Mechanistic Study on the Shape Transition of Block Copolymer

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Mechanistic Study on the Shape Transition of Block Copolymer Particles Driven by Length-Controlled Nanorod Surfactants Kang Hee Ku, Ji Ho Ryu, Jinwoo Kim, Hongseok Yun, Chongyong Nam, Jae Man Shin, Youngkwon Kim, Se Gyu Jang, Won Bo Lee, and Bumjoon J. Kim Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04020 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on November 1, 2018

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Chemistry of Materials

Mechanistic Study on the Shape Transition of Block Copolymer Particles Driven by Length-Controlled Nanorod Surfactants Kang Hee Ku1, Ji Ho Ryu2, Jinwoo Kim1, Hongseok Yun1, Chongyong Nam2, Jae Man Shin1, Youngkwon Kim1, Se Gyu Jang3, Won Bo Lee2,*, Bumjoon J. Kim1,* 1 Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science

and Technology (KAIST), Daejeon 34141, Republic of Korea 2 School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea 3 Functional Composite Materials Research Center, Korea Institute of Science and Technology (KIST), Jeonbuk 55324, Republic of Korea *E-mail: [email protected] (B. J. K.), [email protected] (W.B.L.)

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ABSTRACT Interface engineering of evaporative emulsion droplets containing block copolymers (BCPs) provides an effective route to generate non-spherical particles. Here, we demonstrate the impact of length-controlled nanorods (NRs) on the interfacial properties of BCP emulsions to produce anisotropic BCP particles. A series of lamellae- and cylinder-forming polystyreneb-poly(4-vinylpyridine) (PS-b-P4VP) and a series of NRs with different lengths (l) are coassembled, and selective arrangement of the NRs on the P4VP domain at the particle surface enables the production of striped football (prolate) and convex lens-shaped (oblate) particles. In particular, the ratio of the NR length to the size of the NR-hosting domain (l/L), which is varied from 0.07 to 3.60, is the key parameter in determining the location of the NRs in the BCP particles as well as the final particle shape. The oblate particles are generated only in the range of 0.36 ≤ l/L ≤ 0.96, whereas the prolate particles are produced for much wider range of l/L ≥ 0.83 without upper limit. This difference is attributed to larger entropic penalty for the NRs confined within the P4VP cylinders than the entropic penalty for those within the lamellae. To better understand and support our experimental observations, we performed dissipative particle dynamics simulation and calculated the free energy for the NR/BCP assembly within the emulsion droplets.


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INTRODUCTION Polymer particles with anisotropic shapes have gained growing interest due to their unique optical, rheological, structural, and coating properties.1-7 In a brief span of years, the self-assembly of block copolymers (BCPs) within interface-engineered emulsion droplets has been established as a simple and powerful technique in producing anisotropic particles with unconventional nanostructures.8-23 For example, the use of two different surfactants that have selective interaction to each block of BCPs can effectively modulate the interfacial properties of BCP particles and, thus, enable fine tuning of particle shape.19-21, 24-27 Inorganic nanoparticles (NPs) have been successfully applied as surfactants in oil-inwater emulsion systems owing to their high adsorption energy at the interface.28-32 The ability of NPs as surfactants can be systematically controlled depending on their size, shape, and surface properties.33-39 Of note, controlled assembly of nanorods (NRs) can provide unique and novel physical properties that originate from the anisotropic shape of the NRs.40-42 For example, noble metal NRs, such as gold or silver, are optically active due to the excitation of surface plasmons in the NRs, which can be tuned by changing the chemical composition, length, and inter-particle distance of the NRs.43, 44 Despite their interesting and attractive properties, much fewer studies on the morphological behavior of BCP/NR assembly have been conducted compared to those on the assembly with spherical NPs.45-54 Balazs group reported that the incorporation of NRs into the minority phase of the phase-separating polymer blend yields a bicontinuous morphology with enhanced electrical and mechanical properties.52 Recently, Xu and co-workers reported a library of NR assemblies in the BCP thin films depending on the size and length of NRs.53, 54 While most of the previous works studied the BCP/NR assembly in bulk or thin film system, the NR assembly in three-dimensional BCP emulsion droplets has been rarely studied.



Previously, we reported the effect of NR length on the shape of BCP particles and observed that the transition of particle shape strongly depends on the ratio of the NR length to the size of the NR-hosting BCP domain (l/L).29 Nevertheless, thermodynamic interaction parameters to control the NR assembly and the transition of the particle shape have not been well understood. In addition, understanding the relationship among the NR geometry, the NR assembly within the particle, and the resulting particle shape and structure is crucial for the future design of anisotropically shaped BCP particles. In this article, we describe the shape control of polystyrene-b-poly(4-vinylpyridine) (PS-b-P4VP) particles (i.e. sphere, striped football (prolate) and convex lens (oblate)) by precisely tuning the assembly manner of length-controlled NRs within BCP emulsion droplets. Particularly, we attempt to understand how the interplay of thermodynamic parameters affects the assembly of NRs at the emulsion interface and the final shape of BCP particles, based on model experiments and related theoretical calculations. A dramatic shape transition of BCP particles was observed depending on the l/L values and the structure of BCP microdomains (i.e. lamellae and cylinders). Due to the larger entropic penalty to accommodate the NRs within P4VP cylinders than that for the NRs within lamellae, the formation of oblate particles was observed in a limited l/L range of 0.36 ≤ l/L ≤ 0.96. By contrast, prolate particles were produced for much wider range of l/L ≥ 0.83. The shape transition of BCP particles depending on l/L values was supported by dissipative particle dynamics (DPD) simulation.


