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Mar 22, 2018 - On the other hand, in dilute solutions, the self-assembly behaviors of shape amphiphiles are much .... HOOMD,48a,49 and some data with ...
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Self-Assembly of Giant Amphiphiles Based on Polymer-Tethered Nanoparticle in Selective Solvents Qingxiao Li, Zheng Wang, Yuhua Yin, Run Jiang, and Baohui Li* School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China S Supporting Information *

ABSTRACT: We study the self-assembly and formation process of vesicles of giant molecular shape amphiphiles in a selective solvent using the Brownian dynamics approach. Each amphiphile is composed of one hydrophilic nanoparticle tethered with one to five hydrophobic polymer tail(s), and the number of coarse-grained beads in each polymer tail is comparable to the number of repeating units in shape amphiphile used in the experiments. The effects of various parameters, such as the number of polymer tails, the length of each tail, the concentration of amphiphile beads, the size of the nanoparticle, and the temperature of the system on the self-assembled aggregate morphologies, are investigated. Morphological phase diagrams are constructed in different parameter spaces, and multiple morphological transitions are predicted and explained based on packing parameter. The formation pathways of vesicles are examined systematically, and mechanism II is identified for the first time in such shape amphiphilic systems. Transition between mechanism I and mechanism II can occur by varying several parameters, and principles controlling the different pathways are elucidated. The simulation results are compared with available experimental and simulation results of related systems.

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INTRODUCTION Polymer-tethered nanoparticles constitute a class of prototype “shape amphiphiles” or geometric objects made of hydrophilic and hydrophobic parts.1−15 These novel materials have much in common with traditional molecular amphiphiles, but here the “head group” may be molecular nanoparticles (MNPs) with persistent shape and volume, or may vary in size, symmetry, and surface chemistry, and can also be formed by covalently bonded or folded/assembled cage structures.1−17 These functionalized MNPs are covalently connected with polymer tail(s), forming typical molecular shape amphiphiles. The shape amphiphiles have been observed or predicted to self-assemble into a variety of highly diverse, thermodynamically stable and metastable structures in solutions,1−5 in thin film,2 or in the bulk.2,18−26 This new class of materials provides a broad platform for structural engineering, biotechnology, optoelectronic, and others and opens up numerous possibilities in the bottom-up fabrication of well-defined nanostructures with technological relevance.3 Cheng’s group has systematically studied the self-assembly of giant molecular shape amphiphiles constructed by two major functionalized nanoparticles, namely, carboxylic acid-functionalized [60]fullerence (AC60)1 and polyhedral oligomeric silsesquioxanes (APOSS),4 tethered with one or two hydrophobic polystyrene (PS) chain(s) at one junction point (PSnAC60/APOSS or 2PSn-AC60) in selective solvents. They observed that when the 1,4-dioxane/dimethylformamide (DMF) mixture was used as common solvent and water as selective solvent, the series of PSn-AC60 form spherical micelles, whereas the series of 2PSn-AC60 form bilayer vesicles in the low © XXXX American Chemical Society

molecular concentration range (≤0.25 wt %). In the high molecular concentration (>0.25 wt %) range, however, morphological transitions of aggregates from spherical to cylindrical micelles and further to bilayer vesicles were observed with increasing the molecular concentration and/or the lengths of PS tail for the series PSn-AC60; in contrast, bilayer vesicles remained for the series of 2PSn-AC60.1 They further observed that PSn-APOSS self-assemble into aggregates in selective solvents, and the morphology can be tuned from bilayer vesicles to worm-like cylinders and finally to spherical micelles with increasing the degree of ionization of the carboxylic acid.4 These experimental studies also clearly showed the synergistic influence of molecular topology, the lengths of PS tail, and molecular concentration on the self-assembled structures. Computer simulations have been used to predict the intriguing self-assembled structures of these shape amphiphiles in selective solvents.27,28 Wang’s group investigated effects of the number and the length of hydrophobic tails and the size of the hydrophilic head on the self-assembled structures of shape amphiphiles in selective solvents employing the dissipative particle dynamics simulation.27,28 They found that model shape amphiphiles with two or three tails prefer to form vesicles, while amphiphiles with one tail form vesicles for short tail (the size of a hydrophilic H-bead is 1.5−2.0 times a tail bead in their case)27,28 and spherical micelles for longer tail.27 Received: January 25, 2018 Revised: March 22, 2018

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DOI: 10.1021/acs.macromol.8b00189 Macromolecules XXXX, XXX, XXX−XXX

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tration, the number and the length of the polymer tails, the system temperature, and the size of the hydrophilic head bead to investigate their effects on self-assembly structures and formation pathways of vesicles.

