ON THE MECHANICS OF ELLIPSOIDAL FULLERENES INSIDE OPEN CARBON NANOCONES: A NOVEL NUMERICAL APPROACH

Abstract

In this research, mechanics of concentric ellipsoidal fullerenes inside open carbon nanocones (CNCs) is investigated. To this end, using continuum approximation in conjunction with Lennard-Jones (LJ) potential function, quadruple-integral expressions associated with van der Waals (vdW) potential energy and interaction force are first derived. For determination of these expressions, it is assumed that the fullerene molecule enters the open CNC through the small end or wide end. Thereafter, an efficient approach based on the differential quadrature (DQ) method is proposed to numerically evaluate the obtained quadruple integrals. The proposed method takes advantage of computing multidimensional integrals efficiently with using appropriate number of grid points. By introducing DQ-based operational matrices of differentiation and integration, the quadruple-integral expressions are estimated over their domains. Moreover, new semianalytical expressions are introduced in terms of triple integrals to evaluate vdW interactions. The validity and accuracy of the introduced numerical method are proved by comparing the results obtained through this method with ones achieved via the semianalytical expressions. The ease of implementation and quick answer of the demonstrated numerical solution enable us to comprehensively examine the effects of different geometrical parameters such as small end radius wide end radius and vertex angle of nanocone on the distributions of vdW potential energy and interaction force. The results reveal that the ellipsoidal fullerene undergoes an asymmetrical motion along the axis of open CNC.