Laterally Nanostructured Vesicles, Polygonal Sheets, and

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Article Cite This: Macromolecules 2019, 52, 3680−3688

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Laterally Nanostructured Vesicles, Polygonal Sheets, and Anisotropically Patched Micelles from Solution-State Self-Assembly of Miktoarm Star Quaterpolymers: A Simulation Study Jiaping Wu, Zheng Wang, Yuhua Yin, Run Jiang, and Baohui Li* School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Nankai University, Tianjin, 300071, China Downloaded via JAMES COOK UNIV on August 25, 2019 at 06:38:59 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: The self-assembly of miktoarm star quaterpolymers, composed of one solvophilic arm and three solvophobic arms connected at a common junction point, in dilute solutions has been investigated using a simulated annealing technique. By tuning the strength of incompatibility between the different solvophobic arms (α) or the quaterpolymer composition, unique multicompartment aggregates are predicted and their formation mechanisms are elucidated. It is the competition between the interfacial energy and the surface energy that results in the morphological transitions. At large α values, interfacial energy dominates over the system, and hence, hexagonally shaped laterally patterned nanosheets with smaller interfacial areas always form to decrease the interfacial energy. The smaller interfacial area of this morphology comes from the high local order of the three-colored short-cylinders where any three centers of mass of the nearestneighboring A, B, and C domains constitute an approximately regular triangle. The paving of the nearly rigid triangles results in the hexagonal shape of the whole nanosheet. At relatively small α values, transitions from vesicles to nanosheets and further to micelles are observed with increasing the volume fraction of the solvophilic arm, f P. The vesicles can be of lateral patterns with six protrusions which distributed symmetrically, and each corresponds to a packing defect of the three-colored short-cylinders. Micelles can be highly anisotropic and multiple-patched. The higher curvature of micelles favors the maximal contact for the solvophilic arm with solvent molecules. The morphological sequence obtained with increasing f P has a similar trend to that obtained with decreasing α. Our simulation results are compared with related experiments. The self-assembly of miktoarm star quaterpolymers could provide a powerful strategy for fabricating nanoscaled multicompartment aggregates with special shape and morphology, which may offer tremendous potential in nanotechnology.

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INTRODUCTION Aggregates self-assembled spontaneously from amphiphilic block copolymers in dilute solutions can be used in emerging nanotechnologies1−3 and have received considerable interest in the last few decades.4−6 The self-assembly of amphiphilic diblock copolymers in a dilute solution has been well documented,7−9 and three general morphologies10,11 of spherical micelles, worm-like micelles, and vesicles usually resulted along with some intriguing morphologies.12,13 Multicompartment aggregates of subdivided solvophobic domains can emerge in the solution-state self-assembly of linear polymer systems with three chemical species with two of them being solvophobic, such as ABC triblocks,14−18 ABCA quaterblocks,19,20 ABCBA21 pentablocks, and blends of two diblock copolymers of AB/BC.22−25 However, aggregates obtained from these linear polymers are usually in a concentric arrangement of core−shell−corona domains.14 The most efficient strategy to obtain multicompartment aggregates is using miktoarm star polymers such as ABC star terpolymers which have been extensively investigated in both experiments26−34 and theoretical or simulation studies.35−40 The constraint of the ends of A, B, and C arms meeting at a © 2019 American Chemical Society

common junction point suppresses the formation of concentric domains and leads to more elaborate structures. For example, Lodge and co-workers observed a variety of nonconcentric multicompartment aggregates such as hamburgers, segmented worms, toroids, Y-junctions, segmented circular or nanostructured polygonal bilayer sheets, nanostructured vesicles, bowl shaped semivesicles, and raspberry-like micelles in their systematic experimental studies26,28−31 of self-assembly of μ[poly(ethylethylene)][poly(ethylene oxide)][poly(perfluoropropylene oxide)] (μ-EOF) miktoarm star terpolymers in aqueous solution. Despite these previous studies, some issues remain poorly understood still for the ABC miktoarm star terpolymer systems, such as the stability and the formation mechanism of the polygonal-shaped bilayer sheets and the details of the observed surface feature on the vesicles.28,29 In a multicompartment aggregate of ABC star terpolymers, the two segregated solvophobic domains can facilitate the Received: March 4, 2019 Revised: April 29, 2019 Published: May 7, 2019 3680

