Insight into the Polymerization-Induced Self-Assembly via a Realistic

Aug 9, 2019 - The dynamic process of polymerization-induced self-assembly (PISA) is simulated by the dissipative particle dynamics method coupled with...
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Insight into the Polymerization-Induced Self-Assembly via a Realistic Computer Simulation Strategy Yu-Dou Yan,†,∥ Yao-Hong Xue,‡,∥ Huan-Yu Zhao,† Hong Liu,*,†,§ Zhong-Yuan Lu,† and Feng-Long Gu§

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†

Laboratory of Theoretical and Computational Chemistry, State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun 130023, China ‡ Information Science School, Guangdong University of Finance and Economics, Guangzhou 510320, China § Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry, South China Normal University, Guangzhou 510006, China S Supporting Information *

ABSTRACT: The dynamic process of polymerization-induced selfassembly (PISA) is simulated by the dissipative particle dynamics method coupled with the stochastic reaction model. Meaningful comparisons between simulation and experimental results are made. Typical microscopic self-assembly structures are analyzed, and possible dynamic pathways of their formation are proposed. We find that increasing the length of the hydrophobic block leads to the decrease of the size of the vesicle chamber, which further yields the coexistence of vesicles and compound micelles. Moreover, PISA with fast polymerization is proved to experience a different pathway of transition, in which the hydrophobic and hydrophilic blocks undergo a typical flip-flop process to form the final vesicle structure. The simulation study can act as a theoretical guide to achieve the better design or fine regulation of new PISA systems and relevant functional materials.

1. INTRODUCTION Amphiphilic block copolymers (BCPs) can self-assemble to form a variety of morphologies, for example, vesicles, micelles, etc.1−7 These self-assembled structures can be widely used in different fields such as biomedicines, coating materials, sensors, nanolithography, and so on.8−14 The classical techniques of self-assembly commonly request the accomplished synthesis of BCPs via polymerization beforehand. Because of the difference of hydrophilicity between different blocks, the BCPs are able to form various kinds of morphologies for reaching the thermodynamically steady state. Nevertheless, the whole processing technique is not merely complicated but also requires extra purification process after the polymerization. On the other hand, this classical self-assembly technique is only feasible within a rather dilute aqueous phase, which is practically impossible for industrial manufacturing. For overcoming these drawbacks of classical self-assembly methods, a new technique, so-called “polymerization-induced self-assembly” (PISA), has attracted more attention in recent years. Generally, PISA is a technique that can synthesize amphiphilic BCPs by the polymerization reaction via inducing the soluble initiators or macro-CTAs (macromolecular chain-transfer agents) in selective solvent condition. During the process, the newly generated hydrophobic block turns slightly dominating with the growth of its length in polymerization. The aggregation driving force gradually strengthens with the © XXXX American Chemical Society

change of the ratio of hydrophobic and hydrophilic block lengths, which in turn yields the self-assembly of BCPs accompanied with the polymerization. As a consequence, a series of complicated morphologies can be generated in situ by the PISA process. Compared to classical self-assembly means, PISA has apparent advantages. For example, on the basis of a quite simple flowchart, PISA is able to take place in a highconcentration solution (even as high as 50%) which is expected to be applied in industrial processing. Besides, a variety of morphologies can be generated in PISA, which supplies different potential applications. In the recent decade, the experimentalists had made great progress on the investigation of PISA. Pan and co-workers had studied the PISA process of poly(4-vinyl pyridine) and styrene in the solution of cyclohexane, as well as poly(acrylic acid) and styrene in the solution of methanol.15−17 By analyzing the polymerization kinetics, they had clarified the mechanism of the formation of micelles. Arms and co-workers had reported a typical aqueous dispersion polymerization system to in situ prepare nanoemulsions and vesicles by the PISA of poly(glycerol monomethacrylate) (PGMA)18−20 and 2-hydroxypropyl methacrylate.5,21,22 The experiments exhibited the Received: May 23, 2019 Revised: July 26, 2019

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DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX

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experimental data to reflect the characteristics of the experiment. The dynamic process of PISA can be reasonably reproduced in simulations, and the simulation results are able to accordingly guide to design or develop new PISA systems in the experiment. This strategy is validated by simulating a true experimental PISA system, that is, the preparation of poly(acrylic acid)-b-polystyrene (PAA-b-PS) assemblies in methanol solution, which was proposed by He and coworkers.16 Meaningful comparisons between simulation and experimental results are made. Typical microscopic selfassembly structures are analyzed, and possible dynamic pathways of their formation are proposed. As a typical nonequilibrium self-assembly process, PISA shows a clear pathway of the transition from the dispersed small micelles to wormlike micelles that further fuse to form lamella micelles. The lamella micelle spontaneously bends and changes into a closed vesicle morphology, and several neighboring vesicles further fuse into one large columnar vesicle ultimately. We find that increasing the length of the hydrophobic block leads to the decrease of the size of the vesicle chamber, which further yields the coexistence of vesicles and compound micelles. Moreover, PISA with fast polymerization is proved to experience a different pathway of transition as compared to that with slow or medium polymerization, in which the hydrophobic and hydrophilic blocks undergo a typical flip-flop process to form the final vesicle structure. The construction of this simulation study is beneficial to discover the crucial factors in different PISA systems and is possible to suggest to improve the experimental technology in the future. The simulation study can act as a theoretical guide to achieve the better design or fine regulation of new PISA systems and relevant functional materials.

