Adsorption-desorption kinetics, effect

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

Figure 6.17 Effect of a slow rate of adsorption-desorption kinetics on the shape of the band profile and its asymmetry. Dimensionless plot of Q versus frf. Chromatogram calculated with the Lapidus and Amundson model, with Nap = 5. Reprinted by permission of Kluwer Academic Publishing, from S. Golshan-Shirazi and G. Guiochon, NATO ASl Series C, vol 383, 61 (Fig. 6), with kind permission of Springer Science and Business Media.

Figure 3 illustrates the effect of the adsorption/desorption kinetics on the transient profile, in the absence of surface diffusion, where KJKd = 1, i.e., half the surface sites are occupied at equilibrium. The results are presented as i/i() versus r 1/2 in order to emphasize the short-time behavior. At very short times, i.e., the largest r 1/2, the UME response is identical for all values of Ka, since under these conditions, the diffusion field adjacent to the electrode is much smaller than the tip/sample separation and so does not sense the presence of the substrate (30,33). At times sufficient for the dif-... 

When the adsorption/desorption kinetics are slow compared to the rate of diffusional mass transfer through the tip/substrate gap, the system responds sluggishly to depletion of the solution component of the adsorbate close to the interface and the current-time characteristics tend towards those predicted for an inert substrate. As the kinetics increase, the response to the perturbation in the interfacial equilibrium is more rapid and, at short to moderate times, the additional source of protons from the induced-desorption process increases the current compared to that for an inert surface. This occurs up to a limit where the interfacial kinetics are sufficiently fast that the adsorption/desorption process is essentially always at equilibrium on the time scale of SECM measurements. For the case shown in Figure 3 this is effectively reached when Ka = Kd= 1000. In the absence of surface diffusion, at times sufficiently long for the system to attain a true steady state, the UME currents for all kinetic cases approach the value for an inert substrate. In this situation, the adsorption/desorption process reaches a new equilibrium (governed by the local solution concentration of the target species adjacent to the substrate/solution interface) and the tip current depends only on the rate of (hindered) diffusion through solution. 

Thus, the most suitable route for obtaining information on the adsorption/desorption kinetics is from the short-time transient behavior. Under these conditions, surface diffusion effects are negligible and the short-time current response depends only on Ka, Kd, and A for a given tip/substrate separation. Provided that an independent measurement of A can be made, an absolute assignment of the interfacial kinetics is possible. Furthermore, analysis of the long-time current allows the importance, and magnitude, of surface diffusion to be determined. 

G.D. Weatherbee and C.H. Bartholomew, Effects of support on hydrogen adsorption/ desorption kinetics of nickel, J. Catal, 1984, 87, 55. 

As one extends this analysis to the chain growth probabilities and methane selectivities, an immediate conclusion reached is that, one has to include the effect of the alkali promoters on the CO adsorption kinetics and on olefin reincorporation steps as well. Since, no direct data on CO adsorption/desorption kinetics is available at the moment, we will leave this as a postulate. 

Furthermore, modeling of the esterification reaction was attempted in the presence of silica nanoparticles during the formation of aliphatic polyester nanocomposites. From the experimental data, it was found that on increasing the Si02 content in esterification, the rate of water production decreases [47]. In addition, it was clear that the total quantity of water released does not depend on the nanoparticle concentration. This suggests that the existence of the particles does not influence the esterification reaction itself. Their main effect is to adsorb the produced water before it evaporates, altering in this way the water evaporation curve. The simplest model for this phenomenon is to assume very fast water adsorption/desorption kinetics on the Si02 particles. In this case, the evaporation kinetics must be explicitly taken into account because it is no more very fast compared to the other phenomena that occur. 

Manifestly enough, many non-linear effects influence the overall adsorption-desorption kinetics. In particular, we mention a possible dependence of Z on m + M (Z is expected to decrease with M for sufficiently high coverage) and of xd on M (because xd exp(y Z(M)/kB T)). If the resulting nonlinearities are sufficiently strong, the considered dependences might result in oscillatory behaviours too. 

