvation force, which relates directly to surface force experiments. We find that its decay length is neither qualitatively nor quantitatively close to the large decay lengths measured in experiments and conclude that the latter cannot be accounted for by the primitive model. The anomalously large decay lengths found in surface force measurements require an explanation that lies beyond primitive models.
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Affiliation(s)
- P Cats
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - R Evans
- HH Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - A Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, Freiburg 79104, Germany
| | - R van Roij
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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20
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Sprik M. Electric-field-based Poisson-Boltzmann theory: Treating mobile charge as polarization. Phys Rev E 2021; 103:022803. [PMID: 33736023 DOI: 10.1103/physreve.103.022803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2020] [Accepted: 02/08/2021] [Indexed: 12/18/2022]
Abstract
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of an electrolyte can then be treated as a composite nonuniform dielectric body. Writing the electrostatic interactions as an integral over electric-field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua [J. L. Ericksen, Arch. Rational Mech. Anal. 183, 299 (2007)AVRMAW0003-952710.1007/s00205-006-0042-4]. The Maxwell field equations are enforced by extending the set of variational parameters by a vector potential representing the dielectric displacement which is fully transverse in a dielectric system without embedded external charge. The electric-field energy density in this representation is a function of the vector potential and the sum of ionic and solvent polarization making the mutual screening explicit. Transverse polarization is accounted for by construction, lifting the restriction to longitudinal polarization inherent in the electrostatic potential based formulation of Poisson-Boltzmann mean field theory.
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Affiliation(s)
- Michiel Sprik
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England, United Kingdom
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21
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Qing L, Zhao S, Wang ZG. Surface Charge Density in Electrical Double Layer Capacitors with Nanoscale Cathode-Anode Separation. J Phys Chem B 2021; 125:625-636. [PMID: 33405923 DOI: 10.1021/acs.jpcb.0c09332] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Using a dynamic density functional theory, we study the charging dynamics, the final equilibrium structure, and the energy storage in an electrical double layer capacitor with nanoscale cathode-anode separation in a slit geometry. We derive a simple expression for the surface charge density that naturally separates the effects of the charge polarization due to the ions from those due to the polarization of the dielectric medium and allows a more intuitive understanding of how the ion distribution within the cell affects the surface charge density. We find that charge neutrality in the half-cell does not hold during the dynamic charging process for any cathode-anode separation, and also does not hold at the final equilibrium state for small separations. Therefore, the charge accumulation in the half-cell in general does not equal the surface charge density. The relationships between the surface charge density and the charge accumulation within the half-cell are systematically investigated by tuning the electrolyte concentration, cathode-anode separation, and applied voltage. For high electrolyte concentrations, we observe charge inversion at which the charge accumulation exceeds the surface charge at special values of the separation. In addition, we find that the energy density has a maximum at intermediate electrolyte concentrations for a high applied voltage.
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Affiliation(s)
- Leying Qing
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237, China.,Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Shuangliang Zhao
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East China University of Science and Technology, Shanghai, 200237, China.,Guangxi Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology and School of Chemistry and Chemical Engineering, Guangxi University, Nanning, 530004, China
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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22
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Zeman J, Kondrat S, Holm C. Bulk ionic screening lengths from extremely large-scale molecular dynamics simulations. Chem Commun (Camb) 2020; 56:15635-15638. [PMID: 33283802 DOI: 10.1039/d0cc05023g] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Recent experiments have reported anomalously large screening lengths of interactions between charged surfaces confining concentrated electrolytes and ionic liquids. Termed underscreening, this effect was ascribed to bulk properties of dense ionic systems. Herein, we study bulk ionic screening with extremely large-scale molecular dynamics simulations, allowing us to assess the range of distances relevant to the experiments. Our results yield two screening lengths satisfying distinct scaling relations. However, with an accuracy of 10-5kBT in interionic potentials of mean force, we find no signs of underscreening, suggesting that other than bulk effects might be at play in the experiments.
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Affiliation(s)
- Johannes Zeman
- Institute for Computational Physics, University of Stuttgart, D-70569 Stuttgart, Germany.