gradual evolution of the assemblies from spherical morphologies to micelles. D’Agosto et al.23 and Yan et al.24 had both studied the influence of different topologies of the hydrophilic and hydrophobic blocks on the morphology of PISA, respectively. An and co-workers25,26 and Zhang et al.27,28 had investigated the PISA process by mixing the growth of homopolymers which are the same as the hydrophobic or hydrophilic blocks. By regulating the ratio of generated BCPs and homopolymers, different morphologies of self-assembly structures could be effectively presented. Yuan and coworkers29,30 considered to introduce the supramolecular interaction, for example, the host−guest interaction in PISA to obtain the well dispersion of hydrophobic monomers in solution so that aqueous dispersion polymerization is realized in PISA. Besides, Boyer and co-workers had studied the lightmediated photoinduced PISA and its potential bioapplications.14,31,32 All of the experimental studies could herein indicate that by finely regulating the ratio of the two blocks, the degree of polymerization, solvent quality, monomer concentration, or other controlling factors,1,5,15−22,24,29,33−38 a variety of different morphologies can be reasonably obtained. PISA is a typical nonequilibrium self-assembly process because the polymerization takes place concurrently with the self-assembly process. As compared to experimental means, computer simulation is naturally more appropriate on understanding this dynamic process because it supplies a microscopic or mesoscopic picture. Besides, the in situ observation of PISA in computer simulations is almost not accessible in experiments. It is also possible in computer simulations to make the systematic and continuous regulation of parameters, which are controlling factors to determine the results of PISA. Therefore, it is a feasible way to clearly obtain the overview of the PISA process and grasp the intrinsic mechanism of the formation of typical morphologies. However, as compared to the number of experimental achievements, computer simulation studies on the PISA process are scarcely reported. Wang and co-workers39,40 had recently used dissipative particle dynamics (DPD) to simulate the PISA process and studied the influence of reaction rate, size of macro-CTA, and concentration on the kinetics of PISA. Besides, Shupanov et al. had also used DPD combined with the Monte Carlo scheme to study the PISA as well as the relevant micellar polymerization process based on the BCP surfactants, in which the phase diagrams of the micelle states were constructed depending on the polymer concentration and the asymmetry of the composition for various reaction conditions.41,42 Nakagawa and Noguchi43,44 had also simulated the similar polymerization of amphiphilic molecules on the surface of the oil droplet, who had discovered that the polymerization could efficiently induce the transition of equilibrated selfassembly structures to other structures. Nevertheless, the only few simulation works are still based on generic model studies, and the authors mainly aimed to conveying proof-of-concept insights. A systematic realistic simulation strategy is urgently demanding so that typical experimental PISA systems can be reasonably reproduced, and crucial controlling factors can be discovered by computer simulations to inversely guide to improve the experimental technology. In this paper, the dynamic process of PISA is simulated by the particle-based DPD simulation method coupled with our in-house stochastic reaction model. This simulation model can be approximately mapped to the practical experimental PISA system. The input simulation parameters are obtained from the

2. MODEL AND SIMULATION DETAILS We will show how the coarse-grained (CG) simulation strategy is carried out by focusing on an experimentally important system. He and co-workers had reported an easy-going route to prepare PAA-b-PSt assemblies with different morphologies through a dispersion polymerization of styrene in methanol with the trithiocarbonated PAA as the macro-CTA.16 On the basis of the study of various assembly morphologies and their transitions with the growth of the PSt block, the authors had suggested that the controlling factors such as polymerization conversion, St/PAA feed ratio, and methanol amount may be crucial to regulate the assembly morphologies. Focusing on this specific reaction, for systematically elucidating the influences of the above factors and for further clarifying the mechanisms for the formation of vesicles and micelles, a model system containing the molecules of acrylic acid, styrene, and methanol is needed. Considering the system of He et al.,16 the macro-CTA is simply represented by the hydrophilic PAA in our model. The polymerization takes place with the growth of a hydrophobic PSt block. The experiment is performed in the methanol solution. Notably, the solvent here is methanol instead of water, and, thus to be exact, PAA and PSt should be solvenphilic and solvenphobic blocks. For simplicity, we still use the terms hydrophilic and hydrophobic to describe the affinities of the components to the solvent. We then consider to build a CG model containing three types of beads, that is, A, B, and S, where A represents the hydrophilic AA molecule, B represents the styrene molecule, and S represents methanol molecules, respectively. According to the structural characterB

DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. (a) Schematic illustration of the coarse-graining scheme for the three components, that is, the AA molecule is represented by one A-type bead, the styrene molecule is represented by one B-type bead, and a lump of two methanol molecules together is represented by one S-type bead. (b) The principal RAFT reaction during the PISA process (top panel) and the illustration of the growth of the hydrophobic block during the polymerization in our CG model (bottom panel). (c) Initial configuration of the PISA system with the macro-CTAs labeled as red chains and the styrene molecules as green beads. The methanol molecules are omitted for clarity. Notably, for clearer illustration, this configuration is generated with obviously much lower concentrations of PAA and St than those in the practical simulations.

