CB Diblock Copolymer Mixture

Jul 16, 2014 - Christina L. Ting , Brad H. Jones , Amalie L. Frischknecht , Erik D. Spoerke , Mark J. Stevens. Soft Matter 2015 11 (34), 6800-6807 ...
1 downloads 0 Views 4MB Size
Download PDF
Article pubs.acs.org/Langmuir

Asymmetric Vesicle Constructed by AB/CB Diblock Copolymer Mixture and Its Behavior: A Monte Carlo Study Jie Cui, Yuanyuan Han,* and Wei Jiang* State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China S Supporting Information *

ABSTRACT: Asymmetric vesicles constructed from AB/CB diblock copolymer mixture in a selective solvent for A and C blocks are studied using Monte Carlo simulation. The effects of the mixed ratio of the two diblock copolymers, the solution pH, and the hydrophilic chain length on the distributions of hydrophilic blocks on the surfaces of asymmetric vesicles are studied systematically. The simulation results show that asymmetric vesicle, in which the inner and outer surfaces are constructed from different hydrophilic blocks, can be obtained from AB/CB diblock copolymer mixture. The formation of ABC or CBA three-layer asymmetric vesicle depends on the composition of the mixture, the chain length of hydrophilic block, and the solution pH. The hydrophilic block with the same charge (induced by the solution pH), or longer chain length, or lower content in the mixture is more likely to distribute on the outer surface of the vesicle. Moreover, the transition from ABC to CBA three-layer asymmetric vesicle in which blocks C are charged can occur by adjusting the composition of the mixture. On the other hand, the investigations of the interfacial energy density of asymmetric vesicles elucidate the distribution regularity of hydrophilic blocks. When the hydrophilic chain lengths are equal, the difference between the outer and inner interfacial energies is the main factor that determines the asymmetric vesicle structures; that is, the distributions of different hydrophilic blocks on asymmetric vesicles always tend to gain the largest difference between the outer and inner interfacial energies. However, when the hydrophilic chain lengths are different, the chain conformational entropy becomes the main driving force for determining the distribution of hydrophilic blocks on asymmetric vesicles. the inner surface of the asymmetric vesicles. Liu et al.10 have studied the aggregate morphologies of the amphiphilic triblock copolymer poly(acrylic acid)-b-polystyrene-b-poly(4-vinylpyridine) (PAA26−PS890−P4VP40) as a function of pH in DMF/ THF/H2O mixtures. They found that the triblock copolymers can self-assemble into asymmetric vesicles when the pH is 1 or 14. Vesicles obtained at pH 1 contain P4VP chains on the outside and PAA chains on the inside, while those obtained at pH 14 contain PAA chains outside and P4VP chains inside. They attributed this phenomenon to the difference in repulsive interactions within the PAA or P4VP corona under different pH conditions. In general, ABC triblock copolymers8−15 or even more sophisticated block copolymers such as ABCA tetrablock copolymers16−18 are used to prepare asymmetric vesicles. However, the synthesis of well-defined multiblock copolymer is relatively difficult and expensive. As compared to synthesizing multiblock copolymers, blending block copolymers provides a more convenient and economical solution for the preparation

I. INTRODUCTION Asymmetric vesicles are vesicular aggregates formed by amphiphilic block copolymers with different corona and/or core-forming blocks located on the inner and outer hydrophilic and/or hydrophobic leaflets, respectively. Much research1−7 indicates that asymmetric vesicles have distinctive advantages in some application areas, especially in biomedical science. Meier’s group1,8 has pointed out that many potential technical applications of reconstitutions of cell membranes inserted with proteins depend on the correct orientation of the protein, and the correct orientation of the inserted protein further depends on the asymmetric property of the vesicle membrane. Therefore, the investigations of the membrane structure of asymmetric vesicle have attracted a lot of attention in recent years. People found that the hydrophilic chain length and the solution pH may affect the membrane structures of asymmetric vesicles. Njikang et al.9 have studied poly(tert-butyl acrylate)-bpoly(2-cinnamoyloxyethyl methacrylate)-b-poly(glyceryl monomethacrylate) (PtBA107−PCEMA193−PGMA115) triblock copolymer micelles in solution. They observed various morphologies including asymmetric vesicles. In their study, the longer hydrophilic chains (PGMA) always located at the outer surface, whereas the shorter PtBA chains always located at © 2014 American Chemical Society

