Conductivity variation with composition

So from electrical data, it is possible to get information on partial thermodynamic functions of the salt and then develop thermodynamic models for quantitative interpretation of the conductivity variation with composition. These models are not very different from those already developed for molten salt mixtures or metallic alloys. 

Mahesh, S., and S.C. Joshi. 2015. Thermal conductivity variations with composition of gelatin-silica aerogel-sodium dodecyl sulfate with functionahzed multi-walled caibon nanotube doping in their composites. International Journal of Heat and Mass Transfer 87 606-615. 

Resistivities of 1 to 100,000 ohm-cm can be achieved and are proportional to cost. Various carbon fibers and powders are available with wide variations in conductivity yields in composites. 

Solid solutions are very common among structurally related compounds. Just as metallic elements of similar structure and atomic properties form alloys, certain chemical compounds can be combined to produce derivative solid solutions, which may permit realization of properties not found in either of the precursors. The combinations of binary compounds with common anion or common cation element, such as the isovalent alloys of IV-VI, III-V, II-VI, or I-VII members, are of considerable scientific and technological interest as their solid-state properties (e.g., electric and optical such as type of conductivity, current carrier density, band gap) modulate regularly over a wide range through variations in composition. A general descriptive scheme for such alloys is as follows [41]. 

Fig. 4.2 Typical variations in ionic conductivity with composition. In all cases, variations in alkali or silver content are very low compared to the observed variation in log a (a) influence of the network modifier (LijS) (b) influence of a doping salt (c) mixed alkali effect (d) mixed anion effect. References for data are indicated in Souquet and Perera (1990).

For the four typical variations in ionic conductivity with composition illustrated in Fig. 4.2, thermodynamic interpretations and predictions have been advanced. 

A series of works by Matsuda et al. composed perhaps the first systematic study to explore the physical foundation for such a mixing effect. Using PC/DME as a model system, they investigated the dependence of vapor pressure, dielectric constant, and viscosity on solvent composition, and they correlated these variations with ion conductions. It was found that the dielectric constant varied with solvent composition by following an almost linear relation, with slight positive deviations, while viscosity always showed a pronounced negative deviation from what a linear relation would predict (Figure 6b). For such binary solvent systems, approximate quantifications... 

Fig.36. Variation in electrical conductivity (o) with molecular weight for polyethylene composites filled with 4% by volume carbon black, demonstrating the effects of orientation (I), degradation (II) and flow-induced segregation of carbon black aggregates (III). ( ) injection moulded (O) compression moulded (unoriented) [181]...

We emphasize that the use of g in these equations may be justified only if /—a, because of the Edwards cancellation theorem (Section 6). We should expect a metal-insulator transition to occur for some value of in the neighbourhood of For several liquid systems there is experimental evidence that the interference term in (52) is absent. Thus for liquid TeTl alloys, with variation of composition and temperature, for a less than the Ioffe-Regel value e2/3hai the conductivity is proportional to the square of the Pauli paramagnetic susceptibility and then to 2. These results are due to Cutler (1977). Warren (1970a, b, 1972a, b) examined... 

The structure of liquid silicates suggested in the last few sections was presented as a reasonable interpretation of conductance, viscous flow, and density measurements and the variation of the heats of activation with composition, for example. What evidence for the chains, rings, and icebergs is given from spectral approaches such as Roman and NMR If all is well in the earlier interpretation, it should be possible to see evidence of the structures in the spectral peaks. 

Most engineering materials are isotropic in nature, and thus they have the same properties in all directions. For such materials we do not need to be concerned about the variation of properties with direction. But in anisotropic materials such as (he fibrous or composite materials, (he properties may change with direction. For example, some of the properties of wood along the grain are different than those in (he direction normal to the grain. In such cases the thermal conductivity may need to be expressed as a tensor quantity to account for the variation with direction. I he treatment of such advanced topics is beyond the scope of tlus text, and we will assume the thermal conductivity of a material to be independent of direction. 

T0 at the outer surface prescribes, but does not eliminate, the consequent radial variation of Tg and hence of n values for Tg, the radial average gas temperature, may be computed in terms of 7rR2Xj0 and the thermal conductivities by the procedure of Verweij (90). The provision of a chemical sink to remove reaction products from the gas, for example by refrigeration of the discharge tube (36) or by absorption on a chemically reactive surface (41, 42, 43, 44) is also associated with concentration gradients, that is with the variation with position of the detailed composition of the gas an analysis of the kinetics of the diffusion processes involved has been given by Emeleus and Beck (22). 

Published information on urethane polymerization detail largely concerns thermoset urethane elastomers systems.4 13 In particular, the work of Macosko et. al. is called to attention. The present paper supplements this literature with information on the full course of linear thermoplastic urethane elastomer formation conducted under random melt polymerization conditions in a slightly modified Brabender PlastiCorder reactor. Viscosity and temperature variations with time were continuously recorded and the effects of several relevant polymerization variables - temperature, composition, catalyst, stabilizer, macroglycol acid number, shortstop - are reported. The paper will also be seen to provide additional insight into the nature and behavior of thermoplastic polyurethane elastomers. 

The next step the modeller faces is the determination of all physico-chemical parameters and the suitable correlations for computing their changes with the variations in composition, temperature and pressure at different points in the reactor (in general axially and radially) and also along the depth of the catalyst pellets. These parameters include physical parameters such as specific heats, densities, viscosities etc. transport parameters such as diflfusivities and thermal conductivities kinetic parameters as discussed earlier as well as thermodynamic parameters such as equilibrium constants and heats of reactions. 

Figure 4 shows the variation with temperature of the equilibrium mole fractions for a few feed gas compositions. The curves in Sections A and B represent the equilibrium state for mixtures initially composed of 3.4% hydrogen sulfide and 5.9% carbon monoxide in the absence and presence of 15% water vapor, respectively. Helium made up the balance in each gas mixture. Species present at less than the micromolar fraction level were ignored. To conduct the same computer program on each gas mixture, an extremely low concentration of water vapor (4.5 X 10"5% ) was assumed in cases A and C of Figure 4. Sections C and D in this figure illustrate the effect of 7% water vapor for a sulfur dioxide-carbon monoxide mixture at the low concentration level. As expected, both hydrogen sulfide and hydrogen were present with the water vapor, and the concentrations of hydrogen sulfide and carbonyl sulfide increased with temperature up to 700 °C.

---