istics of the three types of molecules, we propose the following mapping scheme: the AA molecule is represented by one Atype CG bead, the styrene molecule is represented by one Btype CG bead, and a lump of two methanol molecules together is represented by one S-type bead. The details are displayed in Figure 1a. Commonly, in PISA systems, the controlled radical polymerization is mostly applied, for example, the reactions such as nitroxide-mediated polymerization,45 atom-transfer radical polymerization,46 reversible addition−fragmentation chain transfer (RAFT),47 and so on. For example, in the reaction of He et al.,16 the macro-CTA is synthesized by the RAFT polymerization of AA monomers. Then, the selfassembly can take place in the solution of methanol, in which the macro-CTA is induced by the initiator such as 2,2′azobisisobutyronitrile (AIBN). In our simulation, the macroCTA is considered as the short chain of An, with the end bead simply handled as connecting a reactive A-type bead, which plays the role of the reacting end of the macro-CTA to grow the hydrophobic block. Thus, the RAFT reaction process and its mapping scheme to the corresponding CG level can be presented in Figure 1b. As suggested in ref 49, a basic assumption in the DPD method is that all beads possess comparable masses and volumes. It is not difficult to obtain the molar masses of each type of beads from their respective underlying molecular formula, as shown in Table 1. Although the masses of the beads are different, we assume that we still can use the mean molar mass of the beads to define a single mass unit: m = ∑i=A−S(φi × Mi). Because PISA is able to take place with high concentration of polymers, we specifically set the volume fraction of the reactants as high as 20% and the feeding ratios of the three types of beads as φA = 0.04, φB = 0.16, and φS = 0.8, as listed in Table 1. Therefore, we can easily obtain the value of the averaged single mass unit m = 70.81 g/mol. Accordingly, the average density of the system can be reasonably calculated as ρ = ρAφA + ρBφB + ρSφS = 0.821 g/

Table 1. Molar Mass (M), Density (ρ), Solubility Parameter (δ), and the Volume Fraction (φ) of Each Type of CG Bead bead type

A

B

S

corresponding molecule(s) M (g/mol) ρ (g/cm3)a δ (cal/cm3)1/2b Φ

acrylic acid 72.06 1.05 12.0 0.04

styrene 104.15 0.909 9.3 0.16

2× methanol 64.08 0.7918 14.5 0.8

a

The density of each component is obtained from the handbook of ref 48 which represents the densities of the pure components at room temperature. Here, we make the approximation that the densities of the components do not change a lot at reaction temperature. bThe solubility parameters of the components are obtained from the handbook of ref 48.

cm3. From this mean molar mass and the average density, we can obtain the average volume of the bead as v0 = 143.2 Å3. In classical DPD simulations, the bead number density is chosen as ρ = ρn = 3.0. Thus, following the handling of DPD simulations in ref 49, we obtain L = (v0ρn)1/3 = 7.5 Å, that is, we can define the length scale of the simulation roughly as 7.5 Å. This length scale denotes that there are roughly three DPD beads in a small cell of size L.3 As conventionally used in DPD simulations, the interaction radius of beads rc is set equal to L. For easy numerical handling and for avoiding the finite size effect during simulations, we construct the simulation box of size (50L)3 with reduced bead number density ρn = 3.0; consequently, our DPD model consists of 375 000 movable beads. In DPD, the time evolution of interacting beads is governed by Newton’s equations of motion.50 Interbead interactions are characterized by pairwise conservative, dissipative, and random forces acting on bead i by bead j. They are given by FijC = −αijωC(rij)eij C

(1) DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules FijD = −γωD(rij)(vij·eij)eij

(2)

FijR = σωR (rij)ξijΔt −1/2eij

(3)

Å3 in this study. Therefore, the values of χij between different components are obtained. The empirical relation between the Flory−Huggins χ parameter and DPD interaction parameter can be used to evaluate the DPD interaction parameter between different species

where rij = ri − rj, rij = |rij|, eij = rij/rij, and vij = vi − vj. ξij is a random number with zero mean and unit variance. For easy numerical handling, the cutoff radius, the bead mass, and the temperature are often set to be the units, that is, rc = m = kBT = 1. aij is the repulsion strength, which describes the maximum repulsion between interacting beads. ωC, ωD, and ωR are the three weight functions for the conservative, dissipative, and random forces, respectively. For the conservative force, ωC(rij) = 1 − rij/rc for rij < rc and ωC(rij) = 0 for rij ≥ rc ωD(rij) and ωR(rij) have a relation according to the fluctuation−dissipation theorem51

χ = (0.286 ± 0.002)(αij − αii)

(12)

where αii (=25) and αij are the DPD interaction parameters between the same and different types of species, respectively. The calculated DPD interaction parameters between different components, αij, are shown in Table 2. Table 2. DPD Interaction Parameters between Different Types of Beads in the Simulation of PISA

ωD(rij) = [ωR (rij)]2

(4)

bead type

A

B

S

σ 2 = 2γkBT

A B S

25.00

(5)

28.90 25.00

26.90 37.10 25.00

Here, we choose a simple form of ωD and ωR according to Groot and Warren52 2 l o o o1 − (rij/rc) (r < rc) ωD(rij) = [ωR (rij)]2 = m o o o0 (r ≥ rc) n

