Shape-Anisotropic Diblock Copolymer Particles from Evaporative

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Shape-Anisotropic Diblock Copolymer Particles from Evaporative Emulsions: Experiment and Theory Kang Hee Ku,† Young Jun Lee,† YongJoo Kim,*,‡ and Bumjoon J. Kim*,† †

Department of Chemical and Biomolecular Engineering and ‡KAIST Institute for NanoCentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea

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S Supporting Information *

ABSTRACT: Self-assembly of block copolymers (BCPs) in evaporative emulsion provides a simple and effective route for the preparation of anisotropic particles with controlled shape and size. Understanding of thermodynamic phenomena associated with the bending/stretching of the BCP chains confined within the particles is necessary to enable precise control of the shape and microstructure of the particles. Herein, we report the systematic design of shapeanisotropic diblock copolymer (dBCP) particles based on a new theoretical model that includes entropic penalty associated with bending of dBCP chains upon deformation of the particles. First, we produced convex lens-shaped (oblate) and football-shaped (prolate) polystyrene-b-polydimethylsiloxane (PSb-PDMS) particles, where the aspect ratios (AR, defined as the major axis length divided by minor axis length) were varied. Of note, the AR of the oblate particles increased almost linearly up to 10 as the particle size increased, whereas the increase of AR for the prolate particles was limited to 2.0. For oblate particles, the high bending energy of the curved cylinders at the periphery of a particle can be released by increasing the AR of particle. However, the relatively low bending energy of curved lamellae of prolate particles prevents the particles from having a high AR. Furthermore, our theoretical model that considers these bending energies successfully explains the experimental observations on the variation of particle shape depending on the particle size and the dBCP molecular weight.

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INTRODUCTION Programmed design and engineering of particle shape is necessary to meet specific needs for desired applications of shape-controlled polymer particles. Recently, self-assembly of block copolymers (BCPs) within interface-engineered emulsion droplets has been an effective strategy for producing anisotropically shaped polymeric particles.1−14 In this approach, droplets containing BCPs act as soft and mobile templates, where spontaneous deformation of particle shape can be driven by bending/stretching of self-assembled polymer chains.15−18 Therefore, the assembled structure of the BCPs is critical in determining the final shape and morphology of the particle. For example, spherical particles are typically formed when diblock copolymers (dBCPs) with the assembly structures of threedimensionally isotropic symmetry such as body-centered cubic and gyroid phase are confined in emulsion droplets (Scheme 1a).19,20 By contrast, if the microphase-separated structure of dBCPs inside the particles has an anisotropic symmetry (i.e., cylinders or lamellae) and the different blocks of dBCPs have non-preferential interaction to the particle surface (i.e., neutral surrounding condition), the resulting particles have either a convex lens shape (oblate)21−26 or football shape (prolate)25−28 depending on the self-assembled dBCP structure (Scheme 1b). However, most of the theoretical studies have been limited to studying the internal nanostructure of the dBCPs within the spherical-shaped particle.29−34 © XXXX American Chemical Society

Scheme 1. Schematics of dBCP Phases in Bulk (S: Spheres; G: Gyroid; C: Cylinders; and L: lamellae) and the Corresponding Structure of Polymer Particle

Received: November 17, 2018 Revised: January 4, 2019

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DOI: 10.1021/acs.macromol.8b02465 Macromolecules XXXX, XXX, XXX−XXX