Received: April 30, 2014 Revised: July 15, 2014 Published: July 16, 2014 9219

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

the neighbor is a solvent molecule, exchange move is attempted. If the exchange does not violate the bond length restriction and retains no bond crossing, the exchange is allowed. This process constitutes a single movement. If the exchange would break two chain connections, it is not allowed. If the exchange creates a single break in the chain, the solvent molecule will continue to exchange with subsequent monomers along the chain until reconnection of a bond. The acceptance or rejection of the attempted move is further governed by the Metropolis importance sampling rule:28 if the energy change ΔE is negative, the exchange is accepted. Otherwise, the exchange is accepted with a probability of p = exp[−ΔE/(kBT)], where ΔE = ∑ijΔNijεij is the energy change caused by the attempted move; ΔNij is the number difference of the nearest neighbor pairs between components i and j before and after the movement, where i, j = A, B, C, and S (solvent), respectively; εij is the interaction energy between i and j; and kB is the Boltzmann constant and assumed to be 1 in the whole simulation. The parameter T is the reduced temperature. To obtain equilibrium structures, the annealing method was implemented. The inverse temperature 1/T changed gradually from 0 (representing the athermal state of T = ∞) to a given positive value 0.075 (representing a lower temperature). The annealing process was achieved by 300 time steps. In other words, the annealing rate (i.e., the increasing rate of 1/T) was set as 0.00025 per time step. In each time step, 7000 Monte Carlo Steps (MCS) were performed and were chosen as the time unit in this work. In one MCS, on the average, each monomer has attempted one exchange move. After 300 time steps, keeping 1/T = 0.075 unchanged, another 200 time steps were carried out to confirm that the final structures are in equilibrium state. In this work, two kinds of AB/CB diblock copolymer mixtures are considered. One is A3B4/C3B4 in which the hydrophilic chain lengths of blocks A and C are equal, and the other is A2B4/C3B4 in which the hydrophilic chain length of block A is shorter than that of C (the subscripts represent the monomer number of corresponding blocks). The volume fraction of the diblock copolymers in the solution is set as a constant, that is, cAB + cCB = 7%. The volume fraction of AB diblock copolymer ( fAB) in the diblock copolymer mixture is varied from 10% to 50%, and fAB + f CB = 100%. In the selective solvent, blocks A and C are hydrophilic and block B is hydrophobic. Therefore, the interaction energies εAS and εCS are set as −1, while εBS is set as positive, corresponding to the amphiphilic nature of diblock copolymers. The interaction energies are εAB = 1, εBC = 1, and εAC = 3 to mimic the incompatibilities among the A, B, and C blocks. All other selfinteractions between the same components (i.e., εAA, εBB, εCC, and εSS) are set as zero unless specified otherwise. The value of εBS is crucial for the diblock copolymer mixture to self-assemble into vesicle in the selective solvent. It is found that the A3B4 and A2B4 diblock copolymers can form perfect vesicles when εBS = 7 and 5, respectively. Thus, to obtain fine and stable vesicles, εBS is set as 7 for A3B4/C3B4 diblock copolymer mixture, while it is set as εBS = fA2B4 × 5 + f C3B4 × 7 for A2B4/C3B4 diblock copolymer mixture.

of asymmetric vesicle. One can simply blend AB/CB diblock copolymers together (in which A and C blocks are hydrophilic and B blocks are hydrophobic) to form ABC (CBA) three-layer asymmetric vesicles. Luo and Eisenberg19 have investigated the vesicles formed by a diblock copolymer mixture of PS300− PAA11/PS310−P4VP33. Experimental results show that the P4VP chains tend to locate at the outside of the vesicles, while the inside corona of the vesicles consisted of PAA chains. They attributed this phenomenon to the fact that the P4VP chains are much longer than the PAA chains, and at the same time the P4VP chains are positively charged, which results in a repulsive interaction in solution. Zhuang et al.20 have simulated the self-assembly behavior of AB/CB diblock copolymer mixtures in selective solvent for A and C blocks using realspace self-consistent field theory (SCFT). Their simulation results also indicate that when the hydrophilic chain lengths of blocks A and C are different, the longer chains tend to distribute on the outer surface of the vesicle. Recently, we have investigated the asymmetric vesicles formed by the AB/BC diblock copolymer mixture based on hydrogen bonding using Monte Carlo simulation. The AB and BC diblock copolymers can be connected and then form “pseudo” ABC triblock copolymers via the hydrogen bonding. The simulation results indicate that both the vesicle structures and the vesicle formation pathway of such “pseudo” ABC triblock copolymers highly depend on the hydrogen bonding.21 As compared to the block chain length, the mixed ratio of AB/CB diblock copolymer mixtures and the solution pH can be more easily controlled in experiment. However, it remains unclear just how the mixed ratio and the pH of solution affect the membrane structure of asymmetric vesicles. On the other hand, in our previous work,21 the effect of the hydrogen bonding on the asymmetric vesicle structures and their formation were elucidated. However, which hydrophilic chains (A or C) can distribute on the outer (or inner) surface of the vesicle and the factors determining the distribution of hydrophilic blocks (such as the mixed ratio of the two diblock copolymers, the solution pH, and the hydrophilic chain length) were not investigated. Therefore, in this study, we employed Monte Carlo simulation to investigate the asymmetric vesicles formed by AB/CB diblock copolymer mixture in solvents selective for corona-forming blocks A and C. The purpose is to give an easy way to control the distribution of hydrophilic blocks on asymmetric vesicles membranes and an insight into the competing effect among the block chain length, the mixed ratio, and the solution pH.