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EXPERIMENTAL SECTION

Materials. Four different polystyrene-b-poly(4-vinylpyridine) (PS-b-P4VP) BCPs: PS27k-bP4VP7k (dispersity (Ð) = 1.15), PS50k-b- P4VP17k (Ð = 1.08), PS10k-b- P4VP10k (Ð = 1.08), and PS19k-b-P4VP22k (Ð = 1.15) were purchased from Polymer Source, Inc. (Subscripts indicate the number average molecular weight (Mn) of each block). 3-n-pentadecylphenol (PDP) and cetyl trimethylammonium bromide (CTAB, 98%) were purchased from Sigma-Aldrich, and copper acetylacetonate (Cu(acac)2), platinum acetylacetonate (Pt(acac)2), oleic acid, oleylamine, 1-2hexadecanediol, and 1-octadecene were purchased from Aldrich, and used as received without purification. Synthesis of Length-controlled CuPt NRs. CuPt NRs were synthesized by the thermal decomposition method with the standard air free technique, as described in the previous studies.55-57 See the Supporting Information and Figure S1 for the detailed synthetic procedure. Cu(acac)2 and Pt(acac)2 were dissolved in 1-octadecene. Then, calculated amount of oleic acid, oleylamine and 1,2-hexadecanediol were added to the reaction mixture. The solution was heated and stirred at 120 °C under a nitrogen atmosphere for 20 min, and then the temperature was increased to 225 °C and kept for 30 min. Finally, the solution was cooled down to room temperature, and the product was precipitated in a 50:50 mixture of hexane and acetone at 3600 rpm for 10 min. Preparation of BCP Particles. A chloroform solution of PS-b-P4VP (10 mg/mL) was prepared as a disperse phase. To provide strong favorable interaction between the CuPt NRs and the selective domain (i.e. P4VP) of the BCP chains, PDP was introduced as the small molecule linker between P4VP block and alkyl ligands of NRs, as previously reported.11, 58 The mole fraction of PDP to P4VP units were adjusted to 0.2 for lamellae-forming BCPs, and 0.5 for



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PS27k-b-P4VP7k and 0.3 for PS50k-b-P4VP17k. The sizes of P4VP(PDP) domain (L) for the lamellae-forming PS10k-b-P4VP10k(PDP)0.2 (LAM14) and PS19k-b-P4VP22k(PDP)0.2 (LAM20) were measured to be 13.8 and 20.2 nm, and the L values for the cylinder-forming PS27k-bP4VP7k(PDP)0.5 (CYL21) and PS50k-b-P4VP17k(PDP)0.3 (CYL34) were measured to be 20.7 and 33.7 nm, respectively. The information of the polymer-PDP complexes used in this study is summarized in Table 1. Then, CuPt NRs were added to the polymer solution, and stirred for 24 h. In our system, the volume fraction of NRs (NR) = 0.015 was used to provide neutral surrounding conditions for both lamellar and cylindrical BCPs, and elucidate the effect of the NR length on the particle morphology. The effect of NR on the morphology of the particle was investigated by varying NR from 0.01 to 0.12, and summarized in Figures S2 and S3. And the optimal range of NR was determined to obtain prolate (0.015 ≤ NR ≤ 0.030) or oblate (0.010 ≤

NR ≤ 0.020) particles. To produce BCP particles, the mixed chloroform solution (200 μL) was emulsified in aqueous solution of CTAB (0.5 wt%, 2.5 mL) using a homogenizer for 1 min at 20,000 rpm. The organic solvent was slowly evaporated at room temperature for 24 h. The sample was washed with DI water to remove the large excess of remaining surfactants by repeated centrifugations performed at 13,000 rpm for 10 min. The BCP particles were redispersed in DI water and used for further characterization. Table 1. Characteristic of PS-b-P4VP(PDP) BCPs used in this study. PS-b-P4VP(PDP)

Mn [kg/mol]

Equilibrium morphology

Mole fraction of PDP to P4VP units

Size of P4VP(PDP) (L, nm)a

LAM14

PS10k-b-P4VP10k(PDP)0.2

20

LAM

0.2

13.8

LAM20


41

LAM

0.2

20.2

CYL21


34

CYL

0.5

20.7

CYL34


67

CYL

0.3

33.7

a

Domain sizes were measured by TEM.


