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The renormalized charge of a simple two-dimensional model of colloidalsuspension was determined by solving the hypernetted chain approximation andOrnstein-Zernike equations. At the infinite dilution limit, the asymptoticbehavior of the correlations functions is used to define the effectiveinteractions between the components of the system and these effectiveinteractions were compared to those derived from the Poisson-Boltzmann theory.The results we obtained show that, in contrast to the mean-field theory, therenormalized charge does not saturate, but exhibits a maximum value and thendecays monotonically as the bare charge increases. The results also suggestthat beyond the counterion layer near to the macroion surface, the ionic cloudis 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 thecorrelations between microions

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