III. RESULTS AND DISCUSSION In the current study, we mainly focus on the effects of the mixed ratio of the two diblock copolymers, the solution pH, and the chain length of the hydrophilic blocks on the membrane structures of the asymmetric vesicles formed by AB/CB diblock copolymer mixtures. The asymmetric vesicles can be obtained from homogeneous initial state through the annealing method. The details including the interaction parameter settings were introduced in section II. A. Effect of the Mixed Ratio of the Two Diblock Copolymers. To investigate the effect of the mixed ratio of the two diblock copolymers on vesicle membrane structure, we focus on the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture in this section. The volume fraction of A3B4 in the mixture (fA3B4) is varied from 10% to 50%. First, vesicles with the mixed ratio of fA3B4 = 50% (i.e., equal content for the two diblock copolymers) are studied. Figure 1

II. MODEL AND METHOD The lattice Monte Carlo simulation method is used in this study. The system is embedded in a simple cubic lattice of volume V = L × L × L with L = 50. Periodic boundary conditions are imposed in all three directions. The system is filled with polymers and solvents. Each monomer or solvent molecule occupies one lattice site, and they are self- and mutually avoiding, which insures that one monomer or solvent molecule occupies only one lattice site. The single-site bond fluctuation model proposed by Carmesin and Kremer22 and by Larson23,24 was used in this study. The permitted bond length is 1 and √2; thus, each lattice site has 18 nearest neighbor sites in a threedimensional space. The evolution of the chain configuration is achieved through the motions of monomer. Each step of the motion is generated through a microrelaxation model, which has proven to be highly efficient in relaxing local chain conformation on the lattice.25−27 The microrelaxation mode is defined as follows: A monomer is randomly chosen to exchange with one of its 18 nearest neighbors. If 9220

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

Figure 1. Possible membrane structures of the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture when fA3B4 = 50%. Parts (b) and (d) are the cross sections corresponding to (a) and (c), respectively. Parts (e) and (f) are the variations of densities of components A and C with r in (a) and (c), respectively. (r is the radii around the mass center of the vesicle.)

shows two kinds of asymmetric vesicle structures obtained from different initial states. The blocks A, B, and C are drawn and represented by blue, red, and green, respectively. From the snapshots of the vesicle shown in Figure 1a (or Figure 1c) and the corresponding cross sections shown in Figure 1b (or Figure 1d), we can see that the inner surface of the vesicle is covered almost completely by block A (or block C), whereas the outer surface is covered by both blocks A and C. The vesicle membrane has different inner and outer hydrophilic surfaces. This asymmetric membrane structure can be further identified by the density distribution of blocks A and C along the radii of the vesicles. The radial density distributions of blocks A and C over a spherical shell within r − 1 to r (r is the radii around the mass center of the vesicle) are, respectively, calculated and shown in Figure 1e,f. Taking Figure 1e as an example, we can see that the densities of blocks A and C are zero at the mass center of the vesicle. Two peaks for the density distribution curve of block A correspond to the densities of block A at the inner and outer surfaces of the vesicle shown in Figure 1a, respectively. This means that A segments locate on both the inner and the outer surfaces of the vesicle. However, only one peak corresponding to the density of block C at the outer surface of the vesicle can be seen on the density distribution curve of block C, meaning that C segments only locate on the outer surface of the vesicle. Figure 1e further indicates that the inner surface of the vesicle shown in Figure 1a is almost completely covered by A segments, while the outer surface is covered by both A and C segments. In addition, the simulation result shows that whether the inner surface of vesicles is covered by A (Figure 1b) or C (Figure 1d) segments depends on the initial state of the system. We randomly selected more than 10 initial states and found that the possibility for forming asymmetric vesicles with either A or C segments locating on the inner surface is equal. This is because all characteristics (including chain length, hydrophilicity, and interactions with other components) of blocks A and C are identical. Subsequently, we studied the cases in which the contents of the two diblock copolymers are not equal. Figure 2 shows the asymmetric vesicle structures formed by the diblock copolymer mixture when the volume fraction of A3B4 in the mixture (fA3B4) decreases from 40% to 10%. The snapshots of vesicle outer surface (Figure 2a−d) and vesicle cross sections (Figure 2a′−d′) clearly show that A segments always locate on the outer surface of vesicles and can barely be observed in the inner

Figure 2. Membrane structures of the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture with different fA3B4. Parts (a′)− (d′) are the cross sections corresponding to (a)−(d), respectively.

surfaces when fA3B4 is decreased from 40% to 10%. A decrease in fA3B4 means that block A becomes the minor component as compared to block C in the mixture. Figure 2 indicates that the diblock copolymer with lower content tends to locate on the outer surface of vesicles. To deeply understand the phenomenon shown in Figure 2, the energy densities ρE(r) over a spherical shell within r − 1 to r (r is the radii around the mass center of the vesicle) are calculated. The definition of ρE(r) is ρE (r ) =

∑ ij

Nij(r )εij kBT

/∑ ni(r ) i

(1)

where i, j = A, B, C, and S (solvent); r is the radii around the mass center of the vesicle; εij is the interaction energy introduced in section II; Nij(r) is the contact number between different species; and ni(r) is the number of monomers (or solvents) in the spherical shell within r − 1 to r. Figure 3 shows the variations of ρE(r) with r when fA3B4 = 40% and 10% (the red and green curves), respectively. It is seen that there are two peaks on each curve. The peak positions are r ≈ 7 and r ≈ 11, respectively. To further determine the peak positions in vesicle membrane, variations of densities of hydrophilic blocks (black line) and hydrophobic blocks (gray line) with r are also given in Figure 3. Two intersections of the black and gray curves are observed in Figure 3. The positions of the two intersections correspond, respectively, to the positions of the inner and outer hydrophobic−hydrophilic interfaces of the vesicle and are almost the same as the positions of the peaks 9221

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

Figure 3. Variations of the densities of energy and components A+C and B with r in the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture when fA3B4 = 10% and 40%, respectively. (r is the radii around the mass center of the vesicle.)

