Basic Kinetics on Surfaces

Understanding the kinetics of a catalytic conversion requires atomistic-level insights into the dynamics of the fundamental gas-surface interactions. Catalytic reactions at surfaces often involve several elementary reaction steps that might exhibit different dynamics and result in overall complex kinetic behavior. In this section, we will focus on basic processes that can occur in a very simple reaction on a surface with a single facet. More complex systems will be discussed in section 2.1.2. Figure 2.1 illustrates the most important ele-mentary processes. In a collision between a molecule and a surface translational and/or internal energy is exchanged. Subsequently, the molecule might scatter back into the vac-uum, or it might not escape the potential well and become adsorbed. In the latter case, the species might be trapped in a physisorbed precursor state first, diffuse at the surface and finally chemisorb. The adsorbed molecule may undergo a chemical reaction and desorb, if it gains sufficient thermal energy.

Scattering

Atoms or molecules can be scattered from a surface elastically or inelastically. In elastic scattering, the kinetic energy of the species is conserved and the angle of incidence is equal to the angle of scattering [75]. In inelastic scattering, molecules that impinge on the surface gain or loses perpendicular momentum but the parallel momentum is conserved.

The angular distribution of inelastically scattered molecules is broader than that for elastic scattering. For instance, molecules with masses like CO, O₂, or heavier will exchange perpendicular momentum with the surface and thus heat or cool the surface [21].

Chemisorption and Physisorption

The adsorption of a molecule is a complex process that usually can be divided into two stages. First there is physisorption, a relatively weak and long-range dipolar interaction between the adsorbate and the surface. Van der Waals interactions cause attractive po-tentials between the surface and the adsorbate at large distances. Closer to the surface, electronic repulsion becomes dominant, which leads to an increase of the potential energy and defines apotential well, in which the molecule can be trapped. Secondly, chemisorp-tion occurs when a chemical bond is formed between the adsorbate and the surface. In this case, the potential of the system decreases along the reaction coordinate until the chemical bond is formed. Often chemisorption follows an initially formed physisorbed precursor state [76].

Trapping Trapping describes the adsorption of a species from the gas phase into a gas–

surface potential well. The adsorbate thermally equilibrates to the surface. It is mostly associated with non-activated, non-dissociative physisorption [20, 21]. In order to be trapped, the incident species must lose sufficient momentum along the surface normal, for instance through coupling to its momentum parallel to the surface or to surface phonons.

Hence, the trapping probability will decrease with increasing energy of the impinging species. However, the trapping probability depends on numerous further parameters such as surface temperature, mass, and chemical structure of the adsorbate [20, 77, 78]. Trap-ping might be followed by desorption, this process is called trapping-desorption. The intensity of the desorbing signal is a cosine distribution around the surface normal and the kinetic energy corresponds to a Maxwell-Boltzmann velocity distribution characteristic for the surface temperature [20, 21, 75].

Precursor States A species that has been trapped on a surface might be in a precursor state. The lifetime of a precursor state is short compared to the lifetime of the strongly adsorbed state. Precursor states can exist over sites that are available for chemisorp-tion (intrinsic precursor), but it can also exist over surface sites that are occupied by chemisorbed species (extrinsic presursor). Extrinsic precursor states ensure high sticking probabilities of adsorbates up to high surface coverages, since impinging molecules get trapped and can diffuse along the surface until they find a site available for chemisorp-tion. Physisorption can also be followed by desorption, which then corresponds to the phenomenon of trapping-desorption, which has been discussed before 2.1.1. Figure 2.2 illustrates the different precursor states and the possible pathways of their conversion [20, 76, 77].

Sticking Sticking refers to the formation of a chemisorbed species. Often it is formed from a weaker bonded physisorbed precursor state. The fraction of the impinging gas phase molecules that stick to a surface is the sticking coefficient S, which is generally a function of the coverage Θ. Langmuir assumed that molecules impinging on a site occupied by a chemisorbed species will scatter back while species arriving at empty sited will stick with a probabilityS0. According to this model, the sticking probability SL(Θ) decreases

2.1 Kinetics at Gas-Surface Interfaces

Figure 2.2: Illustration of the adsorption into a precursor state over an empty site (intrinsic precursor) and over a site occupied by a chemisorbed species (extrinsic precur-sor). The formation of the intrinsic precursor state can be directly followed by chemisorption. During the lifetime of the extrinsic precursor, the adsorbate can diffuse along the surface to find a site available for chemisorption.

linearly with the density of empty sites and thus with the surface coverage Θ.

