Physics Letters A 373 (2009) 3174–3181

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Physics Letters A

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Structure transitions of polymer-mediated colloidal crystals

C.R. Han a, J.G. Cao a, L.W. Zhou a,∗, X.C. Pang b, J.L. Huang b,∗, L.F. Zhang a, J.P. Huang a,∗,1

a Department of Physics and Surface Physics Laboratory (National Key Laboratory), Fudan University, Shanghai 200433, Chinab The Key Laboratory of Molecular Engineering of Polymer, State Education Ministry of China, Department of Macromolecular Science, Fudan University, Shanghai 200433, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 31 January 2009Received in revised form 25 June 2009Accepted 27 June 2009Available online 1 July 2009Communicated by R. Wu

PACS:47.57.-s42.70.Qs47.57.J-

Keywords:Structures transitionsColloidal crystalsSelf-assemblyBand structures

The self-assembled colloidal crystals with structure transitions were realized experimentally on substrateswith polymer brushes. Such polymer-mediated colloidal crystals were found to experience a series ofin-layer structure transitions including stable columnar, polycrystalline, mixed square-hexagonal, square,hexagonal structures when the mass ratio of colloidal particles to free polymers was adjusted from 0.125to 10. Among these structures, a large area interfacial square structure was proved to be a body-centeredtetragonal (BCT) structure in three dimensions in the polymer-mediated colloidal crystals.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Colloidal crystals are materials with periodic structures typi-cally made by the self-assembly of submicrometer colloidal par-ticles. Self-assembled colloidal crystals present rich phase be-haviours which can be used to fabricate nanomaterials with highperformance in size-dependent optical, electrical, and mechanicalproperties [1–5], and especially in photonic band gaps [6–11]. Itis highly desirable to fabricate colloidal crystals with various sta-ble crystalline structures [12–14]. For instance, if such crystalswere available, they could serve as photonic band gap materi-als [10,11,15–17], which is of particular importance in optoelec-tronic applications that require the manipulation of photons, e.g.,as photonic components in telecommunication devices, lasers, andsensors. In monodisperse colloidal systems, the random hexagonalclose-packed or face-centered-cubic structures with high symme-try can be formed by self-assembly methods [18,19]. Various tech-niques, such as dip coating [20], electrochemical growth [21], self-assembly with electrodes [22], evaporation [23] have been used forthe fabrication of large colloidal crystals with a given structure and

* Corresponding authors.E-mail addresses: lwzhou@fudan.edu.cn (L.W. Zhou), jlhuang@fudan.edu.cn

(J.L. Huang), jphuang@fudan.edu.cn (J.P. Huang).1 Tel.: +86 21 55665227; fax: +86 21 55665239.

0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.physleta.2009.06.050

fewer defects. All the methods mentioned above utilize a smoothand “hard” substrate to grow the colloidal crystals. The hard sub-strate served as the confinement to the system and permitted col-loidal spheres to be assembled into highly ordered structures [24].It has been reported that monodispersed colloidal spheres sequen-tially organized themselves into ordered 3D structures when theyare subjected to physical confinement [25]. Using these methods,the three-dimensional colloidal crystal with given structures canbe achieved.

In recent years, several methods have been developed to tunethe transition of the structures of the colloidal crystals. Dif-ferent structures which were random hexagonal close packing,face-centered cubic, body-centered cubic, body-centered tetrago-nal, body-centered orthorhombic, and space-filling tetragonal wererealized and the phase behaviours were controlled by varyingthe solvent salt concentration and external electric field [26,27].Also the structure transformation from body-centered tetragonalto face-centered cubic had achieved by tuning the magnetic andelectric fields [28]. The patterned substrates can also be used todirect the crystallization of the colloidal suspension and permit totune the symmetry and the growth direction of the colloidal crys-tal [29–31].

In this Letter, we report an experimental self-assembly methodto achieve colloidal crystal with various structures and structuretransition and thus verify the previous theoretical findings by Renand Ma [32]. The colloidal crystal is composed of colloidal particles

