Learning nature’s assembly language with polymers - Oliver Xie; Alexander E. Cohen; Martin Z. Bazant; Bradley D. Olsen (Proceedings of the National Academy of Sciences, 2026)
The self-assembly of matter into ordered structures is ubiquitous throughout nature and engineered systems. Programming a material’s macroscopic properties via molecular-level structural control is a grand scientific challenge, requiring methods for inverse design that can design a targeted molecule to achieve a given self-assembled structure. One model system that serves as a common proving ground for inverse design algorithms is block copolymers. In these systems, self-consistent field-theory (SCFT) provides a robust thermodynamic model for predicting self-assembly for a given molecular sequence. This work presents a computational algorithm which learns the reverse translation, allowing a target structure to be achieved by varying molecular sequence. The algorithm is based on development of an adjoint solution of the SCFT equations allowing incorporation of automatic differentiation. The power of this algorithm is demonstrated by inverse designing polymer sequences to yield equilibrium structures, resolving the long-standing dilemma of navigating the combinatorial explosion of sequence possibilities offered by complex copolymer designs. The inverse designed sequences show that the algorithm learns to modulate unfavorable block interactions to stabilize these complex morphologies. By learning how to program self-assembly at the molecular-level using only a thermodynamic model, this work opens the door to similar computational inverse design across other soft matter systems.