Polygonal Micellar Aggregates of a Triblock Terpolymer Containing a

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Polygonal Micellar Aggregates of a Triblock Terpolymer Containing a Liquid Crystalline Block Xiaoyu Li,† Yang Gao,† Xiangjun Xing,*,‡ and Guojun Liu*,† †

Department of Chemistry, Queen’s University, 90 Bader Lane, Kingston, Ontario, Canada Department of Physics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

‡

S Supporting Information *

ABSTRACT: Block copolymers self-assemble in block-selective solvents into diverse nanometer-sized micellar aggregates (MAs). Understanding the formation mechanisms of these morphologies is challenging but important for the design and synthesis of block copolymer architectural materials. Here we report our discovery that polygonal or enclosed cylindrical MAs bearing sharp bends can be formed from a triblock terpolymer containing a liquid crystalline block. We propose that the sharp bends are formed mainly to enable approximately straight sides in which the liquid crystalline packing of the core block is facilitated and the cylinder bending energy is reduced. However, this energy reduction is counteracted by an energy increase due to the concentration of smectic edge dislocations at the vertices. Thus, polygonal MAs are formed only when the toroidal MAs are sufficiently small and the cylinders experience significant bending. We theoretically estimate critical toroidal size below which the transition from round toroids to polygons occurs. This estimated size agrees with our experimental observations, supporting our hypothesis and analysis.

I. INTRODUCTION The synthesis of advanced functional materials with intricate structures is a central theme of modern material science and chemistry.1−8 Block copolymer micellization in block-selective solvents offers a robust and versatile approach toward novel and complex nanostructures. In these solvents, the insoluble block(s) of different copolymer chains aggregates to form a nanostructure of a particular shape that is decorated and dispersed in the solvent by chains of the soluble block(s).9 The morphologies of self-assembled block copolymer micellar aggregates (MAs) are remarkably diverse and have been of tremendous interest in the past two decades. The shapes or morphologies of block copolymer MAs affect their performance in applications. For example, cylindrical micelles may be better than spherical micelles for controlled drug release because of their longer circulation times in animal bloodstreams.10 Also, cylindrical micelles are better suited than spherical micelles for the reinforcement of epoxy resins.11 Meanwhile, spherical micelles are more effective than cylindrical micelles in reducing the friction of lubricating base oils.12 Thus, MA morphologies are of critical importance for their functions, and the understanding of the formation mechanisms of MAs is essential for morphological control. In the case of diblock copolymers consisting of two covalently linked random-coil A and B chains, the equilibrium MA morphology is governed by the competition between the stretching energies of the insoluble and soluble chains as well as the interfacial energy between the insoluble block and the solvent.9 Adjusting these energy scales by tuning the relative lengths of the soluble and insoluble blocks or by changing the © 2013 American Chemical Society

quality of the solvent toward the insoluble block allows one to achieve controlled production of diblock copolymer MAs with spherical, cylindrical, or vesicular morphologies.9 In contrast, the MA morphologies of ABC triblock terpolymers are much more diverse and complex and depend on many other experimental factors.13 Recently, various exotic micellar morphologies from this family of polymers have been discovered, including helices,14−16 toroidal MAs,17−21 Janus MAs,22,23 spiral-like MAs,24 and MAs with multicompartmental cores25,26 and patchy coronas.27−29 Aside from adding another block, changing a coil block into a crystalline or liquid crystalline (LC) block can fundamentally change the micellization behavior of a diblock copolymer. For example, Manners, Winnik, and co-workers have produced MAs with unusual shapes from diblock copolymers bearing a crystalline insoluble block, and the exotic shapes have included blocky cylinders30−32 and scarf.31 Discher and co-workers determined that their diblock copolymers bearing an insoluble crystalline block formed vesicular MAs at compositions when a coil−coil diblock copolymer would have formed spherical or cylindrical micells.33 Even the introduction of a LC block with a packing energy much lower than that of crystallization can lead to the formation of unusual MAs. For example, Li, Keller, and co-workers discovered that diblock copolymer bearing a LC insoluble block preferred cylindrical micelles over spherical micelles.34,35 When vesicles were formed, they were faceted Received: June 26, 2013 Revised: August 22, 2013 Published: September 6, 2013 7436

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Scheme 1. Chemical and Schematic Structures of PAA65-b-PCEMA54-b-PFOEMA16

