Anisotropy, thermal conductivity

Halpin-Tsai model [18] allows describing the thermal conductivity of composites containing fillers which have a fiber or disc shape. This model is used to take in consideration the composite anisotropy. Thermal conductivity could be given by the following equation (Eq 7) ... 

We saw in Section 3.2 that the knowledge of low-temperature specific heat is extremely important to understand the physical properties of a solid. The measurements of heat capacity are not, conceptually, more difficult than those of thermal conductivity. On the contrary, some problems such as the anisotropy of materials are not present, and the shape of the sample to be measured is usually unimportant. Nevertheless, from a technical... 

Hooker C, Ubbelohd AR, Young D. Anisotropy of thermal conductance in near-ideal graphite. Proceedings of the Royal Society of London Series A. Mathematical and Physical Sciences. 1965 284(1396) 17 ff. 

Low density PE foam sheets having a thickness of 10 mm were cut from a block produced by compression moulding and their thermal conductivities over the temperature range from 24 to 50C determined. The evolution of the properties along the block was analysed and the cell structure, apparent mean cell diameter, anisotropy, mean cell wall thickness and relative fraction of polymer determined using quantitative image analysis and a previously reported model utilised to predict the thermal conductivity of the foams. 30 refs. 

Various other instances of hydrodynamic and electrohydrodynamic instabilities in nematic and, to a lesser extent, smectic liquid crystals have been investigated. No attempt is made here to review this work. For the present discussion, it is sufficient to note that (a) most of the work has dealt with oriented layers having anisotropic properties, and (b) some interesting instabilities arise in oriented layers which do not occur for isotropic materials. An example of the latter is cellular convection in a fluid layer confined between horizontal plates maintained at different temperatures. With an isotropic fluid, convection can arise only if the lower plate is hotter than the upper plate. Then, fluid near the lower plate is less dense and tends to rise while fluid near the upper plate is denser and tends to sink. With an oriented layer, however, convection can arise even when the upper plate is hotter if the anisotropy of thermal conduction properties is of a particular type (8). 

As indicated above, much interest exists in dynamic behavior of thin aligned layers of nematic liquid crystals. It is not surprising to find, therefore, that measurement of the anisotropy of transport properties has been the objective of many studies of thermotropic systems. The literature on anisotropic thermal conductivity in nematic liquid crystals has been reviewed recently by Rajan and Picot (12). Among the studies of anisotropic diffusion are those of Yun and Fredrickson (13), Bline... 

Mathis, N.E., Measurement of Thermal Conductivity Anisotropy in Polymer Materials, PhD thesis, Chemical Engineering Department, University of New Brunswick, Fredericton, N.B., Canada, 1996. 

Furthermore, it is not surprising that the thermal conductivity of melts increases with hydrostatic pressure. This effect is clearly shown in Fig. 2.3 [19]. As long as thermosets are unfilled, their thermal conductivity is very similar to amorphous thermoplastics. Anisotropy in thermoplastic polymers also plays a significant role in the thermal conductivity. Highly drawn semi-crystalline polymer samples can have a much higher thermal conductivity as a result of the orientation of the polymer chains in the direction of the draw. 

Equation (3) has several other important implications which can be directly confirmed by finite-frequency probes. One example is the motion-narrowing effect in NMR experiments which is expected to disappear when l/r is below the chemical-shift-anisotropy (CSA) width. Indeed the NMR results of Tycko et al. [16] indicate that for a CSA width of 18.2 kHz the line broadens below 190 K and develops a powder pattern at lower temperature. This is in fair agreement with the 200 K calculated from Eq. (3). They also concluded that the thermal activation energy is around 260 meV below TV, again close to the values we calculated. The glassy dynamics can be probed by other experiments such as sound attenuation, microwave absorption, and thermal conductivity. In particular the characteristic temperature will depend on probe frequency. Such studies are essential to fully understand the low-temperature orientational dynamics. 

It exhibits anisotropic physical properties as a result of its crystallographic structure of well-separated parallel sheets of carbon atoms. Thus graphite single cry.stals exhibit far higher electrical and thermal conductivity parallel to the layers of carbon atoms than perpendicular to them. Macroscopically, however, this anisotropy is seldom observable due to the random orientation of the individual particles. 

Figure 4. Calculated properties vs. temperature and anisotropy coefficient (p) elastic modulus, MPa, along Y/Z-axes (a) and its relative difference, %, to X-axis (b) thermal conductivity, W/mK, along Y/Z-axes (c) and its relative difference, %, to X-axis (d).

The main bottleneck in this case will be in relaxation on the Y-Z plane (perpendicular to gradient), since there will be the most property mismatch and restricted movement of the parts of the whole specimen. Interesting, that relative anisotropy in elastic module between X and Y/Z components is not large (2-3%), but depends on temperature and anisotropy coefficient in a complicated way (Fig.4a and b). On the other hand, differences in values of thermal conductivity between X and Y/Z are almost the same for different anisotropy, but change strongly with the temperature (Fig.4c and d). The results for Y/Z-plane could be summarised in Table 1. 

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