(474i) Preliminary Validation of an Improved Approach-to-Contact Method for Determining the Hamaker Constant of Solid Materials Using Atomic Force Microscopy

The Hamaker constant, A, quantifies the 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, explosives detection systems, next-generation solar cells, tissue engineering technologies, and biomimetic polymers. Such estimates are often obtained using atomic force microscopy (AFM) in contact sampling mode. This work is concerned with continuing improvements to an existing approach-to-contact method, originally developed by Fronczak et al. (2017, Langmuir 33, 714-725), that relates A to the deflection of the AFM cantilever tip at first contact with the surface, d_c. Topographical features on interacting surfaces lead to local variations in surface separation at the nanoscale, which results in a distribution of d_c-values for given interacting surfaces of interest.

Here, we present a dynamic model of an AFM cantilever approaching a surface of arbitrary roughness. This model provides the framework for which an experimentally-obtained d_c-distribution can be used to extract an accurate value of A to describe the interaction between the cantilever and the surface of interest. For various surfaces, we discuss the impact of the cantilever approach speed, v_c, on the shape and magnitude of the resulting d_c-distribution. An effective A can be obtained for a particular substrate and v_c by minimizing the sum of squares error between the d_c-distributions generated from the dynamic model and the quasi-static limit (i.e. when v_c approaches 0). The effective A approaches the “true” A at sufficiently slow cantilever approach speeds, and this trend has been validated computationally for various model surfaces. Therefore, the behavior of the cantilever is well-described by the quasi-static model and so d_c-values obtained experimentally may be properly compared with those predicted using the previously-developed quasi-static model (Stevenson et al. J. Phys. Chem. C 2020, 124, 3014-3027).

Finally, we present a preliminary experimental validation of the approach-to-contact method through comparison of predicted d_c-distributions to those obtained from AFM measurements for an amorphous silica surface. Assuming that the roughness features of a single scan are descriptive of an entire surface, we utilize fast Fourier transforms to generate many similar surfaces by transposing surface features while maintaining the same amplitude spectrum and root-mean-squared roughness as the original scanned surface. Applying the quasi-static approach-to-contact model with these surface permutations as input parameters, we then generate a statistically averaged d_c-distribution describing the entire surface and use this distribution to compare with those obtained experimentally. The Hamaker constant of amorphous silica determined through the improved approach-to-contact method compares favorably to literature values and is reported with a significant reduction in uncertainty compared to the previous approach-to-contact method.