Aspect Ratio-Controlled Synthesis of Uniform Colloidal Block

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Aspect Ratio-Controlled Synthesis of Uniform Colloidal Block Copolymer Ellipsoids from Evaporative Emulsions Jae Man Shin, YongJoo Kim, Kang Hee Ku, Young Jun Lee, Eun Ji Kim, Gi-Ra Yi, and Bumjoon J. Kim Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b01821 • Publication Date (Web): 06 Aug 2018 Downloaded from http://pubs.acs.org on August 7, 2018

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Chemistry of Materials

Aspect Ratio-Controlled Synthesis of Uniform Colloidal Block Copolymer Ellipsoids from Evaporative Emulsions Jae Man Shin1, YongJoo Kim2, Kang Hee Ku1, Young Jun Lee1, Eun Ji Kim1, Gi-Ra Yi*,3 and Bumjoon J. Kim*,1,2

1

Department of Chemical and Biomolecular Engineering, 2KAIST Institute for NanoCentury,

Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea 3

School of Chemical Engineering, Sungkyunkwan University, Suwon 16419, Republic of Korea

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

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ABSTRACT Block copolymers (BCPs) confined in evaporative emulsions can assemble into ellipsoidal particles when solvent evaporation is faster than polymer diffusion within the droplet. Here, we report the synthesis of monodisperse, ellipsoidal polystyrene-block-1,4-polybutadiene (PS-b-PB) BCP particles with tunable aspect ratios (ARs) ranging from 1.0 to 2.2, and particle sizes ranging from 0.1 to 5 μm by membrane emulsification and subsequent solvent evaporation. The ratio of the propagation distance (lp) of ordered BCP domains perpendicular to the particle surface to the particle size (rBCP), or lp/rBCP, was found to be a critical parameter dictating the particle shape, where lp/rBCP >1 yielded ellipsoids. We show that the AR of colloidal BCP ellipsoids can be precisely controlled by varying particle size (i.e., membrane pore size) and BCP molecular weight, as predicted by theoretical calculations of the free energy of particle elongation including three terms: (1) the interfacial energy between the two blocks of the BCP; (2) the entropic penalty associated with stretching of the BCP chains upon elongation of the particles; and (3) surface energy between the BCP particles and the surrounding medium. Finally, using the resulting ARcontrolled and highly monodisperse colloidal ellipsoids, we systematically investigated the effects of AR on the homogeneity of colloidal coatings obtained by drop-casting the ellipsoids into films.


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INTRODUCTION Anisotropically shaped particles have received significant attention for their unique shapedependent properties in the context of photonics, rheology, phase behavior, and packing structure, among others.1–7 Recent studies have shown that the self-assembly of block copolymer (BCP) confined in emulsion droplets8–10 can be an effective route to generate non-spherical microparticles.11–25 Droplets containing BCPs act as soft and mobile templates that, upon solvent evaporation, deform into asymmetric particles, including prolate ellipsoids and oblate convex lensshaped particles with well-ordered internal nanostructures, in order to minimize the free energy penalty associated with bending of BCP chains. Further development of such approaches toward non-spherical BCP particles with well-controlled shape and internal nanostructure is needed for the production of tailorable particles for implementation in applications such as optical lenses, sensors, catalysts, and dielectric resonators.15,26–29 Nevertheless, it has been a great challenge to produce highly monodisperse ellipsoidal particles of BCPs with precisely-controlled aspect ratios (ARs) and sizes, which is a critical requirement for implementing the particles into most of the applications mentioned above. Previously, we demonstrated that tuning the evaporation rate of solvent from BCP-containing emulsions induces a transition in the shape of polystyrene-block-polybutadiene (PS-b-PB) BCP particles from onion-like spheres to ellipsoids with striped lamellae.30 In this report, we demonstrate the precise control of the AR of monodisperse PS-b-PB ellipsoid particles synthesized on large scales. In addition, the uniformity of the AR and size of the generated ellipsoids enabled systematic analysis and development of theoretical models that support the formation mechanism of these particles. These studies yielded the following conclusions regarding the formation of 3 ACS Paragon Plus Environment


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monodisperse ellipsoids with well-defined ARs: 1) the successful formation of ellipsoidal particles requires the propagation of lamellae oriented perpendicular to the particle surface into the core during solvent evaporation, where the propagation distance (lp) of these perpendicular lamellae should be larger than the particle radius; 2) under conditions yielding ellipsoid formation, the AR can be precisely controlled by tuning particle size and BCP molecular weight (Mn). As the ellipsoid size and overall Mn of BCP increased from 0.1 to 5 μm and from 59 to 216 kDa, respectively, the AR of the ellipsoids increased from 1.00 to 2.16. Particle ARs were quantitatively predicted by a theoretical model that calculates the degree of particle elongation, expressed as a function of three terms associated with the interfacial energy between the two blocks of the BCP, the entropic penalty of chain stretching, and the surface energy between the particle and the surrounding medium. Finally, using monodisperse AR-controlled BCP particles, we systematically investigated the coating properties of the colloidal solutions, which yielded films with varying degrees of homogeneity with respect to ellipsoid AR.


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EXPERIMENTAL Materials Three different symmetric poly(styrene-b-1,4-butadiene) (PS-b-PB) BCPs were purchased from Polymer Source, Inc: (1) PS34k-b-PB25k (subscripts indicate the number-average molecular weight (Mn) of each block), dispersity (Ð ): 1.20); (2) PS67k-b-PB75k (Ð : 1.08); and (3) PS112k-b-PB104k (Ð : 1.06). Sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide (CTAB) were purchased from Sigma Aldrich. Benzene, toluene, p-xylene and tetrahydrofuran (THF) were purchased from Samchun Chemical and used as received. Preparation of PS-b-PB Colloidal Particles by Membrane Emulsification A solution containing 10 mg/mL of PS-b-PB (PS34k-b-PB25k, PS67k-b-PB75k, or PS112k-b-PB104k) in toluene (4 mL) was emulsified in a continuous phase (CP) containing 5 mg/mL SDS in deionized (DI) water (80 mL) using a Shirasu porous glass (SPG) membrane device.31 Monodisperse emulsion droplets of PS-b-PB were generated by passing the organic phase through the SPG membrane. To control droplet size, membranes with various pore sizes (dpore = 5.1, 2.1, 1.1, 0.5 and 0.2 μm) were employed. After emulsification, the organic solvent was evaporated at 30 ºC while stirring at 250 rpm. To vary the evaporation rate, 80 mL of the emulsion was separated into four different containers with varied interfacial area between the emulsion and air (Aemul/air = 26.4 and 0.1 cm2).30 Evaporation rate was quantified as φ values, defined as the volumetric rate of solvent loss per droplet volume in units of h-1. To obtain φ values for each evaporation condition, a plot of volume of individual droplets (VD) as a function of evaporation time (tevap) was constructed by measuring the residual solvent in the sample at different tevap using gas chromatography (GC). This plot was fitted with the relation VD(t) = (V0/ND)exp(−φtevap) to yield φ 5 ACS Paragon Plus Environment


