262909 Measuring Hamaker Constants by Atomic Force Microscopy From the “Jump-Into-Contact” Distance: Quasi-Static Models and Dynamic Simulations
The Hamaker constant is a quantitative measure of the fundamental attractive van der Waals interactions among particles, between particles and a flat surface, and other geometries. It plays an important role in numerous phenomena and behaviors of materials, such as colloidal stability, interfacial adhesion, and nanoparticle self-assembly.
Improved methods and procedures for determining the Hamaker constant from atomic force microscopy (AFM) measurements are presented. A quasi-static analysis is used to correct an earlier method based on the “jump-into-contact” distance represented by the delta d-value, accounting for the tip-surface interaction forces or energies. It is further extended to three tip-surface models in addition to the simplest sphere-plane model. The sensitivity of all four models to predicting the delta d-values and from them the Hamaker constants is investigated. A mechanical-energy-based analysis is also reported. It predicts the same results as the quasi-static force analysis, but offers additional insights on the mechanical stability of the tip.
In addition, a novel dynamic analysis of the tip motion is developed to simulate the tip motion for determining the time-dependent tip deflection as a function of two dimensionless groups, a and b. The parameter a is the ratio of the characteristic time of the tip to the time scale of the tip motion. The parameter b involves some characteristic properties of the tip, i.e. the radius of curvature and the spring constant, and an operational parameter, which is the initial tip height relative to the surface. Effective delta d-values depend on the number of data points sampled from the dynamic curve describing the motion of the tip. As the number of data points increases, the thus-determined dynamic delta d-value decreases. As the approaching speed of the cantilever decreases, the dynamic delta d-value approaches the quasi-static delta d-value. Therefore, the dynamic analysis provides insights on how to improve the experimental procedures for obtaining more accurate and reliable Hamaker constants.
Finally, the quasi-static delta d-values are compared with the dynamic AFM data for three model systems of glass (amorphous SiO2), polystyrene, and crystalline copper phthalocyanine (CuPc). The measured data are in fair agreement with the predictions from four models using the literature values of the Hamaker constants. To further test the methods quantitatively, additional measurements with improved experimental procedures, AFM instrument designs, and tips and materials, are needed.