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The details for the optimization of surfactant conditions are described in the Supporting Information (Figure S1). Then, the polymer solution was emulsified in an aqueous solution containing a mixture of SDS and PVA using a homogenizer for 30 s at 15000 rpm. The organic solvent (chloroform) was slowly evaporated at room temperature for 24 h while stirring at 250 rpm. The sample was washed with DI water to remove the large excess of remaining surfactants by repeated centrifugations performed at 13000 rpm for 10 min. The dBCP particles were redispersed in DI water and used for further characterization. Characterization. To observe the surfaces and internal structures of the particles, field-emission scanning electron microscopy (SEM) (Hitachi S-4800) and transmission electron microscopy (TEM) (JEOL 2000FX) were used. The samples were prepared by drop-casting dBCP particle suspensions onto the silicon wafers and TEM grids coated with a 20 nm thick carbon film. To investigate the morphology evolution process by cryo-EM, 2 μL of sample was prepared on the grid, blotted for 9 s, and plunge-frozen in liquid ethane using a Vitrobot Mark IV (FEI) with 100% humidity at 4 °C. Specimens were imaged on a Titan Krios TEM equipped with a field emission source (FEI) and operated at an acceleration voltage of 300 kV. Micrographs were recorded using a Falcon II direct electron detector (FEI). Development of Theoretical Model. For PS-b-PDMS, χ and b in the eqs 1 and 2 were set to 0.26 and 0.6 nm, respectively, and γPS and γPDMS were set to 9.36 and 8.44 mJ/m2, respectively, from the contact angle measurements of each polymer film upon addition of water with SDS and PVA above the critical micelle concentration. Then, the free energy of particle deformation is a function of fitting parameters (α and β), the volume and AR of the dBCP particle, and the number of cylinders in radius from the central cylinder for oblate particle or the number of lamellae for prolate particle from center to edge (n). Therefore, for each dBCP particle volume, free energy was minimized with optimized n and AR. The curvature C and volume of curved layers Vc were numerically calculated from given geometries of oblate and prolate particles. The fitting parameters were optimized to α = 0.9 and β = 0.85 for the plot of AR as a function of width of the oblate particle (W) from experimental data collected from PS31K-b-PDMS17K particles. For the PS11K-b-PDMS5K oblate particles and PS16K-b-PDMS17K prolate particles, AR plots were obtained using same fitting parameters as for the case of PS31K-b-PDMS17K. The PDMS volume fraction (f PDMS) was set to 0.34 and 0.5 for oblate and prolate particle, respectively. For the calculation of free energy in Figure 6 and Figures S9 and S10, the degree of polymerization (N) was fixed to 527 for both types of particles to study the effect of structure (i.e., f PDMS) of dBCP on the AR of particle. The total volume of polymer chains in single particle was set to the volume of sphere with diameter of 1000, 2000, and 3000 nm. The details for the free energy calculation are described in the Supporting Information.

One insight into the development of a theoretical model to explain the self-assembly of prolate dBCP particles was provided by the Fredrickson group.27,35 In their work, the free energy of polymer chains was developed with three contributions: (1) interfacial energy between the different blocks of dBCP, (2) entropic penalty associated with dBCP chain stretching, and (3) surface energy between the particle surface and the surrounding medium. According to this model, a particle stretches to satisfy the commensurability condition between the lamellae spacing of dBCPs and the finite droplet size.36−39 However, this model is limited to the special case of striped prolate particles with the assumption of unbent lamellar stacks. For the particles with highly anisotropic shape such as stretched prolate particles or flat oblate particles,21,22 the large curvature along the particle surface (i.e., at the pole sides of the oblate and prolate particles) can lead to a large bending of the actual dBCP structure, which induces significant deviations from the ideal dBCP structure. Rather, the bending energy can play a significant role in the deformation of the actual particles. Therefore, we believe that understanding the relationship between the energy contribution from the bending of dBCP layers and the resulting particle shape is essential to extend our knowledge for accurate design of anisotropically shaped dBCP particles. In this article, we report a systematic design of shapeanisotropic dBCP particles based on our new theoretical model that additionally considers the contribution of the entropic penalty associated with the bending of the dBCP chains in the free energy equation. First, oblate and prolate particles were produced from solvent-evaporative emulsion droplets containing cylinder- and lamella-forming polystyrene-b-polydimethylsiloxane (PS-b-PDMS) dBCPs. The cylinder-forming dBCPs showed a dramatic increase of aspect ratio (AR) of oblate particle (i.e., from 1.8 to 9.4 according to the increase of the particle diameter from 0.5 to 7.0 μm), producing almost flat particles for large particle sizes. However, in the case of the lamella-forming dBCPs, the deformation of the particle shape from sphere to prolate was restricted, increasing the AR value only up to 2.0 even for very large particle size (i.e., 6.0 μm). To understand this difference, we paid special attention to the bending energy of the dBCP chains in addition to the previously described contributions to the free energy. We observed that for the case of oblate particles a significant reduction of the bending energy could compensate for the increase of surface energy of highly anistropic structure, enabling the production of highly deformed particles. Moreover, fine-tuning of the particle shape by controlling the particle size and the molecular weight (Mn) of PS-b-PDMS dBCP was demonstrated experimentally, and the observations were well explained by our theoretical model.

