1
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Agrawal NR, Duan C, Wang R. Nature of Overcharging and Charge Inversion in Electrical Double Layers. J Phys Chem B 2024; 128:303-311. [PMID: 38150660 DOI: 10.1021/acs.jpcb.3c04739] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2023]
Abstract
Understanding overcharging and charge inversion is one of the long-standing challenges in soft matter and biophysics. To study these phenomena, we employ the modified Gaussian renormalized fluctuation theory, which allows for the self-consistent accounting of spatially varying ionic strength as well as the spatial variations in dielectric permittivity and excluded volume effects. The underlying dependence of overcharging on the electrostatic coupling is elucidated by varying the surface charge, counterion valency, and dielectric contrast. Consistent with simulations, three characteristic regimes corresponding to weak, moderate, and strong coupling are identified. Important features like the inversion of zeta potential, crowding, and ionic layering at the surface are successfully captured. For weak coupling, there is no overcharging. In the moderate coupling regime, overcharging increases with the surface charge. Finally, in the strong coupling regime, ionic crowding and saturation in overcharging are observed. Our theory predicts a nonmonotonic dependence of charge inversion on multivalent salt concentration as well as the addition of monovalent salt, in quantitative agreement with experiments.
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Affiliation(s)
- Nikhil R Agrawal
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720-1462, United States
| | - Chao Duan
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720-1462, United States
| | - Rui Wang
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720-1462, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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2
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Wu H, Liang C, Jeong J, Aluru NR. From ab initio to continuum: Linking multiple scales using deep-learned forces. J Chem Phys 2023; 159:184108. [PMID: 37947511 DOI: 10.1063/5.0166927] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2023] [Accepted: 10/18/2023] [Indexed: 11/12/2023] Open
Abstract
We develop a deep learning-based algorithm, called DeepForce, to link ab initio physics with the continuum theory to predict concentration profiles of confined water. We show that the deep-learned forces can be used to predict the structural properties of water confined in a nanochannel with quantum scale accuracy by solving the continuum theory given by Nernst-Planck equation. The DeepForce model has an excellent predictive performance with a relative error less than 7.6% not only for confined water in small channel systems (L < 6 nm) but also for confined water in large channel systems (L = 20 nm) which are computationally inaccessible through the high accuracy ab initio molecular dynamics simulations. Finally, we note that classical Molecular dynamics simulations can be inaccurate in capturing the interfacial physics of water in confinement (L < 4.0 nm) when quantum scale physics are neglected.
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Affiliation(s)
- Haiyi Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Chenxing Liang
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Jinu Jeong
- Department of Mechanical Science and Engineering, The University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - N R Aluru
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
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3
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Aluru NR, Aydin F, Bazant MZ, Blankschtein D, Brozena AH, de Souza JP, Elimelech M, Faucher S, Fourkas JT, Koman VB, Kuehne M, Kulik HJ, Li HK, Li Y, Li Z, Majumdar A, Martis J, Misra RP, Noy A, Pham TA, Qu H, Rayabharam A, Reed MA, Ritt CL, Schwegler E, Siwy Z, Strano MS, Wang Y, Yao YC, Zhan C, Zhang Z. Fluids and Electrolytes under Confinement in Single-Digit Nanopores. Chem Rev 2023; 123:2737-2831. [PMID: 36898130 PMCID: PMC10037271 DOI: 10.1021/acs.chemrev.2c00155] [Citation(s) in RCA: 18] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/12/2023]
Abstract
Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.
