A method to quantitatively evaluate the Hamaker constant using the jump-into-contact effect in atomic force microscopy

Abstract

We find that the 'jump-into-contact' of the cantilever in the atomic force microscope (AFM) is caused by an inherent instability in the motion of the AFM cantilever. The analysis is based on a simple model of the cantilever moving in a nonlinear force field. We show that the 'jump-into-contact' distance can be used to find the interaction of the cantilever tip with the surface. In the specific context of the attractive van der Waals interaction, this method can be realized as a new method of measuring the Hamaker constant for materials. The Hamaker constant is determined from the deflection of the cantilever at the 'jump-into-contact' using the force constant of the cantilever and the tip radius of curvature, all of which can be obtained by measurements. The results have been verified experimentally on a sample of cleaved mica, a sample of Si wafer with natural oxide and a silver film, using a number of cantilevers with different spring constants. We emphasize that the method described here is applicable only to surfaces that have van der Waals interaction as the tip-sample interaction. We also find that the tip to sample separation at the 'jump-into-contact' is simply related to the cantilever deflection at this point, and this provides a method to exactly locate the surface.

Morphology of polymeric powders in Laser Sintering (LS): From Polyamide to new PEEK powders

“…Van der Waals' forces are often taken into account to evaluate the intermolecular interactions responsible of macroscopic properties between the particles of a given material [37]. In this scenario, the Hamaker constant is a force constant able to predict or estimate the interparticle interactions by considering the physic-chemical nature of the materials involved [38][39][40][41][42]. In general, in the interaction of two spheres, the smaller the Hamaker constant is, the smaller the Van der Waals' forces are likely to be [43] and therefore the better the particles will flow.…”

Nanofluids: Stability, phase diagram, rheology and applications

“…In practice, it is difficult to calculate or directly measure the forces. Hamaker constants have been calculated using Lifshitz theory, and forces calculated via aggregation rate, electrophoresis, particle force light scattering (PFLS) and, more recently, atomic force microscope (AFM) and differential electrophoresis (Anderson, Velegol, & Garoff, 2000;Das, Sreeram, & Raychaudhuri, 2007;Lifshitz, 1956;Muir, Meagher, & Gee, 2001;Seog et al, 2002;van de Ven & Mason, 1976a, 1976bVelegol, Holtzer, Radović-Moreno, & Cuppett, 2007).…”

Assembly of Gold Nanowires by Sedimentation from Suspension: Experiments and Simulation

“…The following values of the Hamaker constants were used: A Au =40×10 −20 J, A w =3.73×10 −20 J, and A m =5.0×10 −20 J 74, 75. In Eq.…”