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Recent experiments on weak polyelectrolyte brushes found marked shifts in theeffective p$K_\mathrm{A}$ that are linear in the logarithm of the saltconcentration. Comparing explicit-particle simulations with mean-fieldcalculations we show that for high grafting densities the salt concentrationeffect can be explained using the ideal Donnan theory, but for low graftingdensities the full shift is due to a combination of the Donnan effect and thepolyelectrolyte effect. The latter originates from electrostatic correlationswhich are neglected in the Donnan picture and which are only approximatelyincluded in the mean-field theory. Moreover, we demonstrate that the magnitudeof the polyelectrolyte effect is almost invariant with respect to saltconcentration but depends on the grafting density of the brush. This invarianceis due to a complex cancellation of multiple effects. Based on our results, weshow how the experimentally determined p$K_\mathrm{A}$ shifts may be used toinfer the grafting density of brushes, a parameter that is difficult to measuredirectly.

Explaining Giant Apparent $\mathrm{p}K_\mathrm{A}$ Shifts in Weak Polyelectrolyte Brushes