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 DOI: 10.1021/acs.jpclett.4c01829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [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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Travesset A. Nonlinear Poisson-Boltzmann solutions for charged parallel plates: When opposite charges repel. J Chem Phys 2024; 161:054903. [PMID: 39087898 DOI: 10.1063/5.0221826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2024] [Accepted: 07/12/2024] [Indexed: 08/02/2024] Open
Abstract
I present an exact solution of the Poisson-Boltzmann equation for two parallel plates and discuss the solution properties. I discuss in more detail plates with opposite charges: In this case, there are two critical separations, Lc,1 < Lc,2. For separations less than Lc,1, the force between plates is repulsive. It switches to attractive at Lc,1, but with the electric potential having the same sign on both plates. For L > Lc,2, the force remains attractive, and the potential at the plates has the same sign as the charge on each plate. I also describe charge regulation, determined by pKa, and provide formulas for both the critical distance where oppositely charged plates repel and their charging process. The implications of these results for the nanoparticle assembly, as driven by electrostatic interactions, are also discussed.
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Affiliation(s)
- Alex Travesset
- Department of Physics and Astronomy, Iowa State University and Ames Lab, Ames, Iowa 50011, USA
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3
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Berlinger SA, Küpers V, Dudenas PJ, Schinski D, Flagg L, Lamberty ZD, McCloskey BD, Winter M, Frechette J. Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer. Proc Natl Acad Sci U S A 2024; 121:e2404669121. [PMID: 39047037 PMCID: PMC11295052 DOI: 10.1073/pnas.2404669121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 06/20/2024] [Indexed: 07/27/2024] Open
Abstract
Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI)2], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI)2], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.
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Affiliation(s)
- Sarah A. Berlinger
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
| | - Verena Küpers
- Münster Electrochemical Energy Technology, University of Münster, Münster48149, Germany
| | - Peter J. Dudenas
- Polymer Processing Group, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD20899
| | - Devin Schinski
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
| | - Lucas Flagg
- Polymer Processing Group, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD20899
| | - Zachary D. Lamberty
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
| | - Bryan D. McCloskey
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
- Energy Storage and Distributed Resources Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
| | - Martin Winter
- Münster Electrochemical Energy Technology, University of Münster, Münster48149, Germany
- Helmholtz-Institute Münster Ionics in Energy Storage, Münster48149, Germany
| | - Joelle Frechette
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA94720
- Energy Storage and Distributed Resources Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
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4
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Forsman J, Ribar D, Woodward CE. An efficient method to establish electrostatic screening lengths of restricted primitive model electrolytes. Phys Chem Chem Phys 2024; 26:19921-19933. [PMID: 38990567 DOI: 10.1039/d4cp00546e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/12/2024]
Abstract
We present a novel, and computationally cheap, way to estimate electrostatic screening lengths from simulations of restricted primitive model (RPM) electrolytes. We demonstrate that the method is accurate by comparisons with simulated long-ranged parts of the charge density, at various Bjerrum lengths, salt concentrations and ion diameters. We find substantial underscreening in low dielectric solvent, but with an "aqueous" solvent, there is instead overscreening, the degree of which increases with ion size. Our method also offers a possible path to (future) more accurate classical density functional treatments of ionic fluids.
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Affiliation(s)
- Jan Forsman
- Computational Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden.
| | - 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
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5
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Buyukdagli S. Systematic Incorporation of Ionic Hard-Core Size into the Debye-Hückel Theory via the Cumulant Expansion of the Schwinger-Dyson Equations. J Chem Theory Comput 2024; 20:2729-2739. [PMID: 38518257 DOI: 10.1021/acs.jctc.4c00011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/24/2024]
Abstract
The Debye-Hückel (DH) formalism of bulk electrolytes equivalent to the Gaussian-level closure of the electrostatic Schwinger-Dyson identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By comparing the monovalent ion activity and pressure predictions of our cumulant-corrected DH (CCDH) theory with hypernetted-chain results and Monte Carlo simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar to molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that, via the adjustment of the hydrated ion radii, CCDH formalism can equally reproduce the nonuniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.
