The multivariate interaction between Au and TiO₂ colloids: the role of surface potential, concentration, and defects

The established DLVO theory explains colloidal stability by the electrostatic repulsion between electrical double layers. While the routinely measured zeta potential can estimate the charges of double layers, it is only an average surface property which might deviate from the local environment. Moreover, other factors such as the ionic strength and the presence of defects should also be considered. To investigate this multivariate problem, here we model the interaction between a negatively charged Au particle and a negatively charged TiO₂ surface containing positive/neutral defects (e.g. surface hydroxyls) based on the finite element method, over 6000 conditions of these 6 parameters: V_Part (particle potential), V_Surf (surface potential), V_Def (defect potential), DD (defect density), Conc (salt concentration), and R (particle radius). Using logistic regression, the relative importance of these factors is determined: V_Surf > V_Part > DD > Conc > R > V_Def, which agrees with the conventional wisdom that the surface (and zeta) potential is indeed the most decisive descriptor for colloidal interactions, and the salt concentration is also important for charge screening. However, when defects are present, it appears that their density is more influential than their potential. To predict the fate of interactions more confidently with all the factors, we train a support vector machine (SVM) with the simulation data, which achieves 97% accuracy in determining whether adsorption is favorable on the support. The trained SVM including a graphical user interface for querying the prediction is freely available online for comparing with other materials and models. We anticipate that our model can stimulate further colloidal studies examining the importance of the local environment, while simultaneously considering multiple factors.