Role of Nanoparticle Selectivity in the Symmetry Breaking of

Article pubs.acs.org/JPCC

Role of Nanoparticle Selectivity in the Symmetry Breaking of Cylindrically Confined Block Copolymers Jay Hoon Park,† Jun Yin,† Vibha Kalra,‡ and Yong Lak Joo*,† †

School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States

‡

S Supporting Information *

ABSTRACT: We have comprehensively studied the effect of nanoparticle selectivity on the self-assembly of symmetrical block copolymer (BCP) under cylindrical confinement using simulation and experiment. For the simulation, a coarse-grained molecular dynamics (CGMD) simulation has been utilized, and we investigated the confined assembly using nanoparticles with three different interactions with block copolymer: (i) neutral to both A (wall-attractive) and B (wall-repulsive) phases, (ii) B domain selective, and (iii) A domain selective. It is predicted that nonselective (neutral) nanoparticles (NPs) tend to be placed near the interface between radially alternating layers of A or B domains, while selective (A or B) NPs swell the corresponding phase, inducing discrete asymmetrical morphologies. We also find that pure asymmetrical BCP forms more radially perforated morphologies, while symmetrical BCP/NP forms more discrete morphologies. Experimentally, we have incorporated gold or magnetite NPs with the matching three types of selectivity toward symmetrical diblock PS-b-PI and electrospun them. The morphologies observed from our study have been quantified by morphological classification numbers to identify the degree of asymmetry formed. The qualitative and quantitative comparisons between experiment and simulation confirm the validity of the simulation tool and shed light on the NP’s role on breaking the symmetry of BCP under cylindrical confinement.

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surfaces13,14 and spherical confinement.15−17 While confined assembly studies of BCP film created numerous potential applications, they are limited by their short length scale and difficulty in separating the nanostructures from the supporting BCP films. One method used to produce continuous long-scale nanostructures is to electrospin BCP into nanofibers. Electrospinning is an electrostatically driven process which forms submicrometer diameter fibers. When the electrical force at the interface of a polymer liquid overcomes the surface tension, a charged jet is ejected.18 The ejected jet then undergoes high deformation (strain (extension) rate ∼10 000 s−1) and rapidly evaporates (∼200 nL/s), resulting in solidified fiber accumulated on the grounded collector.19 These electrospun fibers are widely used as high performance separation, sensing, and filtration devices because of their large surface area to mass ratio.20 Fong and Reneker have an electrospun styrene− butadiene−styrene triblock copolymer solution to produce nanofibers.21 Largely disordered morphology was observed due to extensive elongation and rapid evaporation from electrospinning with such nanofibers. This finding is consistent with other works that reported the formation of irregular morphology.22−24 These nanofibers can be annealed to restore the equilibrium morphology, but it often requires annealing of the fibers above the glass-transition temperature (Tg) of the

INTRODUCTION Nanoparticles (NPs) have attracted much research interest for a wide variety of potential applications in biomedical, optical, and electronic fields.1−4 In particular, nanoparticles are successfully incorporated into a polymer matrix to enhance material properties.5−7 Due to their high surface energy, however, nanoparticles often self-aggregate in the polymer matrix, which prevents utilization of their large interfacial volume. Synergetic effects can arise from periodic spatial placement of the nanoparticles to fully maximize its utility. As one solution, the block copolymer has been used as a template for ordered placement of nanoparticles. Block copolymer (BCP) solutions and melts are known to self-assemble into a variety of nanoscale morphologies including spheres, rods, micelles, lamellae, vesicle tubules, and cylinders8,9 depending on the volume fraction and interaction parameter between different blocks. Self-assembly of BCP has attracted increasing interest in recent years for applications in nanotechnology.10,11 Precise control over the size, shape, and periodicity of these nanoscale microdomains is the key factor in providing opportunities for realization of nanoscale systems. It has been reported that BCP exhibits novel morphologies not seen in the bulk under a confined domain (D) which is commensurate with its equilibrium bulk periodic spacing (L0). Shin et al. confined symmetrical polystyrene-b-polybutadiene (PS-b-PBD) in an alumina nanopore to obtain concentric ring morphology which was not observed in the bulk.12 There are also other types of confinements such as block copolymer in between two flat © 2014 American Chemical Society

Received: December 11, 2013 Revised: February 22, 2014 Published: March 18, 2014 7653

