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 w...