LETTERS PUBLISHED ONLINE: 30 NOVEMBER 2008 DOI: 10.1038/NMAT2338 Probing interfacial equilibration in microsphere crystals formed by DNA-directed assembly Anthony J. Kim 1 * , Raynaldo Scarlett 1 * , Paul L. Biancaniello 2 , Talid Sinno 1 and John C. Crocker 1 † DNA is the premier material for directing nanoscale self-assembly, having been used to produce many complex forms 1–4 . Recently, DNA has been used to direct colloids 5,6 and nanoparticles 7,8 into novel crystalline structures, providing a potential route to fabricating meta-materials 9 with unique optical properties. Although theory 10–12 has sought the crystal phases that minimize total free energy, kinetic barriers 13 remain essentially unstudied. Here we study interfacial equilibration in a DNA-directed microsphere self-assembly system 5,6,14 and carry out corresponding detailed simulations. We introduce a single-nucleotide difference in the DNA strands on two mixed microsphere species, which generates a free-energy penalty 5,15,16 for inserting ‘impurity’ spheres into a ‘host’ sphere crystal, resulting in a reproducible segregation coefficient. Comparison with simulation reveals that, under our experimental conditions, particles can equilibrate only with a few nearest neighbours before burial by the growth front, posing a potential impediment to the growth of complex structures. In earlier studies, we showed that micrometre-sized polymer spheres with single-stranded DNA grafted on their surfaces can form large, close-packed colloidal crystals 5,6 when the DNA strands hybridize to bridge them together. Within this interaction system, some local annealing is possible owing to the fact that bridge formation is a dynamic, reversible process. For crystallization to occur, the microspheres must be highly monodisperse (<4% standard deviation in diameter) and the DNA-induced sphere– sphere binding energy, E b , must be the proper strength—too strong and the particles bind strongly to assemble fractal aggregates, too weak and assembled structures dissociate. One feature of DNA-mediated interactions is that the computed binding energy depends exponentially on the free-energy change, G, for bridge formation (see Supplementary Information), as confirmed by direct interaction measurements 5 . Owing to the strong temperature dependence of G for DNA hybridization 15 , the corresponding temperature window for crystal formation 17 is only ∼0.5 ◦ C wide. Within this temperature range, crystallites nucleate homogeneously in less than 24 h, and grow to a size of a few thousand microspheres within another 12–24 h. To better understand the annealing and equilibration that takes place on the growing crystal interface, we designed a system expected to form a solid-solution alloy (Fig. 1). Specifically, we combined two populations of 0.98-μm-diameter polymer spheres (carboxylate-modified polystyrene, Seradyn) that are essentially identical in their preparation 18 and physical parameters, but that bear short grafted strands of single-stranded DNA whose sequences 1 Department of Chemical and Biomolecular Engineering, The University of Pennsylvania, 220 S. 33rd St. Philadelphia, Pennsylvania 19104, USA, 2 Department of Physics and Astronomy, The University of Pennsylvania, 209 S. 33rd St. Philadelphia, Pennsylvania 19104, USA. *These authors contributed equally to this work. † e-mail: jcrocker@seas.upenn.edu. differ at a single nucleotide-base location (Fig. 1). When additional ‘linker’ DNA strands containing two complementary sequences are added to the solution, hybridization leads to the formation of DNA bridges between particles (Fig. 1b), which in turn give rise to a time-averaged attractive interaction with a ∼15 nm range 5 . The difference in DNA sequence in the two populations of microspheres, ‘A’ and ‘B’, decreases the AB bridge formation energy relative to an AA bridge by an amount G, which can be computed a priori from DNA thermodynamics 15,16 . As the sphere binding energy is an exponential function of the hybridization free energy 5 , the mismatch alters the relative sphere binding energies amongst the different populations according to E AA b E AB b = e (G/kBT ) ≡ α, E AA b E BB b = α 2 , (1) where k B is Boltzmann’s constant and T is the absolute temperature. This result predicts that particle segregation should be rather sensitive to changes in DNA sequence. The typical G for a single nucleotide mismatch is ∼2 k B T relative to a Watson–Crick match 16 , corresponding to a sphere binding-energy ratio of α = e 2 ≈ 7. We can find the minimum AA binding energy required for crystal stability, E AA b = 3.75 k B T , through simulations described below. Thus, if B contains a single mismatch then the binding energy between AB sphere pairs would be seven times smaller than the AA binging energy, or less than 1 k B T . Presumably such B spheres would not bind the growing A crystal significantly, and would be completely excluded. This hypothesis was confirmed by experiment (data not shown). To obtain a smaller difference in sphere binding energy, and therefore produce solid-solution crystals, we place different mismatching bases on both the A and B particles; see Fig. 1c. One system we studied contained GG and GA mismatches on the A and B particles, respectively, and had the smallest accessible G GG/GA ≈ 0.22 k B T per bridge 16 . In this case, equation (1) predicts α = 1.25, corresponding to E b = E AA b −E AB b = (1 −1/α)E AA b = 0.79 k B T , assuming E AA b = 4 k B T . As the pairwise interactions are additive, the energetic cost of inserting one B sphere into a close-packed (12-fold-coordinated) host crystal of A spheres would still be 12E b ≈ 10 k B T , presumably leading to nearly total B exclusion, at least in a fully equilibrated solid-solution crystal. In practice, the absence of solid diffusion in close-packed colloidal systems precludes such bulk equilibration. Instead, we might expect a smaller degree of segregation to occur owing to surface equilibration or kinetic limitations on the crystal interface. 52 NATURE MATERIALS | VOL 8 | JANUARY 2009 | www.nature.com/naturematerials © 2009 Macmillan Publishers Limited. All rights reserved.