(144a) Impact of Surface Roughness on Estimating Hamaker Constants through Non-Contact Atomic Force Microscopy

The adhesion of particles to surfaces plays an important role in a variety of applications including those relevant to pharmaceuticals, semiconductors, colloidal dispersions, and explosives detection. In many cases, the dominant interaction between a particle and a surface is the van der Waals (vdW) force, which is quantified by the Hamaker constant, A. An atomic force microscope (AFM) operating in contact sampling mode can measure the deflection of a cantilever tip as it is brought close to the surface. By measuring the deflection as a function of the tip-surface separation distance, an estimate of the value of A can be obtained. AFM results may be, however, adversely affected by surface properties and contact separation distances. Consequently, Fronczak et al. (2017, Langmuir 33, 714-725; 2018, J Colloid Interface Sci. 517, 213-220) developed a new approach-to-contact method that relates A to the deflection of the cantilever tip at first contact with the surface, d_c, which can be found reliably from AFM experiments. For several surfaces, the estimated values of A were in good agreement with the predictions of the Lifshitz approximation. Despite this method’s demonstrated improvements, the modest experimental errors in d_c are nevertheless increasingly propagated in the estimate of A and, as currently formulated, the method assumes perfectly smooth substrates.

Some degree of surface roughness is experimentally unavoidable. Improvements to the approach-to-contact method can be obtained by explicitly accounting for the topography of the given surface, thereby significantly improving the accuracy of the estimates of A and extending the range of the types of surfaces to which this method can be applied. We therefore present an AFM approach-to-contact method in which the vdW force between a cantilever tip, treated as an effective sphere, and a surface of arbitrary roughness is determined. The underlying surface geometry and roughness can be modeled directly using a surface height function, without the need to simplify the features of the surface or utilize an oversimplified vdW force expression. Since surface roughness is incorporated in the method, such that the resulting vdW force now varies locally along the surface, a distribution of d_c-values is instead obtained for a given value of A. We discuss the effect of surface topography on the resulting d_c-distributions, which indicates that the local surface curvature has a large impact on the measured cantilever deflections. Despite previous approaches to modeling surface roughness, it is clear that roughness cannot be handled in an approximate way, but rather it must be explicitly incorporated. In addition to computational work, we also present a comparison of the predicted d_c-distributions to those obtained from AFM measurements for a model surface. These experiments serve to validate the current work and set the stage for further refinement of the newly-developed model.