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6
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Yang J, Papaderakis AA, Roh JS, Keerthi A, Adams RW, Bissett MA, Radha B, Dryfe RAW. Measuring the Capacitance of Carbon in Ionic Liquids: From Graphite to Graphene. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2024; 128:3674-3684. [PMID: 38476828 PMCID: PMC10926162 DOI: 10.1021/acs.jpcc.3c08269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Revised: 02/01/2024] [Accepted: 02/01/2024] [Indexed: 03/14/2024]
Abstract
The physical electrochemistry of the carbon/ionic liquids interface underpins the processes occurring in a vast range of applications spanning electrochemical energy storage, iontronic devices, and lubrication. Elucidating the charge storage mechanisms at the carbon/electrolyte interface will lead to a better understanding of the operational principles of such systems. Herein, we probe the charge stored at the electrochemical double layer formed between model carbon systems, ranging from single-layer graphene to graphite and the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI). The effect of the number of graphene layers on the overall capacitance of the interface is investigated. We demonstrate that in pure EMIM-TFSI and at moderate potential biases, the electronic properties of graphene and graphite govern the overall capacitance of the interface, while the electrolyte contribution to the latter is less significant. In mixtures of EMIM-TFSI with solvents of varying relative permittivity, the complex interplay between electrolyte ions and solvent molecules is shown to influence the charge stored at the interface, which under certain conditions overcomes the effects of relative permittivity. This work provides additional experimental insights into the continuously advancing topic of electrochemical double-layer structure at the interface between room temperature ionic liquids and carbon materials.
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Affiliation(s)
- Jing Yang
- Department
of Chemistry and Henry Royce Institute, The University of Manchester, Oxford Road, M13
9PL Manchester, U.K.
| | - Athanasios A. Papaderakis
- Department
of Chemistry and Henry Royce Institute, The University of Manchester, Oxford Road, M13
9PL Manchester, U.K.
| | - Ji Soo Roh
- Department
of Materials, The University of Manchester, Oxford Road, M13 9PL Manchester, U.K.
- National
Graphene Institute, The University of Manchester, Oxford Road, M13 9PL Manchester, U.K.
| | - Ashok Keerthi
- Department
of Chemistry and Henry Royce Institute, The University of Manchester, Oxford Road, M13
9PL Manchester, U.K.
- National
Graphene Institute, The University of Manchester, Oxford Road, M13 9PL Manchester, U.K.
| | - Ralph W. Adams
- Department
of Chemistry and Henry Royce Institute, The University of Manchester, Oxford Road, M13
9PL Manchester, U.K.
| | - Mark A. Bissett
- Department
of Materials, The University of Manchester, Oxford Road, M13 9PL Manchester, U.K.
- National
Graphene Institute, The University of Manchester, Oxford Road, M13 9PL Manchester, U.K.
| | - Boya Radha
- Department
of Physics and Astronomy, The University
of Manchester, Oxford
Road, M13 9PL Manchester, U.K.
| | - Robert A. W. Dryfe
- Department
of Chemistry and Henry Royce Institute, The University of Manchester, Oxford Road, M13
9PL Manchester, U.K.
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7
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Xiao T, Zhou Y, Li B. Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions. J Phys Chem B 2024; 128:1029-1039. [PMID: 38235680 DOI: 10.1021/acs.jpcb.3c07233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.
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Affiliation(s)
- Tiejun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
| | - Yun Zhou
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
| | - Bo Li
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
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8
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Xiao T, Song X. A Gaussian field approach to the solvation of spherical ions in electrolyte solutions. J Chem Phys 2024; 160:034102. [PMID: 38226821 DOI: 10.1063/5.0187141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2023] [Accepted: 12/25/2023] [Indexed: 01/17/2024] Open
Abstract
In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.
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Affiliation(s)
- Tiejun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang People's Republic of China
| | - Xueyu Song
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
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9
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Kumari S, Podgornik R. On the nature of screening in charge-regulated macroion solutions. J Chem Phys 2024; 160:014905. [PMID: 38180260 DOI: 10.1063/5.0187324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 12/14/2023] [Indexed: 01/06/2024] Open
Abstract
We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the "uncertainty relation" of the Legendre transform, which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler-Guggenheim-Frumkin model of charge regulation, we then analyze the "screening resonance" and the "overscreening" of the screening properties of the charge-regulated macroion solution.
