Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly

Abstract

We demonstrate a method based on symmetry to predict the structure of self-assembling, multicomponent colloidal mixtures. This method allows us to feasibly enumerate candidate structures from all symmetry groups and is many orders of magnitude more computationally efficient than combinatorial enumeration of these candidates. In turn, this permits us to compute ground-state phase diagrams for multicomponent systems. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, we use this scheme to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, for a model two-dimensional colloidal system, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from certain systems by tuning the mixture composition alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.

Understanding protein-complex assembly through grand canonical maximum entropy modeling

“…The difficulty in using the grand canonical ensemble is that the chemical potentials for specific particle types are unknown. To avoid this problem, previous efforts in studying protein or synthetic particle assembly have either defined the chemical potentials as known 33,[42][43][44][45][46] or used semi-grand canonical ensembles 47 , where particle types may vary in particle number with the total N is fixed.…”

Disentangling Rotational Dynamics and Ordering Transitions in a System of Self-Organizing Protein Nanorods via Rotationally Invariant Latent Representations

“…The emergence of ordered patterns in the systems of interacting particles is one of the foundational phenomena in chemistry, condensed matter physics, materials science, and biology, encompassing areas ranging from the formation of atomic lattices, protein complexes, and lipid membranes, to the self-assembly of viruses and nanoparticles. ,− Correspondingly, understanding of the evolution of such systems and the mechanisms guiding the emergence of the order has remained on the forefront of physical research for over half a century. This effort includes both the theoretical and simulation analysis, , exploring both natural structures, and model systems such as colloidal crystals , that allow for tunability of underpinning interactions. , …”

“…2,4−6 Correspondingly, understanding of the evolution of such systems and the mechanisms guiding the emergence of the order has remained on the forefront of physical research for over half a century. This effort includes both the theoretical and simulation analysis, 7,8 exploring both natural structures, and model systems such as colloidal crystals 2,9 that allow for tunability of underpinning interactions. 10,11 One of the challenges in understanding the dynamics of pattern emergence in these systems is the nature of the descriptors of the systems, i.e., the compact representation of the local and global geometries.…”

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

“…The structure of the superlattice dictates important material properties, e.g. photonic response [10] and catalytic activity [11]; thus much effort has focused on designing particles that self-assemble particular colloidal crystal structures [12][13][14][15][16][17][18][19]. However, less well understood is how to ensure that the equilibrium structure is kinetically accessible via self-assembly.…”