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23
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Kjellander R. A multiple decay-length extension of the Debye-Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes. Phys Chem Chem Phys 2020; 22:23952-23985. [PMID: 33073810 DOI: 10.1039/d0cp02742a] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Poisson-Boltzmann and Debye-Hückel approximations for the pair distributions and mean electrostatic potential in electrolytes predict that these entities have one single decay mode with a decay length equal to the Debye length 1/κD, that is, they have a characteristic contribution that decays with distance r like e-κDr/r. However, in reality, electrolytes have several decay modes e-κr/r, e-κ'r/r etc. with different decay lengths, 1/κ, 1/κ' etc., that in general are different from the Debye length. As an illustration of the significance of multiple decay modes in electrolytes, the present work uses a very simple extension of the Debye-Hückel approximation with two decay lengths, which predicts oscillatory modes when appropriate. This approach gives very accurate results for radial distribution functions and thermodynamic properties of aqueous solutions of monovalent electrolytes for all concentrations investigated, including high ones. It is designed to satisfy necessary statistical mechanical conditions for the distributions. The effective dielectric permittivity of the electrolyte plays an important role in the theory and each mode has its own value of this entity. Electrolytes with high electrostatic coupling, like those with multivalent ions and/or with solvent of low dielectric constant, have decay lengths in dilute solutions that substantially deviate from the Debye length. It is shown that this is caused by nonlinear ion-ion correlation effects and the origin of under-screening, i.e., 1/κ > 1/κD, in dilute symmetric electrolytes is analyzed. The under-screening is accompanied by an increase in the effective dielectric permittivity that is also caused by these correlations. The theoretical results for the decay length are successfully compared with recent experimental data for simple electrolytes in various solvents. The paper includes background material on electrolyte theory and screening in order to be accessible for nonexperts in the field.
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Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden.
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24
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Patsahan O, Meyra A, Ciach A. Correlation functions in mixtures with energetically favoured nearest neighbours of different kind: a size-asymmetric case. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1820091] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- O. Patsahan
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, Lviv, Ukraine
| | - A. Meyra
- IFLYSIB (UNLP, CONICET), La Plata, Argentina
- Depto de Ingenieria Mecánica, UTN-FRLP, La Plata, Argentina
| | - A. Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa, Poland
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25
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de Souza JP, Goodwin ZAH, McEldrew M, Kornyshev AA, Bazant MZ. Interfacial Layering in the Electric Double Layer of Ionic Liquids. PHYSICAL REVIEW LETTERS 2020; 125:116001. [PMID: 32975984 DOI: 10.1103/physrevlett.125.116001] [Citation(s) in RCA: 51] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Accepted: 07/24/2020] [Indexed: 06/11/2023]
Abstract
Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly interacting environment, leading to the formation of discrete layers of charges at interfaces and spin-glass structure in the bulk. Here, we propose a simple theory that captures the coupling between steric and electrostatic forces in ionic liquids. The theory predicts the formation of discrete layers of charge at charged interfaces. Further from the interface, or at low polarization of the electrode, the model outputs slowly decaying oscillations in the charge density with a wavelength of a single ion diameter, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.
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Affiliation(s)
- J Pedro de Souza
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Zachary A H Goodwin
- Department of Physics, CDT Theory and Simulation of Materials, Imperial College of London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Michael McEldrew
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Alexei A Kornyshev
- Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Department of Chemistry, Imperial College of London, Molecular Science Research Hub, White City Campus, London W12 0BZ, United Kingdom
| | - Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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26
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Okamoto R, Koga K, Onuki A. Theory of electrolytes including steric, attractive, and hydration interactions. J Chem Phys 2020; 153:074503. [PMID: 32828079 DOI: 10.1063/5.0015446] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional F for the coarse-grained solvent, cation, and anion densities, including the Debye-Hückel free energy, the Coulombic interaction, and the direct interactions among these three components. These densities fluctuate obeying the distribution ∝exp(-F/kBT). Eliminating the solvent density deviation in F, we obtain the effective non-Coulombic interactions among the ions, which consist of the direct ones and the solvent-mediated ones. We then derive general expressions for the ion correlation, the apparent partial volume, and the activity and osmotic coefficients up to linear order in the average salt density ns. Second, we perform numerical analysis using the Mansoori-Carnahan-Starling-Leland model [J. Chem. Phys. 54, 1523 (1971)] for three-component hardspheres. The effective interactions sensitively depend on the cation and anion sizes due to competition between the steric and hydration effects, which are repulsive between small-large ion pairs and attractive between symmetric pairs. These agree with previous experiments and Collins' rule [Biophys. J. 72, 65 (1997)]. We also give simple approximate expressions for the ionic interaction coefficients valid for any ion sizes.