DOI: 10.1021/acs.macromol.9b00433 Macromolecules 2019, 52, 3680−3688

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Macromolecules storage and delivery of two different agents simultaneously,27 while the solvophilic shell stabilizes these structures in a biological environment. If the star polymer contains more mutually incompatible solvophobic arms, it is expected that the types of agents in the potential delivery vehicles will be more than two. These systems would hold great promise for nanotechnology applications such as drug delivery. Syntheses of miktoarm star polymers with more than three chemical species, like ABCD41−46 quaterpolymers or ABCDE44,45,47 pentapolymers, were achieved controllably. On the selfassembly side, Liu et al.48 observed polymer aggregates such as hollow nanocapsules or vesicles from poly(ethylene glycol)−polystyrene−poly(ε-caprolactone)−poly(acrylic acid) (PEG−PSt−PCL−PAA) miktoarm star quaterpolymers with a hydrophilic PEG arm, two hydrophobic arms of PSt and PCL, and a pH-responsive arm of PAA in a dilute solution. PAA arm exhibits hydrophobicity at pH 3.0, and they proposed that, in this case, the membranes of the vesicles comprise PSt, PCL and at least some PAA segments due to the hydrogen-bonding interactions between PEG and PAA. Lateral nanophase separation, however, was difficult to detect in their system due to the close solubility parameters of the two hydrophobic arms of PSt and PCL. To the best of our knowledge, there are no experimental or theoretical studies on the solution-state self-assembly of miktoarm star quaterpolymers with three mutually incompatible solvophobic arms. Since the parameter space of star quaterpolymer solution systems is quite large, experimental exploration of the phase space is a very costly and time-consuming task. A simulation study can effectively predict the self-assembled morphologies in the large parameter space and hence can provide guidelines for future experimental studies. In this paper, we report the spontaneous self-assembly of miktoarm star quaterpolymers with one solvophilic arm and three solvophobic arms in dilute solutions using computer simulations. The motivation for venturing into such a complex system is to predict the self-assembled morphologies and elucidate their formation mechanisms. It is also expected that a systematic study of star quaterpolymer systems may provide helpful information for understanding the self-assembling behavior of miktoarm ABC star terpolymers and other related complex systems. We focus on the effect of the strength of incompatibility between the different solvophobic arms and the quaterpolymer composition on the geometry, morphology, and internal segregated structures of the self-assembled aggregates. Unique multicompartment aggregates are predicted and their formation mechanisms are elucidated.

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polymerization degree for each model molecule is N = NP + NA + NB + NC + 1. The segment concentration of a system is specified by Φ = nN/V, where n is the number of model molecules in a simulation box. Each segment occupies one lattice site, and two consecutive segments are connected by bonds that can adopt a length of 1, 2 , and 3 lattice spacing, and thus the number of neatest-neighbors for each site is 26. The model molecules are self-avoiding and mutually avoiding. The energy of the system is the objective function in the simulated annealing. Here we consider the nearest-neighboring interactions only, and they are modeled by assigning an energy Eij= εijkBTref to each nearest-neighboring pair of unlike components i and j, where i, j = P, A, B, C, D, and S. Here εij is the reduced interaction energy, kB is the Boltzmann constant and Tref is a reference temperature. It is assumed that εii = 0 and εiD = 0 with i = P, A, B, C, D, and S. In the present paper, the parameters are set as followings. We fix the length of the three solvophobic arms equally (NA = NB = NC = NQ). Thus, the volume fractions of P arm and each one of the A, B, or C arms are f P = NP/N and f Q = NQ/N, respectively. The solvent molecules are assumed to be selective for the P arm only while poor for the other arms, where we fix εPS = −1.0 and εAS = εBS = εCS > 0. The solvophilic arm is incompatible with the three solvophobic arms, where we fix εAP = εBP = εCP = 1.0. The strength of the incompatibility between the three solvophobic arms are identical and tunable by setting εAB = εBC = εAC = αεAS. The segment concentration is fixed at Φ = 0.04 unless otherwise specified. The simulation box is usually fixed at V = 60 × 60 × 60, and we further use a simulation box of V = 80 × 80 × 80 to investigate the reproducibility of the nanostructures and the effect of the segment concentration on the resulting morphologies. Details of the trial move and the annealing procedure are the same as those in the previous work.37 The average contact number for each segment of species m with segments of species n in the nearest-neighboring sites is denoted as Nmn with m, n = A, B, C, P, S. Due to the equal-length of the three solvophobic A, B, and C arms and the symmetric interaction between them, we define NQii = (NAA + NBB + NCC)/3 and NQij = (NAB + NBA + NAC + NCA + NBC + NCB)/6 to represent the average contact numbers between the same type of solvophobic segments and between the different types of solvophobic segments, respectively, and NQP = (NAP + NBP + NCP)/3 and NQS = (NAS + NBS + NCS)/3 to represent the average contact numbers between the solvophobic and solvophilic segments and between the solvophobic segments and solvent molecules, respectively.

