Material transport diffusion coefficients

While now somewhat dated, the book by Horvath [83] discusses additional correlation methods, data sources, and parameters for transport properties of electrolyte solutions, including material on diffusion coefficients and electrical conductivity. 

It is not always recognized that potential sweep voltammetry can be used to obtain quantitative information on charge percolation in polymer films. We now briefly indicate how apparent charge transport diffusion coefficients can be extracted by analyzing such voltammetric parameters as peak current, peak width, and peak potential as a function of scan rate. This analysis is diffusional in concept and perhaps best applied to polymer materials where redox conduction is the predominant mechanism of charge transport. 

Gas diffusion in the nano-porous hydrophobic material under partial pressure gradient and at constant total pressure is theoretically and experimentally investigated. The dusty-gas model is used in which the porous media is presented as a system of hard spherical particles, uniformly distributed in the space. These particles are accepted as gas molecules with infinitely big mass. In the case of gas transport of two-component gas mixture (i = 1,2) the effective diffusion coefficient (Dj)eff of each of the... 

Up to now, no direct measurements of diffusion coefficients have been reported for any system that show the low-temperature upturn just described, and it may well be that for most systems involving hydrogen such effects would occur only at ultra-low temperatures and minuscule diffusion rates. Also, the impurities and imperfections always present in real materials might well trap nearly all the diffusant atoms at the low temperatures at which coherent transport might be expected in ideal material. However, a recent measurement by Kiefl et al. (1989) of the (electronic) spin relaxation rate of muonium in potassium chloride over a range of temperatures gives spectacular support to the concept of coherent tunneling at low temperatures. (See Fig. 6 of Chapter 15 and the associated discussion.)... 

The above sections have focused upon homogeneous systems with a constant composition in which tracer diffusion coefficients give a close approximation to selfdiffusion coefficients. However, a diffusion coefficient can be defined for any transport of material across a solid, whether or not such limitations hold. For example, the diffusion processes taking place when a metal A is in contact with a metal B is usually characterized by the interdiffusion coefficient, which provides a measure of the total mixing that has taken place. The mixing that occurs when two chemical compounds, say oxide AO is in contact with oxide BO, is characterized by the chemical diffusion coefficient (see the Further Reading section for more information). 

It is important to note that Eqs. 5, 8, and 9 were derived entirely from a silicon material balance and the assumption that physical sputtering is the only silicon loss mechanism thus these equations are independent of the kinetic assumptions incorporated into Eqs. 1, 2, and 7. This is an important point because several of these kinetic assumptions are questionable for example, Eq. 2 assumes a radical dominated mechanism for X= 0, but bombardment-induced processes may dominate for small oxide thickness. Moreover, ballistic transport is not included in Eq. 1, but this may be the dominant transport mechanism through the first 40 A of oxide. Finally, the first 40 A of oxide may be annealed by the bombarding ions, so the diffusion coefficient may not be a constant throughout the oxide layer. In spite of these objections, Eq. 2 is a three parameter kinetic model (k, Cs, and D), and it should not be rejected until clear experimental evidence shows that a more complex kinetic scheme is required. 

We will now describe the application of the two principal methods for considering mass transport, namely mass-transfer models and diffusion models, to PET polycondensation. Mass-transfer models group the mass-transfer resistances into one mass-transfer coefficient ktj, with a linear concentration term being added to the material balance of the volatile species. Diffusion models employ Fick s concept for molecular diffusion, i.e. J = — D,v ()c,/rdx, with J being the molar flux and D, j being the mutual diffusion coefficient. In this case, the second derivative of the concentration to x, DiFETd2Ci/dx2, is added to the material balance of the volatile species. 

Rafler et al. showed in an early work [102] that the diffusion coefficient of EG varies with the overall effective polycondensation rate and they proposed a dependency of the diffusion coefficient on the degree of polycondensation. This dependency is obvious, because the diffusion coefficient is proportional to the reciprocal of the viscosity which increases by four orders of magnitude during polycondensation from approximately 0.001 Pas (for Pn = 3) to 67Pas (for Pn = 100) at 280 °C. In later work, Rafler et al. [103, 104, 106] abandoned the varying diffusion coefficient and instead added a convective mass-transport term to the material balance of EG and water. The additional model parameter for convection in the polymer melt and the constant diffusion coefficient were evaluated by data fitting. 

The composition at the permeate-phase interface depends on the partial pressure and saturation vapour pressure of the component. Solvent composition within the membrane may vary considerably between the feed and permeate sides interface in pervaporation. By lowering the pressure at the permeate side, very low concentrations can be achieved while the solvent concentration on the feed-side can be up to 90 per cent by mass. Thus, in contrast to reverse osmosis, where such differences are not observed in practice, the modelling of material transport in pervaporation must take into account the concentration dependence of the diffusion coefficients. 

In a PEMFC, the power density and efficiency are limited by three major factors (1) the ohmic overpotential mainly due to the membrane resistance, (2) the activation overpotential due to slow oxygen reduchon reaction at the electrode/membrane interface, and (3) the concentration overpotential due to mass-transport limitations of oxygen to the electrode surfaced Studies of the solubility and concentration of oxygen in different perfluorinated membrane materials show that the oxygen solubility is enhanced in the fluorocarbon (hydrophobic)-rich zones and hence increases with the hydrophobicity of the membrane. The diffusion coefficient is directly related to the water content of the membrane and is thereby enhanced in membranes containing high water content the result indicates that the aqueous phase is predominantly involved in the diffusion pathway. ... 

Key material properties for SOFC, such as the ionic conductivity as a function of temperature, are available in refs 36—39. In addition, Todd and Young ° compiled extensive data and presented estimation methods for the calculation of diffusion coefficients, thermal conductivities, and viscosities for both pure components and mixtures of a wide variety of gases commonly encountered in SOFCs. Another excellent source of transport properties for gases and mixtures involved in a SOFC is the CHEMKIN thermodynamic database. ... 

Fick (F2) proposed one of the more useful relationships for describing molecular material transport. The Fick diffusion coefficient is identified... 

In thermal transport there was need of considering only temperature as the driving potential. However, in the case of multicomponent material transport it is necessary to evaluate the behavior of each component. Such relationships lead to rather complicated expressions when the diffusion of each of the components is considered individually. For this reason it is often appropriate to focus attention on one component and consider the characteristics of the remainder of the components in the phase as invariant. In the present discussion only the behavior of one component will be considered, but it should be realized that the effect of the properties of the phase upon the diffusion coefficient must be taken into account. 

Equation (56) states that the effect of a thermal gradient on the material transport bears a reciprocal relationship to the effect of a composition gradient upon the thermal transport. Examples of Land L are the coefficient of thermal diffusion (S19) and the coefficient of the Dufour effect (D6). The Onsager reciprocity relationships (Dl, 01, 02) are based upon certain linear approximations that have a firm physical foundation only when close to equilibrium. For this reason it is possible that under circumstances in which unusually high potential gradients are encountered the coupling between mutually related effects may be somewhat more complicated than that indicated by Eq. (56). Hirschfelder (BIO, HI) discussed many aspects of these cross linkings of transport phenomena. 

To be specific, permeability is the product of the partition coefficient K and diffusion coefficient D of a solute within a material. The partition coefficient is usually defined as the ratio of solute concentration in the material to the concentration in the solution it is a measure of the interaction between the polymer and the solute. The partition coefficient should decline as a gel shrinks and the average pore size declines, if other interactions between the solute and the gel are unchanged. The diffusion coefficient is also expected to decline as water content falls and obstruction to movement increases. While K is an equilibrium property, D is a transport property, and so these parameters can be evaluated independently. 

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