NON-STATIONARY THERMAL CONDUCTIVITY OF CHAIN STRUCTURES AT LOW TEMPERATURES

Abstract

The matter of thermal conductivity is considered in an approximation, in which the free length of phonons is limited and doesn't depend on temperature, so that the temperature behavior of thermal conductivity coefficient is only determined by thermal capacity. In these conditions the problem of non-stationary thermal conductivity of chain structures at low temperatures (T<<θ, θ for Debye temperature) is solved with the use of the variables separation method. Solutions relating to the areas with both moving and fixed borders are considered. Special choice of border motion law allowed us to bring the initial problem to the problem with fixed borders, but with reformed equation of thermal conductivity. The results obtained can be applied for studying the thermal conductivity of crystal carbon existing in the form of carbine (synthetic polymeric chained structure). The found solutions of the equation of non-stationary thermal conductivity of highly anisotropic crystals can also be used while studying thermal conductivity in melted quartz fibres and highly oriented fibres of polyethylene. Melted quartz fibres have a disordered atomic structure, but with an uninterrupted net of silica-oxygen links. The effective sizes of crystallites in such substance are of the same order as those of separate tetrahedrons of silica dioxide. One may assume that in this case the free length of phonons remains constant, limited only by the size of the crystallites, and the decrease of thermal conductivity coefficient while lowering the temperature is caused only by the decrease of heat capacity. Polyethylene of a higher crystallinity degree has almost the ideal structure of lamellar type. The borders of lamellas scatter phonons, so that the probability of scattering practically doesn't depend on the length of phonon's wave. Thus, in this case the free length of phonons won't remain constant and is determined by the size of lamellas, so that thermal conductivity will be proportional to heat apacity.apacity.

Keywords

• low temperatures
• equation of non-stationary thermal conductivity
• chain structures