With regard to the protocol of describing the growth of the B block, we employ the idea in our previous works57,58 by introducing the reaction probability Pr to model the polymerization in DPD. In each reaction time interval τ = NstepΔt, if an active end meets several reactable beads in the reaction radius (taken the same as the interaction radius for convenience), first it randomly chooses one of the reactable beads as the reacting object. Subsequently, another random number is generated, and by checking if it is smaller than the preset Pr, we decide whether the reacting object will be connected to the active end or not. In the simulations, we adopt reaction probability Pr = 0.0005−0.00005 and the reaction time interval τ = NstepΔt = 1 (i.e., the reaction may take place for once within a DPD time unit), which represents a relatively moderate reaction with regard to the simulation time unit according to our previous experiences. In the initial configuration, we generate a number of reactive An polymer chains, which play the role of macro-CTAs composed of PAA, randomly distributed in the simulation box. On the other hand, the free B-type beads with a total number of 52 500 are also randomly generated in the simulation box, acting as the styrene molecular monomers. The left space of the simulation box is filled with a number of S-type beads (acting as doubly lumped methanol molecules) to construct the solution environment during the PISA process so that the whole bead number density is kept as ρ = 3.0. A series of DPD simulations are carried out in constant-volume and constanttemperature (NVT) conditions. All the simulations are carried out using the GALAMOST package59 with the SKIPSGALAMOST reaction simulation platform.58 The periodic boundary conditions are applied in X, Y, and Z directions. A period of 4 × 104 time step simulation is first conducted to relax the configuration without the polymerization, followed by 5 × 106 time steps with the polymerization switched on to collect the data and observe the evolution and dynamic pathway of PISA. Notably, because the obtained αBS = 37.10 is obviously high enough to lead to the deposition of styrene monomers before the polymerization, we specifically use a smaller value of αBS = 25.0 before the styrene monomer is connected to a chain so that the unreacted styrene molecules can uniformly disperse in the solution. The consideration of this handling is reasonable according to ref 16 in which the

(6)

Groot−Warren-velocity Verlet algorithm50,52 is used here to integrate the Newton’s equations of motion ri(t + Δt ) = ri(t ) + Δtvi(t ) + 1/2(Δt )2 fi (t )

(7)

vĩ (t + Δt ) = vi(t ) + λΔtfi (t )

(8)

fi (t + Δt ) = fi [r(t + Δt ), v(̃ t + Δt )]

(9)

vi(t + Δt ) = vi(t ) + 1/2Δtfi (t ) + fi (t + Δt )

(10)

Here, λ = 0.65 according to ref 52. In DPD, polymers are constructed by connecting the neighboring beads together via the harmonic springs FSij = ∑jCrij. We choose the spring constant C = 10 according to ref 52. In this study, we choose the time step Δt = 0.02 in the DPD simulations. There are several strategies to estimate interaction parameters in DPD simulations.49,50,53 For example, in ref 49, the researchers mapped the binding energies between different species at the atomistic level to define the DPD interaction parameters between the polymer and clay. In another approach, Scocchi and co-workers53 proposed a quite similar route to determine the repulsive DPD parameters by mapping the energy values resulted from the atomistic MD simulations. Here, we use the strategy to estimate the DPD interaction parameters from Flory−Huggins χ-parameters. Because the solubility parameters are obtained in Table 1, the Flory−Huggins interaction parameters χ at 353 K (the experimental temperature is 80 °C) can therefore be calculated via54−56 χij =

(δi − δj)2 vref kBT

(11)

where δi and δj are the solubility parameters for components i and j, respectively, and vref is the reference bead volume. Here, we use the approximation that the reference bead volume vref can be taken as the average size of the bead, which is v0 = 143.2 D

DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX

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On the basis of the preliminary visual cognition of PISA in Figure 2, we focus on the reaction kinetic features of PISA. Figure 3a shows the time evolution of the conversion of

authors had indicated that methanol was chosen as the polymerization medium because it was a good solvent of St and PAA but a nonsolvent of PSt. Figure 1c shows an initial configuration of the PISA system, in which the polymerization has not yet been switched on and the macro-CTAs (red) and free monomers (green) are randomly distributed in the simulation box.

3. RESULTS AND DISCUSSION 3.1. Basic Overview. Our simulation reproduces the PISA process between the PAA-type macro-CTA and styrene monomers in the solution of methanol. With the growth of the PSt block, the morphology transition of the assemblies formed by the generated BCPs is mainly investigated. As a preliminary study, we specifically represent the macro-CTA as a short chain of A5 and the reaction probability as Pr = 0.00005. Figure 2 shows the typical snapshots of the

Figure 3. (a) Time evolution of the conversion of styrene monomers Xm and the monomer concentration decay ln([M0]/[Mt]) during the PISA process. (b) Simulated mass distributions of the PSt blocks in different stages with specific Xm values (scatters). The curves with the same color denote the comparison of the corresponding Poisson distributions obtained from eq 13.

styrene monomers and the monomer concentration decay during the PISA process. It is clear that as the polymerization time proceeds, the monomer conversion Xm increases fast in the early stage and turns slower in the medium stage. Finally, the plot becomes flat and reaches close to 100% at around 106 time steps, which implies the exhaustion of styrene monomers in the solution in the end. On the other hand, the monomer concentration decay is monitored via the time evolution of ln([Mo]/[Mt]), where [Mo] and [Mt] represent the initial and instantaneous concentration of the monomers, respectively.58 It is clear that the plot of ln([Mo]/[Mt]) ∼ t almost shows a linear dependence, implying that this reaction obeys the feature of first-order reaction kinetics. It is in agreement with our acknowledgement of most controlled radical polymerization reactions based on the reaction equation as rp = k[P*][M] (rp: reaction rate; k: reaction rate coefficient; [P*]: concentration of active chain ends which should be constant in controlled radical polymerization; [M]: free monomer concentration), which proves that this model describes the

Figure 2. Typical snapshots of the morphologies in different stages of the PISA process with the macro-CTA as A5 and the feeding ratio A/ B = 1:3. The free B monomers and the solvent S beads are omitted for clarity. The corresponding time of the polymerization and the instantaneous averaged length of B block N̅ B are both labeled below each subfigure.

