An introduction to these clay components can be found in Ishiguro and Koopal, Adv J Colloid Interface Sci 2016.

A correct description of the electrical double layers of clays are quite complicated because the plate surfaces have other characteristics then the edge surface. A further complication is the montmorillonite can swell and in the interlayer also an electrical double layer can devellop. In all simple treatments all these complications are neglected and the surface is considered to have one surface potential that can be described by taking into account different sites on the different surface parts. The relation between proton charge surface potential is then mostly worked out on the basis of a diffuse lyer model or a basic Stern layer model (Stern layer+ diffuse layer). As there is a constant charge surface part (Si-O plate) and a variably charge surface part (edge) the double layer is different from that of simple metal oxides like goethite. The interlayer electrostatics can be described in a simple way with a Donnan model for the electrostatics.

Basically, KAOLINITE is 1:1 Clay mineral while MONTMORILLONITE is 2:1 Clay mineral: Montmonrillonite can swell. Kaolinite has a basal-spacing smaller (0.72nm) due to hydrogen-bonding than Montmotillonite (4nm) depending on the dominant exchangeable cation.

These specifical characteristics can affect the Diffuse Double Layer (DDL) of these two different clay mineral. Also see and compare the differents assumptions made by Gouy-Charpman for the DDL and relate them two the characterisctics of these 2 clays minerals.

I suggest to read the following publication. I find it very helpful. Tombácz, E. & Szekeres, M. (2006) Surface charge heterogeneity of kaolinite in aqueous suspension in comparison with montmorillonite. Applied Clay Science, 34, 105–124.