FULL PAPER DOI: 10.1002/asia.201402146
Dissipative Particle Dynamics Simulation Study on Vesicles Self-Assembled from Amphiphilic Hyperbranched Multiarm Copolymers Yuling Wang,[a] Bin Li,[b] Haibao Jin,[a] Yongfeng Zhou,*[a] Zhongyuan Lu,*[b] and Deyue Yan[a]
Abstract: Hyperbranched multiarm copolymers (HMCs) have been shown to hold great potential as precursors in self-assembly, and many impressive supramolecular structures have been prepared through the self-assembly of HMCs in solution. However, theoretical studies on the corresponding selfassembly mechanism have been greatly lagging behind. Herein, we report the self-assembly of normal or reverse vesicles from amphiphilic HMCs by dissipative particle dynamics (DPD) simulation. The simulation disclosed both the self-assembly mechanisms and dy-
namics of vesicles. It indicates that the self-assembly of HMCs involves several steps, from randomly distributed unimolecular micelles to small spherical micelles, to membrane-like micelles, to finally small vesicles. The membranes are formed through the direct aggregation and lateral fusion of small micelles, and the bending and closing of Keywords: dissipative particle dynamics simulation · hyperbranched multiarm copolymersmicelles · self-assembly · vesicles
Introduction
Up to now, most of the polymeric vesicles are generated from the self-assembly of linear block copolymers, and are denoted as polymersomes.[6a, 8a] The structures as well as the self-assembly mechanisms of polymersomes have been widely studied both experimentally and theoretically by using computer simulations. The simulation work can be divided into atomistic scale simulations and mesoscopic scale simulations. The most widely used simulation techniques are molecular dynamics (MD), Monte Carlo (MC), Brownian dynamics (BD), dissipative particle dynamics (DPD), selfconsistent field theory (SCFT), and density functional theory (DFT). These simulation works are mainly focused on four parts: the first part is about the vesicle self-assembly from block copolymers[9] and dendrimers;[10] the second part is related to the mixtures between lipids, homopolymers, block copolymers, dendrimers, or nanoparticles;[11] the third part is about the fusion, fission, and rupture of vesicles, and the interaction between the vesicle and the membrane;[12] and the forth part is about the microphase separation behavior and shape transformations of vesicles.[13] These theoretical works have greatly broadened our knowledge on polymersomes.[14] Hyperbranched polymers (HBPs) composed of dendritic units, linear units, and terminal units are highly branched macromolecules with a three-dimensional dendritic architecture, and consequently possess special properties, such as a large population of terminal functional groups, lower solution or melt viscosity, and increased solubility.[15] Recently,
Self-assembly of amphiphilic block copolymers has proved to be an excellent and efficient way to construct all kinds of delicate supramolecular structures, and most of the reported studies concern the self-assembly of linear block copolymers such as diblock or triblock copolymers.[1] The self-assembly of amphiphilic block copolymers results in a wide range of aggregates in aqueous solution, including spherical micelles, rods, vesicles, toroids and so on.[1–5] Among them, the selfassembled vesicles with closed membranes have attracted great attention because of their unique hollow structure and potential applications in drug delivery, gene therapy, and as model systems of biomembranes.[6–8]
[a] Dr. Y. Wang, H. Jin, Prof. Y. Zhou, D. Yan School of Chemistry and Chemical Engineering State Key Laboratory of Metal Matrix Composites Shanghai Jiao Tong University 800 Dongchuan Road, Shanghai 200240 (China) E-mail: [email protected] [b] Dr. B. Li, Prof. Z. Lu Institute of Theoretical Chemistry State Key Laboratory of Theoretical and Computational Chemistry Jilin University Changchun 130023 (China) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/asia.201402146.
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the membranes give rise to small vesicles. Finally, large and steady vesicles are formed through the fusion of small vesicles. In addition, the bilayer or monolayer molecular packing modes as well as the mircrophase separation behaviors of HMCs in normal or reverse vesicles have also been studied. These simulation results explore details that cannot be observed in the experiments to a certain degree, and have extended the understanding of the vesicular selfassembly process of HMCs.
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as an extension of block copolymer self-assembly, HBPs have been shown to hold great potential as excellent precursors in self-assembly.[16] Many impressive supramolecular aggregates at all scales and dimensions, such as macroscopic tubes,[17] physical gels,[18] micro- or nanovesicles,[19] spherical micelles,[20] honeycomb films,[21] and large compound vesicles,[22] have been prepared through solution self-assembly, interfacial self-assembly, and hybrid self-assembly of amphiphilic HBPs. Generally, these amphiphilic HBPs are composed of a hydrophobic hyperbranched core and many hydrophilic linear arms, and are known as hyperbranched multiarm copolymers (HMCs). The term “branched polymersomes” (BPs) has been introduced for vesicles self-assembled from amphiphilic HMCs in order to discern them from conventional polymersomes.[19] Up to now, several advances have been made for BPs experimentally. Firstly, normal BPs self-assembled from a HMC with a hydrophobic hyperbranched core and many hydrophilic arms, or vice versa, so-called reverse BPs self-assembled from a HMC with a hydrophilic hyperbranched core and many hydrophobic arms have been obtained.[23] Secondly, BPs can have a bilayer or a monolayer structure depending on the hydrophilic fractions of HMCs, and they will change from bilayer to monolayer with the increase of hydrophilic fractions.[19] Thirdly, BPs are very flexible and can fuse with each other to increase in size.[24] However, basic issues for understanding these experimental phenomena, the self-assembly mechanism as well as the dynamics of the formation of BPs remain unclear. For example, the self-assembly pathway of BPs is unclear; it is not clear why spherical HBPs can microphase separate into a bilayer; and the structural differences between normal and reverse BPs are unclear. It is very difficult to solve all of these problems only by experiments and, accordingly, theoretical simulations are needed. Unfortunately, to our knowledge, no theoretical simulation work on BPs has been done up to now. Very recently, we used DPD simulation to study the micellization process of HMCs.[25] Herein, we report for the first time on DPD simulations of the solution self-assembly of HMCs into BPs. DPD has its own advantages of high computational speed, large integration time step, and covering a much longer time scale, and thus it is very useful for simulating complex soft matter systems.[26] In our simulations, the formation mechanism and dynamics of both
Yongfeng Zhou, Zhongyuan Lu et al.
normal and reverse BPs have been disclosed in detail. In addition, the microphase separation process of HMCs and the bilayer or monolayer molecular packing model in the normal and reverse BPs have also been revealed.