On the other hand, in dilute solutions, the self-assembly behaviors of shape amphiphiles are much less understood than these of amphiphilic block copolymers. For amphiphilic block copolymers in dilute solutions, various self-assembled morphologies have been identified, mechanisms of morphology formation and morphological transitions have been elucidated,29−34 and furthermore, two pathways of vesicle formation have been identified.35−44 In the conventional pathway of vesicle formation (named mechanism I), amphiphilic molecules first self-assemble into spherical micelles, these micelles further transform into bilayer-type structures, and finally the bilayertype structures bend around and close up to form bilayer vesicles.35−41 In the other pathway (named mechanism II), spherical micelles are formed initially similar to that in mechanism I. Subsequently, the spherical micelles transform into semivesicles, and finally solvent molecules diffuse inside the center of semivesicles; hence, the semivesicles grow into complete bilayer vesicles.39−44 Transitions from mechanism I to mechanism II were observed by controlling the selective solvent addition rate,40 or the strength of repulsive interaction between the hydrophobic block and solvent,39,41 or the hydrophobic block length,41 or the copolymer concentration41 of block copolymer systems. For the polymer-tethered shape amphiphile systems, however, the pathway for vesicle formation has not been investigated systematically; only mechanism I has been identified.27 In this paper, we study the self-assembly of shape amphiphiles, possessing one hydrophilic head bead tethered with one to five hydrophobic polymer tail(s) at one junction point, in a selective solvent using Brownian dynamics simulations. We systematically change the amphiphile concen-

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SIMULATION MODEL AND METHOD Coarse-Grained Model. We use a coarse-grained model to investigate the self-assembly of shape amphiphiles of Yu et al.1 Each model amphiphile is composed of one hydrophilic nanoparticle (H-bead) tethered with 1, 2, 3, 4, or 5 hydrophobic polymer tail(s) at one junction point, denoted as Pn-H, 2Pn-H, 3Pn-H, 4Pn-H, or 5Pn-H, respectively, as illustrated schematically in Figure 1. The n in the denotation of model amphiphiles is the number of coarse-grained beads (Pbeads) on each polymer tail, and its value is 16−56 with a step of 8 in our simulations. The junction point is also considered as a coarse-grained bead having the same property as that of a Pbead. The system is placed in a cubic box with periodic boundary conditions. The concentrations of the model amphiphile beads (φ) and of the hydrophilic H-beads (φH) N V +N V N V in the solution are defined as φ = H HV P P and φH = HV H , respectively, where NH and NP are the total numbers of hydrophilic H-beads and hydrophobic P-beads, respectively, in the system; VH, VP, and V are the volumes of an H-bead, a Pbead, and the simulation box, respectively. The nonbonded interactions between P−P, P−H, and H−H pairs are modeled by a modified and shifted Lennard-Jones (SLJ) potential. For two beads at a distance rij, this interaction is given by

⎧ ⎡ 12 ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ ⎛ σ ⎞6 ⎤ ⎪ ⎢⎛ σ ⎞ σ σ ⎥ ⎢ ⎥ ⎜ ⎟ ⎟⎟ − αij⎜⎜ ⎟⎟ − 4εij − αij⎜⎜ ⎟⎟ ⎥ rij < βij + Δij ⎪ 4εij⎢⎜⎜ ⎢ ⎜ ⎟ ⎥ ⎝ rij − Δij ⎠ ⎦ VSLJ(rij) = ⎨ ⎣⎝ rij − Δij ⎠ ⎝ βij ⎠ ⎥⎦ ⎢⎣⎝ βij ⎠ ⎪ ⎪0 rij ≥ βij + Δij ⎩

⎧ 2⎤ ⎡ ⎪− 1 kR 2 ln⎢1 − ⎛⎜ rij ⎞⎟ ⎥ r ≤ R ⎪ 0 ij 0 ⎢⎣ ⎝ R 0 ⎠ ⎥⎦ V (rij) = ⎨ 2 ⎪ ⎪0 rij > R 0 ⎩

where εij is the potential well depth, σ is the diameter of a Pbead, and βij is the cutoff radius, Δij =

di + d j 2

− σ is the shift

distance, in which di and dj are the diameter of ith and jth

(1)

