Supplementary Information:

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1 Supplementary Information: Self assembly of tetrahedral CdSe nanocrystals: effective patchiness via anisotropic steric interaction Michael A. Boles and Dmitri V. Talapin Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois, S1

2 Synthesis of tetrahedral zinc blende CdSe nanocrystals. Tetrahedral CdSe NCs were synthesized based on the recipe provided by Liu et al. 1 Briefly, for 10-nm tetrahedra: In a 50-mL three-neck flask, 1 mmol (78.4 mg) elemental selenium powder (Aldrich, 99.99%) in 15 ml of 1-octadecene (Aldrich, 90%) was degassed for thirty minutes at 100 C and heated for one hour at 250 C to dissolve the selenium, producing a clear-yellow solution. In a separate flask, 1 mmol (267 mg) Cd(ac) 2 2H 2 O (Aldrich, %) was heated to 250 C in air. Using a glass syringe, hot cadmium oleate was quickly injected into stirring Se-ODE with both solutions at 250 C. The temperature drops to ~240 C, is allowed to recover to 250 C, and growth continues at 250 C for 15 minutes. The reaction is cooled to room temperature in air, washed three times with hexane/ethanol, and redispersed in hexane for storage. Addition of ~10 μl excess oleic acid aids long-term stability of the NCs. Large-area images of CdSe tetrahedron superlattices. Figure S1. (a,b) TEM images of CdSe SLs. Scale bars, 50 nm. S2

3 Two-dimensional defects in CdSe tetrahedron superlattices. Figure S2. (a) TEM image of a superlattice domain containing several twin planes marked with dashed red line. Scale bar, 50 nm. (b) Modeled defect structure via mirror reflection of the lattice across twin plane. (c) Unit cell geometry determines rotation angle across twin plane. Assembly of 8-nm CdSe tetrahedra capped with oleic and stearic acid ligands. Figure S3. (a-c) 8-nm tetrahedral CdSe NCs with oleic acid (C 18 ) capping ligands. (d-f) The same NCs capped with stearic acid (C 18 ) ligands. Scale bars, 20 nm. S3

4 Elimination of alternative tetrahedron superlattice structures. Figure S4. (a-c) Candidate SL structures generated by permutation of tetrahedron orientation. (d-g) CdSe SL and three modeled structures viewed from triangles projection. (h-k) CdSe SL and three modeled structures viewed ~45 from triangles projection. (l-o) CdSe SL and three modeled structures viewed from ~60 from triangles projection. S4

5 Particle tracking measurement of superlattice dimensions. Figure S5. (a) TEM image of triangles projection of CdSe superlattice with assigned particle centroid positions marked as red dots. Inset: histogram of centroid separations fitted with three Gaussian profiles for extraction of three distances d 1, d 2, and d 3, each shown as red line segments in TEM image. (b) Similar particle tracking image analysis performed on hexagonal projection of CdSe SL. Scale bars, 20 nm. Distance Measurement (nm) d d d d Table S1. Particle tracking measurements. S5

6 Two-dimensional reconstruction of superlattice using particle tracking measurements. Figure S6. Measured d 1, d 2, and d 3 allow for calculation of superlattice parameters a and b, as well as triangle edge separation (y 1 ), tip overlap (y 2 ), and edge separation (x). Calculation of lattice parameters S6

7 Calculation of spacings y 1, y 2, and x Calculation of tetrahedron separations. 1. Face-face distance arccos Edge-edge distance 1 (in-plane) 90 arctan Edge-edge distance 2 (across planes) Face-vertex distance Vertex-vertex distance 2.56 S7

8 Lattice parameter Length (nm) a b c 9.70 Table S2. Calculated lattice parameters. Geometry Separation (nm) Face face 5.14 Edge edge Edge edge Face vertex 1.84 Vertex vertex 2.56 Table S3. Calculated separations. Figure S7. (a) Sketch of face-face (b) edge-edge 1 (c) edge-edge 2 (d) face-vertex and (e) vertex-vertex interparticle separations. S8

9 Packing fraction without ligands. Figure S8. (a) Approximation of SL structure neglecting ligands using columns of tetrahedra in tip-face contact and edge-edge, vertex-vertex contacts in the horizontal plane. (b) Density estimation obtained by circumscribing triangular prism around tetrahedron. Ignoring ligands, the density can be approximated as S9

10 Packing fraction with ligands. Organic mass fraction obtained from TGA measurement (Fig. S4) can be used to estimate number of ligands per tetrahedron and ligand surface grafting density: / / / / 27.5% / / / / / / / / 3 For simplicity, nanocrystal inorganic core volume and surface area were calculated using equivalent perfect tetrahedron edge length a 2. Oleic acid molecules likely pack more densely when tethered to the NC surface than they do in bulk liquid form. An estimate of ligand shell volume might be made using frozen oleic acid density (ρ OA,solid 0.99 g/cm 3 ): /, 0.99 / / With estimates for core and ligand components of NC volume and measured unit cell dimensions, the space-filling fraction of the CdSe-OA can be estimated: S10

