Study On Correlation Between Heat Conduction And Thermal Expansion Of One - Dimensional Lattice System

With the development of experimental technology, the phenomena that violate Fourier’s law are observed in many thermal experiments in low dimensional nano materials, which indicate that the traditional theory of heat conduction has deficiency in the description of the heat conduction in low dimensional system. Therefore, it is necessary to improve the traditional theory of heat transport.At present, the mode coupling theory based on fluid dynamics and renormalization group theory, have been proposed. They give the same predictions, i.e., the thermal conductivity in one dimensional momentum conservation systems diverges with the system size in power law but the exponents predicted by two theories are not the same, which may be caused by different approximate methods. In2000, Bambi Hu, Baowen Li and Hong Zhao reported their numeric experimental results in a one dimensional classical lattices, which shows that momentum conservation implies anomalous conductivity. Lately, T. Presen and D. K. Campbell also further proved theoretically that for one dimensional momentum conservation lattices with nonvanishing internal pressure must show anomalous heat conduction behavior in the thermodynamic limit. However, the recent work of Hong Zhao shows that asymmetric interparticle interaction of one dimensional momentum conserving lattice systems with nonvanishing internal pressure will produce local mass current which leads to heat carriers suffering additional scattering. The system may present normal heat conduction while the scattering is strong enough, which reveals that the existing thermal conduction theory is also imperfect. Hence, a more complete heat conduction theory should be established based upon the microscopic dynamical mechanism. At the same time, the research also implies that there is an internal correlation between thermal expansion and thermal conductivity.Based on the above considerations, the correlation between thermal expansion properties and thermal conductivity behavior of one dimensional momentum conserving lattice is investigated in the one-dimensional FPU-a(3lattice and one-dimensional asymmetric harmonic interparticle interaction lattice (AHIIL).Firstly, the thermal expansion properties of the models are studied by the numerical simulation. It has found that normal thermal expansion, zero expansion and negative thermal expansion are observed in ID FPU-a(3lattice and ID AHIIL with asymmetric control parameters varies. The numerical calculation and theoretical analysis suggest the following conclusions:1) the expansion coefficient tends to zero under arbitrary parameters of these two systems in the high temperature limit, but in the low temperature limit, the systems show completely different properties. The expansion coefficient of FPU-αβ lattice is still zero, however, it is always divergent for AHIIL under arbitrary asymmetric control parameters;2) The lattice constant should not be less than the average relative displacement between atoms in numerical simulation, otherwise it will get qualitatively wrong results, i.e. the selection of lattice constant will affect the properties of thermal expansion in simulation;3) For models with double well structure potential function, the best initialization should make the relative displacements between atoms obey Boltzmann distribution at corresponding temperatures. Nevertheless, to the case where the zero relative displacement point is not the absolute minimum value of potential function. Special care should be made when calculating the expansion properties at low temperature. Otherwise, some qualitative mistakes will appears.Then, the thermal conduction properties of these two lattice models are discussed qualitatively by Green-Kubo formula in the framework of linear response theory. For the FPU-αβ model, our numerical results and the previous results show that the damped exponent of current correlation functions is increasing with the expansion coefficient increasing. For the AHIIL model, the system exhibits anomalous heat conduction when the potential asymmetric control parameter is small. The normal heat conduction is observed when the control parameter is larger and the numeric calculation of the current correlation function shows that the heat conductivity seems to be a constant independent of temperature. At the fixed temperature, the greater the control parameters, the larger the corresponding thermal expansion coefficient and damped exponent of correlation function. However, the temperature will affect the thermal expansion coefficient, but the damped exponent of heat current correlation functions is independent of temperature under fixed control parameters.In conclusion, our results show that there is a close correlation between the thermal expansion and thermal conduction in one dimensional momentum conserving lattice with asymmetric interpartilce interaction. But the quantitative correlations between them need to be further determined. Our results provide the data support for building a complete heat conduction theory.