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Using Symmetry To Elucidate the Role Of Stoichiometry In Colloidal Crystal Assembly



Nathan Mahynski, Evan Pretti, Vincent K. Shen, Jeetain Mittal


We demonstrate a method based on symmetry to predict the structure of multi-component colloidal mixtures. In this work we focus on two-dimensional systems, for which the method allows us to exhaustively enumerate candidates from all wallpaper groups, guaranteeing all planar symmetries have been explored. In turn, this allows us to compute ground-state phase diagrams for multicomponent lattices. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, this enumeration scheme allows us to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from systems by tuning stoichiometry alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.
Nature Communications


colloidal crystals, self-assembly, wallpaper group


Mahynski, N. , Pretti, E. , Shen, V. and Mittal, J. (2019), Using Symmetry To Elucidate the Role Of Stoichiometry In Colloidal Crystal Assembly, Nature Communications, [online], (Accessed April 15, 2024)
Created May 2, 2019, Updated February 12, 2020