Surface diffusion rates, measurement principles

For the investigation of adsorption/desorption kinetics and surface diffusion rates, SECM is employed to locally perturb adsorption/desorption equilibria and measure the resulting flux of adsorbate from a surface. In this application, the technique is termed scanning electrochemical induced desorption (SECMID) (1), but historically this represents the first use of SECM in an equilibrium perturbation mode of operation. Later developments of this mode are highlighted towards the end of Sec. II.C. The principles of SECMID are illustrated schematically in Figure 2, with specific reference to proton adsorption/desorption at a metal oxide/aqueous interface, although the technique should be applicable to any solid/liquid interface, provided that the adsorbate of interest can be detected amperometrically. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Fig. 10.12. General principles of the SECM feedback mode. The UME, normally a disk electrode of radius r, is used to generate a redox mediator in its oxidised or reduced form (a reduction process is shown here) at a diffusion-controlled rate. As the UME approaches an insulating surface (a) diffusion of Ox to the electrode simply becomes hindered and the recorded limiting current is less than the steady-state value measured when the electrode is placed far from the surface, in the bulk of the solution, /( >). This effect becomes more pronounced as the tip/substrate separation, dKcm, is decreased. As the UME approaches a conducting surface (b) the original form of the redox mediator (Ox) can be regenerated at the substrate establishing a feedback cycle and an additional flux of material to the electrode.

Aromatic Compounds in NaX. Molecular transport of aromatic compounds in zeolite NaX has been studied by both nmr and uptake measurements. On the basis of Equation 4,and if surface barriers are absent, both methods should lead to comparable results. Though uptake measurements by the variable - pressure, constant - volume method by Biilow and coworkers (16,17) apparently are in satisfactory agreement with the nmr data (18), extensive uptake measurements including chromatographic methods are continuously found to yield diffusivities of about two orders of magnitude below these values (19,20). In principle, this discrepancy might be explained by the existence of surface barriers, which remain invisible for nmr studies of intracrystalline diffusion, but which may control the uptake rate. 

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