Self-assembly of three-dimensional open structures using patchy colloidal particles

Abstract

Open structures can display a number of unusual properties, including a negative Poisson's ratio, negative thermal expansion, and holographic elasticity, and have many interesting applications in engineering. However, it is a grand challenge to self-assemble open structures at the colloidal scale, where short-range interactions and low coordination number can leave them mechanically unstable. In this paper we discuss the self-assembly of open structures using triblock Janus particles, which have two large attractive patches that can form multiple bonds, separated by a band with purely hard-sphere repulsion. Such surface patterning leads to open structures that are stabilized by orientational entropy (in an order-by-disorder effect) and selected over close-packed structures by vibrational entropy. For different patch sizes the particles can form into either tetrahedral or octahedral structural motifs which then compose open lattices, including the pyrochlore, the hexagonal tetrastack and the perovskite lattices. Using an analytic theory, we examine the phase diagrams of these possible open and close-packed structures for triblock Janus particles and characterize the mechanical properties of these structures. Our theory leads to rational designs of particles for the self-assembly of three-dimensional colloidal structures that are possible using current experimental techniques.

Activity-Enhanced Self-Assembly of a Colloidal Kagome Lattice

“…24,59,61,62 Additionally, our model exhibits qualitatively similar phase behavior to previous thermodynamic studies on equilibrium triblock Janus colloids. 42,43,55,63 A more complete discussion of this patchy potential and its functional form can be found in the Supporting Information. Below we list the key features of the anisotropic interaction potential, which drives the formation of the kagome lattice:…”

Nonisotropic Self‐Assembly of Nanoparticles: From Compact Packing to Functional Aggregates

“…the patch angular width, was particularly investigated and it was shown that, when this value is high enough to enable one patch to interact simultaneously with the patches of two neighboring particles, ring structures may be promoted leading to a two-dimensional Kagome lattice [199]. It has also been shown theoretically that triblock Janus parti-cles, which have two large attractive patches separated by a repulsive band, can form a 3D pyrochlore lattice [200]. Romano and Sciortino have further demonstrated by performing Monte Carlo simulations that a rational design of the shape and the symmetry of the two patches can drive the patchy particles to crystallize in a single morphology by eliminating the undesired polymorphs [201].…”

Designing pairwise interactions that stabilize open crystals: Truncated square and truncated hexagonal lattices

“…For classes of competing structures that contain free parameters, the values of those parameters are determined by minimizing the chemical potential (using GAMS) under the optimized pair potential (for details see appendix of ref. 25). Any structures that are revealed by this calculation to be more stable than the target lattice are added to the competing pool to be used in the next iteration of the pair potential optimization.…”