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Affiliation(s)
- Sunita Kumari
- Department of Physics, Indian Institute of Technology, Jodhpur 342037, India
| | - Rudolf Podgornik
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
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10
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Srinivasa MK, Lee J, Hyun K, Yoo HD. Modifying Kohlrausch's Law to Describe Nonaqueous Electrolytes for Lithium-Ion Batteries. ACS APPLIED MATERIALS & INTERFACES 2023; 15:59296-59308. [PMID: 38088367 DOI: 10.1021/acsami.3c09396] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2023]
Abstract
To develop next-generation lithium-ion batteries with enhanced stability and safety, it is crucial to understand the physicochemical principles of nonaqueous electrolytes. Kohlrausch's law describes a linear decrease in the molar conductivity (Λ) with respect to the square root of the molarity of strong electrolytes at lower concentrations. This empirical law explains the impeded ionic mobility at higher concentrations due to ionic interactions, i.e., relaxation and asymmetric effects. However, this law does not hold at higher concentrations due to the ionic association that alleviates the ionic interactions and retards the decrease in the Λ. Especially, the anomalously stagnant decrease in the Λ near the solubility limit has not been clearly explained, calling for the consideration of other concentration-dependent factors such as the mean activity coefficient (γ±), viscosity (η), and dielectric constant (ε). Herein, we develop a systematic method to modify Kohlrausch's law. First, we install the ionic association constant, and the theoretical estimation is compared with the experimental results to induce the correction function that is related with the previously neglected concentration-dependent factors. Thus, the induced correction function was close to the rectified linear unit (ReLU) function, which has been widely used in the field of artificial intelligence. The modified Kohlrausch's law with the ReLU-type correction function provides a highly precise and reliable data fitting, and the fitted parameters showed clear concentration dependency and straightforward interpretability. As a result, this method effectively generalized Kohlrausch's law for nonaqueous electrolytes at higher concentrations up to the solubility limit of 3.0-3.5 M. Moreover, the modified Kohlrausch's law inspired us to discover the physical origins of the anomalously stagnant Λ profiles near the solubility limit; and the most relevant physical origin of the anomaly was the concentration dependency of the γ± and η, which grow exponentially above a critical concentration.
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Affiliation(s)
- Madhusudana Koratikere Srinivasa
- Department of Chemistry and Chemical Institute for Functional Materials, Pusan National University, Busan 46241, Republic of Korea
| | - Jeonghyeon Lee
- School of Chemical and Biomolecular Engineering, Pusan National University, Busan 46241, Republic of Korea
| | - Kyu Hyun
- School of Chemical and Biomolecular Engineering, Pusan National University, Busan 46241, Republic of Korea
| | - Hyun Deog Yoo
- Department of Chemistry and Chemical Institute for Functional Materials, Pusan National University, Busan 46241, Republic of Korea
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11
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Ruixuan H, Majee A, Dobnikar J, Podgornik R. Electrostatic interactions between charge regulated spherical macroions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:115. [PMID: 38019363 DOI: 10.1140/epje/s10189-023-00373-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 10/20/2023] [Indexed: 11/30/2023]
Abstract
We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.
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Affiliation(s)
- Hu Ruixuan
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Arghya Majee
- Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany
| | - Jure Dobnikar
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang, China
- Songshan Lake Materials Laboratory, Guangdong, 523808, Dongguan, China
| | - Rudolf Podgornik
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, 325011, Zhejiang, China.
