Size-dependent engineering of methane selectivity in CO₂ electroreduction on single-crystalline copper tetrahedra

While the facet dependence of Cu catalysts in the electrocatalytic CO₂ reduction reaction (e-CO₂RR) is well-established, how particle size dictates product selectivity on identical crystal facets, a critical but underexplored dimension of structure-performance relationships, remains elusive. Herein, we demonstrate a non-monotonic size-dependent selectivity toward methane (CH₄) using (111)-terminated Cu tetrahedra (Cu_tet) with uniform sizes of 20, 42, 55, and 64 nm. Among these, the 55 nm Cu_tet exhibits optimal CH₄ selectivity, delivering a peak Faradaic efficiency (FE_CH4) of 53.6% at -1.0 V versus reversible hydrogen electrode (RHE), while suppressing the competing hydrogen evolution reaction (HER) to 12.3%. In situ spectroscopy and theoretical calculations reveal that this selectivity trend arises from an optimal synergy between edge sites and (111) facet sites. Specifically, edge sites promote CO₂ adsorption and *COOH formation, whereas neighboring facet sites facilitate the key *CO → *CHO step. The 55 nm tetrahedron achieves an optimal edge-to-facet ratio that balances sufficient edge sites for CO₂ activation against limited edge sites to suppress *H-induced HER, thereby maximizing the cooperative relay of *CO from edges to facets for selective CH₄ production. This work establishes particle size as a key design strategy to engineer cooperative active sites on facet-defined nanocrystals, providing an alternative principle for rational catalyst design beyond facet control alone.