Orientation-Dependent London-van der Waals Interaction Energy between Macroscopic Bodies

The aim of this work is to derive formulas for numerical calculations of the orientation-dependent London-van der Waals (vdW) interaction energy (V(A)) between two rectangular bodies with arbitrary dimensions, arranged at arbitrary relative angles (θ) and separations in twisted and coplanar rotational modes. The formulation is made using a simple volume-element-integration method in the framework of the microscopic approach, in which V(A) is the sum of the local vdW energy (Vp) between body 1 and each thin plate constituting body 2. Examples of the calculation results are the following: (1) The θ values that give maximal and minimal values of V(A) depend on their shapes and relative positions. (2) As the bodies come close to each other, the variations of V(A) with θ and thus vdW dispersion torques generated are drastically intensified. (3) Upon increasing the length of crossing rods in twisted configurations, the V(A) values become constant beyond a critical length (depending on θ and separation), where the length effect on V(A) disappears. (4) The distribution curves of Vp show that the region in body 2 which interacts effectively with body 1 (i.e., the effective interaction region) is more sharply localized in the vicinity of the surface (closest to body 1) as the separation is decreased.