SUPPLEMENTARY INFORMATION

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1 Supplementary Information DNA-Programmable Nanoparticle Crystallization Sung Yong Park,* 1 Abigail K. R. Lytton-Jean,* 1 Byeongdu Lee 2, Steven Weigand 3, George C. Schatz 1 and Chad A. Mirkin 1 1 Department of Chemistry and International Institute for Nanotechnology, Northwestern University, 2145 Sheridan Rd., Evanston, IL X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL DND-CAT Synchrotron Research Center, Northwestern University, APS/ANL 432-A004, 9700 S. Cass Ave., Argonne, IL * These authors contributed equally to this work. Small-Angle X-ray Scattering (SAXS) Experiments The SAXS experiments were performed at the Dupont-Northwestern-Dow Collaborative Access Team (DND-CAT) Sector 5 and BESSRC-CAT Sector 12 of the Advanced Photon Source, Argonne National Laboratory with X-rays of wavelength 1.03 Å (12 kev). Aqueous samples were placed in either 1 mm capillary tubes or a flow-cell, both equipped with a temperature controlling system. Temperature was controlled within a 0.1 o C resolution. Two sets of slits were used to define and collimate the X-ray beam, and a pinhole was used to remove parasitic scattering. Samples were irradiated with a 0.3 mm beam, and scattered radiation was 1

2 detected with a CCD area detector. The 2D scattering data were azimuthally averaged, and the resulting 1D profiles of scattered intensity as a function of scattering angle, 2 θ, were transformed into profiles of scattered intensity as a function of scattering vector, q ( = 4π sinθ / λ), using silver behenate as a standard. Standard data correction procedures such as dark current subtraction and absorption correction are applied. In this system, scattering from DNA is negligible as compared to that from electron dense gold; scattering from the buffer and capillary are weak relative to that from the gold, but the buffer data are nonetheless used to reduce the solution sample data to scattering representative of the particles alone. Theoretical Calculation of Structure Factor To theoretically calculate structure factors of several nanoparticle crystal structures, we applied a simplified Debye formula for spherical scatters to the real-space configurations of finite-size nanoparticle crystals 1. For perfect crystals, we can easily obtain the real-space configurations from their basis vectors. Estimation of the number of the nearest neighbors with A-B interactions in a substitutionally-disordered FCC crystalline structure The FCC crystalline configuration with a small degree of disorder, which we obtained using the method in the above section, can be used as a starting point to obtain a configuration of a substitutionally-disordered FCC structure. First we prepare the slightly-disordered FCC crystalline configuration with N particles, as we will describe in the next section. The overall shape of the crystal is assumed to be a cube. Next, we assign the type of each particle in the crystal randomly, to generate an initial configuration. With 2

3 a usual optimization algorithm, we maximize the number of AB nearest neighbors in the cluster. This is equivalent to the energy minimization of the cluster of binary particles with a nearest neighbor attractive interaction between different particles and hard sphere repulsion. The following figure shows a dissection of the resulting cluster with N=4096 particles from the method we described. Figure S1. Dissection of an energy minimized configuration of binary particles in a FCC crystalline structure with small disorder The number of AB nearest neighbors in the cluster is and this is slightly smaller than the number of AB nearest neighbors in a cubical BCC cluster with the same number of particles (=14415). Hence, with an assumption that the averaged number of double stranded DNA in a DNA-linked nanoparticle pair within each cluster is the same, we can conclude that the BCC cluster is slightly more energetically favored than the substitutionally-disordered FCC cluster. Configuration of Face-Centered Cubic (FCC) structure with small disorder 3

4 For an FCC structure with disorder, we can use the real-space configuration from an algorithm in Ref. 24 of the main text. In this algorithm, there is a tunable parameter, the expansion rate of the spheres, that enable one to span from a "maximally random jammed" (MRJ) state with packing fraction of about 0.64 to essentially perfect FCC lattice jammed states with packing fraction of about The former is achieved with relatively fast expansion rates and the latter with relatively slow expansion rates. Here we modify the expansion rate to get a configuration with a packing fraction of , so as to mimic the aggregates in an FCC crystalline structure with a small degree of disorder. Predicted Interparticle Distance. Based on a rigid model, 10 DNA duplexes = ~3.4 nm in length. In the singlecomponent system, there are 40 DNA base pairs and 22 free bases between two linked particles. The free DNA bases are more flexible and have the potential to lie down on the gold surface. If the length of the DNA is calculated, this is equivalent to ~13.6 nm if only the duplex portion is considered and ~21.1 nm if the length of the free DNA bases are included. To determine the center-to-center interparticle distance, the radius of each AuNP must be added to this calculation (7.5 nm) to give a range of nm. The binary system contains 43 DNA base pairs and 22 free bases. This equates to a range of nm for center-to-center interparticle spacing based on the above calculations. Formation of a substitutionally-disordered FCC structure of a binary DNA-linked nanoparticle system As noted in the main text, in certain cases, the binary system can also form a closepacked structure, Fig. S2. This is not a theoretically predicted structure for a DNA-linked 4

