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

Abstract

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 0.85 Cu 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.