Formal Mathematical Analysis of the Existence of the Common Intersection Point in Relation to Determining the Parameters Describing Ion Adsorption at the Oxide/Electrolyte Interface: Comparison of the Triple and Four-Layer Models

For most oxide/electrolyte systems potentiometric titration curves measured for different ionic strengths have a Common Intersection Point (CIP) which corresponds to the Point of Zero Charge (PZC). However, there are systems where a CIP exists but the surface charge at this point does not equal zero (PZC CIP). In this paper theoretical analysis of the systems in which the PZC and CIP do not coincide is presented. It is based on the well-known 2-pK surface charging approach and Triple Layer Model (TLM) as well as the Four Layer Model (FLM) of the electric double layer. The appropriate mathematical criterion for CIP existence was applied with detailed derivations, both for TLM and FLM. Having determined in this manner the parameter values, one can draw proper conclusions about the features of oxide/electrolyte adsorption systems, in which PZC and CIP do not coincide. The values of adsorption parameters are found by fitting simultaneously the obtained theoretical expressions to both of the experimental titration isotherms, and to the individual isotherms of electrolyte cation adsorption measured using radiometric methods.