Adsorption irreversible kinetics

Fig. 38. (a, b) SFG spectra of CO adsorbed on Rh(l 11) at 300K at pressures between 10 and 1000 mbar. (c) Analysis of the on-top CO intensity (surface density), resonance position, and CO coverage as a function of the CO pressure. The open symbols indicate the pressure range of irreversible CO adsorption. The equilibrium CO surface coverage in (c) was calculated from adsorption/desorption kinetics adapted from Pery et al. (314). Copyright (2002) The Combustion Institute. 

The size of a molecule is an important feature because proteins form multiple contacts with the surface (e.g., 77 contact points in the case of the albumin molecule and 703 contact points in the case of the fibrinogen molecule adsorbed on silica [10]). Multipoint binding usually causes adsorption irreversibility having a dynamic nature in the absence of irreversible denaturation. The rates of desorption are, as a rule, much lower than those of adsorption, and in many cases it is virtually impossible to attain the equilibrium state desorbing the adsorbed protein [11]. In other words, the formation of one or several bonds with the surface increases the probability of adsorption of neighboring sites of the same molecule. On the other hand, the desorption of a protein molecule requires the simultaneous rupture of a large number of bonds and, for kinetic reasons, equilibrium is not attained [12-14], This corresponds to a considerable difference between the activation energies for the adsorption and desorption processes [15,16],... 

Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

These assumptions are partially different from those introduced in our previous model.10 In that work, in fact, in order to simplify the kinetic description, we assumed that all the steps involved in the formation of both the chain growth monomer CH2 and water (i.e., Equations 16.3 and 16.4a to 16.4e) were a series of irreversible and consecutive steps. Under this assumption, it was possible to describe the rate of the overall CO conversion process by means of a single rate equation. Nevertheless, from a physical point of view, this hypothesis implies that the surface concentration of the molecular adsorbed CO is nil, with the rate of formation of this species equal to the rate of consumption. However, recent in situ Fourier transform infrared (FT-IR) studies carried out on the same catalyst adopted in this work, at the typical reaction temperature and in an atmosphere composed by H2 and CO, revealed the presence of a significant amount of molecular CO adsorbed on the catalysts surface.17 For these reasons, in the present work, the hypothesis of the irreversible molecular CO adsorption has been removed. 

Hydrogen adsorption was also described as irreversible in our previous mechanism,10 and an empirical kinetic law was used to describe the rate of this step. However, a deeper analysis of literature data revealed that this step is likely in equilibrium, too. On the basis of this evidence, the previously developed model has been modified in this work in order to improve the physical consistency of the proposed mechanism. 

An interesting approach to measuring rates of electron transfer reactions at electrodes is through the study of surface bound molecules (43-451. Molecules can be attached to electrode surfaces by irreversible adsorption or the formation of chemical bonds (461. Electron transfer kinetics to and from surface bound species is simplified because there is no mass transport and because the electron transfer distance is controlled to some degree. 

FIGURE 5.21. Kinetics of irreversible adsorption forFrumkin isotherm interactions between adsorbates. From left to right, aa = 0, — 1, —2, —3, —5. Adapted from Figure 4 of reference 22, with permission from the American Chemical Society. 

The physical meaning of the kinetic parameter m is identical as for surface electrode reaction (Chap. 2.5.1). The electrochemical reversibility is primarily controlled by 03 (Fig. 2.71). The reaction is totally irreversible for log(m) < —3 and electrochemically reversible for log(fo) > 1. Between these intervals, the reaction appears quasireversible, attributed with a quasireversible maximum. Though the absolute net peak current value depends on the adsorption parameter. Fig. 2.71 reveals that the quasireversible interval, together with the position of the maximum, is independent of the adsorption strength. Similar to the surface reactions, the position of the maximum varies with the electron transfer coefficient and the amphtude of the potential modrrlation [92]. 

Because polymer adsorption is effectively irreversible, and because adsorption and floe growth occur simultaneously, flocculation is a non-equilibrium process. As a result, performance is largely determined by the kinetics of adsorption and aggregation. Both of these can be regarded as collision processes involving solid particles and polymer molecules. In each case, collisions can arise due to either Brownian motion or agitation of the suspension. The collision frequency v between particles and polymer molecules can be estimated from °... 

We have studied above a model for the surface reaction A + 5B2 -> 0 on a disordered surface. For the case when the density of active sites S is smaller than the kinetically defined percolation threshold So, a system has no reactive state, the production rate is zero and all sites are covered by A or B particles. This is quite understandable because the active sites form finite clusters which can be completely covered by one-kind species. Due to the natural boundaries of the clusters of active sites and the irreversible character of the studied system (no desorption) the system cannot escape from this case. If one allows desorption of the A particles a reactive state arises, it exists also for the case S > Sq. Here an infinite cluster of active sites exists from which a reactive state of the system can be obtained. If S approaches So from above we observe a smooth change of the values of the phase-transition points which approach each other. At S = So the phase transition points coincide (y 1 = t/2) and no reactive state occurs. This condition defines kinetically the percolation threshold for the present reaction (which is found to be 0.63). The difference with the percolation threshold of Sc = 0.59275 is attributed to the reduced adsorption probability of the B2 particles on percolation clusters compared to the square lattice arising from the two site requirement for adsorption, to balance this effect more compact clusters are needed which means So exceeds Sc. The correlation functions reveal the strong correlations in the reactive state as well as segregation effects. 

When molecules adsorb to a flat substrate, their conformation is modified due to the geometric confinement between the two interfaces and the direct interaction to the substrate. This state can be far from equilibrium if the adsorption process has been fast and irreversible. In this case, the molecules do not have time to sample the whole assembly of thermodynamic states and get trapped kinetically at contact sites. The reversibility is difficult to achieve because of the great size of the molecules and strong adhesion which might exceeds kBT by far. In order to approach an equilibrium state, the sample has to be pre-... 

The reversibility of the adsorption steps in mechanism (4) affects the total number of steady states. As can be seen from Table 1, if two adsorption steps are reversible, boundary steady-state points are absent. Irreversibility of one adsorption step leads to the appearance of one boundary steady-state point in which the concentration of the reversibly adsorbing substance is equal to zero and the irreversibly adsorbing substance occupies all active sites of the catalyst surface. In the case where both adsorption steps are irreversible, there exist two boundary steady-state points (x = 0, y = C2) and (x = Cz, y = 0). In the latter case, at equal kinetic orders of the adsorption steps (n = m) a multiplicity of steady-state solutions is possible, i.e. at pk2 = qk1 (non-rough case) there exists a singular line of steady states connecting two boundary steady-state points. It can manifest itself in the unreproducibility of experimental data in a certain range of the parameters. 

Let us start our investigation with the case when the adsorption steps in mechanism (8) are irreversible [166]. The unsteady-state kinetic model is then of the form... 

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