Colloids and Surfaces, 56 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB (1991) 149-176 Elsevier Science Publishers B.V., Amsterdam 149 The interfacial bending moment: thermodynamics and contributions of the electrostatic interactions Peter A. Kralchevsky, Theodor D. Gurkov and Ivan B. Ivanov’ Laboratory of Thermodynamics and Physico-Chemical Hydrodynamics, Faculty of Chemistry, University of Sofia, 1126 Sofia (Bulgaria) (Received 13 April 1990; accepted 6 September 1990) zyxwvutsrqponmlkjihgfedcbaZYXWVUT Abstract The problem concerning the magnitude and the sign of the interfacial bending moment of the droplets in fluid disperse systems is considered on the basis of a thermodynamic approach. It is demonstrated that the total bending moment can be expressed as a superposition of contributions connected with the different components in the system. Expressions for the contributions of the electric double layer, of the interactions between adsorbed dipoles and of the electrolyte excess osmotic pressure to the value of the bending moment are derived. The effect of a possible incom- plete dissociation of the adsorbed ionic surfactant monolayer is also taken into account. The results show that the van der Waals and the electric double layer interactions provide significant contributions to the bending moment, both of them of the order of 10 pN. Even at high electrolyte concentrations, the electrostatic bending moment can be important owing to the contribution of the Stern layer. The results can be applied to study the curvature dependence of the interfacial tension in microemulsions and in liquid-gas dispersions. 1. INTRODUCTION The effect of curvature on the interfacial tension was first studied by Gibbs in his theory of capillarity [ 11. His approach was developed by Tolman [ 21, who established that a pronounced dependence of the interfacial tension on curvature can exist for very small drops or bubbles, whose radii are comparable with the so-called Tolman parameter S,. (The latter represents the distance between the surface of tension and the equimolecular dividing surface (see Eqn (2.10) below) .) Further development was achieved in the works by Koenig [ 31 and Buff [ 4-61. Kondo [ 71 investigated the role of the choice of the dividing surface in the thermodynamics of curved interfaces (see also Refs [ 8-101). New interest in curvature effects was awakened by the studies on the ther- modynamics of microemulsions [ 11-201. In particular, Miller [ 161 pointedout ‘Present address: Department of Chemical Engineering, Illinois Institute of Technology, Chicago, IL 60616, U.S.A. 0166-6622/91/$03.50 0 1991- Elsevier Science Publishers B.V.