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 d d L 11 k 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 L 1  ¥ and/or L 1 0  .