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RESULTS AND DISCUSSION In this section, we present our simulation results of the solution-state self-assembly of miktoarm star quaterpolymers PABC with one solvophilic (P) arm (of length NP) and three solvophobic arms of equal length (NA = NB = NC = NQ). Typical morphological sequences are presented in terms of the strength of repulsive interaction between the different solvophobic arms, α, or in terms of the arm lengths. Formation mechanisms of laterally nanostructured polygonal sheets, laterally nanostructured vesicles, and anisotropically patched micelles are elucidated. Our simulation results are compared with related experiments. Morphological Sequences as a Function of α. In this subsection, results are presented at fixed interactions of εPS = −1.0, εAS = εBS = εCS = 2.0, εAP = εBP = εCP = 1.0, εAB = εBC = εAC = αεAS, and the arm lengths of NQ = 6 and NP = 4, 6, or 10. Morphological sequences (Figures 1, 3, and 4) and order parameter (Figure 2) are listed as a function of α. Systems with arm lengths of NQ = 12 are also studied to examine the robustness of the results. Hexagonally Shaped and Laterally Patterned Nanosheets. In Figure 1, it is noted that at arm lengths of NQ = NP = 6, nanosheets occur in a wide range of the strength of repulsive interaction between the different solvophobic arms

MODEL AND METHOD

The simulations are performed using the simulated annealing technique,49,50 and the miktoarm star quaterpolymers are modeled by the single-site bond fluctuation model.51−53 The combination of the model and simulation algorithm are known to be a highly efficient strategy in the study of the self-assembly of block copolymers in solutions37 or under confinement,54 and details of the method can be found elsewhere.55 The model system is embedded in a simple cubic lattice of volume V = LxLyLz with periodic boundary conditions in all the three directions. The system is composed of two components: the PABC miktoarm star quaterpolymer model molecules and solvent molecules (S). Each model molecule consists of a solvophilic arm (P) and three solvophobic arms (A, B, and C) connected at a common junction point D. We denote the number of P, A, B, C, and D segments in each molecule as NP, NA, NB, NC, and ND(= 1) respectively. And the 3681

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Figure 1. (a−c) Typical snapshots of self-assembled morphologies as a function of α at NP = NQ = 6, the segment concentration Φ = 0.04, and the simulation box V = 603. Plots in parts b and c are viewed in two perpendicular directions, and the solvophilic P segments are not shown for clarity. (d) Dashed lines are added along the edges of the nanosheet formed at α = 4.0 to guide the eyes. (e) Variations of distribution of the centers of mass of A, B, and C domains with increasing α. Color scheme: yellow for the solvophilic P segments; gray, green, and blue for the solvophobic A, B, and C segments, respectively; and red for the unselective junction point D.

