Role of Electrostatic Energy Barriers in the Expansion of Lamellar Crystals

Abstract

The method of Fourier transforms has been used in the investigation of the electrical forces between the platelets of the montmorillonite crystal. The potential-energy curve, as a function of the distance 2D between the platelets, is shown to have two turning points. The one with the smaller value of D is a minimum and is therefore a point of stable equilibrium, while the one with the larger value of D is a maximum and is a point of unstable equilibrium. For small separations of the platelets the potential energy is positive and increases with decreasing separation, while at large separations the potential energy is negative and decreases linearly with increasing separation. The foregoing is shown to be in complete accord with accumulated experimental findings over the years. Physically, the basis of the shape of the energy curve is that at small separations the repulsive ion—solvent and ion-image forces prevail whereas at intermediate distances the attractive surface-ion terms become important; finally the surface—surface terms dominate at larger distances. It is also shown that by suitable expansions the Fourier transform method can be used to generate the required sets of electrostatic images developed in an earlier work by the optical analog.