Polymers phonon scattering

As with other disordered materials, the thermal condnctivities of polymers are low due to phonon scattering. As a resnlt, even thongh polymers tend to have heat capacities of the same order of magnitude as metals (1.5 to 3.5 J/g K), their thermal conductivities (0.1 to 1.0 W/m K) are 1000 times lower than metals. Polymers, therefore, are generally good insulators, as long as their use temperature is below their thermal stability temperature. Few correlations for heat capacity and thermal conductivity of polymers... 

In general, the exact functional form of the scattering law is complex. For most experiments on hydrogeneous polymers at low temperatures, the scattering probability has been taken to be proportional to the one-phonon scattering cross-section 74, 34) for crystals of cubic symmetry, namely ... 

When the concentration of chain interruptions is sufficiently high such that the left hand side of equation 1.3 is small, then the wave function will be localised. The possible limits for the conductivity arise from the chain interruptions and/or phonon scattering. All the above factors suggest that in high-quality conducting polymers the electronic mean free path could be much larger than the structural coherence length and real metallic features could be observed. 

Lerner [189] found that oxidized PAN fibers subjected to heat treatment temperatures of 715-945 K are semiconductors. The room temperature conductivity is dominated by the contributions of impurity states, but these are not related to defects in the polymer. There is a decrease in conductivity on ageing in air caused by a decrease in the electron-phonon scattering time. The conductivity increases at temperatures above 473 K, as the samples aged in air outgas. 

In conducting carbon films there is a juxtaposition of sp islands and an sp network that resembles the conjugated chain in a polymer (linear sp bond) with sp defects (o- defects as in a-Ge). In the case of high molecular weight and relatively few sp defects, even relatively weak interchain coupling is sufficient to avoid onedimensional localization. This phenomenon leads to coherent transport with a mean free path that is limited by the mean separation between chain imperfections or by phonon scattering. 

In the case of amorphous polymers, the phonon mean free path is an extremely small constant (a few angstroms) due to phonon scattering from numerous defects, leading to a very low thermal conductivity of polymers (Agari et al. 1997). The thermal conductivity depends on the degree of crystallinity because vibration and movement/rotation of macromolecular chains transfer heat energy. 

Hida S, Shiga T, Maruyama S, Elliott JA, Shiomi J (2012) Influence of thermal boundary resistance and interfacial phonon scattering on heat conduction of carbon nanotube/polymer composites. Trans Jpn Soc Mech Eng Part B 78(787) 634-643 Hilmi Y, Seyhana TA, Servet T, Metin T, Wolfgang B, Karl S (2010) Electric field effects on CNTs/vinyl ester suspensions and the resulting electrical and thermal composite properties. Compos Sci Technol 70(14) 2102-2110... 

Cross-section for multi-phonon scattering of neutrons by crystalline polyethylene. J. Polymer Sci., Part B, 6, 83—86 (1968a). 

The achievement of high performance polymers with electrical and mechanical properties that approach intrinsic values will provide the opportunity to explore the intrinsic mechanisms of transport. For example, the study of the temperature dependence, pressure dependence, etc of phonon scattering in quasi-one-dimensional (quasi-id) metals with sufficient interchain interaction to avoid Id localization will surely be of interest. On the other hand, in the disordered conductor limit, hopping processes in anisotropic... 

In some cases (amorphous materials as polymers or glasses), the scattering of phonons with tunnelling states is also relevant. This process leads to an approximate [40-42,94,95] dependence as T1 2 of k (see Table 3.4) and to a plateau in the 2K < T < 20K range (see Fig. 3.18). 

Currently worldwide six conventional (generic INll type) high resolution instruments are in operation and one is under construction. Two zero-field instruments that are suitable for polymer investigation are available. In addition, several installations for other purposes such as large angle scattering or phonon line width analysis exist (see Table 2.1 for more details). 

Polymer molecules in a solution undergo random thermal motions, which give rise to space and time fluctuations of the polymer concentration. If the concentration of the polymer solution is dilute enough, the interaction between individual polymer molecules is negligible. Then the random motions of the polymer can be described as a three dimensional random walk, which is characterized by the diffusion coefficient D. Light is scattered by the density fluctuations of the polymer solution. The propagation of phonons is overdamped in water and becomes a simple diffusion process. In the case of polymer networks, however, such a situation can never be attained because the interaction between chains (in... 

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