Diffusion coefficient significance

Apart from impurities, the formation of surfactant aggregates at the interface makes the adsorption process slower than expected from diffusion. Applying the classical diffusion model to such data would result in a diffusion coefficient significantly smaller than physically reasonable and hence a barrier mechanism would have to be postulated. It will be shown below that a correct consideration of surface aggregation processes allow to quantitatively describe such systems in the framework of a purely diffusion controlled mechanism. 

The permeation of flavor, aroma, and solvent molecules in polymers follows the same physics as the permeation of small molecules. However, there are two significant differences. For these larger molecules, the diffusion coefficients are much lower and the solubihty coefficients are much higher. This means... 

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

Multicomponent Mixtures No simple, practical estimation methods have been developed for predicting multicomponent hquid-diffusion coefficients. Several theories have been developed, but the necessity for extensive activity data, pure component and mixture volumes, mixture viscosity data, and tracer and binaiy diffusion coefficients have significantly limited the utihty of the theories (see Reid et al.). 

Give an approximate expression for the time t required for significant diffusion to take place over a distance x in terms of x, and the diffusion coefficient, D. A component is made from an alloy of copper with 18% by weight of zinc. The... 

The scaling dependence of the diffusion coefficient on N and Cobs Iso poses a number of questions. While the original scaling predictions, based on reptation dynamics [26,38], oc N, have been verified by some measurements [91,98], significant discrepancies have been reported too [95,96]. Attempts to interpret existing data in terms of alternative models, e.g., by the so-called hydrodynamic scaling model [96], fail to describe observations [100,101]. 

The measurement of transport numbers by the above electrochemical methods entails a significant amount of experimental effort to generate high-quality data. In addition, the methods do not appear applicable to many of the newer non-haloalu-minate ionic liquid systems. An interesting alternative to the above method utilizes the NMR-generated self-diffusion coefficient data discussed above. If both the cation (Dr+) and anion (Dx ) self-diffusion coefficients are measured, then both the cation (tR+) and anion (tx ) transport numbers can be determined by using the following Equations (3.6-6) and (3.6-7) [41, 44] ... 

The effect of temperature is complex since there are two conflicting factors, (a) a decrease in the oxygen concentration which results in a decrease in and (b) an increase in the diffusion coefficient that increases about 3% per degree K rise in temperature. In a closed system from which oxygen cannot escape there is a linear increase in rate with temperature that corresponds with the increase in the diffusion coefficient. However, in an open system although the rate follows that for the closed system initially, the rate starts to decrease at about 70°C due to the decrease in oxygen solubility, which at that temperature becomes more significant than the increase in the diffusion coefficient see Section 2.1). 

The hydrodynamic drag experienced by the diffusing molecule is caused by interactions with the surrounding fluid and the surfaces of the gel fibers. This effect is expected to be significant for large and medium-size molecules. Einstein [108] used arguments from the random Brownian motion of particles to find that the diffusion coefficient for a single molecule in a fluid is proportional to the temperature and inversely proportional to the frictional coefficient by... 

The EMD studies are performed without any external electric field. The applicability of the EMD results to useful situations is based on the validity of the Nemst-Planck equation, Eq. (10). From Eq. (10), the current can be computed from the diffusion coefficient obtained from EMD simulations. It is well known that Eq. (10) is valid only for a dilute concentration of ions, in the absence of significant ion-ion interactions, and a macroscopic theory can apply. Intuitively, the Nemst-Planck theory can be expected to fail when there is a significant confinement effect or ion-wall interaction and at high electric... 

An important result of this study is the conclusion of a particle-size-dependent COads surface mobility. The value obtained for large Ft particles is significantly smaller than Deo at a solid/gas interface. However, Kobayashi and co-workers, using solid state NMR, performed measurements of the tracer diffusion coefficient Deo at the solid/electrolyte interface and for Ft-black particles (about 5nm grain... 

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