Results and Discussion In our simulations, a DPD model for HMCs was constructed (see Figure 1; details of the model are given in the Experimental Section). A typical vesicle-forming amphiphilic HMC, a so-called HBPO-star-PEO, is shown in Figure S1 in
Figure 1. Ball-and-stick model of a HMC containing 41 beads, in which the hydrophobic hyperbranched core is composed of grey beads (A beads) and the hydrophilic arms are composed of black beads (B beads).
the Supporting Information. It consists of a hydrophobic hyperbranched poly(3-ethyl-3-oxetanemethanol) (HBPO) core and many hydrophilic polyethylene oxide (PEO) arms. Taking HBPO-star-PEO as an example to explain the DPD model, one “A” bead (the grey bead) in the model signifies one repeat unit in the HBPO core, while one “B” bead (the black bead) denotes three repeat units in the PEO arms. One “C” bead refers to six water molecules, the solvent for the self-assembly process. For the simulation, no artificial manipulation on the vesicle formation was used. Accordingly, we started from randomly distributed HMCs in dilute solution and traced the steps of vesicle formation. 1. Vesicle Formation Pathway
Abstract in Chinese:
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There are three interaction parameters for HMCs. One is the repulsive parameter between the hydrophobic core (A beads) and the solvent (C beads), as indicated by aAC ; the second one is the repulsive parameter between the hydrophilic arm (B beads) and the solvent (C beads), as indicated by aBC ; the third one is the repulsive parameter between the hydrophobic core (A beads) and the hydrophilic arm (B beads), as indicated by aAB. To reduce the parameter space of this system, we fixed the interaction parameters as aAB = 70, aAC = 150, and aBC = 26. These parameters reflect the fact
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tion (Figure 2 a). The subsequent self-assembly process can be classified into four stages: at the first stage, randomly distributed HMCs aggregate into small micelles within a short time (Figure 2 b, within 1.0 104 simulation steps); at the second stage, the small micelles merge into membrane-like structures (Figure 2 c and 2 d) with a long simulation time until 3.0 105 simulation steps; at the third stage, the undulation of the membranes, which induces a bending of the membrane (Figure 2 e, Figure S2 in the Supporting Information), occurs at 5.0 105 simulation steps to finally form small vesicles by closing the curving membranes (at 7.0 105 simulation steps, Figure 2 f); at the fourth stage, stable vesicles are obtained through the fusion of smaller ones (Figure 2 g–j). The cross-sectional view of the particles shown in Figure 2 j illustrates that they are hollow vesicles with segregated hydrophobic cores and hydrophilic arms (Figure 3 a). Figure 3 b shows the density distribution from the center of mass to the outside of the vesicle across the vesicle membrane (arrow direction in Figure 3 a). The density distribution profile of arms (B beads) has two peaks, while that of cores (A beads) has only one peak, thus indicating that the vesicle has the typical “arm-core-arm” structural characteristic of normal vesicles. Moreover, the first peak of the arms is slightly higher than the Figure 2. Time series of morphologies of normal vesicles self-assembled from HMCs at the initial state (a), second peak, which means that 1.00 104 steps (b), 1.00 105 steps (c), 3.00 105 steps (d), 5.00 105 steps (e), 7.00 105 steps (f), 1.00 106 steps (g), 1.45 106 steps (h), 1.50 106 steps (i), and 2.00 106 steps (j) in a line model. The hydrophobic cores the density of the internal vesiare shown in grey and hydrophilic arms are shown in black. Water beads are not shown for clarity. (k) Plot of cle surface is slightly larger the conservative energy between the core beads and water, EAC, versus simulation time. than that of the external vesicle surface. The fusion of small vesicles into big vesicles widely occurs that, in each HMC, the hyperbranched core is hydrophobic at the fourth stage of the self-assembly process. For instance, and the arms are hydrophilic, and that the core and arms two small vesicles in Figure 2 h (indicated by black circles) are incompatible.[26d] merge into one vesicle in Figure 2 i. For further information, The self-assembly process of HMCs in dilute solution is ila complete fusion process is shown in the Supporting Inforlustrated in Figure 2. HMCs are randomly distributed in mation (Figure S3). water as unimolecular micelles at the initial setup configura-
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Figure 3. (a) Cross-sectional view of the vesicle shown in a line mode rather than a ball-and-stick model for clarity and better resolution. Water beads are omitted for clarity. (b) Density distribution of segments A and B across the membrane.
such as unimolecular micelle aggregates (UMAs).[25] Evidently, such a lateral fusion process is energetically favorable. The self-assembly mechanism of BPs from HMCs is further illustrated in Figure 5 a. The HMCs first exist as unimolecular micelles in the solvent and then aggregate into small micelles with a segregated hydrophobic core and hydrophilic arms at stage 1 through microphase separation. Subsequently, at stage 2, the small micelles
We also studied the time evolution of an energy index, EAC, to characterize the self-assembly process. EAC is defined as the conservative energy between the hyperbranched core (A) of HMCs and the solvent (C) per particle:[26c] EAC ¼
X 1 beads
2 r =Nbeads aAC 1 AC RC 2
As shown in Figure 2 k, EAC decreased sharply and quickly when HMCs were changed from unimolecular micelles to small spherical micelles, which exist at the first stage of the self-assembly process (stage 1). This indicates that the selfassembly process minimizes the interaction energy between the hydrophobic core and the solvents. At stage 2, EAC decreased slowly and then reached a dynamic equilibrium due to the formation of membranes. At stage 3, EAC again decreased (see the magnified inset in Figure 2 k), which is attributed to the bending and closing of membranes to form small vesicles. At stage 4, a new equilibrium of EAC was reached and the small vesicles evolved into big ones through fusion.
