Adsorbate diffusion coefficient

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. 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Ruthven (gen. refs.) summarizes methods for the measurement of effective pore diffusivities that can be used to obtain tortuosity factors by comparison with the estimated pore diffusion coefficient of the adsorbate. Molecular diffusivities can be estimated with the methods in Sec. 6. 

The diffusion coefficient in these phases D,j is usually considerably smaller than that in fluid-filled pores however, the adsorbate concentration is often much larger. Thus, the diffusion rate can be smaller or larger than can be expected for pore diffusion, depending on the magnitude of the flmd/solid partition coefficient. 

To illustrate, consider the hmiting case in which the feed stream and the two liquid takeoff streams of Fig. 22-45 are each zero, thus resulting in batch operation. At steady state the rate of adsorbed carty-up will equal the rate of downward dispersion, or afV = DAdC/dh. Here a is the surface area of a bubble,/is the frequency of bubble formation. D is the dispersion (effective diffusion) coefficient based on the column cross-sectional area A, and C is the concentration at height h within the column. 

Lateral density fluctuations are mostly confined to the adsorbed water layer. The lateral density distributions are conveniently characterized by scatter plots of oxygen coordinates in the surface plane. Fig. 6 shows such scatter plots of water molecules in the first (left) and second layer (right) near the Hg(l 11) surface. Here, a dot is plotted at the oxygen atom position at intervals of 0.1 ps. In the first layer, the oxygen distribution clearly shows the structure of the substrate lattice. In the second layer, the distribution is almost isotropic. In the first layer, the oxygen motion is predominantly oscillatory rather than diffusive. The self-diffusion coefficient in the adsorbate layer is strongly reduced compared to the second or third layer [127]. The data in Fig. 6 are qualitatively similar to those obtained in the group of Berkowitz and coworkers [62,128-130]. These authors compared the structure near Pt(lOO) and Pt(lll) in detail and also noted that the motion of water in the first layer is oscillatory about equilibrium positions and thus characteristic of a solid phase, while the motion in the second layer has more... 

Frequently, adsorption proceeds via a mobile precursor, in which the adsorbate diffuses over the surface in a physisorbed state before finding a free site. In such cases the rate of adsorption and the sticking coefficient are constant until a relatively high coverage is reached, after which the sticking probability declines rapidly. If the precursor resides only on empty surface sites it is called an intrinsic precursor, while if it exits on already occupied sites it is called extrinsic. Here we simply note such effects, without further discussion. 

Transport Properties Although the densities of SCFs can approach those of conventional liquids, transport properties are more favorable because viscosities remain lower and diffusion coefficients remain higher. Furthermore, CO2 diffuses through condensed-liquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. For example, at 35°C the estimated pyrene diffusion coefficient in polymethylmethacrylate increases by 4 orders of magnitude when the CO2 content is increased from 8 to 17 wt % with pressure [Cao, Johnston, and Webber, Macromolecules, 38(4), 1335-1340 (2005)]. 

Radon is a noble gas and is therefore not readily ionized or chemically reactive. Its properties in terrestrial material will be controlled by its solubility in melt and fluid as well as its diffusion coefficients. Compared with the lighter noble gases, Rn diffuses more slowly and has a lower solubility in water. It will also more readily adsorb onto surface that the lighter rare gases. It can, however be lost by degassing in magmatic systems (Condomines et al. 2003). More information about the behavior of Rn can be found in Ivanovich and Harmon (1992). 

Therefore, the detailed analysis of concentration of defects in surface-adjacent layer and in the volume of adsorbent as well as assessment of the values of diffusion coefficients of defects and particles of various gases in material of adsorbent are very important for understanding the processes of both reversible and irreversible change in electrophysical characteristics of semiconductor during low temperature (if compared to the temperature of creation of defects) interaction with gaseous phase. 

The specified decrease of the radical concentration in the gas phase near the film surface and in tiie layer adsorbed on the film is caused by the fact that interaction of these prides with cetene molecules becomes stronger as concentration of the latter increases. Another reason for the decrease of the radical concentration is the decrease of the diffusion coefficients of active particles in the gas and on the siu-face. This results in a growth of the time it takes for active particles from a gas phase to reach the film surface. Furthermore, it leads to an increase in the time it takes for active particles in the adsorption layer to reach the centers of chemisorption. 

NMR signals are highly sensitive to the unusual behavior of pore fluids because of the characteristic effect of pore confinement on surface adsorption and molecular motion. Increased surface adsorption leads to modifications of the spin-lattice (T,) and spin-spin (T2) relaxation times, enhances NMR signal intensities and produces distinct chemical shifts for gaseous versus adsorbed phases [17-22]. Changes in molecular motions due to molecular collision frequencies and altered adsorbate residence times again modify the relaxation times [26], and also result in a time-dependence of the NMR measured molecular diffusion coefficient [26-27]. 

Thus, the time that is necessary to attain a certain coverage, 6, or the time necessary to cover the surface completely (9 = 1) is inversely proportional to the square of the bulk concentration (cf. Fig. 4.10b). Assuming molecular diffusion only, 8 is of the order of 2 minutes for a concentration of 10 5 M adsorbate when the diffusion coefficient D is 10 5 cm2 s1 and rmax = 4 1010 mol cm 2 1). Considering that transport to the surface is usually by turbulent diffusion, such a calculation illustrates that the formation of an adsorption layer is relatively rapid at concentrations above 10 6 M. But it can become slow at concentrations lower than 10 6 M. 

Surface diffusion considerably influences the mass transfer inside the intraparticle space of a porus adsorbent. The surface diffusion coefficient Ds can be expressed by... 

These results were extended by Tilton et a/.(n8) to adsorption of eosin-labeled BSA on polymer surfaces. They also found a component that surface diffuses, with coefficients ranging from 1.2 x 10 9 to 2.6 x 10 9cm2/s, depending on surface type. In this study, intersecting TIR laser beams rather than a focused stripe were used to define the spatial intensity variation. Surface diffusion was even noted for the most irreversibly adsorbed eosin-labeled BSA components this was evident on samples rinsed for long periods with unlabeled BSA after exposure to eosin-labeled BSA. The surface diffusion coefficient of the irreversibly bound BSA was found to be a strong function of adsorbed concentration.(n9)... 

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