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values, where V0 is the total volume of the droplets and ND is the number of droplets. In this work, two representative conditions were used primarily, namely φ = 0.26 h-1 (Aemul/air = 26.4 cm2) to form ellipsoids, and φ = 0.03 h-1 (Aemul/air = 0.1 cm2) to form onion-like particles. Drying of Suspensions Containing Particles for Observation of the Coffee-ring Effect Before drop-casting the colloidal suspensions, residual SDS was thoroughly removed by repeated centrifugation and re-dispersion in DI water (at least 5 times), and the substrates (glass slides purchased from Marienfeld) were washed and sonicated in acetone and ethanol. To observe the particle deposition patterns as a function of AR, particle suspensions (1 μL, Ф = 0.15, i.e. the particle volume fraction in the suspension) with varying ARs were drop-casted onto glass slides and dried in air. Deposition patterns were observed by optical microscopy. For larger scale drop evaporation, 0.5 mL of suspensions (Ф = 0.15) with varying AR were placed on the glass slide and dried in air. To evaluate the homogeneity of the film, 3 μL of DI water was dispensed more than 5 times in random locations on the film. The water contact angle (WCA) values were measured and averaged using a KRUSS DSA 30 drop shape analysis program. Characterization Field-emission scanning electron microscopy (FE-SEM) (Nova230) and transmission electron microscopy (TEM) (JEOL 2000FX) were used to characterize particle shape and internal morphology. Particle dispersions were stained with an aqueous solution of 0.2 wt% osmium tetraoxide (OsO4), which selectively stains PB. After staining, the samples were washed with DI water to remove excess surfactant by repeated centrifugation at 12,000 rpm. For SEM samples, the particle suspension was drop-casted onto silicon wafers, which were then dried and sputtered with platinum. For TEM, the particle suspension was drop-casted onto TEM grids coated with 206 ACS Paragon Plus Environment

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30 nm thick carbon layers, and dried in air. To investigate the internal structures of the BCP particles by cross-sectional TEM, the samples were prepared by drop-casting the particle suspensions onto an epoxy film and drying the treated film. Then, the dried samples were exposed to OsO4 vapor to selectively crosslink the PB domains of PS-b-PB. Then, the epoxy-supported films were cured in an oven at 60 °C for 24 h. The epoxy-supported films were then microtomed with a diamond knife at room temperature into 50 nm slices. GC was used to measure the residual amount of toluene in the emulsions, which was extracted using benzene prior to the measurements as follows: 0.5 mL of dispersion was withdrawn at designated tevap, and 5 μL of internal standard (p-xylene) was added. An equimolar amount of CTAB relative to the SDS in the solution was then added to form an electrostatic surfactant complex, since the high polarity of SDS precludes its elution from the GC column.32,33 Benzene (0.5 mL) was added as the extracting solvent, and the mixture was vortexed for 1 min. The mixture was stored at 4 ºC, and the supernatant organic phase was subjected to GC analysis. To measure the saturated concentration of toluene in the CP (Csat) as a function of SDS concentrations (CSDS), 1 mL of CP and 1 mL of toluene were combined and vortexed for 1 min. After 1 d, separation of the toluene phase from the aqueous phase was observed, and 0.2 mL of the bottom aqueous phase was withdrawn. Internal standard (2 μL of p-xylene) was added and the solution was diluted to a total volume of 1 mL in THF for GC. Csat values at 30 ºC were measured to be 0.70, 1.23, and 6.89 mg/mL for CSDS = 0, 5, and 20 mg/mL, respectively. Calculation of Ellipsoid AR



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Similar to the previous model developed by Fredrickson,12,14 the total free energy of elongation of BCP particles with n-layered lamellae into ellipsoids with L and S as the lengths of the major and minor axes, respsectively, is described by

𝐹 𝑘𝑏 𝑇

=

𝜋

𝜒

√ 𝑆2 ( 12𝑏2 6

2𝑛2 +1

𝜋 2 𝐿3 𝑆 2

𝑛

48𝑁 2 𝑏5 𝑛

)+

+ 2

𝜋(𝛾𝑃𝑆 +𝛾𝑃𝐵 ) 4(1+𝛽Σ)𝛼

𝑆 2 [1 +

𝐿 sin−1 √1−𝑆 2 /𝐿2 𝑆√1−𝑆 2 /𝐿2

]

[1]

where kb is the Boltzmann constant, T is temperature,  is the Flory-Huggins interaction parameter between the two blocks of the BCP, b is the statistical segment length, N is the degree of polymerization, PS is the interfacial tension between the PS block and the surrounding aqueous medium, PB is the interfacial tension between the PB block and the surrounding aqueous medium, ∑ is the ratio of the volume to the surface area of the particles, and  and  are fitting parameters for the term associated with the interfacial energy between the BCP particles and the surrounding media. For PS-b-PB,  and b were set to 0.04 and 0.6 nm, respectively, and PS and PB were set to 30.0 mJ/m2 and 3.6 mJ/m2, respectively, from contact angle measurements of each polymer film upon addition of water with SDS above the critical micelle concentration (CMC). Thus, the free energy of particle elongation becomes a function of fitting parameters, the volume and AR of the BCP particle, and the number of layers. Therefore, for each BCP particle volume, free energy was minimized with optimized n and S values to obtain AR as a function of L. The fitting parameters were optimized to  = 1.96 and  = 1.85 nm for the plot of AR as a function of L from experimental data collected from monodisperse PS67k-b-PB75k BCP ellipsoidal particles. For the PS34k-b-PB25k and PS112k-b-PB104k particles, AR plots were obtained using same fitting parameters as for the PS67k-b-PB75k case.