≥ 1.0 and finally approaches 1. Figure 2a indicates that when α ≥ 1.0, the triangles composed of any three nearest-neighboring points in Figure 1e are approximately equilateral ones. That is, the self-assembled nanosheet is a piece of paving composed of a number of tilings with each having a rigid shape of an approximately equilateral triangle, which results in the hexagonal shape of the whole nanosheet. On the other hand, the larger pdi value at α < 1.0 indicates that a larger deviation from the ideal hexagonal arrangement of A, B, and C domains in the internal of the sheet leads to the nearly circular shape of the nanosheet. The average contact numbers between different species are calculated, and these between the same type and the different types of solvophobic segments, NQii and NQij, respectively, between a solvophobic segment and solvophilic segments NQP, between a solvophobic segment and solvent molecules NQS, and between a solvophilic segment and solvent molecules NPS are plotted as a function of α in Figure 2b. It is noted that with the increase of α, NQij decreases rapidly, while NQS and NQP increase slightly and NPS decreases slightly. It should be noted that the interfacial energy (the energy between the solvophobic domains) and the surface energy (the total energy minus the interfacial energy) of the aggregates are proportional to αεASNQij and 3εASNQS + 3εAPNQP + εPS NPS, respectively. Furthermore, the interfacial area is proportional to average contact number between the different types of solvophobic segments NQij. When α = 0, the interfacial energy is zero, and hence the surface energy dominates over the system. In this case, the relatively smaller NQS and NQP and relatively larger NPS (due to εPS < 0), as shown in Figure 2b at α = 0, correspond to lower surface energy. The average contact number NQij, however, reaches a maximum value, indicating that the interfacial area is largest at α = 0. With the increase of α, the interfacial energy becomes large and gradually dominates over the system so that cannot be ignored, and hence the interfacial area, proportional to NQij, decreases to decrease the interfacial energy. On the other hand, based on the curves in Figure 2b, it can be deduced that the surface energy of the system, represented by the contact number of NQS, NQP, and NPS, slightly increases with α. Comparing Figure 2b with Figures 1 and 2a, we note that the hexagonally shaped nanosheet corresponds to a lower pdi and a lower NQij values. That is, when the centers of mass of any three nearest-

(α). As seen in Figure 1, circularly shaped nanosheets with mixed A, B, and C segments are formed when α = 0. With the increase of α, phase separation occurs between the three solvophobic arms in the internal of the nanosheets, and an approximately hexagonal array of three-colored short-cylinders is formed. A remarkable feature is the appearance of the hexagonal shape of each nanosheet formed when α ≥ 1.0 as indicated in Figure 1, parts b and d. The hexagonal array of the three-colored short-cylinders should come from the bulk phase of ABC miktoarm star terpolymers where (6,6,6) tiling patterns form in the case of NA = NB = NC and symmetric interaction parameters (εAB = εBC = εAC).56 Details of the aggregates, such as the junction point distribution, chain packing motif, and aspect ratio of the nanosheets are presented in Figures S1−S3 in the Supporting Information. The junction points distribute on the core surface irregularly at α < 0.4, gather around the interfaces among the A, B, and C domains on the surface or in the internal of the nanosheets at 0.6 ≤ α ≤ 1.5 when phase separation between the A, B, and C domains occurs or the three-colored short-cylinders form, and arrange in a straight line at the interfaces among the A, B, and C domains in the interior of the nanosheets at α ≥ 2.0 (Figure S1). To elucidate the mechanism for the hexagonal shape of the nanosheets, we analyze the morphologies quantitatively. We plot the calculated centers of mass of each A, B, or C domain in Figure 1e, where the hexagonal arrangement of A, B, and C domains and the hexagonal shape of the overall nanosheets are clearly seen. We further calculate the polydispersity index (pdi) of the angles β formed by any three nearest-neighboring points in Figure 1e (boundary points are excluded in the calculations) as a function of α, and the result is plotted in Figure 2a. It should be noted that pdi = 1 corresponds to an ideal hexagonal arrangement of A, B, and C domains where all the angles formed by any three centers of mass of nearest-neighboring A, B, and C domains are in 60°, and hence the centers of mass of any three nearest-neighboring A, B, and C domains should constitutes an equilateral or regular triangle. On the other hand, a disordered arrangement of the centers of mass of nearest-neighboring A, B, and C domains would lead to a larger pdi value. Hence pdi can be used as a local order parameter. Figure 2a shows that with the increase of α, pdi decreases rapidly when α < 1.0, then decreases slowly when α 3682

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Figure 2. Variations of (a) the index of polydispersity pdi of the angles β and (b) the average contact numbers of NQij, NQii, NQS, NQP, and NPS with α for the nanosheets shown in Figure 1.