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
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12
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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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13
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Chowdhury A, Borgia A, Ghosh S, Sottini A, Mitra S, Eapen RS, Borgia MB, Yang T, Galvanetto N, Ivanović MT, Łukijańczuk P, Zhu R, Nettels D, Kundagrami A, Schuler B. Driving forces of the complex formation between highly charged disordered proteins. Proc Natl Acad Sci U S A 2023; 120:e2304036120. [PMID: 37796987 PMCID: PMC10576128 DOI: 10.1073/pnas.2304036120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 08/22/2023] [Indexed: 10/07/2023] Open
Abstract
Highly disordered complexes between oppositely charged intrinsically disordered proteins present a new paradigm of biomolecular interactions. Here, we investigate the driving forces of such interactions for the example of the highly positively charged linker histone H1 and its highly negatively charged chaperone, prothymosin α (ProTα). Temperature-dependent single-molecule Förster resonance energy transfer (FRET) experiments and isothermal titration calorimetry reveal ProTα-H1 binding to be enthalpically unfavorable, and salt-dependent affinity measurements suggest counterion release entropy to be an important thermodynamic driving force. Using single-molecule FRET, we also identify ternary complexes between ProTα and H1 in addition to the heterodimer at equilibrium and show how they contribute to the thermodynamics observed in ensemble experiments. Finally, we explain the observed thermodynamics quantitatively with a mean-field polyelectrolyte theory that treats counterion release explicitly. ProTα-H1 complex formation resembles the interactions between synthetic polyelectrolytes, and the underlying principles are likely to be of broad relevance for interactions between charged biomolecules in general.
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Affiliation(s)
- Aritra Chowdhury
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Alessandro Borgia
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Souradeep Ghosh
- Department of Physical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research Kolkata, Mohanpur741246, India
| | - Andrea Sottini
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Soumik Mitra
- Department of Physical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research Kolkata, Mohanpur741246, India
| | - Rohan S. Eapen
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | | | - Tianjin Yang
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Nicola Galvanetto
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
- Department of Physics, University of Zurich, Zurich8057, Switzerland
| | - Miloš T. Ivanović
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Paweł Łukijańczuk
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Ruijing Zhu
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Daniel Nettels
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
| | - Arindam Kundagrami
- Department of Physical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research Kolkata, Mohanpur741246, India
| | - Benjamin Schuler
- Department of Biochemistry, University of Zurich, Zurich8057, Switzerland
- Department of Physics, University of Zurich, Zurich8057, Switzerland
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14
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Xiao T, Song X. A Gaussian field approach to the planar electric double layer structures in electrolyte solutions. J Chem Phys 2023; 158:2887562. [PMID: 37125713 DOI: 10.1063/5.0138568] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 04/17/2023] [Indexed: 05/02/2023] Open
Abstract
In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.
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Affiliation(s)
- Tiejun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
| | - Xueyu Song
- Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
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15
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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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16
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Tong J, Peng B, Kontogeorgis GM, Liang X. Behavior of the aqueous sodium chloride solutions from molecular simulations and theories. J Mol Liq 2023. [DOI: 10.1016/j.molliq.2022.121086] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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17
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On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Theory of charge asymmetric electrolytes. Onsager’s approach revisited. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120163] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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19
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Bespalova M, Behjatian A, Karedla N, Walker-Gibbons R, Krishnan M. Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule–Solvent Interface. Macromolecules 2022; 55:6200-6210. [PMID: 35910310 PMCID: PMC9330769 DOI: 10.1021/acs.macromol.2c00657] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
A DNA molecule is
highly electrically charged in solution. The
electrical potential at the molecular surface is known to vary strongly
with the local geometry of the double helix and plays a pivotal role
in DNA–protein interactions. Further out from the molecular
surface, the electrical field propagating into the surrounding electrolyte
bears fingerprints of the three-dimensional arrangement of the charged
atoms in the molecule. However, precise extraction of the structural
information encoded in the electrostatic “far field”
has remained experimentally challenging. Here, we report an optical
microscopy-based approach that detects the field distribution surrounding
a charged molecule in solution, revealing geometric features such
as the radius and the average rise per basepair of the double helix
with up to sub-Angstrom precision, comparable with traditional molecular
structure determination techniques like X-ray crystallography and
nuclear magnetic resonance. Moreover, measurement of the helical radius
furnishes an unprecedented view of both hydration and the arrangement
of cations at the molecule–solvent interface. We demonstrate
that a probe in the electrostatic far field delivers structural and
chemical information on macromolecules, opening up a new dimension
in the study of charged molecules and interfaces in solution.
