Measuring Transient Reaction Rates from Nonstationary Catalysts

Up to now, methods for measuring rates of reactions on catalysts required long measurement times involving signal averaging over many experiments. This imposed a requirement that the catalyst return to its original state at the end of each experiment—a complete reversibility requirement. For real catalysts, fulfilling the reversibility requirement is often impossible—catalysts under reaction conditions may change their chemical composition and structure as they become activated or while they are being poisoned through use. It is therefore desirable to develop high-speed methods where transient rates can be quickly measured while catalysts are changing. In this work, we present velocity-resolved kinetics using high-repetition-rate pulsed laser ionization and high-speed ion imaging detection. The reaction is initiated by a single molecular beam pulse incident at the surface, and the product formation rate is observed by a sequence of pulses produced by a high-repetition-rate laser. Ion imaging provides the desorbing product flux (reaction rate) as a function of reaction time for each laser pulse. We demonstrate the principle of this approach by rate measurements on two simple reactions: CO desorption from and CO oxidation on the 332 facet of Pd. This approach overcomes the time-consuming scanning of the delay between CO and laser pulses needed in past experiments and delivers a data acquisition rate that is 10–1000 times higher. We are able to record kinetic traces of CO2 formation while a CO beam titrates oxygen atoms from an O-saturated surface. This approach also allows measurements of reaction rates under diffusion-controlled conditions.


Treatment of Diffusion
We use Fick's second law to account for CO diffusion which becomes important at later times in titration experiments. Assuming circular symmetry, Fick's law describes diffusion through a ring with eq S1, written in polar coordinates.
In our application, the center of circular symmetry is crossing point of the center lines of the two molecular beams on the Pd surface. The coordinate system is sketched in figure S1. The CO beam axis is rotated by only 30° from the symmetry axis introducing a slightly elliptical CO spatial profile; but this is a small effect that we approximate as circular. We simulate the diffusion on the surface in a uniform sized radial grid, with being the radial width of each grid element and being the radial distance from center of circular 0 symmetry (coordinate system origin) to the spatial element .
Here, is an integer from 0, 1, …, . max Using finite differences, eq S1 can be expressed as: The result from eq S3 is identical to a formulation that can be found in reference 1, treating diffusion in a single component systems; however, we require a treatment of a two-component system. This is necessary because of site blocking effects that make the diffusion of two components dependent on one another. See figure S2.
Fick's law can be recast using the finite difference method into a circularly symmetric grid-hopping formalism (eq S4, comparable to reference 2): where is the hopping rate constant of n associated with the spatial element .

H,
We also need to consider that the perimeter of each grid element in polar coordinates increases with increasing radial distance-for example, the rate of hopping from to will be favored over that from + 1 to as the diffusion circumference is larger for the former. The resulting grid hopping rate constants -1 are simply related to the diffusion coefficients: The hopping transition rate for spatial element (eq S4) consists of 4 contributions: transitions from -1 and to and trasnitions from to and . The advantage formulating the diffusion problem in this way is that the diffusion of multiple species can be easily coupled to one another. This is done by introducing an occupation factor, , to each contribution of eq S4 reflecting the binding site occupation of the spatial element to which the transition is described (e.g. to the term the occupation of is . The modified form of eq S4 yields: where is the occupation factor for the species n. We define in the following way: where is the concentration of species m in spatial element and its concentration at maximum max coverage. This approach means that the diffusive transport of species n is hindered by coverages of species m. This is justified for CO and O on Pd, because both species are most stably bound at the same 3-fold site.
The rate formulation at the origin and outer edge of the coordinate system, i.e. at and , is given = 0 = max by eq's. S10 and S11.
At (eq S11) the system may be closed-diffusion beyond this point is not possible-ensuring mass max conservation as the system evolves. Alternatively, the system may be open-molecules can diffuse beyond but cannot return back, which yields eq S12: We used the open termination condition in our analysis, but tested the closed termination. We found no differences because the simulated cell size was big enough.

Comparison of CO diffusion rates
In figure S3 we compare the fitted CO diffusion coefficient from this work to previous reports of CO

Estimation of the reaction front speed
In figure S4, we show the radial concentration profiles of CO* and O* at several late titration times. The rather steep decrease of both concentration profiles indicates a diffusion-controlled regime. The quasistationary CO 2 production is confined near the reaction front. In the titration experiment, the oxygen coverage steadily decays, while the CO coverage builds up. The reaction moves out from the center toward the outer flanks where the CO coverage steadily removes O*. An established characteristic for diffusioncontrolled reactions is the reaction front propagation speed. We use plots like those shown in figure S4 to estimate the reaction front speed that is shown in figure 10 of the main text. Figure S1: The coordinate system used for diffusion reaction modelling with key definitions.   The stationary CO 2 formation rate as a function of the radial distance associated with the coverage profiles from the above plot. From the temporal evolution of the peak maximum the reaction front speed is estimated.