Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly involves an inevitable divergence in chemical potential. The divergence and its detailed structure are controlled by the spectrum of the transfer matrix, which summarizes all of self-assembly design degrees of freedom. By analyzing the transfer matrix, we map out the phase boundary between the designable structures and the unstructured aggregates, driven by the level of cross-talk.
@article{arxiv.2103.02010,
title = {Topological Design of Heterogeneous Self-Assembly},
author = {Andrei A. Klishin and Michael P. Brenner},
journal= {arXiv preprint arXiv:2103.02010},
year = {2021}
}