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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Marcia Barbosa, Mar 21, 2015 Available from: Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

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**ABSTRACT:**In the previous publication [A.E. Yaroshchuk, Asymptotic behavior in the pressure-driven separations of ions of different mobilities in charged porous membranes, J. Membr. Sci.], it has been found that strong separations of counterions of different mobilities (but the same charge) occur only at moderate to large membrane Péclet numbers. At realistic transmembrane pressure differences, the mode of moderate to large membrane Péclet numbers occurs only for membranes with relatively large pores. For them, the applicability of widely used homogeneous approximation becomes disputable. Therefore, the heterogeneity of ion distribution inside pores has been taken into account for the model of straight cylindrical capillaries. The account for microheterogeneity by means of non-linearized Poisson–Boltzmann equation has revealed the existence of optimal fixed charge densities as well as of optimal pore sizes. The latter are rather large (say, 8nm for decinormal feed solutions). The active layer thickness of membranes with such pore sizes has to be essentially larger than in conventional NF membranes to diminish concentrational polarization. Thus, ‘optimal’ charged membranes for the pressure-driven separation of ions of different mobilities are quite different from conventional NF membranes. The latter are fine-porous, thin and only slightly charged while the former should be relatively coarse-porous, thick and have a large fixed charge density. To be effective, that fixed charge should be compensated by counterions involved in convective solution transfer (the so called electrokinetic charge). The existence of an extended hydrodynamically immobile layer near the pore surface noticeably diminishes the membrane separation efficiency. That is especially so if ions retain their electo-diffusional mobility within that layer.Journal of Membrane Science 03/2000; 167(2):149-161. DOI:10.1016/S0376-7388(99)00280-X · 4.91 Impact Factor - [Show abstract] [Hide abstract]

**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 02/2014; 35(4). DOI:10.1002/jcc.23446 · 3.60 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The paper is the summary of lectures given in Sao Carlos, Brazil during the 2004 Summer School on Statistical Mechanics. My objective was to provide the students with some basic tools necessary to study the thermody- namics of Coulomb systems. I have restricted myself to simple models and techniques, which nevertheless, when used correctly can give a clear insight into the fundamental physics behind various complex phenomena that appear when the interactions between the system's constituents are dominated by the long ranged Coulomb force.Brazilian Journal of Physics 09/2004; 34. DOI:10.1590/S0103-97332004000600006 · 0.68 Impact Factor