(240g) Design of Optimal Metallic Surface Reconstructions for Heterogeneous Catalysis

Transition metal nanoparticles have been used to enhance the reactivity of catalysts by introducing significantly more surface area per amount of precious metal. Furthermore, some reactions show additional increase in reactivity on a per area basis due to the relative abundance of under-coordinated surface sties on nanoclusters [1]. Recently, synthesis methods such as electrochemical deposition, galvanic displacement, and the formation of near surface alloys have enabled the formation of nanostructured surfaces with pits, grooves, and multimetallic sites designed to introduce unique controls over the reactivity of surface sites [2,3]. The formation of these structures results in a combinatorial number of surface designs to be proposed, and leads to the challenging task of identifying the most reactive surface to target for catalyst design. To support this effort, we propose the use of mathematical optimization models to help guide this materials design process [4].

As a design space, we consider the choices of whether to place an atom or not in a periodic tile representing several layers around an infinite catalyst surface. We can generically model the characteristics of reaction sites with suitable descriptors, such as the coordination or generalized coordination number, and indicate if a site constitutes an ideal location for a desired chemical reaction [5,6,7]. Symmetry-breaking constraints are introduced to eliminate the significant number of equivalent representations of a design and are necessary to solve the model for reasonable tile sizes. The resulting model can be solved to identify the pattern of modifications to the base crystallographic plane that results in a maximal packing of ideal reaction sites per unit area.

While the developed framework can be applied with some basic approximations of stability, it is desirable to develop additional simplified structure function models to predict if designs are likely to be stable under reactive conditions. In order to determine which nanostructured designs are stable, we first enumerated a set of over one hundred Pt surfaces with modifications from the face centered cubic (FCC) {111} plane. The surface energy of these reconstructions and several reference Pt crystal configurations was calculated via density functional theory (DFT) using the RPBE exchange correlation functional and a linear extrapolation method [8].

This analysis yielded a number of reconstructions whose excess from the FCC {111} surface energy was low enough to make them plausible under normal conditions. In order to incorporate this information into our mathematical optimization model, we regressed a simplified structure-function relationship between the coordination of surface atoms and the surface energy evaluated by DFT. This allows us to predict the surface energy of nanostructured surfaces to within a small error by simply counting up the number of sites at a particular coordination. Furthermore, the contribution of different coordination numbers to surface energy was found to be roughly linear, suggesting that a simple bond counting model was sufficient to capture the trend in the data.

Given such a bond-counting model, we were able to explicitly incorporate constraints in our optimization model that required the predicted surface energy of designs to fall below a threshold of surface energy. We show that the choice of threshold can be chosen to correspond to the surface energy of the least stable simple crystal plane that is exhibited in experimental conditions. Alternatively, the optimization model can be iteratively solved while the threshold is scanned through a range of values to generate a Pareto-optimal frontier representing the tradeoff of stability against reactivity of nanostructured surfaces. The resulting surfaces were further evaluated via DFT to more accurately determine their actual stability and reactivity. The outcome of this framework is a systematic way to identify patterns of nanostructure that can be of interest for further study.

References

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[2] Calle-Vallejo F., Koper M. T. M., Bandarenka A. S., “Tailoring the catalytic activity of electrodes with monolayer amounts of foreign metals,” Chemical Society Reviews, 42(12):5210–30, 2013.

[3] Stamenkovic V. R., Mun B. S., Mayrhofer K. J. J., Ross P. N., Markovic N. M., “Effect of surface composition on electronic structure, stability, and electrocatalytic properties of Pt-transition metal alloys: Pt-skin versus Pt-skeleton surfaces,” Journal of the American Chemical Society, 128(27):8813–8819, 2006.

[4] Hanselman C. L., Gounaris C. E., “A mathematical optimization framework for the design of nanopatterned surfaces,” AIChE Journal, 62(9):3250–3263, 2016.

[5] Nørskov J. K., Bligaard T., Logadottir A., Bahn S., Hansen L. B., Bollinger M., Bengaard H., Hammer B., Sljivancanin Z., Mavrikakis M., Xu Y., Dahl S., Jacobsen C. J. H., “Universality in heterogeneous catalysis,” Journal of Catalysis, 209(2):275–278, 2002.

[6] Calle-Vallejo F., Martínez J. I., García-Lastra J. M., Sautet P., Loffreda D., “Fast prediction of adsorption properties for platinum nanocatalysts with generalized coordination numbers,” Angewandte Chemie - International Edition, 53(32):8316–8319, 2014.

[7] Calle-Vallejo F., Loffreda D., Koper M. T. M., Sautet P., “Introducing structural sensitivity into adsorption-energy scaling relations by means of coordination numbers,” Nature Chemistry, 7(5):403–410, 2015.

[8] Zhang W. B., Chen C., Zhang S. Y., “Equilibrium crystal shape of Ni from first principles,” Journal of Physical Chemistry C, 117(41):21274–21280, 2013.