A multiscale theory framework predicts size- and ordering-dependent activity in Pt–Cu oxygen reduction reaction catalysts

Optimizing the oxygen reduction reaction (ORR) performance of Pt-based alloy nanocatalysts requires a quantitative understanding of how catalytic activity and durability depend on nanoparticle composition, size, and atomic ordering. In this work, we present a multiscale theoretical framework that integrates density functional theory (DFT), machine-learning-accelerated cluster expansions, and kinetic and Metropolis Monte Carlo simulations to predict the structural evolution and ORR activity of octahedral Pt-Cu nanoparticles under acidic conditions. Our model captures the configurational complexity of experimentally relevant (4 to 10 nm) particles and reveals that disordered Pt_0.85Cu_0.15 nanoparticles exhibit optimal mass activity near 5 nm and a saturated specific activity plateau at ~6 nm, driven by the high density of catalytically active Pt(111) terrace sites. We further identify a size-dependent crossover in catalytic performance between ordered and disordered Pt-Cu particles, governed by subsurface atomic ordering and the distribution of *OH binding energies. These findings provide mechanistic insights and design strategies for tailoring surface and subsurface structure to enhance the catalytic efficiency of alloy nanocatalysts.