Figure 4. The evolution from spherical micelles to sheet-like micelles at the simulation stage of 1.70 104 steps (a), 1.75 104 steps (b), 1.80 104 steps (c), 1.85 104 steps (d), 2.05 104 steps (e), 2.10 104 steps (f), and 2.15 104 steps (g). The morphologies self-assembled from HMCs are shown in a line mode. The hyperbranched hydrophobic cores (A) are shown in grey and the hydrophilic linear arms (B) are shown in black. (h) Scheme for the lateral fusion of a small micelle with a membrane.
At stage 2, the small spherical micelles turned into membranes; however, it is not easy to understand the pathway leading to this change just from looking at Figure 2 b–2 d. Therefore, three particles in sequential fusion (Figure 4 a–g) were taken out from the simulation snapshots to further display the pathway. At the beginning, a sheet-like structure was observed with two micelles around (Figure 4 a). Then, one of the small micelles merged with the sheet through lateral fusion when it was close enough (Figure 4 b–4 d). Subsequently, the residual small micelle also merged with the sheet through lateral fusion (Figure 4 e–4 g). In this manner, a bigger sheet was obtained. According to these results, one can conclude that the membrane is formed through sequential lateral aggregation and fusion of small micelles into small sheets (Figure 4 h). To our surprise, only lateral fusion occurred when the small micelles merged into sheets, which guaranteed the formation of two-dimensional membranes rather than three-dimensional large multimolecular micelles
further aggregate into membranes through continuous lateral aggregation and fusion, as shown in Figure 4 h. At stage 3, membrane bending and closing happens, and small vesicles are formed. At stage 4, small vesicles merge into big ones through sequential membrane fusion. In the self-assembly of polymersomes from linear block copolymers, the widely accepted mechanism is as follows: amphiphilic block copolymers first aggregate into small spherical micelles, which then grow into rod-like micelles; subsequently, the rods transform into sheet- or membranelike structures, and finally vesicles are formed through the bending and closing of membranes.[27, 14d] This mechanism is also suitable to the formation of lipid vesicles (liposomes). Thus, when comparing the self-assembly mechanism of conventional polymersomes to that of BPs, it can be seen that they are similar despite the fact that in the self-assembly of BPs no rod-like micelles are formed and the membranes are
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wanted to study the structure of BPs through simulation by exploring the packing model as well as the microphase separation of HMCs in the vesicle membranes. As shown in Figure 5 b,c, there are two molecular packing modes in normal BPs. In order to clearly discern the molecular packing model in the cross-sectional view, we arbitrarily labeled HMCs with different colors. When HMCs have a small hydrophilic fraction, that is, the copolymer has a relatively large hyperbranched core but short hydrophilic arms, evidently a bilayer structure can be observed (Figure 5 b). In this packing model, each HMC undergoes a full “A–B”-type microphase separaFigure 5. (a) Self-assembly mechanism of normal vesicles from HMCs. (b–d) Cross-sectional views of a normal tion, in which “A” designates vesicle (b, c) and a reverse vesicle (d) formed by hyperbranched multiarm copolymers. The magnified particles the hyperbranched core and in panels b, c, and d represent the bilayer structure and the monolayer structure of normal vesicles, and the bilayer structure of reverse vesicles, respectively. Hyperbranched core: white, blue, and green beads; linear “B” denotes the hydrophilic arms: pink, red, and purple beads. Water beads are omitted for clarity. arms. Two “A–B”-type HMCs are packed together in a headto-tail manner to form the bilayer. When HMCs have directly formed through the aggregation and fusion of small a large hydrophilic fraction, that is, the copolymer has a relaspherical micelles. However, in the self-assembly of conventively small hyperbranched core but long hydrophilic arms, tional polymersomes, the “sphere-to-rod” and “rod-to-mema monolayer structure can be evidently observed (Figbrane” transitions are necessary pathways. ure 5 c). In this packing model, each HMC undergoes an Besides on normal vesicles, we also performed DPD simu“A–B–A”-type microphase separation to form the monolaylations on reverse vesicles self-assembled from HMCs with er. Such a hydrophilic fraction-dependent bilayer and monohydrophilic hyperbranched cores and many hydrophobic layer packing model agrees well with the experimental linear arms in water. For the simulation, the same molecular data.[19a] The bilayer and monolayer structures of normal model as that shown in Figure 1 was used for each HMC while the parameters were changed to aAB = 70, aAC = 26, vesicles from HMCs are also schematically shown in Figure 5 a. and aBC = 150. According to these parameters, in each HMC, Next, we also studied the structure of reverse BPs through the hyperbranched core (A beads) is hydrophilic and the simulations. As shown in Figure 5 d, reverse BPs have a biarms (B beads) are hydrophobic, and the core and arms are layer structure. Most interestingly, only the bilayer structure incompatible. is possible with a continuous increase in the hydrophilic Based on the simulation results (Figure 6), we conclude fraction, and no monolayer structure can be observed. In that the formation pathway of reverse vesicles (Figure S4 in other words, HMCs can only undergo an “A–B”-type microthe Supporting Information) is the same as that of normal phase separation, and such a microphase separation is indevesicles, which consists of the aforementioned four stages. pendent of the hydrophilic fraction of the polymers. Thus, Membranes are also formed by aggregation and lateral reverse BPs are different from normal ones with regard to fusion of small micelles. However, the dynamics of the forthe membrane structure. The reason for this difference can mation of reverse BPs are faster than those of normal BPs. be easily understood. If the reverse vesicles had a monolayer Stable big vesicles can be obtained within 1.0 106 simulastructure, the hydrophilic hyperbranched polymer in a HMC tion steps (Figure 6 g). We attribute this to the faster microshould be greatly deformed to locate both in the outside phase separation process of HMCs in reverse vesicles, which and inside shells of the vesicles, which is energetically unfavwill be discussed in the following section. orable. By contrast, less deformation is needed for each HMC to adopt a bilayer structure. 2. The Structure of Vesicle Membranes As mentioned above, BPs have been shown experimentally to possess a bilayer or a monolayer structure.[19] We also
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dynamics simulations. Both the self-assembly pathways and the dynamics of as-prepared vesicles, so-called branched polymersomes, have been disclosed in detail. The results indicate some differences in the self-assembly mechanism for branched polymersomes and conventional polymersomes from linear block copolymers. No “sphere-to-rod” and “rodto-membrane” transitions have been observed. By contrast, a direct “sphere-to-membrane” transition has been found. In addition, the molecular packing models and microphase separation behaviors of hyperbranched multiarm copolymers in normal and reverse branched polymersomes have also been studied. The results indicate that normal branched polymersomes can have either a bilayer or a monolayer structure depending on the hydrophilic fraction, while reverse branched polymersomes only possess a bilayer structure. These simulation results provide some details on the self-assembly of branched polymersomes, which not only support the experimental data but also give new insight into the self-assembly of hyperbranched multiarm copolymers.
