Internal mass transport

Summing up this section, we would like to note that understanding size effects in electrocatalysis requires the application of appropriate model systems that on the one hand represent the intrinsic properties of supported metal nanoparticles, such as small size and interaction with their support, and on the other allow straightforward separation between kinetic, ohmic, and mass transport (internal and external) losses and control of readsorption effects. This requirement is met, for example, by metal particles and nanoparticle arrays on flat nonporous supports. Their investigation allows unambiguous access to reaction kinetics and control of catalyst structure. However, in order to understand how catalysts will behave in the fuel cell environment, these studies must be complemented with GDE and MEA tests to account for the presence of aqueous electrolyte in model experiments. 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

Parker, F. L., Churchill, M. A., Andrew, R. W., Frederick, B. J., Carrigan, P. H. Jr., Cragwall, J. S. Jr., Jones, S. L., Struxness, E. G. and Morton, R. J. (1966). Dilution, dispersion and mass transport of radionuclides in the Clinch-Tennessee Rivers, page 35 in Disposal of Radioactive Wastes into Seas, Oceans and Surface Waters, IAEA Publication No. STI/PUB/126 (International Atomic Energy Agency, Vienna). 

Gunn, R. D., Clark, J. P., King, C. J. Mass transport in freeze-drying, basic studies and processing implications, p. 79-98. International Institute of Refrigeration (Comm. X, Lausanne 1969)... 

Ary given catalytic material can be abstracted based on the same underlying similar architecture — for ease of comparison, we describe the catalytic material as a porous network with the active centers responsible for the conversion of educts to products distributed on the internal surface of the pores and the external surface area. Generally, the conversion of any given educt by the aid of the catalytic material is divided into a number of consecutive steps. Figure 11.13 illustrates these different steps. The governing transport phenomenon outside the catalyst responsible for mass transport is the convective fluid flow. This changes dramatically close to the catalyst surface from a certain boundary onwards, named the hydrodynamic boundary layer, mass transport toward and from the catalyst surface only takes place... 

This complex easily looses CO, which enables co-ordination of a molecule of alkene. As a result the complexes with bulky phosphite ligands are very reactive towards otherwise unreactive substrates such as internal or 2,2-dialkyl 1-alkenes. The rate of reaction reaches the same values as those found with the triphenylphosphine catalysts for monosubstituted 1-alkenes, i.e. up to 15,000 mol of product per mol of rhodium complex per hour at 90 °C and 10-30 bar. When 1-alkenes are subjected to hydroformylation with these monodentate bulky phosphite catalysts an extremely rapid hydroformylation takes place with turnover frequencies up to 170,000 mole of product per mol of rhodium per hour [65], A moderate linearity of 65% can be achieved. Due to the very fast consumption of CO the mass transport of CO can become rate determining and thus hydroformylation slows down or stops. The low CO concentration also results in highly unsaturated rhodium complexes giving a rapid isomerisation of terminal to internal alkenes. In the extreme situation this means that it makes no difference whether we start from terminal or internal alkenes. 

Operating temperature has a significant influence on PEFC performance. An increase in temperature lowers the internal resistance of the cell, mainly by decreasing the ohmic resistance of the electrolyte. In addition, mass transport limitations are reduced at higher temperatures. 

As indicated by Fig. 23 and Fig. 24, the source function can be highly asymmetrical. For the liquid droplet corresponding to Fig. 23, one would expect the internal temperature to be higher near the back and front of the sphere because of the spikes in the source function in those regions. As a result, the evaporation rate should be enhanced at the rear stagnation point and the front of the sphere. To calculate the evaporation rate when internal heating occurs, one must solve the full problem of conduction within the sphere coupled with convective heat and mass transport in the surrounding gas. 

It is possible to make nonstoichiometric solids that have ionic conductivities as high as 0.1-1000 S m-1 (essentially the same as for liquid electrolytes) yet negligible electronic conductances. Such solid electrolytes are needed for high energy density electrical cells, fuel cells, and advanced batteries (Chapter 15), in which mass transport of ions between electrodes is necessary but internal leakage of electrons intended for the external circuit... 

Formal kinetic investigations (performed only with acidic ion exchange catalysts) revealed, in most cases, the first-order rate law with respect to the alkene oxide [285,310,312] or that reaction order was assumed [309,311]. Strong influence of mass transport (mainly internal diffusion in the polymer mass) was indicated in several cases [285,309, 310,312,314]. The first-order kinetics with respect to alkene oxide is in agreement with the mechanism proposed for the same reaction in homogeneous acidic medium [309,315—317], viz. 

Finally, mechanisms besides diffusional transport of mass between internal interfaces can contribute to diffusional creep. For instance, single crystals containing dislocations exhibit limited creep if the dislocations act as sources and sinks, depending on their orientation with respect to an applied stress (see Exercise 16.3). 

Techniques which allow one to monitor the boundary layer as a function of time, such as total internal reflection fluorescence (TIRF) spectroscopy 4 43), permit a quantitative evaluation of interfacial mass transport processes using, for example, fluorescently-tagged macromolecules which do not adsorb, such as fluorescein-labeled dextran 40 ... 

One can deal with mixed mass transport by ratioing the X value of the test compound to that of an internal standard such as Cp2Fe0/+, for which the electrode mechanism is known to be independent of scan rate at very low v. 

Due to the fact that protein adsorption in fluidized beds is accomplished by binding of macromolecules to the internal surface of porous particles, the primary mass transport limitations found in packed beds of porous matrices remain valid. Protein transport takes place from the bulk fluid to the outer adsorbent surface commonly described by a film diffusion model, and within the pores to the internal surface known as pore diffusion. The diffusion coefficient D of proteins may be estimated by the semi-empirical correlation of Poison [65] from the absolute temperature T, the solution viscosity rj, and the molecular weight of the protein MA as denoted in Eq. (16). 

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