SL(Θ) =S0 Θ_sat is the saturation coverage andn is the order of the adsorption process.

However, in many studies the sticking probability was found to stay high up to high coverages, caused by a precursor-mediated sticking. In this process, adsorbates can first be trapped in an extrinsic precursor state that enables them to diffuse along the covered surface to find sites available for chemisorption. Thus, the rate of this precursor-mediated sticking depends on the rate of diffusion of the extrinsic precursor to sites which are available for chemisorption and on the rate of chemisorption from these intrinsic precursor state. This coverage-dependent sticking probability S(Θ) was described by Kisliuk as follows: S0 is the sticking probability on the pristine surface. The precursor state parameter KP

is a measure for the effect of the precursor on the sticking probability. If K_P=1, the precursor plays no role in the chemisorption process and the sticking probability decreases linearly with increasing coverage, which corresponds to the Langmuir model. Assuming a nearly random distribution of empty and filled sites, which is most likely true for Θ≈0 and Θ ≈ 1, K_P is given by the ratio between the probabilities of desorption from the extrinsic precursor statePde and adsorption from the intrinsic precursor statePai:

K = S0P_de

(2.3)

Figure 2.3: The effect of the precursor state parameter on the coverage-dependent sticking probabilityS relative to the initial sticking probability (S₀). K=1 corresponds to no effect of the precursor states (Langmuir model). K=0.01 corresponds to a strong precursor effect on the chemisorption rate, such as for large organic molecules.

Qualitatively, the precursor states lead to increased sticking when the desorption prob-ability from the extrinsic precursor state is low and the adsorption probprob-ability from the intrinsic precursor state is high [79]. Figure 2.3 illustrates the effect of changing precursor state parameters on the coverage dependent sticking probability. The studies in this thesis show that for relatively large molecules such as organic compounds with masses higher than 50 amu, the sticking probability is high until high surface coverages indicating a low desorption rate from the extrinsic precursor states and a high adsorption rate from intrinsic precursor.

Diffusion and Desorption

After an adsorbed species has entered the potential well of a surface, it can diffuse across the surface or desorb into the gas phase. For diffusion on the energetically corrugated sur-face, the adsorbate has to overcome the energetic barrier to hop from one potential well to the next one. The activation barrier for diffusion is generally lower than the activation barrier for desorption. As both processes are driven by thermal fluctuations, the surface temperature critically governs the rates of diffusion and desorption.

The root mean square distance< x² >^1/2 that an adsorbate diffuses within it’s residence timeton a uniform two-dimensional surface is given by

2.1 Kinetics at Gas-Surface Interfaces

< x² >^1/2=

√

4Dt (2.4)

withDrepresenting the diffusion coefficient. The diffusion constant is described by an Ar-rhenius equation with the pre-exponential factorD₀ and the activation energy for diffusion Edif f. The rate of desorption ^−dΘ_dt is given by

−dΘ with Θ the coverage,nthe desorption order,k₀ the pre-exponential factor for desorption, andEdes the activation barrier for desorption.[20, 75]

Bimolecular Reactions on Surfaces

Figure 2.4 illustrates two principle ways of bimolecular reactions on surfaces, Langmuir-Hinselwood (LH) and Eley-Rideal (ER). Most reactions proceed by the LH mechanism, in which both reactants are fully accommodated on the surface before they react. The adsorption process of both reactants might follow the steps that are described above:

Physisorption in a precursor state, diffusion between different sites, and chemisorption with and without dissociation. Finally, the adsorbates can react and desorb into the gas phase. The formation rate of the product AB^dΘ_dt^ABout of the reactants A and B in an elementary reaction step is given by:

with Θ_A and Θ_B representing the surface coverages of species A and B, E_act^LH is the activation energy for the reaction, andk^LH₀ is the pre-exponential factor.

The ER mechanism describes a far rare type of bimolecular reactions. Here, the reaction occurs between an adsorbate and an incident species, which has not equilibrated to the surface. Evidence for LH or ER mechanisms can be found by molecular beam studies [20, 21].