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Affiliation(s)
- Ryuichi Okamoto
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
| | - Kenichiro Koga
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
| | - Akira Onuki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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27
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Fetisov EO, Mundy CJ, Schenter GK, Benmore CJ, Fulton JL, Kathmann SM. Nanometer-Scale Correlations in Aqueous Salt Solutions. J Phys Chem Lett 2020; 11:2598-2604. [PMID: 32163289 DOI: 10.1021/acs.jpclett.0c00322] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The intermediate-range (1-4 nm) correlation of cations, anions, and water in aqueous alkaline earth salt solutions is measured using synchrotron X-ray diffraction. We differentiate from the entire solution structure factor, SX(Q), a separate region at low Q (<1.5 Å-1) containing local diffraction maxima (prepeaks) that indicate nanometer-scale oscillatory behavior. These features are quantitatively reproduced with classical molecular dynamics simulations. At high concentrations, the prepeaks emerge from correlations arising from the existence of small quasi close-packed lattice-like structures comprised of cation hydration spheres. We also analyze the concentration dependence of the prepeak and discuss the overall results in light of the rich literature dealing with intermediate-range correlations underlying universal phenomena in concentrated electrolytes.
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Affiliation(s)
- Evgenii O Fetisov
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Christopher J Mundy
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Gregory K Schenter
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Chris J Benmore
- Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - John L Fulton
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Shawn M Kathmann
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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28
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Coles SW, Park C, Nikam R, Kanduč M, Dzubiella J, Rotenberg B. Correlation Length in Concentrated Electrolytes: Insights from All-Atom Molecular Dynamics Simulations. J Phys Chem B 2020; 124:1778-1786. [PMID: 32031810 DOI: 10.1021/acs.jpcb.9b10542] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We study the correlation length of the charge-charge pair correlations in concentrated electrolyte solutions by means of all-atom, explicit-solvent molecular dynamics simulations. We investigate LiCl and NaI in water, which constitute highly soluble, prototypical salts for experiments, as well as two more complex, molecular electrolyte systems of lithium bis(trifluoromethane)sulfonimide (LiTFSI), a salt commonly employed in electrochemical storage systems, in water, and in an organic solvent mixture of dimethoxyethane and dioxolane. Our simulations support the recent experimental observations as well as theoretical predictions of a nonmonotonic behavior of the correlation length with increasing salt concentration. We observe a Debye-Hückel like regime at low concentration, followed by a minimum reached when d/λD ≃ 1, where λD is the Debye correlation length and d is the effective ionic diameter, and an increasing correlation length with salt concentration in very concentrated electrolytes. As in the experiments, we find that the screening length in the concentrated regime follows a universal scaling law as a function d/λD for all studied salts. However, the scaling exponent is significantly lower than the experimentally measured one and lies in the range of the theoretical predictions based on much simpler electrolyte models.
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Affiliation(s)
- Samuel W Coles
- Sorbonne Université, CNRS, Physicochimie des électrolytes et Nanosystèmes Interfaciaux, UMR PHENIX, 4 pl. Jussieu, F-75005 Paris, France
| | - Chanbum Park
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
| | - Rohit Nikam
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
| | - Matej Kanduč
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
| | - Joachim Dzubiella
- Research Group for Simulations of Energy Materials, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany.,Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Physicochimie des électrolytes et Nanosystèmes Interfaciaux, UMR PHENIX, F-75005 Paris, France
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29
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Adar RM, Safran SA, Diamant H, Andelman D. Screening length for finite-size ions in concentrated electrolytes. Phys Rev E 2019; 100:042615. [PMID: 31771021 DOI: 10.1103/physreve.100.042615] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Indexed: 11/07/2022]
Abstract
The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.