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Affiliation(s)
- Maria Bespalova
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K
| | - Ali Behjatian
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K
| | - Narain Karedla
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K
| | - Rowan Walker-Gibbons
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K
| | - Madhavi Krishnan
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K
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20
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Kumari S, Dwivedi S, Podgornik R. On the nature of screening in Voorn–Overbeek type theories. J Chem Phys 2022; 156:244901. [DOI: 10.1063/5.0091721] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By using a recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn–Overbeek-type theories, which remains valid also in the cases where the entropy of the charged component(s) is not given by the ideal gas form as in the Debye–Hückel theory. The screening length consistent with the non-electrostatic terms in the free energy ansatz for the Flory–Huggins and Voorn–Overbeek type theories, derived from the local curvature properties of the Legendre transform, has distinctly different behavior than the often invoked standard Debye screening length, though it reduces to it in some special cases.
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Affiliation(s)
- Sunita Kumari
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shikha Dwivedi
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Rudolf Podgornik
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
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21
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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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22
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Gregory KP, Elliott GR, Robertson H, Kumar A, Wanless EJ, Webber GB, Craig VSJ, Andersson GG, Page AJ. Understanding specific ion effects and the Hofmeister series. Phys Chem Chem Phys 2022; 24:12682-12718. [PMID: 35543205 DOI: 10.1039/d2cp00847e] [Citation(s) in RCA: 87] [Impact Index Per Article: 43.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Specific ion effects (SIE), encompassing the Hofmeister Series, have been known for more than 130 years since Hofmeister and Lewith's foundational work. SIEs are ubiquitous and are observed across the medical, biological, chemical and industrial sciences. Nevertheless, no general predictive theory has yet been able to explain ion specificity across these fields; it remains impossible to predict when, how, and to what magnitude, a SIE will be observed. In part, this is due to the complexity of real systems in which ions, counterions, solvents and cosolutes all play varying roles, which give rise to anomalies and reversals in anticipated SIEs. Herein we review the historical explanations for SIE in water and the key ion properties that have been attributed to them. Systems where the Hofmeister series is perturbed or reversed are explored, as is the behaviour of ions at the liquid-vapour interface. We discuss SIEs in mixed electrolytes, nonaqueous solvents, and in highly concentrated electrolyte solutions - exciting frontiers in this field with particular relevance to biological and electrochemical applications. We conclude the perspective by summarising the challenges and opportunities facing this SIE research that highlight potential pathways towards a general predictive theory of SIE.
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Affiliation(s)
- Kasimir P Gregory
- Discipline of Chemistry, School of Environmental and Life Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia. .,Department of Materials Physics, Research School of Physics, Australian National University, Canberra, ACT 0200, Australia
| | - Gareth R Elliott
- Discipline of Chemistry, School of Environmental and Life Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia.
| | - Hayden Robertson
- Discipline of Chemistry, School of Environmental and Life Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia.
| | - Anand Kumar
- Flinders Institute of Nanoscale Science and Technology, College of Science and Engineering, Flinders University, South Australia 5001, Australia
| | - Erica J Wanless
- Discipline of Chemistry, School of Environmental and Life Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia.
| | - Grant B Webber
- School of Engineering, The University of Newcastle, Callaghan, New South Wales 2308, Australia
| | - Vincent S J Craig
- Department of Materials Physics, Research School of Physics, Australian National University, Canberra, ACT 0200, Australia
| | - Gunther G Andersson
- Flinders Institute of Nanoscale Science and Technology, College of Science and Engineering, Flinders University, South Australia 5001, Australia
| | - Alister J Page
- Discipline of Chemistry, School of Environmental and Life Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia.