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Characterization. Thermal gravimetric analysis (TGA) was used to calculate the weight fraction of CuPt core and organic ligands of CuPt NRs. The volume of NRs was calculated by using the densities of oleylamine (0.813 g/cm3), oleic acid (0.895 g/cm3), Cu (8.96 g/cm3), and Pt (21.45 g/cm3). Field-emission scanning electron microscopy (SEM) (Hitachi S-4800), transmission electron microscopy (TEM) (JEOL 2000FX) were used to observe the surfaces and internal structures of the particles. The samples were prepared by drop-casting BCP particle suspensions onto the silicon wafers or TEM grids coated with a 20 nm thick carbon film. For the TEM analysis, the prepared samples were exposed to I2 vapor to selectively stain the P4VP domains of PS-b-P4VP. Dissipative Particle Dynamics (DPD) Simulation. All of the simulations were performed using the LAMMPS simulation package. The initial configuration is constructed by randomly placing polymer, solvent, and NRs without consideration of overlap between beads in a cubic box of size 𝐿′ × 𝐿′ × 𝐿′. The box size 𝐿′ is determined as 43.68 𝑟𝑐 for the number density of system 𝜌 to be 3 with 250000 beads. Periodic boundary conditions to all directions are applied. The simulations were performed during 106Δ𝑡 with timestep Δ𝑡 = 0.018. In our simulation, we set the temperature 𝑇 = 1, mass of all beads 𝑚 = 1, and cut-off radius 𝑟𝑐 = 1. The BCP was modeled by linearly connecting PS beads ((1 ― 𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃))𝑁 = 𝑁𝑃𝑆) and P4VP(PDP) beads (𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃)𝑁 = 𝑁𝑃4𝑉𝑃(𝑃𝐷𝑃)), where 𝑁 and 𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃) are the length of BCP, and the composition fraction of P4VP(PDP) beads to 𝑁, respectively. The values of 𝑁 were set to 10 for the case of 𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃) = 0.5 and 20 for the case of 𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃) = 0.25 to provide sufficient chain length for shorter block to form inner packing structure. The model of NR was described by consecutive 𝑁𝑟𝑜𝑑 beads, which is selectively favorable to P4VP(PDP) domain. In order to investigate the dependence of selective localization of NRs on the P4VP(PDP) domain as a function of 𝑁𝑟𝑜𝑑, the length of NR (𝑁𝑟𝑜𝑑) was varied from 3 to 28.



In addition, to remove the effect of volume fraction of solvent on the particle morphology, we fixed the volume fraction of solvents at 𝜙𝑠 = 0.8 to assure that particle has spherical structure, where 𝜙𝑃𝑆/𝑃4𝑉𝑃(𝑃𝐷𝑃) + 𝜙𝑟𝑜𝑑 + 𝜙𝑠 = 1.59 Reflecting the experimental results, the volume fraction of NRs was also fixed at 𝜙𝑟𝑜𝑑 = 0.03 for fP4VP(PDP) = 0.5 and 𝜙𝑟𝑜𝑑 = 0.02 for fP4VP(PDP) = 0.3. We also calculated the characteristic lengths of self-assembled structures by performing the BCP melt simulations. The characteristic lengths of lamellar and cylinder structures were 𝐿𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃) = 0.5 = 5.38 𝑟𝑐 and 𝐿𝑓𝑃4𝑉𝑃(𝑃𝐷𝑃) = 0.25 = 3.83 𝑟𝑐. Simulation details are described in the Supporting Information.


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RESULTS

Figure 1. Schematic illustration for the fabrication of PS-b-P4VP(PDP) particles including length-controlled CuPt NRs through the ‘emulsion-encapsulation and evaporation process’; (a) Schematic illustration of a series of lamellae-forming BCPs (LAM14 and LAM20) and cylinder-forming BCPs (CYL21 and CYL34); (b) TEM images of CuPt NRs with different lengths ranging from 2.3 to 49.7 nm with a fixed width of 2.3 nm. Scale bars are 20 nm.

A series of lamellae- and cylinder-forming PS-b-P4VP(PDP) particles were produced by solvent evaporation from chloroform-in-water emulsion droplets containing BCPs and length-controlled CuPt NRs (Figure 1(a)). To investigate the effect of the NR length to NRhosting domain size ratio (l/L) on the structure of BCP particles, CuPt NRs with varied l ranging from 2.3 to 49.7 nm were prepared.56, 57 Figure 1(b) and Figure S1 show the CuPt NRs with l of 2.3 nm (NR-2), 7.5 nm (NR-8), 12.4 nm (NR-12), 16.8 nm (NR-17), 19.9 nm (NR-20), 25.5 nm (NR-26), 32.4 nm (NR-32), and 49.7 nm (NR-50) with a fixed width of 2.3 nm. The l/L values for the four different BCP systems (i.e. LAM14, LAM20, CYL21, and CYL34) are summarized in Table 2. The values of l/L for the cylinder- and lamellae-forming BCPs were tunable from 0.07 to 2.40, and from 0.11 to 3.60, respectively. The volume fraction of NRs (NR) = 0.015 was fixed for all of the experiments to elucidate the effect of the NR length on the NR position and the particle morphology.