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RESULTS AND DISCUSSION

The dBCP should have a high Flory−Huggins interaction parameter (χ) to produce dBCP particles with large extents of deformation due to the high bulk elasticity, which is proportional to χ1/2.27 PS-b-PDMS BCPs can be an attractive candidate due to the reasonably high χPS−PDMS value of 0.27,40 which can induce a long-range-ordered cylindrical and lamellar microdomains on the sub-10 nm length scale.41−43 To compare the shape anisotropies of the dBCP particles depending on the particle size and dBCP structure, we employed two different PSb-PDMS dBCPs (i.e., cylinder-forming PS31K-b-PDMS17K and lamella-forming PS16K-b-PDMS17K). Oblate and prolate particles were produced by solvent evaporation-driven self-assembly of PS-b-PDMS from emulsion droplets. A mixture of PS- and PDMS-selective surfactants, SDS and PVA, was used to generate a neutral interface between each of the dBCPs blocks and the surrounding aqueous medium (Figure 1a).44 Figure 1b shows the SEM images of oblate PS-b-PDMS particles. Regularly arranged dimple structures were observed on the surface of the

EXPERIMENTAL SECTION

Materials. Two different cylinder-forming PS-b-PDMS dBCPs (PS31K-b-PDMS17K (dispersity (Đ) = 1.08) and PS11K-b-PDMS5K (Đ = 1.18)) and lamella-forming PS16K-b-PDMS17K (Đ = 1.18) were purchased from Polymer Source, Inc. (subscripts indicate the number-average molecular weight (Mn) of each block). Sodium dodecyl sulfate (SDS) and poly(vinyl alcohol) (PVA) (the weightaverage molecular weight (Mw) = 13K−23K, 87−89% hydrolyzed) were purchased from Sigma-Aldrich and used as received without purification. Preparation of dBCP Particles. A chloroform solution of PS-bPDMS (10 mg/mL, 500 μL) was prepared as a disperse phase. To provide neutral surrounding conditions for both cylindrical and lamellar dBCPs, a mixture of SDS and PVA (10 mg/mL, 10 mL, 2:1 w/w for the cylindrical dBCPs and 1:1 w/w for the lamellar dBCPs) was prepared. B

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Figure 2. (a, b) Schematic illustration showing the morphological evolution of oblate dBCP particles from a chloroform-in-water emulsion droplet. (c−e) Cryo-EM images of PS-b-PDMS particles acquired at evaporation times of (c) 3 h, (d) 6 h, and (e) 12 h.