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Affiliation(s)
- Ram M Adar
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Samuel A Safran
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Haim Diamant
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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30
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Adibnia V, Shrestha BR, Mirbagheri M, Murschel F, De Crescenzo G, Banquy X. Electrostatic Screening Length in "Soft" Electrolyte Solutions. ACS Macro Lett 2019; 8:1017-1021. [PMID: 35619477 DOI: 10.1021/acsmacrolett.9b00437] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Using the Surface Forces Apparatus on solutions of polymeric ions, the effect of specific ion-ion correlations is evaluated on the characteristic decay length, λ, of screened electrostatic interactions between charged surfaces. Electrolyte solutions composed of point charges surrounded by repulsive polymeric shells were used to elucidate the role of ions size and size asymmetry between co- and counterions on the screening of electrostatic forces. In electrolytes composed of large polymeric cations and small point-charge anions, because of the steric and excluded volume effects, the screening length follows the simple scaling relation λ ∼ d, where d is the characteristic size of the large cation. It is also reported that both co- and counterion sizes affect the thickness of the electrical double layer and influence the screened electrostatic interactions. In solutions of polymeric cation/anion pairs, the screening length is shown to depend on an asymmetry factor. These results provide insights into correlation effects in electrolytes, which were so far unreachable experimentally and help elucidate such effects in electronics, energy storage devices, and biomedical systems.
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Affiliation(s)
- Vahid Adibnia
- Faculty of Pharmacy, Université de Montréal, 2900 Édouard-Montpetit, Montreal, Quebec H3C 3J7, Canada
- Department of Chemical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079,
succ. Centre-Ville, Montreal, Quebec H3C 3A7, Canada
| | - Buddha Ratna Shrestha
- Faculty of Pharmacy, Université de Montréal, 2900 Édouard-Montpetit, Montreal, Quebec H3C 3J7, Canada
| | - Marziye Mirbagheri
- Faculty of Pharmacy, Université de Montréal, 2900 Édouard-Montpetit, Montreal, Quebec H3C 3J7, Canada
- Department of Chemical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079,
succ. Centre-Ville, Montreal, Quebec H3C 3A7, Canada
| | - Frederic Murschel
- Faculty of Pharmacy, Université de Montréal, 2900 Édouard-Montpetit, Montreal, Quebec H3C 3J7, Canada
| | - Gregory De Crescenzo
- Department of Chemical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079,
succ. Centre-Ville, Montreal, Quebec H3C 3A7, Canada
| | - Xavier Banquy
- Faculty of Pharmacy, Université de Montréal, 2900 Édouard-Montpetit, Montreal, Quebec H3C 3J7, Canada
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31
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Kjellander R. The intimate relationship between the dielectric response and the decay of intermolecular correlations and surface forces in electrolytes. SOFT MATTER 2019; 15:5866-5895. [PMID: 31243425 DOI: 10.1039/c9sm00712a] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A general, exact theory for the decay of interactions between any particles immersed in electrolytes, including surface forces between macroscopic bodies, is derived in a self-contained, physically transparent manner. It is valid for electrolytes at any density, including ionic gases, molten salts, ionic liquids, and electrolyte solutions with molecular solvent at any concentration. The ions, the solvent and any other particles in the system can have any sizes, any shapes and arbitrary internal charge distributions. The spatial propagation of the interactions in electrolytes has several decay modes with different decay lengths that are given by the solutions, κν, ν = 1, 2,…, to a general equation for the screening parameter κ; an equation that describes the dielectric response. There can exist simultaneous decay modes with plain exponential decay and modes with damped oscillatory exponential decay, as observed experimentally and theoretically. In the limit of zero ionic density, the decay length 1/κν of the mode with the longest range approaches the Debye length 1/κD. The coupling between fluctuations in number density and charge density, described by the density-charge correlation function HNQ(r), makes all decay modes of pair correlations and interaction free energies identical to those of the screened electrostatic potential, and hence they have the same values for the screening parameters. The density-density and charge-charge correlation functions, HNN(r) and HQQ(r), also have these decay modes. For the exceptional case of charge-inversion invariant systems, HNQ(r) is identically zero for symmetry reasons and HNN(r) and HQQ(r) have, instead, decay modes with different decay lengths.
