Abstract
A novel method using Lifshitz continuum theory to account for the effects of surface roughness was developed. The method treats roughness as a diffuse film whose dielectric properties vary continuously between those of the substrate and those of the solvent: AFM measurements of surface topography are used to deduce the volume-fraction profile of substrate in solvent which in turn is converted into a dielectric-permittivity profile using the Clausius-Mossoti equation as a mixing rule. Calculations show orders of magnitude of reduction in the van der Waals force between rough surfaces at contact compared with smooth surfaces, with the amount of reduction dependent on the shape of the volume-fraction profile as well as the total depth of the roughness. These predictions help account for discrepancies observed previously between the Total Internal Reflection Microscopy (TIRM) data and calculations for smooth polystyrene surfaces in water, with or without physisorbed polymer, without introducing any adjustable parameters.
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