The same evolutionary strategies we used for the design of macroscopic granular molecules (see 3/3/13 entry) can also be applied to the design of more microscopic systems.  In collaboration with Juan de Pablo’s group at U of Chicago’s Institute for Molecular Engineering, we showed that this makes it possible to optimize the self-assembly of nano-scale domain patterns in thin films of diblock copolymers.

Directed assembly of block polymers is rapidly becoming a viable strategy for lithographic patterning of nanoscopic features. One of the key attributes of directed assembly is that an underlying chemical or topographic substrate pattern used to direct assembly need not exhibit a direct correspondence with the sought after block polymer morphology, and past work has largely relied on trial-and-error approaches to design appropriate patterns. In this work, a computational evolutionary strategy is proposed to solve this optimization problem. By combining the Cahn–Hilliard equation, which is used to find the equilibrium morphology, and the covariance-matrix evolutionary strategy, which is used to optimize the combined outcome of particular substrate–copolymer combinations, we arrive at an efficient method for design of substrates leading to non-trivial, desirable outcomes.

1. •Jian Qin, Gurdaman S. Khaira, Yongrui Su, Grant P. Garner, Marc Miskin, Heinrich M. Jaeger, and Juan J. de Pablo, “Optimizing directed self-assembled morphology”, Soft Matter 9, 11467–11472 (2103). pdf file
   

The image above is from the inside cover of the corresponding issue of Soft Matter. The background shows the spontaneously micro-phase-separated domain pattern (similar to a disordered fingerprint) in the absence of markers on the substrate. The colors red and blue indicate the domains in which one of the two blocks of the copolymer dominates. The typical domain spacing is ~50nm (see also the 12/30/2000 entry). The two rows of squares in the foreground show how marker placement, optimized via the evolutionary algorithm, makes it possible to direct the copolymer domain pattern into self-assembling the 10 letters S.O.F.T.M.A.T.T.E.R.