phase) dominates the formation of perpendicular orientation of BCPs at the surface.16,47,48 For our case of using dual surfactants, the neutral interface between the dBCPs and the surrounding medium allows both blocks to be exposed to the surrounding, resulting in the perpendicular orientation of the dBCP domains relative to the particle surface.21,22,26 This is followed by the propagation of polymer ordering into the particle center upon further solvent evaporation,49 and the particle starts to deform into nonspherical shape (i.e., oblate particle for cylinder-forming dBCPs). Finally, well-ordered oblate particles are formed after complete evaporation of the solvent (Figure 2b). These schematic diagrams are in good agreement with the cryoelectron micrographs acquired at different evaporation times (the emulsion samples were vitrified by liquified nitrogen at evaporation times of 1, 3, 6, and 12 h) as shown in Figure S3b and Figure 2c−e. The initial chloroform emulsion droplet had a spherical shape, with no observable microphase-separated dBCP domain (Figure S3a,b). After solvent evaporation for 3 h, a sufficient amount of chloroform still remained within the dBCP particle, such that the dBCP phase separation was observed only near the particle surface. Larger intercylinder spacing and domain thickness (61.7 and 33.3 nm, respectively) were observed due to the symmetric swelling of both PS and PDMS domains by residual chloroform molecules in the particles. Notably, the PDMS cylinders were oriented perpendicular to the particle surface, which was attributed to the balanced interfacial interaction between the two different domains of the dBCP particles and the surrounding medium (Figure 2c). Further evaporation until 6 h revealed the propagation of perpendicular cylinders from the surface to the particle center (Figure 2d). At this point, the particles started to deform into an oblate shape. The remaining chloroform solvent was removed until 12 h, resulting in the formation of oblate particles with long-range lateral order of the hexagonal dBCP structures (Figure 2e). To explore the effect of the size of the particles on their shape, a series of oblate PS31K-b-PDMS17K particles were produced with different widths (W) in a broad range from 300 nm to 7 μm. Figure 3 shows the side and top views of the PS-b-PDMS particles with three representative W of 500 nm, 1.2 μm, and 2.5 μm. All the particles had regularly ordered cylinders whose domain size and center-to-center distance were 23.3 and 41.4 nm, respectively. To analyze the anisotropy of the particle shape, the aspect ratio (AR = W/H) defined by W divided by the height (H) of the oblate particles was measured from the side view of

Figure 1. (a) Schematic illustration for production of oblate PS31K-bPDMS17K particles from chloroform-in-water emulsion droplets. (b) SEM images of oblate particles and (c) TEM images of oblate particles tilted at angles of 0°, 20°, 40°, and 80°. (d) SEM and (e) TEM images with fast Fourier transform (FFT) (inset) of 10 μm sized oblate PS31Kb-PDMS17K particle having regularly arranged PDMS cylinders.

oblate particles. The internal morphology of the particles was characterized by the TEM image as shown in Figure 1c. The particles had hexagonally arranged dark PDMS domains, which indicated the formation of standing-up cylinders normal to the surface of the particle. From the tilted TEM images, the axially stacked morphology of PS and PDMS was observed, showing overlapped vertical cylinders. Importantly, extremely high degree of lateral order was found to extend over the entire area of all the particles, even for the particles with sizes larger than 10 μm, as shown in the SEM and TEM images with fast Fourier transform (FFT) (Figure 1d,e). A high-degree ordering of the cylinders was further proved by a Voronoi diagram constructed from the locations of the PDMS domain center in the oblate particles, where the center of every domain had six nearest neighbors (Figure S2). To elucidate the formation mechanism of oblate dBCP particles, we examined how dBCPs assemble within the emulsion droplets during the solvent evaporation by investigating the particle structure and morphology using cryo-fixation of emulsion droplet at different stages of evaporation. In general, the emulsion droplets form spherical shape to minimize the interfacial area between the droplet and the surrounding aqueous phase. When dBCP-containing emulsions are subjected to evaporation, the size of the dBCP-containing droplets decreases and, thus, the concentration of the dBCP increases until the nucleation of ordered (microphase-separated) dBCP domains initiates near the interface between the droplet and the surrounding medium (Figure 2a).45,46 The slow solvent evaporation condition in our experimental system provides sufficient time for dBCP chains to reach an energetically stable state. As a result, the thermodynamic effect (neutral interfacial interactions between dBCPs and the surrounding aqueous C