Figure 4. Variations of the energy densities with r in the artificially well-layered asymmetric vesicle (a) and the asymmetric vesicles spontaneously formed by A3B4/C3B4 diblock copolymer mixture with fA3B4 = 25% (b), respectively. (r is the radii around the mass center of the vesicle.)

on the curves of ρE(r), indicating that the two peaks on the curves of ρE(r) correspond to the inner and outer interfacial energy densities, respectively. The peak values in the curves of ρE(r) show that the outer interfacial energy density (r ≈ 11) is higher than the inner interfacial energy density (r ≈ 7) in both cases ( fA3B4 = 40% and 10%). Luo and Eisenberg29 once proposed a vesicle stability mechanism when they investigated vesicles formed by the mixture of PS−PAA with different PAA chain lengths. They think that if the repulsion outside the vesicle is stronger than that inside the vesicle, the curvature of vesicle will be maintained in a thermodynamically stable manner. This stability mechanism can explain our simulation results of why the minor component tends to distribute on the outer surface of the vesicle. Because the distribution of minor component A on the outer surface of the vesicle increases the contact number between A and C blocks, herein it increases the repulsions outside the vesicle. This is a benefit for vesicle stabilization. An interesting phenomenon can be observed in the simulations. Because blocks A and C are incompatible, why did not we find well-layered vesicles with all blocks A (lower content) locating on the inner surface and all blocks C (higher content) locating on the outer surface of the vesicle even if the inner surface area is much smaller than the outer surface area? This distribution can decrease the system energy due to the complete phase separation between incompatible A and C blocks. However, we never find such kind of vesicles. Does this mean that the well-layered asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture cannot exist in a thermodynamically stable manner? To answer this question, an extra test is done to investigate whether the perfect well-layered asymmetric vesicle structure in which the hydrophilic blocks with lower content locate on the inner surface while the hydrophilic blocks with higher content locate on the outer surface of the vesicle can exist stably. First, a perfect asymmetric vesicle is artificially made as follows: a symmetric vesicle is obtained by the self-assembly of pure C3B4 diblock copolymer, then the blocks C at the inner surface of the vesicle are artificially changed to be blocks A. Thus, a welllayered ABC (from inside to outside) three-layer asymmetric vesicle is formed (Figure 4a). It is found that fA3B4 ≈ 25% in this artificial asymmetric vesicle. We take this artificially made asymmetric vesicle as the initial state and run the system for a

very long time. The simulation result shows that the vesicle structure is almost unchanged (Figure S1 in the Supporting Information). This indicates that this kind of well-layered structure is thermodynamically stable. However, it can not be spontaneously formed by the self-assembly of diblock copolymer mixture with similar fA3B4 from a homogeneous state; that is, the diblock copolymer mixture with fA3B4 = 25% can only form asymmetric vesicle with A segments locating on the outer surface of the vesicle (Figure 4b), and this vesicle structure was further proved to be stable (Figures S3−5 in the Supporting Information). From the curves of ρE(r) for these two asymmetric vesicles shown in Figure 4, we can see that, although the system energy for the artificial vesicle (Figure 4a) is lower than that for the spontaneously formed vesicle (Figure 4b), the difference between the outer and inner interfacial energy densities for the spontaneously formed vesicle is much larger than that for the artificial vesicle. This indicates that the larger difference of the interfacial energy is more favorable for the stabilization of the vesicle membrane structure. Therefore, the well-layered asymmetric vesicle can not be obtained by solely changing the mixed ratio of the mixture. From the above simulation results, it can be found that the effect of interactive enthalpy between A and C blocks determines the distribution of blocks A and C on the vesicle membrane formed by A3B4/C3B4 diblock copolymer mixture, because the larger difference between the outer and inner interfacial energy densities originates from the interactive enthalpy between A and C blocks. B. Effect of the Solution pH. In this section, the effect of the solution pH on vesicle membrane structures formed by the A3B4/C3B4 diblock copolymer mixture is investigated. According to the experimental results,10,19 the P4VP (or PAA) blocks tend to be protonated (or ionized) in the solution with lower (or higher) pH values, which results in the repulsions among the segments of the P4VP (or PAA) blocks. Taking P4VP as an example, the P4VP blocks will be protonated when pH is 3. The degree of protonation of P4VP will increase with decreasing pH value,19 which primarily results in the increase of repulsions among the P4VP segments. To simulate the repulsions among the protonated P4VP segments, we employed an approximate method to tackle the repulsions stemming from the protonation of blocks. The repulsive interaction energy between blocks C (εCC) is introduced in this 9222

