Diffusional mass transport

For small K, i.e., K = 0.5 in Fig. 17, the response of the equilibrium to the depletion of species Red] in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing... 

For the diffusional monitor the steady state mass transport... 

In Section III, emphasis was placed on flux kinetics across the cultured monolayer-filter support system where the passage of hydrophilic molecular species differing in molecular size and charge by the paracellular route was transmonolayer-controlled. In this situation, the mass transport barriers of the ABLs on the donor and receiver sides of the Transwell inserts were inconsequential, as evidenced by the lack of stirring effects on the flux kinetics. In this present section, the objective is to give quantitative insights into the permeability of the ABL as a function of hydrodynamic conditions imposed by stirring. The objective is accomplished with selected corticosteroid permeants which have been useful in rat intestinal absorption studies to demonstrate the interplay of membrane and ABL diffusional kinetics (Ho et al., 1977 Komiya et al., 1980). 

Little is known about the mechanisms that cause the three other current extrema ]2 to J4. The kinetic and diffusional contributions of the characteristic currents Ji to J4 show a different concentration dependence. While the diffusion current is found to be roughly proportional to Cp, the kinetic current shows an exponent of 2 < <2.5 [Ha3]. No dependence of the characteristic currents to ]4 on doping kind and density is observed. This indicates again that to ]4 depend on mass transport and reaction kinetics rather than on charge supply. For n-type electrodes, of course, strong illumination is necessary in order to generate a sufficient number of minority carriers to support the currents. 

UMEs decrease the effects of non-Earadaic currents and of the iR drop. At usual timescales, diffusional transport becomes stationary after short settling times, and the enhanced mass transport leads to a decrease of reaction effects. On the other hand, in voltammetry very high scan rates (i up to 10 Vs ) become accessible, which is important for the study of very fast chemical steps. For organic reactions, minimization of the iR drop is of practical value and highly nonpolar solvents (e.g. benzene or hexane [8]) have been used with low or vanishing concentrations of supporting electrolyte. In scanning electrochemical microscopy (SECM [70]), the small size of UMEs is exploited to locahze electrode processes in the gm scale. 

In the presence of the spacer (Fig. 17.35a), an initially high photocurrent value ( 6 mA/cm2) is achieved, but, due to the larger spacing between the two electrodes, the diffusion of the electron mediator is not fast enough to supply new reduced mediator to the Ti02/dye interface from which, under irradiation, is constantly depleted. Thus, a steady photocurrent value, significantly lower than the initial spike, is attained after a few seconds. In Fig. 17.35b, the reduced diffusional path for the electron mediator allows for a more effective mass transport that accounts for the generation of a stable photocurrent without the observation of photoanodic relaxation processes. 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

In practical applications, where the maximum yield of a product or electricity in electrochemical energy conversion systems at the lowest energy cost is desirable, the rate of mass transport should be fast enough in order not to limit the overall rate of the process. For electroanalytical applications, such as polarography or gas sensors, on the other hand, the reaction must be limited by the transport of the reactant since the bulk concentration which is of interest is evaluated from the limiting con-vective-diffusional current. 

Equation (69) holds universally, but eqn. (70) applies only to a potential step mean perturbation in the case of semi-infinite linear diffusion. For other mean perturbations or other types of (diffusional) mass transport, eqn. (70) should be replaced by the appropriate expression for F(tm). A survey of such expressions was given in a recent review by Sluyters-Rehbach and Sluyters [53], Unfortunately, most of them are of uncomfortable complexity. Therefore it may be preferable to make use of the less rigorous, but more simple, F(tra ) function that can... 

So, the term [A0a0 + AR aR ] co-1/2 (1 — i) resembles the Warburg impedance corresponding to diffusional mass transport of A, O and R, with a mobile equilibrium between A and 0, i.e. kQ -> °°, whereupon the term in g = kQ /co would vanish. If, however, kQ has a finite value, the faradaic impedance is enlarged by the Gerischer impedance expressed by the term containing g. 

J.W. Cahn and R.W. Balluffi. Diffusional mass-transport in polycrystals containing stationary or migrating grain boundaries. Scripta Metall. Mater., 13(6) 499-502, 1979. 

Most electrodes are of the planar type and can be affected by such factors as convectional mass transport within the sample in which they are immersed. Any type of turbulence will tend to increase the supply of ions to an electrode surface, above and beyond that of diffusional supply. This can have an effect on the magnitude of sensor response and give rise to erroneous results. Diffusion to a large planar electrode can be approximated to be perpendicular to the electrode surface. However, when electrodes become very small, the diffusion profile is hemispherical, mass transport is greatly increased (Fig. 9) and diffusion becomes much less of a limiting factor in the sensor response [109]. Thus, turbulence has a much smaller effect and this means that very small microelectrodes display stir-independent responses. Also the small size of micro-... 

Viscosity. In many applications a low viscosity is desirable so that mass transport by diffusion or convection will extend the time range for mass transport by pure diffusional control to periods as long as 40-50 s, which can be advantageous to electroanalytical techniques such as chronopotentiometry.34 At low temperatures the solvent may not appear to crystallize, but may form a rigid glass whose viscosity is so high that mass transport practically ceases the experimentalist must be alert to this possibility. 

In this book we are concerned only with mass transport, or diffusion, in solids. Self-diffusion refers to atoms diffusing among others of the same type (e.g., in pure metals). Interdiffusion is the diffusion of two dissimilar substances (a diffusion couple) into one another. Impurity diffusion refers to the transport of dilute solute atoms in a host solvent. In solids, diffusion is several orders of magnitude slower than in liquids or gases. Nonetheless, diffusional processes are important to study because they are basic to our understanding of how solid-liquid, solid-vapor, and solid-solid reactions proceed, as well as [solid-solid] phase transformations in single-phase materials. 

Studies with porous catalyst particles conducted during the late 1930s established that, for very rapid reactions, the activity of a catalyst per unit volume declined with increasing particle size. Mathematical analysis of this problem revealed the cause to be insufficient intraparticle mass transfer. The engineering implications of the interaction between diffusional mass transport and reaction rate were pointed out concurrently by Damkohler [4], Zeldovich [5], and Thiele [6]. Thiele, in particular, demonstrated that the fractional reduction in catalyst particle activity due to intraparticle mass transfer, r, is a function of a dimensionless parameter, 0, now known as the Thiele parameter. 

Many reaction processes of industrial importance occur in microporous solids (catalysis, electrolysis, shale retorting, etc.). Access to the interior of the solid is by diffusional transport and the transport of mass is usually described by Fick s law. The parameter describing the ease of mass transport is the effective diffusivity, De, where... 

The conservation equations for mass and enthalpy for this special situation have already been given with eqs 76 and 62. As there is no diffusional mass transport inside the pellet, the overall catalyst effectiveness factor is identical to the film effectiveness factor i/cxl which is defined as the ratio of the effective reaction rate under surface conditions divided by the intrinsic chemical rate under bulk fluid phase conditions (see eq 61). For an nth order, irreversible reaction we have the following expression ... 

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