An analysis of Pareto fronts for programmable self-assembly.

We study how the energy landscape for particles with short-range interactions varies as one increases the range of the interaction potential. We start with the local minima for 6 ≤ N ≤ 12 sticky hard spheres, which interact with a delta-function potential at their point of contact, and use numerical continuation to evolve the clusters as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters (local minima) merge, until at long ranges only one or two clusters are left. We compare the corresponding bifurcation diagrams for different potentials and find them to be insensitive to the interaction strength or particular potential at short range; they are identical up to about 5% of particle diameter and very similar up to 8%. The bifurcation diagrams vary significantly for ranges of 30% or longer, with more variation generally with the Lennard-Jones family than the Morse family of potentials. For most merge events, the range at which the merge occurs is possible to predict from the geometry of the starting sticky hard sphere cluster; an exception to this rule occurs with so-called nonharmonic clusters, which have a zero eigenvalue in their Hessian and undergo a more global rearrangement. arXiv:1908.09896v1 [cond-mat.soft]