The variety of publications reporting high-entropy alloy (HEA) catalysts with exceptional activities creates a survivor bias, implying that the mixing entropy directly increases the activity. However, many screening studies show a different picture. In a multielement composition-activity space, often a low to medium entropic 2- or 3-element composition emerges as the most active catalyst. In this work, we investigate the relationship between the complexity of an alloy, which can be expressed in mixing entropy, and its maximum possible activity using theory and statistical modeling. Based on our analysis, we propose a hypothesis for the surface complexity-activity relationship of HEA catalysts. Namely, the intrinsic activity of an alloyed surface is defined by two opposing forces: positive ligand interactions that enhance the activity and the statistical dilution of active sites. As a result, the relationship between the surface complexity-activity shows qualitatively a volcano-like behavior. At first, adding elements increases the activity due to favorable ligand interactions. Yet, at some point, the catalytic benefit from increasing the complexity of the surface gets outweighed by the dilution of the catalytic sites. Correspondingly, this hypothesis states that there is an optimal ratio between the surface complexity and catalytic activity.
Mints et al. (Mon,) studied this question.