(2)

where the FENE spring constant k = 30.0ε/σ2 and the maximum allowable separation is set to R0 = 1.5σ. Brownian Dynamics Simulation. The self-assembly of the model amphiphiles is simulated using Brownian dynamics which has been used to study the self-assembly of polymertethered nanoparticle in the bulk and in dense solutions.18−26 In the Brownian dynamics, the motion of each bead in the system is governed by the Langevin equation

Figure 1. Schematic of model amphiphiles: one hydrophilic nanoparticle tethered with one (Pn-H), two (2Pn-H), three (3Pn-H), four (4Pn-H), and five (5Pn-H) hydrophobic polymer tail(s) at one junction point. Color scheme: red for hydrophilic nanoparticle (Hbead) and green for hydrophobic P-beads.

mi rï (t ) = Fic(ri(t )) + FiR (t ) − γi vi(t )

beads, respectively. The parameter αij (0 ≤ αij ≤ 1) reflects the hydrophilic or hydrophobic properties of beads.45,46 In εij, βij, Δij, di, dj and αij, the subscript i, j = P or H for a P-bead or an Hbead, respectively. The adjacent beads in the shape amphiphiles are connected via the finitely extensible nonlinear elastic (FENE) springs25,26,47

(3)

where mi, ri, vi, and γi are the mass, the position, the velocity, and the friction coefficient, respectively of the ith bead; t is time; Fci and FRi are conservative and random force, respectively. We set γP = 1.0 for P-bead and γH = dHγP for H-bead. The effect of solvent is implicitly treated by the random force which satisfies the fluctuation dissipation theorem B

DOI: 10.1021/acs.macromol.8b00189 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules ⟨FiR (t )FRj (t ′)⟩ = 6γikBTδijδ(t − t ′)

Comparisons between Simulation Results and Experiment Observations. As previous experiments have studied the self-assembly of shape amphiphiles composed of one hydrophilic particle tethered with 1−2 hydrophobic PS tail(s) (PSn-AC60 and 2PSn-AC60) in selective solvent,1 we first focus on shape amphiphiles with compositions similar to the experimental ones to determine the model parameters. Figure 2 shows the morphological phase diagram and typical snapshots obtained from three types of amphiphiles, P48-H, 2P24-H, and 2P32-H, at various amphiphile concentrations. It is noted that the morphology of aggregates from P48-H system changes from spherical micelles at φ = 1.4% to a mixed morphology of spherical and cylindrical micelles in the range of φ = 2.0−2.6% and further to worm-like or cylindrical micelles in the range of φ = 3.2%−4.4%. For systems consisting of molecules 2P24-H and 2P32-H, only vesicles are observed with increasing φ in the range of 1.4%−4.4%. These simulation results are consistent with previous experimental findings of Yu et al.1 In their experiments, they used 1,4-dioxane/DMF mixture as the common solvent and water as the selective solvent for the amphiphiles PS44-AC60, 2PS24-AC60, and 2PS32-AC60. They observed that for the PS44-AC60 system the self-assembled morphology changes from spherical micelles in the molecular concentration range of c = 0.1−0.5 wt %, to a mixed morphology of spherical and cylindrical micelles in the range of c = 0.75−1.0 wt %, and finally to pure cylindrical micelles in the range of c = 1.5−2.0 wt %, while for 2PS24-AC60 and 2PS32AC60 systems, morphologies of aggregates are always the bilayer vesicles in the range of c = 0.1−2.0 wt %. Our simulation results are also consistent with previous simulation predictions of molecular shape amphiphiles possessing a hydrophilic head tethered with 1−3 hydrophobic tails where the length of each tail is 5−31.27 We also tried other sets of parameters and found that the set of parameters listed in Figure 2 are the best that can reproduce the experimental results. Therefore, we used this set of parameters in obtaining the following results, unless otherwise specified. Effect of Various Parameters on Aggregate Morphology: Phase Diagrams. The effects of the number of hydrophobic polymer tails in each shape amphiphile and the reduced temperature T* on the self-assembled morphologies are investigated, and a phase diagram of representative morphologies is constructed as shown in Figure 3. It is noted that spherical micelles are formed by P16-H molecules in the studied T* range, in which compact and bigger spherical micelles are formed at lower T* (= 0.7−1.0) range while swollen and smaller micelles are formed at T* = 1.1−1.2. With increasing T*, the number of spherical micelles in the system increases whereas the average size of each micelle decreases. For 2P16-H molecules, the morphology of aggregate changes from a mixture of vesicles and spherical micelles at T* = 0.7 to vesicles in the range of T* = 0.8−1.2. For 3P16-H and 4P16-H molecules, transitions from mixed morphology of vesicles and spherical micelles to vesicles and further to large compound micelles (LCMs) are observed with the increase of T*. For 5P16-H molecules, the morphology changes from vesicles in the range of T* = 0.7−0.8 to LCMs in the range of T* = 0.9−1.2. Figure 3 also shows that with increasing the number of hydrophobic tails morphology changes from spherical micelles to vesicles, and further to LCMs at a given T*, which is similar to those observed in diblock copolymer dilute solutions where Eisenberg et al. found that morphological transitions of polystyrene-b-poly(acrylic acid) (PS-b-PAA) aggregates from