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Affiliation(s)
- Narayana R Aluru
- Oden Institute for Computational Engineering and Sciences, Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, 78712TexasUnited States
| | - Fikret Aydin
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
| | - Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Daniel Blankschtein
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Alexandra H Brozena
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland20742, United States
| | - J Pedro de Souza
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Menachem Elimelech
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut06520-8286, United States
| | - Samuel Faucher
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - John T Fourkas
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland20742, United States
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland20742, United States
- Maryland NanoCenter, University of Maryland, College Park, Maryland20742, United States
| | - Volodymyr B Koman
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Matthias Kuehne
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Hao-Kun Li
- Department of Mechanical Engineering, Stanford University, Stanford, California94305, United States
| | - Yuhao Li
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
| | - Zhongwu Li
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
| | - Arun Majumdar
- Department of Mechanical Engineering, Stanford University, Stanford, California94305, United States
| | - Joel Martis
- Department of Mechanical Engineering, Stanford University, Stanford, California94305, United States
| | - Rahul Prasanna Misra
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - Aleksandr Noy
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
- School of Natural Sciences, University of California Merced, Merced, California95344, United States
| | - Tuan Anh Pham
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
| | - Haoran Qu
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland20742, United States
| | - Archith Rayabharam
- Oden Institute for Computational Engineering and Sciences, Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, 78712TexasUnited States
| | - Mark A Reed
- Department of Electrical Engineering, Yale University, 15 Prospect Street, New Haven, Connecticut06520, United States
| | - Cody L Ritt
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut06520-8286, United States
| | - Eric Schwegler
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
| | - Zuzanna Siwy
- Department of Physics and Astronomy, Department of Chemistry, Department of Biomedical Engineering, University of California, Irvine, Irvine92697, United States
| | - Michael S Strano
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States
| | - YuHuang Wang
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland20742, United States
- Maryland NanoCenter, University of Maryland, College Park, Maryland20742, United States
| | - Yun-Chiao Yao
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
- School of Natural Sciences, University of California Merced, Merced, California95344, United States
| | - Cheng Zhan
- Materials Science Division, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, Livermore, California94550, United States
| | - Ze Zhang
- Department of Mechanical Engineering, Stanford University, Stanford, California94305, United States
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4
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Yu J, Shukla G, Fornari RP, Arcelus O, Shodiev A, de Silva P, Franco AA. Gaining Insight into the Electrochemical Interface Dynamics in an Organic Redox Flow Battery with a Kinetic Monte Carlo Approach. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2022; 18:e2107720. [PMID: 35841122 DOI: 10.1002/smll.202107720] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Revised: 05/20/2022] [Indexed: 06/15/2023]
Abstract
Finding low-cost and nontoxic redox couples for organic redox flow batteries is challenging due to unrevealed reaction mechanisms and side reactions. In this study, a 3D kinetic Monte Carlo model to study the electrode-anolyte interface of a methyl viologen-based organic redox flow battery is presented. This model captures various electrode processes, such as ionic displacement and degradation of active materials. The workflow consists of input parameters obtained from density functional theory calculations, a kinetic Monte Carlo algorithm to simulate the discharging process, and an electric double layer model to account for the electric field distribution near the electrode surface. Galvanostatic discharge is simulated at different anolyte concentrations and input current densities, which demonstrate that the model captured the formation of the electrical double layer due to ionic transport. The simulated electrochemical kinetics (potential, charge density) are found to be in agreement with the Nernst equation and the obtained EDL structure corresponded with published molecular dynamics results. The model's flexibility allows further applications of simulating the behavior of different redox couples and makes it possible to consider other molecular-scale phenomena. This study paves the way for computational screening of active species by assessing their potential kinetics in electrochemical environments.
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Affiliation(s)
- Jia Yu
- Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université de Picardie Jules Verne, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
| | - Garima Shukla
- Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université de Picardie Jules Verne, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
| | - Rocco Peter Fornari
- Department of Energy Conversion and Storage, Technical University of Denmark, Anker Engelunds Vej, Building 301, Kongens Lyngby, 2800, Denmark
| | - Oier Arcelus
- Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université de Picardie Jules Verne, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
| | - Abbos Shodiev
- Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université de Picardie Jules Verne, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
| | - Piotr de Silva
- Department of Energy Conversion and Storage, Technical University of Denmark, Anker Engelunds Vej, Building 301, Kongens Lyngby, 2800, Denmark
| | - Alejandro A Franco
- Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université de Picardie Jules Verne, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- ALISTORE-European Research Institute, FR CNRS 3104, Hub de l'Energie, 15 rue Baudelocque, Amiens Cedex, 80039, France
- Institut Universitaire de France, 103 Boulevard Saint Michel, Paris, 75005, France
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5
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Agrawal NR, Wang R. Electrostatic Correlation Induced Ion Condensation and Charge Inversion in Multivalent Electrolytes. J Chem Theory Comput 2022; 18:6271-6280. [PMID: 36136891 DOI: 10.1021/acs.jctc.2c00607] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The study of the electrical double layer lies at the heart of colloidal and interfacial science. The standard mean-field Poisson-Boltzmann (PB) theory is incapable of modeling many phenomena originating from ion correlation. An important example is charge inversion or overcharging of electrical double layers in multivalent electrolyte solutions. Existing theories aiming to include correlations cannot capture the non-monotonic dependence of charge inversion on salt concentration because they have not systematically accounted for the inhomogeneous nature of correlations from surface to the bulk and the excluded volume effect of ions and solvent molecules. In this work, we modify the Gaussian renormalized fluctuation theory by including the excluded volume effect to study ion condensation and charge inversion. A boundary layer approach is developed to accurately model the giant difference in ion correlations between the condensed layer near the surface and the diffuse layer outside. The theory is used to study charge inversion in multivalent electrolytes and their mixtures. We predict a surface charge induced formation of a three-dimensional condensed layer, which is necessary but not sufficient for charge inversion. The value of the effective surface potential is found to depend non-monotonically on the bulk salt concentration. Our results also show a non-monotonic reduction in charge inversion in monovalent and multivalent electrolyte mixtures. Our work is the first to qualitatively reproduce experimental and simulation observations and explains the underlying physics.