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RESULTS and DISCUSSION PS-b-PB BCP ellipsoidal particles were produced by solvent evaporation from monodisperse emulsions formed by membrane emulsification. Three lamellae-forming symmetric BCPs with different overall molecular weights (PS34k-b-PB25k, PS67k-b-PB75k, and PS112k-b-PB104k) were dissolved in toluene. Following the emulsification of the BCP solutions into an aqueous solution containing 5 mg/mL of SDS surfactant, particles were produced upon evaporation of toluene, where evaporation rate was controlled by varying the interfacial area between the emulsion and the air (Aemul/air).30 In this work, φ = 0.26 h-1 (Aemul/air = 26.4 cm2) was the most frequently used, yielding predominantly PS-b-PB ellipsoids. Using four membranes with pore diameters (dpore) of 0.2, 0.5, 1.1, and 2.1 μm,31,34,35 various ellipsoidal particles were obtained as summarized in Table 1, which shows four key parameters, L, S, AR, and particle volume, obtained by analyzing more than 200 particles per batch using ImageJ.36 Importantly, all of the ellipsoidal particles produced in these studies can be considered monodisperse since their coefficients of variation (CV) were ca. 10 %. The diameter (dBCP) and volume of analogous spherical particles with onion-like morphologies produced at a slower evaporation rate (φ = 0.03 h-1) are also shown in Table 1 as control systems.30 For emulsions produced from membranes with the same dpore, the volume of the resulting ellipsoidal particles was found to be similar to that of the spherical particles generated using slower evaporation rates.



Table 1. Dimensions (major axis (L), minor axis (S) and AR (L/S)) and volume of the ellipsoidal BCP particles produced from BCPs with different Mn and from membranes with different dpore. The dBCP and volume of spherical particles, produced identical conditions as the corresponding ellipsoidal particles but with a much lower φ value of 0.03 h-1, are also provided.

PS67k-b-PB75k

PS112k-b-PB104k

Mn

PS34k-b-PB25k

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Ellipsoids

Spheres (Onions)

dpore (μm)

L (μm)

S (μm)

AR (L/S)

2.1

2.77 ± 0.25

1.28 ± 0.13

2.16

2.38×100 1.56 ± 0.14 1.99×100

1.1

1.44 ± 0.15

0.79 ± 0.06

1.82

4.71×10-1 1.00 ± 0.09 5.24×10-1

0.5

0.62 ± 0.06

0.41 ± 0.03

1.51

5.46×10-2 0.43 ± 0.04 4.16×10-2

0.2

0.24 ± 0.03

0.19 ± 0.02

1.23

4.54×10-3 0.20 ± 0.03 4.19×10-3

2.1

2.29 ± 0.25

1.17 ± 0.10

1.96

1.64×100 1.48 ± 0.15 1.70×100

1.1

1.33 ± 0.13

0.80 ± 0.06

1.67

4.46×10-1 0.99 ± 0.10 5.08×10-1

0.5

0.60 ± 0.06

0.44 ± 0.03

1.36

6.08×10-2 0.45 ± 0.05 4.77×10-2

0.2

0.21 ± 0.02

0.18 ± 0.02

1.16

3.56×10-3 0.20 ± 0.02 4.19×10-3

2.1

1.94 ± 0.15

1.39 ± 0.07

1.39

1.97×100 1.51 ± 0.15 1.80×100

1.1

1.11 ± 0.11

0.87 ± 0.08

1.27

4.40×10-1 0.98 ± 0.11 4.93×10-1

0.5

0.55 ± 0.04

0.46 ± 0.02

1.18

6.09×10-2 0.44 ± 0.05 4.46×10-2

0.2

0.20 ± 0.02

0.19 ± 0.02

1.04

3.78×10-3 0.20 ± 0.03 4.19×10-3

Volume (μm3)

dBCP (μm)

Volume (μm3)

Understanding Ellipsoid Formation from Evaporative Emulsions The solvent evaporation rate is an important parameter governing the morphological transition from onion-like to ellipsoidal particles,30 but this transition is also significantly influenced by particle size.37 Therefore, in this section, we first try to understand how BCPs assemble during solvent evaporation from BCP-containing emulsions. Then, we develop a simple,


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but quantitative model for predicting the propagation distance of lamellae (lp) from the particle surface into the core, which explains the size-dependent particle shape and morphology.

Figure 1. (a) Schematic illustration showing the stages of ellipsoid formation from BCPcontaining emulsion droplets. This schematic is aligned with accompanying microscopy images of emulsion containing PS112k-b-PB104k produced from membranes with dpore = 1.1 μm at different evaporation times (tevap). (b) Optical microscopy image of an as-prepared emulsion (tevap = 0 h) with an average droplet diameter of 4 μm. TEM images of BCP particles obtained at different evaporation times: (c) tevap = 6 h, (d) tevap = 8 h, and (e) tevap = 15 h. Evaporation conditions were fixed at φ = 0.26 h-1. In TEM images, PB domains appear dark due to OsO4 staining.

