Phonon wavelength, dominant

In this temperature range, the number of phonons is small, and their scattering is due to lattice defects or to crystal boundaries. Of the two processes of scattering, the latter is of more importance since, at low temperatures, the dominant phonon wavelength is larger than the size of the lattice imperfections. As a consequence Aph is usually temperature independent. Hence, the temperature dependence of the thermal conductivity is that of the specific heat ... 

At temperatures where the dominant phonon wavelengths of interchain modes are of the order of the cross-link distance, a pronounced effect of cross-linking on thermal conductivity and thermal expansion was found. Both quantities were strongly determined by anharmonic contributions of the binding potential. Elastic mechanical parameters or specific heat, which can be described in the harmonic approximations, showed no influence of cross-linking. The interpretation that the... 

At low temperatures, Ac, may fall even below that of the matrix. The cause is a thermal boundary resistance between the filler and the matrix, which is a pl enomenon of phonon mismatch. This resistance, the Kapitza resistance, varies as T and is dominant at low temperatures. If the dominant phonon wavelength --T ) becomes larger than the particle diameter, this effect disappears. Whether or not Ac is increased or decreased, depends on the predominance of the Kapitza resistance and the thermal shortcut in the filler particles. At a fixed temperature, this is a function of the filler diameter, as shown in Fig. 12. Small particles can be used to reduce Ac below that of the matrix. Illustrative examples [ are shown in... 

At cryogenic temperatures, interchain interaction, governs most pol3mier properties, as is evident for elasticity and most thermal properties. Dominant phonon wavelengths become large enough to estabUsh a similar intra- and interchain phonon flux. 

At low temperatures, mechanical properties such as elasticity or strength are less influenced by morphology than they are at ambient temperatures, because both amorphous and crystalline domains are frozen. In some poljrmers, crystallites and tie molecules cause an increase of ultimate strain. As to thermal transport properties, phonon scattering at crystallite boundaries is dominant below 20 K. At very low temperatures, ie, <1 K, the phonon wavelengths are too great to allow resolution of morphological details. Dielectric and mechanical losses are influenced by crystalline structures, eg, cancellation of dipoles. 

When 10 K phonon propagation (intra- and interchain modes) the thermal energy is smaller than the interchain binding energy and for a three-dimensional flexible system, 5 holds for the density of states. This results in the well-known Debye relation,... 

When 2 K < 1 < 10 K the dominant phonon wavelengths are so large that stretching modes predominate, i.e.,... 

In amorphous polymers, discontinuities are caused by the heterogeneous chemical structure of molecular chains or by massive cross-link points in thermoset plastics. Their influence on thermal conductivity depends on their mean cross-link distance D relative to the dominant phonon wavelength ... 

At RT, thermal conductivities of carbon fiber composites with high tensile fibers differ from those of high modulus fibers and are much higher than the thermal conductivity of the epoxy matrix. Below 7 K, they become similar within 25% and lower than the thermal conductivity of the epoxy matrix (37,47). The similarity is owing to the fact that at low temperatures only long phonon wavelengths are activated they cannot resolve different graphite microstructures of different carbon fiber types which are dominant at RT (36,43). In most cases, the specific heat of composites is lower than that of the polymeric matrix. 

As already observed for some isotropic polynuclear clusters [30 - 32], slow relaxation of the magnetization in an external magnetic field can occur because of the inefficient transfer of energy to the environment, for example, the helium bath, and consequent reabsorption of the emitted phonon by the spin system. The phenomenon, also known as phonon bottleneck (PB), was first introduced by Van Vleck [33]. It is characteristic of low temperatures, where relaxation is dominated by the direct process between closely spaced levels, and results from the low density of phonons with such a long wavelength to match the small energy separation... 

The vibrations within a molecular crystal cell are not only a result of molecular motions, but also the relative motions between neighboring molecules. Dominant features of the THz spectra are the sharp absorption peaks caused by phonon modes directly related to the crystalline structure [14], This result originates from the molecular vibrational modes and intramolecular vibrations associated, for example, with RDX [39], Consequently, vibrational modes are unique and distinctive feature of the crystalline explosive materials. The presence of broad features might also be caused by scattering from a structure with dimensions comparable to the THz wavelength. This can occur in materials that contain fibers or grains [37],... 

Depending on the time and length scales, different transport laws can be used. When the objects have comparable size to the wavelength of energy carrier, wave phenomena, that is, reflection, refraction, diffraction, etc., dominate the energy transport mechanism. When the time scale of interest (t) is of the order of collision time scale (t ), time-dependent wave mechanics must be used. Schrodinger s equation must be used for electrons and phonons. Maxwell s equation must be used for photons ... 

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