Why is there preferential adsorption of a common ion during preparation of colloids by peptization?

There was a similar question asked [here](https://chemistry.stackexchange.com/a/129613/105771) on Chem SE, but the answer was not very satisfactory to me, so I am asking a fresh question.


Peptization is the process of creating a colloid from a precipitate by shaking it with a suitable electrolyte. In this process, the rule of preferential adsorption is followed which states ([source](https://qr.ae/pG981d)) that:



> 
> The Particle Constituting the Dispersed Phase adsorb only those ion preferentially which are more related chemically to it or which are common with the Lattice ion of Dispersed phase
> 
> 
> 


So what is the reason behind this selectivity? I think it might have to do with the lattice of the precipitate, because the precipitate is in a solid-state and even after being dispersed it will also remain in the solid-state but as small particles.


So, do the lattice ions try to extend their lattice by adsorption and in this process get separated into small particles? Lattice ion adsorption puts little strain on the lattice structure, because having a similar dimension they simply fit into the gaps in the edges of the crystal, whereas ions other than lattice ions will create some distortion because of its dissimilar dimension?


I found a paper related to this and according to this paper size and deformation of lattice can play an important role in adsorbtion of ions



> 
> Fajans and Erdey-Grdz (7) pointed out that in addition to solubility
> other factors, such as deformation, size of the adsorbed ions, and
> dissociability of the adsorption complex formed have to be taken into
> 
> 
> ADSORPTION ON IONIC LATTICES 1029 account. Moreover, the charge
> (valence) of the adsorbed ions and the deformability of the lattice
> ions will play a part. Considering the many factors that influence the
> adsorbability, it is quite plausible that the socalled
> Paneth-Fajans-Otto Hahn rule can be only of a highly approximate
> character.
> 
> 
> 


**Reference**


I.M. Kolthoff, "Adsorption on Ionic Lattices", *J. Phys. Chem.*, 1936, **40**(8), 1027–1040, ([Link to the article](https://pubs.acs.org/doi/pdf/10.1021/j150377a008))


