Hamaker constants and dispersion forces interactions of materials are of increasing interest and the advent of atomic force microscopy ͑AFM͒ force measurements represents a new opportunity for quantitative studies of these interactions. A critical problem is the determination of a force-distance relation for realistic AFM probes. Due to the inadequacies of existing power-law sphere-plane models to describe the probe-sample system, we present a new parametric tip force-distance relation ͑PT/FDR͒. A surface integration method is developed to compute the interactions between arbitrarily shaped bodies. The method is based on the Hamaker pairwise integration in a continuous fashion, reducing the six-dimensional integration to a four-dimensional scheme. With this method, the PT/FDR is obtained and a nonlinear fitting routine is used to extract the model parameters and the Hamaker constant from AFM force-distance data. From the sensitivity analysis of the fitting of synthesized AFM force-distance data, one finds that, for large tip radius ͑compared to separation͒, the force is proportional to the product of the Hamaker constant and tip radius. Unique determination of the Hamaker constant can be achieved if a small radius tip is used in the AFM scan. By fitting to literature data, the effectiveness of the PT/FDR is shown.

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Coalescence of a Maxwell viscoelastic sphere to a frictionless and flat rigid plane is analyzed to study the transition from initial elastic adhesion to viscous sintering. Deformation is driven by surface tractions due to the surface energy. The formulation for surface forces consistently combines direct van der Waals attraction across the gap ahead of the contact edge with curvature-based tractions normal to the sphere surface. These two contributions to the surface traction result in two different modes of contact growth. The initial elastic contact and the early stage of time-dependent contact growth are in a zipping mode of contact closure dominated by direct attractive forces. The later stage of sintering is by stretching of the contact and is dominated by curvature-based tractions. The transition from the initial elastic contact to the zipping mode of contact growth is viscoelastic. For a given sphere radius, kinetics of the zipping mode of contact growth scale with a characteristic viscous sintering time. However, this mode is not part of the existing sintering models because direct attractive tractions were neglected in previous analyses of sintering. This stage of coalescence does not have unique scaling with sphere radius. The transition from the zipping to stretching mode of contact growth occurs at a contact radius that depends on sphere radius. The stretching mode of contact growth is in good agreement with previous analyses of viscous sintering.