Experimental Section Simulation Method and Details DPD Method DPD is a mesoscopic simulation technique introduced by Hoogerbrugge and Koelman in 1992.[28] A DPD bead represents a group of atoms or a volume of fluid that is large on the atomistic scale but still macroscopically small.[26a] The force experienced by bead i is composed of three *C
*D
parts: a conservative force F , a dissipative force F , and a random force *R
F . Each force is pairwise additive: *
Fi ¼
X *C *D *R *s F ij þ F ij þ F ij þ F ij
ð1Þ
j6¼i
The sum runs over all other beads within a certain cutoff radius Rc. The different parts of the forces are given by: * *C F ij ¼ aij wC rij eij
ð2Þ
* * * *D F ij ¼ gwD rij vij eij eij
ð3Þ
*R * * F ij ¼ swR r ij xij Dt1=2 eij
ð4Þ
* * * * * *
* * where r ij ¼ r i r j , rij ¼ r ij , eij ¼ r ij =rij , with r i and r j being the positions * * * * * of bead i and bead j, respectively; vij ¼ vi vj , with vi and vj being the velocities of bead i and bead j, respectively. aij is a constant which describes the maximum repulsion between interacting beads. g and s are the amplitudes of dissipative and random forces, respectively. wC, wD, and wR are three weight functions for the conservative, dissipative, and random forces, respectively. For the conservative force, we chose wCACHTUNGRE(rij) = 1rij/RC for rij < RC and wCACHTUNGRE(rij) = 0 for rij RC. wDACHTUNGRE(rij) and wRACHTUNGRE(rij) follow a certain relation according to the fluctuation-dissipation theorem,
Figure 6. DPD simulations on the self-assembly of reverse vesicles from HMCs in water at the initial state (a) and at the simulation stage of 2.5 104 steps (b), 5.0 104 steps (c), 1.5 105 steps (d), 3.0 105 steps (e), 4.0 105 steps (f), and 1.0 106 steps (g) in a line model. The hydrophilic hyperbranched cores are shown in grey and hydrophobic linear arms are shown in black. Water beads are not shown for clarity.
wD ðrÞ ¼ ½wR ðrÞ2 , s2 ¼ 2gkB T
Conclusions
ð5Þ
Here we chose a simple form of wD and wR following Groot and Warren,
In this paper, the vesicular self-assembly of amphiphilic hyperbranched multiarm copolymers in dilute aqueous solution has been studied systematically by dissipative particle
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D
R
2
(
w ðrÞ ¼ w ðrÞ ¼
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ð6Þ
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xij in Equation (4) is a random number with zero mean and unit variance, chosen independently for each interacting pair of beads at each time step Dt. A modified version of the velocity-Verlet algorithm is used here to integrate the equations of motion. For easy numerical handling, we have chosen the cutoff radius (Rc), the bead mass (m), and the temperature i.e., ffi RC = m = kBT = 1. As (kBT) as the units of the simulated system, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a consequence, the unit of time t is t ¼ RC m=kB T ¼ 1.
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The interaction parameter between the same type of bead aii equals 25 to correctly describe the compressibility of water, and 1 = 3 is the number density in our simulations. The spring force between connected polymer *S
beads is F ij ¼ Crij, and the spring constant C is set to be 4.0, which is enough to keep adjacent beads connected together along the polymer backbone.[26e] Simulation Details The DPD models of hyperbranched multiarm copolymers have a hyperbranched core and several linear arms. A denoting the hydrophobic core DPD bead, B denoting the hydrophilic arm DPD bead, and the solvent beads denoted by C are included explicitly in the simulations. The beads in the hyperbranched core include dendritic units that have three connections and linear units that have only two connections. The systems are constructed in a cubic box of size L3 with the side length L equal to 60 in periodic boundary conditions. The number density is kept at 1 = 3, and thus 6.48 105 DPD beads are considered in a simulation. The bead concentration, which is defined by the volume fraction of the hyperbranched multiarm copolymer beads (since all kinds of beads possess the same volume), is used to characterize the concentration of the hyperbranched multiarm copolymers and is set as 5 % throughout the simulations. The characteristics of the beads (either hydrophobic or hydrophilic) are determined by the value of the interaction parameter aij. The interaction parameter between the same type of beads, aii, is set as 25, to reflect the correct compressibility of water. Therefore in our simulations, aij-aii > 0 implies that i-type and j-type DPD beads “dislike” each other, while aijaii < 0 implies the contrary. A three-body potential is added on the consecutive triplets of the backbone beads to control the main chain rigidity, Uq = kqACHTUNGRE(1cosACHTUNGRE(qq0)), where kq is the bond angle potential constant, q is the bond angle between the two bonds connecting particles (i1, i) and (i, i + 1), and q0 = 0 is the equilibrium bond angle. In this simulation, we set kq = 4.0 and q = 1.91. A total of 2.0 106 time steps simulation with a step size of 0.02 was performed for each system considered in this study. 2.0 106 time steps were selected for the DPD simulations because all the systems studied here reach equilibrium under this condition. All DPD simulations were performed by using the HOOMD package on a NVIDIA Tesla C2050 GPU processor.[29]
Acknowledgements The authors thank the National Basic Research Program (2013CB834506), the National Natural Science Foundation of China (91127047), and China National Funds for Distinguished Young Scientists (21225420).
