Geometric effects on non-DLVO forces: Relevance for nanosystems

In this paper, the surface element integration (SEI) method was used derive analytical force/potential versus distance profiles for two non-DLVO forces: Lewis acid-base and solvation forces. These forces are highly relevant in a variety of systems, from bacterial adhesion, nanoparticle suspension stability to atomic force microscopy (AFM) profiles. The SEI-derived expressions were compared with the more commonly utilized Derjaguin approximations in order to assess the effect of curvature on the resulting interaction for the test cases of sphere-flat plate and equally sized spheres. For acid-base interactions, the deviation was found to be significant for particles up to 40 nm in diameter for the conventionally used decay length (λ = 1 nm) for water. The resulting expressions show that accounting in curvature for acid-base interactions is important even for simple smooth geometric shapes, recovering the Derjaguin expression at smaller values of λ/R. These results allow for correction of the acid-base force/potential versus distance from the Derjaguin-derived expressions using simple functions of λ/R. Conversely, for the solvation force the deviation was far less significant due to the oscillatory nature of the potential damping out effects and the smaller order of magnitude range of the solvation decay length, indicating that for solvation forces the Derjaguin approximation is suitable for most conceivable cases.