(713d) Using Atomic Force Microscopy to Estimate Hamaker Constants of Solid Materials: Effect of Repulsive Interactions

Understanding particle adhesion is crucial for a wide range of industries, such as microelectronics, pharmaceuticals, and defense. While multiple forces give rise to the phenomena of adhesion, van der Waals (vdW) forces are of particular interest, whose strength is quantified through the Hamaker constant, A. The atomic force microscope (AFM) proves effective at estimating the value of A for diverse materials as it can characterize the surface topography and measure particle-surface forces. Recently, an AFM-based method for estimating A with low uncertainty was proposed (Stevenson et al., 2023, J. Phys. Chem. C, 127, 19, 9371-9379). This approach-to-contact (AtC) method directly accounted for the surface roughness of the substrate and utilized the distributions of the deflections at first contact (d_c) obtained in AFM experiments in order to generate values of A. Although this method yielded accurate estimates of A with small errors for various solid materials, the method neglected, however, the repulsive interactions that are known to arise between the AFM cantilever tip and the substrate.

We therefore investigate the effects of the AFM tip-surface repulsive interactions on the existing AtC method. We demonstrate that the repulsive forces slightly alter the predicted d_c-distributions, which in turn affects somewhat the estimated values of A. In addition, accounting for these repulsive forces allows for the direct determination of the AFM tip-surface force when the AFM tip is in direct contact with the substrate, without having to use a fixed (and arbitrary) minimum gap distance between the tip and surface as is commonly done. We show that the repulsive forces have a significant effect on the resulting pull-off deflections (d­_PO). Consequently, and in contrast to what follows from using the minimum gap distance, the explicit accounting of repulsion yields accurate predictions of the d­_PO­-distributions for substrates with arbitrary surface roughness. We also present improved AFM-based methods for obtaining accurate estimates of A, both from the AtC and pull-off portions of the AFM deflection curve. Finally, the new model predicts that the magnitudes of and are not correlated for certain surface geometries. A set of AFM experiments performed on ultra-smooth sapphire surfaces that are tilted at various angles from the horizontal validates these predictions.