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23
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Silva GM, Liang X, Kontogeorgis GM. Investigation of the Limits of the Linearized Poisson-Boltzmann Equation. J Phys Chem B 2022; 126:4112-4131. [PMID: 35623090 DOI: 10.1021/acs.jpcb.2c02758] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
This work presents a comparison between a numerical solution of the Poisson-Boltzmann equation and the analytical solution of its linearized version through the Debye-Hückel equations considering both size-dissimilar and common ion diameters approaches. In order to verify the limits in which the linearized Poisson-Boltzmann equation is capable to satisfactorily reproduce the nonlinear version of Poisson-Boltzmann, we calculate mean ionic activity coefficients for different types of electrolytes as various temperatures. The divergence between the linearized and full Poisson-Boltzmann equations is higher for lower molalities, and both solutions tend to converge toward higher molalities. For electrolytes of lower valencies (1:1, 1:2, 2:1, and 1:3) and higher distances of closest approach, the full version of the Debye-Hückel equation is capable of representing the activity coefficients with a low divergence from the nonlinear Poisson-Boltzmann. The size-dissimilar full version of Debye-Hückel represents a clear improvement over the extended version that uses only common ion diameters when compared to the numerical solution of the Poisson-Boltzmann equation. We have derived a salt-specific index (Θ) to gradually classify electrolytes in order of increasing influence of nonlinear ion-ion interactions, which differentiate the Debye-Hückel equations from the nonlinear Poisson-Boltzmann equation.
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Affiliation(s)
- Gabriel M Silva
- Center for Energy Resources Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Xiaodong Liang
- Center for Energy Resources Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Georgios M Kontogeorgis
- Center for Energy Resources Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
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24
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Bültmann M, Härtel A. The primitive model in classical density functional theory: beyond the standard mean-field approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:235101. [PMID: 35294927 DOI: 10.1088/1361-648x/ac5e7a] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 03/16/2022] [Indexed: 06/14/2023]
Abstract
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory (DFT) the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation of the pair potential for an uncharged reference system of hard spheres. This mean-field electrostatic term particularly contributes at particle separations that are forbidden due to hard-core overlap. In this work we modify the mean-field contribution such that the pair potential is constant for distances smaller than the contact distance of the ions. We motivate our modification by the underlying splitting of the potential, which is similar to the splitting of the Weeks-Chandler-Andersen potential and leads to higher-order terms in the respective expansion of the functional around the reference system. The resulting formalism involves weighted densities similar to the ones found in fundamental measure theory. To test our modifications, we analyze and compare density profiles, direct and total correlation functions, and the thermodynamic consistency of the functional via a widely established sum rule and the virial pressure formula for our modified functional, for established functionals, and for data from computer simulations. We found that our modifications clearly show improvements compared to the standard mean-field functional, especially when predicting layering effects and direct correlation functions in high concentration scenarios; for the latter we also find improved consistency when calculated via different thermodynamic routes. In conclusion, we demonstrate how modifications toward higher order corrections beyond mean-field functionals can be made and how they perform, by this providing a basis for systematic future improvements in classical DFT for the description of electrostatic interactions.
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Affiliation(s)
- Moritz Bültmann
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
| | - Andreas Härtel
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
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25
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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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26
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Nandy M, Lahiri BB, Philip J. Inter-droplet force between magnetically polarizable Pickering oil-in-water nanoemulsions stabilized with γ-Al 2O 3 nanoparticles: Role of electrostatic and electric dipolar interactions. J Colloid Interface Sci 2021; 607:1671-1686. [PMID: 34592554 DOI: 10.1016/j.jcis.2021.09.025] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Revised: 09/03/2021] [Accepted: 09/04/2021] [Indexed: 12/30/2022]
Abstract
HYPOTHESIS The presence of nanoparticles at oil-water interface influences the interaction forces between Pickering emulsions. When charged nanoparticles are at the oil-water interface of an electrostatically stabilized emulsion, in addition to the screened Coulombic interaction, electric dipolar force also influences the total inter-droplet force profiles. An in-depth understanding of the effects of such electric dipolar forces is essential for designing colloidally stable Pickering nanoemulsions for various applications. EXPERIMENTS Inter-droplet forces between γ-Al2O3 nanoparticle stabilized oil-in-water nanoemulsion, containing superparamagnetic nanoparticles (magnetically polarizable) in the oil phase, are measured using the magnetic-chaining technique at different pH and salt concentrations. The role of mono-, di- and tri-valent salts on the inter-droplet force profiles are assessed. FINDINGS Force measurement studies reveal a lowering of inter-droplet spacing, within the linear chains, for higher salt concentrations due to an increased screening. Strong interfacial attachment of the charged nanoparticles results in the formation of an asymmetric charge cloud leading to an electric dipolar interaction. Incorporating the contributions of electric dipolar and screened Coulombic interactions, the theoretically estimated total repulsive force magnitudes are in good agreement with the experimental data. The obtained results offer better insights into the nature of colloidal force between charged particle stabilized nanoemulsions.
