Correlation functions, macroions

A. M. Walsh, R. D. Coalson. Lattice field theory for spherical macroions in solution Calculation of equilibrium pair correlation function. J Chem Phys 700 1559-1566, 1994. 

The superscripts c and p denote counterions and macroions, respectively, and the subscripts 0 and 1 describe the state (0 for nonbonded and 1 for bonded) of the corresponding counterion. The partial correlation functions are related to the regular correlation functions, hab(r) = g"h(r) — 1, by the relation pahabpb = [p" H"/ p/ ]()0, where 00 denotes the first element of the matrix. HNC-like [70, 71] and the MSA-like [72-74] closures have been proposed to solve the WOZ equation. For the former we have,... 

In the next two figures we discuss the pair-correlation functions as obtained from the two-density theory and computer simulations. First, in Fig. 3 we compare the counterion-counterion pair-distribution function as obtained theoretically (lines) and from simulations (symbols). The numerical calculations apply to cp = 0.0001 and ce = 0.005 mol dm-3 the results show that the theory underestimates the counterion-counterion correlation. Next, in Fig. 4 the macroion-counterion pair-distribution is shown for the same set of parameters. Finally, in Fig. 5 the macroion-macroion pair-distribution functions are calculated by both theoretical approaches at cp = 0.0001 mol dm-3 solution and for zp = —10 and —30. 

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10-12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in... 

In Fig. 8 we show the results for a —12 +1 electrolyte with the macroion concentration cp = 0.01 mol/dm3. The lines represent the results for the system where r) = 0 (pure Coulomb potential), while the symbols represent the results for r = —3.18 nm and A = 1.5 (cf Eq. (19)). The macroion-counterion pair distribution function (Fig. 8b) shows, as expected, that an attractive short-range potential causes higher accumulation of monovalent counterions around the macroions. As a consequence the counterions become strongly correlated as indicated by the shape of the counterion-counterion pair distribution func-... 

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