double layer interaction is derived from solution of the Pois-A novel method, the surface element integration (SEI), is develson-Boltzmann equation (1,10,11). Exact evaluation of oped to determine the van der Waals and electrostatic double layer both these types of interaction energy is achieved only interactions between a particle and an infinite flat plate from the through rigorous numerical treatments (12,14,(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28). Alcorresponding interactions per unit area between two infinite flat though several simpler techniques for determination of the plates. Comparison with the Hamaker expression for nonretarded interaction energy are available, they are mostly approximate van der Waals interaction reveals that the new technique gives (10,11,(29)(30)(31)(32)(33). Approximations in the evaluation of the the exact interaction energy between a spherical particle and a interaction energy often result in misleading and anomalous flat plate. Available analytical expressions for the electrostatic doutheoretical predictions of several properties of colloidal sysble layer interaction energy between two infinite flat plates, based on the linearized Poisson-Boltzmann equation, are used in SEI tems.
to obtain the sphere-flat plate interaction energy. These sphere-
The involved mathematics associated with rigorous evaluflat plate interaction energies determined using SEI are compared ation of the interaction energies restricts their application to with the corresponding interaction energies obtained from a derelatively simple geometric shapes of the particles. Barring tailed numerical solution of the Poisson-Boltzmann equation the specific applications to two infinite parallel flat plates, based on finite element analysis. The comparisons reveal that SEI or two spherical particles, these methods can hardly be apscales the flat plate interaction to the corresponding sphere-flat plied to determine the interaction energy for other shapes and plate geometry exactly, while the scaling based on the conventional geometries. For instance, the nonlinear Poisson-Boltzmann Derjaguin approximation technique grossly overpredicts the interequation can be solved analytically to give exact results only action energy for small particles and low electrolyte concentrain case of two infinite parallel flat plates (16,17, 24). Even tions.