5 nanoparticle system 2. This is observed when AuNP-X and AuNP-Y are combined above the T m of region 2, followed by slow cooling. The formation of the different crystal structures is attributed to a competition between the entropic and enthalpic contributions involved in the assembly process at different temperatures. From an entropic standpoint, a close-packed structure is favored over a non-close-packed structure because the entropy of the entire system can be maximized if the aggregated state possesses the smallest volume possible (ref 22 and 26 in main text). Therefore, if AuNPs begin to assemble near the DNA T m, where the DNA binding strength is very weak and the enthalpic contribution is small, the entropic contribution will dominate the assembly process and a close-packed structure forms. However, as the temperature decreases, the enthalpic contribution associated with DNA hybridization will govern and direct the assembly to the non-close-packed structure which maximizes the number of DNA hybridization events. Hence, we would expect a morphological transition from a close-packed structure to a non-close-packed structure at a certain temperature. However, in actuality, we do not observe this transition directly in the current setup. This could be related to the slow DNA dehybridization process or nanoparticle dissociation process at temperatures lower than the DNA T m. Moreover, the dissociation becomes slower, due to the multiple DNA linkages and the potential for cooperative binding interactions between the neighboring DNA stands. Thus, these factors can prevent restructuring events which are required for the transition. Under these circumstances, we choose a different annealing scheme to form a non-close-packed structure. If the AuNP assembly is initiated several degrees below the DNA T m, the enthalpic contribution associated with DNA hybridization will 5

6 drive the assembly to the non-close-packed structure which maximizes the number of DNA hybridization events. Figure S2. SAXS result of binary DNA-linked nanoparticles. After slow-cooling from above the T m of region 2, the AuNPs form a substitutionally-disordered FCC structure (Red and Blue line). The peak positions are consistent with the peak positions of theoretical calculation with a perfect FCC crystal (Green line). 6

7 Binary Samples with Different Aspect Ratios Combining a short region 1 AuNP-X and long region 1 AuNP-Y (Fig. 4b from main text) results in a BCC structure that is more thermally-stable. Unlike the original setup, peaks related to a BCC structure are present when the particles are combined below the T m and when the particles re-associate after melting apart. Figure S3. Asymmetric binary sample from Fig 4b in main text. A small peak at q q0 ~1.4 is visible. The presence of this peak is required for BCC structure to form. This peak is present when the particles are combined below the T m and when the particles re-associate after melting apart. The importance of aspect ratio was further addressed by looking at samples using small AuNPs (10 nm) with short region 1 and large AuNPs (15 nm) with long region 1 (Fig. 4c 7

8 main text). These samples formed crystals with a BCC structure that exhibit even greater stability such that the BCC structure can be achieved independent of pathway (i.e. slow cooling from above T m vs. combining and annealing below T m ). Hence, the binary sample begins to form a BCC structure both when combined below the T m and after melting apart and re-associating with slow cooling. In Fig S4, we observed that the first peak is significantly lower than the second peak. This peak actually corresponds to the (100) direction, which is forbidden in a BCC structure if all particles have the same size. This indicates that one size particle is at the body center position while the other size of particle is located at the corners of the BCC lattice. Thus we experimentally verified (using two different particle sizes 10 and 15 nm) that the BCC structure is indeed CsCl. When the particle size of AuNP-X and AuNP-Y are the same, the CsCl structure made by AuNP-X and AuNP-Y is BCC. 8

9 Figure S4. Binary sample begins to form BCC structure both when combined below the T m and after melting apart and re-associating with slow cooling. 9

10 Dissipative Particle Dynamics (DPD) Simulation We also use Dissipative Particle Simulation (DPD) (Ref 28 and 29 in main text) to get a realistic BCC Configuration. The details of the simulation will be published elsewhere. Effects of polydisperse particles We studied the effect of nanoparticle polydispersity on the crystal structure formation. In our simulations, we used 100 particles. We assume that all particles are the same, and the interaction between the particles is attractive, so they can aggregate. For the attractive potential, we used the same attractive potential as in the above section. The details of the simulation method are similar to the above section. Figure S5 shows the time-averaged structure factors of aggregates of monodisperse single-component particles and of polydisperse particles, where we assigned the polydispersity of the particles to be 20 %. As we can see in the figure, the crystalline structure of the aggregates with polydisperse particles is less defined than the monodisperse particles. 10

11 Figure S5. Dissipative Particle Dynamics (DPD) simulation result of single-component DNAlinked nanoparticle aggregates. We present the result using monodisperse particles (Red line) and using particles with 20 % polydispersity (Blue lines). Compared with the theoretical calculations with a perfect FCC crystal, the cluster with monodisperse particles has a more defined crystalline structure than with polydisperse particles. 1. Guiner, A. & Fournet, G. Small-Angle Scattering of X-Rays (Wiley, New York, 1955). 2. Tkachenko, A.V., Morphological diversity of DNA-colloid self_assembly. Phys. Rev. Lett. 89, (2002). 11