When BCP-containing emulsions are subjected to evaporation, solvent is transported from the inside of the droplets to the air through multiple steps, resulting in BCP particles as shown in Figure 1(a). First, solvent inside the emulsion is transported by diffusion from the droplet to the continuous phase (CP, red arrows, step 1), driven continuously by evaporation of solvent from the 11 ACS Paragon Plus Environment


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CP through the emulsion/air interface (purple arrows, step 1).38,39 Thereby, the droplet diameter decreases gradually and the BCPs are concentrated near the droplet surface, at which lamellar domains form perpendicular to the surface (step 2). Further evaporation leads to propagation of these perpendicular domains into the droplet center, and the particle starts to deform into an ellipsoidal shape (step 3). Finally, well-ordered ellipsoids are formed after complete evaporation of solvent (step 4). These schematic diagrams are in good agreement with optical and electron micrographs acquired at different evaporation times (tevap) as shown in Figure 1(b-e). Before evaporation, the average diameter of emulsion droplets formed from a membrane with dpore = 1.1 μm was 4 μm, which decreased gradually upon continuous solvent diffusion/evaporation (Figure 1(b)). After solvent evaporation for 6 h, the BCPs formed ordered structures at the surface of the particle, oriented perpendicular to the surface (Figure 1(c)). However, no clear morphology was observed near the particle center due to the significant amount of toluene still remaining inside the droplet, which supported the formation of lamellar domains from the particle surface. Further evaporation until tevap = 8 h revealed propagation of perpendicular lamellae from the surface to the particle center (Figure 1(d)). At this point, the particles started to elongate into ellipsoidal shapes. The remaining toluene solvent was evaporated until tevap = 15 h to generate ellipsoids with wellordered BCP structures (Figure 1(e)). Therefore, to develop a quantitative analytical model to describe the formation of ellipsoidal particles, it is important to understand steps 2 and 3 depicted in Figure 1(a), in which sufficiently high solvent concentration gradient in the radial direction drives the propagation of the perpendicularly-oriented BCP structures into the center of the particles.


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Figure 2. TEM images of PS112k-b-PB104k ellipsoidal particles produced from membranes with various pore sizes (dpore = 0.5, 1.1, and 2.1 μm) at different tevap of 6, 8, 9, 15, and 20 h. The Aemul/air was fixed at 26.4 cm2 for a constant solvent evaporation rate of φ = 0.26 h-1. Emulsion samples were acquired at each tevap and crosslinked immediately with OsO4 aqueous solution to minimize undesired morphological changes during TEM sample preparation.

Figure 2 summarizes the evolution of the monodisperse droplets of PS112k-b-PB104k with three different diameters, which were produced by varying the dpore = 2.1, 1.1, 0.5 μm, at different tevap = 6, 8, 9, 15, and 20 h. For dpore = 2.1 μm, lamellar BCP domains were observed at the particle surface when tevap = 8 h (Figure 2(a, b)). The BCP structures propagated further inward at tevap = 9 h and showed a more clear striped lamellar morphology (Figure 2(c)). Subsequent elongation into ellipsoids with swollen PB domains in the center (54 nm) were observed at tevap = 15 h (Figure 2(d)) due to preferential escape of toluene through the PB phase.30 The variation of PB domain 13 ACS Paragon Plus Environment


thickness depending on the position in the ellipsoid supports the formation of toluene concentration gradient (Figure S1 and Table S1). Finally, at tevap = 20 h (Figure 2(e)), the observation of ellipsoids with similar domain thicknesses of 33 nm (PS) and 34 nm (PB), suggested the complete removal of toluene. To show the morphological evolution process more clearly, cross-sectional TEM images for dpore = 2.1 μm were taken at each tevap (Figure S2). For dpore = 1.1 μm, although the BCPs formed ordered structures at the particle surface similarly at tevap = 6 - 8 h (Figure 2(f, g)), elongated ellipsoids with swollen PB domains (57 nm) were observed at tevap = 9 h (Figure 2(h)), earlier than that in dpore = 2.1 μm. Similarly, ellipsoids having similar domain thicknesses of PS and PB were observed earlier, starting from tevap = 15 h (Figure 2(i)). The faster morphological evolution within smaller emulsion droplets was even more apparent for particles formed using membranes with dpore = 0.5 μm. Well-ordered ellipsoids with swollen PB domain (55 nm) formed quickly, even before the tevap = 6 h time point (Figure 2(k)), in contrast to two other cases of dpore = 1.1 and 2.1 μm. The thickness of the PB domains reduced rapidly to the size of the PS domains at tevap = 8 h (Figure 2(l-o)) due to the faster solvent removal from the smaller emulsion droplets. Therefore, from the set of TEM images shown in Figure 2, we conclude that lamellar structures first form perpendicular to the droplet/particle surface and then grow inward, which induces a shape change from spherical to ellipsoidal particles. To understand the formation kinetics of the ellipsoidal particles with different particle sizes and quantitatively determine the solvent evaporation rate, we measured the amount of residual toluene in the emulsion at different tevap using gas chromatography (GC) (Table S2). At a given evaporation time, more toluene was found in larger droplets with at least an order of magnitude difference. For example, the residual volume of toluene in each droplet at tevap = 9 h was determined to be 1.74×10-8 µL for dpore = 2.1 µm, 2.50×10-9 µL for dpore = 1.1 µm, 2.35×10-10 µL for dpore = 0.5 µm, and 1.50×10-11 µL for dpore 14 ACS Paragon Plus Environment

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= 0.2 µm. These results are consistent with the slower formation of particle in larger droplets. Once the ordered BCP structures and the PS domain becomes vitrified form near the droplet surface where the solvent concentration is the lowest, the solvent diffusivity from the particle to the surrounding media is expected to be significantly reduced. In the case of smaller particles, the distance through which the perpendicular lamellar structures must propagate is small such that the BCP structures are constructed faster throughout the particle to produce nicely-ordered ellipsoids. By contrast, as the particle radius becomes larger, a longer time is required for the propagation of the BCP structures from the surface into the core, significantly slowing the formation of ellipsoidal particles.37 To understand the particle size-dependent morphological evolution of the BCP particles in a quantitative manner, we defined the propagation distance of perpendicular lamellae from the surface toward the particle center (lp) and attempted to estimate this value. We first adopted a mathematical model developed by Cussler et al.40 that described the formation of BCP structures in thin films upon solvent evaporation. In this model, the key of achieving perpendicular orientation of BCP domains relative to the surface was the formation of substantial solvent concentration gradients at the air-film interface upon rapid solvent evaporation. Consistent with this model, the results in Figures 1 and 2 suggest the presence of sharp toluene concentration gradients radially along the droplet, analogous to the solvent gradients generated normal to BCP film surfaces.40–44 Therefore, we assume that radial diffusion of solvent within the droplet (i.e., from the center to the droplet surface) is slower than the mass transfer of solvent from the droplet to the CP. In such case, time required for complete solvent evaporation (tc) scales with the square of the radius of the droplet:45,46 15 ACS Paragon Plus Environment


