Finite-size effect of the thermal conductivity in one dimensional chain

Abstract

Finite-size effect of the thermal conductivity in one dimensional chain is theoretically investigated with a phenomenological model. Boundary temperature dropping and the spectrum-dependent linear temperature profile within the chain are given self-consistently at high temperatures. A general formula of thermal conductivity is presented and a good agreement with the molecular dynamics simulations is obtained. It is found that while ${\rm{d}}\tfrac{1}{\kappa }/{\rm{d}}\tfrac{1}{{L}}$ decreases with increasing of 1/ L monotonically, the well known linear dependence of thermal resistance 1/ κ on the reciprocal length 1/ L of systems is, however, valid only in two limit cases of $1/L\to \infty $ and/or $1/L\to 0$ .

Keywords

• thermal conductivity
• phonon
• finit-size effect
• spectrum dependent temperature profiles
• non-equilibrium transport