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

section. The cutoff radius for calculating the repulsive interaction energy between the protonated segments was chosen to be √3, and the interaction strength between protonated segments was set to be independent of the distance. This model can describe the main feature of the repulsive interactions between protonated blocks to some extent, and at the same time it is with high efficiency. As for the association between the solution pH and the interaction, we assume that the repulsive interaction between protonated segments increases with the protonated degree; that is, higher repulsive interaction refers to higher protonated degree. In this work, εCC was changed from 0.1 (low degree of protonation) to 0.5 (high degree of protonation) to investigate the effect of solution pH on the distributions of hydrophilic blocks A and C on the surfaces of asymmetric vesicles. In addition, on the basis of our simulations, εCC can not be larger than 0.5 to ensure the formation of vesicles. Figure 5 displays the asymmetric vesicle structures formed by A3B4/C3B4 diblock copolymer mixture with fA3B4 = 50% when

Figure 6. Membrane structures of the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture (blocks C are charged, εCC = 0.5) with different fA3B4. Parts (a′)−(d′) are the cross sections corresponding to (a)−(d), respectively.

and the solution pH on the formation of the vesicle membrane structure. The energy densities for several typical fA3B4 are given in Figure 7 to better understand the phenomenon observed in Figures 5 and 6. Figure 7a is the result for fA3B4 = 50%. From the peak values, we can see that the outer interfacial energy density is higher than the inner interfacial energy density. The higher outer interfacial energy mainly results from the repulsions between the charged blocks C located on the outer surface of the vesicle. As discussed in section III.A, the higher outer interfacial energy is favorable for the stabilization of vesicle structure, which explains why the charged blocks always prefer to locate on the outer surface of the vesicle in the case of fA3B4 = 50% (Figure 5). When fA3B4 is decreased to 48% (Figure 7b), the inner interfacial energy density remains almost unchanged as compared to that in the case of fA3B4 = 50% due to the inner surface being occupied by the same component, while the outer interfacial energy density decreases slightly as compared to the case of fA3B4 = 50%. The outer interfacial energy is mainly related to two kinds of repulsions, that is, NACεAC and NCCεCC (NAC is the contact number between bocks A and C, while NCC is the contact number between blocks C). As compared to the case of fA3B4 = 50%, NAC is decreased while NCC is increased on the outer surface of the vesicle when fA3B4 = 48% due to a decrease in the content of blocks A and an increase in the content of blocks C. The slight decrease in the outer interfacial energy observed in Figure 7b indicates that the decrease of NAC has a larger impact on the outer interfacial energy. When further decreasing fA3B4 to 42% (Figure 7c), the outer interfacial energy is much lower. Figure 7c indicates that the effect of the decrease in NAC is much stronger and the difference between the inner and outer interfacial energy becomes smaller with a decrease in fA3B4 from 48% to 42%. We can imagine that the difference between the inner and outer interfacial energies will keep reducing with further decreasing fA3B4 if the vesicle structure remains unchanged. However, when fA3B4 further decreases to 40% (Figure 7d), the vesicle structure is reversed to prevent the decrease in the difference between the inner and outer interfacial energies. That is, the difference between the inner and outer interfacial energies in the case of fA3B4 = 40% is much larger than that in the case of fA3B4 = 42%. The vesicle structure reversal increases the inner interfacial energy undoubtedly due to the distribution of the charged blocks C in the inner surface. However, it also increases the outer

Figure 5. Membrane structures of the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture ( fA3B4 = 50%) in which blocks C are charged. (a) εCC = 0.1, (b) εCC = 0.3, (c) εCC = 0.5. Parts (a′)− (c′) are the cross sections corresponding to (a)−(c), respectively.

εCC = 0.1, 0.3, and 0.5, respectively. It is seen that all of the charged blocks C locate on the outer surface of the vesicle (Figure 5a−c), while most of the blocks A locate on the inner surface of the vesicle (Figure 5a′−c′) in all three cases shown in Figure 5. This simulation result reveals that the charged block C always tend to locate on the outer surface of the vesicle, even if its protonation degree is as low as εCC = 0.1. This is consistent with the experimental results observed by Luo and Eisenberg19 in the vesicles formed by a mixture of PS300− PAA11/PS310−P4VP33 (molar ratio is 2:3) when the solution pH is 3. The 4-VP units are protonated and therefore positively charged at pH 3. They think that being charged is one of the reasons that P4VP chains are more likely to locate on the outer surface of the vesicle. Figure 6a−d and a′−d′ displays the asymmetric vesicle structures obtained with decreasing fA3B4. It is seen that the charged block C tends to distribute on the outer surface, while the uncharged block A preferentially distributes on the inner surface of the vesicle when decreasing fA3B4 to 42%. However, reversed vesicle membrane structure is observed by further decreasing fA3B4 to 40%. Moreover, it is found that the vesicle structures for 40% ≤ fA3B4 ≤ 42% are not unique; that is, vesicles with both blocks A and C located on the inner surface can be observed when changing the initial state (Figure S5 in the Supporting Information). This simulation result indicates that there is competition between the effects of the mixed ratio 9223

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

Figure 7. Variations of the energy densities of the asymmetric vesicles formed by A3B4/C3B4 diblock copolymer mixture (blocks C are charged, εCC = 0.5) with r when fA3B4 = 50% (a), 48% (b), 42% (c), and 40% (d), respectively. (r is the radii around the mass center of the vesicle.) The snapshots are the vesicle membrane structures correspondingly.