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Dissipative Particle Dynamics Simulation Study on Vesicles Self-Assembled from Amphiphilic Hyperbranched Multiarm Copolymers Yuling Wang,[a] Bin Li,[b] Haibao Jin,[a] Yongfeng Zhou,*[a] Zhongyuan Lu,*[b] and Deyue Yan[a]
Abstract: Hyperbranched multiarm copolymers (HMCs) have been shown to hold great potential as precursors in self-assembly, and many impressive supramolecular structures have been prepared through the self-assembly of HMCs in solution. However, theoretical studies on the corresponding selfassembly mechanism have been greatly lagging behind. Herein, we report the self-assembly of normal or reverse vesicles from amphiphilic HMCs by dissipative particle dynamics (DPD) simulation. The simulation disclosed both the self-assembly mechanisms and dy-
namics of vesicles. It indicates that the self-assembly of HMCs involves several steps, from randomly distributed unimolecular micelles to small spherical micelles, to membrane-like micelles, to finally small vesicles. The membranes are formed through the direct aggregation and lateral fusion of small micelles, and the bending and closing of Keywords: dissipative particle dynamics simulation · hyperbranched multiarm copolymersmicelles · self-assembly · vesicles
Introduction
Up to now, most of the polymeric vesicles are generated from the self-assembly of linear block copolymers, and are denoted as polymersomes.[6a, 8a] The structures as well as the self-assembly mechanisms of polymersomes have been widely studied both experimentally and theoretically by using computer simulations. The simulation work can be divided into atomistic scale simulations and mesoscopic scale simulations. The most widely used simulation techniques are molecular dynamics (MD), Monte Carlo (MC), Brownian dynamics (BD), dissipative particle dynamics (DPD), selfconsistent field theory (SCFT), and density functional theory (DFT). These simulation works are mainly focused on four parts: the first part is about the vesicle self-assembly from block copolymers[9] and dendrimers;[10] the second part is related to the mixtures between lipids, homopolymers, block copolymers, dendrimers, or nanoparticles;[11] the third part is about the fusion, fission, and rupture of vesicles, and the interaction between the vesicle and the membrane;[12] and the forth part is about the microphase separation behavior and shape transformations of vesicles.[13] These theoretical works have greatly broadened our knowledge on polymersomes.[14] Hyperbranched polymers (HBPs) composed of dendritic units, linear units, and terminal units are highly branched macromolecules with a three-dimensional dendritic architecture, and consequently possess special properties, such as a large population of terminal functional groups, lower solution or melt viscosity, and increased solubility.[15] Recently,
Self-assembly of amphiphilic block copolymers has proved to be an excellent and efficient way to construct all kinds of delicate supramolecular structures, and most of the reported studies concern the self-assembly of linear block copolymers such as diblock or triblock copolymers.[1] The self-assembly of amphiphilic block copolymers results in a wide range of aggregates in aqueous solution, including spherical micelles, rods, vesicles, toroids and so on.[1–5] Among them, the selfassembled vesicles with closed membranes have attracted great attention because of their unique hollow structure and potential applications in drug delivery, gene therapy, and as model systems of biomembranes.[6–8]
[a] Dr. Y. Wang, H. Jin, Prof. Y. Zhou, D. Yan School of Chemistry and Chemical Engineering State Key Laboratory of Metal Matrix Composites Shanghai Jiao Tong University 800 Dongchuan Road, Shanghai 200240 (China) E-mail: [email protected] [b] Dr. B. Li, Prof. Z. Lu Institute of Theoretical Chemistry State Key Laboratory of Theoretical and Computational Chemistry Jilin University Changchun 130023 (China) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/asia.201402146.
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the membranes give rise to small vesicles. Finally, large and steady vesicles are formed through the fusion of small vesicles. In addition, the bilayer or monolayer molecular packing modes as well as the mircrophase separation behaviors of HMCs in normal or reverse vesicles have also been studied. These simulation results explore details that cannot be observed in the experiments to a certain degree, and have extended the understanding of the vesicular selfassembly process of HMCs.
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as an extension of block copolymer self-assembly, HBPs have been shown to hold great potential as excellent precursors in self-assembly.[16] Many impressive supramolecular aggregates at all scales and dimensions, such as macroscopic tubes,[17] physical gels,[18] micro- or nanovesicles,[19] spherical micelles,[20] honeycomb films,[21] and large compound vesicles,[22] have been prepared through solution self-assembly, interfacial self-assembly, and hybrid self-assembly of amphiphilic HBPs. Generally, these amphiphilic HBPs are composed of a hydrophobic hyperbranched core and many hydrophilic linear arms, and are known as hyperbranched multiarm copolymers (HMCs). The term “branched polymersomes” (BPs) has been introduced for vesicles self-assembled from amphiphilic HMCs in order to discern them from conventional polymersomes.[19] Up to now, several advances have been made for BPs experimentally. Firstly, normal BPs self-assembled from a HMC with a hydrophobic hyperbranched core and many hydrophilic arms, or vice versa, so-called reverse BPs self-assembled from a HMC with a hydrophilic hyperbranched core and many hydrophobic arms have been obtained.[23] Secondly, BPs can have a bilayer or a monolayer structure depending on the hydrophilic fractions of HMCs, and they will change from bilayer to monolayer with the increase of hydrophilic fractions.[19] Thirdly, BPs are very flexible and can fuse with each other to increase in size.[24] However, basic issues for understanding these experimental phenomena, the self-assembly mechanism as well as the dynamics of the formation of BPs remain unclear. For example, the self-assembly pathway of BPs is unclear; it is not clear why spherical HBPs can microphase separate into a bilayer; and the structural differences between normal and reverse BPs are unclear. It is very difficult to solve all of these problems only by experiments and, accordingly, theoretical simulations are needed. Unfortunately, to our knowledge, no theoretical simulation work on BPs has been done up to now. Very recently, we used DPD simulation to study the micellization process of HMCs.[25] Herein, we report for the first time on DPD simulations of the solution self-assembly of HMCs into BPs. DPD has its own advantages of high computational speed, large integration time step, and covering a much longer time scale, and thus it is very useful for simulating complex soft matter systems.[26] In our simulations, the formation mechanism and dynamics of both
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normal and reverse BPs have been disclosed in detail. In addition, the microphase separation process of HMCs and the bilayer or monolayer molecular packing model in the normal and reverse BPs have also been revealed.