Figure 1. (a−c) TEM images and (d, e) AFM images of PAA65-b-PCEMA54-b-PFOEMA16 MAs prepared at 1.0 mg/mL in TFT/MeOH at f TFT = 10%. Specimens for images a−d were aero-sprayed, and that for image e was prepared through a “wet MA deposition process”. TEM samples were stained with OsO4. (f) Schematic structures and representative TEM images for toroid, racket-shaped MA, and some polygonal MAs.

rather than round.36−38 We recently studied the micellization behavior of a series of ABC triblock terpolymer bearing an insoluble LC C block in solvents that was good only for the A block and poor for the B and C blocks.39 These polymers preferred core−shell−corona cylindrical micelles presumably to facilitate LC packing of the C core block. In this paper, we report results of a detailed study of the selfassembly behavior of an ABC triblock terpolymer that we have studied before.39 Under conditions that we used in the past, this polymer self-assembled mostly into cylinders. After adjusting some of the experimental parameters, we have discovered in this study that we could also produce cylinders that were folded into either round toroids or polygons that have the shapes of quadrilaterals, triangles, eyes, and rackets. As will be argued later, these polygons are formed mainly due to the smectic ordering of the insoluble C block in the core of the cylinders.

the perfluorooctyl groups are bulky and rod-like, as illustrated by the ovals in Scheme 1. Furthermore, our previous 19F NMR and WAXS studies have established that the PFOEMA block formed an isotropic phase at 70 °C and a SmA phase at room temperature in a solvent mixture of α,α,α-trifluorotoluene (TFT) and methanol (MeOH) at a TFT volume fraction ( f TFT) of 10%. The SmA-to-isotropic (AI) transition was determined to be around 68 °C. The polygonal MAs were produced together with MAs of other morphologies in three steps. First, the terpolymer was stirred overnight at 1.0 mg/mL at room temperature in TFT/ MeOH at f TFT = 10%. Only the PAA chains were soluble in this mixture. In the second step, the solution was heated to and held at 70 °C (above the AI transition of the PFOEMA block) for 2 h to fully or partially disorder the PFOEMA LC phase. In the third step, the solution was cooled naturally to 21 °C in an oil bath and was held at this temperature for 2 days before analysis. To visualize the MAs, their solutions were aero-sprayed onto carbon-coated grids. The dry MAs were then stained by osmium tetroxide (OsO4, PCEMA-selective) and subsequently viewed via transmission electron microscopy (TEM). The purpose of aero-spraying was to atomize the MA solution into a fine fog and to speed up solvent evaporation to be within fractions of a second while the solution droplets flew from the spraying nozzle to the collecting TEM grid. This fast solvent evaporation froze the skeletal structure of the MAs and

II. RESULTS AND DISCUSSION MA Aggregates. The polygonal MAs were prepared from poly(acrylic acid)65-block-poly(2-cinnamoyloxyethyl methacrylate)54-block-poly(perfluorooctylethyl methacrylate)16 (PAA65b-PCEMA54-b-PFOEMA16, Scheme 1), where the subscripts denote the repeat unit numbers for the different blocks. This terpolymer was derived from a precursor that was synthesized via anionic polymerization and had a low polydispersity index of 1.04.39 The PFOEMA block is liquid crystalline and forms a smectic-A (SmA) phase at room temperature (21 °C) because 7437