dx.doi.org/10.1021/jp412145j | J. Phys. Chem. C 2014, 118, 7653−7668

The Journal of Physical Chemistry C

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BCP, resulting in the loss of fiber morphology. To overcome such limitations, one can coaxially electrospin the BCP core along with a thermally stable shell to preserve the fiber morphology while annealing the fibers above the Tg of BCP. Kalra et al. used silica as a sheath layer to the symmetrical polystyrene-b-polyisoprene (PS-b-PI) core and successfully obtained the PS-b-PI concentric ring from annealing.25 Similarly, Ma et al. used poly(methylmethacrylate-co-methacrylic acid) (P(MMA-co-MMA)) as the shell and poly(styrene-block-isoprene-block-styrene) as the core material and successfully annealed at high temperature to obtain the equilibrium concentric ring morphology.26 This confined assembly of BCP is a well-known phenomenon as observed by a number of experimental and simulation studies.27−29 Although there are many factors that contribute to this phenomenon, the general consensus is that it is the combined result of commensurability, polymer-surface condition, and the confining geometry that affects the confined assembly of BCP. These novel BCP structures can be formed only under cylindrical confinement, but they have limited potential applications from the materials standpoint due to its lack of functionality. Many groups have studied selectively adding surface-modified NPs to a block copolymer in film to demonstrate added functionality and morphology change induced by increasing the size of the NP-selective block copolymer domain.30−32 Using this idea, Kalra et al. successfully incorporated selective magnetite NPs in the symmetrical PS-b-PI core phase in electrospinning and demonstrated the selectivity and dispersion of such particles into one of the polymer domains in electrospun BCP nanofibers.33 They also successfully demonstrated the added functionality of these self-assembled materials with magnetic NPs and also showed evolution of BCP morphology by swelling of the PI domain with addition of the selective NPs.33 These continuous materials, with high surface area-to-mass ratio and good production rate, showed good promises in applications such as magnetic storage media and catalysts. The science of polymer/nanoparticle confined assembly has undeniably made significant progress in recent years. However, there has not been a study that deals with how exactly NPs can affect the self-assembly of BCP under a special condition like cylindrical confinement, and this special condition is a significant factor in self-assembly study because the resulting morphology is clearly different from that of bulk or film. In this study, we aim to examine the effect of NP selectivity on its placement and BCP morphology under cylindrical confinement. Experimentally, we have incorporated (i) styreneattractive NPs, (ii) isoprene-attractive NPs, and (iii) neutral NPs to a symmetrical PS-b-PI diblock copolymer by exchanging the ligand of the NP. Three types of BCP/NP composite solutions were electrospun, and the internal structure was observed to examine the effect of NP selectivity on BCP selfassembly under cylindrical confinement. In addition, we use computer simulation to gain further insights into these phenomena. Some recent simulation studies that involved BCP in cylindrical confinement have been useful in analyzing some of the novel morphologies formed in electrospinning experiment.34−36 For this study, we have used coarse-grained molecular dynamics simulation to investigate the location and three-dimensional structures of nanoparticles within cylindrically confined, symmetrical BCP/NP and how its selectivity can affect the block copolymer by breaking the symmetry of

lamellae-forming BCP. The coarse-grained MD method was chosen to greatly reduce computational time and to impose long time scale physics such as shear and elongation flows and thermal annealing in the future. There are recent simulation studies of BCP under cylindrical confinement37−39 and BCP/ NP nanocomposite self-assembly under two-dimensional confinements,40−42 but no other studies have dealt with simulation of the BCP/NP composite in cylindrical 3-D structures. Our most recent simulation work has dealt with cylindrically confined assemblies of asymmetrical BCP and BCP/NP and provided insight into the mechanisms behind the confined nanocomposite self-assembly.43 In the current study, we have primarily investigated the role of NP selectivity, concentration, and confinement dimension on self-assembly of symmetrical BCP where we aimed to break the symmetry of BCP by swelling of the NP-preferred phase and induce asymmetrical morphologies. By introducing a quantified morphological description, we can analyze the degree of symmetry breakage. Finally, we compared the predicted morphologies with our recent experimental results to reveal the 3-D structures and validate the simulation. By examining the role of NP selectivity on confined assembly by experiment and simulation, we gain the ability to fine tune the nanostructure for appropriate application.

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COMPUTATIONAL AND EXPERIMENTAL METHODS Simulation Parameters. Block Copolymer Modeling. The model block copolymer chains in the current coarse-grained MD study consist of minor (A) and major (B) blocks of monomers. Within a polymer chain, the neighboring monomers are connected by a finitely extensible nonlinear elastic (FENE) potential ⎡ ⎛ r ⎞⎤ 1 2 ln⎢1 − ⎜ u FENE(r ) = − kR max ⎟⎥ ⎢⎣ 2 ⎝ R max ⎠⎥⎦

(1)

where the spring constant k is 30 and the maximum extensibility Rmax is 1.5, as used by Kremer and Grest to simulate polymer beads.44 Monomers in each block have excluded volume interactions between them and are modeled by Weeks−Chandler−Anderson (WCA) potential45 ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ u REP(r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ + ε = u LJ(r ) + ε , r ≤ 21/6 ⎝r⎠ ⎦ ⎣⎝ r ⎠ u REP(r ) = 0, r > 21/6 (2)

where r is the separation distance between beads and σ and ε are the Lennard-Jones parameters. An attractive potential between like monomers (i.e., A−A or B−B) was used to incorporate the physics of microphase separation between the A and B species. The attractive potential, as described by Horsch et al.46 to model the equilibrium properties of diblock copolymer melts, is again a LJ potential that is cut and shifted at values that differ from those presented in eq 2. ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ u ATT(r ) = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ + u LJ(2.5), r ≤ 2.5, ⎝r⎠ ⎦ ⎣⎝ r ⎠ u ATT(r ) = 0, r > 2.5 7654

(3)