Figure 8. Membrane structures of the asymmetric vesicles formed by A2B4/C3B4 diblock copolymer mixture with different fA2B4. Parts (a′)−(e′) are the cross sections corresponding to (a)−(e), respectively.

interfacial energy significantly due to the large increase in NAC, which results from the distribution of almost all of the blocks A on the outer surface of the vesicle. Therefore, the difference between the inner and outer interfacial energies is increased rather than decreased in the case of fA3B4 = 40%. Figure 7d illustrates that the reversed vesicle structure has a larger difference between the inner and outer interfacial energies as compared to that in the case of fA3B4 = 42%. These simulation results indicate that the system prefers to spontaneously form an asymmetric vesicle with a larger difference between the outer and inner interfacial energies. This further indicates that the difference between the outer and inner interfacial energy is the main factor in determining the vesicle membrane structure. C. Effect of the Hydrophilic Chain Length. The A2B4/ C3B4 diblock copolymer mixture, in which the hydrophilic chain length of block A is shorter than that of block C, is introduced in this section to investigate the effect of hydrophilic chain length on vesicle membrane structure. First, the vesicle structure formed by the diblock copolymer mixture with fA2B4 = 50% is studied. The simulation results are shown in Figure 8a,a′. It can be seen that all of the longer hydrophilic blocks C locate on the outer surface of the vesicle (Figure 8a), while most of the shorter hydrophilic blocks A locate on the inner surface of the vesicle (Figure 8a′). The simulation results indicate that if the chain lengths of hydrophilic blocks are different, longer hydrophilic chains always tend to locate on the outer surface of the vesicle. This phenomenon can be explained by the chain conformational

entropy. Longer polymer chains on the outer surface can realize their conformation more freely than those on the inner surface of the vesicle due to the spacial confinement. This means that conformational entropy would be lost additionally if the longer polymer chains distribute on the inner surface of the vesicle. Therefore, it is the entropy-driven result that the longer hydrophilic chains occupy the outer surface of the vesicle. This entropy-driven chain segregation between hydrophilic blocks with different chain lengths is consistent with the simulation result observed in symmetric vesicles reported by Ji and Ding.27 The simulation result (Figure 8a,a′) that longer hydrophilic chains prefer to distribute on the outer surface while shorter chains prefer to distribute on the inner surface of asymmetric vesicles has already been observed in many experimental9,19 and simulation20 studies. On the other hand, according to the simulation results shown in sections III.A and III.B, the mixed ratio also plays an important role in determining the distribution of hydrophilic chains in asymmetric vesicle. However, the cooperative effect of the block chain length and the mixed ratio has not been studied. Therefore, the vesicles formed by the A2B4/C3B4 diblock copolymer mixtures with fA2B4 ranging from 40% to 10% are studied in this section. It is noteworthy that the shorter hydrophilic block A turns to be the minor component in the mixture when fA2B4 ranges from 40% to 10%. As stated in section III.A, the minor component prefers to locate on the outer surface of the vesicle. However, from Figure 8b,c and b′,c′, it can be seen that almost all of the shorter blocks A locate on the inner surface of the vesicle, while 9224

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

Figure 9. Variations of the energy densities of the asymmetric vesicles formed by A2B4/C3B4 diblock copolymer mixture with r when fA2B4 = 10%, 20%, and 30%, respectively. (r is the radii around the mass center of the vesicle.) The snapshots are the vesicle membrane structures correspondingly.

Figure 10. Membrane structures of the asymmetric vesicles formed by A2B4/C3B4 diblock copolymer mixture (blocks A are charged and εAA = 0.5) with different fA2B4. Parts (a′)−(e′) are the cross sections corresponding to (a)−(e), respectively.

the higher inner interfacial energy density comes from the distribution of hydrophilic blocks A and C both in the inner surface. This result seems to be inconsistent with the vesicle stabilization criterion given in sections III.A and III.B; that is, the vesicles with higher outer interfacial energy are stable. In fact, this phenomenon results from the competition between the effects of chain conformational entropy and interactive enthalpy between A and C blocks. The effect of chain conformational entropy impels the longer chains to preferentially distribute on the outer surface to reduce the entropy loss, while the effect of interactive enthalpy between A and C blocks tends to make the minor component (shorter A blocks) distribute on the outer surface to increase the outer interfacial energy and at the same time decrease the inner interfacial energy of the vesicle. Apparently, the distribution of longer chains on the outer surface of vesicle (Figure 8) and the ρE(r) curves shown in Figure 9a,b both indicate that the chain conformational entropy has a larger effect on the distribution of hydrophilic blocks on asymmetric vesicles. In other words, the distribution of hydrophilic blocks with different chain length is mainly an entropy-driven process. For the purpose of comparison, charged blocks A are introduced into the A2B4/C3B4 diblock copolymer mixture. The simulation result for εAA = 0.5 is given in Figure 10. From the vesicle structure shown in Figure 10a,a′, it is seen that the longer chains (blocks C) still tend to locate on the outer surface of the vesicle, while the charged shorter chains (block A) tend

