New structure of electrical double layer to modify triple-layer model at oxide-water interface

Purpose Triple-layer model (TLM) is distinct from other surface complexation models (SCMs) with the charged beta-layer between solid surface and diffuse layer. However, its structure of electrical double layer, i.e., three capacitors connected in series, produced an uncharged beta-layer according to the rule of capacitors in the electrical circuit theory. The objective of this study was to modify TLM with the development of a new structure of electrical double layer and mathematical models for the charge-potential relationships. Methods The rule of capacitors in the electrical circuit theory was used to modify the electrical double layer in TLM. Published acid-based titration experiments on goethite in KNO3 solution by Yates and Healy (J Colloid Interface Sci 52:222-228, 1975) was used to demonstrate the modified TLM. Simulation study of the modified TLM for goethite was carried out by changing pH from 4.0 to 10.0 and ionic strength of KNO3 solution from 0.001 to 0.100 mol.l(-1). Results The finite size of ions in aqueous solution determined the parallel connection of the two capacitors, which were described by the constant capacitance model (CCM) and the diffuse layer model (DLM). A new concept termed as ion size factor delta, which was governed by the radius r of hydrated ion, was proposed to quantify the percentages of surface area occupied by the CCM and DLM capacitors. A new characteristic relationship of the modified TLM was derived to be a linear relationship between net surface charge and square root of ionic strength when the surface potential was small. The experimental results verified the characteristic relationship, and the ion size factor was validated by the success in estimating the dielectric constant of the CCM capacitor and the radii of hydrated ions (K+ and NO3-). The CCM capacitor occupied 33.8% of the area of goethite surface. Simulation results showed that substantial amount of charge was at the compact layer, and it contributed 14.6% to 74.4% of the net surface charge. Conclusion New electrical double layer with structure of connection of the two capacitors in parallel eliminated the internal flaw of the classical TLM, modified the classical TLM into a general model which unified CCM and DLM, and supported the core of the classical TLM (i.e., the charged compact layer and the diffuse layer).