11 Figure S9. TGA of CdSe-OA NCs used in assembly experiments. Measurement of tetrahedron core edge length, estimation of vertex curvature. Figure S10. (a) TEM image of randomly-oriented CdSe NCs. Inset: Gaussian profile fit of manually-collected core edge length measurements. Scale bar, 20 nm. (b) TEM image of a tetrahedral CdSe NC with a face in the imaging plane. Scale bar, 2 nm. (c) Sketch of triangle with rounded vertices. With measured average edge length (a 1 ) and some assumption for vertex radius of curvature (r), the edge length of the equivalent perfect tetrahedron (a 2 ) can be estimated. With measured average edge length 9.23 nm and estimated vertex radius of curvature r 0.5 nm the equivalent perfect tetrahedron edge length a 2 can be estimated: S11

12 Estimation of surface curvature. The radius of curvature of a tetrahedron vertex was estimated from TEM images (Fig. S4). For flat tetrahedron faces, the radius of curvature of the equivalent sphere was estimated by drawing a circle through three points whose positions are determined by the end of the ligand alkyl tail radiating outwards from the NC surface as shown at right. 0, sin, cos sin, cos Where arccos arctan 2 Figure S11. Estimation of equivalent radius of tetrahedron face. Drawing a circle through points p 1, p 2, and p 3 allows for estimation of R face. For this we find an equivalent radius of 17.4 nm. Subtraction of 2-nm extended ligand length gives R face 15.4 nm. S12

13 Calculation of ligand potential in good solvent. According to Flory-Krigbaum theory, 2 the free energy of interpenetration of two chains brought from infinite separation together in volume dv may be expressed as Where v s is Kuhn segment volume (for polyethylene, v s ~ 0.2 nm 3 ), v i is solvent molecular volume (for TCE, v i ~ 0.1 nm 3 ), and χ is the Flory-Huggins chain-solvent interaction parameter (for polyethylene- TCE, χ ~ 0). Assuming uniform segment density parallel to the tethering surface, the free energy of mixing may be rewritten for one-dimensional mixing Where b is length of the Kuhn segment. The one-dimensional segment density distribution function φ is derived from the geometry of the cone-shaped volume available to a ligand of alkyl chain cross-sectional area A chain and headgroup area A head, tethered to a sphere of radius R Normalization of the segment density distribution function such that 1 gives We set. We create by reflection of across the y-axis and translation by d in the +x-direction The overlap integral S 12 was evaluated analytically using Mathematica ln2 ln 2 S13

14 Osmotic repulsion between two ligands in good solvent as a function of surface separation and grafting surface curvature. Using parameters relevant to our experiments (v s ~ 0.2 nm 3, v i ~ 0.1 nm 3, χ ~ 0, L = 2 nm), the osmotic repulsion for two ligands brought from infinite separation to moderate interpenetration (L < d < 2L) was plotted for several grafting surface radii. Figure S12. (a) Overlapping segment density distribution functions contribute to osmotic repulsion. (b) Repulsive energy for selected grafting surface radii. Calculation of ligand potential in bad solvent or vacuum. The van der Waals-dispersion energy of attraction between two hydrocarbon chains in vacuum is given by Salem: Where energy (E) depends on hydrocarbon Hamaker coefficient (-0.1 kcal/mol of methylene units), basic unit length (0.127 nm), close-packing separation distance (0.49 nm), and length of molecular overlap, L. With Salem s conclusion that E ~ L, and with the attractive energy for stearic acid (given as -8.4 kcal/mol, or k B T/molecule), we may relate interaction length and interaction strength: S14

15 Where length of molecular overlap L is replaced with our measure of overlap, 2L OA -d, in nanometers. The reported E stearic acid is recovered for full overlap of C 18 molecules (2L-d = 2 nm). To estimate elastic repulsion energy between oleic acid ligands bound to CdSe tetrahedron faces, we referenced experimental measurement of Young moduli of hydrocarbon SAMs on gold given by Del Rio et al., 4 reported to be on the order of 1 GPa for C 18 -length alkanethiol molecules. The elastic modulus (E) can be related to elastic repulsion energy: 1 2 Where A o is the original cross-sectional area through which the force is applied, L o is the original length of the object, and ΔL is the amount by which the length of the object changes. Using E = 10 9 N/m 2, A o = 0.25 nm 2, L o = 2 nm, and ΔL = 2L-d, we obtain an expression for the elastic energy: The full potential (vdw + elastic) for two (2-nm length) face-bound ligands can therefore be represented as This potential features a shallow minimum of k B T at small surface separation distance d face-face 3.75 nm (Fig. S13). Figure S13. The sum of van der Waals and elastic potentials between two ligands tethered to a flat surface produces an estimate for equilibrium face-face separation distance of 1.88L OA or ~3.76 nm. S15

16 (1) Liu, L.; Zhuang, Z.; Xie, T.; Wang, Y.-G.; Li, J.; Peng, Q.; Li, Y. Journal of the American Chemical Society 2009, 131, (2) Napper, D. H. Journal of Colloid and Interface Science 1977, 58, 390. (3) Salem, L. J. Chem. Phys. 1962, 37, (4) W., D. F.; Cherno, J.; A., F. D.; F., C. R. Appl. Phys. Lett. 2009, 94. S16