Experimental Validation of a New Method for Estimating the Hamaker Constants of Solid Materials via Atomic Force Microscopy: Utilizing Both Approach-to-Contact and Pull-Off Deflections

Abstract

Accurate predictions of the Hamaker constants, A, of a broad range of solid materials can be obtained from both the distributions of the deflections at first contact, dc, and the pull-off deflections, dPO, determined via atomic force microscopy (AFM). Using a model that describes both the attractive van der Waals (vdW) forces and the repulsive steric interactions between a sphere (AFM probe) and a substrate with arbitrary surface roughness, the comparison of model-predicted and experimentally obtained deflection distributions yields unique pairs of A and the effective diameters, σ, of the materials comprising the AFM probe and substrate. Four different AFM probes were contacted against five different substrates to determine the dc- and dPO-distributions from experimental AFM deflection-distance (DD) curves. AFM image scans were obtained along each substrate in the vicinity of where the DD curves were collected in order to generate the model-predicted dc- and dPO-distributions. The difference between the model-predicted and experimental distributions was quantified with the Wasserstein distance, which yielded best estimates of A and σ, along with meaningful asymmetric error estimates of both parameters. The obtained values of the self-Hamaker constants for several solid materials are in good agreement with the Lifshitz theory predictions. The estimated values of σ are consistent with the corresponding atomic sizes appearing in the literature. The model that incorporates both the attractive vdW and repulsive steric interactions also indicates that dynamic effects are negligible for dPO and give rise to similar relative changes of dc that were observed in previous studies.