The origin of the particle-size-dependent selectivity in 1-butene isomerization and hydrogenation on Pd/Al2O3 catalysts

The selectivity of 1-butene hydrogenation/isomerization on Pd catalysts is known to be particle size dependent. Here we show that combining well-defined model catalysts, atmospheric pressure reaction kinetics, DFT calculations and microkinetic modeling enables to rationalize the particle size effect based on the abundance and the specific properties of the contributing surface facets.

In the full hydrogenation to n-butane 9*, the intermediates 2-butyl 8* or 1-butyl 7* are involved, see reactions R6, R8, R9, and R10, Supplementary We estimated Gibbs free energies of adsorption by adjusting pertinent electronic energies for the zero-point energy correction and the entropy correction at 373 K, approximated by the harmonic oscillator model. Hereby we invoked the vibrational degrees of freedom of a complex that involves the adsorbate and the metal centers directly involved in the adsorption as well as the direct metal neighbors of the latter centers. Surface species were assumed not to engage in frustrated rotations or translations. The standard pressure of these free energies is 1 bar for species in the gas phase, while for adsorbed molecules, treated as lattice gas, the standard surface concentration is 0.5. 14,15 For species in the gas phase, we also considered the rotational degrees of freedom. For molecular species in the gas phase, these corrections were determined using the program Gaussian 09, 16 at the analogous level of theory using basis sets of the double zeta type.
Modes with vibrational frequencies below 100 cm −1 or imaginary frequencies (of at most 50 cm −1 ) were assigned a frequency of 100 cm −1 for evaluating the entropy term.
Adsorption energies ΔGads and reaction energies ΔGr, were calculated according to where Gads are free energy values of adsorption complexes, and the term Ggas + Gslab is the sum of total free energy values of the molecule in the gas phase and the bare Pd surface, respectively,

Evaluation of rate constants
We calculated the rate constant ki(fwd) of the i-th forward reaction step as Here Ga(i) is the standard state Gibbs activation free energy of reaction i (kJ mol -1 ) containing the terms as specified in the previous section, A is the pre-exponential factor, kB is the Boltzmann constant (J K -1 ), h is Planck's constant (J s), T is the temperature (K), and R is the gas constant (kJ K -1 mol -1 ). The Gibbs free energies of the initial states and the corresponding transition state structures were calculated in advance, see Supplementary Note 1. Following our previous work, 12 we evaluated rates using these rate constants times surface concentrations times the actual surface area of our catalyst in experiment.
Assuming the adsorption reactions A1, A2, as well as those reverse to D1, and D2,

Supplementary
Here, the mass of the molecule m is in kg, the Boltzmann constant kB in J K -1 , and the temperature S6

Strategy for determining the amount of blocked sites
According to scanning tunneling microscopy (STM) characterization, 22 2-butene blocks Nbs = 2-3 metal centers, which we use as basic unit of "site" at the surface Pd(110). A similar value of Nbs was also deduced in our previously calculated structure of 2-butene on Pd(110). 12  Conversely, we used Nsb values decreased by one on all surfaces for the nearly saturated intermediates 7*, 8*, and 9* which are only bound through one C-metal bond.

Micro-kinetic modeling, adapted rate constants of the desorption reactions
Micro-kinetic modeling was carried out using rate constants derived from Gibbs free reaction energies and activation energies as just described, Supplementary Table 2 As in our previous work, we carried out a sensitivity analysis 17 regarding the formation of nbutane, to elucidate the influence of individual elementary reactions within the network. 12 To this S7 end, the rate constants ki were perturbed, one at a time, increasing their values by 10%. At the same time, the equilibrium constant i eq of reaction i, remained unchanged to maintain the thermodynamic equilibrium condition. Hence, for each elementary reaction step i of the reaction network, a calculation with the perturbed parameter ki was carried out to determine the variation of the output quantity Xk. In this work, we chose X0 = 9% as output quantity, i.e., 9% of the product n-butane was formed. For a rate constant ki, the normalized sensitivity coefficient NSCi is expressed as: The value (positive or negative) of NSCi indicates the magnitude of the influence of reaction i on the formation of the products.
Supplementary Figure 6 shows the impact on the formation rate of the hydrogenation product, n-butane. Accordingly, the adsorption A1 of 1-butene, the hydrogenation R6 of 1-butene, and the hydrogenation R8 of 2-butyl 8* have the highest positive sensitivity coefficient for reactions on Pd(111) and Pd(110), whereas we obtained large negative coefficients NSCi for the desorption D1 of trans-2-butene.
As we identified the fast desorption reaction to be responsible for the rather low hydrogenation activity, we subsequently explored likely causes of this observation. The desorption is controlled by the desorption energy of an adsorbate. i.e., the negative of the corresponding adsorption energy on a metal surface. The calculated desorption energy, in turn, is affected by the chosen exchangecorrelation functional and the associated gain of entropy. While calculations using the PBE functional have their advantages in describing reactions, they have been shown to underestimate desorption energies, on the example of hydrocarbons at Pt(111). 23 Using the BEEF-vdW functional, which had been reported to yield more realistic adsorption/desorption energeties, 23

Catalytic batch reactor measurements and activity/selectivity
The clean samples were transferred under UHV to the reaction cell, where catalytic measurements were performed at atmospheric pressure. The model catalysts were exposed to the reaction mixture (high-purity P1-butene: 5 mbar; PH2: 10 mbar; Ar added to 1 bar) at a temperature of 373 K. Kinetic measurements were carried out in a batch mode with the gas recirculating over the catalyst by a metal bellows pump (reactor volume exchanged 5 times per minute). The reaction products were analyzed by on-line gas chromatography (GC), using a HP-PLOT/Al2O3 column (50m×0.53mm) capillary column and a flame ionization detector FID. 30 Retention times and sensitivity factors for the reactant and products were calibrated using different gas mixtures.
Employing Al2O3 films on NiAl(110) as "inert" catalysts, the absence of background (wall) and support reactions was confirmed.
To avoid the formation of β-palladium hydride, the pressure PH2 of H2 was kept well below the required threshold pressure (about 20 and 200 mbar at room temperature and 373 K, respectively). 40 Consequently, the catalytic reactions were started on well-defined clean surfaces of the Pd NPs. Given the "mild" reaction conditions, major structural/compositional changes of the Pd nanoparticles can be largely excluded. When the reaction was stopped and the reaction cell recharged with the original reaction mixture, hardly any differences in the GC reaction profiles were observed.
In any case, we focused on the initial activity and selectivity of the model catalysts i.e., after 10 min reaction time, when both the cleanliness and structure were hardly affected. Supplementary Table 8 reports the turnover frequencies of the various catalysts for 1-butene isomerization and hydrogenation, the selectivity (the iso/hydro ratio), and the trans-2-butene/cis-2-butene ratio.