Results and Discussion In our simulations, a DPD model for HMCs was constructed (see Figure 1; details of the model are given in the Experimental Section). A typical vesicle-forming amphiphilic HMC, a so-called HBPO-star-PEO, is shown in Figure S1 in
Figure 1. Ball-and-stick model of a HMC containing 41 beads, in which the hydrophobic hyperbranched core is composed of grey beads (A beads) and the hydrophilic arms are composed of black beads (B beads).
the Supporting Information. It consists of a hydrophobic hyperbranched poly(3-ethyl-3-oxetanemethanol) (HBPO) core and many hydrophilic polyethylene oxide (PEO) arms. Taking HBPO-star-PEO as an example to explain the DPD model, one “A” bead (the grey bead) in the model signifies one repeat unit in the HBPO core, while one “B” bead (the black bead) denotes three repeat units in the PEO arms. One “C” bead refers to six water molecules, the solvent for the self-assembly process. For the simulation, no artificial manipulation on the vesicle formation was used. Accordingly, we started from randomly distributed HMCs in dilute solution and traced the steps of vesicle formation. 1. Vesicle Formation Pathway
Abstract in Chinese:
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There are three interaction parameters for HMCs. One is the repulsive parameter between the hydrophobic core (A beads) and the solvent (C beads), as indicated by aAC ; the second one is the repulsive parameter between the hydrophilic arm (B beads) and the solvent (C beads), as indicated by aBC ; the third one is the repulsive parameter between the hydrophobic core (A beads) and the hydrophilic arm (B beads), as indicated by aAB. To reduce the parameter space of this system, we fixed the interaction parameters as aAB = 70, aAC = 150, and aBC = 26. These parameters reflect the fact
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tion (Figure 2 a). The subsequent self-assembly process can be classified into four stages: at the first stage, randomly distributed HMCs aggregate into small micelles within a short time (Figure 2 b, within 1.0 104 simulation steps); at the second stage, the small micelles merge into membrane-like structures (Figure 2 c and 2 d) with a long simulation time until 3.0 105 simulation steps; at the third stage, the undulation of the membranes, which induces a bending of the membrane (Figure 2 e, Figure S2 in the Supporting Information), occurs at 5.0 105 simulation steps to finally form small vesicles by closing the curving membranes (at 7.0 105 simulation steps, Figure 2 f); at the fourth stage, stable vesicles are obtained through the fusion of smaller ones (Figure 2 g–j). The cross-sectional view of the particles shown in Figure 2 j illustrates that they are hollow vesicles with segregated hydrophobic cores and hydrophilic arms (Figure 3 a). Figure 3 b shows the density distribution from the center of mass to the outside of the vesicle across the vesicle membrane (arrow direction in Figure 3 a). The density distribution profile of arms (B beads) has two peaks, while that of cores (A beads) has only one peak, thus indicating that the vesicle has the typical “arm-core-arm” structural characteristic of normal vesicles. Moreover, the first peak of the arms is slightly higher than the Figure 2. Time series of morphologies of normal vesicles self-assembled from HMCs at the initial state (a), second peak, which means that 1.00 104 steps (b), 1.00 105 steps (c), 3.00 105 steps (d), 5.00 105 steps (e), 7.00 105 steps (f), 1.00 106 steps (g), 1.45 106 steps (h), 1.50 106 steps (i), and 2.00 106 steps (j) in a line model. The hydrophobic cores the density of the internal vesiare shown in grey and hydrophilic arms are shown in black. Water beads are not shown for clarity. (k) Plot of cle surface is slightly larger the conservative energy between the core beads and water, EAC, versus simulation time. than that of the external vesicle surface. The fusion of small vesicles into big vesicles widely occurs that, in each HMC, the hyperbranched core is hydrophobic at the fourth stage of the self-assembly process. For instance, and the arms are hydrophilic, and that the core and arms two small vesicles in Figure 2 h (indicated by black circles) are incompatible.[26d] merge into one vesicle in Figure 2 i. For further information, The self-assembly process of HMCs in dilute solution is ila complete fusion process is shown in the Supporting Inforlustrated in Figure 2. HMCs are randomly distributed in mation (Figure S3). water as unimolecular micelles at the initial setup configura-
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Figure 3. (a) Cross-sectional view of the vesicle shown in a line mode rather than a ball-and-stick model for clarity and better resolution. Water beads are omitted for clarity. (b) Density distribution of segments A and B across the membrane.
such as unimolecular micelle aggregates (UMAs).[25] Evidently, such a lateral fusion process is energetically favorable. The self-assembly mechanism of BPs from HMCs is further illustrated in Figure 5 a. The HMCs first exist as unimolecular micelles in the solvent and then aggregate into small micelles with a segregated hydrophobic core and hydrophilic arms at stage 1 through microphase separation. Subsequently, at stage 2, the small micelles
We also studied the time evolution of an energy index, EAC, to characterize the self-assembly process. EAC is defined as the conservative energy between the hyperbranched core (A) of HMCs and the solvent (C) per particle:[26c] EAC ¼
X 1 beads
2 r =Nbeads aAC 1 AC RC 2
As shown in Figure 2 k, EAC decreased sharply and quickly when HMCs were changed from unimolecular micelles to small spherical micelles, which exist at the first stage of the self-assembly process (stage 1). This indicates that the selfassembly process minimizes the interaction energy between the hydrophobic core and the solvents. At stage 2, EAC decreased slowly and then reached a dynamic equilibrium due to the formation of membranes. At stage 3, EAC again decreased (see the magnified inset in Figure 2 k), which is attributed to the bending and closing of membranes to form small vesicles. At stage 4, a new equilibrium of EAC was reached and the small vesicles evolved into big ones through fusion.
