C. L. Choy

Thermal conductivity of polymers

Abstract In this review we have concentrated on the interpretation of three essential aspects of the thermal conductivity K of polymers: the temperature dependence, the crystallinity dependence and the orientation effect. K for all amorphous polymers is approximately equal in magnitude and characterized by a T2 dependence below 0.5K, a plateau region between 5 and 15K and a slow increase at yet higher temperatures. While a number of models involving different phonon scattering mechanisms are capable of explaining these features, further corroborating evidence would be needed to explain the ad hoc assumptions involved. For semicrystalline polymers K shows both strong crystallinity and temperature dependence, with a distinctive cross-over point at about 10K. These marked features can now be understood as the result of the interplay between two competing factors: the intrinsically higher conductivity in the crystalline regions, and the reduction in K due to an additional phonon scattering mechanism which becomes important at low temperature. This scattering could arise from either the correlation in the spatial fluctuation of the sound velocity in the polymer or the acoustic mismatch at the interfaces between the crystallites and the amorphous matrix. Orientation produces a very large anisotropy in semicrystalline polymers, which however decreases at low temperature and becomes insignificant below 10K. This feature can again be understood in terms of the same competing mechanisms if one realizes that the molecular chains in the crystallites are essentially lined up along the direction of orientation thus offering very little thermal resistance along this direction. For polyethylene with an extrusion ratio of 25 the thermal conductivity at 100K along the extrusion direction is 91 mW/cm K, a value extremely high for polymers and close to that of stainless steel. At this temperature the anisotropy is only about 20, yet because of the different temperature dependence of the thermal conductivity along and perpendicular to the extrusion direction, we predict an anisotropy as high as 60 at room temperature.

Thermal conductivity of highly oriented polyethylene

Abstract We have measured the thermal conductivity of oriented polyethylene both along and perpendicular to the draw direction for draw ratio λ between 1–25 and in the temperature range of 120 to 320K. The results for λ ⩽ 5 have been analysed in terms of the modified Maxwell model while the further increase of thermal conductivity along the draw direction at higher λ has been explained by the Takayanagi model. The Youngs modulus and thermal conductivity along the draw direction for the sample with λ = 25 were found to be 64 GN/m2 (at 220K) and 140 mW/cm K (at 300K), respectively, which are extremely high values for polymers. This material, which is a good electrical insulator and yet has a high thermal conductivity, may be useful in electrical applications requiring large dissipation of heat.

Thermal conductivity of semicrystalline polymers — a model

Abstract The thermal conductivity of semicrystalline polymers, regarded as two-phase materials, is discussed in terms of the Maxwell model generalized to the case where the inclusions are thermally anisotropic. The predicted effect of orientation agrees well with the large anisotropy observed in oriented polymers. The conductivity of the crystallites normal to the chain axes has also been extracted using this model. A recently proposed model for composites which incorporates interfacial boundary resistance has been applied to the low temperature data for poly(ethylene terephthalate), not only explaining the decrease of conductivity with crystallinity, but also allowing the effective crystallite shape and the boundary resistance to be determined. The latter is found to vary as T−2.

Anistropic thermal expansion of oriented crystalline polymers

Abstract The linear thermal expansitivity of oriented high-density polyethylene (HDPE) and polypropylene (PP) with draw ratio between 1 and 18 has been measured between 120 and 300 K. The expansivity perpendicular to the draw direction z (α ⊥ ) increases with λ, because of the alignment of the crystallite chain axes along ẑ; the expansivity parallel to z (α ue302 ) decreases very sharply with λ, becoming negative at about λ = 3 for HDPE and λ = 7 for PP — a consequence of the negative expansivity of the crystalline phase along its chain axis and the constraining effect of the stiff intercrystalline bridges. A model treating the drawn crystalline polymer as a composite consisting of partly aligned crystallites embedded in an isotropic amorphous matrix is adequate for explaining the behaviour of α⊥, whereas a parallel-series model can give reasonable estimates of α ue302 for ultra-oriented samples, which is largely independent of λ and decreases with increasing temperature. However, neither model can account for the behaviour of α ue302 at low draw ratio.

Thermal conductivity of amorphous alloys above room temperature

The thermal conductivity of ten amorphous alloys has been measured between 280 and 500 K. The thermal conductivity, K, can be separated into the electronic (Ke) and phonon (Kph) contributions. The electronic thermal conductivity, deduced from the Wiedemann–Franz law, varies almost linearly with temperature, whereas the phonon thermal conductivity shows a slower increase. At 300 K, Kph accounts for 34–49% of K. The phonon mean free path l is 12.5 A for the binary alloy Fe80B20, but l decreases as the number of chemical components increases, reaching 7 A for the five‐component alloys Fe32Ni36Cr14P12B6 and Co66Fe4Mo2B12Si16. The metal‐metal glasses, Cu70Zr30 and Cu45Zr55, have l values slightly larger than 11 A, indicating that they have short‐range order similar to that of Fe80B20.

