Conductometric evidence for accurate dissociation behaviour of surface groups on nanorods

The surface charge of nanoparticles is usually quantified under the assumption that strong electrolytes fully dissociate in aqueous systems. Here, we demonstrate the effect of counterion condensation on charge through meticulous corrections to the individual dissociation constants. By considering the electrostatic potential energy of charged moieties on the particle surface and by applying Poisson-Boltzmann statistics to assess the electrostatic double layer surrounding the particles, we were able to simulate experimental potentiometric and conductometric titration curves for both solutions and colloidal systems with decent correlation. As such, we can predict that due to counterion condensation, our chosen rod-like particles (phosphorylated cellulose nanocrystals) never carry more than 0.5 mmol g^-1 charge, amounting to a mere fraction of the theoretical maximum of 2 mmol g^-1. In addition, we gained insight into the role of carbonate impurities in the system, which reliably indicate the first equivalence point of the highly charged nanorods by causing the brief rise in conductivity before a plateau is reached. We therefore discourage the interpretation of conductometry curves for nanoparticles by traditional linearization. Instead, we propose a more reliable method for nanoparticle charge determination from the conductometric data based on calculating the fraction of counterions entering the bulk solution instead of merely observing conductivity or pH.