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minimized the chance for morphological transitions. Figures 1a−c show TEM images of specimens thus prepared. The MAs thus prepared were a mixture of spheres, cylinders, θ-shaped MAs, figure 8-shaped MAs, approximately circular toroids, and polygonal MAs. The polygons, as illustrated in Figure 1f, resembled quadrilaterals, triangles, eyes, and rackets that possessed 4, 3, 2, and 1 vertices, respectively. In contrast, the circular toroids possessed no sharp bends. Since only the PAA block was soluble in the solvent mixture, the MAs should have a core−shell−corona structure with PAA as the soluble corona. The block sequence of the polymer dictated that PCEMA should have formed the shell and PFOEMA constituted the core. This core−shell structure was supported by the high-magnification TEM images for the eyeshaped, triangular, and quadrilateral MAs shown in Figure 1f. The projection of the folded cylinders in these polygons had a dark rim and light core because these regions corresponded to the OsO4-stained PCEMA and the unstained PFOEMA domains, respectively. The PAA corona was barely visible in this case, but it was clearly visible if it was selectively stained with uranyl acetate (UO2(Ac)2), as shown in Figure S1 (Supporting Information). The cylindrical, spherical, and toroidal MAs as well as other polygonal MAs should also possess a similar core−shell−corona structure. More experimental evidence supporting this chain packing motif of cylindrical MAs in this sample can be found in our previous publication.39 MA Distributions. We obtained many TEM images similar to Figure 1a for a batch of MA sample prepared using the protocol described above and counted a total of 2400 MAs. Of these MAs, 23% were either polygonal or toroidal. While toroids included circular or slightly deformed circular objects that did not bear sharp bends, MAs assuming “figure 8” or “θ” shapes were excluded from this analysis because they were complex polygons of less interest for this study. Of the toroidal and polygonal MAs, the relative populations of toroidal, racketshaped, eye-shaped, triangular, and quadrilateral MAs were 17%, 11%, 13%, 29%, and 30%, respectively. We also determined the circumferences of the polygonal MAs using methods described in Figure S3 and plotted the variation in the number fraction of each type of MAs as a function of their circumference in Figure 2. Their average circumferences were 1250 ± 506, 947 ± 399, 577 ± 191, 394 ± 128, and 214 ± 82 nm, respectively, for toroidal, racket-shaped, eye-shaped, triangular, and quadrilateral MAs. Evidently, the average circumference decreased as the number of vertices increased for a polygon. Origin of the Polygonal MAs. Before rationalizing polygon formation, we ruled out that these structures were artifacts formed during microscopic specimen preparation. For this purpose, one experiment involved aero-spraying the MA sample onto freshly cleft mica surfaces and then analyzing the sprayed sample by atomic force microscopy (AFM). Figure 1d shows an AFM image thus obtained. Evidently, polygons were observed in this case as well. Therefore, polygonal MAs did not result from some unusual interactions between the terpolymer and the carbon coating of the TEM grids. One may still plausibly argue that these polygons were derived from toroids during TEM and AFM specimen preparation because of toroid deformation due to impact force on the toroids as they landed on a TEM grid or a mica plate or due to capillary or surface tension forces during solvent evaporation. However, if toroids did deform during TEM or AFM specimen preparation, the

Figure 2. Histograms showing the relative population change for each type of MA as a function of their circumferences. The solid lines are included for visual guidance.

larger toroids should have deformed preferentially rather than the small ones. Additionally, we have also prepared AFM specimens via a wet deposition process (see Supporting Information for detailed experimental procedures). In this case, the MAs were deposited in solution onto an aminemodified silicon wafer by attractive interactions between the amino groups on the silicon wafer and carboxyl groups on the MA surfaces. Since these electrostatic and hydrogen bonding interactions were short-ranged relative to the radii of curvatures of the polygon vertices, these forces were unlikely to cause large-scale deformations such as formation of the sharp bends from the toroidal MAs. Furthermore, an adsorbed toroid was unlikely to deform substantially during solvent evaporation because of the attractions between MAs and the substrate. Therefore, this AFM specimen protocol differed fundamentally from the aero-spraying method. Nevertheless, specimens thus prepared again contained polygons, as shown in the AFM image in Figure 1e. Thus, polygonal MAs existed in the original MA solution before aero-spaying, or they were intrinsic MA structures in the solution. The PAA coronal chains or the shell-forming PCEMA block could not have been responsible for polygonal MA formation. Previously, various cylindrical and toroidal MAs bearing PAA coronal chains have been reported.40,41 However, these structures contained no sharp bends. Cylindrical micelles bearing PCEMA cores have been previously reported by us.42,43 Again, these cylindrical MAs were worm-like and contained no sharp bends. Therefore, the PFOEMA core was most likely responsible for the sharp bends observed in our polygonal MAs. As mentioned earlier, the polygons were prepared by heating and then cooling the copolymer in TFT/methanol at f TFT = 10%. This tortuous procedure was used because irregular aggregates and ill-defined cylinders as shown in Figure 3a were produced by stirring the copolymer in this solvent mixture at room temperature. Heating the copolymer at 70 °C for 2 h yielded vesicles that seemed to consist of fused core−shell− corona spherical particles as well as nonaggregated spherical particles, as revealed by the TEM and AFM images of Figure 3b,c. It was only during or after cooling that polygons together with other MAs were formed. Our systematic microscopic analysis of the MAs formed after sample cooling and aging at 7438

