Addressing the electrostatic component of protons binding to aquatic nanoparticles beyond the Non-Ideal Competitive Adsorption (NICA)-Donnan level: Theory and application to analysis of proton titration data for humic matter.

Hypothesis: Charge descriptors of aquatic nanoparticles (NPs) are evaluated from proton titration curves measured at different salt concentrations and routinely analysed by the Non-Ideal Competitive Adsorption-Donnan (NICAD) model. This model, however, suffers from approximations regarding particle electrostatics, which may bias particle charge estimation. Implementation of Poisson-Boltzmann (PB) theory within consistent treatment of NPs protolytic data is expected to address NICAD shortcomings.

Experiments: An alternative to NICAD is elaborated on the basis of nonlinearized PB equation for soft particle electrostatics to properly unravel the electrostatic and chemical components of proton binding to NPs. A numerical package is developed for automated analysis of proton titration curves and proton affinity spectra at different salt concentrations. The performance of the method is illustrated for humic matter nanoparticles with different charge and size, and compared to that of NICAD.

Findings: Unlike NICAD, PB-based treatment successfully reproduces particle charge dependence on pH for practical salt concentrations from the thin to thick electric double layer limit. Donnan representation in NICAD leads to moderate to dramatic misestimations of proton affinity and binding heterogeneity depending on particle size to Debye layer thickness ratio. Interpretation of NPs protolytic properties with PB theory further avoids adjustment of the 'particle Donnan volume' empirically introduced in NICAD.