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FFT (Figure 4f). However, in comparison to the oblate particles, the AR of the prolate particles had a weaker dependence on the particle size, showing an AR increase from 1.2 to 2.0 when L was increased from 0.5 to 2.3 μm. Then, the AR became nearly saturated with further increase in L. To explain the different behaviors for the increase of AR as a function of the size of oblate and prolate particles, we developed a theoretical model based on strong segregation theory to calculate the total free energy of the elongated particle. Specifically, we added a term that describes the bending energy of dBCP chains to the free energy equation developed from the previous studies.27 The total free energy of the oblate particle (Fob) with a width of W and a height of H, and consisting of nlayered (from the center to the periphery) dBCP cylinders, can be expressed as the following equation: 2π f Fob = k bT 3b2

Figure 3. (a−c) Side-view SEM, (d−f) top-view SEM, and (g−i) topview TEM images of oblate PS31K-b-PDMS17K particles with different widths of (a, d, g) 500 nm, (b, e, h) 1.2 μm, and (c, f, i) 2.5 μm. The scale bars are 500 nm.

χ HW (2n − 1) 6

π 3(1 −

f )2 W 4H

π 2(1 −

f )2 L0 4C 2Vc

512(1 − f )2 N 2b5 ÄÅ π[(1 − f )γPS + fγPDMS] 2ÅÅÅÅ H2 W ÅÅÅ1 + + α ÅÅ 2(1 + β Σ) 2W 2 1 − H2/W 2 ÅÇ ÉÑ Ñ 1 + 1 − H2/W 2 ÑÑÑ ÑÑ × ln Ñ 1 − 1 − H2/W 2 ÑÑÑÖ (1) +

the SEM image over 200 particles for each sample. We observed that the shape anisotropy of the dBCP particles strongly depends on their respective sizes. For example, as the W increased from 0.5 to 2.5 μm, the H of oblate particle increased by a smaller amount (i.e., from 240 to 510 nm), resulting in a significant increase of AR from 2.1 to 4.9. Next, to compare the trends in the particle size dependent AR increase for the different particle shapes, we produced a series of dBCP particles containing lamella-forming PS16K-b-PDMS17K (f PDMS = 0.5) (Figure 4a). In this case, neutral wetting of dBCP domains to the chloroform/water interface resulted in the nucleation of lamellae perpendicular to the interface when the chloroform evaporated.27,36 Further propagation of the lamellae to the center of the particle enabled the formation of axially stacked lamellar structure, producing prolate particles, as shown in Figure 4b. TEM images in Figures 4c−e show the prolate particles with different lengths (L) ranging from 530 nm to 2.3 μm. All particles had axially stacked PS/PDMS lamellae whose domain size was 16.1 nm. In addition, a high extent of lamellar ordering was found over the entire area of all the particles, even for the 5 μm sized particles, as shown in the TEM images with

96(1 − f )2 N 2b5(2n − 1)2

+

Similarly, the total free energy of prolate particle (Fpr) with a major axis of L and a minor axis of S, consisting of n-layered (from center to edge) dBCP lamellae, can be expressed as the following equation: χ 2 π 3L3S2 S + k bT 6 192N 2b5(2n − 1)2 π[(1 − f )γPS + fγPDMS] 2 π 2L0 4C 2Vc S + + 2 5 2(1 + β Σ)α 1024N b ÄÅ ÉÑ ÅÅ Ñ L sin−1 1 − S2/L2 ÑÑÑ ÅÅ ÑÑ × ÅÅÅ1 + ÑÑ ÅÅ ÑÑÖ S 1 − S2/L2 ÅÇ Fpr

=

(2n − 1)π 3b2

(2)

