Wall "thickness" effects on Raman spectrum shift, thermal conductivity, and Young's modulus of single walled nanotubes

We theoretically demonstrate that at a finite temperature, an effective wall thickness of a single walled carbon nanotube (SWNT) should be $W=W_s+W_d$, where $W_s$ is the static thickness defined as the extension of the outmost electronic orbit and $W_d$ the dynamic thickness due to thermal vibration of atoms. Both molecular simulations and a theoretical analysis show that $W_d$ is proportional to $\sqrt{T}$. We find that the increase of dynamic thickness with temperature is the main mechanism of Raman spectrum shift. The introduction of dynamic thickness changes some conclusions about the Young's modulus and reduces the values of thermal conductivity.