Monte Carlo algorithms for charged lattice gases

Levrel, Lucas; Maggs, A. C.

doi:10.1103/physreve.72.016715

Cited by 17 publications

(17 citation statements)

References 21 publications

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“…10 Interested readers are encouraged to consult this original reference and additional references for further development and improvement of the method. 11,12,18 Because our model is the rst application to polymers, we reproduce some of the key steps in the derivation. We start with the electrostatic energy functional in the form of…”

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confidence: 99%

“…For computational efficiency, we adopt a lattice formulation by combining the bond uctuation model (BFM), 7,8 a standard lattice Monte Carlo method for polymers, 9 with a local algorithm developed by Maggs et al [10][11][12] for computing the electrostatic interactions. This algorithm requires a computational effort of order N, 10 and can be directly implemented on a lattice, making it naturally compatible with lattice models of polymers.…”

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confidence: 99%

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Effects of dielectric inhomogeneity in polyelectrolyte solutions

Nakamura

Wang

2013

Soft Matter

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We illustrate the effects of dielectric inhomogeneity on the statistical Polyelectrolytes in solution form an important class of macromolecules that are essential in biology and colloidal science, and have been the subject of intensive theoretical and experimental investigations; see ref. 1 for an extensive review of the issues and relevant literature.The standard model for polyelectrolytes in solution typically assumes some chain models for the polymer, such as the beadspring model, 2 lattice model 3 or Gaussian thread model, 4 in implicit solvents. The charges are taken to interact with Coulomb potential in a dielectric medium, with a uniform dielectric constant of the solvent. Some studies account for the solvent explicitly by treating the solvent molecules as LennardJones particles, 5 but the electrostatic interactions are still included at the level of dielectric continuum with a uniform dielectric constant. In reality, however, the typically hydrophobic polymer backbone can have a very different dielectric response than the solvent, which will alter the electrostatic interactions between the charges in the vicinity of the polymer. While the use of a uniform dielectric constant of the solvent can be rationalized when the segmental concentration of the polymer is low, as in the case of dilute, good-solvent conditions, it can no longer be justied when the polymer concentration becomes high. The latter can correspond either to a concentrated bulk solution, or to a single polymer in or near a collapsed or partially collapsed state. Even under dilute, goodsolvent conditions, the degree of charge condensation can be affected by the local dielectric response of the polymer backbone. 6In this communication, we demonstrate the importance of including the dielectric inhomogeneity in modeling polyelectrolytes in solution by considering a single polyelectrolyte chain in solvent with no added salt. The decrease of the local dielectric response in the vicinity of the polymer leads to two effects: rst, it alters (strengthens) the Coulomb interactions between the charged species, and second, it expels the counterions from the polymer-rich regions due to the unfavorable solvation energy. The combination of these two effects substantially inuences the chain conformation and degree of charge condensation. For example, we show that upon decreasing the dielectric constant of the polymer backbone from that of the solvent, a collapsed polyelectrolyte chain can turn into the coil state.For computational efficiency, we adopt a lattice formulation by combining the bond uctuation model (BFM), 7,8 a standard lattice Monte Carlo method for polymers, 9 with a local algorithm developed by Maggs et al.10-12 for computing the electrostatic interactions. This algorithm requires a computational effort of order N, 10 and can be directly implemented on a lattice, making it naturally compatible with lattice models of polymers. Furthermore, the dielectric difference between the polymer and the solvent can be easily incorporated. Thus, the la...

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confidence: 99%

Effects of dielectric inhomogeneity in polyelectrolyte solutions

Nakamura

Wang

2013

Soft Matter

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“…Sampling the partition function requires updates generating fluctuations of the variables, {r j }, E and σ. We refer the reader to previous work 6,8,20 for particle updates and bulk field updates. We note that the demonstration requires an integral over the surface charge σ; thus even if charges in the volume are discrete those on surfaces should be sampled continuously.…”

Section: Algorithmmentioning

confidence: 99%

Boundary conditions in local electrostatics algorithms

Levrel

Maggs

2008

The Journal of Chemical Physics

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We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We first show how to implement constant-potential, Dirichlet boundary conditions by introducing extra Monte Carlo moves to the algorithm. Second, we show the interest of the algorithm for studying systems which require anisotropic electrostatic boundary conditions for simulating planar geometries such as membranes.

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“…A lattice Monte Carlo algorithm, based on the use of the electric field E(r) for Coulomb systems, was introduced by Maggs and collaborators. [17][18][19] The field E in this algorithm is purely "local" on an interpolating grid. Although a benchmark study of the molecular dynamics version of this method based on a single core revealed no speed advantages over traditional fast electrostatic (Fourier-based) algorithms, excellent efficiencies are obtained on parallel clusters.…”

Section: Introductionmentioning

confidence: 99%

“…The local Monte Carlo simulation algorithm proposed by Maggs and co-workers [17][18][19] applies Metropolis sampling a) Electronic mail: zgw@caltech.edu together with Gauss's law constraint for a fluctuating electric field. The configuration sampling involves two kinds of updates: (1) the electric field on the grid for a given particle configuration, subject to the constraint of Gauss's law, and (2) the position of the charged particles, also subject to the constraint of Gauss's law.…”

Section: Introductionmentioning

confidence: 99%

Improved local lattice Monte Carlo simulation for charged systems

Jiang

Wang

2018

The Journal of Chemical Physics

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Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)] proposed a local lattice Monte Carlo algorithm for simulating charged systems based on Gauss's law, which scales with the particle number N as O(N). This method includes two degrees of freedom: the configuration of the mobile charged particles and the electric field. In this work, we consider two important issues in the implementation of the method, the acceptance rate of configurational change (particle move) and the ergodicity in the phase space sampled by the electric field. We propose a simple method to improve the acceptance rate of particle moves based on the superposition principle for electric field. Furthermore, we introduce an additional updating step for the field, named "open-circuit update," to ensure that the system is fully ergodic under periodic boundary conditions. We apply this improved local Monte Carlo simulation to an electrolyte solution confined between two low dielectric plates. The results show excellent agreement with previous theoretical work.

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Monte Carlo algorithms for charged lattice gases

Cited by 17 publications

References 21 publications

Effects of dielectric inhomogeneity in polyelectrolyte solutions

Effects of dielectric inhomogeneity in polyelectrolyte solutions

Boundary conditions in local electrostatics algorithms

Improved local lattice Monte Carlo simulation for charged systems

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