𝑟2

𝑡𝑐 ~ 𝐷

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[2]

where r is the radius of the droplet and D is the diffusivity of solvent (toluene) within the droplet. Equation [2] indicates a strong dependence of tc on droplet size, which is consistent with our observations in Figure 2. Furthermore, Cussler et al. expressed the solvent concentration profile at the film surface as a function of drying time by assuming that the film is very thick (i.e., that the film surface is far from the substrate). This expression yielded the characteristic time of the system (τ), which is important in determining the solvent concentration profile within the film and the starting point of BCP nucleation. This characteristic time is given as:

𝜏 =

𝐷𝐻 2 𝑘2

[3]

where H is the partition coefficient of solvent between the droplet and CP, and k is the mass transfer coefficient of solvent at the CP-droplet interface. The concentration profile at time τ provides an estimate for the distance into the film that perpendicular orientation can be sustained. Therefore, by assuming that a droplet surface is sufficiently far from the center (i.e., in large droplets similar to the thick BCP film case), the propagation distance of perpendicularly orientated BCP nanostructures can be estimated as l ~ (Dt)1/2 until the evaporation time equals to DH2/k2, at which point the perpendicular orientation of BCP domain will be sustained. Therefore, lp can be expressed as: 𝑙𝑝 =

𝐷𝐻 𝑘

[4]

The lp values in our system can be determined by estimating the coefficients in equation [4]. First, the partition coefficient (H) of the poly(styrene-b-butadiene-b-styrene) (SBS) and toluene system 16 ACS Paragon Plus Environment

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at 30 ºC was estimated to be 618 from the literature.47 The diffusivity of toluene (D) within the droplet was obtained from the following equation:48–50 D = Do (1−Фp)2 (1−2χp-sФp)

[5]

where Do is the solvent self-diffusivity, Фp is the volume fraction of polymer and χp-s is the Flory– Huggins interaction parameter between the polymer components and the solvent. Since the diffusion of toluene is limited near the particle surface where the Фp is the highest,51–53 we calculated the D value of toluene at the particle surface. We can assume that the BCPs start to vitrify at the Фp value where the glass transition temperature (Tg) of PS chains in toluene reaches the temperature of the system (30 ºC). Therefore, we used the Fox equation54 for PS and toluene to find the Фp of PS that yields a Tg = 30 ºC as following: 1 𝑇𝑔

𝑤𝑝

=𝑇

𝑔,𝑝

𝑤

+𝑇𝑠

𝑔,𝑠

[6]

where the Tg,p of neat PS (373 K) and Tg,s of toluene (=137.5 K) were used to calculate the weight fraction of polymer (wp), which yielded the volume fraction Фp of 0.842.55 The Do of toluene at 30 º

C was estimated to be 10-8 cm2/s from the literature.47 Inserting all of these values into equation

[5] with χPS-tol = 0.34, we obtained D = 1.07×10-10 cm2/s. To estimate the value of the mass transfer coefficient (k, cm/s), the mass balance of solvent (toluene) in the CP is derived based on previous reports describing solvent evaporation from emulsion droplets:39,56–58 𝑑𝐶

𝑉𝑒𝑚𝑢𝑙 𝑑𝑡 = 𝑁4𝜋𝑅 2 𝑘(𝐻𝐶𝑑 − 𝐶) − 𝑘𝑒𝑚𝑢𝑙/𝑎𝑖𝑟 𝐴𝑒𝑚𝑢𝑙/𝑎𝑖𝑟 𝐶

[7]

where Vemul is the volume of the entire emulsion, C is the concentration of solvent in the CP, N is the number of droplets, R is the droplet radius, k is the mass transfer coefficient of solvent at the 17 ACS Paragon Plus Environment


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droplet/CP interface, Cd is the concentration of solvent inside the droplet, and kemul/air is the mass transfer coefficient at the CP/air interface. On the right-hand side of equation [7], the first term represents the rate of the interfacial mass transfer of solvent from the droplet to the CP, and the second term is the evaporation rate of solvent from the CP to the air. In particular, among the two different mass transfer coefficients (k and kemul/air), the k value is most important in this system since it directly affects the structure formation of BCP domains at the droplet surface. The k and kemul/air values were determined by analyzing the C vs. tevap profiles obtained from the equation [7] for the evaporation of toluene from toluene-in-water emulsion without BCPs (Figure S3). There are two stages of solvent removal in the C vs. tevap curve. In the early stage, the CP is saturated with solvent, where the quantity of the evaporated solvent is compensated by the solvent transferred from the droplet to the CP and C remains constant (i.e., C = Csat). In the later stage, C decreases exponentially, since solvent removal is dominated by evaporation from the CP to the air. Therefore, the interfacial mass transfer into the CP becomes negligible at the later stage, and first term in the equation [7] can be approximated as 0. Integrating equation [7] in this case gives: 𝐶 = 𝐶0 𝑒𝑥𝑝(−𝑘𝑒𝑚𝑢𝑙/𝑎𝑖𝑟

𝐴𝑒𝑚𝑢𝑙/𝑎𝑖𝑟 𝑉𝑒𝑚𝑢𝑙

𝑡)

[8]

where C0 is the initial concentration of the organic solvent (i.e., toluene). To determine kemul/air, fitting the curve with equation [8] provides an exponential decay constant of kemul/airAemul/air/Vemul =1.64 h-1. For ellipsoid-forming solvent evaporation conditions used in our work (i.e., Vemul = 20 mL, Aemul/air = 26.4 cm2), kemul/air was estimated to be kemul/air = 3.45×10-4 cm/s. In the early stage of solvent evaporation, dC/dt = 0 and solving equation [7] for k gives:

𝑘=

𝑘𝑒𝑚𝑢𝑙/𝑎𝑖𝑟 𝐴𝑒𝑚𝑢𝑙/𝑎𝑖𝑟 𝐶𝑠𝑎𝑡 𝑁4𝜋𝑅 2 (𝐻𝐶𝑑 −𝐶𝑠𝑎𝑡 )

[9] 18

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Using the obtained value of kemul/air = 3.45×10-4 cm/s, k was calculated to be k = 4.21×10-4 cm/s. More detailed description of the estimation of k and kemul/air values is provided in the Supporting Information. Finally, using the estimates above, perpendicular lamellae are predicted to grow from droplet surface toward the center until lp = (1.07×10-10 cm2/s)(618)/(4.21×10-4 cm/s)=1.57 μm (equation [4]).



