Topological Design of Heterogeneous Self-Assembly

TL;DR

This paper develops a thermodynamic framework for understanding how the topology of self-assembled structures from heterogeneous components can be controlled, revealing the role of transfer matrix spectra in phase behavior.

Contribution

It introduces a theoretical approach linking transfer matrix spectra to the designability and phase boundaries of self-assembled structures from heterogeneous building blocks.

Findings

Divergence in chemical potential is fundamental to self-assembly.

Transfer matrix spectrum determines the phase boundary.

Cross-talk influences the transition between structured and unstructured phases.

Abstract

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.