(73g) Experimental Determination of the Hamaker Constants of Various Solid Materials with Improved Accuracy Using Atomic Force Microscopy

The Hamaker constant, A, quantifies the strength of the attractive van der Waals (vdW) force, which is the dominant force acting between solid materials at nanometer-scale separation distances. Accurate estimates of A are key for understanding and potentially controlling interfacial interactions in, for example, pharmaceutical products, semiconductors, colloidal dispersions, and explosives detection. Various experimental methods have been employed to determine A, but recent work has focused on the use of atomic force microscopy (AFM) in contact sampling mode in order to generate estimates of A for a broad range of materials. The current authors presented the important first steps needed for the development of an improved experimental AFM-based method to estimate A with high accuracy solely from the approach-to-contact portion of the AFM-generated deflection curve (Stevenson et al. J. Phys. Chem. C 2020, 124, 3014-3027). Even for relatively smooth substrates, such as amorphous silica, the AFM tip-surface vdW force varies significantly along the substrate during an AFM contact sampling experiment. Hence, a characteristic distribution of deflections at first contact, d_c, or a d_c-distribution, is obtained for a given substrate and set of AFM cantilever properties. The resulting d_c-distribution is therefore not just dependent upon A, but also acts as an important “signature” of both the overall geometry and inherent surface roughness of the substrate.

This current work presents the development of a robust method to extract an accurate value of A from an experimentally obtained d_c-distribution for a particular substrate. By inputting a range of d_c-values, the Hamaker constant of a given substrate, with a given surface roughness, is estimated by minimizing the relative entropy between the experimental (or true) and model-predicted (the surface with its given roughness) d_c-distributions. A self-consistency check of the method is first performed computationally to ensure that the outputted Hamaker constant is similar to that of the chosen input value for various surface geometries and for various slow-enough AFM cantilever approach speeds. Due to the difficulty in performing AFM imaging and force experiments on the exact same region on the surface, we also present a method that utilizes the spatial Fourier transform of the surface in order to generate representative images of the surface with the same overall surface characteristics. Then, the self-Hamaker constant of several solid materials (e.g., amorphous silica and sapphire) is determined experimentally from an AFM surface scan of the given substrate and by using a colloidal probe with a defined radius. The outputted self-Hamaker constants are found to be in excellent agreement with the predictions from the Lifshitz theory, which now are also obtained with greatly reduced errors, illustrating the robustness of this new approach-to-contact method.