Interaction of two parallel colloidal plates in an electrolyte mixture of univalent and divalent ions

Abstract

We consider the electric double layer interaction energy per unit area of two, equally charged, parallel, colloidal plates at separation 2 h in an aqueous electrolyte mixture containing univalent and divalent ions. The Gouy-Chapman model of the double layer is used and the potential ψ0 at the plates is assumed independent of plate separation. An expression is obtained for the interaction energy which is based on the assumption that the potential at the plane midway between the plates is the sum of the potentials produced by each of the plates in the absence of the other (linear super-position approximation). This provides a good approximation to the interaction energy at large separations which is proportional to exp (−2 κh) where 1/κ is the Debye-Huckel thickness of the diffuse layer. This approximation is the leading term in an expansion for the interaction energy, the second term of which is also obtained. The formulae for the general electrolyte mixture are applied to the two particular electrolytes, of valency types 1−1 + 2−2 and 1−1 + 2−1, where the first valency of each electrolyte in a mixture refers to the coagulating ion oppositely charged to the plates. Introducing the Hamaker-van der Waals interaction energy between infinitely thick plates, both the methods of zero potential barrier and of zero force are used to define the coagulation conditions in the D.L.V.O. theory of colloid stability. Plots between the coagulating concentrations of the two binary electrolytes in each mixture are obtained for values of ψ0 in the range 0–100 mV. For ψ0≲25 mV the 1−1 + 2−2 mixture shows additivity but with further increase in ψ0 this changes to sensitization. With the 1−1 +2−1 mixture, approximate additivity is obtained at ψ0≲50 mV and at higher ψ0 some superadditivity at the 2−1 end and sensitisation at the 1−1 end set in. Although the linear superposition approximation produces mutual antagonism at the 2−1 end for the higher potentials, this is completely eliminated for ψ0≲100 mV when the second term in our expansion for the energy is included.