C.R. Han et al. / Physics Letters A 373 (2009) 3174–3181 3175

and free polymers on a substrate with a soft polymer brush, andit is named as “polymer–colloidal particles–polymer brush” (PCB)colloidal crystal. This method of making PCB colloidal crystals andother colloidal structures is called a PCB method. Here the poly-mer brush [33–38] is used to modulate the softness of substrates.Using a polymer brush is an efficient way to control and stabilizethe symmetry of the first layer of the colloidal structure. Differentto previous “hard” or short range interactive substrate, it is foundthat “soft and flexible” polymer brush substrate may lead to a longrange force between substrate and particles, and among particles.This long range force stabilizes the order of the nanometer sizedparticles and controls the symmetry of the structure formed in adesired direction. The free polymers are homogeneously dispersedin the solution which provides a depletion force (also called an en-tropic excluded volume force) [32,39–42]. It is known that the de-pletion force can cause a lot of phase separation behaviours in col-loidal systems [43–46]. For example, when the colloidal–polymermixture was coated onto a solid surface, columnar and lamellarstructures can be found [4]. In our polymer–colloidal particles–polymer brush colloidal system, a brush-mediated long-range in-teraction between the colloidal particles competes with the stericpacking effect of the particles themselves, and generates a seriesof ordered structures, which undergo symmetry-changing transi-tions [32]. In the experiment, we fixed the quantity of the freepolymers and changed the mass ratio of colloidal particles to freepolymers from 0.125 to 10. It was found that the colloidal parti-cle structures undergo a series of transitions from amorphous, topolycrystalline, to columnar, to mixed square-hexagonal, to densesquare, to mixed hexagonal-square, and to hexagonal structures onthe polymer brush. The profiles of the polymer brush substrateswere investigated by both the scanning probe microscope (SPM)and scanning electronic microscope (SEM) before colloidal parti-cles were layered on and after they were rinsed off. As a result,the deformation of the polymer brush substrate shows the interac-tion of the polymer brush and the colloidal particles. The spectraof different phases of colloidal structures show different photonicband gaps as well.

2. Experiment

The single- or multi-layered PCB colloidal crystals are composedof colloidal particles, free polymers, and polymer brush by us-ing a self-assembly method. The colloidal particles are polystyrene(PS) nanometer-sized spheres 5030A (Duke Scientific Corporation,Fremont USA), which have an average diameter (D) of 300 nm.The size uniformity (The standard deviation of the mean diam-eter expressed as a percentage of the mean diameter) is lessthan 3%. The free polymer is poly(ethylene oxide) (PEO) whichhas a molecular weight of about 20,000. The polymer brushis poly(methyl methacrylate) (PMMA) and was prepared by thesurface-initiated atom transfer radical polymerization method [47].The silane initiator used in this polymerization was (11-(2-bromo-2-methyl)propionyloxy)undecyltrichlorosilane [48].

The details of the preparation procedure of the PMMA poly-mer brush contain three steps. Step 1: the 1 cm × 1 cm siliconwafers were cleaned consequently by de-ionized water ( min),acetone (20 min), methanol (5 min), H2SO4/H2O2 (volume ratiois 7/3 for 1 h), and de-ionized H2O (10 min), and then dried ina nitrogen flow. Step 2: pre-cleaned silicon wafers were put intoa silane/toluene solution (a mixture of 10–20 μl silane initiatorand 10 ml toluene solvent) at 15 ◦C for 15 h. Then the silicon-wafers-grafted initiator was removed from the solution and rinsedby toluene, acetone, methanol, and de-ionized water. Finally, theywere dried with nitrogen and deposited in a drying box [48]. Step3: The initiator wafers were immersed in a homogeneous maroonsolution composed of methyl methacrylate (MMA) (5 g, 50 mmol),

CuBr (71 mg, 0.5 mmol), bipyridine (156 mg, 1 mmol), degassedH2O (1 ml), and MeOH (4 ml). After freeze-drawing for three times,the ampule were put into a thermostatic oil bath at 30 ◦C for 22 h.After completion of the polymerization, the substrate was cleanedby sonication in tetrahydrofuran (THF) for 20 min, and dried ina nitrogen flow. The polymer brush thicknesses of 400 nm weredetermined by ellipsometer and the step measurement, which areconsistent with each other. This thickness is comparable to the di-ameter of the colloidal particles.