Figure 4. (a) Schematic illustration for generation of prolate PS16K-b-PDMS17K particles from chloroform-in-water emulsion droplets. (b) SEM and (c−e) TEM images of prolate particles with different major axes of (c) 530 nm, (d) 1.1 μm, and (e) 2.3 μm. (f) TEM image with FFT (inset) of 5 μm sized prolate PS16K-b-PDMS17K particle having axially stacked PDMS lamellae. The scale bars are 500 nm. D

DOI: 10.1021/acs.macromol.8b02465 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules where kb is the Boltzmann constant, T is the temperature, χ is the incompatibility parameter of dBCP, b is the monomer length of dBCP, N is the degree of polymerization of dBCP, f is the volume fraction of minority (PDMS) block, γPS is the interfacial tension between PS domain and surrounding, γPDMS is the interfacial tension between PDMS domain and surrounding, and Σ is the ratio of volume to surface area of particle. α and β are the fitting parameters for the surface energy term between dBCPs and surrounding. The first and second terms on the right-hand side (rhs) of eqs 1 and 2 present the interfacial energies between the two blocks and the chain stretching energy of the dBCPs, respectively, assuming that the oblate particle consists of closepacked cylinder pillars while the prolate particle consists of axially stacked lamellae (Scheme 2). The third term of both of

blocks and the stretching energy of dBCP chains) are minimized when the dBCPs are self-asembled into cylinders or lamellae with L0 as the periodicity.38,39 Consequently, dBCP particles adjust their AR values to satisfy the commensurability condition when the major axis (W of oblate particle and L of prolate particle) is a multiple of L0. Therefore, a harmonic-like free energy behavior is observed near commensurate points (bulk elasticity). When the particle deforms from sphere to oblate or prolate particles, the bending penalty of dBCPs can be released by reducing the curvature of curved layer. However, simultaneously, the surface energy increases due to the increased surface area of dBCP particle. Thus, the competition of these energy contributions determines the final AR of both oblate and prolate dBCP particles. For each particle volume, we numerically calculated the optimized AR for both particle types by minimizing the total free energy. As demonstrated in Figures 3 and 4, the size of a particle is an important parameter that governs the shape of the dBCP particle. To elucidate the effect of particle size on the particle shape, we compared the AR values of a series of PS31K-bPDMS17K oblate and PS16K-b-PDMS17K prolate particles with different major axes. In Figure 5, the AR values for the oblate

Scheme 2. Schematic Illustration of (a) the Oblate Particle Composed of Hexagonally Packed Cylinder Pillars and (b) the Prolate Particle Composed of Axially Stacked Lamellaea

Figure 5. Plots of experimentally measured (●) and theoretically calculated () AR as a function of the major axis (W or L) for representative populations of PS31K-b-PDMS17K oblate (red) and PS16Kb-PDMS17K prolate (green) particles.

a

The scheme illustrates the bending of the dBCP domains along the curved surface of the anisotropic particles, which is particularly emphasized near at the edge of the particles.

particles (red) and prolate particles (green) are plotted as a function of the major axis length (W of oblate particle and L of prolate particle). Also, the black lines were produced from the calculations using the model described above. For the calculation, N and f were set to 527 and 0.34, respectively, to describe PS31K-b-PDMS17K, and those were set to 382 and 0.50, respectively, to describe PS16K-b-PDMS17K. The calculated AR values were well-matched with values that were experimentally observed. As the size of the particles increased, the increase in the volume of the particles resulted in greater contributions of bulk elastic energy and bending energy but in relatively smaller surface energy contributions attributed to the reduced surfaceto-volume ratio. Importantly, the trends of the AR values at larger major axis length were different for the two types of particles. For the oblate particles, the AR values increased almost linearly as a function of W. For example, when the W of the particle increased from 300 to 7000 nm, the AR increased from 1.7 to 9.8. According to this change (an increase in the W value by a factor of 23), the H of the particle was increased by a much smaller amount (i.e., from 150 to 680 nm, a factor of only 4.5)