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Figure 3. TEM (a, b, e) and AFM topography (c, d) and phase (f) images of PAA65-b-PCEMA54-b-PFOEMA16 MAs at different stages before polygon formation: (a) specimen of MAs prepared by stirring the copolymer at 1.0 mg/mL in TFT/MeOH at f TFT = 10% for 2 months; (b, c) specimen of MAs prepared by initially stirring the copolymer in the mixed solvent at room temperature (21 °C) and then heating at 70 °C for 2 h; (d) specimen of MAs that had been quenched to 21 °C in 3 min and then held at 21 °C for 15 min, and (e, f) specimen of MAs that was quenched to and held at 21 °C for 1/2 h. The specimen in (a) was stained by the PCEMA-selective OsO4, and those shown in (b) and (e) were stained by PAA-selective uranyl acetate.

Figure 3d shows an AFM height image of such a specimen. Compared with the image shown in Figure 3c, new structures such as ruptured vesicles (one being the second marked structure from the top) and plate-like structures (other three marked structures) were seen. After holding this sample at room temperature for another 15 min, lace-like structures were seen (Figure 3e,f). The holes in these laces were encompassed by toroids, which were fused to the knitted plate-like regions of the laces. The fact that the plate-like regions of the lacelike intermediates eventually disappeared suggests the perforation of the plates as a possible mechanism for toroid formation. Further, the polygons formed probably from the localized bending of the cylinders that made up the toroids. Theoretical Analysis. We will next theoretically explain why small toroids tend to form sharp bends and transform themselves into polygons by showing that the polygons are energetically favored under these conditions. Energetic arguments apply only to systems that are in global or local

room temperature revealed that the cooling protocol and the sample stirring speed (shearing rate) used affected polygon formation. For example, polygon population was reduced by increasing the sample stirring rate or using a staged cooling protocol, which involved holding the sample at each of a series of gradually decreasing temperatures for a finite period of time.39 In the extreme of cooling the sample to 55 °C, holding it there for 2 weeks, and then cooling it to room temperature, mostly cylindrical aggregates were produced. Significant polygons and toroids were produced by quickly cooling the sample after its removal from a 70 °C oil bath or coiling it naturally in the bath. We followed the morphological transition from vesicles and spheres to polygons and other MAs in one case. Here, a heated sample was withdrawn from an oil bath and hand-shaken in air to cool the sample to room temperature. The cooling took ∼3 min. The sample was then held at room temperature for 15 min before an aliquot was taken and aero-sprayed for AFM analysis. 7439

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Scheme 2. Schematic Illustration of a Toroidal MA, a Quadrilateral MA, and the Packing of the Perfluorooctyl Groups at a Sharp Vertex and in the Straight Sections of a Quadrilateral MAa

a

Dislocation defects at the sharp bends help localize the bending strain at these vertices rather than spreading the strain through the entire toroid.

near the bend, where d is the smectic layer spacing and is 1.6 nm for the current system.46 The bending angle of the SmA phase at a vertex caused by the dislocations is given by Δθ = d/ D, while D = 8 nm is the diameter of the LC core. Hence Δθ is about 0.2 rad or 11°. The radius of curvature R′ of two arcs (after the insertion of dislocation pairs) is then

thermodynamic equilibrium. As mentioned above, polygon formation was path dependent. Thus, kinetics might have played a major role in polygon formation. The inability for our system to reach global equilibrium also explained why different MAs including spheres, cylinders, and various polygons coexisted. Despite this, we argue that an equilibrium between the toroids and polygons probably still existed because the interconversion between the two required little local chain motion or only local cylinder bending or straightening.44,45 To formulate the cylinder bending energy, we assume, based on the results of prior studies involving cylindrical MAs with smectic LC blocks,34,35,37 that the SmA layers formed inside the PFOEMA core are perpendicular to the long axis of the cylinders, as illustrated in the last structure of Scheme 2. For toroidal MAs with no smectic dislocation, the smectic layers are compressed at the inner side of the cylinder but are stretched on the outer side. Let B represent the compressional modulus of the smectic layers, which has the dimension of energy per unit volume. If we further define the radius of the toroid as R and the diameter of the PFOEMA cylindrical domain as D, the free energy penalty associated with the deformation of the smectic phase is Fcirc =