The effect of oxidizing atmospheres on the reduction of NO over rhodium surfaces has been investigated by kinetic and IR characterization studies with NO + CO + 02 mixtures on Rh(lll) [63], Similar kinetics was observed in the absence of oxygen in the gas phase, and the same adsorbed species were detected on the surface as well. This result contrasts with that from the molecular beam work [44], where 02 inhibits the reaction, perhaps because of the different relative adsorption probabilities of the three gas-phase species in the two types of experiments. On the other hand, it was also determined that the consumption of 02 is rate limited by the NO + CO adsorption-desorption... 

Having chosen a particular model for the electrical properties of the interface, e.g., the TIM, it is necessary to incorporate the same model into the kinetic analysis. Just as electrical double layer (EDL) properties influence equilibrium partitioning between solid and liquid phases, they can also be expected to affect the rates of elementary reaction steps. An illustration of the effect of the EDL on adsorption/desorption reaction steps is shown schematically in Figure 7. In the case of lead ion adsorption onto a positively charged surface, the rate of adsorption is diminished and the rate of desorption enhanced relative to the case where there are no EDL effects. 

As an example of the manner in which EDL effects are incorporated into the kinetic analysis, consider the following bimolecu-lar adsorption/desorption mechanism ... 

Pawela Crew and Madix [144] have investigated desorption of propylene and propane from Ag(llO) with the emphasis put on the anomalous effects of weak chemisorption on desorption kinetics of alkenes. Molecular conformation of styrene on Ag(lOO) related to the catalytic epoxidation of terminal alkenes has been studied by Williams etal. [145]. IR studies of the adsorption structures of 1,3-butadiene at Ag(lll) and Au(lll) surfaces have been published by Osaka et al. [146]. 

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

Thus for each zone, during a given cycle, the adsorption-desorption process is separated into two distinct events with F or G describing the kinetics of each event. Such an approach is of course valid only for first order rate reactions. In the limit of low concentration, (such as that resulting from slow leaching from a repository) the reaction sites on the rock will not approach saturation and the number of reaction sites can be considered to remain constant during adsorption. Therefore, for a single species in solution at tracer concentrations the reaction should approximate a first order reaction (i.e., where no complications such as concentration effects, step-wise dehydration, dissociation, etc., are present). 

Figure 53 shows relative rates of C02 formation under steady-state conditions that were recorded with various single-crystal surfaces of Pd as well as with a polycrystalline Pd wire (173). It must be noted that with these experiments no determination of the effective surface areas was performed so that no absolute turnover numbers per cm2 are obtained. Instead, the reaction rates were normalized to their respective maximum values. As can be seen from Fig. 53, all data points are close to a common line which indicates that, in fact, with this reaction the activity is influenced very little by the surface structure. As has been outlined in Section II, the adsorption of CO exhibits essentially quite similar behavior on single-crystal planes with varying orientation. Since the adsorption-desorption equilibrium of CO forms an important step in the overall kinetics of steady-state C02 formation, this effect forms at least a qualitative basis on which the structural insensitivity may be made plausible. 

Specific kinetic effect. This would apply to the sulfided monolayer catalyst. Cobalt may affect adsorption-desorption properties or intrinsic activity of vacancies. No definitive data exist to support this proposal. 

Sorption to surfaces can have important effects on the rates of contaminant transformation, but these effects may be very different, depending on how the mechanism of sorption (i.e., hydrophobic partitioning, donor-acceptor interactions, or ligand exchange) relates to the mechanism of contaminant transformation (i.e., reaction in solution, reaction at surface sites, etc.). In general, however, the contributions of each compartment can be treated as additive as long as the kinetics of adsorption/desorption are fast, relative to contaminant transformation (168). Just as with the effect of pH (Section 4.2.3), each term is simply the product of the reactant concentrations in the compartment and the corresponding rate constant. 

---