Assembly of planar chiral superlattices from achiral building blocks

Abstract

The spontaneous assembly of chiral structures from building blocks that lack chirality is fundamentally important for colloidal chemistry and has implications for the formation of advanced optical materials. Here, we find that purified achiral gold tetrahedron-shaped nanoparticles assemble into two-dimensional superlattices that exhibit planar chirality under a balance of repulsive electrostatic and attractive van der Waals and depletion forces. A model accounting for these interactions shows that the growth of planar structures is kinetically preferred over similar three-dimensional products, explaining their selective formation. Exploration and mapping of different packing symmetries demonstrates that the hexagonal chiral phase forms exclusively because of geometric constraints imposed by the presence of constituent tetrahedra with sharp tips. A formation mechanism is proposed in which the chiral phase nucleates from within a related 2D achiral phase by clockwise or counterclockwise rotation of tetrahedra about their central axis. These results lay the scientific foundation for the high-throughput assembly of planar chiral metamaterials.

Fig. 1. Purification and assembly of Au tetrahedra.

a Schematic of purification methodology in which Ag shells are grown around as-synthesized samples containing a mixture of particle shapes. Small differences in the internal twinning of Au cores are accentuated in Ag shells, allowing for selective precipitation and separation of a desired morphology, e.g. tetrahedra (Td). b Purified Au Td@Ag cube particles. c Analysis of the distribution of nanoparticle shape products from as-synthesized (n = 7,612) and purified samples (n = 10,259). d Left and right-handed planar chiral hexagonal superlattices of tetrahedra with insets indicating orientation. e Schematic of the 2D chiral hexagonal phase, f hexagonal repeat unit, and g top and side views of Td dimers that constitute the structure. Scale bars: b 50 nm; d 100 nm.

Fig. 2. Analysis of growth modes for chiral hexagonal superlattices.

a Net pairwise interaction potentials for 2D and 3D chiral superlattices built from tetrahedron (Td)-shaped particles. Inset illustrates the structure of hexadecyltrimethylammonium chloride (CTAC) and its ability to form both solution-phase micelles and positively charged bilayers on Au surfaces separated by a distance, d. The x and y positions of the potential minimum as defined as d^* and U_tot^*, respectively. b Calculation of attachment energies for a single Td particle to top c, side c, and trimer g positions on a superlattice. c, d Illustration and SEM image of Td attachment at favorable side positions driving lateral (2D) growth. c, e–h Illustration and SEM images of sequential Td attachment at unfavorable monomer e, dimer f, and trimer g top positions before a favorable tetramer h can form, allowing for out-of-plane (3D) growth. i SEM image of the 3D analogue of planar chiral hexagonal superlattices generated via assembly under thermodynamic conditions. All scale bars are 100 nm.

Fig. 3. Understanding the stability of different 2D tetrahedra lattices.

Schematic illustration of the lattice, hexagonal repeat unit, and particle-particle overlap area for: a achiral (1), b achiral (2), and c chiral (3) structures described in the text. The closest distance two particles can approach (d_min) is set by the specific packing geometry. d Comparison of different superlattice energies as a function of hexadecyltrimethylammonium chloride (CTAC) concentration showing the ultimate stability of the chiral hexagonal (3) phase. e Illustration of the rounding of tips and edges as a result of selective oxidation of gold tetrahedra (Td) particles. f SEM images of the solvent evaporation-based assembly of Td particles with different tip radii (R), indicated in yellow. g Calculated concentration-dependent phase stability of achiral (1) and chiral (3) structures as a function of Td tip radius; separate lines are for Td with differing edge lengths. h Phase diagram predicting the stability of achiral (1) or chiral (3) structures at the endpoint of the assembly process based on particle size and tip radius; blue line is calculated phase boundary while red and purple dots indicate experimental observation of the achiral or chiral structures, respectively. All scale bars are 100 nm.

Fig. 4. Particle rotation explains the achiral-chiral phase transition.

a Tetrahedra (Td) packed into the achiral (1) structure may b undergo clockwise (CW) or counterclockwise (CCW) rotation to generate chiral enantiomers that c can form a denser lattice with more favorable interparticle attractions. d Definition of structural parameters for chiral superlattices including L, the Td edge length, D, the tip offset, and θ, the particle rotation angle. e Model calculations comparing the interaction potential (U_tot^*) as a function of rotation angle. Minimums in the plots define the optimal rotation angle (θ^*), which shift to higher values with increasing hexdecyltrimethylammonium chloride (CTAC) concentration. f Optimal rotation angle for L = 66.3 nm edge length Td at different CTAC concentrations showing the predicted value at the endpoint of the assembly process of θ_endpoint = 20°. g Calculated optimal rotation angles (θ^*) of chiral hexagonal assemblies for Td of varying edge length. Scale bar is 100 nm.