Conductivity of bulk dispersions

Electrolytically evolved gas bubbles affect three components of the cell voltage and change the macro- and microscopic current distributions in electrolyzers. Dispersed in the bulk electrolyte, they increase ohmic losses in the cell and, if nonuniformly distributed in the direction parallel to the electrode, they deflect current from regions where they are more concentrated to regions of lower void fraction. Bubbles attached to or located very near the electrodes likewise present ohmic resistance, and also, by making the microscopic current distribution nonuniform, increase the effective current density on the electrode, which adds to the electrode kinetic polarization. Evolution of gas bubbles stirs the electrolyte and thus reduces the supersaturation of product gas at the electrode, thereby lowering the concentration polarization of the electrode. Thus electrolytically evolved gas bubbles affect the electrolyte conductivity, electrode current distribution, and concentration overpotential and the effects depend on the location of the bubbles in the cell. Discussed in this section are the conductivity of bulk dispersions and the electrical effects of bubbles attached to or very near the electrode. Readers interested in the effect of bubbles dispersed in the bulk on the macroscopic current distribution in electrolyzers should see a recent review of Vogt.31... 

Departures of the electrokinetic behavior of real systems from that described by the equations reported occurs most often because of breakdown of two of the assumptions above because of marked surface conductivity (particularly in dilute solutions, where the bulk conductivity is low) and because of a small characteristic size of the disperse-phase elements (e.g., breakdown of the condition of bg <5 r in extremely fine-porous diaphragms). A number of more complicated equations allowing for these factors have been proposed. 

Ionically conducting polymers and their relevance to lithium batteries were mentioned in a previous section. However, there are several developments which contain both ionically conducting materials and other supporting agents which improve both the bulk conductivity of these materials and the properties of the anode (Li)/electrolyte interface in terms of resistivity, passivity, reversibility, and corrosion protection. A typical example is a composite electrolyte system comprised of polyethylene oxide, lithium salt, and A1203 particles dispersed in the polymeric matrices, as demonstrated by Peled et al. [182], By adding alumina particles, a new conduction mechanism is available, which involved surface conductivity of ions on and among the particles. This enhances considerably the overall conductivity of the composite electrolyte system. There are also a number of other reports that demonstrate the potential of these solid electrolyte systems [183],... 

Though numerous groups have fabricated CNT-polymer composites, mechanical behaviour has not been the main focus of such studies. The bulk of the work has focused on studying the effect of the addition of CNT on the crystallization behaviour and on the electrical conductivity and improving dispersion by employing different techniques, as described earlier. 

Another model of experimental interest concerns the case of a highly conductive shell around practically non-conductive material. It may be applied to macromolecules or colloidal particles in electrolyte solution which usually have counterion atmospheres so that the field may displace freely movable ionic charges on their surfaces. The resulting dielectric effect turns out to be equivalent to a simple Maxwell-Wagner dispersion of particles having an apparent bulk conductivity of... 

In this section, we compare BTE and MD predictions of bulk thermal conductivity of silicon to the available experimental data [74] over a temperature range of 500K to lOOOK (Fig. 4). The BTE predictions are obtained from the full phonon dispersion model described in section 2.3. This full phonon dispersion model involves an adjustable parameter, the Gruneisen constant (y), which is set... 

SOI and strained silicon transistors are comparable to or smaller than the phonon s mean free path (which, for silicon, has been estimated as 300 nm at 300K) [53], In this limit, the film surfaces alter the phonon dispersion relations [76], and the phonon-surface scattering may become the predominant scattering mechanism [3, 53], Since phonons are the main carriers of thermal energy in silicon, these effects alter the thermal conductivity, which differs from that of bulk silicon [10, 36, 77], Measurements of the thermal conductivities of silicon films of thicknesses down to 74 nm found a reduction of 50% with respect to the bulk value at 300K [53], This reduction depends on the temperature and the thickness of the film [3, 53],... 

Polyurethane pre-polymer or thermoplastic polyurethanes are prepared by the reaction of polyester or polyether diols with diisocyanates. The reaction can be conducted in bulk, in a solvent, or in an aqueous solution or dispersion. Unless the reaction is carried out at an elevated temperature a catalyst is required. Organotin compounds are the prime catalyst for this reaction. 

Very few CPs are produced in bulk quantities. Polyphenylene sulfide, a member of the third generation of polymers, was produced in bulk quantities many years before CPs were established and its dopability was elucidated. Polyethylenedioxythiophene is commercially available as a water-based colloidal dispersion (Baytron P water dispersion), and presumably as dispersible powders. The powders with a conductivity of 5-10 S/cm can be dispersed in thermoplastic polymers and in organic solvents such as xylene. Polyaniline doped with dodecylbenzene sulfonic acid and complexed with zinc dodecylbenzene sulfonate is commercially available as a powder, which can be dispersed in polyolefins. The same polymer doped with p-toluenesulfonic acid is also available as a dispersible powder, Ormecon, and in a predispersed form for solution processing in polar and nonpolar media. Based on Ormecon PANi, there are many commercial products marketed for many different applications. 

The second equation is the bulk effective resistivity due to particle surface resistivity for a cubic array of mono-dispersed particles with the direction of the electric field aligned with the poles and volume conduction neglected. The constriction resistance is included in the integration of Equations 3.8. These equations are a weak function of the particle geometry. 

Gas bubbles dispersed in the bulk electrolyte, common in industrial electrolysis, are essentially randomly distributed spheres having zero conductivity. There are a number of different approaches to describing the effect of such dispersions on the overall conductivity. Simplification of the problem is possible when the dispersed phase is dilute or when a limited range of void fraction is considered. Some writers discuss media in which the dispersed phase occupies well-defined lattice positions while others treat random dispersions. One may also consider spheres of equal size or dispersions containing a distribution of sizes. I classify the approaches by the type of dispersion they aim to describe and compare the theory for these classes to appropriate experimental data. 

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