One of the major factors that controls the swelling and exfoliation behavior of layered inorganic materials is the van der Waals (vdW) interaction. The vdW force, considered to be a weak interaction in many cases, has a strong influence on the structure and properties of colloidal and nano-materials, especially the swelling and exfoliation of nanometer-thick platelets in inorganic layered materials. However, since the vdW force is ultimately a quantum mechanical interaction, additive behavior is typically not a good assumption, and so accurate theoretical evaluation of vdW interactions is limited to just a few special cases. Among the various theoretical methods, Lifshitz theory is successful and popular due to its solid theoretical foundation and satisfying accuracy at length scales greater than 5 nm. However, the Lifshitz theory has two significant drawbacks: it is exact only for a few special geometries, and it ignores the discrete atomic structure of matter at very short range ( 2 nm).;To overcome the above drawbacks in the prediction of the vdW interaction in layered inorganic materials, we explore the use of the Coupled Dipole Method (CDM), an approximate method for computing the many-body interaction of nanoscale bodies composed of discrete atoms. Since it is quite difficult to experimentally measure the vdW interaction between nanoscale clusters of atoms with different specific geometries, we compare CDM calculations of vdW interactions with predictions from various existing approaches in order to study the performance of the CDM. First, we analytically solved the CDM equations for the case of a single pair of atoms, comparing the result with the London equation for two interacting atoms, and established a relationship between parameters used in these two methods. For the interaction of two nanoscale atomic clusters, we compared CDM predictions with those from pairwise summation and the Hamaker method. For spherical clusters, the orientation effects are studied. For platelets, edge and thickness effects are studied. Finally, the CDM is applied to compute the vdW interaction of crystal lattice sheets of muscovite mica and compared with the results of the Hamaker method. Due to the complexity of the crystal lattice, we coarse-grained the crystal lattice in various ways and studied the effect on vdW interaction energy. Our studies show that the CDM yields similar results as the Hamaker method for platelets at large separations. One can compensate for edge effects in order to obtain smoothly varying interaction energy curves for large platelets.
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