sheets is also driven by the decrease of the interfacial area when α is increased. Therefore, it is also the competition between the interfacial energy and the surface energy that results in the morphological transition from vesicles to hexagonally shaped and laterally patterned nanosheets. Multiple-Patched Anisotropic Micelles. Figure 4 shows the typical morphologies obtained at the solvophilic arm length NP = 10. Morphological transitions with the sequence from spherical micelles (α = 0) → 4-patched micelles (α = 0.6) → 6-patched micelles (α = 1.3) → 8-patched two-core micelles (α = 1.5) → 11-patched five-core micelles (α = 1.8) → hexagonally shaped and laterally patterned nanosheets (α ≥ 2.0) are observed with the increase of α. When α ≤ 1.8, several micelles are formed in one system, and it is interesting to notice that the micelles are highly ordered and anisotropic. It should be noted that the center domain in the micelle core can be A, B, or C randomly in the 4-patched or 6-patched micelles or can be the combination of any two of them in the two-core micelles due to the equal length of the three solvophobic arms and the symmetric interaction between them. Similarly, in the five-core micelles, the center includes one A, one B, and one C domain, and the remaining two domains are the same as that in the two-core micelles. It is interesting to notice that a 6patched micelle can be regarded as a minimum repeating unit of the laterally patterned nanosheets, while a n-core micelle is a combination of n 6-patched micelles when n ≥ 2. These micelles are highly anisotropic both in composition and in shape (with a large aspect ratio). On the other hand, a 4patched micelle is of a nearly spherical shape. From Figure S4b, it is noticed that the morphological transitions from spherical micelles to patched micelles further to hexagonally shaped and laterally patterned nanosheets are also driven by the decrease of the interfacial area of the system with increasing α, because when α is larger, the interfacial energy between different solvophobic domains dominates. On the other hand, the average contact number between a solvophilic segment and solvent molecules, NPS, decreases with increasing α. This is because the attractive energy between the solvophilic arm and the solvent molecules dominates in systems of copolymers with a longer solvophilic arm (NP = 10) when α is relatively small, and micelles favor the contact between the solvophilic arm and solvent molecules (a large NPS), especially the spherical shape of the 4-patched micelles allows a maximal value of NPS. From Figures 1, 3, and 4, it is noted that hexagonally shaped laterally patterned nanosheets always form in the large α case, independent of the quaterpolymer composition. This is because this type of sheets have smaller interfacial area (NQij) than the corresponding morphology of circular shaped

neighboring A, B, and C domains constitute an approximately regular triangle, the system has a smaller interfacial area, while the paving of the nearly rigid triangles results in the sheet morphology and polygonal boundary of the aggregate. Sheet morphology with a polygonal boundary has a surface energy slightly higher than that with a circular boundary. The above result indicates that when α is small, a nanosheet with a circular boundary forms to decrease the surface energy where the aggregate has a large interfacial area. When α is larger, a nanosheet with a hexagonal boundary forms to decrease the interfacial area, and hence the interfacial energy is decreased at the cost of slightly increasing the surface energy. Therefore, it is the competition between the interfacial energy and the surface energy that results in the transition of nanosheets from circular boundary to hexagonally shaped boundary. Laterally Patterned Vesicles. When the solvophilic arm length is NP = 4, morphological transitions with the sequence from spherical nonphase-separated vesicles (0 ≤ α ≤ 0.2) → laterally patterned vesicles (0.4 ≤ α ≤ 1.0) → hexagonally shaped and laterally patterned nanosheets (α ≥ 1.5) occur with the increase of α as shown in Figure 3a. Our further results show that the resulting morphologies do not depend on the size of the simulation box or the segment concentration (Φ) when Φ is not too small. Gradually larger vesicles are obtained with increasing Φ at α = 0.9 in a larger simulation box of V = 803 as shown in Figure 3b. When phase separation occurs between the solvophobic arms, the solvophobic shell of vesicles is composed of three-colored short-cylinders (or small wedges whose diameter slightly decreases from outside to inside along the radial direction), as shown in section III of Figure 3b. A remarkable feature in this case is that small spherical protrusions always form on the solvophobic shell of a vesicle. Furthermore, the protrusions on each vesicle shell are usually six in number, and they constitute the six vertexes of an approximately regular octahedron, as illustrated in Figure 3c. Each protrusion is found located on a structure defect site formed when the hexagonally arranged three-colored shortcylinders are forced to be packed on a spherical shell. Two types of defects are observed. In one of them, a bigger shortcylinder is formed by one type of solvophobic arms and located along the shell surface, while a smaller sphere formed by another type of solvophobic arms is stacked on the shortcylinder (Figure 3d). In the other type of defect, the coordination number of the center short-cylinder or/and that of its neighbor short-cylinders deviates from six (Figure 3e). On the other hand, each vesicle is of or is nearly of spherical surfaces without obvious edges, except the presence of the protrusions. As shown from Figure S4a, the transition from vesicles to hexagonally shaped and laterally patterned nano3683