The sample preparation process of PCB colloidal crystals is thefollowing: firstly, 0.01 g PEO was dissolved in 20 ml methanol sol-vent (methanol/water volume ratio of 4:1) to make free polymersolution A. The colloidal PS particles were then added into 2 mlof free polymer solution A according to the PS/PEO mass ratiofrom 0.125 to 10. The mixtures were made uniform by ultrasonicdispersion for 10 min. The polymer-brush-attached square siliconchips were immersed into the methanol solvent (methanol/watervolume ratio of 4:1) for 20 min at 30 ◦C for pre-inteneration ofthe polymer brushes. The chips were then immersed verticallyinto the colloidal-polymer mixture with different PS/PEO mass ra-tio for 20 h. After the solvent was evaporated at 40 ◦C, severaldifferent colloidal structures were found such as the hexagonal,hexagonal-square mixture, square or columnar. In the prepara-tion of PCB colloidal crystals, the mass of PEO was kept constantwhile the concentration of the PS particles was varied accordingto PS/PEO mass ratios ranging from 0.125 to 10. The transition ofthe colloid structures occurs with the increase of the nanoparti-cle concentration. After the solvent was completely evaporated, thetwo-dimensional filling fraction of columnar, square, and hexago-nal structures were calculated by Image-Pro, and found increasingfrom columnar (0.3516), via square (0.6333), to hexagonal (0.8104)structures. The ability to control structures of colloidal crystals us-ing a polymer brush layer and free polymer is quite unique in com-parison with other self-assembly methods. The methanol/watersolvent used in our experiment is the same as that used in PMMApolymerization [48]. From this we could deduce that PMMA couldbe dissolved in the methanol/water solvent, and the polymer brushis soft in the solvent at 40 ◦C.

3. Results and discussion

The SEM observation is an intuitive way to determine thestructures of materials in this study. Fig. 1 shows self-assembledcolloidal crystals on substrates with polymer brush thickness of400 nm and the transition of structures from amorphous, viacolumnar, polycrystalline, mixed square-hexagonal, dense square,mixed hexagonal-square, and to hexagonal structures. In the ex-periment, it is found that the transition of these structures can becontrolled by varying the mass ratio of the colloidal PS particles tothe free PEO polymers. When the PS/PEO mass ratio ranges from0 to 0.2, the distribution of colloidal particles is random. When theratio was increased from 0.2 to 1, the columnar structures werediscovered. Especially, when the ratio was 0.3, the columnar struc-ture reached its maximum. The maximum area of the columnarstructures can be as large as 10 000 μm2. We can see the colloidalparticles arranged along nearly one direction to form the colum-nar structure on the 1 cm × 1 cm polymer brush substrate. Thissuggests that the polymer brush provides the colloidal particles along-range anisotropic force. Here, the anisotropy means the orga-nization direction of the particles on the surface of the polymerbrush. The anisotropic interaction originates from the stretchingenergy cost of polymer brush chains which depends strongly onthe aggregation style of the colloidal particles. To minimize the freeenergy, the nanoparticles aggregate at the polymer brush-air inter-face choosing a baguette shape and growing anisotropically alonga one-dimensional direction, resulting in columnar structures [49].

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Fig. 1. (Color online.) Structure transition of colloidal crystals with increasing ratio of PS/PEO from 0.125 to 10. From left to right, the colloidal crystals transform fromamorphous, to columnar, to polycrystalline, to mixed square-hexagonal, to dense square, to mixed hexagonal-square, and to hexagonal structures. In this figure, A denotes“amorphous”, C denotes “columnar”, S denotes “square”, S+H denotes “mixed square-hexagonal” (the area of square structure is larger than that of hexagonal one), H+Sdenotes “mixed hexagonal-square” (hexagonal area is more than square one), and H denotes “hexagonal”. The ratios of 0.3, 4 and 10 are the places where the correspondingcolloidal structures reach their maxima.

When the ratio increased from 1 to 4, the short-ranged orderedpolycrystalline structures changed to the mixed square-hexagonal.During this change, both the square and hexagonal structures in-creased with the mass ratio. However, the area of square structureincreased faster than that of hexagonal one and reached the max-imum at a PS/PEO mass ratio of 4. At this optimal ratio we foundthat the maximum region of the square structure of the body cen-tered tetragonal (bct) can be over 10 000 μm2. The inset in Fig. 1(S) is the magnification of the square structure, which is the (100)face of the BCT structure. Fig. 2A represents the large region ofsquared structure when the PS/PEO ratio is 4. The inset on theright corner of Fig. 2 is the magnification of the correspondingstructures. When the PS/PEO mass ratio increased from 4 to 10,the mixed hexagonal-square structure was occupied by increasinghexagonal structure (H). When the ratio is larger than 10, mostof the area is covered by the hexagonal structure. The maximumregion of the hexagonal structures is 0.1 cm × 0.1 cm in our ex-periment. Fig. 2B shows the large area hexagonal structure. Thearea could be even larger if we keep the extra circumstances (tem-perature, stability, uniformity of the polymer brush) more stable.Such transitions conform to the sequence from disorder to orderedstructures, and from short-range to long-range orders.

