(187ab) Accounting for Counterion Association In Prediction of Colloidal Stability
The methodology of a generalized model  for colloidal stability has been validated against experimentally measured values of the stability ratio and critical coagulation concentrations (CCC), for electrolytes with mono or divalent cation, i.e., potassium chloride and magnesium chloride, respectively. Besides the classical DLVO theory the generalized model accounts for the interplay between colloidal interactions and the association of cations with the particles surface charge groups. The model parameters are obtained or estimated purely based on information available in the literature. For the monovalent salt the predictions agree well with the experimental data from literature , forecasting both the CCC values and stability ratios quantitatively. For the divalent salt the predictions for large values of the stability ratio tend to deviate from the experimental results, but it is noted that the onset of stability, i.e., the CCC, and small stability ratios are correctly forecast. Moreover, a comparison of the above results with those neglecting the effect of counterion association with the particles surface charge groups indicates that the latter substantially overestimates stability ratios in the presence of high salt concentrations, in the case of the monovalent salt, and leads to unrealistic large values of the CCC for the divalent salt. Including the association of cations with the particles surface charge groups can explain the relative low values of experimental CCC for divalent salts compared to the theoretical predictions by the classical DLVO theory neglecting ion association, which is a point of interest in solid-liquid separation processes.
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