Self-assembly of multi-flavored two-dimensional binary colloidal crystals

We systematically investigate the assembly of binary, “multi-flavored” colloidal mixtures in two-dimensional space using various computational and theoretical approaches. These mixtures mimic DNA-coated colloids where... [ view full abstract ]

We systematically investigate the assembly of binary, “multi-flavored” colloidal mixtures in two-dimensional space using various computational and theoretical approaches. These mixtures mimic DNA-coated colloids where multiple different sequences of single stranded DNA are attached to the surface of the colloids.  Consequently, by tuning the concentration of complementary sequences on different colloids, all pairwise interactions may be tuned independently.  This introduces additional degrees of freedom over more traditional binary mixtures with fixed mixing rules, which is anticipated to open new avenues for directed self-assembly.  At present, colloidal self-assembly into non-trivial two-dimensional lattices tends to require either high pressures for isotropically interacting particles, or the introduction of directionally anisotropic interactions. Here we demonstrate tunable assembly into a plethora of morphologies which requires neither of these conditions. We develop a minimal model that defines a three-dimensional phase space containing one dimension for each pairwise interaction, then employ various computational techniques to map out regions of this phase space in which the system self-assembles into different structures. We then illustrate a simple theory, similar to the so-called “complementary contact model,” that is capable of reproducing these results for size-symmetric mixtures. This reveals how to target different structures by tuning pairwise interactions, solution stoichiometry, or both. Concerning particle size-asymmetry, we find that domains in this model’s phase space, corresponding to different morphologies, tend to undergo a continuous “rotation” whose magnitude is proportional to that of the size-asymmetry. Such continuity enables one to estimate the relative stability of different lattices for arbitrary size-asymmetries. Owing to its simplicity and accuracy, we expect this theory to serve as a valuable design tool for engineering binary colloidal crystals from multi-flavored components.