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The higher cutoff means that this is not purely repulsive and that monomers of the same type are attracted to each other. The thermostat used was a dissipative particle dynamics (DPD) thermostat. We point the readers to the previous simulation work done by Kalra et al. to learn more about the potentials and thermostat used.47 The chain length of the polymer was fixed at ten beads throughout the simulations. Each phase was assigned with five beads, i.e., A:B = 5:5. The site density ρ and the temperature kBT were kept fixed at 0.85 and 1.0, respectively. The number of beads in a fixed box size was determined based on the site density. Nanoparticle Modeling. The NP size was set at 1 in MD units, which is equivalent to a nanoparticle size of ∼1 nm in this system where BCP is described by a bead-spring polymer chain with 10 beads.47 The size of the NP ensured that the results were not peculiar to the particle size of one Kuhn monomer.47 When the simulation results were compared with the experimental results, the NP fractions were chosen to match the experimental setup. The NP attraction toward A, B, and wall phases was varied to match A-attractive, B-attractive, and neutral NPs. Wall Modeling. To apply the cylindrical confinement on the diblock copolymer, a fixed cylindrical wall diameter was set in x and y directions. Immobile beads with diameter of 1 MD unit were aligned cylindrically on the BCP and BCP/NP to set up the wall. Thus, periodic boundary condition was only applied in the axial, z direction. The diameter of the wall was set to range from 4.6 to 47.92, which is about 0.5 to 5 times bigger than the polymer domain spacing (∼9.1). The cylindrical wall layer was given attraction potential to the A phase. If the NP prefers the A phase over the B phase, it is set to be attracted toward the wall as well. When the NP prefers the B phase, however, the NP is repulsive from the wall. The strength of attraction of the NP toward the wall and phase A is set to be the same. Simulation Details. The velocity Verlet algorithm was used to integrate the equations of motion. The MD integration time step size, Δt, was fixed at 0.005. A cell list algorithm was used to make the code efficient,48 and the cutoff was set to be 2.5. To prevent undue periodic boundary artifacts, we varied the radius and height (z-axis length) of the system until stacked disk morphology was attained. When the dimensionless periodic height of the box size, Lz, was set at 9.54, the system attained the most stable form of a stacked disk at equilibrium. For the dimensions of radii we used in this study, the aforementioned Lz values attained the equilibrium structure (see Supporting Information S7). The simulations were run for a sufficiently long time until variables such as pressure, potential energy, radius of gyration, and mean squared end-to-end distance remained constant. The order parameter, O, which is the largest eigenvalue of the Saupe tensor,49 was monitored and stabilized along with the other variables when MD time was approximately 2000, which is about 400 000 time steps for our simulation. The current simulations were typically run until MD time reaches 10000, or 2 000 000 time steps to insure the formation of the BCP equilibrium morphology. The parameters used in this system are summarized in Table 1. Experimental Procedures. Nanoparticle Synthesis. Hydrogen tetrachloroaurate (HAuCl4, Aldrich), tetraoctylammonium bromide (TOABr, 99%, Aldrich), sodium borohydride (NaBH4, 99%), 1-decanethiol (DT, 96%, Aldrich), and thiolterminated polystyrene (1) (P4422-SSH, Polymer Source, Inc.)

Table 1. Variables Used in MD Simulation parameters

symbol

value (MD units)

temperature monomer size NP diameter NP monomer mass chain length bead density diameter of cylindrical confinement z-axis periodic length Flory−Huggins parameter*N MD integration time step length of polymer domain

kBT σ σp m N ρ D Lz χN Δt L0

1 1 1 1 10 0.85 4.6−47.9 6.36−15.90 53.3 0.005 ∼9.1

were used. According to Brust’s two-phase protocol,50 gold nanoparticles encapsulated with decanethiolate and P4422-SSH monolayer shells were processed by two-phase reduction of HAuCl4 and a synthetic modification.51 In general, with the help of phase transfer reagent TOABr (36 mM), AuCl4from the precursor HAuCl4 (10 mM) dissolved in deionized water was first transferred from aqueous solution to toluene solution, followed by capping agents (21 mM) adding, e.g., decanethiol, P4422-SSH with 2:1 thiol/Au mole ratio. Then, the Au precursors were reduced by aqueous NaBH4 with controllable dropping, turning the clear solution into dark brown/dark red. After 4 h of stirring at room temperature, the reaction was completed and ready for further particle purification, which was operated by a rotary evaporator (at ∼50 °C) and followed by ethanol cleaning to purify the encapsulated Au particles. The average size of the as-synthesized gold nanoparticles (DT−Au2 nm) turns out to be 2.0 ± 0.7 nm. Coaxial Electrospinning. Symmetrical PS-b-PI (molecular weight of 45 000−46 000 g/mol for PS and PI blocks), with a polydispersity index (PDI) of 1.07, was purchased from Polymer Source. The symmetrical PS-b-PI BCP was mixed in THF with the Au NP, where separate samples with the mass fraction of the Au NP relative to BCP ranging from 1 to 10 wt % were made. Typically, the polymer solution had ∼15 wt % BCP/NP in THF. The BCP/NP solution was used as a core layer solution for a coaxial electrospinning setup where the silica precursor from the tetra(ethyl) ortho silicate (TEOS) sol−gel synthesis method was used as the shell layer. To produce the sol−gel solution, a homogeneous solution with molar ratio of TEOS:EtOH:H2O:HCl of 1:2:2:0.01 was made. After vigorous mixing, the solution was placed in a 50 °C oven to accelerate the sol−gel transition. After ripening for 3−4 h, the solution is ready to be electrospun. The flow rate between the core and shell was fixed at 0.01−0.015 mL/min, with ∼20 kV charge, and fibers were deposited at a grounded collector 15 cm away from the tip of the solution syringe. Charaterization of the Electrospun Nanofiber. To examine the nanostructure inside the nanofiber, we had microtomed the electrospun fiber samples. The sample was first embedded in epoxy resin and cured under an oven at 50 °C to harden the epoxy. Then the sample was microtomed at 70−80 nm thickness using a Leica Ultramicrotome. After the cut sample was recovered on a copper grid, it was stained with osmium tetraoxide to differentiate between the PS and PI phase under TEM. A Tecnai T-12 TEM was used to observe the nanostructure of the sample. 7655



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Figure 1. Simulation snapshot results for symmetrical BCP in (a) bulk, cylindrical confinement with (b) neutral interaction between the wall and BCP and (c) selective attraction between the wall and BCP. The cross sections across and along the cylinder axis are shown in (d), (e), (f) at the top row and bottom row, respectively. From left to right, the images in (d) represent the experimental TEM image of the PS-b-PI core with a silica shell, (e) the simulation snapshots of neutral interaction, and (f) A (blue phase)−wall attraction. The scale bar in the TEM image represents 200 nm.