eqs 1 and 2 indicates the bending energies of curved cylinders at the periphery of the oblate particle (Scheme 2a and Figure S5a) and of the curved lamellae at the edges of prolate particle (Scheme 2b and Figure S5b), respectively, where L0 is the bulk periodicity, C is the curvature of curved layer, and Vc is the total volume of curved layers.50−53 When the cylinders and lamellae of dBCPs are stacked within the oblate and prolate particles, respectively, they are bent along with the particle surface. As a result, the dBCP chains cost high entropic penalty for bending either cylinders or lamellae compared to the unbent bulk cylinders and lamellae. This bending energy can be calculated by multiplying elastic modulus of bulk dBCPs (cylinders for oblate particles and lamellae for prolate particles) by square of curvature of curved layers, as described in the eqs 1 and 2 (see the Supporting Information and Figures S4−S6 for details). The last term in the equation is the surface energy between the dBCPs and the surrounding medium. The first two terms on the rhs of the equations (the interfacial interaction between two E

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Figure 6. Plots of calculated bending energy/surface energy per chain as a function of AR for the (a) oblate particle and (b) prolate particle. (c) Total free energy per chain as a function of AR for the oblate (red) and prolate (green) particles with N = 527 and diameter of spherical emulsion = 2000 nm.

Figure 7. Influence of the molecular weight of the dBCPs on the shape anisotropy of the oblate particles: (a) Plots of experimentally measured (●) and calculated () AR values as a function of the W for representative PS31K-b-PDMS17K (red) and PS11K-b-PDMS5K (blue) particles. (b−d) Side-view SEM and TEM images of (b) PS31K-b-PDMS17K and (c, d) PS11K-b-PDMS5K oblate particles, which show different AR at a given W value.

(Figure S7). By contrast, the increase of the AR for the prolate particles was saturated to near 2.0 even for the very large L. To understand the difference in the AR value between the oblate and prolate particles in terms of the particle size, we calculated the free energies of the oblate and prolate particles with different AR values. Figures 6a and 6b are the plots of bending energy and surface energy per chain of both types of particles as a function of AR. The total volume of polymer chains in a single particle was set to the volume of sphere with a diameter of 2000 nm. We used a fixed N (= 527) to understand the effect of the polymer structure (i.e., f PDMS) on the AR of the particle. For both types of the particles, curvature C and volume of curved layer Vc are decreased as the AR of particle is increased (Figure S8). As a result, the bending energy of the dBCP structures at the periphery of oblate particle and edges of prolate particle is reduced. However, the amount of reduced bending energy is much larger for the oblate particles since the volume of the curved cylinder stacks at the periphery of the oblate particles (approximately πWL0t as shown in Figures S5a and S8a) is much larger than that of the lamellar stacks at the edges of prolate (approximately 2L0A as shown in Figures S5b and S8c), which results in 1 order of magnitude difference in the bending energy as shown in Figures 6a and 6b. Consequently, for the oblate particle, the decrease of the bending energy with increasing AR can compensate for the corresponding increase of the surface energy. By contrast, for the prolate particles, the reduction of the bending energy for the higher AR was insufficient to yield the particles with larger surface area. As a result, the total free energy

is minimized at a much higher value of AR (= 6.63) for the oblate particle compared with the prolate particle (AR value = 2.12) from Figure 6c. We also constructed the free energy plots with different droplet diameters of 1000 and 3000 nm in Figures S9 and S10, respectively. In the case of the oblate particles, the thermodynamically stable AR value increased from 3.94 to 9.02 as the diameter of particle increased from 1000 to 3000 nm. For the larger particle, because of the relatively reduced surface energy contribution (Figure S10a), the AR of the particle increased to release high entropic penalty for bending cylinders. However, for the prolate particle, the surface energy contribution is still dominant compared to the contribution from the bending energy (Figure S10b), resulting in only a slight increase of AR even for the 3000 nm sized particle. Following our quantitative analysis in the previous section, we can further modulate the shape anisotropy of oblate particles by varying the molecular weight (Mn). Figures 7b−d show sideview SEM and TEM images of oblate PS31K-b-PDMS17K (Mn = 48 kg/mol, N = 527) and PS11K-b-PDMS5K (Mn = 16 kg/mol, N = 173) particles. Both the dBCPs show cylindrical structure. All of the PS11K-b-PDMS5K particles were found to be oblate with regularly ordered PDMS cylinders that had a domain size of 7.5 nm and a center-to-center distance of 16.4 nm. Figure 7a shows the plots of experimentally observed and theoretically calculated AR values as a function of W for representative populations of particles (>200 particles). For the case of smaller Mn (16 kg/ mol), a much slower increase of AR in terms of the particle size was observed compared with the case of larger Mn (48 kg/mol). F

