Adsorption sticking coefficient

Another limitation of tire Langmuir model is that it does not account for multilayer adsorption. The Braunauer, Ennnett and Teller (BET) model is a refinement of Langmuir adsorption in which multiple layers of adsorbates are allowed [29, 31]. In the BET model, the particles in each layer act as the adsorption sites for the subsequent layers. There are many refinements to this approach, in which parameters such as sticking coefficient, activation energy, etc, are considered to be different for each layer. 

Very recently, considerable effort has been devoted to the simulation of the oscillatory behavior which has been observed experimentally in various surface reactions. So far, the most studied reaction is the catalytic oxidation of carbon monoxide, where it is well known that oscillations are coupled to reversible reconstructions of the surface via structure-sensitive sticking coefficients of the reactants. A careful evaluation of the simulation results is necessary in order to ensure that oscillations remain in the thermodynamic limit. The roles of surface diffusion of the reactants versus direct adsorption from the gas phase, at the onset of selforganization and synchronized behavior, is a topic which merits further investigation. 

This is our principal result for the rate of desorption from an adsorbate that remains in quasi-equihbrium throughout desorption. Noteworthy is the clear separation into a dynamic factor, the sticking coefficient S 6, T), and a thermodynamic factor involving single-particle partition functions and the chemical potential of the adsorbate. The sticking coefficient is a measure of the efficiency of energy transfer in adsorption. Since energy supply from the... 

Note that if sticking is controled by site-exclusion only, i.e., if S 6,T) = 5 o(P)(l — 0), this rate is that of a first-order reaction at low coverage. This simple picture breaks down when either the sticking coefficient depends dilferently on the coverage, as it does for instance for precursor-mediated adsorption, or when lateral interactions become important. It then does not make much physical sense to talk about the order of the desorption process. 

The sticking coefficient at zero coverage, Sq T), contains the dynamic information about the energy transfer from the adsorbing particle to the sohd which gives rise to its temperature dependence, for instance, an exponential Boltzmann factor for activated adsorption. 

To get the equilibrium sticking coefficient we assume that at an ambient pressure Pq the adsorbate is in equilibrium at a temperature T with partial coverages Hq, m, and Iq. We then increase the pressure slightly to p = Pq- - AP and linearize the rate equations in the increase in the precursor coverages Am = (m) —m and Al = (/) — Iq. If adsorption into and desorption from the precursors is much faster than transitions from the precursors into the adsorbed state, we can ignore terms proportional to An = n) -6 on the right-hand side of Eqs. (70-72) and also assume that the precursors will be in a steady state. It has been shown that the sticking... 

For adsorbates out of local equilibrium, an analytic approach to the kinetic lattice gas model is a powerful theoretical tool by which, in addition to numerical results, explicit formulas can be obtained to elucidate the underlying physics. This allows one to extract simplified pictures of and approximations to complicated processes, as shown above with precursor-mediated adsorption as an example. This task of theory is increasingly overlooked with the trend to using cheaper computer power for numerical simulations. Unfortunately, many of the simulations of adsorbate kinetics are based on unnecessarily oversimplified assumptions (for example, constant sticking coefficients, constant prefactors etc.) which rarely are spelled out because the physics has been introduced in terms of a set of computational instructions rather than formulating the theory rigorously, e.g., based on a master equation. 

For alkali modified noble and sp-metals (e.g. Cu, Al, Ag and Au), where the CO adsorption bond is rather weak, due to negligible backdonation of electronic density from the metal, the presence of an alkali metal has a weaker effect on CO adsorption. A promotional effect in CO adsorption (increase in the initial sticking coefficient and strengthening of the chemisorptive CO bond) has been observed for K- or Cs-modified Cu surfaces as well as for the CO-K(or Na)/Al(100) system.6,43 In the latter system dissociative adsorption of CO is induced in the presence of alkali species.43... 

This backdonation of electron density from the metal surface also results in an unusually low N-N streching frequency in the a-N2 state compared to the one in the y-N2 state, i.e. 1415 cm 1 and 2100 cm"1, respectively, for Fe(l 11)68. Thus the propensity for dissociation of the a-N2 state is comparatively higher and this state is considered as a precursor for dissociation. Because of the weak adsorption of the y-state both the corresponding adsorption rate and saturation coverage for molecular nitrogen are strongly dependent on the adsorption temperature. At room temperature on most transition metals the initial sticking coefficient does not exceed 10 3. 