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Table 2. l of CuPt NRs used in this study; l/L values for PS10k-b-P4VP10k(PDP)0.2 (LAM14), PS19k-b-P4VP22k(PDP)0.2 (LAM20), PS27k-b-P4VP7k(PDP)0.5 (CYL21), and PS50k-bP4VP17k(PDP)0.3 (CYL34). CuPt NRs

NR-2

NR-8

NR-12

NR-17

NR-20

NR-26

NR-32

NR-50

l (nm)

2.3

7.5

12.4

16.8

19.9

25.5

32.4

49.7

l/LLAM14

0.17

0.54

0.90

1.21

1.44

1.85

2.35

3.60

l/LLAM20

0.11

0.38

0.61

0.83

0.99

1.26

1.60

2.46

l/LCYL21

0.11

0.36

0.59

0.81

0.96

1.23

1.57

2.40

l/LCYL34

0.07

0.22

0.37

0.50

0.60

0.76

0.96

1.47

First, the effect of NR addition on the morphology of lamellae-forming BCP particles was investigated using two different lamellae-forming BCPs (LAM14 and LAM20). Figure 2(a) shows the TEM images of LAM14 particles stabilized by CTAB only. Spherical BCP particles with radially-stacked lamellar morphology (onion-shaped particles) were formed with the PS half-layer at the outermost particle surface due to favorable interaction between CTAB surfactants and PS block.30 By contrast, the addition of a small amount of CuPt NRs (NR-12,

NR = 0.015) led to an interesting transition in the overall shape of the particles from sphere to prolate with axially stacked lamellar morphology (Figures 2(b) and (c)). This structural transition can be attributed to the segregation of NR-12 to the P4VP/water interface during the particle formation. Since the NRs and CTAB have preferences to each of the different blocks, they serve as dual surfactants to interact with PS and P4VP chains, respectively. Consequently, the perpendicularly-oriented lamellae structure is first formed at the particle surface, followed by the propagation of the BCP ordering into the particle center, eventually resulting in the formation of the prolate particles.14, 20, 30


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Figure 2. (a-c) TEM and SEM images of LAM14 particles (a) stabilized by CTAB only, and (b, c) stabilized by both CTAB and NR-12 surfactants. Segregation of NRs at the surface of the particle induced the morphological transition from spherical to prolate particles. (d) SEM and TEM images of LAM14 and LAM20 particles including NRs with different lengths. The transition of the particle shape was observed from sphere (green boxes) to prolate particles (red boxes) with increase of length of NRs. The scale bars are 200 nm. P4VP(PDP) domains appear dark due to staining with I2.



In order to systematically evaluate the effect of l/L value on the shape and internal morphology of BCP particles, LAM14 and LAM20 particles, whose L values are 13.8 and 20.2 nm, respectively, were prepared using NR-8, NR-12, NR-20, and NR-32 (NR = 0.015). Figure 2(d) shows a morphological transition of the BCP particles upon the increase of NR length. When the NR-8 was added (first column in Figure 2(d)), the particles showed no change in the shape: the NRs were well incorporated within the P4VP(PDP) domain of the BCP particles, and, thus, CTAB molecule could be considered as a sole surfactant. Meanwhile, a morphological transition from spherical to prolate particles was observed for LAM14 by the addition of NR-12 (second column in Figure 2(d)). In this case, the value of l/LLAM14 (= 0.90) was large enough to exclude NRs to the particle surface due to the increased entropic penalty associated with the stretching of BCP chains to host the long NRs. In contrast to the case of LAM14, when LAM20 BCPs (l/LLAM20 = 0.61) with larger P4VP domain size was used, NR12 was still located within the P4VP(PDP) domain and no change in the particle shape was observed, maintaining the spherical shape. However, the addition of the longer NRs (i.e., NR20 and NR-32) induced the change in the overall shape of the BCP particles from sphere to prolate (as shown in the third and fourth columns in Figure 2(d)). Importantly, all of the particles were found to have prolate shape within the range of experimentally producible l/L (i.e., l/L ≤ 3.60).


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Figure 3. (a-c) TEM and SEM images of (a-c) CYL21 particles (a) stabilized by CTAB only, and (b, c) stabilized by both CTAB and NR-12 surfactants. Segregation of NRs at the surface of the particle induced the morphological transition from spherical to oblate particles. The scale bars are 200 nm. (d) SEM and TEM images of CYL21 and CYL34 particles including different NRs. The transition of the particle shape was observed from sphere (green boxes) to oblate particles (red boxes), and to irregular shaped sphere with rough surface (blue boxes) with the increase of l. The scale bars are 100 nm.



