Electrolytes, asymmetric

Marmur [12] has presented a guide to the appropriate choice of approximate solution to the Poisson-Boltzmann equation (Eq. V-5) for planar surfaces in an asymmetrical electrolyte. The solution to the Poisson-Boltzmann equation around a spherical charged particle is very important to colloid science. Explicit solutions cannot be obtained but there are extensive tabulations, known as the LOW tables [13]. For small values of o, an approximate equation is [9, 14]... 

The first term on the right-hand side of this equation is zero, since it is simply the sum of the electrical charge in solution, which must be zero for a neutral electrolyte solution. The third term is also zero for electrolytes with equal numbers of positive and negative ions, such as NaCl and MgSC>4. It would not be zero for asymmetric electrolytes such as CaCE. However, in the Debye-Huckel approach, all terms except the second are ignored for all ionic solutions. Substitution of the resulting expression into equation (7.20) gives the linear second-order differential equation... 

Chiral alcohols isolated from reduction of ketones at a mercury cathode in aqueous methanol containing an asymmetric electrolyte. Data from refs. [34] and [35]. 

For asymmetrical electrolytes the ionic strength is the same for, say, 1 2 as for 2 1 solutes namely, 3 M as verified by substitution into the summation (and remembering the stoichiometry of the dissociation ). Therefore in a 0.01 M solution of 2 1 electrolyte... 

Blum, L. and Hoeye, J.S. Mean spherical model for asymmetric electrolytes 2 hemodynamic properties and the pair correlation function. 7. Phys. Chem. 1977, 81, 1311-1316. 

Surface Charge Density-Surface Potential Relationship Asymmetrical Electrolyte... 

Gouy himself already treated the (2-1) and (1-2) cases (G. Gouy, Compt. Rend. 149 (1909) 654 J. Phys. (4) 9 (1910) 457) D.C. Grahame, (J. Chem. Phys. 21 (1953) 1054) and S. Levine and J.E. Jones Kolloid-Z 230 (1969) 306) revisited and extended it, the latter authors included mixtures. R. de Levle (J. Electroanal. Chem. 278 (1990) 17) tabulated equations for o, O and y (min) and gave y(x) profiles. Asymmetrical electrolytes have also been considered in theories involving a more advanced model than Polsson-Boltzmann (see sec. 3.8). 

A.L. Loeb, J.Th.G. Overbeek and P.H. WIersema. The Electrical Double Layer around a Spherical Colloid Particle, M.I.T. Press (1961). (Covers symmetrical and asymmetrical electrolytes, ionic components of charge and Gibbs energies.)... 

Table 7 Chiral Secondary Alcohols Isolated from Reduction of Ketones at a Mercury Cathode in Aqueous Methanol Containing an Asymmetric Electrolyte...

Spherical micelles or globular proteins in solution can be considered as an asymmetric electrolyte solution where the ionic species grossly differ in charge and size. Taking into account these asymmetries, an extension of WOZ equa-... 

Hribar, B., Krienke, H., Kalyuzhnyi, Yu.V., and Vlachy, V. Dilute solutions of highly asymmetrical electrolytes in the primitive model approximation. Journal of Molecular Liquids, 1997, 73, No. 4, p. 277-289. 

Linse, P. Highly asymmetric electrolyte - comparison between one-component and 2-component models at different levels of approximations. Journal of Chemical Physics, 1991, 94, No. 5, p. 3817-3828. 

Vlachy, V., Marshall, C.H., and Haymet, A.D.J. Highly asymmetric electrolytes - a comparison of Monte-Carlo simulations and the HNC integral-equation. Journal of the... 

Kalyuzhnyi, Yu.V., Vlachy, V., Holovko, M.F., and Stell, G. Multidensity integral-equation theory for highly asymmetric electrolyte-solutions. Journal of Chemical Physics, 1995, 102, No. 14, p. 5770-5780. 

Kalyuzhnyi, Yu.V., Blum, L., Holovko, M.F., and Protsykevytch, I.A. Primitive model for highly asymmetric electrolytes, associative mean spherical approximation. Physica A, 1997, 236, No. 1-2, p. 85-96. 

Chan, D.Y.C. A simple algorithm for calculating electrical double layer interactions in asymmetric electrolytes. Poisson-Boltzmann theory. J. Colloid Interface Sci. 2002, 245 (2), 307-310 Devereeux, O.F. deBruyn, P.L. Interaction of Plane Parallel Double Layers, MIT Press Cambridge, 1963. 

Fig. 4. Simulated binodal curves for size-asymmetric electrolyte systems with different X values. Circles, A = 1 diamonds, X = 0.75 squares, X = 0.5 triangles, X = 0.25.

In this paper, we have reviewed some recent applications of the HPTMC method. We have attempted to demonstrate its versatility and usefulness with examples for Lennard-Jones fluids, asymmetric electrolytes, homopolymer solutions and blends, block copolymer and random copolymer solutions, semiflexible polymer solutions, and mixtures. For these systems, the proposed method can be orders of magnitude more efficient than traditional grand canonical or Gibbs ensemble simulation techniques. More importantly, the new method is remarkably simple and can be incorporated into existing simulation codes with minor modifications. We expect it to find widespread use in the simulation of complex, many-molecule systems. 

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