(4)

where kB is the Boltzmann constant and T is the temperature. All simulations are carried out in an NVT ensemble with HOOMD,48a,49 and some data with GALAMOST.48b In our simulations, reduced units are used where σ, εPP, and the mass of a P-bead mP are the units of length, energy, and mass, respectively; i.e., σ = dP = 1.0, εPP = 1.0, mP = 1.0, with the time τ = σ mP /εPP , and the reduced temperature of the system T* = kBT/εPP. We fix the mass of an H-bead at mH = 20.0, the cutoff radius at βPP = 3.0, βHH = 21/6, and change parameters αPP and αHH in the range of 0.8−1.0 and 0−0.5 to reflect hydrophobicity of the P-beads and the hydrophilicity of the Hbeads, respectively. εHH, βPH, and εPH are also changed to reproduce the available experimental results. The diameter of an H-bead dH, the concentration of amphiphilic beads φ, and the reduced temperature of the system T* are changed in the ranges of 2−5, 1.4%−4.4%, and 0.7−1.2, respectively, to investigate their effects on the self-assembly behavior. The simulation box side length is set at 100 in our simulations; the size effect is checked with larger simulation box of side length 140 for systems with φ = 3.2% and T*=1.2, and good reproducibility is obtained. Integration time step of δt = 0.005 is used, and the simulations last 2.0 × 108 or 4.0 × 108 time steps.

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RESULTS AND DISCUSSION In this section, we present the Brownian dynamics simulation results of self-assembly and formation process of vesicles of shape amphiphiles consisting of a hydrophilic H-bead tethered with 1−5 hydrophobic tail(s) in a selective solvent. The simulated self-assembled morphologies are compared with available experimental observations to validate the model and method we used (Figure 2). The effects of the number of

Figure 2. (a) Self-assembled morphology phase diagram and (b) typical snapshots of the amphiphiles P48-H, 2P24-H, and 2P32-H at different amphiphile concentrations and T* = 1.2. Color scheme is the same as that in Figure 1. Each arrow points to the cross-sectional slice of the corresponding snapshot. The other parameters are αPP = αPH = 0.8, αHH = 0.1, βPH = 3.0σ, εPH = 1.0, εHH = 0.5, and dH = 3.0.

hydrophobic tails, the system temperature, the hydrophobic tail length, and the hydrophilic bead size on morphologies of the self-assembled aggregates are illustrated by constructing the morphological phase diagrams (Figures 3 and 4). Morphological transitions are explained based on packing parameter (Tables 1 and 2). The formation pathways of vesicles are systematically examined (Figures 5−7, Figures S1−S3), and the principles controlling the pathways are elucidated (Table 3, Figure S4). C

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Figure 3. (a) Morphological phase diagram and (b) representative snapshots of aggregates formed by P16-H, 2P16-H, 316-H, 4P16-H, and 5P16-H molecules at different temperatures when φ = 3.2%. The color scheme and the meaning of arrows are the same as those in Figure 2.

