Critical Length of Double-Walled Carbon Nanotubes Based Oscillators

The critical lengths of an oscillator based on double-walled carbon nanotubes(DWCNTs)are studied by energy minimization and molecular dynamics simulation.Van der Waals(vdW)potential energy in DWCNTs is shown to be changed periodically with the lattice matching of the inner and outer tubes by using atomistic models with energy minimization method.If the coincidence length between the inner and outer tubes is long enough,the restoring force cannot drive the DWCNT to slide over the vdW potential barrier to assure the DWCNT acts as an oscillator.The critical coincidence lengths of the oscillators are predicted by a very simple equation and then confirmed with energy minimization method for both the zigzag/zigzag system and the armchair/armchair system.The critical length of the armchair/armchair system is much larger than that of the zigzag/zigzag system.The vdW potential energy fluctuation of the armchair/armchair system is weaker than that of the zigzag/zigzag system.So it is easier to slide over the barrier for the armchair/armchair system.The critical lengths of zigzag/zigzag DWCNTbased oscillator are found increasing along with temperature,by molecular dynamics simulations.

Effective attractive potential between identical dielectric molecules via Lifshitz theory

A general theory of Van der Waals forces developed by Lifshitz based on quantum electrodynamics theory is applied in the range R?λ0( where the Casimir effects may be neglected) to construct Van der Waals attractive potential between identical dielectric molecules in rarefied media in order that the effective attractive potential between the like-molecules (including the repeat units) is offered. A closed form solution for the integral formulation of the attractive potential between like-particles is first obtained based on certain assumptions made in this work. On the basis of the theory of electric polarization, the derived expression in terms of bulk properties is then compared with the well-known London formula, the former differs from the latter only by the fact $\frac{4}{\pi }or\frac{4}{\pi }\left( {\frac{{\varepsilon _\infty + 2}}{3}} \right)^2 $ The validity of the effective potential can be verified by testing cases composed of several types of dielectric materials. The computed results are presented in this paper, and comparisons with the results computed by London dispersion formula, as well as the recommended values in virtue of the experimental and theoretical techniques, are also presented. The effective potential of polyethylene is also computed to demonstrate the effectiveness of the developed model, and it is found that the computed well depth fall within a reasonable range of accuracy.