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Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden.
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32
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Kamysbayev V, Srivastava V, Ludwig NB, Borkiewicz OJ, Zhang H, Ilavsky J, Lee B, Chapman KW, Vaikuntanathan S, Talapin DV. Nanocrystals in Molten Salts and Ionic Liquids: Experimental Observation of Ionic Correlations Extending beyond the Debye Length. ACS NANO 2019; 13:5760-5770. [PMID: 30964280 DOI: 10.1021/acsnano.9b01292] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
The nature of the interface between the solute and the solvent in a colloidal solution has attracted attention for a long time. For example, the surface of colloidal nanocrystals (NCs) is specially designed to impart colloidal stability in a variety of polar and nonpolar solvents. This work focuses on a special type of colloids where the solvent is a molten inorganic salt or organic ionic liquid. The stability of such colloids is hard to rationalize because solvents with high density of mobile charges efficiently screen the electrostatic double-layer repulsion, and purely ionic molten salts represent an extreme case where the Debye length is only ∼1 Å. We present a detailed investigation of NC dispersions in molten salts and ionic liquids using small-angle X-ray scattering (SAXS), atomic pair distribution function (PDF) analysis and molecular dynamics (MD) simulations. Our SAXS analysis confirms that a wide variety of NCs (Pt, CdSe/CdS, InP, InAs, ZrO2) can be uniformly dispersed in molten salts like AlCl3/NaCl/KCl (AlCl3/AlCl4-) and NaSCN/KSCN and in ionic liquids like 1-butyl-3-methylimidazolium halides (BMIM+X-, where X = Cl, Br, I). By using a combination of PDF analysis and molecular modeling, we demonstrate that the NC surface induces a solvent restructuring with electrostatic correlations extending an order of magnitude beyond the Debye screening length. These strong oscillatory ion-ion correlations, which are not accounted by the traditional mechanisms of steric and electrostatic stabilization of colloids, offer additional insight into solvent-solute interactions and enable apparently "impossible" colloidal stabilization in highly ionized media.
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Affiliation(s)
- Vladislav Kamysbayev
- Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Vishwas Srivastava
- Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Nicholas B Ludwig
- Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Olaf J Borkiewicz
- X-ray Science Division, Advanced Photon Source , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Hao Zhang
- Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
| | - Jan Ilavsky
- X-ray Science Division, Advanced Photon Source , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Byeongdu Lee
- X-ray Science Division, Advanced Photon Source , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Karena W Chapman
- X-ray Science Division, Advanced Photon Source , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | | | - Dmitri V Talapin
- Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States
- Center for Nanoscale Materials , Argonne National Laboratory , Argonne , Illinois 60439 , United States
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33
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Bresme F, Robotham O, Chio WIK, Gonzalez MA, Kornyshev A. Debye screening, overscreening and specific adsorption in solutions of organic ions. Phys Chem Chem Phys 2018; 20:27684-27693. [PMID: 30376022 DOI: 10.1039/c8cp04924f] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Tetrabutylammonium (TBA) and tetraphenylborate (TPB) ions dissolved in dichloroethane (DCE) are widely used in electrochemistry of liquid-liquid interfaces. Unlike alkali halide solutions in water, TBA-TPB-DCE solutions feature large organic ions and a solvent with a dielectric constant almost one order of magnitude lower than that of water. This is expected to dramatically amplify the impact of ionic correlations in the properties of the solution. Here we report atomistic simulations of TBA-TPB-DCE solutions and analyze ion correlations, clustering, and charge screening effects. We target concentrations in the range of 0.01-0.25 molal (m), hence exploring concentration regimes typical for many experimental investigations. We show that the transition from monotonic to oscillatory decay of the charge density, which signals the onset of strong ion correlations, takes place in this concentration interval, leading to overscreening effects. Furthermore, we investigate the distribution and adsorption of ions at the DCE-air interface. Unlike what is observed for small inorganic ions in water at similar concentrations, we find that TPB and TBA ions accumulate near the DCE surface, resulting in significant interfacial clustering and adsorption at concentrations ∼0.25 m. TPB ions adsorb more strongly leading to free energy wells of ∼1-2 kBT. The adsorption modifies significantly the electrostatic potential of the DCE-air interface, which undergoes a shift of 0.2 V in going from pure DCE to TBA-TPB-DCE solutions at 0.25 m.