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laterally patterned nanosheets and further to patched micelles or from hexagonally shaped laterally patterned nanosheets to multiple-patched micelles are observed at 0.4 ≤ α ≤ 1.0, and 1.5 ≤ α ≤ 1.8, respectively. In the cases with α > 0, the resulting aggregates have a shape usually deviating from spherical due to the competition between the interfacial energy and the surface energy. The effects of arm length on the morphologies are examined by increasing the solvophobic arm length to NQ = 12 while keeping all the other parameters the same as those in Figures 1, 3, and 4, and typical morphologies are presented in Figure S5. It is noted that the morphologies and morphological sequence obtained for the case at NQ = 12 are similar to those from the case at NQ = 6. These comparisons indicate that the predicted morphologies and morphological transitions are robust, independent of the arm length. Morphological Sequences as a Function of Arm Lengths. It is noted that, in the small α case, the resulting morphologies depend on both α and f P. Simulations are further carried out to investigate the effects of α and f P, focusing on the small α case of α = 2/3 and εAS = εBS = εCS = 3.0, while the other interaction parameters are the same as those used in the last subsection. In this subsection, morphological sequences are presented as a function of arm length NP for a system with NQ = 9 (Figure 5) or of NQ for a system with NP = 2 (Figure 6). Effect of the Solvophilic Arm Length. As shown in Figure 5 for the system with NQ= 9 and α = 2/3, a morphological transition from laterally patterned nanosheets to multiplepatched micelles is observed with the increase of NP. It is interesting to notice that 4-patched micelles occur in a wide range of NP values when NP is larger than NQ (NP ≥ 12). The decreased size of the 4-patched micelles observed with the increase of NP is due to the fact that a longer solvophilic block favors higher surface curvature and smaller core dimensions.2 The trend of morphological sequence in Figure 5 is consistent with that for morphologies shown in Figures 1, 3, and 4 for the model molecules with NQ = 6, where with increasing f P the same morphological sequences from laterally patterned nanosheets to multiple-patched micelles are observed at 1.5 ≤ α ≤ 1.8. This comparison indicates that the same morphological sequences occurs at a smaller α value for model molecules with a longer NQ; that is, an increase of NQ is somewhat equivalent to an increase of α. The morphological sequence in Figure 5 is also similar to that shown in Figure 4 but in the direction of decreasing α for a system with a relatively long NP, indicating that an increase of NP is

Figure 3. Typical snapshots of self-assembled morphologies obtained when NP = 4, and NQ = 6 as a function of (a) α and (b) Φ at α = 0.9 and V = 803, where isosurface contour plots of (I) solvophobic domains (ABC) in one color, (II) solvophobic domains (ABC) in different colors, and (III) only A domains are shown. (c) Lines are added by connecting the neighboring protrusions on the vesicle formed at α = 1.0 to guide the eyes. (d, e) Defects are indicated for the vesicle formed at α = 0.9, Φ = 0.055. The color scheme is the same as that used in Figure 1.

nanosheets, or vesicles, or spherical micelles formed at α = 0, as shown in Figures 2b and S4. Hence, they can decrease the dominating interfacial energy. These results indicate that a polygonal-shaped nanosheet is stable for the star quaterpolymer system, which is quite different from diblock copolymer or surfactant solution systems. In the small α case, the resulting morphologies depend on both α and the volume fraction of the solvophilic P arm f P. Morphological transitions from vesicles to nanosheets further to spherical micelles are observed with increasing f P at α = 0. This transition trend is basically consistent with that deduced based on the packing parameter of surfactant systems.57,58 In the case of α = 0, micelles and vesicles are all spherical in shape to decrease the dominating surface energy, while the nanosheet (with a circular boundary) is an intermediate morphology between vesicles and spherical micelles. In the intermediate α values, with increasing f P, morphological sequences from laterally patterned vesicles to

Figure 4. Plots of typical snapshots of self-assembled morphologies as a function of α when NP = 10 and NQ = 6. (a) All types of segments (PABCD) are shown. (b) Just one micelle in each system with only solvophobic (ABC) domains shown and viewed in two perpendicular directions (isosurface contour shown at α > 0). The color scheme is the same as that used in Figure 1. 3684

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Figure 5. Typical morphologies as a function of the solvophilic arm length NP when NQ = 9, with isosurface contour of the solvophobic domains (ABC) shown. The number of model molecules was fixed at 288 for all the systems, and V = 803 for NP ≥ 36. The color scheme is the same as that used in Figure 1.