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RESULTS AND DISCUSSION In this section, we first show our finding of pure symmetrical BCP under cylindrical confinement by coarse-grained molecular dynamics (CGMD). We then compare the simulation prediction with electrospun symmetrical BCP to validate the tool. Then we incorporate three different types of NPs to a symmetrical BCP and induce morphological change. Then finally, we compare the comprehensive experiment and simulation results by examining the morphological similarities both qualitatively and quantitatively. Pure Symmetrical BCP. First, we induced cylindrical confinement on pure symmetrical BCP and compared the selfassembled structures with those in the bulk. In bulk, the symmetrical BCP self-assembles into the well-known lamellae phase. Under cylindrical confinement, the lamella is curled and forms stacked disks alternating between A and B phases. As shown in Figure 1b, alternating disks of A and B phases are stacked along the cylinder axis when the cylindrical wall covering the BCP (not shown) does not have preferential attraction toward one of the BCP phases. When one of the BCP phases is preferred by the wall, as shown in Figure 1c, the wall is wetted by more a attractive phase, and the BCP selfassembles into concentric rings. The morphological difference between Figure 1b and Figure 1c shows clearly that the interaction of the wall and BCP phase can yield different morphologies under cylindrical confinement. The self-assembly

of symmetrical BCP under cylindrical confinement to form either a concentric ring or stacked disk morphologies was observed in other theoretical predictions as well.28,29,52,53 The simulation results are then compared with the equivalent experimental ones in Figure 1d,e, and f. A symmetrical PS-b-PI BCP was coaxially electrospun with a silica precursor shell layer. Figure 1d shows the cross-section of the nanofiber after thermal annealing. Clearly, the cross sections are more similar between Figure 1d and f (selective wall) than Figure 1d and e (neutral wall). The similarities between simulation and experiment not only validate the simulation results but also confirm the presence of preferential wetting of the PS-b-PI with the silica shell layer. Throughout the current study, the phase that exhibits a preferred interaction with the cylinder wall is denoted as the phase A (colored as blue), while the other phase without attractive wall interaction and thus repulsive to the wall is assigned as the phase B (colored as green). Having confirmed the preferential attraction of the cylindrical silica wall to one of the BCP phases in our experiments, we then studied the effect of the confinement dimensions on the self-assembly of BCP. Generally, as D/L0 is increased, the number of concentric rings is increased as well. The number of rings increases when D/L0 is commensurate with an integer multiple of block copolymer domains, i.e., from 1.5 to 2.0 and from 2.5 to 3.0, which makes intuitive sense (see Supporting Information S1). However, when D/L0 is increased from 3.5 to 7656



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Figure 2. Snapshots of the symmetrical BCP/neutral NP nanocomposite equilibrium morphologies at different NP loading. The blue and green beads represent A and B phases of the symmetrical BCP, respectively. The red beads represent the neutral NPs.

Figure 3. Concentration profile of cylindrically confined BCP with neutral NP for (a) 10%, (b) 20%, and (c) 30% at D/L0 = 5.6. Blue dash-dotted line = A, green dashed line = B, and solid red line = NP. The radial concentration profile examines the A, B, and NP from the core to the wall on the left side and right side, where the former ranges from 0 to −1, while the latter ranges from 0 to 1. The radial distance from the center has been normalized by the confinement diameter. For each set, the top images show the full morphology seen from above, while the bottom images show the same views for NPs only.

layers. As D/L0 gets bigger, the difference of polymeric beads among the layers gets bigger as well. Thus, when D/L0 = 4.0, even though the confinement diameter is commensurate with the integer multiple of the BCP domain size, the number of layers is not necessarily increased when compared with 3.0 < D/L0 < 4.0. When the confinement diameter is smaller than the domain spacing (D/L0 < 1.0), the physical confinement overrules the chemical affinity of the BCP to the wall, and both BCP phases can be found along the wall. This effect of extreme physical confinement, also known as frustration of the BCP caused by

4.0, the number of layers is not increased. It should be noted that this observation is consistent with the theoretical prediction by Yu et al., where the number of rings is not increased to five until D/L0 = 4.3.53 Under a cylindrical confinement with a selective wall, it should be noted that the circumference of the alternating A and B layer gets bigger as we inspect it from the core to outward radially toward the wall. Since the thicknesses of the alternating layers are similar (∼4.5), the outer layer typically has more polymeric beads than the inner one. One exception is the A phase that is wetting the wall area, where its thickness is about one-half of the other 7657



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Figure 4. Snapshots of the symmetrical BCP/selective NP nanocomposite equilibrium morphologies at different NP loadings. The blue and green beads represent A and B phases of the symmetrical BCP, respectively. The red bead represents the selective NP which is set to be selective toward the A phase. The morphologies shown in inset are the minority domain, or B phase, with the NP and A phases blanked out.

NPs take up the possible spaces in the interface between A and B, they are forced to spread out evenly into the A and B domains. This phenomenon shows how the physical limitation of the most chemically favorable space forces particles to look for the next option. The NP placements in A and B phases are more apparent when we examine the concentration profile when D/L0 = 5.6 in Figure 3. As the concentration of NPs is increased, more NPs are seen at the center of A and B domains. It is noted that the highest NP concentration peaks are found at the interface between A and B phases even when NP volume percentage is 30%, emphasizing that the neutral NP prioritizes its placement between A and B. As the NP concentration is increased, the interfacial area will eventually be filled up by NPs, and eventually the rest of NPs smear into A and B phases. It should also be noted that NP placement begins to resemble a bulk neutral NP concentration profile seen in ref 47, as D/L0 is increased to 5.6 (see Supporting Information S3 for concentration profiles at other D/L0 values). As the diameter becomes larger, the curvature of the concentric layers near the wall becomes smaller, thus the system approaches planar lamellae. The difference between the polymer beads then should become smaller. The unique feature observed with the confined system is the presence of the NP-dominant region in small D/L0 of 2.0 (see Supporting Information S3) with NP loading of 20% and 30%. This observation implies that the NPs will likely form a major domain in a confined space. Interplay between Selective Nanoparticle and Symmetrical Block Copolymer in Confined Assembly. In this section, we studied the self-assembly of the selective NP/ symmetrical BCP composite in bulk and under confinement. Figure 4 shows the equilibrium morphologies of symmetrical BCP and A (blue)-selective NPs. The lamella is preserved, or the symmetry of the BCP is not broken, up to NP loading of 10%. As the NP loading is increased to 20% then to 30%, we observe onset of symmetry breakage and the formation of bicontinuous morphologies. When NP loading = 40%, the A phase swells up even more, and the volumetric ratio between