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Affiliation(s)
- Nikhil R Agrawal
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720-1462, United States
| | - Rui Wang
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720-1462, United States.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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6
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Wu H, Aluru NR. Deep learning-based quasi-continuum theory for structure of confined fluids. J Chem Phys 2022; 157:084121. [DOI: 10.1063/5.0096481] [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
Predicting the structural properties of water and simple fluids confined in nanometer scale pores and channels is essential in, for example, energy storage and biomolecular systems. Classical continuum theories fail to accurately capture the interfacial structure of fluids. In this work, we develop a deep learning-based quasi-continuum theory (DL-QT) to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid and water confined in a nano channel. The deep learning model is built based on a convolutional encoder-decoder network (CED) and is applied for high dimensional surrogate modeling to relate the fluid properties to the fluid-fluid potential. The CED model is then combined with the interatomic potential-based continuum theory to determine the concentration profiles of a confined LJ fluid and confined water. We show that the DL-QT model exhibits a robust predictive performance for a confined LJ fluid under various thermodynamic states and water confined in a nanochannel of different widths. The DL-QT model seamlessly connects the molecular physics at nanoscale with the continuum theory by using the deep learning model.
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Affiliation(s)
- Haiyi Wu
- Mechanical Engineering, The University of Texas at Austin, United States of America
| | - N. R. Aluru
- Oden Institute and Mechanical Engineering, The University of Texas at Austin, United States of America
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7
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Frank K, Bernau C, Buyel J. Spherical nanoparticles can be used as non-penetrating tracers to determine the extra-particle void volume in packed-bed chromatography columns. J Chromatogr A 2022; 1675:463174. [DOI: 10.1016/j.chroma.2022.463174] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 05/20/2022] [Accepted: 05/21/2022] [Indexed: 11/24/2022]
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8
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Rojano AE, Córdoba A, Walther JH, Zambrano HA. Effect of charge inversion on nanoconfined flow of multivalent ionic solutions. Phys Chem Chem Phys 2022; 24:4935-4943. [DOI: 10.1039/d1cp02102h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A comprehensive understanding of fluid dynamics of dilute electrolyte solutions in nanoconfinement is essential to develop more efficient nanofluidic devices. In nanoconduits, the electrical double layer can occupy a considerable...
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9
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Gillespie D, Valiskó M, Boda D. Electrostatic correlations in electrolytes: Contribution of screening ion interactions to the excess chemical potential. J Chem Phys 2021; 155:221102. [PMID: 34911314 DOI: 10.1063/5.0068521] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new theory for the electrostatic component of the chemical potential for homogeneous electrolytes modeled with the primitive model is developed. This Mean Countershell Approximation (MCSA) is an analytic theory derived by including the interactions between the ions' screening clouds. At molar concentrations, these contribute substantially to the excess chemical potential but are absent in classical Debye-Hückel and Mean Spherical Approximation (MSA) theories. Simulations show that the MCSA is highly accurate, including at the low dielectric constants of ionic liquids. While sharing a mathematical framework with the MSA, the MCSA has simpler formulas and is qualitatively more accurate when there is ion size asymmetry.