π 2BD4 64R

R′ =

1 Rd = R + δR R≈R+ πD 1 − Δθ /π

(2)

where δR = Rd/πD is the change of radius of curvature due to the insertion of a pair of dislocations. Note that we have kept only linear term in Δθ/π. The percentage of error introduced by this approximation is roughly (Δθ/π)2 × 100% = 4%. This reduces the curvature energy in eq 1 by the following amount: δFcirc = −

π 2BD4 πBdD3 δ R ≈ − 32R 32R2

(3)

Note that while the radius of curvature changes as the dislocations are inserted, the total contour length of the toroid remains fixed. On the other hand, the free energy per unit length of an edge dislocation is given by

(1)

⎛ λ ⎞2 ⎞ 1 d 2B ⎛ Fe = ln⎜⎜1 + ⎜ 3 ⎟ ⎟⎟ ⎝a⎠⎠ L 8π ⎝

This energy is inversely proportional to R and hence becomes large for small toroids. Note that additional energy costs may come from the other two blocks of the terpolymer, but we assume them to be subdominant to that of the SmA layers, i.e., eq 1. We now consider the free energy cost for the insertion of a smectic dislocation into a circular toroid with radius R. If this cost is positive, the circular toroids are stable. If this cost is negative, however, dislocations will spontaneously nucleate and circular toroids will become unstable. More careful consideration suggests that the insertion of a single dislocation into a circular toroid is not energetically optimal: the curvature at the antipodal point would become even higher than its original value. This extra bending energy can be relieved by the insertion of another dislocation at the antipodal point. The resulting toroid is eye-shaped, with a pair of dislocations at two antipodal points. This pair of defects divides the toroid into two circular arcs of equal length and curvature. Since there is one more SmA layer on the outer side of the toroid, the contour length of the outer side is longer than that of the inner side by d

(4)

where a is the core size of the edge dislocation, L is the length of the dislocation line, and λ3 represents the penetration length of bending deformation of nematic order (for details, see section 9.3 of the textbook by Chaikin and Lubensky).47 The length of the dislocation line can be written as αD, where α is a number between 0 and 1 and its precise value can be determined only by a more microscopic calculation, which is beyond the scope of this study. The free energy cost for inserting two dislocation lines is then δFdefects =

⎛ λ ⎞2 ⎞ αd 2BD ⎛ ln⎜⎜1 + ⎜ 3 ⎟ ⎟⎟ ⎝a⎠⎠ 4π ⎝

(5)

which is independent of the radius of toroid. The net free energy cost for the insertion of a pair of edge dislocations at two antipodal points is then given by the sum of eqs 5 and 3: 7440

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⎛ λ ⎞2 ⎞ πBdD3 αd 2BD ⎛ + ln⎜⎜1 + ⎜ 3 ⎟ ⎟⎟ ⎝a⎠⎠ 32R 4π ⎝

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PFOEMA core was increased to 11 ± 2 nm from 8 ± 2 nm. Figure S5 shows a TEM image of the MAs aero-sprayed. This copolymer formed mostly cylindrical MAs. Occasionally, polygonal MAs were seen. The polygons were indeed much larger than those prepared from PAA65 -b-PCEMA 54 -bPFOEM16. While the observed R* increasing trend agreed with the theoretical prediction, we could not rule out a possible contribution to the observed trend from the thicker PCEMA layer in the PAA120-b-PCEMA100-b-PFOEMA22 polygons. Because of possible kinetic origin for the polygons reported in this paper, they possessed different shapes and wide size distributions. It would be interesting to discover systems where polygons are favored thermodynamically and examine if our theory still applies. For completion, we have also derived an expression for the total free energy for a polygonal MA with their number of defects given by eq 8. The free energy expression is given in eq S6 of the Supporting Information. Last, we want to point out that the above analysis does not apply to the case of racket-shaped micelles. These micelles have a Y-junction, where three cylindrical MAs join each other and form an orientational defect, i.e., disclination. Additional dislocations may relieve the deformation of the smectic layers in the junction. “Figure 8” MAs with an X-junction, where four cylindrical MAs join each other, have also been observed in our system. The formation of Y-junction and X-junction is however not likely driven by the minimization of the elastic energy of smectic layers. Hence, no inference can be made about the size of racket-shaped micelles based on free energy minimization of smectic layers. Indeed, as one can see from Figure 3, the circumference distribution of the racket-shaped toroids is much wider than polygonal MAs. Because of the limitation of space, we shall not discuss the energetics of X and Y junctions in this work.