the curvature, was experimentally observed with PS-b-PBD confined in an aluminum nanopore.12 When the nanopore dimension is smaller than the BCP’s domain spacing, the BCP does not have enough space to pack in more chemically favorable morphology or concentric ring phases and instead formed stacked disk morphology. Qualitatively similar axial morphology was observed when we axially cut our simulation result at D/L0 = 0.5. From the similarity between the two, we believe that BCP chain packing frustration indeed occurs when D/L0 = 0.5, and the 3-D structure from ref 12 would match with our prediction in S1 (Supporting Information). Interplay between the Neutral Nanoparticle and Symmetrical Block Copolymer in Confined Assembly. We first examined the self-assembly of BCP and the neutral NP nanocomposite in bulk and under cylindrical confinement. The simulated bulk equilibrium morphologies for the neutral NP and symmetrical BCP are shown in Figure 2. As expected, most of the NPs are found at the interface between A and B phases. It should be noted that as the NP loading is increased above 20% NPs are found in the center of A and B domains as well. The onset of lamellae disruption is observed when the NP loading is increased 40%, and more disordered morphology is observed at 50%. This result is in good agreement with the simulated predictions of the BCP/NP composite by Shultz et al.,54 where disordered morphology was observed when neutral NP loading was greater than or equal to 40% at χN ∼ 50. Then we examined the neutral NPs in BCP under cylindrical confinement. The BCP morphology is largely unaffected by addition of the neutral NPs for 1.0 ≤ D/L0 ≤ 4.0 (see Supporting Information S2). When NP concentration is 10%, the NPs are observed along the interface of alternating A and B phases. This is consistent with the bulk result shown in Figure 2b and other bulk simulation results where neutral NPs are placed at the interface between A and B phases.47,54 As the concentration is increased, the NPs are found in both BCP phases as well, which is the same trend as observed with the bulk system in Figure 2c and 2d. After a certain amount of 7658



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Figure 5. Snapshots of simulation results with the inclusion of B-attractive NPs into symmetric BCP with concentration of (a) 0% (pure BCP), (b) 10%, (c) 20%, and (d) 30% are shown in a wide range of D/L0. The top rows show the full morphology seen from the top, while the bottom one shows core morphologies. If the core is A phase, the wall is shown as well.

Figure 6. Concentration profile of cylindrically confined BCP with B-attractive NP for (a) 10%, (b) 20%, and (c) 30% at D/L0 = 5.6. Blue dashdotted line = A, green dashed line = B, and red straight line = NP. The radial concentration profile examines the A, B, and NP from the core to the wall on the left side and right side, where the former ranges from 0 to −1, while the latter ranges from 0 to 1. The radial distance from the center has been normalized by the confinement diameter. For each set, the top images show the full morphology seen from above, while the bottom images show the core A morphologies.

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Figure 7. Snapshots of simulation results with (a) NP−B attractive NPs with concentration of 30% and (c) 40%, compared with pure BCP with chain fraction of (b) A:B = 4:6 and (d) 3:7. For each set of figures, the top row shows the full morphology seen from the top, while the bottom row shows the axial core morphology.

the A domain and B domain becomes 7 to 3. As a result, we observe the formation of B cylinders as seen in Figure 4e. As the concentration of the NP is increased further, we expect to see more discrete B morphology, such as a spheroid. This result is again similar to the previously predicted results by Shultz et al.54 where the onset of symmetry breakage was observed when NP loading was higher than 20%, and then perforated lamellae and cylinder were observed as the NP loading was increased further at χN ∼ 50. We then studied the effect of the selective nanoparticles on confined symmetrical BCPs. Unlike the bulk system, changing the NP selectivity between the A and B phases can yield different outcomes due to the presence of the A domain-

selective cylindrical wall. We expect that the NP/BCP interactions, when combined with cylindrical confinement, will greatly affect the BCP self-assembly. With each NP/BCP interaction, the concentration of the NP is increased, in 10% increments, from 10 vol % up to 30 vol % to examine the evolution of BCP morphology due to the swelling of the NPpreferred BCP phase. We incorporated NPs that are attracted to the wall-repulsive B phase. The NPs are also set to dislike the wall phase, following the chemical affinity of the B phase. Figure 5 shows the NPs incorporated with various concentrations within a range of D/L0. Unlike the neutral NPs, the BCP morphologies are influenced by the inclusion of selective NPs. Since these 7660



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Figure 8. Quantification of morphologies formed. It explains how the morphologies are categorized based on the number of layers of domains (including both A and B) (L), the number of radially and axially interconnected domains (I), and the number of axially perforated domains (P).