Next, we examined the effect of the NR addition on the morphology of the particles with two different cylinder-forming BCPs (CYL21 and CYL34). As shown in Figures 3(a) to (c), the spherical BCP particles with coiled cylindrical P4VP(PDP) domains (CYL21) were transformed to oblate particles by the addition of NR-12. In this case, the NR surfactant induced nucleation of the perpendicularly-ordered cylinders at the particle surface, exposing the end cap of the P4VP(PDP) cylinder to the surface. Finally, propagation of the cylinders completed the long-range lateral order of the hexagonally-packed cylinders, resulting in the formation of oblate particles.21, 28, 29 The l/L-dependent phase behavior of cylinder-forming BCP particles was studied by CYL21 and CYL34 with a series of NR-2, NR-8, NR-20, NR-32, and NR-50 surfactants (NR = 0.015). Different from the observations from the lamellae-forming BCPs, the cylindrical forming BCP particles experienced different morphological transitions from spherical to oblate particles, and to irregular shaped spherical particles, as shown in the SEM and TEM images in Figure 3(d). First, when the value of l/L was small, (i.e. NR-2 for CYL21, and NR-2 and NR-8 for CYL34), NRs were incorporated within the P4VP(PDP) domain, and spherical particles were observed. As shown in the third column in Figure 3(d), oblate particles were produced when the l of NRs increased, accompanied by positioning of the NRs at the particle surface. This transition was observed only within a specific range of l/L (i.e., NR-8 and NR-20 for CYL21 and NR-20 and NR-32 for CYL34). Also, the critical length of NRs for the shape transition from sphere to oblate was higher for CYL34 (l = 19.9 nm) than that for CYL21 (l = 7.4 nm). It is worth to note that further increase of NR length produced irregular particles with rough surface, while all of the NRs were clearly segregated at the outer surface of the BCP particle (Figure S4).


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Figure 4. Summary of morphological transition of CYL21 (●), CYL34 (■), LAM14 (◆), and LAM20 (▲) particles depending on l/L values.

To highlight the importance of l/L parameter in determining the shape of both lamellaeand cylinder-forming BCP particles, we summarized the morphological behavior of the BCP particles containing eight different NRs in Figure 4. First, the critical l/L value for cylinderforming BCP particles to show the transition of particle shape from spherical to oblate particle (l/LS-O, CYL) was 0.36, whereas, for lamellae-forming BCP particles, the transition of particle shape from spherical to prolate particle occurred at much higher value (l/LS-P, LAM = 0.83). In addition, for the particles containing cylinder-forming BCPs, the oblate particles were produced within an l/L range from 0.36 to 0.96. By contrast, all of the NRs, whose l/L values were larger than 0.83, enabled to generate prolate particles for the lamellar-forming BCPs. In summary, the l/L is a key parameter to determine the position of the NRs as well as the shape of the BCP particles.



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DISCUSSION Thermodynamically, the structure of polymer particle composed of NRs and BCPs is determined by minimizing the total free energy of the system, which can be expressed as the sum of total enthalpic and entropic free energies of the multi-components. Therefore, our key observation on the shape transformation of BCP particles induced by l/L–dependent positioning and orientation of NRs must arise from the shift of the free energy balance of the system. In this section, i) calculation on the free energy shift of the system will be conducted to understand l/L–dependent NR position and orientation, and ii) the assembly of BCPs and NRs will be simulated using DPD method to describe the shape transition of BCP particles from sphere to ellipsoids (i.e. oblate and prolate). The governing equation for total free energy change upon co-assembly of NRs and BCPs in evaporative emulsion can be expressed as53, 54 ΔG = (Δ𝐻NR ― BCP + Δ𝐻NR ― aque + Δ𝐻BCP ― aque + Δ𝐻NR ― NR) –T(Δ𝑆con +Δ𝑆trans +Δ𝑆orient)

(1)

where Δ𝐻NR ― BCP, Δ𝐻NR ― aque, and Δ𝐻BCP ― aque refer to the enthalpic contributions from interactions between the NRs and BCPs, the NRs and aqueous medium, and the BCPs and aqueous medium, respectively, and Δ𝐻NR ― NR is the enthalpy change arising from favorable side-to-side inter-particle interaction of NRs. Δ𝑆con, Δ𝑆trans, and Δ𝑆orient stand for the entropic changes upon NR incorporation due to the conformational change of the polymer chain, the translational entropy of the NRs, and the orientational entropy of the NRs, respectively.


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Scheme 1. Schematic illustration of the positioning of NRs depending on the l/L values; (a) localization of NRs within P4VP(PDP) domain of the BCP particle (low l/L), (b) segregation of NRs at the particle surface (high l/L).

Here, we consider two limiting cases of NR positioning: 1) low l/L values where NRs are incorporated inside the P4VP(PDP) domain of BCP particles, and 2) high l/L values where NRs are excluded to the interface between the P4VP(PDP) domain and surrounding medium of BCP particles. For the first case, as shown in Scheme 1(a), the location of NRs within the P4VP(PDP) domain is attributed to the strong, favorable interaction between the aliphatic chain of PDP and oleic acid/oleylamine ligands on the surface of the CuPt NRs. In this case, the enthalpic gain from NR and P4VP(PDP) interaction (Δ𝐻NR ― BCP) must be able to compensate the conformational entropic penalty of the polymer chains (Δ𝑆con) when the NRs were incorporated in the P4VP(PDP). The increase of l/L results in the increase of the conformational entropic penalty for the polymers, and thus the NRs cannot stay inside the P4VP(PDP) domain when this entropic penalty exceeds the enthalpic energy gain. As a result, the spherical particles were observed when l/L < 0.83 for lamellar BCPs and l/L < 0.36 for cylindrical BCPs. On the other hand, at high l/L values (i.e. l/L ≥ 0.83 and l/L ≥ 0.36 for the lamellae- and cylinderforming BCPs, respectively), it becomes more energetically favorable to segregate the NRs to the surface of emulsion droplet by reducing the entropic penalty (Δ𝑆con) and increasing the



