Diffusion bulk phase

Hiittig (32) has demonstrated that solid-solid reactions involving bulk phase diffusion take place at tempera-tures>0-52 ( X) only, those involving surfirce processes (i.e., sintering) occur at temperatures <0-52 but >0-25 r . The relation to volume and surface defect mobifey has been demonstrated by Bevan, Shelton and Anderson (33) by electronic conductivity measurements. 

It is seldom possible to predict diffusion rates in porous materials by simply correcting bulk-phase diffusivities for the reduction in cross-sectional area due to the solid phase. There are several reasons for this ... 

The exponent n for the partial pressure is 0.5 provided that the bulk phase diffusion of atomic hydrogen is the only rate-limiting step. In this case Equation 14.10 is named Sievert s law. The hydrogen separation factor 5 is sometimes used to specify membrane quality. It is defined as... 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

As in die case of die diffusion properties, die viscous properties of die molten salts and slags, which play an important role in die movement of bulk phases, are also very stiiicture-seiisitive, and will be refeiTed to in specific examples. For example, die viscosity of liquid silicates are in die range 1-100 poise. The viscosities of molten metals are very similar from one metal to anodier, but die numerical value is usually in die range 1-10 centipoise. This range should be compared widi die familiar case of water at room temperature, which has a viscosity of one centipoise. An empirical relationship which has been proposed for die temperature dependence of die viscosity of liquids as an AiTlienius expression is... 

SPV- from the electric field of the polycation, which leads to a first-order back ET kinetics. Since the addition of NaCl interferes with the electrostatic binding of SPV- by QPh-14, SPV- can escape into the bulk phase by diffusion. Therefore, the back ET occurs via a bimolecular process when NaCl is added. 

An interfacial reaction is accompanied by a diffusion process which provides reactants from the bulk phase to the interface. When the reaction rate is faster than the diffusion rate, the overall reaction has to be governed by the diffusion rate of the reactant. Diffusion, in general, takes place in the stagnant layers (the region on both sides of the interface) and is not disturbed even under the stirring of a bulk region. 

Both reactions are slow compared to the film diffusion in the liquid phase13-15. Hence, the reactions can be assumed to take place predominantly in the bulk phase of the liquid. The rate of mass transfer can be calculated using Equation 7.2. The interfacial concentration can be calculated using Henry Law. Mass transfer coefficients, interfacial area and gas hold-up data are required. Gas hold-up is defined as ... 

The adsorption of GFP molecules on mesoporous silicas takes place in three fundamental steps. First, the protein molecules in the bulk phase are transported close to the silica, either by convection or diffusion. Second, the protein is adsorbed on the surface of the silicas by electrostatic and Coulomb interactions which are mostly the dominant forces to be at stake. Third, the adsorbed proteins diffuse into the inner of pores and channels. 

The surface potential is not accessible by direct experimental measurement it can be calculated from the experimentally determined surface charge (Eqs. 3.1 - 3.3) by Eqs. (3.3a) and (3.3b). The zeta potential, calculated from electrophoretic measurements is typically lower than the surface potential, y, calculated from diffuse double layer theory. The zeta potential reflects the potential difference between the plane of shear and the bulk phase. The distance between the surface and the shear plane cannot be defined rigorously. 

In industrial PET synthesis, two or three phases are involved in every reaction step and mass transport within and between the phases plays a dominant role. The solubility of TPA in the complex mixture within the esterification reactor is critical. Esterification and melt-phase polycondensation take place in the liquid phase and volatile by-products have to be transferred to the gas phase. The effective removal of the volatile by-products from the reaction zone is essential to ensure high reaction rates and low concentrations of undesirable side products. This process includes diffusion of molecules through the bulk phase, as well as mass transfer through the liquid/gas interface. In solid-state polycondensation (SSP), the volatile by-products diffuse through the solid and traverse the solid/gas interface. The situation is further complicated by the co-existence of amorphous and crystalline phases within the solid particles. 

The features of the electro-oxidative polymerization can he explained as follows. The molecular weight of the obtained polymer stayed constant during the polymerization, because the polymerization proceeds heterogeneously in the diffusion layer of electrode. The C-0 coupling reaction is predominant, probably because the phenol is adsorbed and oriented on the electrode surface. The polymerization started from the dimer is much suppressed, because the dimer diffuses from the bulk phase into the diffusion layer very slowly. 

Typical cathode performance curves obtained at 650°C with an oxidant composition (12.6% 02/18.4% C02/69% N2) that is anticipated for use in MCFCs, and a common baseline composition (33% 02/67% CO2) are presented in Figure 6-3 (20,49). The baseline composition contains O2 and CO2 in the stoichiometric ratio that is needed in the electrochemical reaction at the cathode (Equation (6-2)). With this gas composition, little or no diffusion limitations occur in the cathode because the reactants are provided primarily by bulk flow. The other gas composition, which contains a substantial fraction of N2, yields a cathode performance that is limited by gas phase diffusion from dilution by an inert gas. 

The octanol/buffer represents a partition coefficient between two bulk phases it is less affected by the structure of the analyte and therefore it cannot be used to predict the exact value of liposome membrane-to-buffer Xp, which is also affected by the geometry of the analyte (41 4). However, it is accepted and established that the octanol-to-buffer can help to predict transmembrane passive diffusion (40). In the case of liposomes such as Doxil, in which the internal aqueous phase (intraliposome aqueous phase) is different from the external liposome aqueous medium due to large differences in the composition and pH of these two aqueous phases, there are two different liposome membrane-to-aqueous phase partition coefficients this is referred to as asymmetry in the membrane-to-aqueous media partition coefficient. 

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