Supporting Information. Phase Diagram, Design of Monolayer Binary Colloidal Crystals and. Their Fabrication Based on Ethanol-Assisted Self-Assembly at

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1 Supporting Information Phase Diagram, Design of Monolayer Binary Colloidal Crystals and Their Fabrication Based on Ethanol-Assisted Self-Assembly at Air/Water Interface Zhengfei Dai, Yue Li, Guotao Duan, Lichao Jia, Weiping Cai * Key Lab of Materials Physics, Anhui Key Lab of Nanomaterials and Nanotechnology, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 200, P.R. China Figure S Zhengfei Dai et al. N S/L =0.. LS 6 =0.25. LS 9. LS 2 =0.5 =0.75 =0.25. LS V S/L Figure S. N S/L as a function of V S/L under different values from Eq.(). Each plot corresponds to the denoted values. Address correspondence to: yueli@issp.ac.cn; wpcai@issp.ac.cn. Tel: (+86) (Office); Fax: (+86)

2 Figure S2 Zhengfei Dai et al. (a) b c d e f g h i j (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure S2. (a): The photo of the bcc on a glass slide (the experiment conditions: ΦS/L=0.75, VS/L =0.048). (b)- (j): FESEM images corresponding to the areas marked in (a). The sample consists of more than 95% LS9 bcc phase. The insets are some local magnified images. The arrows in (c), (g) and (j) indicate the sparely existent phases LS0, LS6, LS2 in the sample, respectively. 2

3 Chart S Zhengfei Dai, et al. (a) (b) Chart S. The geometrical analysis for the reasonable ranges of and N S/L. (a) Lower and upper limit of. (b): Geometrical analysis of N S/L(max). The symbol d denotes the diameter of small sphere.

4 . Determination of the range for For the size ratio ( ) of the colloidal spheres, obviously, the small-spheres should, at least, be bigger than the size of the interstices among the three close packed large spheres, as illustrated in Chart Sa. Based on the geometrical relation, the lower limit of is thus expressed as: 2 S / (min) = (S) 6 Φ L Likewise, the small spheres cannot be too large; otherwise they would influence on the self-assembly of large spheres and the structural stability of the monolayer bccs. Here, the maximal size of the small sphere could be defined as the diameter corresponding to the inscribed circle of the triangle from the centers of three-close packed large spheres, as illustrated in Chart Sa. The upper limit of is thus subject to S / (max) = (S2) Φ L Consequently, the range for can be determined to be 2 ΦS/L, or For instance, for the large sphere with 2000 nm in diameter, the corresponding small spheres size should be in the range from 54 nm to 54 nm for a monolayer bcc with high quality. 4

5 2. Determination of the ranges for N S/L For the upper limit of N S/L, or the N S/L(max), under the assumption of monolayer close-packed arrangement of the small spheres, the number J of the small spheres on the each side of the triangle ABC, as illustrated in Chart Sb, should be subject to D d J = + = + (S) d Φ where d is the diameter of small sphere. Correspondingly, the maximal number N S (max) of the small spheres in ABC N S (max) = J ( J + ) (S4) 2 So, from Eqs.(S, S4), the maximal number ratio of the small to large spheres N S/L(max) can be expressed as N (max) = J ( J + ) = ( + ) ( + 2) (S5) Φ Φ or, N S/L(max) depends on the size ratio, as illustrated in curve a in Figure 2. Because of the integer s requirement of the sphere number, however, the real N S/L(max) should be a step-like function of, or N (max) = Int( + ) Int( + 2) (S5) Φ Φ where Int (x) is the largest integer less than or equal to x. The corresponding results are shown in curve b (fold-line) in Figure 2, and should be smaller than the values of curve a in Figure 2. 5

6 Further, when the value is small, however, the monolayer close-packed arrangement of the small spheres could be unstable in structure. As previously demonstrated S, the self-assembly of hard-sphere binary structures is dominated by the nanoscaled forces (gravity and interparticle forces) and the packing of spheres is entropically driven and energetically favored. S2, S For the binary colloidal crystals, the free energy (E) of small spheres could be divided into two parts: (i) gravity potential energy (E g ); (ii) size-dependent interparticle interaction energy (E i ). In a word, E = E g + E i. According to the previous report, S4 for the small spheres, the interaction with the large spheres is much stronger than that with other small spheres. So their interactions with large spheres play the essential role in the E i of small spheres. In Charts S2 (a) and (b), the is the same, the E i should be similar, and so the E g directly determines the stability of the LS 6 binary structures. It is geometrically known that the gravity potential energy of small spheres in Chart S2(b) is lower than that in Chart S2(a), because the height (h) of small sphere for the former is lower than that for the latter, as more clearly illustrated in Charts S2(e, f) (or h 2 <h ) at =0.267, which indicates a lower overall energy and hence a stable structure. Likewise, for the patterns LS 2 shown in Chart S2(c, d), the former has a larger and a higher E g of small spheres, demonstrating an instability of the LS 2 structure compared with the latter. In this case, the small spheres should be arranged in a special way, instead of normal monolayer close-packed arrangement. N S/L (max) could be lower for better structural stability, as illustrated in curve c (fold-line) in Figure 2. There are three regions in Figure 2. When (N S/L, ) is in region A, the structure is stable. The patterns in region B are possible but instable. In region C, the bccs are impossible or inexistent. 6

7 Chart S2 Zhengfei Dai et al. Chart S2. Schematic illustration of monolayer close-packed small spheres with unstable and stable arrangements, respectively. (a) =0.267 for unstable LS 6 pattern; (b) =0.267 for stable LS 6 pattern; (c) =0.267 for unstable LS 2 pattern and (d) =0.74 for stable LS 2 pattern. (e) and (f) are the vertical sections along the two circle center lines in (a) and (b), respectively. REFERENCES S. Bishop, K. J. M.; Wilmer, C. E.; Soh, S.; Grzybowski, B. A., Nanoscale Forces and Their Uses in Self-Assembly. Small 2009, 5,

8 S2. Shimmin, R. G.; DiMauro, A. J.; Braun, P. V., Slow vertical deposition of colloidal crystals: A Langmuir-Blodgett process? Langmuir 2006, 22, S. Eldridge, M. D.; Madden, P. A.; Frenkel, D., Entropy-Driven Formation of a Superlattice in a Hard-Sphere Binary Mixture. Nature 99, 65 (644), 5-7. S4. Ohara, P. C.; Leff, D. V.; Heath, J. R.; Gelbart, W. M., Crystallization of Opals from Polydisperse Nanoparticles. Phys. Rev. Lett. 995, 75,