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enthalpic gain from covering the particle surface with a layer of NRs (Δ𝐻NR ― aque +Δ 𝐻BCP ― aque) as depicted in Scheme 1(b).60

Scheme 2. Schematic illustration of three different cases of NR orientation at the surface of BCP particles: (a) parallel (𝜙 = 0o), (b) perpendicular (𝜙 = 90o), and (c) orientation angle of 𝜙 to the tangential plane of the particle surface. In the case of the NRs segregated at the particle surface, the most significant enthalpic energy gain is expected to come from the reduction of the large, unfavorable interfacial interactions between the BCP emulsion and the surrounding (Δ𝐻BCP ― aque). Particularly, the interfacial area occupied by the NRs depends on the orientation of the NRs at the particle surface (Scheme 2), and therefore, the free energy is a strong function of the orientation of the NRs (Δ𝑆orient in equation (1)). More specifically, the total free energy change caused by the addition of NRs (∆𝐺) can be expressed in terms of the orientation angle (𝜙) of cylindrical NRs positioned at the P4VP(PDP)/surrounding interface as follows: ∆𝐺0 = ― (2𝑟𝑙 𝑠𝑖𝑛𝜃)𝛾𝐵𝐶𝑃/𝑎𝑞𝑢𝑒 + 2(𝑟𝑙𝜃 + 𝑟2(𝜃 ― 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃))𝛾𝑁𝑅/𝑎𝑞𝑢𝑒 + (2𝑟𝑙(𝜋 ― 𝜃) + 2𝑟2(𝜋 ― 𝜃 + 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃))𝛾𝑁𝑅/𝐵𝐶𝑃 + 𝐸𝑝𝑜𝑙,0

(2)

𝑟2(𝜃 ― 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃) ∆𝐺𝜙 = ― 𝛾𝐵𝐶𝑃/𝑎𝑞𝑢𝑒 𝑠𝑖𝑛𝜙

(

)

(3)

((

+ 𝑟𝜃

𝑟 + ℎ𝑡𝑎𝑛𝜙 𝑡𝑎𝑛𝜙

)

)

+ 𝑟2(𝜃 + 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃) 𝛾𝑁𝑅/𝑎𝑞𝑢𝑒


Page 19 of 32 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


(

+ 2𝜋𝑟𝑙 ― 𝑟𝜃

(

)

)

𝑟 + ℎ𝑡𝑎𝑛𝜙 + 𝑟2(2𝜋 ― 𝜃 ― 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃) 𝛾 𝑡𝑎𝑛𝜙

+ 𝐸𝑝𝑜𝑙,𝜙 (𝑤ℎ𝑒𝑟𝑒

𝑁𝑅/𝐵𝐶𝑃

𝑟 𝑟 < tan 𝜙 < ) 𝑙―ℎ ℎ

𝜋𝑟2 ∆𝐺𝜙 = ― 𝛾 + (𝜋𝑟2 + 2𝜋𝑟ℎ)𝛾𝑁𝑅/𝑎𝑞𝑢𝑒 𝑠𝑖𝑛𝜙 𝐵𝐶𝑃/𝑎𝑞𝑢𝑒

( )

(4) 𝑟 +(𝜋𝑟2 + 2𝜋𝑟(𝑙 ― ℎ)𝛾𝑁𝑅/𝐵𝐶𝑃 + 𝐸𝑝𝑜𝑙,𝜙 (𝑤ℎ𝑒𝑟𝑒 < tan 𝜙) ℎ where ∆𝐺0 and ∆𝐺𝜙 are the free energy differences when the tangential angle of NRs at the particle surface is 0° (parallel orientation, Scheme 2(a)) and ϕ (ϕ ≤ 90°, Schemes 2(b) and (c)), respectively; r and l are the radius and length of the NR cylinder, respectively; 𝛾 denotes the interfacial tension between the two phases; cos 𝜃 is the ratio of the difference in 𝛾 between the NRs and the polymer and aqueous phases to that between the polymer and aqueous phase (𝑐𝑜𝑠𝜃 = (𝛾𝑁𝑅/𝐵𝐶𝑃 ― 𝛾𝑁𝑅/𝑎𝑞𝑢𝑒) 𝛾𝐵𝐶𝑃/aque); h is the immersion depth of the NRs into the aqueous phase when assembled normal to the interface; and 𝐸𝑝𝑜𝑙,0 and 𝐸𝑝𝑜𝑙,𝜙 are the stretching penalties of P4VP(PDP) chains to circumvent NRs when the tangential angle of NRs is 0° and 𝜙, respectively.26, 61 The first negative term in the equations (2) to (4) indicates the decrease in the interfacial energy between the particle and surrounding medium due to the segregation of NRs at the interface. For example, in the case of NR-20, the interfacial area occupied by NRs, which corresponds to the reduced interfacial area between aqueous phase and polymer particle, is plotted as a function of 𝜙, as shown in Figure 5. When the NRs orient parallel to the particle surface (𝜙 = 0o), 5-fold decrease of interfacial area between the polymer and aqueous medium can be generated compared with that in perpendicular orientation (𝜙 = 90o). Importantly, such difference of the interfacial areas between the two orientations was strongly dependent on the



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NR length that the NRs in parallel orientation reduced the interfacial area by 2-fold and 8-fold for NR-8 and NR-32, respectively. (Figure S5).