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Affiliation(s)
- Dirk Gillespie
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, Illinois 60612, USA
| | - Mónika Valiskó
- Modeling and Simulation of Complex Molecular Systems Research Group, Center for Natural Sciences, Faculty of Engineering, University of Pannonia, Veszprém, Hungary
| | - Dezső Boda
- Modeling and Simulation of Complex Molecular Systems Research Group, Center for Natural Sciences, Faculty of Engineering, University of Pannonia, Veszprém, Hungary
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10
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Fertig D, Valiskó M, Boda D. Rectification of bipolar nanopores in multivalent electrolytes: effect of charge inversion and strong ionic correlations. Phys Chem Chem Phys 2020; 22:19033-19045. [PMID: 32812580 DOI: 10.1039/d0cp03237a] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Bipolar nanopores have powerful rectification properties due to the asymmetry in the charge pattern on the wall of the nanopore. In particular, bipolar nanopores have positive and negative surface charges along the pore axis. Rectification is strong if the radius of the nanopore is small compared to the screening length of the electrolyte so that both cations and anions have depletion zones in the respective regions. The depths of these depletion zones is sensitive to sign of the external voltage. In this work, we are interested in the effect of the presence of strong ionic correlations (both between ions and between ions and surface charge) due to the presence of multivalent ions and large surface charges. We show that strong ionic correlations cause leakage of the coions, a phenomenon that is absent in mean field theories. In this modeling study, we use both the mean-field Poisson-Nernst-Planck (PNP) theory and a particle simulation method, Local Equilibrium Monte Carlo (LEMC), to show that phenomena such as overcharging and charge inversion cannot be reproduced with PNP, while LEMC is able to produce nonmonotonic dependence of currents and rectification as a function of surface charge strength.
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Affiliation(s)
- Dávid Fertig
- Department of Physical Chemistry, University of Pannonia, P. O. Box 158, H-8201 Veszprém, Hungary.
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11
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Craven GT, Lubbers N, Barros K, Tretiak S. Machine learning approaches for structural and thermodynamic properties of a Lennard-Jones fluid. J Chem Phys 2020; 153:104502. [DOI: 10.1063/5.0017894] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Galen T. Craven
- Theoretical Division and Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Nicholas Lubbers
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Kipton Barros
- Theoretical Division and Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Sergei Tretiak
- Theoretical Division, Center for Nonlinear Studies (CNLS), and Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
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12
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Voukadinova A, Gillespie D. Energetics of counterion adsorption in the electrical double layer. J Chem Phys 2019; 150:154706. [PMID: 31005115 DOI: 10.1063/1.5087835] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The energetics of the electrical double layer (EDL) is studied in a systematic way to define how different components of the chemical potential help or hinder cation adsorption at a negatively charged wall. Specifically, the steric (i.e., excluded-volume interactions), mean electrostatic, and screening (i.e., electrostatic correlations beyond the mean field) components were computed using classical density functional theory of the primitive model of ions (i.e., ions as charged, hard spheres in a background dielectric). The reduced physics of the primitive model allows for an extensive analysis over a large parameter space: cation valences +1, +2, and +3, cation diameters 0.15, 0.30, 0.60, and 0.90 nm, bulk concentrations ranging from 1 µM to 1M, and surface charges ranging from 0 to -0.50 C/m2. Our results show that all components are necessary to understand the physics of the EDL. The screening component is always significant; for small monovalent cations such as K+, it is generally much larger than the steric component, and for multivalent ions, charge inversion cannot occur without it. At moderate surface charges, the screening component makes the electrostatic potential less negative than in classical Poisson-Boltzmann theory, sometimes even positive (charge inversion). At high surface charges, this is overcome by the repulsive potential of the steric component as the first ion layer becomes extremely crowded. Large negative electrostatic potentials counteract this to draw even more cations into the first layer. Although we used an approximate model of the EDL, the physics inherent in these trends appears to be quite general.
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Affiliation(s)
- Adelina Voukadinova
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, Illinois 60612-3833, USA
| | - Dirk Gillespie
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, Illinois 60612-3833, USA
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