Optimal control of electrostatic self-assembly of binary monolayers

A simple macroscopic model is used to determine an optimal annealing schedule for self-assembly of binary monolayers of spherical particles. The model assumes that a single rate-controlling mechanism is responsible for the formation of spatially ordered structures and that its rate follows an Arrhenius form. The optimal schedule is derived in an analytical form using classical optimization methods. Molecular dynamics simulations of the self-assembly demonstrate that the proposed schedule outperforms other schedules commonly used for simulated annealing. In general, the term self-assembly refers to a non-intrusive process that transforms a system of components from a less to a more ordered state. There are numerous examples of selfassembly [1] including colloids [2], suspensions [3] and biological systems [4]. This work is motivated by self-assembly in model systems proposed by Grzybowski et al [5]. Those systems are horizontal monolayers of oppositely charged millimeter-size spherical particles placed inside a large square container. In such systems, the electrostatic interactions alone are not sufficient for arranging randomly placed particles into ordered lattices, as the particles are trapped in meta-stable states. To escape those traps, the container was subjected to vibration in the horizontal plane. With properly chosen vibration parameters it was possible on the one hand to escape meta-stable states and, on the other hand, preserve ordered lattice states. While Grzybowski et al were able to choose vibration parameters leading to self-assembly, their search strategy was heuristic and limited to very basic vibration histories. Our goal here is to develop an optimal strategy for guiding self-assembly in systems similar to those considered by Grzybowski et al. We note that the setup in [5] is not the only way to 1 Author to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 053014 1367-2630/09/053014+10$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft