SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION doi: /nature12739 A. SUPPLEMENTARY MATERIALS AND METHODS I. Synthesis and Assembly of DNA-Nanoparticle Conjugates. All oligonucleotides used in this work were synthesized on a MM48 solid-support DNA synthesizer (BioAutomation) using reagents purchased from Glen Research (Table S1). DNA strands were purified by reverse phase HPLC (Agilent) followed by standard deprotection protocols. Citrate-capped gold nanoparticles (AuNPs, Ted Pella) were used as received with no further modification. DNA-functionalization of AuNPs with thiol-modified oligonucleotides was carried out according to procedures that are detailed extensively elsewhere 1,2. Briefly, thiolated oligonucleotides (Sequences 1-2) were treated with a solution of 100 mm dithiothreitol (DTT, ph = 8) for approximately 1 hour and subsequently purified using Nap-5 size exclusion columns (GE Healthcare) to remove remaining DTT. The surfactant Tween-20 was added to the solution of AuNPs to bring the final surfactant concentration to 0.01 vol%, followed by the addition of the purified thiolated DNA (approximately 4-5 nmol per ml AuNPs) to form an initial loose loading of oligonucleotides on the surface of the particles. A 5M solution of sodium chloride (NaCl) was slowly added to the nanoparticle solution over the next several hours in a salt aging process to increase the density of DNA on the particle surface by shielding against electrostatic repulsion between strands. After bringing the final salt concentration to 0.5 M NaCl, the particles were allowed to sit overnight, followed by purification by three rounds of centrifugation (15000 rpm; times varied from min. depending on the nanoparticle size), removal of supernatant, and resuspension of the nanoparticle pellet with Nanopure water (18.2 MΩ, Millipore) to remove any unreacted DNA, salt, and surfactant. After removal of the supernatant following the final round of centrifugation, salt was added to the purified particles to bring the final concentration once more to 0.5 M NaCl, which is the salt concentration at which all the subsequent assembly 2 1

2 RESEARCH SUPPLEMENTARY INFORMATION experiments are performed. Particle and DNA concentrations were measured on a Cary 5000 UV/vis spectrophotometer (Agilent) using known extinction coefficients from the Ted Pella website ( for particles and the IDT Oligo Analyzer ( for oligonucleotides. DNA-AuNPs were assembled into aggregates through the addition of DNA linker strands (Sequences 3-5). The linker strands contain a recognition region that is complementary to the sequence attached to the AuNPs as well as a short four to six base pair-long sticky end that engages in hybridization to the complementary sticky end on neighboring particles to initiate particle aggregation. A single base pair flexor is located between the recognition region and the sticky end which does not participate in hybridization but which provides flexibility to the sticky end during particle assembly and crystallization. The length of the linker was increased through the incorporation of 25mer block units between the recognition sequence and the sticky end. To impart rigidity to this region, complementary strands (or block duplexes, Sequence 9 in Table S1) were hybridized to the block region of the linker. Upon addition of the DNA linker strands, the DNA-AuNP solution changed from the characteristic red color of the particle surface plasmon resonance to a cloudy, purple color indicative of aggregate formation. Visible aggregates settled out of solution over the course of an hour and were transferred to 200 µl standard PCR tubes (Applied Biosciences) for thermal annealing. The melting transition of a particular superlattice is measured by conducting a thermal denaturation experiment by monitoring the extinction of the AuNPs at 520 nm while increasing the temperature from 25 C to 75 C at a ramp rate of 0.25 C/min. The melting temperature is identified in the curve where the extinction at 520 nm increases due to the dissociation of the aggregate. The melting curves for DNA-AuNPs assembled as described above show a 3 2

3 SUPPLEMENTARY INFORMATION RESEARCH characteristic sharp melting transition that is the result of cooperative binding of strands between particles 3. Table S1. DNA Sequences Thiolated Strands # Sequence Name Sequence 1 AuNP-bound Strand 5 -TCA-ACT-ATT-CCT-ACC-TAC-(Spacer)-SH- 3 2 AuNP-bound Strand 5 -TCC-ACT-CAT-ACT-CAG-CAA-(Spacer)-SH- 3 Linker Strands # Sequence Name Sequence 3 b.c.c. Linker for 1 5 -GTA-GGT-AGG-AAT-AGT-TGA-(Flexor)-TTCCTT- 4 b.c.c. Linker for 2 5 f.c.c. Linker for 1 6 d25 f.c.c. Linker for TTG-CTG-AGT-ATG-AGT-GGA-(Flexor)- AAGGAA GTA-GGT-AGG-AAT-AGT-TGA-(Flexor)-GCGC- 3 5 GTA-GGT-AGG-AAT-AGT-TGA-A-(T 5 -AGT-CAC- GAC-GAG-TCA-T 5 -A)-GCGC- 3 Other Strands # Sequence Name Sequence 7 Spacer for AAAAAAAA- 3 or 5 -(Spacer18) 5-3 or 5 -(Spacer18) Flexor for A-3 or 5 -Spacer Block Duplex for 6 5 -A 5 -TGA-CTC-GTC-GTG-ACT-A Spacer 18 refers to the Spacer 18 modified phosphoramidite manufactured by Glen Research. 2. All Spacers and Flexors (and all combinations) were used in the experiments described in this work, but no difference other than interparticle spacing was observed, i.e. there was no effect on the resulting equilibrium crystal shape. II. Superlattice Growth by Slow Cooling. The nanoparticle aggregates exhibit no appreciable degree of ordering following DNA linker addition and prior to any thermal annealing. The transition from disordered aggregates to ordered superlattices typically occurs following thermal annealing at a temperature a few degrees below the melting temperature of the aggregate 2,4. However, to date, thermal annealing below the aggregate melting temperatures has never produced single crystalline domains with well-defined facets (Figure S6). In this work, the transition from disordered aggregates to crystalline 4 3

4 RESEARCH SUPPLEMENTARY INFORMATION superlattices was initiated by starting at a temperature above the melting temperature and slowly cooling to room temperature. For the b.c.c. and CsCl systems, the starting temperature was 55 C while the starting temperature for the f.c.c. system was slightly higher, at 60 C, due to the increased linker strength of the self-complementary (5 GCGC-3 ) sticky end. All slow-cooling experiments were performed on a Veriti Thermal Cycler 96-well instrument (Life Technologies) at a cooling rate of 0.1 C/10 minutes from the starting temperature to 25 C. The full slow cooling procedure typically took approximately 2-3 days to complete. III. Superlattice Structural Characterization. i. Small Angle X-ray Scattering (SAXS) All synchrotron SAXS experiments were conducted at the Dow-Northwestern-Dupont Collaborative Access Team (DND-CAT) Beamline 5ID-D at the Advanced Photon Source (APS) at Argonne National Laboratory. Experiments were collected with 10 kev (wavelength λ = 1.24Å) collimated X-rays calibrated against a silver behenate standard. Exposure times of 0.1 and 1 second were used. Approximately 40 µl of the sample was loaded into a 1.5 mm quartz capillary (Charles Supper) and placed into a sample stage in the path of the X-ray beam. Twodimensional scattering data were collected on a CCD area detector and converted to 1D data by taking a radial average of the 2D data to generate plots of scattering intensity I(q) as a function of the scattering vector q (q = 4πsinθ/λ, where θ and λ are the scattering angle and wavelength of the X-rays used, respectively). The particle form factor F(q), the scattering due to individual dispersed particles in solution, was subtracted from the experimental data to obtain the lattice structure factor S(q). Form factor subtraction, radial averaging, and other SAXS data analysis were performed in Igor using the Irena and Nika macros (available free of charge from the APS at usaxs.xray.aps.anl.gov/staff/ilavsky/irena.html). Modeled SAXS data were generated using 5 4

5 SUPPLEMENTARY INFORMATION RESEARCH PowderCell (available free of charge from the Federal Institute for Materials Research and Testing at a software package that is used for generating theoretical scattering pattern for atomic lattices but which provides a good approximation for the experimental data obtained in this work. ii. Silica Embedding Following slow-cooling, the solution-phase lattices were transferred to the solid state via silica encapsulation using a slightly modified procedure from that described in Auyeung et al. 5. Silica encapsulation is necessary for direct visualization by electron microscopy because the solution-phase lattices collapse in the vacuum environment of the microscope. The slow-cooled samples (e.g. lattices containing approximately 1 nm 20 nm AuNPs) were transferred to a 1.5 ml Eppendorf tube and the volume was brought up to 500 µl with a solution of phosphate buffered saline (PBS) with a salt concentration of 0.5 M NaCl. 2 µl of the quaternary ammonium salt, N-trimethoxysilylpropyl-N,N,N-trimethylammonium chloride (TMSPA), was added to the solution of nanoparticle assemblies and the tube was placed on a thermomixer (Eppendorf) to shake at room temperature at a rate of 750 rpm. The tube was left for minutes to allow the TMSPA to electrostatically associate to the negatively-charged phosphate backbone of the DNA. Subsequently, 4 µl of triethoxysilane (TES) was added to the solution to initiate silica growth first around the DNA where the TMPSA has associated and eventually around the entire lattice. Both the TMSPA and the TES were added in large excess relative to the calculated number of phosphate groups on the DNA contained in the superlattice samples. The mixture was left on the thermomixer at 750 rpm for four days, during which a cloudy precipitate formed above the nanoparticle aggregate that is presumably silica that has undergone bulk precipitation in solution. Note that the shaking rate was intentionally kept low such that the dark 5

6 RESEARCH SUPPLEMENTARY INFORMATION nanoparticle aggregate remained intact at the bottom of the tube. After four days, the supernatant was removed carefully with a pipette so as to not disturb the pellet of nanoparticle aggregates sitting in the bottom of the tube. The aggregates were then carefully removed with a pipette and transferred to a fresh Eppendorf tube and filled with Nanopure water. Without silica embedding, the addition of water to a solution of nanoparticle superlattices results in lattice dissociation due to the absence of salt that is required for DNA hybridization. The solution was then purified by three rounds of centrifugation (5 min@15000 rpm), removal of supernatant, and resuspension in fresh water. After the final round of centrifugation, the supernatant was removed to yield a dark, black pellet that was subsequently dried in vacuo. Note that not all of the bulk silica was removed during the purification process, resulting in visible excess silica chunks in the electron microscopy images. Figure S1shows the SAXS data for the 20 nm b.c.c. superlattices before (black trace) and after silica encapsulation (red trace). Note that both the lattice symmetry and lattice parameter are both preserved during silica encapsulation. Figure S1. SAXS data of silica-embedded b.c.c. superlattices comprised of 20 nm AuNPs (red trace) plotted with the SAXS data of the corresponding solution-phase lattice (black trace)

7 SUPPLEMENTARY INFORMATION RESEARCH iii. Lattice Parameter Calculation from the SAXS Data The nearest neighbor distance d (in nanometers) between particles in a superlattice can be calculated from the position of the first scattering peak q 0 in a SAXS pattern using the following relationship: where C is a constant that is derived using the nearest neighbor distance between two particles of a given lattice and the distance between two planes associated with the peak q 0. Once the nearest neighbor distance is calculated from the SAXS data, the lattice parameter can be related to the nearest neighbor distance through geometrical relationships summarized in Figure S2. Note that for a simple cubic lattice, the nearest neighbor distance is equal to the lattice parameter. The values for q 0, C, and a are summarized in Table S

8 RESEARCH SUPPLEMENTARY INFORMATION Table S2. Constants for lattice parameter calculations. Lattice q 0 [hkl] f.c.c. [111] b.c.c./cscl [110] C Lattice Parameter a Figure S2. The relationship between the nearest neighbor distance d and the lattice parameter for a f.c.c. and b.c.c./cscl lattice. The lattice projection shown is the view along the zone axis specified. IV. Electron Microscopy. i. Transmission Electron Microscopy (TEM) TEM images were obtained at the Northwestern University Atomic and Nanoscale Characterization Experimental Center (NUANCE) on a Hitachi HD2300 STEM in z-contrast and SE mode at an accelerating voltage of 200 kv. Solid-state silica-embedded lattices were resuspended in approximately 250 µl of water and the solution was vortexed and briefly sonicated to break up large aggregates. A small volume (approximately 20 µl) of the sample was directly dropcast onto a copper TEM grid (Formvar/Carbon on 200 mesh, Ted Pella) for imaging. Tilt experiments as seen in Figure 3b in the main text were performed in situ in the STEM instrument. 8

9 SUPPLEMENTARY INFORMATION RESEARCH ii. Scanning Electron Microscopy (SEM) SEM images were obtained at the Northwestern University Atomic and Nanoscale Characterization Experimental Center (NUANCE) on a Hitachi SEM SU8030 instrument at an accelerating voltage of 3 kv. Solid-state silica-embedded lattices were resuspended in approximately 250 µl of ethanol and the solution was vortexed and briefly sonicated to break up large aggregates. Approximately 10 µl of the vortexed solution was directly dropcast onto a silicon wafer cut with a diamond scribe (Ted Pella) to a size appropriate for imaging. V. Molecular Dynamics (MD) Simulations. i. Modeling DNA-AuNPs for Wulff Structure Prediction The crystallization of charged colloids has been extensively studied via MD simulations by using coarse-grained models that require effective pair potentials that include electrostatic repulsions and short-range attractions between the colloids. Phenomenological colloidal models on DNA-AuNPs have captured the main features of the phase diagram for this system 2,7,8 as well as the coalescence dynamics into b.c.c. structures 9. Here, we used a detailed model 10 that includes the grafted DNA chains to find the attractive pair potential between DNA-AuNPs to validate and extend the colloidal models 2,9 in order to study the shape of grains of DNA-AuNPs assembled into b.c.c. and f.c.c. crystals via MD simulations. In the model, each DNA-AuNP building block is coarse-grained into a single spherical bead interacting via an effective electrostatic repulsion and an attraction due to complementary sticky ends. The crystallization of DNA-AuNPs occurs at high salt concentration when the Debye length ( ) is smaller than the size of the particles (2R). Moreover, the effective surface charge density ( eff ) of the DNA-AuNPs is strongly reduced due to the ions that penetrate the rigid

10 RESEARCH SUPPLEMENTARY INFORMATION dsdna layer of the particles. Therefore, we use a linearized mean field approach valid for R/ >>1 and eff << 1 to compute the effective electrostatic repulsion (electric-double layer interaction) between two charged spheres of core radii R 1 = R 2 = R separated by a distance r = r 2R, which, in units of thermal energy k B T, is expressed as 11 : U repulsive ( r )= (4πε 0 ε r /k B T) (R M ) 2 exp(-(r-2r)/ ), where R M = R 1 R 2 / (R 1 + R 2 ) is the average radius of two DNA-AuNPs, is the Debye length, and is the surface potential given by = /ε 0 ε r where ε 0 is vacuum permittivity and ε r is the relative permittivity of the solvent, and is the surface charge density of the particles. For the typical experimental values of salt concentrations from = 0.2M and up to = 0.5M NaCl, the surface charge density at the core radius R, which includes the radius of the gold nanoparticle and the dsdna portion of the DNA-AuNPs, is strongly reduced by the counterions that penetrate the DNA-AuNPs. In this case the surface potential should be = eff /ε 0 ε r where eff is the effective charge of the particles obtained from density functional theory (DFT) and confirmed by explicit ions MD simulations (Figure S3) 12. The final potential in units of k B T is then given by: U repulsive ( r ) = (4π) 2 l b (R/2) ( eff /e) 2 exp(-(r-2r)/ ), where l b =e 2 /4πε 0 ε r k B T is the Bjerrum length; though in water l b = 0.7 nm, in a dense media of ions and DNA it can be of the order of 2 nm. For the design parameters used here, a 20 nm gold core with 150 grafted DNA chains (10 ssdna bases + 18 dsdna base pairs (bp) + 6 bases for sticky end), the hydrodynamic size of this DNA-AuNP is 2R = 34.0 nm and the total charge is Q DNA-AuNP = 150 (10 1e+18 2e+6 1e) = 7800e where e is the unit charge. The effective surface charge density from DFT 12 is eff ~ 0.1e/nm 2, and the bare Debye length is = 0.43 nm at = 10

11 SUPPLEMENTARY INFORMATION RESEARCH 0.5M NaCl. For these values, the pre-coefficient in the electrostatic potential is (4π) 2 l b (R M ) ( eff /e) 2 ~ 0.6 (R M )/nm, which is an approximation since in the DFT the water and hard cores of the ions are only included implicitly 12. We note that the MD simulation results (when the short range interaction described below is included) are rather insensitive to this pre-coefficient (we tested it up to about 100 (R M )/nm) provided the range of the exponential decay or Debye length is not below the lower bound, 0.43 nm, which suggests that the range of the repulsion is important and should be computed for each DNA sticky end length. That is, the functional form of the repulsive electrostatic potential, which contains the hard core of the DNA-AuNPs proportional to exp(2r/ ) and a repulsive soft barrier proportional to exp(-r/ ) is adequate. However, its origin may be due to a combination of different effects including entropic effects of the DNA sticky ends. Figure S3. (a) Schematic of the DNA-AuNP without salt ions shown and (b) schematic of the smear ionic cloud distribution obtained from DFT calculations where excellent agreement between DFT calculations and MD simulations is demonstrated 12. The attractive potential U attractive of complementary sticky end hybridization can be expressed in two ways as discussed in the colloidal phenomenological models for DNA- AuNPs 2,9 : 11

12 RESEARCH SUPPLEMENTARY INFORMATION Δ or Δ, where relates to the DNA coverage, Δ represents the overlapping volume of the two DNA-AuNPs, V is the hydrodynamic volume of the DNA-AuNP, while Δ represents the overlapping area 2 and A is the hydrodynamic surface area of DNA-AuNP. If two DNA-AuNPs have equal size, the overlapping volume reduces to a cubic function Δ π, and the overlapping area reduces to a linear function Δ π, where a, b, c and a, b are constants dependent upon the geometric constants of the DNA-AuNP (e.g. size of the gold core, length of the DNA chains) 2. Figure S4. Shape of attractive potential following the rules of (a) overlapping volume Δ ; (b) overlapping area Δ. Design parameters: 20nm AuNPs covered by 150 DNA chains of 18bp dsdna. For the case of 20 nm AuNPs covered by 150 DNA chains of 18bp dsdna (Figure 2 in the main text), the shape of potential following the rule of Δ or Δ is given in Figure S4. Given that the colloidal model can be constructed in different ways, we used the detailed model with

13 SUPPLEMENTARY INFORMATION RESEARCH explicit DNA chains 10 to justify the form of the effective attraction. We set two building blocks at a fixed distance, tracked the potential from sticky end hybridizations, and obtained the mean potential. By varying the distance, we can plot the effective attractive potential versus distance (Figure S5). At long distances ( ), U attractive can fit into a linear function, which suggests using the rule of overlapping area Δ for this case with short DNA chains. Note that is the hydrodynamic distance at equilibrium (Table 1 in the main text). If two DNA- AuNPs are closer than this distance, the excluded volume of the dense DNA cloud will break down the rule of Δ ; however, the repulsive electrostatic potential will increase exponentially to diminish the importance of the attraction. Figure S5. (a) Simulation snapshot of two building blocks at a fixed distance r for attractive potential estimation, generated with the Visual Molecular Dynamics Package 13. Design parameters are: 20 nm AuNP with 150 DNA strands, each strand has a dsdna part of 18 base pairs. (b) Attractive potential U attractive versus distance r (in units of 2 nm). Grey bars represent the standard deviation of each point. At long distances, U attractive can fit into a linear model:, with a coefficient of determination R 2 = For binary b.c.c. systems, there are two types of DNA-AuNPs (with complementary sticky ends) labeled A and B. Interaction between A and B is composed of both the attraction and repulsion parts, while interaction between A and A or between B and B is purely repulsive. 13

14 RESEARCH SUPPLEMENTARY INFORMATION For f.c.c. systems, there is only one type of DNA-AuNP with self-complementary sticky ends, and thus the universal pair potential is a combination of both contributions. With this colloidal model, we carried out MD simulations with the LAMMPS package 14 (available at Simulations started from a dilute liquid with packing density 0.01, and were performed at ~0.95 T melt (the melting temperature) for 10 8 time steps. Each time step is t=0.002 in the units of σ ε, with σ and m equals to the size and mass of one bead respectively, and ε. The shape for the b.c.c. system was confirmed to be a (110)-enclosed rhombic dodecahedron (Figure 3e in the main text), but the f.c.c. system did not show a clear polyhedron (Figure S14d). See the Supplementary Videos for a visualization of the simulated formation of microcrystals from a b.c.c. and f.c.c. system of interacting particles modeled as a single bead. The videos show that near the melting temperature, few nuclei form, allowing the growth of single grains. However, the f.c.c. grains are initially more spherical (in agreement with the surface energy calculations from the detailed model described below) and shapes that have internal strain (such as icosahedra and decahedra) result due to the low energy associated with defects in f.c.c. nanoparticles, which suggests that crystals of DNA-AuNPs in the closed packed f.c.c. structure have similar defects and shapes to those found in metallic (atomistic) nanoparticles. This modeling approach is robust for describing the growth of b.c.c. equilibrium shapes, even with a range of values of eff. However, the colloidal model is more phenomenological than the detailed model and, as explained above, is not general for all sets of design parameters (e.g. gold core size, dsdna length, and DNA coverage per NP). Therefore, we applied the more detailed model with explicit DNA chains to the estimation of surface energies, as explained in

15 SUPPLEMENTARY INFORMATION RESEARCH the following section. In particular, this detailed approach is sensitive to the length of the DNA and it incorporates the highly kinetic hybridization events required to form crystals 6. This kinetic hybridization leads to fluctuations in thermodynamic quantities (such as in the mean hybridization energy shown in Fig. S7), which are partly manifested in variation in the five independent simulations used to calculate the surface energies in Table 1. Fluctuations in the mean surface energies could explain the inability of some DNA-AuNPs systems to form Wulff shapes. For example, in b.c.c. crystals, when the DNA length increases to 98bp, the calculated surface energies are γ 110: γ 100: γ 111 = 1:1.76 ± 0.45:1.36 ± 0.36, leading to nearly spherical crystal grains instead of Wulff shapes, which is in agreement with experimental observation. 15

16 RESEARCH SUPPLEMENTARY INFORMATION ii. Modeling DNA-AuNPs for Surface Energy Calculations We performed MD simulations on a robust model 10,15 with explicit DNA chains to estimate surface energies. Figure S6. Schematic of the coarse-grained model used in the MD simulations. (a) Model of an individual DNA chain composed of three segments (sticky end, double stranded recognition sequence, and a spacer). (b) Model of the AuNP. (c) Simulation snapshot of two interacting DNA-AuNPs. Figure adapted from Li, T.I.N.G. et al. 10. a. Scale-accurate Coarse-Grained Model We used a scale-accurate coarse-grained model 10 which includes experimentallyconsistent sizes and stiffness values for double-stranded DNA (dsdna) and single-stranded DNA (ssdna) (see Figure S6 for a schematic representation of this model). Approximately 5 dsdna base pairs are represented by one coarse-grained bead of diameter 2nm, and 2-3 ssdna bases are represented by one bead of diameter 1nm. The number of DNA chains per 16

17 SUPPLEMENTARY INFORMATION RESEARCH particle, varied with the size of the nanoparticle, is kept consistent with experimental values 16. The attraction between complementary sticky ends is modeled by the Lennard-Jones potential. This model has been shown to be robust and reliable in accurately recovering the self-assembly processes of all reported symmetries achievable to date with DNA-programmable assembly 10, and is excellent in representing DNA hybridization kinetics and the optimal energy level per sticky end 6. MD simulations were performed with the HOOMD-Blue package 17,18 (available at on graphics cards. Additional details of the model and the simulation protocol can be found elsewhere 6,10,15. b. Assumptions By definition, surface energy is the excess free energy at the surface of a material compared to the bulk. However, to keep within the capability of molecular modeling, several assumptions were made: (1) Entropy remains constant upon the exposure of surfaces, which is a general assumption made in both ab initio calculations and MD simulation studies on surface energy. This assumption is reasonable since DNA chains wiggle freely and DNA hybridizations are thermally active events. 6 (2) Only the potential decrease caused by hybridization events of the sticky ends is considered; other sources of potentials are neglected. (3) The lattice parameter remains constant, i.e. there is no lattice relaxation upon surface exposure. (4) The crystal modeled is a perfect crystal, assuming no crystallographic defects and only weak thermal fluctuation of nanoparticles (nanoparticles are allowed to rotate)

18 RESEARCH SUPPLEMENTARY INFORMATION c. Surface Energy Estimation Method We calculated the surface energy with the above model and the stated assumptions. The first step was to build a perfect superlattice of DNA-assembled AuNPs, with its interparticle distance d (in nm) approximated by the following equation 19 : d = r NP,A + r NP,B (x)+0.8 where r NP,A, r NP,B are the radii of the two nanoparticle cores, and x is the total number of nucleobases between the two particles. The second step was to obtain the relaxed interparticle distance, as the resolution of DNA length decreased while coarse-graining the nucleobases. We put the superlattice in an openboundary box (box size is sufficiently large), ran MD simulations to relax the positions of the nanoparticles, and then estimated the nearest neighbor distance from the radial distribution function g(r). The third step was to rebuild a superlattice with the relaxed interparticle distance, and rotated it to put a specific surface orientation perpendicular to the z-direction, as in Figure 4 in the main text. Note that DNA chains were randomly attached on each building block, and each building block was generated independently. We then tracked the potentials of two systems: a bulk superlattice with periodic boundary conditions, and another one with two surfaces exposed by opening the boundary on z-direction. The centers of the nanoparticles are fixed while running MD simulations; otherwise, a crystal composed of ~100 building blocks may not stay stable 6. Nonetheless, the nanoparticles could rotate freely. Since it is a daunting task to calculate the free energy of this complex system, we approximate the free energy with the time average of potential energies in this study: E 18

19 SUPPLEMENTARY INFORMATION RESEARCH, as in Figure S7. About five independent and identical simulation runs were carried out to get the energy for each system. Figure S7. Time average of potentials of the sticky ends. Top: bulk material; middle: surface (110) exposed; bottom: surface (100) exposed. U hybridization has a unit of k B T/ε, where sticky end binding strength is ε, scaled to 42.3 kj/mol to match the specific DNA sequence in experiments. iii. Wulff Shape Identification The orientational dependence of the surface energy determines the equilibrium shape of a crystal and governs the stability of a surface 20. With the ratios of surface energies estimated from MD simulations, we applied the WulffMaker software 21 to calculate and display its corresponding Wulff polyhedron. Figure S8 shows the corresponding Wulff polyhedra of b.c.c. and f.c.c. superlattices. 19

