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Jiang J, Wang ZG. Improved local lattice Monte Carlo simulation for charged systems. J Chem Phys 2018; 148:114105. [DOI: 10.1063/1.5023491] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jian Jiang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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2
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Tasios N, Samin S, van Roij R, Dijkstra M. Microphase Separation in Oil-Water Mixtures Containing Hydrophilic and Hydrophobic Ions. PHYSICAL REVIEW LETTERS 2017; 119:218001. [PMID: 29219402 DOI: 10.1103/physrevlett.119.218001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Indexed: 06/07/2023]
Abstract
We develop a lattice-based Monte Carlo simulation method for charged mixtures capable of treating dielectric heterogeneities. Using this method, we study oil-water mixtures containing an antagonistic salt, with hydrophilic cations and hydrophobic anions. Our simulations reveal several phases with a spatially modulated solvent composition, in which the ions partition between water-rich and water-poor regions according to their affinity. In addition to the recently observed lamellar phase, we find tubular and droplet phases, reminiscent of those found in block copolymers and surfactant systems. Interestingly, these structures stem from ion-mediated interactions, which allows for tuning of the phase behavior via the concentrations, the ionic properties, and the temperature.
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Affiliation(s)
- Nikos Tasios
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| | - Sela Samin
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
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Girotto M, Colla T, Dos Santos AP, Levin Y. Lattice Model of an Ionic Liquid at an Electrified Interface. J Phys Chem B 2017; 121:6408-6415. [PMID: 28590756 DOI: 10.1021/acs.jpcb.7b02258] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We study ionic liquids interacting with electrified interfaces. The ionic fluid is modeled as a Coulomb lattice gas. We compare the ionic density profiles calculated using a popular modified Poisson-Boltzmann equation with the explicit Monte Carlo simulations. The modified Poisson-Boltzmann theory fails to capture the structural features of the double layer and is also unable to correctly predict the ionic density at the electrified interface. The lattice Monte Carlo simulations qualitatively capture the coarse-grained structure of the double layer in the continuum. We propose a convolution relation that semiquantitatively relates the ionic density profiles of a continuum ionic liquid and its lattice counterpart near an electrified interface.
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Affiliation(s)
- Matheus Girotto
- Instituto de Física, Universidade Federal do Rio Grande do Sul , Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS Brazil
| | - Thiago Colla
- Instituto de Física, Universidade Federal de Ouro Preto , CEP 35400-000, Ouro Preto, MG Brazil
| | - Alexandre P Dos Santos
- Instituto de Física, Universidade Federal do Rio Grande do Sul , Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul , Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS Brazil
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Duan X, Nakamura I. A new lattice Monte Carlo simulation for dielectric saturation in ion-containing liquids. SOFT MATTER 2015; 11:3566-3571. [PMID: 25807274 DOI: 10.1039/c5sm00336a] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We develop a new, rapid method for the lattice Monte Carlo simulation of ion-containing liquids that accounts for the effects of the reorganization of solvent dipoles under external electrostatic fields. Our results are in reasonable agreement with the analytical solutions to the dielectric continuum theory of Booth for single ions, ion pairs, and ionic cross-links. We also illustrate the substantial disparity between the dielectric functions for like and unlike charges on the nanometer scale. Our simulation rationalizes the experimental data for the dependence of the bulk dielectric value of water on ion concentrations in terms of saturated dipoles near ions.
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Affiliation(s)
- Xiaozheng Duan
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China.
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Laghaei R, Kowallis W, Evans DG, Coalson RD. Calculation of Iron Transport through Human H-chain Ferritin. J Phys Chem A 2014; 118:7442-53. [DOI: 10.1021/jp500198u] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Rozita Laghaei
- Department
of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - William Kowallis
- Department
of Chemistry, Carlow University, Pittsburgh, Pennsylvania 15213, United States
| | - Deborah G. Evans
- The
Nanoscience and Microsystems Program and the Department of Chemistry
and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131-0001, United States
| | - Rob D. Coalson
- Department
of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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Wei GW. Multiscale Multiphysics and Multidomain Models I: Basic Theory. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2013; 12:10.1142/S021963361341006X. [PMID: 25382892 PMCID: PMC4220694 DOI: 10.1142/s021963361341006x] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.
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Affiliation(s)
- Guo-Wei Wei
- Department of Mathematics Michigan State University, MI 48824, USA Department of Electrical and Computer Engineering Michigan State University, MI 48824, USA Department of Biochemistry and Molecular Biology Michigan State University, MI 48824, USA
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Wei GW, Zheng Q, Chen Z, Xia K. Variational multiscale models for charge transport. SIAM REVIEW. SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS 2012; 54:699-754. [PMID: 23172978 PMCID: PMC3501390 DOI: 10.1137/110845690] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.
