Adsorption of Cetylpyridinium Chloride at Silica Nanoparticle/Water Interfaces (II): Dependence of Surface Aggregation on Particle Size.

Herein, we report a thermodynamic model that relates the adsorption (aggregation) parameters of surfactants at solid/liquid interfaces to particle radius ( r ). The adsorption (aggregation) parameters include adsorption amounts, equilibrium constants (or the standard Gibbs free energy changes), the critical surface micelle concentration (csmc), and the average aggregation number of surface micelles ( n ). The model predicts the size dependence of the surface aggregation of surfactants, which is determined by the changes in the interfacial tension and the molar volume of surface components caused by adsorption. In addition, the adsorption of cetylpyridinium chloride (CPyCl), a cationic surfactant, on silica nanoparticles with different r values (ca. 6-61 nm) was determined at 298 K and pH 4, showing an obvious size dependence, consistent with the prediction of the model. With an increase in r , the adsorption isotherm changes from the double-plateau type to the Langmuir type, accompanied by obvious changes in the adsorption parameters. The size-dependent adsorption data can be well described using the model equations, indicating that the model presented here is acceptable. In addition, the model can extract information on the interfacial tensions from adsorption data. We think that the model deepens the understanding of the aggregation phenomena of surfactants at solid/liquid interfaces.