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We study the adsorption-desorption transition of polyelectrolyte chains ontoplanar, cylindrical and spherical surfaces with arbitrarily high surface chargedensities by massive Monte Carlo computer simulations. We examine in detail howthe well known scaling relations for the threshold transition-demarcating theadsorbed and desorbed domains of a polyelectrolyte near weakly chargedsurfaces-are altered for highly charged interfaces. In virtue of high surfacepotentials and large surface charge densities, the Debye-Hueckel approximationis often not feasible and the nonlinear Poisson-Boltzmann approach should beimplemented. At low salt conditions, for instance, the electrostatic potentialfrom the nonlinear Poisson--Boltzmann equation is smaller than theDebye-Hueckel result, such that the required critical surface charge densityfor polyelectrolyte adsorption $\sigma_c$ increases. The nonlinear relationbetween the surface charge density and electrostatic potential leads to asharply increasing critical surface charge density with growing ionic strength,imposing an additional limit to the critical salt concentration above which nopolyelectrolyte adsorption occurs at all. We contrast our simulations findingswith the known scaling results for weak critical polyelectrolyte adsorptiononto oppositely charged surfaces for the three standard geometries. Finally, wediscuss some applications of our results for some physical-chemical andbiophysical systems.

Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces: the nonlinear Poisson-Boltzmann approach