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Figure 3. (a-d) SEM images of PS112k-b-PB104k ellipsoids prepared using membranes with different dpore: (a) 0.2 µm; (b) 0.5 µm; (c) 1.1 µm; and (d) 2.1 µm, all corresponding to the case where (e) lp > rBCP. Insets are magnified TEM images. (f) SEM and (g) TEM images of PS112k-b-PB104k 20 ACS Paragon Plus Environment

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particles prepared using membranes with dpore = 5.1 µm, corresponding to the case where (h) lp < rBCP. Evaporation conditions was fixed at φ = 0.26 h-1.

Considering lp = 1.57 μm as a criterion for the propagation of the BCP structure from the surface towards the center of the particles, the morphological evolution of BCP particles was investigated as a function of emulsion droplet/particle size. Figure 3 shows that monodisperse, well-ordered PS112k-b-PB104k ellipsoids can be generated from membranes with dpore = 0.2 - 2.1 μm (Figure 3(a-d)), whereas, in the case of dpore = 5.1 μm (Figure 3(f, g)), most of the particles showed non-ellipsoidal shape. Given that the lamellae formed perpendicular to the particle surface must propagate into the particle center for the generation of ellipsoids, we expect the ratio of lp value relative to the particle radius after complete evaporation of solvent (𝑟𝐵𝐶𝑃 =

𝑑𝐵𝐶𝑃 2

) to be an

important parameter determining the formation of ellipsoidal particles. For this study, we considered the rBCP of spherical particles having similar particle volumes as those of ellipsoids generated from membranes with the same dpore (as summarized in Table 1) because the radius of the spherical droplet at the starting point of elongation is similar to the rBCP value. The radii of spherical particles obtained from membranes with dpore = 0.2, 0.5, 1.1, 2.1, and 5.1 μm were found to be rBCP = 0.10, 0.22, 0.50, 0.74, and 1.85 μm, respectively, where the corresponding SEM images of these spherical particles are provided in Figure S4. Since the rBCP values are lower than lp = 1.57 μm (lp > rBCP), the perpendicular lamellae propagate to the particle center successfully, consistent with the uniform-sized and well-ordered ellipsoids formed from membranes with dpore = 0.2 – 2.1 µm (Figure 3(a-e)). However, since the large particles produced from membranes with dpore = 5.1 μm have rBCP = 1.85 μm, which is larger than the estimated critical value of lp = 1.57 21 ACS Paragon Plus Environment


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μm (lp < rBCP), the perpendicular lamellae at the surface are not expected to reach the particle center. Therefore, even though the perpendicular lamellae are initially formed near the particle surface, ellipsoid formation is non-uniform as shown in Figure 3(f) due to the orientation shift of the lamellae from perpendicular to parallel at some point between the particle surface and the core (Figure 3(h)). Indeed, Figure 3(g) shows the TEM images of resulting intermediate (cone-shaped) particles having lamellae with mixed orientations relative to the surface (consisting of parallel lamellae inside the hemisphere of the particle, and perpendicular lamellae inside the cone-like part). Such mixed orientation inside the particle suggests that the perpendicular lamellae do not fully propagate to the particle center, and the orientation of BCP shifts from perpendicular to parallel inside the particle. Therefore, the observed particle morphologies support our hypothesis that when lp < rBCP, perpendicular lamellae will grow only a finite distance from the particle surface before reaching the particle center. Overall, the estimation of the critical lp = 1.57 μm of the system explains the propagation of the perpendicularly oriented BCP particles with respect to particle size and thus provides design criteria for the successful formation of ellipsoidal BCP particles.

Figure 4. SEM images of PS112k-b-PB104k particles obtained by emulsification through membranes with dpore = 5.1 μm at different SDS concentrations (CSDS) in the CP: CSDS = (a) 5 and (b) 20 mg/mL. (c) Histograms show the percentage of ellipsoids (black) compared to other particle morphologies (red). 22 ACS Paragon Plus Environment

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To enhance the size controllability of ellipsoids, we attempted to increase the lp of the system by increasing the CSDS. The presence of more surfactant in the CP enhances the extraction capacity of toluene to the CP (Csat) by serving as toluene reservoir. Figure 4 shows the SEM images of PS112k-b-PB104k particles obtained using membranes with dpore = 5.1 μm at different CSDS of (a) 5 and (b) 20 mg/mL. The corresponding histograms in Figure 4(c) show the fraction of ellipsoidal particles in each batch. Indeed, remarkable increase of the percentage of ellipsoids in the batch from 30% to 89% was achieved, as the CSDS was increased from 5 to 20 mg/mL. It should be noted that the increased ellipsoid formation is not due to the change in interfacial tension between the droplet and the surrounding media, since CSDS = 5 mg/mL is already above the critical micelle concentration (CMC) of SDS (2.36 mg/mL).59 Rather, the increase of CSDS to 20 mg/mL enhances the solubility of toluene in the CP (i.e., increasing Csat), as reported in previous work showing the solubility of organic compounds in aqueous phase to increase with surfactant concentration, even above the CMC.60 Accordingly, GC measurements revealed a significant increase of Csat from 1.23 to 6.89 mg/mL upon increasing CSDS from 5 to 20 mg/mL. As a result, the additional toluene in the CP decreases the mass transfer rate due to the reduced concentration difference of toluene between the droplet and the CP.58,61,62 Therefore, the lp value of the system is expected to increase, consistent with the salient increase in the percentage of ellipsoids (from 30 to 89%) with increasing CSDS.



Precise Control of AR in Ellipsoids

Figure 5. TEM images demonstrating the ability to control the AR of ellipsoidal particles by variation of the Mn of PS-b-PB and the membrane dpore.