NPs favor the B phase, the NPs effectively increase the volume of the B phase, leading to a smaller total number of alternating layers even at 10% NP concentration. A higher effective volume fraction of the B phase breaks the original symmetry between A and B, allows the discrete layers of B phases to be connected, and eventually leads to the formation of novel A morphologies, as the A phase becomes the minor phase. As seen from Figure 5, the morphological differences are more evident among different NP concentrations when D/L0 ≥ 2.0. As the confinement on BCP is lessened, the circumferential boundary of the outermost A layer increases, which allows more penetration by the swollen B and NP matrix phase. This in turn results in more diverse A morphologies, such as cylinders, stacked disks, and horseshoe morphologies. These morphologies were seen from our previous simulation of confined assembly of asymmetrical BCP40 and in other theories and simulations as well.52,53 The effects of the NP concentrations are well illustrated in the radial NP concentration profile in Figure 6. When NP loading is 10%, the NPs are found evenly at the center of the B domain. As the concentration is increased to 20%, the number of NPs near the center of the B domain increases further. As NP concentration is increased further to 30%, there are more NPs than B near the center of the B domain. It is also notable that in the core region (r ∼ 0) the NPs are forming their own domain rather than being located at the center of the B domain. Note that this core region was occupied by the A phase when the NP concentration was low ( I with pure asymmetrical BCP, and I > P with symmetrical BCP/NP. When NP loading is at 40%, the difference between asymmetrical BCP and symmetrical BCP/NP is more apparent than lower NP loading. This difference implies that the NP’s influence on self-assembly becomes greater as NP loading is increased, resulting in different confined assembly. Generally, the core morphology is radially curved for BCP (P > I), while more discrete morphologies are observed for BCP/NP (I > P). The only exception is when P = 1 and I = 0 for D/L0 = 3.0 for the A5-B5NP2.5 case. Here, a stacked disk of core A morphology is observed, and it is more representative of discrete morphology rather than curvy morphology. This is the only instance discrete morphology is observed even when P > I. Thus, we can conclude that when the B phase is swollen the BCP/NP composite exhibits discrete morphologies and the pure asymmetrical BCP exhibits a perforated curvy morphology. Third, we incorporated the NPs into the wall attractive A phase. Following the chemical properties of A, the NPs are equally attracted to the wall. Figure 9 shows the snapshots of simulation results incorporating different concentrations of Aattractive NPs in a wide range of D/L0. Similar to the B-NP attractive case from Figure 6, we observed the evolution of BCP morphology due to the swelling of the A phase by NPs. The difference here is that some fractions of NPs are found along

radially and axially interconnected domains (I), and the number of axially perforated domains (P). If either P or I is greater than 0, symmetry between A and B is broken, and asymmetrical morphology is observed. The degree of asymmetry is increased as P and I numbers become bigger. The comparison between P and I numbers reveals the type of the core minor block morphology. If P > I, the core minor block forms a perforated and radially curved shape. If I > P, it forms discrete domains. On the basis of this classification, we have analyzed the core minor phase BCP morphologies from Figure 7 and tabulated the morphological zones in Table 2. Note that the L numbers Table 2. Morphological Zones for A-Minority Phases

match for all D/L0 for pure BCP. In the case of symmetrical BCP/NP, however, the NP incorporation results in more erratic change of L numbers as D/L0 is increased from 2.0 to 4.0 . For instance, when D/L0 = 2.0, the NP cluster forms its

Figure 9. Snapshots of simulation results with the inclusion of A-attractive NPs into symmetric BCP with concentration of (a) 0% (pure BCP), (b) 10%, (c) 20%, and (d) 30% are shown in a wide range of D/L0. The top rows show the full morphology seen from the top, while the bottom shows core B morphologies. 7662



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Figure 10. Concentration profile of cylindrically confined BCP with A-attractive NP for (a) 10%, (b) 20%, and (c) 30% at D/L0 = 5.6. Blue dashdotted line = A, green dashed line = B, and red straight line = NP. The radial concentration profile examines the A, B, and NP from the core to the wall on the left side and right ride, where the former ranges from 0 to −1, while the latter ranges from 0 to 1. The radial distance from the center has been normalized by the confinement diameter. For each set, the top images show the full morphology seen from the top, while the bottom images show the core B morphologies.

compared with symmetrical BCP. Thus, even when D/L0 = 3.0, L4 is not observed and results in slower transition of L numbers as D/L0 is increased. Then we note the effect of NP inclusion to induce Adominant confined assembly. The morphology formed with symmetrical BCP/NP results in more discrete morphologies when compared with its pure asymmetrical BCP counterpart. The morphological difference between pure BCP and BCP/NP is actually more apparent than the B-dominant case as indicated by much higher P numbers than I numbers. The driving force behind major phase swelling with NPs in the A-dominant case is toward the wall layer and core A layer, when compared with the B-dominant one where its driving force is only toward the core (remember the B phase is repulsive against the wall). Thus, the bidirectional driving force results in formation of more asymmetrical morphology in the A-dominant BCP/NP case as observed qualitatively from Figure 11 and quantitatively from higher P numbers of 5−6 in general. Then we compared the radial concentration profile of A, B, and NP for all three NP attraction cases at 10% NP concentration for D/L0 = 0.5 (see the Supporting Information S6). Qualitatively, the radial morphologies were all distorted for all NP attraction cases. The same observation was made from the radial concentration profile as well. Even though the A phase should be wetting the wall, because of the extreme physical confinement, the BCP chains are frustrated and the BCP phases and NPs found evenly in radial direction. This observation was true whether the NPs were attracted to wall, A, B, or neutral. Here, the extreme physical confinement dominates and ignores the chemical affinity between the BCP and the wall. When we examined the axial morphologies, the BCPs are seen stacking across the cylindrical axis, just like the pure BCP in S1 (Supporting Information). Because the confined space here is still big enough for the unchained NPs to move around, they follow their affinity toward the BCP. The NPs are seen at the wall even when the NP is attracted to the B

