Article

# Debye-Hückel-Bjerrum theory for charged colloids

Instituto de Fı́sica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre (RS), Brazil

Physica A: Statistical Mechanics and its Applications (Impact Factor: 1.72). 09/1998; 258(3-4):341-351. DOI: 10.1016/S0378-4371(98)00238-6 Source: arXiv

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**ABSTRACT:**The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model (PM), all ions are approximated as nonoverlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman (J. Comput. Phys. 1978, 29, 35), with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting in efficient sampling of pair-correlation functions for highly asymmetric ionic mixtures. For three-dimensional fluids, ion size and charge-ratios larger than 1000 can be treated, corresponding to hitherto computationally not accessed micrometer-sized colloidal spheres in 1-1 electrolyte. Effective colloidal charge numbers are extracted from our PM results. For moderately large ion size and charge-asymmetries, we present molecular dynamics simulation results that agree well with the approximate HNC pair correlations. © 2013 Wiley Periodicals, Inc.Journal of Computational Chemistry 10/2013; · 3.60 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The electrostatic interaction between finite charge distributions, ρ(r), in a neutralizing background is considered as an extension of the one component plasma (OCP) model of point charges. A general form for the interaction potential is obtained which can be applied to molecular theories of many simple charged fluids and mixtures and to the molecular dynamics (MD) simulation of such systems. The formalism is applied to the study of a fluid of Gaussian charges in a neutralizing background by MD simulation and using hypernetted-chain integral equation theory. The treatment of these interactions is extended to a periodic system using a Fourier Transform formulation and, for a rapidly decaying charge distribution, an application of the Ewald method. The contributions of the self-energy and neutralizing background to the system's energy are explicitly included in the formulation. Calculations reveal differences in behavior from the OCP model when the Wigner-Seitz radius is of order and less than the Gaussian charge density decay length. For certain parameter values these systems can exhibit a multiple occupancy crystalline phase at high density which undergoes re-entrant melting at higher density. An exploration of the effects of the various length scales of the system on the equation of state and radial distribution function is made.The Journal of Chemical Physics 01/2014; 140(2):024506. · 3.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the role played by the correlations between the screening counterions in the thermodynamic behavior as a colloidal suspension. A local density functional based on the one component plasma theory is employed to incorporate this effect into the Poisson–Boltzmann theory for this problem. The Helmholtz free energy for this system is derived, showing no indication of phase separation.Physica A: Statistical Mechanics and its Applications 02/2002; 304(s 1–2):170–176. · 1.72 Impact Factor

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