Diffusion coefficient, of adsorbates

Figure 23. The lateral diffusion coefficient of adsorbed FITC-/8-lg in thin films as a function of added Tween 20. (a), o/w thin films formed from aqueous non-homogenized solutions of /3-lg at 3 mg/ml ( ), o/w thin films formed from 10% v/v n-tetradecane emulsion or emulsion subnatant samples of FITC-/3-lg, initial protein concentration 3 mg/ml ( ), a/w thin films formed from aqueous non-homogenized solutions of /3-lg at 0.2 mg/ml.

Theoretical modeling has now to include surface diffusion of the adsorbates, where this effect may be restricted to adsorbed CO as the fastest surface species. In the system of ODEs presented in Fig. 7.6, Eq. 7.1 has to now be supplemented by the additional term DAu, where D is the diffusion coefficient of adsorbed CO with concentration u, and the resulting partial differential equations may then be solved numerically. 

Wherein C is coal particle gas absorbing concentration where diffusion radius is r, kg/m is coal particle gas absorbing concentration with equilibrium state, kg/m is the dissociate gas concentration within coal particle cranny, kg/m D is the diffusion coefficient of adsorbing gas, rrf/s a is mass exchange coefficient at coal particle surface between adsorb gas to dissociate gas, m/s r is the radius of coal particle, m. 

However, it has been demonstrated that the FEM-method is capable of monitoring adsorbate motion or diffusion on a substrate via fluctuations in the electron emission. In fact, the method has become one of the most important tools for measuring the diffusion coefficient of adsorbates on metal surfaces [90GOM]. In one experiment the temporal variation of the emitted electrons has been studied on the picosecond time-scale, thus allowing the observation of the motion of a single adsorbed atom [93HEI]. Recently the method has been extended to study fluctuations in the course of a surface chemical reaction in adsorbed molecular adlayers on a Pt-substrate [99SUC]. 

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. 

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. 

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. 

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)... 

Relaxation times T, and T2 depend on the motion of molecules which contain the nuclei (236) and their measurement often leads to the various kinetic parameters for the adsorbed molecules, the knowledge of which is essential for the understanding of the mechanism of many zeolite-mediated processes. The diffusion coefficient of the reactants and products in a catalytic reaction, which can be determined from NMR, is often rate limiting. Relaxation studies can also determine surface coverage by the sorbed species and provide information about the distribution of adsorption energy between the different sites on the surface of a catalyst. For these reasons a great deal of NMR work has been done with adsorbed species in zeolites in the course of the last twenty years. From the applied viewpoint the emphasis is on water and hydrocarbons as guest molecules from the fundamental viewpoint species such as Xe, SF6, H2, CH4, and NH3 are of special interest. 

The delocalized state can be considered to be a transition state, and transition state theory [105], a well-known methodology for the calculation of the kinetics of events, [12,88,106-108] can be applied. In the present model description of diffusion in a zeolite, the transition state methodology for the calculation of the self-diffusion coefficient of molecules in zeolites with linear channels and different dimensionalities of the channel system is applied [88], The transition state, defined by the delocalized state of movement of molecules adsorbed in zeolites, is established during the solution of the equation of motion of molecules whose adsorption is described by a model Hamiltonian, which describes the zeolite as a three-dimensional array of N identical cells, each containing N0 identical sites [104], This result is very interesting, since adsorption and diffusion states in zeolites have been noticed [88],... 

The pressure and temperature dependent diffusion coefficient of the adsorbate in the carrier gas is approximated according to Gilliland [18] ... 

The primary requirement for an economic separation process is an adsorbent with high selectivity and capacity. The selectivity may depend upon differences in either kinetics or thermodynamic equilibrium of adsorption. Differences in diffusion rates between molecules, due to steric effects, can be large enough to provide transient selectivity. The separation factor is the ratio between the diffusion coefficients of the molecules. 

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