Figure 4. The evolution from spherical micelles to sheet-like micelles at the simulation stage of 1.70 104 steps (a), 1.75 104 steps (b), 1.80 104 steps (c), 1.85 104 steps (d), 2.05 104 steps (e), 2.10 104 steps (f), and 2.15 104 steps (g). The morphologies self-assembled from HMCs are shown in a line mode. The hyperbranched hydrophobic cores (A) are shown in grey and the hydrophilic linear arms (B) are shown in black. (h) Scheme for the lateral fusion of a small micelle with a membrane.
At stage 2, the small spherical micelles turned into membranes; however, it is not easy to understand the pathway leading to this change just from looking at Figure 2 b–2 d. Therefore, three particles in sequential fusion (Figure 4 a–g) were taken out from the simulation snapshots to further display the pathway. At the beginning, a sheet-like structure was observed with two micelles around (Figure 4 a). Then, one of the small micelles merged with the sheet through lateral fusion when it was close enough (Figure 4 b–4 d). Subsequently, the residual small micelle also merged with the sheet through lateral fusion (Figure 4 e–4 g). In this manner, a bigger sheet was obtained. According to these results, one can conclude that the membrane is formed through sequential lateral aggregation and fusion of small micelles into small sheets (Figure 4 h). To our surprise, only lateral fusion occurred when the small micelles merged into sheets, which guaranteed the formation of two-dimensional membranes rather than three-dimensional large multimolecular micelles
further aggregate into membranes through continuous lateral aggregation and fusion, as shown in Figure 4 h. At stage 3, membrane bending and closing happens, and small vesicles are formed. At stage 4, small vesicles merge into big ones through sequential membrane fusion. In the self-assembly of polymersomes from linear block copolymers, the widely accepted mechanism is as follows: amphiphilic block copolymers first aggregate into small spherical micelles, which then grow into rod-like micelles; subsequently, the rods transform into sheet- or membranelike structures, and finally vesicles are formed through the bending and closing of membranes.[27, 14d] This mechanism is also suitable to the formation of lipid vesicles (liposomes). Thus, when comparing the self-assembly mechanism of conventional polymersomes to that of BPs, it can be seen that they are similar despite the fact that in the self-assembly of BPs no rod-like micelles are formed and the membranes are
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wanted to study the structure of BPs through simulation by exploring the packing model as well as the microphase separation of HMCs in the vesicle membranes. As shown in Figure 5 b,c, there are two molecular packing modes in normal BPs. In order to clearly discern the molecular packing model in the cross-sectional view, we arbitrarily labeled HMCs with different colors. When HMCs have a small hydrophilic fraction, that is, the copolymer has a relatively large hyperbranched core but short hydrophilic arms, evidently a bilayer structure can be observed (Figure 5 b). In this packing model, each HMC undergoes a full “A–B”-type microphase separaFigure 5. (a) Self-assembly mechanism of normal vesicles from HMCs. (b–d) Cross-sectional views of a normal tion, in which “A” designates vesicle (b, c) and a reverse vesicle (d) formed by hyperbranched multiarm copolymers. The magnified particles the hyperbranched core and in panels b, c, and d represent the bilayer structure and the monolayer structure of normal vesicles, and the bilayer structure of reverse vesicles, respectively. Hyperbranched core: white, blue, and green beads; linear “B” denotes the hydrophilic arms: pink, red, and purple beads. Water beads are omitted for clarity. arms. Two “A–B”-type HMCs are packed together in a headto-tail manner to form the bilayer. When HMCs have directly formed through the aggregation and fusion of small a large hydrophilic fraction, that is, the copolymer has a relaspherical micelles. However, in the self-assembly of conventively small hyperbranched core but long hydrophilic arms, tional polymersomes, the “sphere-to-rod” and “rod-to-mema monolayer structure can be evidently observed (Figbrane” transitions are necessary pathways. ure 5 c). In this packing model, each HMC undergoes an Besides on normal vesicles, we also performed DPD simu“A–B–A”-type microphase separation to form the monolaylations on reverse vesicles self-assembled from HMCs with er. Such a hydrophilic fraction-dependent bilayer and monohydrophilic hyperbranched cores and many hydrophobic layer packing model agrees well with the experimental linear arms in water. For the simulation, the same molecular data.[19a] The bilayer and monolayer structures of normal model as that shown in Figure 1 was used for each HMC while the parameters were changed to aAB = 70, aAC = 26, vesicles from HMCs are also schematically shown in Figure 5 a. and aBC = 150. According to these parameters, in each HMC, Next, we also studied the structure of reverse BPs through the hyperbranched core (A beads) is hydrophilic and the simulations. As shown in Figure 5 d, reverse BPs have a biarms (B beads) are hydrophobic, and the core and arms are layer structure. Most interestingly, only the bilayer structure incompatible. is possible with a continuous increase in the hydrophilic Based on the simulation results (Figure 6), we conclude fraction, and no monolayer structure can be observed. In that the formation pathway of reverse vesicles (Figure S4 in other words, HMCs can only undergo an “A–B”-type microthe Supporting Information) is the same as that of normal phase separation, and such a microphase separation is indevesicles, which consists of the aforementioned four stages. pendent of the hydrophilic fraction of the polymers. Thus, Membranes are also formed by aggregation and lateral reverse BPs are different from normal ones with regard to fusion of small micelles. However, the dynamics of the forthe membrane structure. The reason for this difference can mation of reverse BPs are faster than those of normal BPs. be easily understood. If the reverse vesicles had a monolayer Stable big vesicles can be obtained within 1.0 106 simulastructure, the hydrophilic hyperbranched polymer in a HMC tion steps (Figure 6 g). We attribute this to the faster microshould be greatly deformed to locate both in the outside phase separation process of HMCs in reverse vesicles, which and inside shells of the vesicles, which is energetically unfavwill be discussed in the following section. orable. By contrast, less deformation is needed for each HMC to adopt a bilayer structure. 2. The Structure of Vesicle Membranes As mentioned above, BPs have been shown experimentally to possess a bilayer or a monolayer structure.[19] We also
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dynamics simulations. Both the self-assembly pathways and the dynamics of as-prepared vesicles, so-called branched polymersomes, have been disclosed in detail. The results indicate some differences in the self-assembly mechanism for branched polymersomes and conventional polymersomes from linear block copolymers. No “sphere-to-rod” and “rodto-membrane” transitions have been observed. By contrast, a direct “sphere-to-membrane” transition has been found. In addition, the molecular packing models and microphase separation behaviors of hyperbranched multiarm copolymers in normal and reverse branched polymersomes have also been studied. The results indicate that normal branched polymersomes can have either a bilayer or a monolayer structure depending on the hydrophilic fraction, while reverse branched polymersomes only possess a bilayer structure. These simulation results provide some details on the self-assembly of branched polymersomes, which not only support the experimental data but also give new insight into the self-assembly of hyperbranched multiarm copolymers.
