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

Abstract

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 1 κ / d 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 → ∞ and/or 1 / L → 0 .