The same sequence of morphologies has been observed in the diblock copolymer PS-b-PAA in mixture of DMF/water solution when increasing of the volume fraction of hydrophilic (PAA) block.29,50 The increase of H-bead size is increasing the volume fraction of hydrophilic H-bead in the amphiphile. The morphological transitions with increasing dH are consistent with those observed in diblock copolymer system.29,50 On the other hand, with the increase of n in 2Pn-H, the morphological transitions from cylindrical micelles to vesicles and from a mixed morphology of cylindrical and spherical micelles to cylindrical micelles further to vesicles are obtained at dH = 3.5 and 4.0, respectively. Considering that the increase of n in 2PnH is increasing the volume fraction of the P-beads in the amphiphile, the morphological transitions with increasing n in 2Pn-H shown in Figure 4 are consistent with that observed in the shape amphiphiles PSn-AC60 in mixture of 1,4-dioxane/ DMF/water solution with increasing the volume fraction of the hydrophobic PS tail.1 The morphological transitions observed in Figures 3 and 4 can be understood based on the packing parameter, Ns. For a V surfactant molecule, it is defined51−53 Ns = a Lc , where Vc is the

spherical micelles, through cylindrical micelles and vesicles, to LCMs as the molar percentage of the hydrophilic PAA block deceases.29,50 In our case, the increase of the number of hydrophobic tails is increasing the molar percentage of the Pbeads, i.e., decreasing the molar percentage of the hydrophilic H-beads. Therefore, the morphological transitions with increasing the number of polymer tails in Figure 3 are composition induced, similar to that in the diblock copolymer system. The cylindrical micelles are not observed between the spherical micelles and vesicles in Figure 3, which may be due to the longer length of each polymer tail so that the compositions corresponding to the cylindrical micelles are missing in Figure 3. The effects of the size of hydrophilic H-bead and the length of each polymer tail on the self-assembled morphologies are investigated, and a phase diagram in the space of dH ∼ n is constructed for the 2Pn-H system as shown in Figure 4. It is noted that with the increase of the H-bead size the morphology of aggregate basically changes from LCMs to vesicles, to cylindrical micelles, to a mixed morphology of cylindrical and spherical micelles, and finally to spherical micelles with only an exception that cylindrical micelles do not occur when n = 56.

e c

volume of the hydrophobic chain, ae the equilibrium area per molecule at the aggregate interface, and Lc the length of the hydrophobic chain. In our case, Vc corresponds to the total volume of all the P-beads in each shape amphiphile, ae the cross-sectional area per H-bead, and Lc the square root of the mean-square end-to-end distance averaged for each tail. The values of Ns as a function of the number of polymer tails in each shape amphiphile m and the reduced temperature T* and as a function of the length of each tail n and the diameter of each Hbead dH are listed in Tables 1 and 2, respectively. In Tables 1 Table 1. Value of Ns = Vc/aeLc as a function of m and T*

Figure 4. Morphological phase diagram of aggregates for 2Pn-H system as a function of the size of hydrophilic H-bead and the length of each hydrophobic tail at φ = 3.8% and T* = 1.2. D

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Macromolecules Table 2. Value of Ns = Vc/aeLc as a function of n and dH

and 2, the corresponding morphologies are the same as those in Figures 3 and 4, respectively, and different morphologies are indicated with different colors. From these tables, it is noted that spherical micelles are with Ns ≤ 0.3, cylindrical micelles with 0.336 ≤ Ns ≤ 0.459, and vesicles with 0.442 ≤ Ns ≤ 1.079. These results are largely consistent with the criterion for the surfactants where spherical micelles form when Ns ≤ 1/3, cylindrical micelles form when 1/3 < Ns ≤ 1/2, and vesicles when Ns > 1/2. The difference in the boundary values of Ns for vesicles shown in Tables 1 and 2 with that for the surfactants may be due to the difference in molecular structures. On the other hand, an obvious difference between our result and that of the surfactants is that large compound micelles are obtained with Ns from the up boundary of vesicles to a larger value of 1.958, mixed morphologies of spherical micelles and vesicles are obtained when T* is lower (in Table 1) with a Ns range overlapping with that for the vesicles, and mixed morphologies of spherical and cylindrical micelles are obtained with a Ns range between those of spherical and cylindrical micelles (in Table 2). From Tables 1 and 2, it is noted that the variations of both m and dH can lead to larger changes in the value of Ns and therefore result in rich morphological transitions, whereas the variation of T* leads to a relatively smaller change in the value of Ns but it also results in morphological transitions. On the other hand, the n value leads to a relatively larger change in the value of Ns, especially when dH is small, but it only results in a fewer morphological transitions. This is because the larger changes in Ns occur in the vesicle and the large compound micelle regimes whose Ns window is larger. Formation Pathway of Vesicles. In Figures 3 and 4, it is noted that vesicles can be formed in a relatively large parameter space in the phase diagrams. The formation pathways of vesicles are investigated. Figure 5 shows a typical formation process of vesicles formed by the 2P16-H molecules. It is noted that at quite early stage of the simulation the system forms a lot of small aggregates where the hydrophobic P-beads are inside and the hydrophilic H-beads are outside (Figure 5a). Neighboring small aggregates merge together forming spherical micelles (Figure 5b), and some spherical micelles further evolve into cylindrical micelles and further to curled bilayer disk. At the time step of 5.8 × 107δt, spherical micelles, a cylindrical micelle, and a curled bilayer disk coexist in the system (Figure 5c). The cylindrical micelle further evolves into a curled bilayer disk; hence, two curled bilayer disks coexist with two spherical micelles in the system (Figure 5d). One of the curled disk further rolls up its edge evolving into a vesicle, while the other curled disk rolls up its edge evolving into a bowl-like micelle (Figure 5e), and with further increasing of the simulation time, the bowl-like micelle finally closes up evolving into a vesicle (Figure 5f). Each vesicle coalesces with a spherical micelle