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For example, at the same W = 3 μm, the PS11K-b-PDMS5K particles had an AR of 2.2, whereas the PS31K-b-PDMS17K particles showed a much higher AR of 6.4. This is because the energetic penalty for bending of dBCP chains within the particle is higher for the larger Mn BCP chain, which can be relieved by increasing the AR value of the particles. Again, the predictions from our theoretical model show an excellent agreement with the experimental observations for dBCP particles with different Mn. Therefore, our theoretical model can be used for systematic design of the shapes of the prolate and oblate dBCP particles. The increase of particle size, molecular weight, and Flory− Huggins interaction parameter results in more elongated prolate or flat oblate particles due to the increase of the elastic contribution of the dBCP chains to the free energy. In another way, if the interfacial energy on the particle surface is decreased using different surfactant pairs while a neutral surrounding interface (γPS/surr ≅ γPDMS/surr) is satisfied, the AR of the particle will also increase.

ACKNOWLEDGMENTS This research was supported by the Korea Research Foundation Grant, funded by the Korean Government ( 2 01 7 M 3 D 1 A 1 0 3 95 5 3 , 2 0 1 5 M 1 A 2 A 2 0 5 75 0 9 , a n d 2018R1D1A1B07040671). This work was supported by the KETEP and the MOTIE of the Republic of Korea (20163030013620 and 20163010012470). We gratefully acknowledge Prof. Ho Min Kim and Dr. Seong-Gyu Lee at KAIST for the cryo-EM. Also, we acknowledge Prof. Gila Stein and Dr. Hongseok Yun for the helpful discussions.

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CONCLUSIONS Using a concerted experimental and modeling effort, we demonstrated a systematic modulation of shape anisotropy of prolate and oblate dBCP particles by evaporative emulsion droplets. These characteristics are controlled by the Flory−Huggins interaction parameter, molecular weight, and composition of the dBCP. We observed that the AR of the oblate particles was more sensitive to the variation of the particle size compared to that of the prolate particles. The difference was theoretically understood based on the modified model that additionally considers the bending energy of dBCP polymer chains along the curvature at the periphery of the elongated particles in addition to the previously described contributions (i.e., the surface energy, the interfacial energy, and the bulk elasticity). High bending energy of the curved cylinders at the periphery of the oblate particles can result in large elongation of the particles. Also, our experimental observations on the AR change of the dBCP particles with different Mn were quantitatively explained based on the calculations by our model. We believe that our study provides a comprehensive understanding of thermodynamic parameters in manipulating the shape and inner structure of dBCP particles, which is very important for a variety of practical applications of anisotropically shaped particles such as coating, emulsions, and smart materials. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02465.

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Additional TEM and SEM images of particles; detailed free energy calculation (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (B.J.K.). *E-mail: [email protected] (Y.J.K.). ORCID

Kang Hee Ku: 0000-0002-6405-8127 Bumjoon J. Kim: 0000-0001-7783-9689 Notes

The authors declare no competing financial interest. G

DOI: 10.1021/acs.macromol.8b02465 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b02465 Macromolecules XXXX, XXX, XXX−XXX