The adsorption in the a-N2 state proceeds mainly via previous adsorption in the y-N2 state. Direct adsorption in the a-N2 state corresponds to a rather low sticking coefficient ( 10 3) but is the only adsorption route at higher... 

Figure 2.23. Changes in the initial sticking coefficient for N2 dissociative adsorption on K-covered Fe(Ul) as a function of K coverage. Ta=430 K.72 Reprinted with permission from Elsevier Science.

Here we have utilized Eq. (147) and assumed that the electronic ground state of the transition state has been raised by AE (to refer partition functions to the transition state s own ground state) and qto-vih is referred with respect to the bottom of the potential, as in Fig. 3.10. Expression (156) shows that the adsorption rate per area is the collision number for that area times a factor So(T), the so-called sticking coefficient, which must always be smaller than one. The sticking coefficient describes how many of the incident atoms were successful in reaching the adsorbed state... 

Hence, according to the transition state theory, adsorption becomes more likely if the molecule in the mobile physisorbed precursor state retains its freedom to rotate and vibrate as it did in the gas phase. Of course, this situation corresponds to minimal entropy loss in the adsorption process. In general, the transition from the gas phase into confinement in two dimensions will always be associated with a loss in entropy and the sticking coefficient is normally smaller than unity. 

Clearly, the sticking coefficient for the direct adsorption process is small since a considerable amount of entropy is lost when the molecule is frozen in on an adsorption site. In fact, adsorption of most molecules occurs via a mobile precursor state. Nevertheless, direct adsorption does occur, but it is usually coupled with the activated dissociation of a highly stable molecule. An example is the dissociative adsorption of CH4, with sticking coefScients of the order 10 -10 . In this case the sticking coefficient not only contains the partition functions but also an exponential... 

If we now assume that this surface at temperature T is in equilibrium with a gas then the adsorption rate equals the desorption rate. Since the atoms/molecules are physisorbed in a weak adsorption potential there are no barriers and the sticking coefficient (the probability that a molecule adsorbs) is unity. This is not entirely consistent since there is an entropic barrier to direct adsorption on a specific site from the gas phase. Nevertheless, a lower sticking probability does not change the overall characteristics of the model. Hence, at equilibrium we have... 

Unraveling catalytic mechanisms in terms of elementary reactions and determining the kinetic parameters of such steps is at the heart of understanding catalytic reactions at the molecular level. As explained in Chapters 1 and 2, catalysis is a cyclic event that consists of elementary reaction steps. Hence, to determine the kinetics of a catalytic reaction mechanism, we need the kinetic parameters of these individual reaction steps. Unfortunately, these are rarely available. Here we discuss how sticking coefficients, activation energies and pre-exponential factors can be determined for elementary steps as adsorption, desorption, dissociation and recombination. 

The rate of adsorption of a gas on a surface is determined by the rate of collision between the gas and the surface and by the sticking coefficient ... 

To describe the adsorption, we need to know the sticking coefficient. As discussed in Chapter 3, it can conveniently be expressed in the Arrhenius form ... 

Measuring the uptake of a gas by a surface as a function of the dose to which the surface is exposed is the most straightforward way to determine a sticking coefficient. In such experiments, great care should be taken to ensure that gas and surface are in thermal equilibrium. In addition, we need to determine the coverage, either by surface sensitive methods (XPS, AES, IR) or by thermal desorption and ensure that adsorption is not accompanied by desorption. 

Figure 7.1. Uptake curves for first and second order adsorption as a function of gas dose given in Pascal seconds. In this example, the sticking coefficient is strongly activated, with an activation energy of 60 kj moTb...

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. 

Table 7.1. Sticking coefficients for dissociative adsorption of selected gases.

Figure 7.5. Sticking coefficients along with differential heats of adsorption as measured by microcalorimetry for ethylene and acetylene on Rh(lOO). [Adapted from R. Kose, W.A. Brown and D.A. King, Chem. Rhys. Lett. 311 (1999) 109.]...

Having estimated the sticking coefficient of nitrogen on the Fe(lll) surface above, we now consider the desorption of nitrogen, for which the kinetic parameters are readily derived from a TPD experiment. Combining adsorption and desorption enables us to calculate the equilibrium constant of dissociative nitrogen adsorption from... 

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