The proportions of different structures in the colloidal crystalfilms with area of 4 mm × 8 mm were shown in Fig. 3. At thePS/PEO mass ratio of 0.3, the proportion of the column structureis 40%. At the ratio of PS/PEO of 4, 55% of the area of 4 mm ×8 mm is square structure and 35% is hexagonal. The largest regionof the square structure is 100 μm × 100 μm (see Fig. 2A for themorphology of a large region of the square structure). The smallsquare region is several micrometer-size. At the ratio of 10, nearly80% of the film is covered by hexagonal structure.

Fig. 4 shows the topography of the polymer brush which wasprepared by surface-initiated atom transfer radical polymeriza-tion. Panel A is the SPM topography of the polymer brush bythe step measurement which denotes the polymer brush thickness(400 nm). It is consistent with the result in panel B which showsthe SEM image of the cross-section of PMMA polymer brush.

To reveal the function of both polymer brush and free polymerin the formation of structure-changeable colloidal crystals, we havecompared four different combinations of the PEO polymers andthe polymer brush with the same concentration of PS particles,see Fig. 5. This figure shows four different combinations of PEOpolymers and polymer brush in order to illuminate the interactionin colloidal structures. Fig. 5a shows the closely packed hexagonalstructure assembled from a monodispersed colloidal suspension ona silicon substrate without polymer brush and free polymers. Inthis case, the structures other than the hexagonal ones are difficultto find. The small areas of the hexagonal and square structures asshown in Fig. 5b were formed with a monodispersed colloidal sus-pension with free polymers, but without polymer brush. There area few short range phases in Fig. 5b but only one phase in Fig. 5a;this is due to the depletion effect between colloidal particles andthe free polymers [39–42]. Fig. 5c is a sample made by using thepolymer brush but without free polymers. Both long range orderedhexagonal and square structures are found in this sample, but itis clear that the closely packed hexagonal structure covers a widerarea than the square structure does. The long-range ordered struc-tures are due to the effect of the soft polymer brush substrate.Fig. 5d shows the sample made with both polymer brush andfree polymers, and several large areas of square structures wereformed. The structures in Figs. 5c and d are more ordered thanthat in Fig. 5b. It is because the polymer brush has a long range

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Fig. 2. (Color online.) (A) The SEM image of the large region square structure with the PS/PEO ratio of 4. (B) The SEM image of the large region hexagonal structure with thePS/PEO ratio of 10. The insets on the right corner are the magnification of the corresponding structures.

effect on the colloidal particles and stabilizes the ordered structureformed in the free polymer-colloidal mixtures. Fig. 5d is the resultof two interactions which are the attractive depletion force dueto the large entropy of polymer brushes and free polymers, andthe repulsive steric force between colloidal particles. PS/PEO massratio of 4 was kept in Figs. 5b and d. It shows that the free poly-mers have an important effect on enriching the phase behaviourof the colloidal particle structures. However, the square structuresare much easier to be stabilized on a soft substrate (Fig. 5d) thanon a hard one (Fig. 5b).

To understand the formation process of colloidal crystal struc-ture, we have also paid attention to the first layer structures byviewing the deformation of the polymer brush after the PS parti-cles were rinsed off. The morphology of polymer brush was madeby immersing the PCB colloidal crystals into the THF solvent for4 days at 20 ◦C to dissolve PS particles, plus a sonication in thesame THF solution for 1 min to remove traces of the PS parti-cles. Figs. 6a and b are the SEM top views of the morphology ofpolymer brushes grafted on the silicon substrate after colloidalparticles have been removed. From each of these pictures, wefind the profiles of the first layer of colloidal particles left onthe polymer brush and these are consistent with phase structuresof the corresponding three-dimensional colloidal crystals. Fig. 6a

Fig. 3. (Color online.) The proportion of different structures in the colloidal crystalfilms with area of 4 mm × 8 mm corresponds to the mass ratio of PS/PEO from1 to 10 when the thickness of polymer brush is comparable to the size of the PSparticles. Solid curves are a guide for the eye.

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Fig. 4. (Color online.) Patterns of the polymer brush. (A) The step measurement by SPM which indicates that the thickness of the polymer brush is about 400 nm. (B) SEMimage of cross-section of PMMA polymer brush.