morphologies in different stages of the PISA process. It can be found from Figure 2 that at the early stage of PISA (e.g., Figure 2a,b), the PSt block is basically still short; thus, only dispersed small aggregates or micelles are formed in different locations. As the PSt block grows longer, the neighboring small micelles tend to fuse into relatively larger wormlike micelles (e.g., Figure 2c,d). In the medium and late stage of PISA, the PSt block continues to grow longer and the morphology tends to fuse and change into ordered structures. This is a general glance of the transition of the assemblies, and a detailed analysis correlated to geometrical quantities will be shown in the following. E

DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules correct reaction kinetics of PISA. More detailed discussion can be found in our previous study.58 Furthermore, Figure 3b shows the mass distribution of the grown PSt blocks in different stages of polymerization during PISA. Notably, here we additionally show their comparisons with the corresponding Poisson form distributions. Hillmyer and Matsen60 proved that from the theoretical point of view, the kinetics of an equilibrium polymerization basically develops a Poisson distribution of the chain lengths. Similar validations on this issue can be found in relevant works. For example, Farah et al.61 indicated that the polymer size distribution should correspond to a Poisson form function based on an analytical derivation of Akkermans et al.62 Our recent simulation work, based on a kinetic chain growth algorithm,58 supported the Poisson distribution on describing the polymer length in different stages of the controlled polymerization, that is, P(N + 1) =

⟨N ⟩N −N e N!

(13)

where N is the average chain length of the polymers at any specific time during the polymerization, and this value is easy to be calculated in simulations. On the basis of the above explanation, Figure 3b shows a good validation whether our stochastic reaction model is reasonable to describe the PSt block growth in PISA. It is clear that in different stages of the polymerization (labeled by the conversion of monomers Xm), the simulated mass distributions of the PSt blocks can well fit on their corresponding Poisson form distributions obtained by eq 13. As the polymerization proceeds, the peak position of the distribution moves accordingly to the higher NB region. Notably, a general Poisson form as eq 13, which is only dependent on the value of instantaneous NB, can well describe the mass distributions of growing PSt blocks. This result supports our above conclusion that the growth of the PSt block obeys the first-order reaction kinetics. Figure 3a,b indicates that our simulation strategy can reproduce the correct reaction kinetics and mass distributions of the growth of the hydrophobic block during the process of PISA. On the basis of the correct description of polymerization, in the following we mainly focus on the formation and transition of the self-assembly morphologies during PISA. In Figure 4, we present the time evolution of the aggregate number Naggr and the asphericity factor a in the process of PISA. Naggr denotes the number of individual aggregates at a specific time during the PISA process, which can be counted in simulations. The asphericity factor a specifies the averaged feature of the aggregates, which is calculated by63 a=

Figure 4. (a) Time evolution of the number of aggregates Naggr (black plot) and the asphericity factor value a (red plot) during the PISA process. The letters a−i close to each point of the red plot denote that the point corresponds to the asphericity factor of one snapshot in Figure 2 labeled with the same letter. (b) Schematic illustration of the possible pathway of the assembly transition during the PISA process.

form small micelles (Figure 2b) and further fuse into relatively larger ones (Figure 2c). It is also shown in Figure 4a that during the time of 105 to 1.5 × 105, the value of Naggr decreases, whereas the value of a basically increases. Consequently, the small micelles possibly come in contact with each other via the random diffusion, and a kind of sphere−sphere fusion is able to take place to generate an even larger wormlike micelle (Figure 2d), and we can observe the further decrease of Naggr and a slight increase of a in Figure 4a. The following transition is the change from the wormlike micelles (Figure 2d) to the special lamellar micelles (Figure 2e) based on a further fusion. As a possible metastable morphology, we believe that this lamella micelle is of great significance to connect the transition of different morphologies, although we have not yet found direct evidence of it in the in situ experimental observation. At the final stage, the lamella micelle spontaneously bends and curls over because of the enhanced surface tension until a closed vesicle is finally formed (Figure 2f). This curling behavior of the lamella micelle also yields the continuous decrease of the value of a from state (d) to (f) in Figure 4a. Similar mechanism of the formation of vesicles is also reported elsewhere.2,39,64,65 Meanwhile, the neighboring vesicles possibly fuse into a larger one, and as a result, a super large columnar vesicle is ultimately observed (Figure 2g−i). The preliminary fusion inevitably yields the aspherical shape of the large vesicle; thus, it is natural to observe the jump of asphericity factor from state (f) to (g) in Figure 4a, whereas a following self-adjustment of the large vesicle after the fusion effectively results in the formation of an almost spherical shape , corresponding to the decrease of the value of a from state (g) to (i) in Figure 4a. In Figure 4b, we schematically show this transition pathway between different assemblies in PISA by simple cartoons. Thus,

(λ 2 − λ1)2 + (λ3 − λ1)2 + (λ3 − λ 2)2 2(λ1 + λ 2 + λ3)2

(14)

where λ1, λ2, and λ3 denote three characteristic radii of an aggregate, that is, two equatorial radius values and one polar radius value. Thus, we can obtain that 0 ≤ a ≤ 1, and a smaller value of a approaching 0 indicates that the aggregate is close to a sphere, whereas a larger value of a indicates that it is close to a cylindrical shape. By correlating Figure 4 with the corresponding snapshots in Figure 2, we can find that at the early stage of PISA, a lot of dispersed small aggregates are generated shortly after the polymerization is started (corresponding to Figure 2a). With the growth of the PSt block, the neighboring small aggregates gradually combine together to F

