Inverse Optimization Techniques for Targeted Self-Assembly

TL;DR

This paper reviews inverse optimization methods for designing interaction potentials in soft matter systems to achieve targeted self-assembled structures, including both ordered and disordered configurations, with potential applications in material design.

Contribution

It introduces novel inverse statistical-mechanical methodologies that optimize many-body interaction potentials for stabilizing specific target structures, expanding the scope of self-assembly control.

Findings

Inverse approaches can produce stable targeted structures beyond natural self-assembly.

Optimized potentials enable the formation of both crystalline and amorphous structures.

Recent results deepen understanding of the relationship between interactions and collective structure.

Abstract

This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable "target" structures. We are interested in finding the interaction potential, not necessarily pairwise additive or spherically symmetric, that stabilizes a targeted many-body system by generally incorporating complete configurational information. Unlike previous work, our primary interest is in the possible many-body structures that may be generated, some of which may include interesting but known structures, while others may represent entirely new structural motifs. Soft matter systems, such as colloids and polymers, offer a versatile means of realizing the optimized interactions. It is shown that these inverse approaches hold great promise for controlling self-assembly to a degree that surpasses the less-than-optimal path that nature has provided. Indeed, we envision being able to "tailor" potentials that produce varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. The notion of tailoring potentials that correspond to targeted structures is motivated by the rich fundamental statistical-mechanical issues and questions offered by this fascinating inverse problem as well as our recent ability to identify structures that have optimal bulk properties or desirable performance characteristics. Recent results have already led to a deeper basic understanding of the mathematical relationship between the collective structural behavior of many-body systems and their interactions, as well as optimized potentials that enable self-assembly of ordered and disordered particle configurations with novel structural and bulk properties.