somewhat equivalent to a decrease of α. This is because when NP is small or α is large, the interfacial energy dominates the system, whereas when NP is large or α is small, the surface energy dominates the system, where the system favors morphologies with higher curvature to allow a maximal contact for the solvophilic arm with solvent molecules. Polygonal shape does not appear in the sequence shown in Figure 5 due to the small α value (α = 2/3) used in that system. Effect of the Solvophobic Arm Length. Figure 6 shows the typical morphologies as a function of the solvophobic arm length NQ at NP = 2. It is noted that morphological sequence from laterally patterned vesicles to laterally patterned nanosheets is formed with the increase of NQ. It should be noted that the micelle-like morphologies observed in Figure 6 at NQ ≥ 12 is actually sheets when the system or the segment concentration is large enough, as shown in Figure S6. The morphological sequence shown in Figure 6 has a similar trend with that shown in Figure 3 where both systems have a relatively small NP value, indicating further that an increase of NQ is somewhat equivalent to an increase of α. This is because the interfacial energy increases in both cases of increasing NQ and increasing α. Polygonal shape does not appear in the sequence shown in Figure 6 also for the small α value. Polygonal shape occurs when α is larger (Figure S7) for the same quaterpolymer composition. Comparisons between Simulation Results and Previous Experiment Observations. The PEG−PSt−PCLPAA miktoarm star quaterpolymer used in ref 48. includes a pH-responsive arm of PAA, a hydrophilic arm, and two hydrophobic arms of PSt and PCL with close solubility parameters, and there are hydrogen-bonding interactions between PEG and PAA arms. Hence a direct comparison between our simulation results and their experiments is difficult. To our knowledge, there are no reports on the solution-state self-assembly of miktoarm star quaterpolymers with one solvophilic arm and three mutually incompatible solvophobic arms. However, our simulation results can be compared with some related systems. The most closely related one is the system of μ-EOF miktoarm star terpolymers in aqueous solution of Li et al.,28,29 where polygonal-shaped laterally patterned nanosheets were first observed with hexagonally packed F short-cylinder domains immersed in the continuous E matrix. They thought that the nanosheets should be circular in shape instead of polygonal to minimize the edge energy. They observed that with decreasing the

volume fraction of the solvophilic arm, the morphological sequence is from hamburger micelles and segmented worms to polygonal shaped laterally nanostructured bilayers and ultimately to laterally nanostructured vesicles. Hexagonally shaped nanosheets were also observed by Ni et al. in their experimental studies of the self-assembly of linear polymer system consisting of a polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer tail tethered to a fluorinated polyhedral oligomeric silsesquioxane (FPOSS) cage in the 1,4dioxane/water solution.59 With increasing water content, they observed a morphological sequence from spherical and cylindrical micelles to hexagonal shaped and hexagonally patterned nanosheets and further to laterally patterned vesicles. Water is a poor solvent for the PS block and the FPOSS cage while a good solvent for the PEO block in their experiments, and hence, the morphological sequence with the increase of water content should be similar to that with a decrease of the volume fraction of the hydrophilic blocks.1 The morphologies of polygonal-shaped laterally nanostructured sheets and laterally nanostructured vesicles observed in the abovementioned two sets of experiments28,29,59 are qualitatively consistent with those obtained in our predictions. And the morphological sequences observed in these two set of experiments are also qualitatively consistent with that we obtained upon decreasing f P where the morphologies evolve from micelles to hexagonal-shaped laterally patterned nanosheets and further to laterally patterned vesicles at α ≈ 1.0. The only difference is that the hexagonally shaped nanosheets and vesicles are composed of three-colored short-cylinders in our present predictions whereas in their experiments they are composed of one-component short-cylinders in the continuous matrix of the other solvophobic component.28,29,59 Since that the structures with one-component short-cylinders have the same symmetry as those with three-component ones, the formation mechanisms for the hexagonally shaped nanosheets and laterally patterned vesicles we proposed should also apply to the systems of Li et al.28,29 and Ni et al.59 Furthermore, surface features were usually observed on vesicles in the experiments of Li et al.,28,29 and they may have some relation with the protrusions observed on the vesicle shells in our systems. On the other hand, the predicted n-core (n ≥ 1) multiple-patched highly anisotropic micelles, and nanosheets and vesicles composed of three-colored short-cylinders have never been observed or predicted before. It is expected that 3685

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Macromolecules

Figure 6. Typical self-assembled morphologies as a function of the solvophobic arm length NQ when NP = 2. The two rows are viewed in two perpendicular directions for NQ ≥ 4, while the plot in the second row at NQ = 2 is a cross-sectional slice view with four types of segments shown. The color scheme is the same as that used in Figure 1.

our predicted multicompartment aggregates are promising in applications of delivery vehicles.

