Mean-field theory is used to derive criteria for the adsorption of a weakly charged polyelectrolyte molecule from salt solution onto surfaces patterned with charge and topography. For flat surfaces patterned with periodic arrays of charged patches, the adsorbed layer thickness predicted using mean-field theory and that found by Brownian dynamics simulations are in quantitative agreement in the strong-adsorption regime, which corresponds to sufficiently small κ or sufficiently large ∫ eff q∫, where κ is the inverse Debye screening length, eff is an effective surface charge density, and q is the charge on each segment of the polyelectrolyte. Qualitative agreement is obtained in the weak-adsorption regime, and for the case where surfaces are patterned with both charge and topography. For uniformly charged, sinusoidally corrugated surfaces, the theory predicts that the critical temperature required for adsorption can be greater than or less than the corresponding value for a flat surface depending on the relative values of κ and the corrugation wave number. If the surface charge is also allowed to vary sinusoidally, then adsorption is predicted to occur only when the topography crests have a surface charge opposite to that of the polyelectrolyte. Surfaces patterned with rectangular indentations having charged bottoms which are separated by flat charged plateaus are investigated as well. Adsorption is predicted to occur even when the net surface charge is zero, provided that the plateaus have a charge opposite to that of the polyelectrolyte. If the charge on the plateaus and polyelectrolyte is the same, adsorption may still occur if electrostatic attraction from the indentation bottoms is sufficiently strong.
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We thank Professor David Morse for helpful discussions. This material is based on work supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under Grant No. W911-NF-04-1-0265. Our work was also supported in part by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory (ARL) under Cooperative Agreement No. DAAD19-01-2-0014. The content does not necessarily reflect the position or policy of the government, and no official endorsement should be inferred.