Colloidal interactions for a polystyrene particle and a smooth silicon surface: Atomic force microscopy, XDLVO theory, and Surface Element Integration

Abstract

In this study Liftshitz van der Waals, electrostatic and acid base interaction forces of a 4 µm polystyrene particle with flat silicon surfaces were experimentally determined using interfacial interaction energy measurements and atomic force microscopy (AFM). Interfacial forces computed using analytical expressions based on the Surface Element Integration (SEI) technique were compared with the standard Derjaguin Approximation (DA) and Continuum Mechanics Adhesion approaches, namely: Derjaguin, Muller and Toporov (DMT), Johnson, Kendall and Roberts (JKR) and Maugis and Pollock (MP) theories in order to assess the effect of curvature on a sphere-plate geometry. For acid base interactions, the SEI was found to deviate from the DA at small particles radii (less than 100 nm) and over a wide ratio of decay length, λ, to particle size, R. Accounting for curvature for acid base interaction requires geometric factors that are functions of λ/R. For van der Waals force of interaction, the SEI and DA showed large variation at large ratios of interparticle separation, D, to particle radius, R. For Double layer interaction force large variation between SEI and DA was observed for small κa values, and good agreement observed at large κa values. The AFM forces of adhesion of polystyrene in 0.01 mM and 100 mM KCl electrolyte solutions were found to be 2.38 ± 2.15 nN and 9.29 ± 6.89 nN, respectively. These results were found to be consistent with the SEI technique that gave adhesion forces of 4.8 and 10.2 nN at the low and high electrolyte concentrations, respectively. These data are also aligned with Maugis and Pollock (MP) theory that accounts for elasto-plastic deformation, Pe.