Based on our quantitative analysis in the previous section, we produced a series of monodisperse ellipsoidal particles with controlled AR values in a range from 1.0 to 2.2 simply by tuning the membrane dpore from 0.2 – 2.1 µm and the Mn of BCPs as shown in the TEM images of Figure 5. The AR values of ellipsoids were observed to increase strongly with particle size and BCP Mn. For the smallest dpore = 0.2 µm, particles with perpendicular lamellae were nearly spherical, with only slight deformation. For example, in the case of PS67k-b-PB75k, the AR value was only 1.16 (Figure 5(e)). However, the ARs of particles generated from membranes with dpore = 0.5, 1.1 and 2.1 µm increased gradually to 1.36, 1.67 and 1.96 (Figures 5(f-h)), respectively. Comparison of particles formed from the same membrane (dpore = 2.1 µm), revealed a strong 24 ACS Paragon Plus Environment

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increasing of AR and with the Mn of BCP, with AR values of 1.39, 1.96, and 2.16 for PS34k-bPB25k, PS67k-b-PB75k, and PS112k-b-PB104k, respectively, as shown in Figures 5(l), (h), and (d). However, for smaller particles from dpore= 0.2 µm (Figure 5(a, e, i)), the variation in the AR value with molecular weight was less pronounced, from 1.04 for PS34k-b-PB25k (Figure 5(i)) to 1.16 for PS67k-b-PB75k (Figure 5(e)) and 1.23 for PS112k-b-PB104k (Figure 5(a)). Taken together, the final AR was found to depend on both particle size and the Mn of the BCPs, allowing precise control of particle shape, from spherical shapes with AR = 1.04 (dpore = 0.2 µm, PS34k-b-PB25k) to long ellipsoids with AR = 2.16 (dpore = 2.1 µm, PS112k-b-PB104k). Notably, the particles in all of the different batches (Figure S5, Table 1) were found to be monodisperse in shape and size with CV of ~10%.

Figure 6. Plot of AR vs. major axis (L) of size-controlled, monodisperse PS67k-b-PB75k ellipsoids produced from membranes with dpore = 0.2, 0.5, 1.1, and 2.1 µm (black, red, blue, and cyan, respectively) fitted with theoretical calculations (olive). 25 ACS Paragon Plus Environment


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To develop a quantitative understanding of the variation of particle AR as functions of particle size and Mn of BCP, we adopted the theoretical model developed by Fredrickson and coworkers.12,14 According to this model, a particle stretches to satisfy the commensurability condition between the lamellar spacing of BCP domains and the finite droplet size (i.e., the bulk elasticity effect). In more detail, the free energy of the system upon particle evolution was calculated considering three major contributions: 1) the interfacial energy between the two blocks of the BCP, 2) the entropic penalty associated with stretching of BCP chains upon elongation of the particles, and 3) the interfacial energy between the surface of the BCP particles and the surrounding medium (i.e., CP). Therefore, the total free energy associated with the elongation of BCP particles can be described by the sum of three terms corresponding to each contribution as shown in equation [1]. The free energy contribution of the first two terms (i.e., (1) the interfacial energy between the two blocks of the BCP, and (2) the chain stretching penalty of BCPs) is minimized when the BCPs are assembled into lamellar structures with a period of L0 within the particles, where L0 is the periodicity of the BCP domains in bulk phase. Therefore, the BCPs within the particles elongate to satisfy the commensurability condition (i.e., such that the major axis L is multiple of L0). However, at the same time, the energy cost associated with particle surface area in contact with the surrounding aqueous medium opposes particle elongation. The counterbalance of these contributions determines the final AR of the ellipsoidal particles. In Figure 6, AR is plotted as a function of L for monodisperse, PS67k-b-PB75k ellipsoids produced from dpore = 0.2, 0.5, 1.1 and 2.1 µm (black, red, blue, and cyan) along with theoretical calculations based on the above model (olive). In order to calculate the theoretical AR values for 26 ACS Paragon Plus Environment

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different BCP particles as a function of L, we determined the fitting parameters  and  in equation [1] from a scatter plot comprised of 50 data points for each dpore of AR vs. L (black, red, blue, and cyan dots). These experimental data were fitted with theoretical calculations from equation [1] (olive). For PS34k-b-PB25k and PS112k-b-PB104k, predicted AR plots were obtained using the fitting parameters determined from PS67k-b-PB75k particles (Figure S6). The observed ARs of BCP ellipsoids in Figure 5 correspond well with the calculated AR values from the theoretical models. Increasing particle size increased the contribution of bulk elastic energy arising from the increased number of lamellar stacks and decreased the surface energy contribution due to the reduced surface area/volume ratio. As a result, a drastic increase in AR was observed as a function of particle size, both in experimental and calculated values. Additionally, since lower Mn BCPs require greater energetic penalties for chain stretching for a given particle volume, particles with higher Mn BCPs elongated to higher ARs. Importantly, the good agreement of the AR values of monodisperse ellipsoids observed in experiments and theoretical calculations supports the mechanism of ellipsoid formation proposed herein and suggests that ellipsoids with targeted sizes and ARs can be designed simply by appropriate selection of dpore and BCP Mn.

Colloidal Coating of AR-Controlled Ellipsoids To demonstrate the utility of the monodisperse AR-controlled ellipsoids, the properties of colloidal coatings were examined as a function of particle shape by comparing the deposition patterns of suspensions containing ellipsoids with varying AR and similar particle volumes (dpore = 2.1 μm). In this regard, three different particle batches having AR values of 1.00 (spheres), 1.39, 27 ACS Paragon Plus Environment


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and 2.16 were prepared by emulsification using the same dpore = 2.1 μm as shown in Figures 7(ac). The volume fraction of the particle suspensions (Ф) was adjusted to Ф = 0.15, and they were drop-casted and dried on a glass slide. The resulting deposition patterns comprised of particles with AR = 1.00, 1.39, and 2.16 are shown in Figure 7(d-f). Spherical particles (AR = 1.00) concentrated at the edges upon drying, consistent with the coffee-ring effect (Figure 7(d), Supplementary Movie 1). In direct contrast, ellipsoidal particles with AR = 1.39 (Figure 7(e)) and 2.16 (Figure 7(f), Supplementary Movie 2) produced films with uniform particle coverage.