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hydrophobic block is long enough for the BCPs to form a complete core−shell structure. As a consequence, a big columnar vesicle is observed finally. Whereas for A5B̅ 20 in Figure 5c, our simulation shows that the final morphology is a multishell annular vesicle; in other words, inside the vesicle, the hydrophilic and hydrophobic shells are covered by each other for several layers. For its complexity, this kind of multishell annular vesicle is difficult to be observed in experiments, and thus, it is scarcely reported. For further investigation, we focus on this multishell annular vesicle morphology to discover the dynamic pathway of its formation. As shown in Figure 6, during the PISA process with

it is clear to imagine a pathway of the transition from the beginning of dispersed small micelles with a quite short hydrophobic block to fuse to wormlike micelles that further fuse to form lamella micelles. In the following, the lamella micelle bends and changes into a closed vesicle morphology. Several neighboring vesicles further fuse into one large columnar vesicle ultimately. The whole process is simply and visually summarized in Figure 4b. It should be noted that during the whole process of PISA, with the continuous growth of the hydrophobic block, the transition of the assemblies always occurs. Because the assemblies are difficult to find a stable state as the polymerization proceeds, PISA can be considered a typical nonequilibrium or dynamic self-assembly process.66,67 After the free St molecules in the solution are almost exhausted, the growth of the hydrophobic block is ceased. Then, the assemblies have the opportunity to reach a final thermodynamically equilibrium state, implying that the process of PISA is accomplished. 3.2. Influence of Hydrophobic Block Length. Zhang and Eisenberg et al.1,2 and Pan et al.16 had, respectively, investigated the influence of solvent property, chain length, and ratio of hydrophilic and hydrophobic blocks on the transition of morphologies in the self-assembly process. As is known, the self-assembly morphology is mainly determined by the free energy of the system. Therefore, by regulating the stretching condition of the hydrophobic block, which forms the core of the self-assembly structure, the interaction between the two blocks, as well as the interfacial free energy, it is possible to adjust the morphology of BCP in PISA.68,69 In practical experiments, it is commonly used to regulate the BCP chain length by controlling the polymerization time and the feeding ratio of the reactants. Accordingly, in this simulation, we regulate the hydrophilic block length in PISA by adjusting the feeding ratio of the macro-CTA and styrene monomers. Here, we set the feeding ratio of A and B beads as A/B = 1:2, 1:3, and 1:4 (macro-CTA is predefined as A5) so that the anticipated average length of BCP after polymerization is A5B̅ 10, A5B̅ 15, and A5B̅ 20. The final snapshots are shown in Figure 5. It is clear that in Figure 5a for A5B̅ 10, a big spherical

Figure 6. Typical snapshots of the morphologies in different stages of the PISA process with the macro-CTA as A5 and the feeding ratio A/ B = 1:4 (anticipated A5B̅ 20 finally). The free B monomers and the solvent S beads are omitted for clarity. The corresponding time of polymerization and the instantaneous averaged length of B block N̅ B are both labeled below each subfigure.

the feeding ratio A/B = 1:4 (anticipated A5B̅ 20 in the final state), the formation of multishell annular vesicle experiences a different mechanism as compared to that in Figure 2. Figure 6a and 6c shows the same way of transition of the dispersed small micelles to wormlike micelles that fuse into larger lamella micelles. Afterward, they could naturally curl to form closed small vesicles as shown in Figure 6d. A further fusion between neighboring vesicles or between vesicles and compound micelles leads to the formation of a big aspherical vesicle (Figure 6e−h). This big vesicle in the solution obviously suffers from the surface tension at the interface between the hydrophobic and hydrophilic blocks. As a consequence, for accessing a thermodynamically stable state, this vesicle naturally adjusts itself so that it is more close to a spherical shape. On the other hand, the hydrophilic chamber in the vesicle however possibly shrinks itself. We observe that the chamber gradually bends into a circle to finally lead to the formation of multishell compound vesicles (Figure 6f). A

Figure 5. Snapshots of the assembly morphologies with different feeding ratios of reactants, that is, A/B = 1:2 (a), 1:3 (b), and 1:4 (c). The initial concentration of the reactants is set as f = 20%. The anticipated BCP length is labeled below each subfigure. For each subfigure, a corresponding cross-sectional view inside the structure is also presented.

multichamber compound micelle is finally observed. This result is reasonable because the hydrophilic block is too short, which is difficult to form the core of the vesicle without any hydrophilic blocks inside. As a result, Figure 5a is more like an aggregate of several connected micelles, in which the wrapped hydrophilic blocks accommodate in the chambers inside the micelle. In comparison, for A5B̅ 15 in Figure 5b, the generated G

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design another set of simulation with extreme case, that is, the feeding ratio A/B = 1:8 with the macro-CTA set as A5 so that the influence of the reactant concentration can be amplified. Practically, we can obtain that the anticipated final length of BCP is A5B̅ 40 and the initial volume fraction of reactants is preset as 10, 20, and 30%. For achieving an equilibrium state of the long-chain system, a special long enough simulation, that is, more than 5 × 106 time steps, is performed. As shown in Figure 7, our simulation well confirms the experimental