the A blocks near the wall, and thus the inclusion of NPs can affect both the core and outer layers of the A domain. Consequently, the impact of NPs is divided, rather than concentrated, to wall and core regions, when compared to the equivalent B-NP attractive case. Thus, the formation of asymmetrical morphology is less apparent at NP loading lower than 20%. However, when NP loading is increased to 30%, the core and skin A phases are attracted to each other and form more diverse asymmetrical morphologies. The NP concentration profile at D/L0 = 5.6 (Figure 10) shows that as NP loading is increased more NPs are seen along the wall phase. Just as observed from Figure 6, the NPs start to form their own domain in a small space (D/L0 = 1.0), but this time mostly along the wall rather than in the core. This trend is also observed in other self-assembled BCP/NP composites with different D/L0 values (see Supporting Information S5). Even though the A chains have the same attractive potential toward the wall as the NPs, in the limited bound space the NPs are more likely to form their domain than the A phase. The “crowd-out” effect is still observed here, but the NPs in the wall are not freely connected to the core like the Battractive case. Thus, the self-assembly is not affected as severely from the crowd-out effect but rather from the swelling of the A phase by core NPs. As with the B-attractive case, we then compared the BCP/ NP composite with equivalent pure asymmetrical BCP morphologies at 2.0 ≤ D/L0 ≤ 4.0. The qualitative 3-D morphologies are observed in Figure 11, and the quantified morphological classification numbers are tabulated in Table 3. First we note that the A-dominant pure asymmetrical BCP transition from L3 to L4 occurs when D/L0 = 3.5, unlike the Bdominant case and symmetrical BCP where its transition occurs when D/L0 = 3.0. With A-dominant BCP, swelling of the A phase results in a relatively higher increase in the skin A layer than the core A layer. We should also note the core B layer has decreased as well, resulting in more wall phase swelling when 7663



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Figure 11. Snapshots of simulation results with (a) NP-A attractive NPs with concentration of 30% and (c) 40%, compared with pure BCP with chain fraction of (b) A:B = 6:4 and (d) 7:3. For each set of figures, the top row shows the full morphology seen from the top, while the bottom row shows the axial core morphology.

Table 3. Morphological Zones for B-Minority Phases

Figure 12. Comparisons between PS-b-PI/NP electrospun results with simulation results. The NP volume % used in simulation is plotted on the x-axis, while the combination of interconnecting layers (IA + IB) is plotted on the y-axis. The inset images represent the corresponding simulation and experimental TEM images with the similar volumetric A:B ratio. The scale bar on the TEM images is 100 nm.

phase and repulsive against the wall (Figure 12b). This is mostly because the NP is attached to the B chain which is forced to contact the wall, and some of the NPs are found there along with the B chain. Thus, when D/L0 is smaller than the periodic BCP spacing, physical confinement frustrates the BCP chain and ignores the BCP and NP’s chemical affinity toward the wall. 7664



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Comparison with Experiments. To confirm the validity of our simulation tool and experimentally observe NP selectivity’s role on confined assembly, we have electrospun symmetrical PS-b-PI with three different types of NPs. The three different types of NPs are (i) oleic acid-coated FeO3 NP (previous experiment from ref 33) attracted to the PI phase, (ii) styrene oligomer-coated Au NP which is attracted to the PS phase, and (iii) decane thiolated-coated Au NP which is neutral to the PS and PI phase. The overview of morphological classification numbers of selective NPs for experiment and simulation are tabulated in Table 4. Table 4. Comparison of Morphological Zones between Simulation and Experiment A-attractive (Figure 12)

Figure 13. Comparisons between PS-b-PI/NP electrospun results with simulation results. The NP volume % used in simulation is plotted on the x-axis, while the combination of interconnecting layers (IA + IB) is plotted on the y-axis. The inset images represent the corresponding simulation and experimental TEM images with the similar volumetric A:B ratio. The scale bar on the TEM images is 100 nm.

B-attractive (Figure 13)

figures

simulation

experiment

simulation

experiment

12a, 13a 12b, 13b 12c, 13c

L5I0A0B L5I3A1B L6I7A5B




high number of I’s (>2) as opposed to morphologies predicted in Figure 7 with wall-repulsive NP. Again, this is due to the bidirectional attractive driving force of the NP toward the wall and the core morphology. Lastly, neutral Au NPs were added to a symmetrical PS-b-PI and coaxially electrospun with a silica shell layer. The experimental images (Figure 14) clearly demonstrate the preservation of a symmetrical BCP concentric ring morphology regardless of NP loading, which is consistent with our simulated prediction. The NPs are observed along the interface between PS and PI phases in Figure 14(a) and found in both phases as well when NP loading is increased (Figure 14b and 12c). At a quick glance, it is difficult to pinpoint the NP location within the PS-b-PI/Au NP due to the small size of the Au NP (∼2 nm) and its poor contrast with the dark PI phase (stained with OsO4) under TEM. To demonstrate more quantitative analysis of the comparison between experiment and simulation, we attempted to examine NP concentration at each layer of BCP domains. Here, the PI phase is denoted as the A phase, and the PS phase is denoted as the B phase. The layers are sequentially numbered from innermost to outermost. Then, the Au NPs were counted for each polymer layer as well as the interfacial boundary between two layers. If the Au NPs were located at the boundary between two layers within ∼3 nm, which is about 10% of the BCP domain size (∼30 nm), they are considered to be located at the interface. The comparison of the NP concentration profile between simulation and experiment is shown below the experimental and simulation images in Figure 14. The NP fraction is consistently higher than the bordering domains for both simulation and experiment, regardless of NP concentration. We note that some of the experimental cross-sectional images presented in Figures 12, 13, and 14 do not have perfect circular cross sections like the respective simulation results. Most of the experimental results with selective NPs in Figures 12 and 13 are circular in nature, while the ones with neutral NPs in Figure 14 are ellipsoidal. This is due to the difficulty in obtaining perfectly circular cross sections from microtoming the electrospun nanofibers. Yu et al.55 suggested that the BCP morphology can be very different depending on the confinement geometry. We also observed in our previous study with asymmetrical BCPs under cylindrical confinement that the cutting angle can yield different two-dimensional cross-sectional images for the same BCP morphology as well.43 However, most