the longer blocks C locate on the outer surface of the vesicle when fA2B4 ranges from 40% to 30%. These simulation results indicate that, although block A is the minor component, it still tends to distribute on the inner surface of the vesicle due to its shorter chain length. More interestingly, the asymmetric vesicle structures shown in Figure 8b,c and b′,c′ are very similar to the well-layered ABC asymmetric vesicle; that is, the hydrophilic blocks A and C distribute on the inner and outer surfaces of the vesicle, respectively. This means that well-layered asymmetric vesicle can be obtained by adjusting the mixed ratio of the diblock copolymers with different hydrophilic chain length. In addition, when fA2B4 is further decreased (Figure 8d,e and d′,e′), the inner surface of the vesicle consists of both shorter blocks A and longer blocks C. This is because the outer surface of vesicles cannot accommodate too many blocks C. Therefore, some blocks C have to locate on the inner surface of the vesicle. To further understand the stabilization mechanism of vesicles formed by the diblock copolymer mixture with different hydrophilic chain length, ρE(r) values for vesicles with different fA2B4 are also calculated. Figure 9 shows three typical curves of ρE(r) and their corresponding vesicle structures. It can be seen that the inner interfacial energy densities (the peaks at r ≈ 6) are similar (Figure 9a) or even higher (Figure 9b) than the outer interfacial energy densities (the peaks at r ≈ 10.5) when fA2B4 = 10% and 20%, respectively. This abnormal phenomenon disappears when fA2B4 = 30% (Figure 9c). From the inner vesicle structures shown in Figure 8d′,e′, it can be deduced that 9225

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

■

to locate on the inner surface of the vesicle. Moreover, when fA2B4 decreases from 40% to 10% (i.e., the charged blocks A turn to be the minor component), the longer blocks C still preferentially locate on the outer surface of the vesicle (Figure 10b−e and b′−e′). It is noteworthy that the vesicle structure can not be obtained if the effect of solution pH is much stronger (i.e., εAA > 0.5) according to the simulation results. Therefore, the simulation results indicate that, as compared to the joint effects of the mixed ratio and solution pH, the effect of the chain length is a more dominating factor that determines the vesicle membrane structure under the current simulation parameter condition.

AUTHOR INFORMATION

Corresponding Authors

*Tel.: 86-431-85262151. Fax: 86-431-85262126. E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China for General Program (21374118) and Youth Science Funds (21104078).

■

IV. CONCLUSION Asymmetric vesicles constructed from AB/CB diblock copolymer mixture in a selective solvent for A and C blocks have been investigated using Monte Carlo simulation. The effects of the mixed ratio of the two diblock copolymers, the solution pH, and the hydrophilic chain length on the distributions of hydrophilic blocks A and C on the surfaces of asymmetric vesicles are studied systematically. The simulation results show that ABC or CBA (from inner to outer) three-layer asymmetric vesicles can be obtained from the diblock copolymer mixture. The formation of either ABC or CBA asymmetric vesicle further depends on three factors. The hydrophilic block with the same charge (induced by the solution pH), or longer chain length, or lower content in the mixture is more likely to distribute on the outer surface of the vesicle. Moreover, the transition from ABC to CBA three-layer asymmetric vesicle in which blocks C are charged can occur by adjusting the composition of the mixture. The cooperative effects of these three factors on the distribution of hydrophilic blocks on vesicle membrane are investigated. It is found that the effect of the hydrophilic chain length is a more dominating factor that determines the vesicle membrane structure as compared to the effects of the mixed ratio and solution pH under the current simulation parameter condition. Through the proper adjustment of the three factors, well-layered ABC asymmetric vesicles (the inner and outer surfaces are solely occupied by a certain hydrophilic blocks) can be obtained. On other hand, the investigations of the interfacial energy density of asymmetric vesicles elucidate the distribution regularity of hydrophilic blocks. When the hydrophilic chain lengths are equal, the difference between the outer and inner interfacial energies is the main factor that determines the asymmetric vesicle structures; that is, the distributions of different hydrophilic blocks on asymmetric vesicles always tend to gain the largest difference between the outer and inner interfacial energies. However, when the hydrophilic chain lengths are different, the chain conformational entropy becomes the main driving force for determining the distribution of hydrophilic blocks on asymmetric vesicles.

