1Assignment 1(MecE 682. NanoMechanics-Dr.CQ Ru) Problems 1-3The van der Waals attractive potential between any atom of body 1 and any atom of body 2 is given by where C is a constant and ris the distance between the two atoms. 1. Consider two parallel straight atom-chains of the atom-number density ρ1and ρ2per unit length, respectively, apart with a distance D. Determine the vdW attractive potential energy and attractive force per unit length of the body 2, as a function of the distance D. 2. Consider a half-space (body 1), of the atom-number density ρ1, and a parallel infinite slab (body 2), of thickness dand the atom-number density ρ2. Use the known formula for the vdW attractive potential energy per unit surface area between two parallel half-space (see lecture-notes), to derive a formula for the vdW attractive potential energy and attractive force per unit surface area of the slab, as a function of the distance D between these two bodies.
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