Experimental Section Simulation Method and Details DPD Method DPD is a mesoscopic simulation technique introduced by Hoogerbrugge and Koelman in 1992.[28] A DPD bead represents a group of atoms or a volume of fluid that is large on the atomistic scale but still macroscopically small.[26a] The force experienced by bead i is composed of three *C
*D
parts: a conservative force F , a dissipative force F , and a random force *R
F . Each force is pairwise additive: *
Fi ¼
X *C *D *R *s F ij þ F ij þ F ij þ F ij
ð1Þ
j6¼i
The sum runs over all other beads within a certain cutoff radius Rc. The different parts of the forces are given by: * *C F ij ¼ aij wC rij eij
ð2Þ
* * * *D F ij ¼ gwD rij vij eij eij
ð3Þ
*R * * F ij ¼ swR r ij xij Dt1=2 eij
ð4Þ
* * * * * *
* * where r ij ¼ r i r j , rij ¼ r ij , eij ¼ r ij =rij , with r i and r j being the positions * * * * * of bead i and bead j, respectively; vij ¼ vi vj , with vi and vj being the velocities of bead i and bead j, respectively. aij is a constant which describes the maximum repulsion between interacting beads. g and s are the amplitudes of dissipative and random forces, respectively. wC, wD, and wR are three weight functions for the conservative, dissipative, and random forces, respectively. For the conservative force, we chose wCACHTUNGRE(rij) = 1rij/RC for rij < RC and wCACHTUNGRE(rij) = 0 for rij RC. wDACHTUNGRE(rij) and wRACHTUNGRE(rij) follow a certain relation according to the fluctuation-dissipation theorem,
Figure 6. DPD simulations on the self-assembly of reverse vesicles from HMCs in water at the initial state (a) and at the simulation stage of 2.5 104 steps (b), 5.0 104 steps (c), 1.5 105 steps (d), 3.0 105 steps (e), 4.0 105 steps (f), and 1.0 106 steps (g) in a line model. The hydrophilic hyperbranched cores are shown in grey and hydrophobic linear arms are shown in black. Water beads are not shown for clarity.
wD ðrÞ ¼ ½wR ðrÞ2 , s2 ¼ 2gkB T
Conclusions
ð5Þ
Here we chose a simple form of wD and wR following Groot and Warren,
In this paper, the vesicular self-assembly of amphiphilic hyperbranched multiarm copolymers in dilute aqueous solution has been studied systematically by dissipative particle
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D
R
2
(
w ðrÞ ¼ w ðrÞ ¼
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ð6Þ
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xij in Equation (4) is a random number with zero mean and unit variance, chosen independently for each interacting pair of beads at each time step Dt. A modified version of the velocity-Verlet algorithm is used here to integrate the equations of motion. For easy numerical handling, we have chosen the cutoff radius (Rc), the bead mass (m), and the temperature i.e., ffi RC = m = kBT = 1. As (kBT) as the units of the simulated system, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a consequence, the unit of time t is t ¼ RC m=kB T ¼ 1.
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The interaction parameter between the same type of bead aii equals 25 to correctly describe the compressibility of water, and 1 = 3 is the number density in our simulations. The spring force between connected polymer *S
beads is F ij ¼ Crij, and the spring constant C is set to be 4.0, which is enough to keep adjacent beads connected together along the polymer backbone.[26e] Simulation Details The DPD models of hyperbranched multiarm copolymers have a hyperbranched core and several linear arms. A denoting the hydrophobic core DPD bead, B denoting the hydrophilic arm DPD bead, and the solvent beads denoted by C are included explicitly in the simulations. The beads in the hyperbranched core include dendritic units that have three connections and linear units that have only two connections. The systems are constructed in a cubic box of size L3 with the side length L equal to 60 in periodic boundary conditions. The number density is kept at 1 = 3, and thus 6.48 105 DPD beads are considered in a simulation. The bead concentration, which is defined by the volume fraction of the hyperbranched multiarm copolymer beads (since all kinds of beads possess the same volume), is used to characterize the concentration of the hyperbranched multiarm copolymers and is set as 5 % throughout the simulations. The characteristics of the beads (either hydrophobic or hydrophilic) are determined by the value of the interaction parameter aij. The interaction parameter between the same type of beads, aii, is set as 25, to reflect the correct compressibility of water. Therefore in our simulations, aij-aii > 0 implies that i-type and j-type DPD beads “dislike” each other, while aijaii < 0 implies the contrary. A three-body potential is added on the consecutive triplets of the backbone beads to control the main chain rigidity, Uq = kqACHTUNGRE(1cosACHTUNGRE(qq0)), where kq is the bond angle potential constant, q is the bond angle between the two bonds connecting particles (i1, i) and (i, i + 1), and q0 = 0 is the equilibrium bond angle. In this simulation, we set kq = 4.0 and q = 1.91. A total of 2.0 106 time steps simulation with a step size of 0.02 was performed for each system considered in this study. 2.0 106 time steps were selected for the DPD simulations because all the systems studied here reach equilibrium under this condition. All DPD simulations were performed by using the HOOMD package on a NVIDIA Tesla C2050 GPU processor.[29]
Acknowledgements The authors thank the National Basic Research Program (2013CB834506), the National Natural Science Foundation of China (91127047), and China National Funds for Distinguished Young Scientists (21225420).
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