Specific heat and thermal diffusivity of strontium barium niobate (Sr1−xBaxNb2O6) single crystals

The specific heat and thermal diffusivity of Sr1−xBaxNb2O6 (x=0.33 and 0.48) single crystals have been measured between 130 and 500 K, and the sound velocity has been measured at 295 K. At x=0.33 the specific heat shows a broad peak at 335 K, indicating the onset of a ferroelectric phase transition. The peak sharpens and shifts to about 383 K at x=0.48. A jump in the thermal diffusivity D is observed at the transition. Away from the transition, however, D is roughly independent of temperature. There is very little anisotropy in D, with the value along the a axis marginally higher than that along the c axis. Outside the transition region the phonon mean free path l is approximately constant, and has values of 5.1 and 5.6 A, respectively, below and above the transition. The low values of D and l are due to the disorder arising from the random distribution of five Sr/Ba ions over six possible sites in a unit cell.

Thermal diffusivity of polymers by the flash method

Abstract We have adopted the flash method to the measurement of thermal diffusivity α of polymers in the temperature range 100–400K. The pulsed radiant energy from a flash tube is applied to the ‘front’ side of a suspended sample disc, and α is deduced from the exponential decay time constant of the subsequent transient temperature difference between the ‘front’ and the ‘back’ side, while correction against radiation loss is made by measuring the much longer decay time of the back-side temperature. Calibration runs on polycarbonate (PC) samples of several thicknesses show that the method is quick, precise and fairly accurate, and the results obtained are in reasonable agreement with previous determinations. We have also carried out measurements on polyoxymethylene (POM), poly (vinylidene fluoride) (PVF2) and poly (ethylene terephthalate) (PET) and computed their thermal conductivities. Results on POM and PVF2, which are semicrystalline, are analysed in the framework of several two-phase models, and the effect of crystallization (produced by annealing) on the glass transition behaviour of PET has also been studied.

Mechanical relaxations and moduli of oriented semicrystalline polymers

Abstract A systematic investigation was carried out on the mechanical relaxations and moduli of four drawn semicrystalline polymers: polyoxymethylene, polypropylene, polyvinylidene fluoride and polychlorotrifluoroethylene. Low-frequency tensile and torsional measuremnts were made between-140 and 140°C, and ultrasonic measurements of all five moduli were made by the water-tank method between 0 and 60°C. The patterns of relaxations remain essentially unchanged upon orientation, but there is a marked reduction of the height of relaxation peaks associated with the amorphous phase and, correspondingly, a smaller drop of moduli in the relaxation region. This reflects a lowering of molecular mobility in the amorphous phase due to the constraining effect of taut tie-molecules. The modulus C 33 increases sharply with draw ratio λ while the other moduli show little variation, which result from the alignment of molecular chain axes and the production of taut tie-molecules. The λ-dependence of the moduli is consistent with the aggregate model only when the polymer is glassy, that is, when its amorphous phase is comparable in stiffness to the crystalline phase and the polymer can reasonably be regarded as a one-phase material for which the aggregate model is valid.

Ultrasonic studies of three fluoropolymers

Abstract The ultrasonic velocities and attenuations of poly(vinylidene fluoride), poly trifluoroethylene and polychlorotrifluoroethylene at 10 MHz from 170 to 300 K have been measured by the pulse echo-overlap and the pulse-height comparison methods, respectively. Discontinuities in the slopes of the velocity — temperature curves and concurrent sharp rises of attenuations were observed, and were identified with previously reported transitions. An analysis of the fractional changes in the corresponding temperature coefficients was made. The velocity data extrapolated to 0 K by Raos rule were combined with presently available thermal data to yield the effective three-dimensional intermolecular force constants in the Tarasov model, and to confirm the existence of low-frequency vibrational modes contributing to the specific heat of polychlorotrifluoroethylene. The magnitude and temperature dependence of the elastic moduli and the Poisson ratio in relation to those of the velocities are also discussed.

Ultrasonic measurements of the mechanical relaxations and complex stiffnesses in oriented linear polyethylene

Abstract The five complex stiffnesses of highly oriented linear polyethylene produced by hydrostatic extrusion and die drawing have been determined by ultrasonic measurements. The results are compared with the elastic stiffnesses for crystalline polyethylene calculated theoretically. The development of anisotropic mechanical behaviour with draw ratio is discussed in terms of present structural understanding of highly oriented polyethylene. Although the very high stiffnesses obtained at the highest draw ratios are attributed to increasing crystal continuity, it is noted that the development of anisotropy in terms of low-temperature ultrasonic behaviour can be predicted to a good approximation by the reorienting unit aggregate model. This surprising result suggests that the overall orientation may still be the key parameter at low temperatures and high frequencies where there is no molecular mobility in the structure.