Understanding the adhesive behavior of solid particles is a primary concern for improving the efficiency of solid processing, pharmaceutical manufacturing and explosives detection. In solid particulate systems, intermolecular interactions become the dominant, system- governing forces as the size of the particles approaches the micro- and nano-scale. As a result, understanding the forces that govern these interactions is imperative for modeling the adhesive properties of particle-particle and particle-substrate systems. While most intermolecular forces are heavily dependent on sampling conditions (ie. relative humidity and surface charge), the van der Waals (vdW) interaction is ubiquitous and, thus, of upmost importance when characterizing adhesive behavior. The vdW interaction is dependent on three system characteristics: 1) the separation distance between the two surfaces, 2) the surfaces’ geometric features, and 3) the material-dependent “Hamaker” constant, A.
In order to avoid unpredictable contact regime deviations caused by surface roughness, a non-contact method for estimating Hamaker constants is desirable. One current non-contact method for determining A of solid materials uses an atomic force microscope (AFM). First, AFM data are gathered regarding the cantilever tip deflection under the influence of the attractive vdW force between the tip and the solid. Second, a quasi-static analysis is used to fit the dynamic data, which enables one to infer the jump-into-contact distance, Δd, and hence the value of A. Here, we evaluate the validity of this quasi-static method and develop an improved procedure for determining A, which acknowledges explicitly that the cantilever tip motion is dynamic, and not quasi-static.
We begin by correcting an earlier quasi-static method based on the “jump-into-contact” distance for the simplest sphere-plane model. Next, a rigorous dynamic analysis of the tip motion is developed to determine the time-dependent tip deflection. The tip motion is found to deviate from the predictions of the quasi-static analysis except at the limit of very low or zero cantilever speeds. This dynamic analysis also indicates that a “jump-into-contact” distance, which is defined in the quasi-static analysis, cannot be uniquely determined from the dynamic AFM data. Hence, a new method is needed if the quasi-static model is still to be used when interpreting this data.
We introduce a straightforward, non-contact method whereby a unique application of the quasi-static model is used to analyze dynamic AFM data in order to determine an apparent Hamaker constant. The apparent A determined from this test depends upon the cantilever speed and weakly on the spatial resolution δ of the data points, and should converge to the value of A obtained from the quasi-static model in the limit of zero cantilever speed. We employ both theoretical and experimental validation techniques for the method in order to establish a practical strategy to improve the accuracy of Hamaker constant estimation for future intermolecular interaction studies.
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