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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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2
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Kloes G, Bennett TJD, Chapet-Batlle A, Behjatian A, Turberfield AJ, Krishnan M. Far-Field Electrostatic Signatures of Macromolecular 3D Conformation. NANO LETTERS 2022; 22:7834-7840. [PMID: 36125326 PMCID: PMC9562458 DOI: 10.1021/acs.nanolett.2c02485] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
In solution as in vacuum, the electrostatic field distribution in the vicinity of a charged object carries information on its three-dimensional geometry. We report on an experimental study exploring the effect of molecular shape on long-range electrostatic interactions in solution. Working with DNA nanostructures carrying approximately equal amounts of total charge but each in a different three-dimensional conformation, we demonstrate that the geometry of the distribution of charge in a molecule has substantial impact on its electrical interactions. For instance, a tetrahedral structure, which is the most compact distribution of charge we tested, can create a far-field effect that is effectively identical to that of a rod-shaped molecule carrying half the amount of total structural charge. Our experiments demonstrate that escape-time electrometry (ETe) furnishes a rapid and facile method to screen and identify 3D conformations of charged biomolecules or molecular complexes in solution.
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Affiliation(s)
- Gunnar Kloes
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Timothy J. D. Bennett
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Alma Chapet-Batlle
- Clarendon
Laboratory, Department of Physics, University
of Oxford, Parks Road, Oxford OX1
3PU, United Kingdom
| | - Ali Behjatian
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Andrew J. Turberfield
- Clarendon
Laboratory, Department of Physics, University
of Oxford, Parks Road, Oxford OX1
3PU, United Kingdom
- The Kavli
Institute for Nanoscience Discovery, Sherrington Road, Oxford OX1 3QU, United Kingdom
| | - Madhavi Krishnan
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- The Kavli
Institute for Nanoscience Discovery, Sherrington Road, Oxford OX1 3QU, United Kingdom
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3
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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
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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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Kjellander R. The intimate relationship between the dielectric response and the decay of intermolecular correlations and surface forces in electrolytes. SOFT MATTER 2019; 15:5866-5895. [PMID: 31243425 DOI: 10.1039/c9sm00712a] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
A general, exact theory for the decay of interactions between any particles immersed in electrolytes, including surface forces between macroscopic bodies, is derived in a self-contained, physically transparent manner. It is valid for electrolytes at any density, including ionic gases, molten salts, ionic liquids, and electrolyte solutions with molecular solvent at any concentration. The ions, the solvent and any other particles in the system can have any sizes, any shapes and arbitrary internal charge distributions. The spatial propagation of the interactions in electrolytes has several decay modes with different decay lengths that are given by the solutions, κν, ν = 1, 2,…, to a general equation for the screening parameter κ; an equation that describes the dielectric response. There can exist simultaneous decay modes with plain exponential decay and modes with damped oscillatory exponential decay, as observed experimentally and theoretically. In the limit of zero ionic density, the decay length 1/κν of the mode with the longest range approaches the Debye length 1/κD. The coupling between fluctuations in number density and charge density, described by the density-charge correlation function HNQ(r), makes all decay modes of pair correlations and interaction free energies identical to those of the screened electrostatic potential, and hence they have the same values for the screening parameters. The density-density and charge-charge correlation functions, HNN(r) and HQQ(r), also have these decay modes. For the exceptional case of charge-inversion invariant systems, HNQ(r) is identically zero for symmetry reasons and HNN(r) and HQQ(r) have, instead, decay modes with different decay lengths.
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Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden.
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5
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Kjellander R. Focus Article: Oscillatory and long-range monotonic exponential decays of electrostatic interactions in ionic liquids and other electrolytes: The significance of dielectric permittivity and renormalized charges. J Chem Phys 2018; 148:193701. [DOI: 10.1063/1.5010024] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden
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6
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Lošdorfer BoŽič A. From discrete to continuous description of spherical surface charge distributions. SOFT MATTER 2018; 14:1149-1161. [PMID: 29345714 DOI: 10.1039/c7sm02207g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface - characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids - we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.
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Kjellander R. Nonlocal electrostatics in ionic liquids: The key to an understanding of the screening decay length and screened interactions. J Chem Phys 2016; 145:124503. [DOI: 10.1063/1.4962756] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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8
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Everts JC, van der Linden MN, van Blaaderen A, van Roij R. Alternating strings and clusters in suspensions of charged colloids. SOFT MATTER 2016; 12:6610-6620. [PMID: 27439990 DOI: 10.1039/c6sm01283c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.
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Affiliation(s)
- J C Everts
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
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Kjellander R. Decay behavior of screened electrostatic surface forces in ionic liquids: the vital role of non-local electrostatics. Phys Chem Chem Phys 2016; 18:18985-9000. [DOI: 10.1039/c6cp02418a] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
General theory for dense electrolytes shows why both plain exponential and oscillatory electrostatic surface forces can appear in ionic liquids.