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Affiliation(s)
- Guo-Wei Wei
- Department of Mathematics Michigan State University, MI 48824, USA
- Department of Electrical and Computer Engineering Michigan State University, MI 48824, USA
- Address correspondences to Guo-Wei Wei.
| | - Qiong Zheng
- Department of Mathematics Michigan State University, MI 48824, USA
| | - Zhan Chen
- Department of Mathematics Michigan State University, MI 48824, USA
| | - Kelin Xia
- Department of Mathematics Michigan State University, MI 48824, USA
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9
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Zheng Q, Chen D, Wei GW. Second-order Poisson Nernst-Planck solver for ion channel transport. JOURNAL OF COMPUTATIONAL PHYSICS 2011; 230:5239-5262. [PMID: 21552336 PMCID: PMC3087981 DOI: 10.1016/j.jcp.2011.03.020] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements.
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Affiliation(s)
- Qiong Zheng
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Duan Chen
- Department of Mathematics, Michigan State University, MI 48824, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, MI 48824, USA
- Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
- Please address correspondence to Guowei Wei.
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Thompson D, Rottler J. Local Monte Carlo for electrostatics in anisotropic and nonperiodic geometries. J Chem Phys 2008; 128:214102. [DOI: 10.1063/1.2918361] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Karttunen M, Rottler J, Vattulainen I, Sagui C. Chapter 2 Electrostatics in Biomolecular Simulations: Where Are We Now and Where Are We Heading? CURRENT TOPICS IN MEMBRANES 2008. [DOI: 10.1016/s1063-5823(08)00002-1] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Duncan A, Sedgewick RD. Accelerated multiboson algorithm for Coulomb gases with dynamical dielectric effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066711. [PMID: 16907027 DOI: 10.1103/physreve.73.066711] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2006] [Indexed: 05/11/2023]
Abstract
A recent reformulation [Phys. Rev. E 73, 016705 (2006)] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite-temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a spatial lattice by including additional bosonic fields. For large systems, the Monte Carlo algorithm proposed in the above-cited work becomes inefficient due to a low acceptance rate for particle moves in a fixed background multiboson field. We show here how this problem can be circumvented by use of a coupled particle-multiboson update procedure that improves acceptance rates on large lattices by orders of magnitude. The method is tested on a one-component plasma with neutral dielectric particles for a variety of system sizes.
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Affiliation(s)
- A Duncan
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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Duncan A, Sedgewick RD, Coalson RD. Local simulation algorithms for Coulomb gases with dynamical dielectric effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:016705. [PMID: 16486312 DOI: 10.1103/physreve.73.016705] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2005] [Indexed: 05/06/2023]
Abstract
We discuss the application of the local lattice technique of Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)] to problems that involve the motion of objects with different dielectric constants than the background. In these systems, the simulation method produces a spurious interaction force which causes the particles to move in an unphysical manner. We show that this term can be removed using a variant of a method known from high-energy physics simulations, the multiboson method, and demonstrate the effectiveness of this corrective method on a system of neutral particles. We then apply our method to a one-component plasma to show the effect of the spurious interaction term on a charged system.
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Affiliation(s)
- A Duncan
- Department of Physics and Astronomy University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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Maggs AC. Monte Carlo simulation of a model of water. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:040201. [PMID: 16383351 DOI: 10.1103/physreve.72.040201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2005] [Indexed: 05/05/2023]
Abstract
We simulate TIP3P water using a constrained Monte Carlo algorithm to generate electrostatic interactions eliminating the need to sum over long-ranged Coulomb interactions. We study discretization errors when interpolating charges using splines and Gaussians. We compare our implementation to molecular dynamics and Brownian dynamics codes.
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Affiliation(s)
- A C Maggs
- Laboratoire de Physico-Chime Théorique, UMR CNRS-ESPCI 7083, 10 rue Vauquelin, 75231 Paris Cedex 05, France
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Levrel L, Maggs AC. Monte Carlo algorithms for charged lattice gases. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:016715. [PMID: 16090142 DOI: 10.1103/physreve.72.016715] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2005] [Indexed: 05/03/2023]
Abstract
We consider Monte Carlo algorithms for the simulation of charged lattice gases with purely local dynamics. We study the mobility of particles as a function of temperature and show that the poor mobility of particles at low temperatures is due to "trails" or "strings" left behind after particle motion. We introduce modified updates which substantially improve the efficiency of the algorithm in this regime.
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Affiliation(s)
- L Levrel
- Laboratoire de Physico-Chimie Théorique, UMR CNRS-ESPCI 7083, 10 rue Vauquelin, F-75231 Paris Cedex 05, France
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