Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach

Abstract

The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.

Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions

“…and have been reported, each of which requires arithmetic operations. Such numerically suboptimal transforms have been applied in various liquid integral equation studies …”

“…( 24), which gives the alternative iteration rule 25) Fixed point iterations on basis of Eq. ( 24) or (25) have been applied in a number of integral equation studies [21,25,31,37,38,56,57], where different strategies have been applied in computing the Fourier transforms, and various closure relations for the OZ-equations have been used, including the HNC closure. The mixing parameter α in Eq.…”

“…For the sake of simplicity, and since it was shown * mheinen@thphy.uni-duesseldorf.de that enforcing thermodynamic self-consistency leads to a weak accuracy improvement only [15], in the present work we restrict ourselves to the HNC approximation. A variety of liquid integral equation [15][16][17][18][19][20][21] or density functional studies [22][23][24] of the PM have been reported. The HNC equations have been solved for the asymmetric PM by Léger and Levesque [25], in case of non-zero macroion number densities for size asymmetries between micro-and macroions as high as 1:80 and charge asymmetries ranging up to 1:450.…”