An uncertainty budget analysis on the Hamaker constant determined when fitting force-distance curves for a sphere-plate system

The Hamaker constant A governs the van der Waals or Born force between macroscopic bodies. Its value can be determined by fitting theoretical equations to the non-contact force FNC measured using atomic force microscopy during the approach of a colloidal sphere to a flat plate. Starting from a general equation for FNC, this report derives the corresponding relative uncertainty budget expression Δr2A≡ΔA/A2 as a function of weighting factors ωj2 or ϕj2, sensitivity factors Sj,k2, overall relative uncertainties Δr2Xj, relative measurement uncertainties δr2xk, and relative measurement noise Δr2Fm. Case studies and empirical estimates are given to demonstrate its applications.115