20 RESEARCH SUPPLEMENTARY INFORMATION a b c d Figure S8. Wulff polyhedra of b.c.c. and f.c.c. DNA-AuNPs. (a) b.c.c.: (110) rhombic dodecahedron. (b), (c), (d) f.c.c.: (111) octahedron truncated by (100) and (110) faces. B. SUPPLEMENTARY DISCUSSION I. Polycrystalline Superlattices from Annealing Below the Aggregate Melting Temperature. As previously mentioned, nanoparticle crystallization conventionally takes place by annealing the aggregate at a temperature slightly below the melting temperature for a period of time typically ranging from 30 minutes to several hours. The resulting superlattices exhibited highly ordered, micron-sized domains as evidenced by the SAXS data, but no single crystals or shape-controlled crystals have been observed using this annealing method. We hypothesize that this is because the energy required to eliminate grain boundaries to form single crystals is

21 SUPPLEMENTARY INFORMATION RESEARCH sufficiently high such that lattice dissociation (i.e. melting) would occur before single crystal formation. Since the aggregate that initially forms prior to annealing is disordered, the thermal energy supplied is sufficient to cause the reorganization of the particles within the aggregate to organize with respect to one another but not enough for the overall crystal shape to change. Figure S9 shows TEM images of superlattices formed from this approach where grain boundaries and randomly oriented polycrystalline domains can readily be seen. Figure S9. TEM Images of b.c.c. superlattices formed by annealing the aggregate a few degrees below its melting temperature. II. Changing the Cooling Rate To verify our hypothesis that slow cooling is responsible for the formation of faceted microcrystals, the cooling rate was increased and found to produce a greater population of polycrystalline superlattices with irregular morphologies. Figure S10 shows TEM images taken for 20 nm b.c.c. superlattices cooled to room temperature from above the melting temperature at an accelerated rate of 0.1 C/2 min and 1 C/10 minutes (compared to the rate of 0.1 C/10 min used for the majority of experiments in this work). Although some rhombic dodecahedron microcrystals were observed at these faster cooling rates, the majority species were 21

22 RESEARCH SUPPLEMENTARY INFORMATION polycrystalline and the faceted structures were typically smaller and contained more defects than those observed at a slower cooling rate. Figure S10. TEM images of b.c.c. superlattices (with 20 nm AuNPs) cooled at faster rates compared to the rate of 0.1 C/10 minutes used to produce faceted rhombic dodecahedron microcrystals. 22

23 SUPPLEMENTARY INFORMATION RESEARCH III. Additional Electron Microscopy Images Figure S11. SEM Images of the rhombic dodecahedra superlattice crystals formed from a b.c.c. system using 20 nm AuNPs (a,b) and a CsCl system using 20 nm and 15 nm AuNPs (c, d). Figure S12. STEM Images of b.c.c. rhombic dodecahedra superlattice crystals obtained in (a) transmission mode and (b,c) scanning mode. A close up view of the surface of the crystal is shown in (c). Particle size = 20 nm

24 RESEARCH SUPPLEMENTARY INFORMATION Figure S13. STEM Images of CsCl rhombic dodecahedra superlattice crystals obtained in (a) transmission mode and (b,c) scanning mode. Particle sizes = 20 nm and 15 nm. IV. Analysis of the f.c.c. System. The lattice symmetry (i.e. b.c.c. versus f.c.c.) is controlled by changing the sequence of the sticky end on the DNA linker strand (see Table S1) 4. When the sticky end sequence is selfcomplementary, every particle can bind to every other particle in solution and the product after annealing is a f.c.c. superlattice. Alternatively, when the sticky end sequence is non-selfcomplementary, then combining two sets of complementary particles will result in a b.c.c. superlattice. While faceted microcrystals were observed for nanoparticles assembled into a f.c.c. lattice symmetry synthesized using the slow-cooling approach, this system did not produce uniform shapes similar to the rhombic dodecahedron microcrystals obtained for particles packed into a b.c.c. lattice. EM images of the crystals produced for a f.c.c. superlattice are shown in Figure S14a. Crystals with triangular features were commonly observed and, as expected, they were often enclosed by (111) facets with occasional observation of (100) facets (see Figure S15). Attempts were made to drive the system toward uniform microcrystals by changing the length of the DNA linker (in order to adjust the melting temperature) as well as by cycling the temperature within a close range of the melting temperature (i.e. cycling between 55 C and 45 C for 3 cycles

