The Cu–ZnO synergy in methanol synthesis Part 3: Impact of the composition of a selective Cu@ZnO x core–shell catalyst on methanol rate explained by experimental studies and a concentric spheres model

•Selective Cu@ZnOx core–shell catalysts of various compositions were synthesized.•The catalytic sites are of the type CuxZn(1−x)Oy.•A predictive model for determining the core–shell catalysts activity was developed.•A correlation between activity and Zn migrated for three catalyst designs is shown.