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Affiliation(s)
- Fernando Bresme
- Department of Chemistry, Imperial College London, White City Campus, 80 Wood Lane, London W12 0BZ, UK.
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34
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Ludwig NB, Dasbiswas K, Talapin DV, Vaikuntanathan S. Describing screening in dense ionic fluids with a charge-frustrated Ising model. J Chem Phys 2018; 149:164505. [DOI: 10.1063/1.5043410] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nicholas B. Ludwig
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60615, USA
| | - Kinjal Dasbiswas
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
| | - Dmitri V. Talapin
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60615, USA
| | - Suriyanarayanan Vaikuntanathan
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60615, USA
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35
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Coupette F, Lee AA, Härtel A. Screening Lengths in Ionic Fluids. PHYSICAL REVIEW LETTERS 2018; 121:075501. [PMID: 30169089 DOI: 10.1103/physrevlett.121.075501] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Indexed: 06/08/2023]
Abstract
The decay of correlations in ionic fluids is a classical problem in soft matter physics that underpins applications ranging from controlling colloidal self-assembly to batteries and supercapacitors. The conventional wisdom, based on analyzing a solvent-free electrolyte model, suggests that all correlation functions between species decay with a common decay length in the asymptotic far field limit. Nonetheless, a solvent is present in many electrolyte systems. We show using an analytical theory and molecular dynamics simulations that multiple decay lengths can coexist in the asymptotic limit as well as at intermediate distances once a hard sphere solvent is considered. Our analysis provides an explanation for the recently observed discontinuous change in the structural force across a thin film of ionic liquid-solvent mixtures as the composition is varied, as well as reframes recent debates in the literature about the screening length in concentrated electrolytes.
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Affiliation(s)
- Fabian Coupette
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Alpha A Lee
- Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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36
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Affiliation(s)
- Alpha A. Lee
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Jean-Pierre Hansen
- Department of Chemistry, University of Cambridge, Cambridge, UK
- Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX, Sorbonne Université, CNRS, Paris, France
| | - Olivier Bernard
- Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX, Sorbonne Université, CNRS, Paris, France
| | - Benjamin Rotenberg
- Physicochimie des électrolytes et nanosystèmes interfaciaux, UMR PHENIX, Sorbonne Université, CNRS, Paris, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), Amiens Cedex, France
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37
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Kjellander R. Focus Article: Oscillatory and long-range monotonic exponential decays of electrostatic interactions in ionic liquids and other electrolytes: The significance of dielectric permittivity and renormalized charges. J Chem Phys 2018; 148:193701. [DOI: 10.1063/1.5010024] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden
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38
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Rotenberg B, Bernard O, Hansen JP. Underscreening in ionic liquids: a first principles analysis. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:054005. [PMID: 29271363 DOI: 10.1088/1361-648x/aaa3ac] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these 'primitive' and 'semi-primitive' models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length [Formula: see text], which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where [Formula: see text] increases with density beyond a critical density at which the Debye length [Formula: see text] becomes comparable to the ion diameter. In this high density regime the ratio [Formula: see text] increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.
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Affiliation(s)
- Benjamin Rotenberg
- Sorbonne Université, CNRS, Physico-chimie des électrolytes et nano-systèmes interfaciaux, PHENIX, F-75005 Paris, France. Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, 80039 Amiens Cedex, France
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39
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Griffin LR, Browning KL, Clarke SM, Smith AM, Perkin S, Skoda MWA, Norman SE. Direct measurements of ionic liquid layering at a single mica-liquid interface and in nano-films between two mica-liquid interfaces. Phys Chem Chem Phys 2018; 19:297-304. [PMID: 27905590 DOI: 10.1039/c6cp05757h] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
The layering of ionic liquids close to flat, charged interfaces has been identified previously through theoretical and some experimental measurements. Here we present evidence for oscillations in ion density ('layering') in a long chain ionic liquid (1-decyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide) near the interface with mica using two complementary approaches. Neutron reflection at the ionic liquid-mica interface is used to detect structure at a single interface, and surface force balance (SFB) measurements carried out with the same ionic liquid reveal oscillatory density in the liquid confined between two mica sheets. Our findings imply the interfacial structure is not induced by confinement alone. Structural forces between two mica surfaces extend to approximately twice the distance of the density oscillations measured at a single interface and have similar period in both cases.