reasonable explanation on the transition of the inner hydrophilic chamber is that once the chamber is generated aspherically, it is more likely to bend itself instead of changing itself to a spherical shape because it undertakes different forces at different locations (inner or outer shell of the micelle). On the basis of the above analysis of the formation of multishell compound vesicles, we also find that increasing the length of the hydrophobic block leads to the decrease of the size of the vesicle chamber. It further yields the coexistence of vesicles and compound micelles in the PISA system. It should be noted that our simulations also show the dependence of the thickness of the vesicle (the distance from the outer shell to the inner chamber shell) on the average length of the hydrophobic block, which can be found in Figure S1 of the Supporting Information. The simulation result concludes that with the increase of the hydrophobic block, the thickness of the vesicle (black plot of Figure S1) and its ratio to the radius of the vesicle (red plot of Figure S1) increase. As a consequence, the chamber size of the vesicle accordingly decreases. This result partially supports the phenomenon of Figure 5 that for the system of A5B̅ 15 it shows a columnar vesicle morphology, whereas for A5B̅ 20 a typical multishell annular vesicle is obtained because an obviously larger-sized chamber (as compared to the vesicle size) can be formed with A5B̅ 15 than that of A5B̅ 20. We further conduct another set of simulations in which the larger macro-CTA is generated as A10, but the feeding amounts of B beads are the same as those in the systems of Figure 5 so that the anticipated average length of BCP after PISA is A10B̅ 10, A10B̅ 15, A10B̅ 20, and A10B̅ 40. We find that when the size of macro-CTA is doubled, the morphologies of spherical micelles are more often observed in PISA (see Figure S2 in the Supporting Information). Therefore, we can conclude that the ratio of the size of the hydrophobic block and that of the hydrophilic macro-CTA are one of the controlling factors to determine the morphology of BCPs in PISA. When the macroCTA is short, with the increase of the hydrophobic block in the polymerization, the size of the assembly is accordingly increased. It intrinsically yields the decrease of density of the shell on the preliminary micelle at the early stage, which further lowers the energy barrier for the micelle fusion. In comparison, once the size of macro-CTA is set too large, the outer shell of the micelle becomes always thick enough to promote the energy barrier of the fusion between neighboring micelles. In other words, the effect of reducing the shell density by the polymerization is too weak, unless the hydrophobic block can grow obviously much longer than the macro-CTA. As a consequence, the aggregates stay at the morphology of spherical micelles and are not likely to change any more. This result is well supported by the experimental study of Arms and co-workers in which they indicated that for a relatively larger macro-CTA (i.e., PGMA112 macro-CTA), the phase diagram (Figure 7 of ref 70) was dominated by spherical morphologies. In summary, we believe that regulating the ratio of the hydrophilic and hydrophobic blocks is a feasible way to adjust the morphology of BCPs in PISA. 3.3. Influence of the Reactant Concentration. In practical experiments, the concentrations of reactants are often adjusted by increasing the amounts of monomers/macroCTAs or increasing the solvent in PISA. It is proved to be a feasible way to obtain different morphologies of assemblies by simply changing the concentration of the reactants. For getting a full acknowledgement of the effect of concentration, we

Figure 7. Final snapshots of assemblies in PISA with the anticipated length of BCP A5B̅ 40 (the feeding ratio A/B = 1:8 with the macroCTA set as A5) but different initial concentrations of reactants (the initial volume fractions of reactants as (a) 10, (b) 20, and (c) 30%). For each subfigure, a corresponding cross-sectional view inside the structure is also presented.

observations. For the lowest reactant concentration (volume fraction 10%), the final morphology is obviously spherical, as shown in Figure 7a. The sectional view of the inside structure indicates that it is a typical spherical micelle. For the medium concentration with the volume fraction 20%, we can observe the spherical vesicle morphology in PISA (Figure 7b). In comparison, when the volume fraction of reactants is further increased, a more complicated morphology as a multichamber vesicle can be generated (Figure 7c). This result agrees well with the experimental observations of He et al.16 With further analysis, this phenomenon can be explained based on our above discussion on the transition pathway between different assemblies. Obviously, Figure 7b shows an appropriate concentration to form the vesicles. According to our above discussion, a common transition pathway from dispersed small micelles to wormlike micelles and further to lamella micelles is imagined because the formation of the vesicle starts from the spontaneous bending of this lamella micelle. However, when the reactant concentration is set too low (e.g., as in Figure 7a), the transition from dispersed small micelles to the wormlike micelle turns out to be too difficult. Because the concentration is quite low, the diffusion of the dispersed small micelles is not efficient to lead to the fusion between neighboring micelles and further formation of the wormlike large micelle. On the contrary, the morphology remains at the state of preliminarily fused micelles for a long time. Further transition is impossible because they are not able to meet any neighbors in their locations. As a consequence, we may possibly observe the micelle structures with low concentration of reactants. In comparison, when the reactant concentration is set obviously high (e.g., Figure 7c), the late stage of the transition pathway is different, that is, the fusion of neighboring vesicles to form the large columnar vesicle. This fusion involves not merely the mutual touch of vesicles but also the adjustment of their structures to find any defective gaps on the surface so that the vesicles are able to fuse together starting from the gaps and maintain the hollow core structure. When H

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Macromolecules the reactant concentration is too high, a dynamic fusion may still continue, whereas the thermodynamic adjustment of the structure is blocked because another neighboring vesicle in the vicinity joins in this fusion shortly. In other words, a step-bystep fusion process inevitably changes into a cooperative fusion between several vesicles simultaneously. As a consequence, it is not difficult to imagine the formation of a multichamber vesicle based on such kind of cooperative fusion. 3.4. Influence of Polymerization Rate. The driving force of PISA is acknowledged as originated from the growth of the hydrophobic block; thus intuitively, the polymerization rate should be a controlling factor to influence the morphology transition in PISA. As our previous introduction of the model, the reaction probability value Pr is proportional to the rate of polymerization.57,71 Here, we perform another set of simulations with a larger value of Pr (Pr = 0.0005) to design the comparison between fast and slow (Pr = 0.00005) polymerizations in PISA. As shown in Figure 8, the aspherity