Figure 7. (a-c) TEM images of particles with AR of (a) 1.00, (b) 1.39, and (c) 2.16 produced by emulsification using a membrane with dpore = 2.1 μm. Each particle batch was generated by evaporating solvent from (a) a PS112k-b-PB104k-containing emulsion at φ = 0.03 h-1, (b) a PS34k-bPB25k-containing emulsion at φ = 0.26 h-1, and (c) a PS112k-b-PB104k-containing emulsion at φ = 0.26 h-1. (d-f) Optical microscopy images of deposition patterns on glass slides generated by drying 1 μL of suspension (particle volume fraction Ф = 0.15) containing particles with (d) AR = 1.00, 28 ACS Paragon Plus Environment

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(e) AR = 1.39, and (f) AR = 2.16. Scale bars (black) are 200 μm. (g-i) Photographs of large-scale deposition patterns on 18 mm × 18 mm cover glass slides generated by drying 0.5 mL of suspensions (Ф = 0.15) containing particles with (g) AR = 1.00, (h) AR = 1.39, and (i) AR = 2.16. Scale bars (white) are 5 mm. Inset images show water droplets with different contact angles on each coating.

These results are consistent with the previous observations showing suppression of the coffee-ring by changing particle shape. Ring-like deposits are known to appear due to the radially outward capillary flow from the center to the edge of sessile drops upon drying of particle suspensions.63 Whereas spherical particles are pushed to the edge of the sessile drops, ellipsoidal particles resist this capillary flow.64,65 The main reasons for this resistance are 1) the strong adsorption behavior of ellipsoids at the air/water interface, and 2) the increased inter-particle capillary attractive force between elongated particles. When ellipsoids are adsorbed at the interface, strong interparticle interaction between ellipsoids yields clustered structures that significantly deform the interface.66–68 Once these structures are formed, the overall mobility of the ellipsoids is significantly reduced, thus resisting the radially outward flow and producing uniform coatings of ellipsoids (e.g., those with AR = 2.16). Interestingly, the strength of interparticle attraction, which affects the degree of deformation of the air/water interface, is expected to be dependent on the ellipsoid AR. Previous reports demonstrate that the degree of deformation of the air/water interface upon adsorption of ellipsoids increased logarithmically with AR.69 We also observed that the contact angle of sessile drops containing ellipsoids on pristine glass slides increased from 58º to 66º as the AR of the ellipsoids increased from 1.00 to 2.16, reflecting the stronger adsorption of



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the particles to the air/water interface and more severe interfacial deformation by larger AR particles (Figure S7). One advantage of SPG membrane emulsification is that monodisperse particles can be produced on large scales.33,34 Therefore, to validate the observed coating property dependence on the AR in larger scales, 0.5 mL of suspensions of particles with three different ARs (AR = 1.00, 1.31, and 2.16) were drop-casted to fully cover 18 mm × 18 mm cover glass slides and dried. Similar to our observations for smaller batches, spherical particles (AR = 1.00) concentrated at the droplet edges upon drying to produce coffee-ring patterns (Figure 7(g)), whereas more uniform coatings were achieved from ellipsoidal particles with AR = 1.39 (Figure 7(h)) and AR = 2.16 (Figure 7(i)). To stress the differences in deposition patterns from different AR particles, 3 μL of water was dropped to the particle films and the water contact angles (WCA) were measured (inset images). For the coffee-ring patterned film of spherical particles (AR = 1.00) in Figure 7(g), the water droplet spread on the film with vanishingly low WCA. By contrast, stable water droplets were formed on the homogeneous films generated from the ellipsoids (Figure 7(h, i)). However, the average WCA values varied with AR, from 81º for films from AR = 1.39 ellipsoids to 104º for films from AR = 2.16 ellipsoids, suggesting the formation of more densely-populated coatings of ellipsoids with AR = 2.16 than those with AR = 1.39. Overall, we demonstrated that the homogeneity of hydrophobic coatings from particle suspensions can be controlled by the particle AR.


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CONCLUSIONS In this work, we developed synthetic methods that allow precise control of the AR of monodisperse PS-b-PB ellipsoid particles by solvent evaporation from BCP-containing emulsions and elucidated the formation mechanism of ellipsoids through theoretical and experimental investigation of these processes. We estimated the critical lp value required for ellipsoid formation by developing analytical mass transfer models of solvent evaporation from emulsions, and found that the relative ratio of rBCP to lp was critical in determining particle shape. And, we demonstrated that the AR of ellipsoids could be systematically tuned by varying particle size and BCP Mn, which was further supported by theoretical models that quantitatively predicted the degree of particle elongation and show good agreement with experiments. The importance of these uniform, AR-controlled ellipsoids produced on large scales was highlighted by investigating the AR-dependent coating properties of particle suspensions. While drying of ellipsoid suspensions yielded homogeneous coatings, spherical particles concentrated at the droplet edges. We are currently investigating the effect of the BCP Flory-Huggins interaction parameter on particle shape to broaden a range of achievable ellipsoid ARs, and thereby the corresponding colloidal coating properties, among others. We believe that our method of producing the particles with precisely controlled ARs and sizes provides an efficient and commercially-viable route for the development of the particle coatings and colloidal materials with unique optical, mechanical, and stimuli-responsive properties.



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ASSOCIATE CONTENTS Supporting Information. Additional SEM, TEM and cross-sectional TEM images of particles, information about the size and AR of different particles, analysis of solvent evaporation rate, and supplementary movies showing AR-dependent particle deposition processes are provided in the supporting information. This material is available free of charge at http://pubs.acs.org

AUTHOR INFORMATION Corresponding Author [email protected], [email protected]

ACKNOWLEDGMENTS This research was supported by the Korea Research Foundation Grant, funded by the Korean Government

(2012M3A6A7055540,

2017M3D1A1039553,

2017M3A7B8065528).

We

acknowledge additional support for this work from the Research Projects of the KAIST-KUSTAR and the CRH (Climate Change Research Hub) of KAIST. We thank Dr. Rachel Letteri for helpful discussions.


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Table of Contents Aspect Ratio-Controlled Synthesis of Uniform Colloidal Block Copolymer Ellipsoids from Evaporative Emulsions


Aspect Ratio-Controlled Synthesis of Uniform Colloidal Block

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