■

Article

REFERENCES

(1) Stoenescu, R.; Graff, A.; Meier, W. Asymmetric ABC-triblock copolymer membranes induce a directed insertion of membrane proteins. Macromol. Biosci. 2004, 4, 930−935. (2) Kita-Tokarczyk, K.; Grumelard, J.; Haefele, T.; Meier, W. Block copolymer vesicles−using concepts from polymer chemistry to mimic biomembranes. Polymer 2005, 46, 3540−3563. (3) Wittemann, A.; Azzam, T.; Eisenberg, A. Biocompatible polymer vesicles from biamphiphilic triblock copolymers and their interaction with bovine serum albumin. Langmuir 2007, 23, 2224−2230. (4) Lin, J.; Zhu, J.; Chen, T.; Lin, S.; Cai, C.; Zhang, L.; Zhuang, Y.; Wang, X.-S. Drug releasing behavior of hybrid micelles containing polypeptide triblock copolymer. Biomaterials 2009, 30, 108−117. (5) Lee, J. S.; Feijen, J. Biodegradable polymersomes as carriers and release systems for paclitaxel using Oregon Green 488 labeled paclitaxel as a model compound. J. Controlled Release 2012, 158, 312−318. (6) Lee, J. S.; Feijen, J. Polymersomes for drug delivery: design, formation and characterization. J. Controlled Release 2012, 161, 473− 483. (7) Liu, G.; Ma, S.; Li, S.; Cheng, R.; Meng, F.; Liu, H.; Zhong, Z. The highly efficient delivery of exogenous proteins into cells mediated by biodegradable chimaeric polymersomes. Biomaterials 2010, 31, 7575−7585. (8) Stoenescu, R.; Meier, W. Vesicles with asymmetric membranes from amphiphilic ABC triblock copolymers. Chem. Commun. 2002, 3016−3017. (9) Njikang, G.; Han, D.; Wang, J.; Liu, G. ABC triblock copolymer micelle-like aggregates in selective solvents for A and C. Macromolecules 2008, 41, 9727−9735. (10) Liu, F.; Eisenberg, A. Preparation and pH triggered inversion of vesicles from poly (acrylic acid)-block-polystyrene-block-poly (4-vinyl pyridine). J. Am. Chem. Soc. 2003, 125, 15059−15064. (11) Blanazs, A.; Armes, S. P.; Ryan, A. J. Self-assembled block copolymer aggregates: From micelles to vesicles and their biological applications. Macromol. Rapid Commun. 2009, 30, 267−277. (12) Du, J.; Fan, L.; Liu, Q. pH-Sensitive block copolymer vesicles with variable trigger points for drug delivery. Macromolecules 2012, 45, 8275−8283. (13) Fustin, C.-A.; Abetz, V.; Gohy, J.-F. Triblock terpolymer micelles: A personal outlooka. Eur. Phys. J. A 2005, 16, 291−302. (14) Tsitsilianis, C.; Roiter, Y.; Katsampas, I.; Minko, S. Diversity of nanostructured self-assemblies from a pH-responsive ABC terpolymer in aqueous media. Macromolecules 2008, 41, 925−934. (15) Cui, J.; Jiang, W. Vesicle formation and microphase behavior of amphiphilic ABC triblock copolymers in selective solvents: A Monte Carlo Study. Langmuir 2010, 26, 13672−13676. (16) Brannan, A. K.; Bates, F. S. ABCA tetrablock copolymer vesicles. Macromolecules 2004, 37, 8816−8819. (17) Greenall, M. J.; Marques, C. M. Can amphiphile architecture directly control vesicle size? Phys. Rev. Lett. 2013, 110, 088301. (18) Cui, J.; Jiang, W. Structure of ABCA tetrablock copolymer vesicles and their formation in selective solvents: A Monte Carlo study. Langmuir 2011, 27, 10141−10147.

ASSOCIATED CONTENT

* Supporting Information S

Vesicle structure obtained from the artificial asymmetric vesicle after running for a sufficiently long time. Vesicle structures and the formation pathways of the mixture of A3B4/C3B4 with fA3B4 = 25% when the initial state and anneal speeds are changed. Vesicle structures of the mixture of A3B4/C3B4 (blocks C are charged) with fA3B4 = 40% and 42% when the initial state is changed. This material is available free of charge via the Internet at http://pubs.acs.org. 9226

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227

Langmuir

Article

(19) Luo, L.; Eisenberg, A. One-step preparation of block copolymer vesicles with preferentially segregated acidic and basic corona chains. Angew. Chem. 2002, 114, 1043−1046. (20) Zhuang, Y.; Lin, J.; Wang, L.; Zhang, L. Self-assembly behavior of AB/AC diblock copolymer mixtures in dilute solution. J. Phys. Chem. B 2009, 113, 1906−1913. (21) Han, Y.; Cui, J.; Jiang, W. Vesicle structure and formation of AB/BC amphiphile mixture based on hydrogen bonding in a selective solvent: A Monte Carlo study. J. Phys. Chem. B 2012, 116, 9208−9214. (22) Carmesin, I.; Kremer, K. The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions. Macromolecules 1988, 21, 2819−2823. (23) Larson, R. Self-assembly of surfactant liquid crystalline phases by Monte Carlo simulation. J. Chem. Phys. 1989, 91, 2479. (24) Larson, R. Monte Carlo simulation of microstructural transitions in surfactant systems. J. Chem. Phys. 1992, 96, 7904. (25) Hu, W. Structural transformation in the collapse transition of the single flexible homopolymer model. J. Chem. Phys. 1998, 109, 3686. (26) Haire, K.; Carver, T.; Windle, A. A Monte Carlo lattice model for chain diffusion in dense polymer systems and its interlocking with molecular dynamics simulation. Comput. Theor. Polym. Sci. 2001, 11, 17−28. (27) Ji, S.; Ding, J. Spontaneous formation of vesicles from mixed amphiphiles with dispersed molecular weight: Monte Carlo simulation. Langmuir 2006, 22, 553−559. (28) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. Equation of state calculations by fast computing machines. J. Chem. Phys. 1953, 21, 1087. (29) Luo, L.; Eisenberg, A. Thermodynamic stabilization mechanism of block copolymer vesicles. J. Am. Chem. Soc. 2001, 123, 1012−1013.

9227

dx.doi.org/10.1021/la501674a | Langmuir 2014, 30, 9219−9227