Figure 5. Plot of the reduced interfacial area between aqueous phase and polymer particle occupied by NR-20 depending on the orientation angle of 𝜙.

In addition, the 𝐸𝑝𝑜𝑙 can be obtained by integration of pressure function, P(z), with the consideration of P4VP brush located at a certain distance (z) away from the PS/P4VP(PDP) interface (z = 0). The P(z) is given by 2

( )(

3𝜋2 𝐿 P(z) = 8𝑁2𝑏5 2

1―

)

4𝑧2 𝐿2

(5)

where L is the NR-hosting P4VP(PDP) domain size, N is the degree of polymerization of the P4VP, and b is the statistical segment length.34, 60 When the NRs are submerged in BCP (i.e., maximum length of NRs submerged in BCP, dBCP) with an orientation angle of 𝜙 as depicted in Scheme 2(c), P4VP chains would have to stretch or contract to fill the space around the NRs to accommodate the inserted NRs. Such deformation of polymers would produce a larger


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pressure (from equation (5)) relative to those for the parallel (𝜙 = 0o) or perpendicular (𝜙 = 90o) orientation. Therefore, to minimize the stretching of polymer chains, the NRs prefer to orient along the direction of cylinder or lamellae.34, 45, 46, 60 Finally, the difference in the total free energy (∆𝐺𝜙) caused by addition of NR-20 (compared to the state without NRs) was calculated as a sum of interfacial energy and stretching energy of the polymer, where ∆𝐺𝜙 was found to be strong functions of 𝜙 and dBCP. (See the Supporting Information for details). The contour plot of ∆𝐺 shown in Figure 6(a) reveals that ∆𝐺 is minimized in the range of 0° < 𝜙 < 15° (blue color). To determine the most thermodynamically-stable structure, we plotted the minimum value of ∆𝐺 as a function of 𝜙, by varying dBCP at each orientation angle. As shown in Figure 6(b), remarkable decrease of ∆𝐺 for the parallel orientation of NR (𝜙 = 0°) (e.g., decrease of ∆𝐺/𝑘𝐵𝑇 from 120 to 40 as 𝜙 varied from 40° to 0°) was observed. And, as the length of NRs increased, the range of 𝜙 to reduce the total free energy narrowed closer to parallel. For example, NR-32 led to sharp decrease of ∆𝐺 in the range of 0° < 𝜙 < 7°, while NR-8 showed more gradual decrease of ∆𝐺 in the range of 0° < 𝜙 < 30° (Figure S6). Therefore, we expect that all of the NRs are oriented to a certain angle to maximize their cross-sectional area at the particle surface and the tendency for parallel orientation of NRs to the particle surface is stronger for the longer NRs.



Figure 6. (a) Plots of the difference in the total free energy (∆𝐺) caused by addition of NR-20 (compared to the state without NR) as functions of 𝜙 and dBCP; (b) Plots of the minimum value of ∆𝐺 obtained at each 𝜙.

Figure 7. Schematic illustration for the positioning of NRs at the surface of P4VP domain of the BCP particles for (a) lamellae-forming BCPs and (b) cylinder-forming BCPs; DPD simulation results for the BCP/NR assembly in the particles: (a) no change in the particle structure was observed depending on l/L, showing axially-stacked lamellar BCP structures; (b) in contrast, the BCP structure and orientation were significantly changed depending on the l/L value showing vertically (l/L < 1) and randomly (l/L > 1) oriented cylindrical BCP structures.