25 SUPPLEMENTARY INFORMATION RESEARCH at a rate of 0.01 C/min). However, no truncated octahedra as predicted by the Wulff construction were observed by making these adjustments. Figure S14. (a) SEM and TEM images of crystal shapes obtained from a f.c.c. packing of DNAnanoparticles (Scale bars, clockwise starting from top left: 3 µm, 2 µm, 2 µm, 0.5 µm, 2 µm, 2 µm). (b) SAXS data for the f.c.c. superlattices (red trace) show that the crystals also contain some rhcp content (rhcp scattering peaks denoted by the black arrows). The black peaks shown are the expecting scattering peaks for a perfect f.c.c. lattice. (c) The presence of linear streaks between the rings in the 2D SAXS scattering pattern are consistent with the presence of stacking faults in the lattice 22. (d) MD simulations for a system containing self-complementary particles as used to assemble a f.c.c. superlattice produced an equilibrium crystal structure exhibiting no well-defined shape (see Section Vi for simulation details). 25

26 RESEARCH SUPPLEMENTARY INFORMATION Figure S15. SEM Image of a microcrystal consisting of nanoparticles arranged in a f.c.c. lattice. Though no apparent crystal shape is observed, the (111) planes enclosing the crystal can readily be seen. Both scale bars = 1 µm. MD simulations that modeled one set of self-complementary particles, where the DNA- AuNP conjugate was coarse-grained as one bead (see Section V.i. above), supported experimental observations of equilibrium crystal structures with no well-defined geometry (Figure S14d). We hypothesize that this is due to the surface energy of the most stable (111) facet having a similar value to that of the second most stable (100) facet, thereby lowering the energy barrier for crystal defects including stacking faults and twinning. Indeed, when comparing the surface energy values for the two most stable facets of a f.c.c. superlattice, γ (100) : γ (111) was calculated to be 1.15 (see Table 1 in the main text). Figure S14b shows a representative SAXS pattern for a f.c.c. superlattice, where the black arrows indicate peaks that are due to the presence of a random hexagonal close-packed (r.h.c.p.) contaminant that is consistent with stacking fault formation (the crystal structures of f.c.c. and r.h.c.p. differ only in their stacking order). It has been observed that the rhcp lattice is a kinetic product of the thermodynamically more favorable f.c.c. lattice for a system of nanoparticles assembled with self-complementary

27 SUPPLEMENTARY INFORMATION RESEARCH linkers 2. Furthermore, the presence of diffuse scattering and linear streaks around the rings of the f.c.c. 2D SAXS pattern shown in Figure S14c provide further evidence for stacking faults in the system 22. Others work on the crystallization of gold nanoparticles into f.c.c. superlattices using a different (slow drying) assembly approach support our observation of shape polydispersity among the resulting crystals which included amorphous, single crystalline, and polycrystalline clusters 23. While not ruling out the possibility that a truncated octahedron is synthetically possible through DNA-assembly, there is both strong experimental and theoretical evidence suggesting that a large surface energy difference between the first- and second-most favorable planes plays a large role in determining whether uniform crystal shapes are observed for a given system. References 1 Auyeung, E. et al. Synthetically programmable nanoparticle superlattices using a hollow three-dimensional spacer approach. Nat. Nanotechnol. 7, 24-28, (2012). 2 Macfarlane, R. J. et al. Nanoparticle Superlattice Engineering with DNA. Science 334, , (2011). 3 Cutler, J. I., Auyeung, E. & Mirkin, C. A. Spherical Nucleic Acids. J Am Chem Soc 134, , (2012). 4 Park, S. Y. et al. DNA-programmable nanoparticle crystallization. Nature 451, , (2008). 5 Auyeung, E., Macfarlane, R. J., Choi, C. H. J., Cutler, J. I. & Mirkin, C. A. Transitioning DNA-Engineered Nanoparticle Superlattices from Solution to the Solid State. Adv Mater 24, , (2012). 6 Li, T. I. N. G., Sknepnek, R. & de la Cruz, M. O. Thermally Active Hybridization Drives the Crystallization of DNA-Functionalized Nanoparticles. J Am Chem Soc 135, , (2013). 7 Leunissen, M. E. & Frenkel, D. Numerical study of DNA-functionalized microparticles and nanoparticles: Explicit pair potentials and their implications for phase behavior. J. Chem. Phys. 134, (2011). 8 Scarlett, R. T., Crocker, J. C. & Sinno, T. Computational analysis of binary segregation during colloidal crystallization with DNA-mediated interactions. J. Chem. Phys. 132, (2010). 9 Dhakal, S., Kohlstedt, K. L., Schatz, G. C., Mirkin, C. A. & de la Cruz, M. O. Growth Dynamics for DNA Guided Nanoparticle Crystallization. (unpublished). 10 Li, T. I. N. G., Sknepnek, R., Macfarlane, R. J., Mirkin, C. A. & de la Cruz, M. O. Modeling the Crystallization of Spherical Nucleic Acid Nanoparticle Conjugates with Molecular Dynamics Simulations. Nano Lett 12, , (2012)

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