We show that, with topologically flexible seeds which are allowed to explore different growth modes, graphitic cones are inherently more “designable” than flat graphitic disks. The designability of a structure is the number of seed topologies encoding that structure.
We illustrate designability with a simple model, where graphite grows onto C
(5≤n≤30) ring seeds. For a wide range of ring sizes, cones are the most likely topological outcome. Results from the model agree well with data from special cone-rich carbon black samples.
The concept of designability allows entropy to be incorporated into the “pentagon road” model of the formation of curved graphitic structures.