Entropic effects in the self-assembly of open lattices from patchy particles

TL;DR

This paper explores how entropy, specifically rotational and vibrational entropy, can stabilize and favor the formation of open lattice structures in self-assembling patchy particles, simplifying future design strategies.

Contribution

It reveals the stabilizing role of entropy in the self-assembly of open lattices from patchy particles, highlighting mechanisms previously unconsidered.

Findings

Rotational entropy stabilizes open lattices.

Vibrational entropy favors open over close-packed lattices.

Entropy effects enable simplified design of patchy particles.

Abstract

Open lattices are characterized by low volume-fraction arrangements of building blocks, low coordination number, and open spaces between building blocks. The self-assembly of these lattices faces the challenge of mechanical instability due to their open structures. We theoretically investigate the stabilizing effects of entropy in the self-assembly of open lattices from patchy particles. A preliminary account of these findings and their comparison to experiment was presented recently [X. Mao, Q. Chen, S. Granick, \textit{Nat. Mater.}, \textbf{12}, 217 (2013)]. We found that rotational entropy of patchy particles can provide mechanical stability to open lattices, whereas vibrational entropy of patchy particles can lower the free energy of open lattices and thus enables the selection of open lattices verses close-packed lattices which have the same potential energy. These effects open the door to significant simplifications of possible future designs of patchy-particles for open-lattice self-assembly.