Figure 5. Snapshots of vesicle formation from 2P16-H system with φ = 3.2% and T* = 0.8 at different time steps. The color scheme and the meaning of arrows are the same as those in Figure 2.

(Figure 5g), and finally two spherical vesicles are formed in the system (Figure 5h). The formation pathway of vesicles shown in Figure 5 is similar to that previously predicted for the polymer tethered nanoparticle shape amphiphilic systems where dissipative particle dynamics simulation27 was used. And a similar pathway has been identified for amphiphilic diblock copolymers in selective solvents where molecular dynamics,35 Brownian dynamics,36 density functional theory,37 Monte Carlo,39,40 and dissipative particle dynamics38,41 simulations have been used. The same as that named in these previous papers, we call this pathway as mechanism I. Figure 6 shows the typical formation process of vesicles from 5P16-H model molecules. It is noted that the 5P16-H molecules

Figure 6. Snapshots of vesicle formation from the 5P16-H system at different time steps with φ = 3.2% at T* = 0.8. The color scheme and the meaning of arrows are the same as those in Figure 2.

can quickly aggregate at the very beginning of simulation (Figure 6a). Then, neighboring aggregates fuse together to form some big spherical micelles (Figure 6b). H-beads begin to enter into the center of big spherical micelles to form some semivesicles (Figure 6c). The semivesicles continue to absorb neighboring micelles or semivesicles to increase their size and finally they expand outward, resulting in the formation of vesicles which may coexist with small spherical micelles (Figure 6d). The vesicles further merge with micelles (Figure 6e), and finally two spherical vesicles are formed in the system (Figure 6f). It is noted that the morphology changes from spherical micelles to semivesicles and further to vesicles in Figure 6, without the process of forming cylindrical, disk-like, or bowllike micelles. Such a pathway is quite different from that shown in Figure 5. To the best of our knowledge, this is the first time E