Figure 9. (a−f) Typical snapshots of the morphologies in different stages of PISA with the obvious fast growth of hydrophobic B blocks with Pr = 0.0005. The free B monomers and the solvent S beads are omitted for clarity. The corresponding time of polymerization is labeled below each subfigure. (g) Schematic illustration of the possible pathway of the assembly transition during the PISA process with this fast polymerization.

polymerization. As a consequence, the formation of vesicles with fast polymerization is not spontaneously induced by the curling of lamellae. Instead, it obeys a completely different pathway because within the fast polymerization the growth of hydrophobic blocks is accomplished quite early. In the early stage, the amphiphilic BCPs combine to form the large micelles (Figure 9b). With their sizes growing bigger with the polymerization time, the micelles may break up at some critical size and generate even larger irregular spheres. During this reconstruction process, the hydrophobic blocks tend to move toward the shell. Instead, the hydrophilic blocks move to the core, that is, they show the so-called “flip-flop” behavior (Figure 9c−e). After that, a part of the solvent beads are able to randomly diffuse into the core of the structure because the hydrophilic block fills the core position (Figure 9f). After a merging process in the late stage, the core of the structure accommodates more solvent beads and this chamber size is enlarged; as a consequence, an equilibrated vesicle structure is accomplished. A schematic illustration of this transition pathway is shown in Figure 9g. This pathway had also been reported previously in other studies. For example, He and Schmid73 and Han et al.74 had proposed this mechanism of vesicle formation induced by the typical “flip-flop” process in their respective works. Our simulation exactly confirms the rationality of this mechanism.

Figure 8. Dependence of asphericity factor a on the conversion of reactants Xm with fast (Pr = 0.0005) and slow (Pr = 0.00005) polymerizations.

factor a for Pr = 0.0005 basically remains in a smaller level (always lower than 0.18) and its fluctuation amplitude is obviously smaller. By observing the corresponding snapshots, we can only find spherical micelles for this system with fast polymerization. It can be attributed to the fact that for relatively fast polymerization, the fusion of neighboring spherical micelles would be seriously disturbed because the fast reaction had been proved to have the effect of locally mixing the species.72 The aspherity factor a for Pr = 0.00005 apparently changes sharply with Xm. It may be ascribed to the fact that for the slow polymerization, it obviously obeys reaction-limited kinetics. Thus, as the prior dynamics, the diffusion further promotes the opportunity of fusion between micelles. The formed wormlike micelles via the fusion of smaller micelles evidently show much higher values of aspherity factor a in Figure 8. On the basis of the above analysis, we further show the transition pathway of the morphology with fast polymerization, that is, Pr = 0.0005. Figure 9a−f shows that the fast polymerization can yield the formation of the micelle structure, as well as the slow polymerization. However, the intermediate states are not the same. Under the fast polymerization condition, numerous spherical micelles are generated in the early stage, while in the following, we are not able to observe the generation of lamellae structures as that with slow

4. CONCLUSIONS In this paper, the dynamic process of PISA is reproduced by the DPD simulation method coupled with our in-house stochastic reaction model. This model can be approximately mapped to the practical experimental PISA system. The input simulation parameters are obtained from the experimental data I

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to reflect the characteristics of the experiment. The dynamic process of PISA, including the two different dynamics pathways with slow and fast polymerization rates to form the vesicle structure, can be reasonably reproduced in simulations, and the simulation results are able to accordingly guide to design or develop new PISA systems in the experiment. This model is validated by simulating a true experimental PISA system of PAA-b-PS assemblies in methanol solution. Our simulation shows that this reaction obeys the feature of first-order reaction kinetics; thus, our simulation strategy can reproduce the correct reaction kinetics and mass distributions of the BCPs during the process of PISA. As a typical nonequilibrium self-assembly process, PISA shows a clear pathway of the transition in our simulations from the dispersed small micelles to wormlike micelles that further fuse to form lamella micelles. The lamella micelle spontaneously bends and changes into a closed vesicle morphology, and several neighboring vesicles further fuse into one large columnar vesicle ultimately. Our simulations evidently show that regulating the ratio of the hydrophilic and hydrophobic blocks is a feasible way to adjust the morphology in PISA. Increasing the length of the hydrophobic block leads to the decrease of the size of the vesicle chamber, which further yields the coexistence of vesicles and compound micelles. Besides, the concentration of the reactants is also proved to greatly influence the morphologies, which implies that an appropriate concentration range is necessary to form the vesicle structure. Finally, the morphologies are also proved to be affected by the polymerization rate. PISA with fast polymerization experiences a different pathway of transition as compared to that with slow or medium polymerization, in which the hydrophobic and hydrophilic blocks undergo a typical flip-flop process to form the final vesicle structure. The construction of the simulation study is beneficial to confirm the crucial factors in different PISA systems and is possible to suggest to improve the experimental technology in the future.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21774051, 51403022, and 21534004). H.L. gratefully acknowledges the support from the Alexander von Humboldt Foundation.

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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.9b01051.

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REFERENCES

Dependence of the thickness of the vesicle d and its ratio to the radius of the vesicle d/R on the average length of the hydrophobic block m in the system with A5Bm and typical final snapshots of the morphologies in PISA with the macro-CTA as A10 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yao-Hong Xue: 0000-0002-7820-2855 Hong Liu: 0000-0002-7256-5751 Zhong-Yuan Lu: 0000-0001-7884-0091 Author Contributions ∥

Y.-D.Y. and Y.-H.X. contributed equally.

Funding

Any funds used to support the research of the manuscript should be placed here (per journal style). J

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DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.9b01051 Macromolecules XXXX, XXX, XXX−XXX