Toward an Improved Method for Determining the Hamaker Constant of Solid Materials Using Atomic Force Microscopy. I. Quasi-Static Analysis for Arbitrary Surface Roughness

Abstract

The initial development and preliminary validation of improvements to an existing approach-to-contact atomic force microscopy (AFM) method for determining the Hamaker constant, A, of solid materials is presented. The updated method explicitly accounts for the surface topography of the given substrate, which will lead to improved estimates of A and extend the range of the types of the surfaces to which the method can be applied. After deriving a general van der Waals (vdW) force expression between the AFM cantilever tip, treated as an effective sphere, and a surface with arbitrary roughness, the deflection of the cantilever tip at first contact with the surface, d c , is then obtained for all tip locations. Since the vdW force varies locally along the surface, a distribution of d c -values is obtained for a given value of A. For various model surfaces, we discuss the effect of surface roughness on the resulting d cdistributions, which indicates that surface roughness cannot be accounted for in an approximate way. We also present preliminary experimental validation of the updated method, whereby the predicted d c -distribution of a simplified version of an amorphous silica surface is found to compare favorably with the d c -distribution obtained from AFM experiments.

Surface Forces between Nanomagnetite and Silica in Aqueous Ca2+ Solutions Studied with AFM Colloidal Probe Method

“…The calculated snap-in distance was 5.0 nm, which is in fairly good agreement with the experimentally observed snap-in distance at low pH, bearing in mind the accuracy of the nominal cantilever spring constant (some percent) [31]. Also, it should be noted that surface roughness can have an impact on the calculated Hamaker constant [7]. There are also other uncertainties and effects that can affect the evaluated Hamaker constant from the measured force-interaction curves [18,19].…”

“…The measurement of force interactions between particles in predefined conditions was shown to significantly contribute to particle dispersion and adhesion studies [2,3]. Knowledge about the forces acting between particles in aqueous solutions is of fundamental importance in various applications, such as mineral processing, biomedicine, nanoelectronics, and adhesives [4][5][6][7]. Iron oxide nanoparticles have attracted significant research interest due to their superparamagnetic properties [8] and high potential to be used in biomedicine [6].…”

“…For this purpose, using a spherical silica probe allows the application of common theoretical models. The determination of interaction force, double-layer thickness, and surface charges is commonly carried out with the DLVO model [7,13,14]. The electrostatic part of the DLVO model is usually obtained by solving the Poisson-Boltzmann equation within boundary conditions, such as a constant surface potential or a constant surface charge on each boundary [15].…”

“…Specific ion effects and pH dependences can affect both long-range and especially short-range forces, and non-DLVO forces, such as hydrophobic and hydration forces, should be considered [12,16]. Moreover, the roughness has to be considered since the surface roughness can cause a dramatic effect on measured values and, therefore, on the evaluation of the adhesion [17] and affect the Hamaker constant [7,18,19].…”

Toward an Improved Method for Determining the Hamaker Constant of Solid Materials Using Atomic Force Microscopy. II. Dynamic Analysis and Preliminary Validation

“…11−15 The current authors recently presented the important first steps needed for the development of an improved experimental AFM-based method to estimate A with high accuracy solely from the approach-to-contact portion of the deflection curve. 16 In contrast to previous approaches, this new method explicitly accounts for the inherent surface roughness of the substrate. In ref 16, a novel expression for the vdW force between a surface with arbitrary roughness and the AFM cantilever tip, treated as an effective sphere, was obtained.…”