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systems where a transition of the vesicle formation pathway from mechanism II to mechanism I was found when the copolymer concentration was increased.41 For 2P32-H, 2P40-H, 2P48-H, and 2P56-H systems, however, only mechanism II is obtained in the studied φ range. It is found that the pathway of vesicle formation largely depends on the concentration of the hydrophilic H-beads φH in the system, as shown in Table 3. A larger φH (≥1.14%) value usually results in mechanism I, whereas a smaller φH (≤1.12%) value results in mechanism II. Furthermore, the in-between mechanism in which both mechanisms I and II occur in one system is observed when φH = 0.94% and 1.14% in 3P16-H, and 4P16-H, respectively. This may be due to the local fluctuation of φH in these systems. The main difference between mechanisms I and II is that bilayer-sheet structures are formed, and they finally bend around and close up to form vesicles in mechanism I, whereas only spherical micelles and semivesicles are formed as intermediate states in mechanism II. From Figure S4, it is noted that with the increase of the simulation time step, the number of micelles in a system (Figure S4a) decreases (i.e., the average micellar size increases) and the repulsive energy per H-bead (UR) (Figure S4b) increases while the attractive energy per P-bead (UA) (Figure S4c) decreases. The increase of the average micellar size would result in a decrease of the surface area if the micelles are spherical shaped since the surface area of a bigger sphere is smaller than the sum of surface areas of two or more smaller spheres when the volume of the bigger sphere is equal to the volume sum of all the smaller spheres; hence, it results in a decrease of the average distance between a pair of nearestneighboring H-beads and therefore leads to an increase of UR. This is the case for the UR curves in Figure S4b when the time step is smaller than 3 × 107δt. It is also noted that when φH value is larger (for 2P16-H), the UR value is larger than that when φH value is smaller (for 5P16-H) at a given time step although the average micellar size is larger in the latter case. In the larger φH case, the formation of a cylindrical micelle or a bilayer sheet can result in a decrease in UR value than that forming a spherical micelle having the same volume due to the relatively larger surface area of the former. This can be somewhat illustrated from the decrease of the increasing rate of the UR curve for 2P16-H observed when the time step is larger than 3 × 107δt (Figure S4b) where cylindrical micelles and bilayer sheets are formed thereafter. Therefore, mechanism I occurs with bilayer sheet as an intermediate state for vesicle formation to disperse the H-beads when the φH value is larger. In this case, a bilayer sheet further evolves into a vesicle to decrease the higher energy due to the presence of the edge. On the other hand, for a system with a smaller φH value (for 5P16H), the average distance between a pair of nearest-neighboring H-beads is relatively larger even on a spherical structure, while

that such a pathway is identified in the polymer-tethered nanoparticle shape amphiphile solution systems. On the other hand, such a pathway is similar to the mechanism II of vesicle formation that has been identified in systems of amphiphilic block copolymers in a selective solvent in which various simulations including Monte Carlo,39,40 dissipative particle dynamics,41 self-consistent field theory,42 and external potential dynamics method43,44 have been used. Figure 7 shows the typical process of the vesicle formation from 3P16-H molecules. It is interesting to notice that both

Figure 7. Snapshots of vesicle formation from 3P16-H system at different time steps with φ = 3.2% at T*= 0.8, in which I and II represent mechanism I and mechanism II, respectively. The color scheme and the meaning of arrows are the same as those in Figure 2.

mechanisms I and II can be identified in Figure 7. The process of the vesicle formation from 4P16-H molecules is similar to that shown in Figure 7. This may be because the tail number of 3P16-H or 4P16-H molecule is between that of 2P16-H and 5P16H. In addition, we also investigate the effects of the hydrophobic tail length and the amphiphile concentration on the pathway of vesicle formation. It is noted that when the size of the H-bead is fixed at dH = 3.0 and the amphiphile concentration at φ = 3.8% (the case in Figure 4), the pathway of vesicle formation changes from mechanism I (for 2P16-H and 2P24-H) to mechanism II (for 2P32-H, 2P40-H, 2P48-H, and 2P56-H) with increasing the length of each polymer tail from 16 to 56. It is also noted that when φ = 3.2% or 4.4%, the same pathway transition as that when at φ = 3.8% is obtained (see Figures S1 and S2 in the Supporting Information). On the other hand, when the length of the polymer tail is fixed in 2P24-H at T* = 1.2, it is found that the pathway of vesicle formation transforms from mechanism II at φ = 1.4%−2.6% (Figure S3) to mechanism I at φ = 3.2%− 4.4% (Figure S1) with increasing φ. This result is consistent with that obtained from the ABA triblock copolymer solution

Table 3. Effect of Concentration of the Hydrophilic H-Beads φH on the Vesicle Formation Pathway model molecules

2P16-H

2P24-H

3P16-H

4P16-H

5P16-H

2P24-H

2P32-H

2P40-H

2P48-H

2P56-H

φ (%)

3.2 3.8

3.2

3.2

3.2

φH (%)

1.44 1.71

3.2 3.8 4.4 1.14 1.35 1.56

1.14

0.94

0.73

1.4 2.0 2.6 0.50 0.71 0.92

3.2 3.8 4.4 0.94 1.12 1.29

3.2 3.8 4.4 0.80 0.95 1.10

3.2 3.8 4.4 0.70 0.83 0.96

3.2 3.8 4.4 0.62 0.73 0.85

mechanism

I

in-between

II F

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systems with the repulsive energy among the hydrophilic Hbeads and the attractive energy among the hydrophobic Pbeads dominating, respectively. Therefore, bilayer sheets are formed in the former case to reduce the repulsive energy, whereas semivesicles are formed in the latter case to increase the attractive energy. Additionally, the in-between mechanism, in which both mechanisms I and II occur in one system, is also observed. Our simulation results are consistent with available experimental observations and simulation results of molecular shape amphiphile and block copolymer systems.