As seen from Figure 12, the PI-preferring NP was found evenly along the PI and the silica wall phase in the experiment. As the NP loading was increased, a significant change in BCP morphology was observed with cross sections across and along the fiber axis. The BCP has evolved into an apparent bicontinuous phase in Figure 12. The simulation results with similar fraction of A, B, and NP showed good qualitative agreement of the cross sections with the experimental result. We then compared the morphology classification numbers between the experimental and simulation results. Because it is hard to identify axial perforation with 2-dimensional microtomed TEM images, we have omitted P numbers here. In the case of the I numbers, the trend observed between the experiment and simulation is the same, where IA > IB for asymmetrical morphologies. This not only affirms the validity of our simulation but also explains that our experimental result with BCP morphology evolution was achieved due to the swelling of NPs to the PI phase. It also explained the location of NPs along the silica wall, which is caused by the attraction of NPs and the silica wall phase and also indicates that the PI phase is attracted to the silica wall as well. Then, styrene-attractive Au NP was added to a symmetrical PS-b-PI and electrospun with a silica shell layer. The crosssection of the electrospun fiber reveals the nanostructures as shown on the inset of Figure 13. As the NP loading is increased, more asymmetrical morphology is observed qualitatively and described by higher number of I’s. The experimental morphology did not quite match up with what we had anticipated in Figures 5 and 7 with B-attractive NPs in BCP/NP. This is because we originally assumed the NP will follow the same chemical affinity of its selective BCP phase, hence repulsive against the wall. From our experiment, however, it is possible that NPs were in contact with the shell silica precursor solution, which is ethanol-based. The Au NPs, therefore, may have physically placed along the wall, as suggested by the TEM images in Figure 13. Thus, we applied wall-attractive potential to NPs in our simulation and predicted the morphologies shown in Figure 13 at 10 wt %, 20 wt %, and 30 wt % loading. The morphologies now match up nicely, with NPs found along both the wall and the wallrepulsive B-phase or PS phase. Even at L4, we see relatively 7665



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Figure 14. Comparisons between PS-b-PI/NP electrospun results with simulation results. From (a) to (c), the NP loadings are increased from 10% to 30%, and the similar volumetric A:B ratio from experimental results is shown next to the simulation results. The scale bars on the TEM images are 100 nm. Below the experimental and simulation images, the location of the nanoparticle and its fraction in each block copolymer layer and interface domains are plotted.

of the morphologies from ellipsoidal cross sections55 are qualitatively similar to those found in circular cross sections with a similar D/L0.53 In addition, the cross sections with the most apparent ellipsoidal shape are mostly found with the BCP/neutral NPs from Figure 14. With neutral NP loading ≤30%, we expect to see symmetrical concentric ring morphology, and we believe that the morphological variation among the symmetrical morphologies under most twodimensional circular confinement is not as apparent as the asymmetrical ones. Thus, we believe we can make a good correlation between the experimental and simulation results presented in Figures 12, 13, and 14.

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less of the BCP, NP, and wall interactions. We also examined the effect of NP concentration at various D/L0 with three different NP/BCP interactions. For neutral NPs, the NPs prioritize their placement along the interface between A and B, but increased concentration leads to smearing of NPs into A and B. With the selective NPs, the evolution of morphology due to swelling of the preferred phase is observed, eventually leading to a formation of discrete asymmetrical morphologies especially at NP loading higher than 30%. This result is clearly different from the equivalent asymmetrical BCP morphology, which has shown more perforated curvy morphology. This morphological difference is most likely due to the difference in χN and the “crowd-out” effect of NPs in a small confined space. For the A− NP attraction case, the morphology evolution is observed but not as dramatic as B−NP at low concentration because most of the NPs are placed along the wall. However, when NP loading is ≥30%, the bidirectional driving force of the NP toward wall and core A layers drives formation of much more discrete asymmetrical BCP morphologies. In both cases, the NP crowdout effect was observed, especially along the wall for the Aattractive case and in the center for the B-attractive case. Finally, the comparison between the equivalent experiment and simulation confirms the validity of the simulation. This result can help us understand how NP presence can affect the BCP self-assembly under cylindrical confinement, especially for the nanostructure of the electrospun BCP/NP nanofiber. It also

CONCLUSIONS

The systematic studies of the cylindrically confined BCP/NP showed that the pairwise interaction of NP and BCP greatly affects the self-assembly of the BCP/NP nanocomposite. There is a competing force between the physical confinement with the chemical interactions between BCP, NP, and the wall. When D/L0 < 2.0, the physical confinement is more dominant, and morphological differences are minimal regardless of NP incorporation. However, as D/L0 is increased, more diverse morphologies are formed with different interactions and concentrations of NPs as more space becomes available. In the extreme case of D/L0 = 0.5, the frustration of BCP/NP caused by the cylindrical confinement is observed, thus exhibiting similar radially homogeneous morphologies regard7666



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revealed the full 3-D structures of the previously unknown experimental results, rendering the nanostructure applications to magnetic storage media and catalysts more feasible. The current simulation findings shed light on the role of NP selectivity and concentration on confined assembly of BCP/NP under cylindrical confinement, which was previously unknown. This tool can serve as a guidance to predict morphologies with a given fraction of BCP, polymer domain radius, and the conditions and loading of NPs. Gaining control over these nanostructures can bring realization of numerous applications much more efficiently than through numerous trial-and-error. To truly emulate the electrospun system, one has to consider other various factors such as elongational deformation, polydispersity, degradation, and evolution of sol−gel silica. In the end, the coarse-grained MD simulations have strong potential in fully emulating electrospinning experiments, potentially serving as a powerful predictive tool for designing BCP and BCP/NP nanocomposite nanofibers.

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ASSOCIATED CONTENT

S Supporting Information *

Concentration profiles at various ranges of D/L0 for neutral, Battractive, and A-attractive NPs in BCP under cylindrical confinement BCP are available. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was partly supported by Axium Nanofibers, LLC. All the computational works were done using the CBE server in the School of Chemical & Biomolecular Engineering at Cornell University. All of the morphological diagrams were drawn using Qutemol.56 The authors also acknowledge Cornell Centers for Material Research (CCMR) grant NSF DMR-1120296 for material characterization.

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Role of Nanoparticle Selectivity in the Symmetry Breaking of

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