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Affiliation(s)
- Manali Nandy
- Smart Materials Section, Corrosion Science and Technology Division, Materials Characterization Group, Metallurgy and Materials Group, HBNI, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603102, India
| | - B B Lahiri
- Smart Materials Section, Corrosion Science and Technology Division, Materials Characterization Group, Metallurgy and Materials Group, HBNI, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603102, India.
| | - John Philip
- Smart Materials Section, Corrosion Science and Technology Division, Materials Characterization Group, Metallurgy and Materials Group, HBNI, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu 603102, India
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27
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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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28
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Xiao T, Zhou Y. A nonlocal electrostatics model for ions in concentrated primitive electrolyte solutions. Electrochim Acta 2021. [DOI: 10.1016/j.electacta.2021.139040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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29
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Xiao T, Zhou Y. Fast Calculation of Electrostatic Solvation Free Energy in Simple Ionic Fluids Using an Energy-Scaled Debye-Hückel Theory. J Phys Chem Lett 2021; 12:6262-6268. [PMID: 34197123 DOI: 10.1021/acs.jpclett.1c01643] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Continuum theories are useful to compute the solvation free energy in ionic fluids. Herein, the electrostatic solvation free energy (ESFE) in simple ionic fluids is studied with an energy-scaled Debye-Hückel (ESDH) theory. Given the ESFEs of simple spherical ions as input, the ESDH theory is applicable to molecules with various complex geometries and charge distributions. Specifically, the ESDH theory is applied to molecules in a molten salt system, where the predicted ESFEs are in good agreement with molecular dynamics simulation results. Our study sheds light on accurately predicting the ESFE in ionic fluids with phenomenological continuum theories.
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Affiliation(s)
- Tiejun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
| | - Yun Zhou
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
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30
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Outhwaite CW, Bhuiyan LB. On the modified Poisson-Boltzmann closure for primitive model electrolytes at high concentration. J Chem Phys 2021; 155:014504. [PMID: 34241386 DOI: 10.1063/5.0054203] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The modified Poisson-Boltzmann closure is applied to the Kirkwood hierarchy of integral equations to investigate high concentration primitive model electrolytes. Two approximations are considered in the two sphere fluctuation potential problem. The derived damped oscillatory mean electrostatic potentials suggest that this closure should be of use in providing a basis for understanding the large experimental decay lengths found at high electrolyte concentrations.
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Affiliation(s)
- Christopher W Outhwaite
- Department of Applied Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - Lutful Bari Bhuiyan
- Laboratory of Theoretical Physics, Department of Physics, University of Puerto Rico, 17 Avenida Universidad, STE 1701, San Juan, Puerto Rico 00925-2537, USA
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31
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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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32
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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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Xiao T, Song X. A Systematic Way to Extend the Debye-Hückel Theory beyond Dilute Electrolyte Solutions. J Phys Chem A 2021; 125:2173-2183. [PMID: 33661015 DOI: 10.1021/acs.jpca.0c10226] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An extended Debye-Hückel theory with fourth order gradient term is developed for electrolyte solutions; namely, the electric potential φ(r) of the bulk electrolyte solution can be described by ∇2φ(r) = κ2φ(r) + LQ2∇4φ(r), where the parameters κ and LQ are chosen to reproduce the first two roots of the dielectric response function of the bulk solution. Three boundary conditions for solving the electric potential problem are proposed based upon the continuity conditions of involving functions at the dielectric boundary, with which a boundary element method for the electric potential of a solute with a general geometrical shape and charge distribution is derived. Solutions for the electric potential of a spherical ion and a diatomic molecule are found and used to calculate their electrostatic solvation energies. The validity of the theory is successfully demonstrated when applied to binary as well as multicomponent primitive models of electrolyte solutions.
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Affiliation(s)
- Tiejun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, People's Republic of China
| | - Xueyu Song
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011, United States
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On the analogy between the restricted primitive model and capacitor circuits: Semi-empirical alternatives for over- and underscreening in the calculation of mean ionic activity coefficients. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2020.115204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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