Surface diffusion parameters, table

Applications to surface science Table 4.1 Diffusion parameters... 

For this study, mass transfer and surface diffusions coefficients were estimated for each species from single solute batch reactor data by utilizing the multicomponent rate equations for each solute. A numerical procedure was employed to solve the single solute rate equations, and this was coupled with a parameter estimation procedure to estimate the mass transfer and surface diffusion coefficients (20). The program uses the principal axis method of Brent (21) for finding the minimum of a function, and searches for parameter values of mass transfer and surface diffusion coefficients that will minimize the sum of the square of the difference between experimental and computed values of adsorption rates. The mass transfer and surface coefficients estimated for each solute are shown in Table 2. These estimated coefficients were tested with other single solute rate experiments with different initial concentrations and different amounts of adsorbent and were found to predict... 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

Figure 9.4. Dynamic behavior of thermodynamically coupled nonisothermal reaction-diffusion system of catalytic oxidation of CH3OH to CH20 (a) concentration surface, (b) temperature surface. The parameters used are in Table 9.1.

One would physically expect that as pressure increases the solid surface may get smoother due to the filling of small pores and cavities with adsorbed molecules, and as a result the reflection time of gas phase molecules from the surface may become shorter. The values of / in Table 1 are close to unity as expected and they are in an increasing order of n-hexane, carbon tetrachloride and benzene. On the other hand, the parameter a for n-hexane is much higher than that of the others. Since the parameter a in Eq. 3 represents how fast the Knudsen diffiisivity increases with pressure, one would expect a substantial contribution of the Knudsen diffusion for n-hexane to the total permeability at very low pressures. Also the parameter is a measure of how fast the activation energy for surface diffusion decreases with adsorbed concentration. As Table 1 indicates, the surface diffusion permeabilities of n-hexane and carbon tetrachloride are expected to increase more sharply than that of benzene. 

Table 1. Isothermal parameters, pore and surface diffusivities of ethane and propane in Norit...

One question that arises with such an approach is how well the model parameters associated with surface diffusion and the chemical and electrochemical reactions can be extracted from the current, potential and ex situ surface morphology data, given the complex nature of the interactions of the additives with the surface (e.g. see Table 4.3). A key point is that current and potential curves and the surface morphology are very sensitive to changes in the experimental inputs (shown in Table 4.2), indicating that... 

To illustrate the dependence of the mobility function d>y on the concentration of surfactant in the continuous phase, in Fig. 12 we present theoretical curves, calculated in Ref 138 for the nonionic surfactant Triton X-100, for the ionic surfactant SDS ( + 0.1 M NaCl) and for the protein bovine serum albumin (BSA). The parameter values, used to calculated the curves in Fig. 12, are listed in Table 4 and K are parameters of the Langmuir adsorption isotherm used to describe the dependence of surfactant adsorption, surface tension, and Gibbs elasticity on the surfactant concentration (see Tables 1 and 2). As before, we have used the approximation Dj Dj (surface diffusivity equal to the bulk dif-fusivity). The surfactant concentration in Fig. 12 is scaled with the reference concentration cq, which is also given in Table 4 for Triton X-100 and SDS + 0.1 M NaCl, cq is chosen to coincide with the cmc. The driving force, F, was taken to be the buoyancy force for dodecane drops in water. The surface force is identified with the van der Waals attraction the Hamaker function Ajj(A) was calculated by means of Eq. (86) (see below). The mean drop radius in Fig. 12 is a = 20 /pm. As seen in the figure, for such small drops 4>y = 1 for Triton X-100 and BSA, i.e., the drop sur-... 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

Table 5 Full linear surface adsorption-desorption problem parameter values at the Case A2 diffusive transport with surface reaction...

In Part 2 of the PCB story, we introduced the exchange between the water column and the surface sediments in exactly the same way as we describe air/water exchange. That is, we used an exchange velocity, vsedex, or the corresponding exchange rate, ksedex (Table 23.6). Since at this stage the sediment concentration was treated as an external parameter (like the concentration in the air, Ca), this model refinement is not meant to produce new concentrations. Rather we wanted to find out how much the sediment-water interaction would contribute to the total elimination rate of the PCBs from the lake and how it would affect the time to steady-state of the system. As shown in Table 23.6, the contribution of sedex to the total rate is about 20% for both congeners. Furthermore, it turned out that diffusion between the lake and the sediment pore water was much more important than sediment resuspension and reequilibration, at least for the specific assumptions made to describe the physics and sorption equilibria at the sediment surface. 

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