Fig. 5. (Color online.) SEM pictures of the morphology of colloidal crystal structures with different combinations of the free polymer (PEO) and the polymer brush. (a) Thecolloidal crystal sample without free polymer and polymer brush. (b) The colloidal crystal with free polymer, but without polymer brush. (c) The colloidal crystal samplewith polymer brush, but without free polymer. (d) The sample with both polymer brush and free polymer. Upper-right corner shows an enlargement of a part of the squarestructure.

Fig. 6. (Color online.) The SEM pictures of the morphology of polymer brush grafted on silicon substrates after the colloidal particles were rinsed out, for (a) a hexagonalstructure and (b) square structure of colloidal crystals.

shows that the first layer is the hexagonal structure, and the three-dimensional structures are closely packed. Fig. 6b displays that thefirst layer is a square structure, and the three-dimensional struc-ture is BCT. Different phase profiles also confirm that the polymerbrush can interact with the colloidal particles to control the sym-metry of the particle structures and stabilize the in-plane struc-tures of the colloidal crystals.

The PS particles were removed by THF solvent, which is alsoa good solvent for both PMMA and PS, but leaves visible featureson the surface of the PMMA as if there were no swelling of thePMMA surface with the THF. Three possible reasons are list below.First, the PS particles are not cross-linked, and they could be dis-solved by the THF. Second, there are layers of Au on the surfaceof the samples which could prevent the THF from immersing into

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the samples. This is because the samples had made the SEM ob-servation before they were immersed into the THF. Third, the freepolymer PEO which could not dissolve well in THF may protect thesurface of PMMA. Clearly, it is not easy to remove the PS particlesthoroughly. After being immersed into the THF solvent for 4 daysat 20 ◦C, there were still a few layers of PS colloids on the polymerbrush. Therefore we placed the samples in THF solvent for sonica-tion (for 1 min) and found the particles were shaken away fromthe surfaces of polymer brushes. We subsequently produced themorphology of the polymer brush by SEM, see Figs. 6a and b.

It has reported that the BCT structure of the colloidal crystalhad been realized by sedimentation of the colloidal dispersion ofmicrometer spheres in the electrical field [26,27,50]. Both Menget al. [51] and Brevo et al. [52] have talked about the crystalliza-tion behaviour of the colloidal particles at the transition regionsfrom n to n + 1 layers. The formation of square structure occurredin the layer transition region during the increase of the thickness.That is to say, in their systems, the position of the square struc-

Fig. 7. (Color online.) Experimentally measured reflectance spectra of the hexagonaland square colloidal crystals.

ture was between the nth and (n + 1)th layers. While both thenth and (n + 1)th layers were hexagonal regions. Our work is dif-ferent from their works. Firstly, the electrostatic interaction in oursystem is small. The polystyrene spheres with a small quantity ofsulfate radicals on them are negatively charged, but the quantityof the charge is very little. Most part of the surface of the spheresis neutral. So the depletion force which induced by the electro-static effect is small enough to be ignored. Secondly, the largeregion of the square structure is located in the surface of the samelayer but not in the layer transition region. The formation of thesquare structure is mainly induced by the entropic effect of thepolymer brush and the steric packing effect of the colloidal parti-cles. If the brush-mediated interaction between colloidal particlesdominates over the steric packing effect of the colloids, the stablesquare structure forms for possibly large conformational entropyof polymer brush. If the steric packing effect dominates, the stablehexagonal structure forms.

It is well known that, on a hard substrate, a square-structuredcolloidal crystal is not stable, while a hexagon-structured one is.This is due to the fact that the latter has lower free energy thanthe former. However, on a polymer brush-mediated soft substrate,square-structured colloidal crystal can be stable under certain con-centration of colloidal particles (Fig. 5c and Fig. 5d). This is be-cause, on the soft surface of the polymer brush, if the interactionof different components and the entropy of free polymer chainsare omitted, the approximate total free energy density consistsof two parts: repulsive steric energy of colloidal particle and en-ergy due to the entropy of the polymer brush. Here the latter maylead to an attractive interaction between colloidal particles (deple-tion effect). Namely, the total free energy density per unit area,F = Nc Fst − Nbr T Sbr , where Fst is the steric energy of a parti-cle, Sbr is the entropy of a single chain of the polymer brush,Nc and Nbr are the numbers of colloidal particles and chains of

Fig. 8. (Color online.) Numerically simulated band structures of (a) BCT and (b) FCC structures. The first Brillouin zones of the (c) BCT and (d) FCC structures. The red arrowsin (c) and (d) display the measurement direction of the reflectance spectra of square and hexagonal colloidal crystal, respectively. Parameters: D = 300 nm. (For interpretationof the references to color in this figure legend, the reader is referred to the web version of this or Letter.)