the stronger attractive energy between P-beads and between PH-beads dominates the system (Figure S4c), and hence spherical micelles are formed due to their facilitating the largest contact among P-beads. In this case, the size of spherical micelles also increases with increasing the simulation time steps. A larger spherical micelle, however, results in the chain stretching, which corresponds to an entropy loss. To decrease the entropy loss, a larger spherical micelle transforms into a semivesicle, that is, from curved monolayer (spherical micelle) to curved bilayer (semivesicle). A semivesicle also results in the chain stretching with the increases of its size and finally evolves into a vesicle through expanding outward to decrease the curvature of the curved bilayer, resulting in the vesicle formation with mechanism II. Therefore, the two pathways of vesicle formation, mechanisms I and II, correspond to systems with the repulsive energy among the hydrophilic H-beads and the attractive energy among the hydrophobic P-beads dominating, respectively, as shown in Figures S4b and S4c. The only exception in Table 3 is that mechanism II also occurs at a relatively higher φH (=1.29%) value for 2P32-H at φ = 4.4%, which shows the synergistic influence of molecular topology, the lengths of each polymer tail, and bead concentration on the self-assembled structures. It is expected that the longer of the polymer tail is the transition from mechanism II to mechanism I shifts to higher φH value.

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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.8b00189. Snapshots of vesicle formation from 2P24-H (Figure S1) and 2P32-H (Figure S2) systems with φ = 4.4% and T* = 1.2, and snapshots of vesicle formation from 2P24-H (Figure S3) system with φ = 2.6% and T* = 1.2 at different time steps; the variation of (Figure S4a) the number of micelles in the system, (Figure S4b) the repulsive energy per H-bead (UR), and (Figure S4c) the attractive energy per P-bead (UA) with the simulation time steps (PDF)

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CONCLUSIONS We performed Brownian dynamics simulations with implicit solvent to study self-assembly and formation process of vesicles of giant molecular shape amphiphiles in a selective solvent. Each amphiphile is composed of one nanoparticle (H-bead) tethered with 1, 2, 3, 4, or 5 hydrophobic polymer tail(s) at one junction point, and the length of each polymer tail is comparable to the number of repeating units in previous experimental systems. By varying various parameters, such as the number of polymer tails, the length of each polymer tail, the concentration of amphiphile beads, the size of the hydrophilic nanoparticle, and the temperature of the system, various selfassembled morphologies including spherical micelles, a mixture of spherical and worm-like micelles, worm-like or cylindrical micelles, vesicles, and large compound micelles are obtained and morphological phase diagrams are constructed. Multiple morphological transitions are explained based on the calculated packing parameter. The formation pathways of vesicles are examined systematically, and two mechanisms are identified. In mechanism I, micelles are formed first and then transform into bilayer sheets. The bilayer sheets further bend around and close up forming vesicles. In mechanism II, micelles are also formed in the initial stage similar to that in mechanism I, and then they gradually grow up instead of forming bilayer sheets. When the micelle size is large enough, hydrophilic H-beads begin to appear in the micelle core, forming semivesicles which are curved bilayers with a large curvature. Finally, the curved bilayers expand outward forming vesicles. To the best of our knowledge, this is the first time that mechanism II is identified in the shape amphiphile solution systems. Furthermore, transition from mechanism I to mechanism II is predicted either by increasing the length of each polymer tail, or by increasing the number of polymer tails in the amphiphile, or by decreasing the amphiphile bead concentration. It is found that all these processes can decrease the concentration of the hydrophilic Hbeads in the system. The mechanisms I and II correspond to

AUTHOR INFORMATION

Corresponding Author

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

Baohui Li: 0000-0002-8403-1220 Notes

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 21528401), by the PCSIRT (IRT1257), and by the 111 Project (B16027). Q. Li thanks Dr. Youliang Zhu (from Changchun Institute of Applied Chemistry) for his helps in using HOOMD and GALAMOST.

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DOI: 10.1021/acs.macromol.8b00189 Macromolecules XXXX, XXX, XXX−XXX

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