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Affiliation(s)
- Lucy R Griffin
- BP Institute and Department of Chemistry, University of Cambridge, Cambridge, UK.
| | - Kathryn L Browning
- BP Institute and Department of Chemistry, University of Cambridge, Cambridge, UK.
| | - Stuart M Clarke
- BP Institute and Department of Chemistry, University of Cambridge, Cambridge, UK.
| | - Alexander M Smith
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
| | - Susan Perkin
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
| | - M W A Skoda
- ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, UK
| | - Sarah E Norman
- ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, UK
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40
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Gavish N, Elad D, Yochelis A. From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory. J Phys Chem Lett 2018; 9:36-42. [PMID: 29220577 DOI: 10.1021/acs.jpclett.7b03048] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and underscreening, which all impact the emergence of fluid/solid interfaces, and the transport in these systems. Because these phenomena are not captured by existing mean-field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquid mixtures. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing a free energy that consists of short- and long-range interactions, along with an energy dissipation mechanism obtained by Onsager's relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as the interactions that are specified by the free energy. The model equations not only provide insights into transport mechanisms beyond the Stokes-Einstein-Smoluchowski relations but also enable qualitative recovery of three distinct regions in the full range of the nonmonotonic electrical screening length that has been recently observed in experiments in which organic solvent is used to dilute ionic liquids.
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Affiliation(s)
- Nir Gavish
- Department of Mathematics, Technion - IIT , Haifa 3200003, Israel
| | - Doron Elad
- Department of Mathematics, Technion - IIT , Haifa 3200003, Israel
| | - Arik Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev , Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev , Be'er Sheva 8410501, Israel
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41
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Coles S, Smith AM, Fedorov MV, Hausen F, Perkin S. Interfacial structure and structural forces in mixtures of ionic liquid with a polar solvent. Faraday Discuss 2018; 206:427-442. [DOI: 10.1039/c7fd00168a] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Oscillatory and monotonic decay in mixtures of salt and solvent at interfaces with varying surface charge.
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Affiliation(s)
- Samuel W. Coles
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
| | - Alexander M. Smith
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
- Department of Inorganic and Analytical Chemistry
| | - Maxim V. Fedorov
- Department of Physics
- Scottish Universities Physics Alliance (SUPA)
- Strathclyde University
- Glasgow G4 0NG
- UK
| | - Florian Hausen
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
- Institute of Energy and Climate Research
| | - Susan Perkin
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
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42
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Smith AM, Lee AA, Perkin S. Switching the Structural Force in Ionic Liquid-Solvent Mixtures by Varying Composition. PHYSICAL REVIEW LETTERS 2017; 118:096002. [PMID: 28306271 DOI: 10.1103/physrevlett.118.096002] [Citation(s) in RCA: 59] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2016] [Indexed: 06/06/2023]
Abstract
The structure and interactions in electrolytes at high concentration have implications from energy storage to biomolecular interactions. However, many experimental observations are yet to be explained in these mixtures, which are far beyond the regime of validity of mean-field models. Here, we study the structural forces in a mixture of ionic liquid and solvent that is miscible in all proportions at room temperature. Using the surface force balance to measure the force between macroscopic smooth surfaces across the liquid mixtures, we uncover an abrupt increase in the wavelength above a threshold ion concentration. Below the threshold concentration, the wavelength is determined by the size of the solvent molecule, whereas above the threshold, it is the diameter of a cation-anion pair that determines the wavelength.
