Counterion condensation in pH-regulated polyelectrolytes

The effective charge of polyelectrolytes (PEs) plays an essential role in their electrokinetic behaviors and applications such as biosensors and drug delivery. To gain a better understanding of this crucial factor, we consider a charge-regulated PE, which simulates entities such as biomacromolecules and charged dendrimers, in a general electrolyte solution mimicking common experimental conditions. Taking account of the effects of pH and the presence of multiple ionic species, both the effective charge and the phenomenon of counterion condensation (CC) of a charge-regulated PE are investigated for the first time in a realistic manner. We show that the occurrence of CC, which significantly affects the charged property of the PE, depends highly upon those two effects. Our model is verified by the experimental data in the literature, which are unable to be described by the famous Manning theory for polyelectrolytes, and the results gathered provide both necessary theoretical foundation and valuable information for utilizing pH-tunable PEs in relevant applications.