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Affiliation(s)
- Roland Kjellander
- Department of Chemistry and Molecular Biology
- University of Gothenburg
- SE-412 96 Gothenburg
- Sweden
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10
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Mazars M. Yukawa potentials in systems with partial periodic boundary conditions. I. Ewald sums for quasi-two-dimensional systems. Mol Phys 2010. [DOI: 10.1080/00268970701481716] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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11
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Woodward CE, Forsman J. Depletion interaction between spheres in an ideal equilibrium polymer fluid: Exact asymptotic results. J Chem Phys 2010; 133:154902. [DOI: 10.1063/1.3494037] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Boon N, Carvajal Gallardo E, Zheng S, Eggen E, Dijkstra M, van Roij R. Screening of heterogeneous surfaces: charge renormalization of Janus particles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:104104. [PMID: 21389438 DOI: 10.1088/0953-8984/22/10/104104] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.
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Affiliation(s)
- N Boon
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
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Trizac E, El Shawish S, Dobnikar J. Dimeric and dipolar ground state orders in colloidal molecular crystals. AN ACAD BRAS CIENC 2010; 82:87-94. [DOI: 10.1590/s0001-37652010000100008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2008] [Accepted: 04/01/2009] [Indexed: 11/22/2022] Open
Abstract
A two dimensional colloidal suspension subject to a periodic substrate evolves into a colloidal molecular crystal under situationsofstrongconfinement. Wefocusonthelongrangeorientationalordertherebyemerging, inthegroundstate. We study by simulations the situations where in each trap lies a pair of identical colloids, or alternatively a pair of oppositelychargedmacroions. We consider square or triangular geometries for the periodic confinement, together with less symmetric distorted lattices.
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Arenas-Gómez BL, González-Mozuelos P. Charge renormalization of nanoparticles immersed in a molecular electrolyte. J Chem Phys 2010; 132:014903. [DOI: 10.1063/1.3285645] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Trulsson M, Forsman J, Akesson T, Jönsson B. Simulations of latex particles immersed in dendrimer solutions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2009; 25:6106-6112. [PMID: 19466775 DOI: 10.1021/la900102r] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In this work, we present Monte Carlo simulations of mixtures containing negatively charged latex particles and positively charged dendrimers. We focus on the interaction between two latex particles as salt concentration, dendrimer dose, and generation number are varied. Interaction free energies and corresponding stability ratios are calculated. Minimal stability is found near the isoelectric point, i.e., where the amount of adsorbed dendrimer charge matches the charge of the latex particles. Away from the isoelectric point, the stability increases as the latex particles get more and more under- or overcompensated, an increase that is more steep on the overcompensated side. Increasing the dendrimer generation leads to a more "patchy" surface. This heterogeneity is particularly relevant close to the isoelectric point. Given the relative simplicity of the model, the simulation results are in surprisingly good agreement with the experimental data.
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Affiliation(s)
- Martin Trulsson
- Theoretical Chemistry, Chemical Centre, Lund University, P.O. Box 124, S-221 00 Lund, Sweden.
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16
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Eggen E, Dijkstra M, van Roij R. Effective shape and phase behavior of short charged rods. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041401. [PMID: 19518227 DOI: 10.1103/physreve.79.041401] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2008] [Indexed: 05/27/2023]
Abstract
We explicitly calculate the orientation-dependent second virial coefficient of short charged rods in an electrolytic solvent, assuming the rod-rod interactions to be a pairwise sum of hard-core and segmental screened-Coulomb repulsions. From the parallel and isotropically averaged second virial coefficient, we calculate the effective length and diameter of the rods, for charges and screening lengths that vary over several orders of magnitude. Using these effective dimensions, we determine the phase diagram, where we distinguish a low-charge and strong-screening regime with a liquid crystalline nematic and smectic phase, and a high-charge and weak-screening regime with a plastic crystal phase in the phase diagram.
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Affiliation(s)
- Eelco Eggen
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
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González-Mozuelos P, de la Cruz MO. Asymmetric charge renormalization for nanoparticles in aqueous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031901. [PMID: 19391965 DOI: 10.1103/physreve.79.031901] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2008] [Revised: 01/19/2009] [Indexed: 05/27/2023]
Abstract
The effective renormalized charge of nanoparticles in an aqueous electrolyte is essential to determine their solubility. By using a molecular model for the supporting aqueous electrolyte, we find that the effective renormalized charge of the nanoparticles is strongly dependent on the sign of the bare charge. Negatively charged nanoparticles have a lower effective renormalized charge than positively charged nanoparticles. The degree of asymmetry is a nonmonotonic function of the bare charge of the nanoparticle. We show that the effect is due to the asymmetric charge distribution of the water molecules, which we model using a simple three-site molecular structure of point charges.
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Affiliation(s)
- P González-Mozuelos
- Department of Chemistry and Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
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18
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Kung W, Solis FJ, Olvera de la Cruz M. Thermodynamics of ternary electrolytes: Enhanced adsorption of macroions as minority component to liquid interfaces. J Chem Phys 2009; 130:044502. [DOI: 10.1063/1.3065071] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Kjellander R. Fundamental aspects of electrostatic interactions and charge renormalization in electrolyte systems. COLLOID JOURNAL 2007. [DOI: 10.1134/s1061933x07010048] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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