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Affiliation(s)
- Alexander M Smith
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
- Department of Inorganic and Analytical Chemistry, University of Geneva, 1205 Geneva, Switzerland
| | - Alpha A Lee
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Susan Perkin
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
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43
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Lee AA, Perez-Martinez CS, Smith AM, Perkin S. Underscreening in concentrated electrolytes. Faraday Discuss 2017; 199:239-259. [DOI: 10.1039/c6fd00250a] [Citation(s) in RCA: 95] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Screening of a surface charge by an electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.
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Affiliation(s)
- Alpha A. Lee
- John A. Paulson School of Engineering and Applied Sciences
- Harvard University
- Cambridge
- USA
| | - Carla S. Perez-Martinez
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
| | - Alexander M. Smith
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
- Department of Inorganic and Analytical Chemistry
| | - Susan Perkin
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory
- University of Oxford
- Oxford OX1 3QZ
- UK
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44
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Goodwin ZA, Feng G, Kornyshev AA. Mean-Field Theory of Electrical Double Layer In Ionic Liquids with Account of Short-Range Correlations. Electrochim Acta 2017. [DOI: 10.1016/j.electacta.2016.12.092] [Citation(s) in RCA: 86] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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45
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Wilson M. Structure and dynamics in network-forming materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:503001. [PMID: 27779129 DOI: 10.1088/0953-8984/28/50/503001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO2, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX2 stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO2 is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO2 are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.
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Affiliation(s)
- Mark Wilson
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
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46
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Frydel D. The double-layer structure of overscreened surfaces by smeared-out ions. J Chem Phys 2016; 145:184703. [DOI: 10.1063/1.4967257] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Derek Frydel
- Institute for Advanced Study, Shenzhen University, Shenzhen,
Guangdong 518060, China
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47
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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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48
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Smith AM, Lee AA, Perkin S. The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration. J Phys Chem Lett 2016; 7:2157-2163. [PMID: 27216986 DOI: 10.1021/acs.jpclett.6b00867] [Citation(s) in RCA: 290] [Impact Index Per Article: 36.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
According to classical electrolyte theories interactions in dilute (low ion density) electrolytes decay exponentially with distance, with the Debye screening length the characteristic length scale. This decay length decreases monotonically with increasing ion concentration due to effective screening of charges over short distances. Thus, within the Debye model no long-range forces are expected in concentrated electrolytes. Here we reveal, using experimental detection of the interaction between two planar charged surfaces across a wide range of electrolytes, that beyond the dilute (Debye-Hückel) regime the screening length increases with increasing concentration. The screening lengths for all electrolytes studied-including aqueous NaCl solutions, ionic liquids diluted with propylene carbonate, and pure ionic liquids-collapse onto a single curve when scaled by the dielectric constant. This nonmonotonic variation of the screening length with concentration, and its generality across ionic liquids and aqueous salt solutions, demonstrates an important characteristic of concentrated electrolytes of substantial relevance from biology to energy storage.
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Affiliation(s)
- Alexander M Smith
- Department of Chemistry, Physical & Theoretical Chemistry Laboratory, University of Oxford , Oxford OX1 3QZ, United Kingdom
| | - Alpha A Lee
- School of Engineering and Applied Sciences, Harvard University , Cambridge, Massachusetts 02138, United States
| | - Susan Perkin
- Department of Chemistry, Physical & Theoretical Chemistry Laboratory, University of Oxford , Oxford OX1 3QZ, United Kingdom
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49
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Kjellander R. Decay behavior of screened electrostatic surface forces in ionic liquids: the vital role of non-local electrostatics. Phys Chem Chem Phys 2016; 18:18985-9000. [DOI: 10.1039/c6cp02418a] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
General theory for dense electrolytes shows why both plain exponential and oscillatory electrostatic surface forces can appear in ionic liquids.
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Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology
- University of Gothenburg
- SE-412 96 Gothenburg
- Sweden
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50
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Lee AA, Vella D, Perkin S, Goriely A. Unravelling nanoconfined films of ionic liquids. J Chem Phys 2014; 141:094904. [DOI: 10.1063/1.4893714] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alpha A. Lee
- Mathematical Institute, Andrew Wiles Building, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Dominic Vella
- Mathematical Institute, Andrew Wiles Building, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Susan Perkin
- Department of Chemistry, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Alain Goriely
- Mathematical Institute, Andrew Wiles Building, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
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