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polymer brushes in a unit area, respectively [32]. We owe the tran-sitions of the structures (Fig. 1) to the competition between theentropy effect (depletion effect) of the polymer brush and the ef-fect of repulsive particle steric energy. Sbr and Fst are calculated inRef. [3,6], and it is found that both of them are dependent on thecolloidal particle concentration; namely, they would be differentwhen the colloidal structure is different. It is found from the cal-culation that the entropy of the polymer brush of square-structure(Fig. 6b) is about 1.1kB ; but the entropy of the polymer brush ofhexagonal structure is −0.2kB . In this work, the particle concen-tration is defined as the mass ratio of the colloidal particles to thefree polymers on an adjustable polymer brush. When the particleconcentration is about 4, although the repulsive steric energy forthe square structure is higher, the total free energy of the squarestructure (or BCT structure in 3D) is low, and the correspondingstructure is stable. This is because a polymer brush of square struc-ture has very high entropy. Similarly, when PS/PEO = 10, althoughthe entropy of the polymer brush of the hexagonal structure isvery low, the repulsive steric energy for the hexagonal structure isalso low, thus the total free energy of the hexagonal structure islow, and the corresponding structure is stable.

To distinguish the square phase from the hexagonal one, thereflectance spectra of the PCB colloidal crystals were measured.A deuterium–tungsten light source was used to emit light of 1 mWwith wavelength varying from 400 to 1100 nm. The diameter ofthe light beam was 1 mm. The spectrum of the silicon substratewas first measured as a reference. The samples were then illumi-nated by the collimated light source and the incident direction wasinclined to the normal direction of the samples. The reflected lightby the samples was analyzed by a monochromator with a resolvingwavelength varying from 400 nm to 850 nm. The spectra of the re-flected light were obtained as shown in Fig. 7. We experimentallyobserved two peaks in the reflectance spectra: One is located at657 nm for the square structure sample with the PS/PEO mass ra-tio of 4, the other is at 710 nm for the hexagonal structure samplewith the PS/PEO mass ratio of 10. Further, we used the commercialR-soft software to calculate the band structures of the BCT (Fig. 8a)and FCC (Fig. 8b) crystal lattices. In Figs. 8a and b, the arrows showthat there are some local frequency-gaps in a certain wave vectorregion. The red arrows in Figs. 8c and d show the measurementdirection of different structures. The calculated frequency-gap cor-responds to reflectance wavelengths of 660 nm and 707 nm forthe BCT and FCC lattices, respectively. They agree with the ex-perimental result, namely, 657 nm and 710 nm for square andhexagonal structures, respectively. The agreement between our ex-periment and theory shows that the (interfacial) square structureobserved in our experiments has a BCT structure in three dimen-sions, and that the (interfacial) hexagonal structure accords withthe FCC structure in three dimensions.

We have so far proved that the square phase of colloidalcrystals is BCT structure by a comparison between experimen-tal reflectance spectra and their model calculations. The three-dimensional structures other than BCT were proven to be impossi-ble because of giving wrong positions of reflection peaks. We arethus convinced that the square-phased colloidal crystals assembledvia polymer-mediated self-organization has a three-dimensionalBCT structure.

4. Conclusion

By using free polymers and polymer brushes, we have exper-imentally demonstrated a theoretically proposed method [32] forfabricating a class of colloidal crystals with stable tunable crys-talline structures. Such polymer-mediated colloidal crystals werefound to experience a series of in-layer structure transitions in-cluding a stable square structure when we adjusted the mass ratio

of colloidal particles to free polymers. This work presents a newexperimental method to fabricate colloidal crystals with structurestransition, which have practical applications in various fields.

Acknowledgements

We thank R.K. Jing and P.X. Chen for their fruitful discus-sion and support, and L. Xu, Q.M. Zhang, L. Zhou, J.M. Hao, andG. Wang for their expertise. This work was supported by theNational Natural Science Foundation of China under Grant Nos.10334020, 10574027, 10604014, and 10874025. L.F.Z. and J.P.H.also acknowledge the financial support by the Pujiang TalentProject (No. 06PJ14006) of the Science and Technology Commis-sion of Shanghai Municipality, by the Shanghai Education Com-mittee and the Shanghai Education Development Foundation (“ShuGuang” project under Grant No. 05SG01), and by CNKBRSF underGrant No. 2006CB921706.

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