Van der Waals forces: Accurate calculation and assessment of approximate methods in dielectric nanocolloids up to 16 nm

A microscopic method is used to calculate the van der Waals (VDW) forces between large nanocolloids. We assess the reliability of predictions derived from the most commonly used macroscopic method in practice, the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory combined with the Derjaguin approximation, by calculating the VDW interactions using the "coupled dipole method" (CDM). The CDM, which has demonstrated its ability to calculate VDW interactions for small nanoclusters, accounts for all many-body forces, and it does not assume a continuous, homogeneous dielectric function in each material. It is shown that, out of three explored, one of the routinely assumed properties ("small-separation dominance") of VDW forces predicted from the macroscopic method is generally applicable for large spherical dielectric nanoclusters of diameter 16 nm allowing much more efficient CDM calculations. The failure of two other routinely assumed properties, "infinite-depth approximation" and "sphere-cube analogy," demonstrates that the effect of finite-size and shape is important in nanocolloid systems even at the large size of 16 nm.