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Consequently, the parallel orientation of NRs at the emulsion interface affords the assembly of differently structured BCPs within emulsions as follows. First, in the case of the symmetric BCPs, the neutral wetting of BCP domains to the particle surrounding induces the nucleation of lamellae whose lateral direction is perpendicular to the outer interface of the particle. Therefore, the NRs even longer than the size of P4VP domain (i.e., l/L > 1) can be selectively located on the P4VP domain of the particle surface by allowing some degree of rotation of the NRs (ω) within the P4VP domain at the tangential plane (Figure 7(a)). The interface-segregated NRs can drive nucleation of P4VP(PDP) disks from the particle surface, generating prolate particles with axially-stacked lamellar BCP structures. For these reasons, the long NRs with l/L > 1 (i.e., NR-20 (l/LLAM14 = 1.44) and NR-32 (l/LLAM14 = 2.35, l/LLAM20 = 1.60) can produce the prolate particles as demonstrated in the phase diagram described in Figure 2. In the case of cylinder-forming BCPs, the nucleation of the perpendicularly-ordered cylinders is induced by the NRs at the particle surface, exposing the top of the cylinder to the surface (Figure 7(b)). However in the case of l/L > 1, the long NRs cannot be confined within the cross-sectional area of the cylinder anymore. To keep the NRs within the cylinder, they should rotate in a direction normal to the particle surface (i.e., 𝜙 should increase) and penetrate into the P4VP domain, but this is not energetically favorable due to the reduction of interfacial area between BCP particle and surrounding occupied by the NRs (Figure 5). Therefore, we expect that most of the long NRs are still oriented parallel to the particle surface, but in this case, the perpendicularly-oriented P4VP(PDP) cannot be produced. Instead, the randomly-oriented of BCP domains including finger print patterns of P4VP(PDP) domains are observed at the surface of the BCP particle. As a result, the irregular-shaped particles with rough surface were produced as shown in the blue-boxed images in Figure 3(d).



The changes of overall shape and inner morphology of BCP particles driven by addition of NRs with controlled length were further supported by DPD simulation for the NR assembly within the confined BCP emulsions.62, 63 The BCP chain was modeled as linearly connecting PS and P4VP(PDP) beads. The length of BCP beads (NBCP) was set to 10 for the lamellae-forming BCPs, and 20 for the cylinder-forming BCPs to provide sufficient chain length for shorter block to form self-assembled structure. In order to systematically investigate the dependence of selective localization of NRs on the length of NR beads (Nrod), the value of Nrod was varied from 3 to 28. We also calculated the characteristic lengths of self-assembled structures (LLAM and LCYL) by performing the BCP melt simulations.64 The l/L-dependent NR assembly on the particle surface from the DPD simulation was in an excellent agreement with the experimental results. Short NRs (i.e., Nrod /LLAM ≤ 0.93 and Nrod /LCYL ≤ 0.52) were selectively incorporated into favorable P4VP(PDP) domain. Increase of Nrod led to segregation of NRs to the surface of BCP particle, resulting in axially-stacked lamellar structure (Figure 7(a)) or vertically oriented cylindrical structure (Figure 7(b)). For the lamellae-forming BCPs, the axially stacked lamellar structures were obtained in a wide range of 0.93 < Nrod /LLAM ≤ 5.20. However, the perpendicularly oriented cylinders were obtained only when the length of the NRs was within the range of 0.52 ≤ Nrod /LCYL < 1.83. When the value of Nrod /LCYL became larger than 1.83, randomly-oriented cylindrical BCP structures were observed. Therefore, the DPD simulation results provide good agreement with the experimental observations on the l/Ldependent transition of the particle shape and the BCP structure.


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CONCLUSION In summary, we investigated the effect of the length of NR surfactants on the shape and internal morphology of lamellae- and cylinder-forming BCP particles. The lengthdependent positioning of NRs in the BCP particles enabled the systematic modulation of the interfacial properties and induced the formation of anisotropic BCP particles such as prolate and oblate particles. In particular, l/L was the key parameter in determining the location of the NRs in the BCP particles and the particle shape. At small l/L (i.e., l/L < 0.36 for cylinderforming BCPs, and l/L < 0.83 for lamellae-forming BCPs), spherical BCP particles were produced with well dispersed NRs in the P4VP(PDP) domain. By contrast, the longer NRs were segregated at the surface of the BCP emulsion droplets, and were functioned as effective surfactants to induce the selective nucleation of P4VP disks or cylinders from the particle surface. Importantly, the range of l/L for producing oblate particles was limited to a specific region of 0.36 ≤ l/L ≤ 0.96, whereas prolate particles can be formed for much wider range of l/L ≥ 0.83. This discrepancy is mainly attributed to the geometrical difference between the lamellar and cylindrical forming BCPs that cause different degree of energetic penalty to accommodate NRs with different lengths within the P4VP domain. Our experimental observations on the change of the NR positioning and the BCP particle shape were further understood by free energy calculation and DPD simulation. Our study provides a comprehensive understanding of the co-assembly of NRs and BCPs within emulsion droplets especially in manipulating the morphology of the shape-anisotropic BCP particles.



ASSOCIATED CONTENT Supporting Information. Additional TEM and SEM images of NR-containing PS-b-P4VP(PDP) particles; synthetic procedures for CuPt NR surfactants; detailed free energy calculation and DPD simulation method to demonstrate the co-assembly of NRs and BCPs within emulsion droplet. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (B.J.K), [email protected] (W.B.L.)

ACKNOWLEDGEMENTS This research was supported by the Korea Research Foundation Grant, funded by the Korean Government (2017M3A7B8065584). This work was also supported by the Agency for Defense Development of the Republic of Korea, under the contract number UD160085BD. We acknowledge additional support for this work from the Research Projects of the KAISTKUSTAR and Basic Research Program (NK211B) funded by the Korea Institute of Machinery and Materials.


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Mechanistic Study on the Shape Transition of Block Copolymer

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