(6)

This free energy penalty is negative if the radius of toroid is smaller than a critical value: R* =

π 2D2 8αd ln(1 + λ32 /a 2)

(7)

which depends weakly on two unknown microscopic length scales λ3 and a, but not on the elastic modulus B of the smectic phase. Note that R* also depends on an unknown factor α. This simple derivation unambiguously establishes that there is a critical size for the toroids: larger circular toroids are (globally) stable and therefore remain circular and dislocation-free, whereas smaller toroids are unstable toward the proliferation of smectic defects. To obtain a crude estimation of R*, we set the terms λ3 and a to be equal and choose α = 0.5, which corresponds to the median of its possible range. Using the experimentally known values D = 8 nm and d = 1.6 nm, we obtain the critical radius of curvature R* of 142 nm or a critical circumference (C*) of 895 nm. Theoretical vs Experimental Results. Experimental data in Figure 2 suggest that the largest eye-shaped MAs have a circumference of approximately 900 nm. Thus, toroids that have circumferences smaller than ∼900 nm are not stable. This critical circumference observed experimentally is remarkably close to our theoretically estimated C* of 895 nm. The bending angles Δθ that we visually detect for polygonal vertices of Figure 1 are substantially larger than 11°. This indicates that there are multiple dislocations at each vertex. The vertices of the polygonal MAs are therefore grain boundaries where dislocations aggregate and separate two sides or arcs of a polygon with different orientations of smectic order. We expect the arcs between two neighboring grain boundaries to possess a radius of curvature Rc close to R* or 142 nm. If R < R*, it is energetically favorable to nucleate more dislocations, whereas if R > R*, it is favorable to reduce the dislocation numbers in the grain boundaries. We measured the radii of curvature of the arc sections of some polygons and the average value was 156 ± 46 nm. The last value was very close to R*. The small difference is probably due to interaction between defects as well as between defects and curved geometry. The total bending angle of all the curved edges is C/R*, where C is the circumference. The bending angle due to all vertices is then 2π − C/R*. The total number of dislocations on a polygonal MA is then given by Ndefects =

D ⎛⎜ C ⎞⎟ 2π − d⎝ R* ⎠

III. CONCLUSIONS In conclusion, MAs with shapes resembling quadrilaterals, triangles, and eyes were formed from an ABC triblock terpolymer containing an insoluble LC block. These MAs occurred together with toroids and other types of MAs. While the toroids were favored when their diameters were larger than ∼900 nm, polygonal MAs were preferred when their circumferences were small. Sharp bends were formed in the polygons presumably to relieve the bending energy associated with deforming SmA layers that were nicely packed into straight or slightly bent cylinders. This energy reduction was counteracted by an energy increase due to the creation and proliferation of dislocations in the polygon vertices. The balance of this energy yielded the critical circumference of 895 nm, below which a transition from toroid to polygon took place. This theoretically generated value agreed with our experimental observation well, and this agreement supported our theoretical model and analysis. This study suggests that the accommodation of a liquid crystalline phase can provide a sufficient driving force for the generation of new morphologies and points to a new mechanism for tailoring architectural materials and biomimetic materials from block polymers.

(8)

This result indicates the number of defects increases with decreasing circumference and becomes zero when C > 2πR*. Although Figure 2 indicates that MAs with smaller circumference tend to have more vertices, no such relation can be inferred. This was largely due to the neglect of the interactions between defects, as what we have done. Further Comments. Equation 7 predicts that R* increases as D increases. To verify this prediction, we prepared MAs using the same protocol from another triblock terpolymer PAA120-b-PCEMA100-b-PFOEMA22 whose characteristics have been previously reported.39 Because of the increase in the number of FOEMA units to 22 from 16, the D value for the

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ASSOCIATED CONTENT

S Supporting Information *

Experimental details; TEM and AFM images of MAs that are precursory to the polygons; more TEM and AFM images of the polygonal MAs; methods for calculating the perimeters of 7441

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polygons. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (X.X.). *E-mail: [email protected] (G.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.L. thanks the NSERC of Canada for financial support of this research. G.L. also thanks the CRC program for a Canada Research Chair position in Materials Science. X.X. acknowledges the financial support from the Natural Science Foundation of China (Grants 11174196 and 91130012). Dr. Ian Wyman is gratefully thanked for proof-reading this paper.

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dx.doi.org/10.1021/ma401324a | Macromolecules 2013, 46, 7436−7442