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regular octahedron. Each protrusion corresponds to a packing defect of the three-colored short-cylinders formed when the hexagonally arranged three-colored short-cylinders are forced to be packed on a spherical shell. Micelles formed at α > 0 are anisotropic and patched ones, and they are observed in systems with a larger f P, where the higher curvature of micelles favors a maximal contact for the solvophilic arm with solvent molecules. The morphological sequence obtained with increasing the volume fraction of the solvophobic arms f Q (or decreasing f P) has a similar trend to that obtained with increasing α. This is because the interfacial energy increases in both cases of increasing f Q (or decreasing f P) and increasing α. The effects of arm length on the morphologies are examined, and the results indicate that the predicted morphologies and morphological transition are robust. Our simulation results are compared with available experiments, especially with those from ABC star terpolymer systems. These results are also helpful for understanding the formation mechanism of the polygonal shape of the nanosheets and the surface features on vesicles self-assembled from miktoarm star terpolymer systems. They may provide guidelines for related experimental studies, and the predicted nanoscaled multicompartment aggregates could provide broad application in nanotechnology, especially in drug delivery.

CONCLUSION

We performed simulated annealing procedure to investigate the self-assembly of PABC miktoarm star quaterpolymers with one solvophilic arm and three equal-length solvophobic arms in a dilute solution. Morphological transitions are observed by tuning the strength of the repulsive interaction between the solvophobic A, B, and C arms (α) at fixed arm lengths or by tuning the arm lengths at fixed interactions. Unique multicompartment aggregates including nanosheets and vesicles composed of lateral patterns of three-colored short-cylinders and anisotropically multiple-patched micelles are predicted. In particular, a laterally patterned nanosheet with a hexagonal shape always forms in the large α case, independent of the quaterpolymer composition. The formation mechanisms of aggregates with special shape and morphology are elucidated based on the competition between the interfacial energy and the surface energy. In the large α case, the total interfacial energy between different solvophobic domains dominates over the system. The hexagonally shaped laterally patterned nanosheets form due to their smaller interfacial area, and hence they can decrease the dominating interfacial energy. The smaller interfacial area of this morphology comes from the high local order of the threecolored short-cylinders. That is, any three centers of mass of the nearest-neighboring A, B and C domains constitute an approximately regular triangle. The paving of these nearly rigid triangles constitutes the hexagonal shape of the nanosheets. The hexagonally shaped nanosheets can be formed in a large α range and independent of the quaterpolymer composition, indicating that they are stable structures. In the limiting case of α = 0, the resulting morphologies depend on the volume fraction of the solvophilic P arm f P, where a sequence from vesicles to circularly shaped nanosheets further to micelles is observed with increasing f P. In this case, micelles and vesicles are all spherical in shape to decrease the dominating surface energy, while the circular shaped nanosheet is intermediate morphology between vesicles and micelles. At α > 0, the interfacial energy becomes impossible to ignore where phase separation between the different solvophobic arms occurs and thus results in the formation of multicompartment aggregates which are quite different from those obtained at α = 0. The vesicles formed at α > 0 are also composed of lateral patterns of three-colored short-cylinders but on a spherical shell, and they are usually observed with six protrusions constituting the vertexes of an approximately

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00433. The junction point distribution (Figure S1), the chain packing motif (Figure S2), the aspect ratio of the nanosheets (Figure S3), and the average contact numbers (Figure S4) as a function of α and typical snapshots of the self-assembled morphologies as a function of NP and α at NQ = 12, Φ = 0.06, εAS = εBS = εCS = 2.0, and V = 723 (Figure S5), as a function of the segment concentration Φ (Figure S6), and as a function of the solvophobic arm length NQ (Figure S7) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(B.L.) E-mail: [email protected]. ORCID

Baohui Li: 0000-0002-8403-1220 3686

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Macromolecules Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (21574071, 21774066 and 21829301), by the PCSIRT (IRT1257), and by the 111 Project (B16027).

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