Spontaneous Formation of Vesicles from Mixed Amphiphiles with

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Langmuir 2006, 22, 553-559

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Spontaneous Formation of Vesicles from Mixed Amphiphiles with Dispersed Molecular Weight: Monte Carlo Simulation Shichen Ji and Jiandong Ding* Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan UniVersity, Shanghai 200433, China ReceiVed September 14, 2005. In Final Form: October 30, 2005 The spontaneous formation of vesicles from amphiphiles with dispersed molecular weight (MW) as well as with mono-MW has been studied by a lattice Monte Carlo simulation. Both pure and mixed amphiphiles were selfassembled into vesicles under appropriate conditions. When mixed amphiphiles were examined, the amphiphiles with longer hydrophilic blocks preferred to segregate into the outer monolayer of the resultant vesicles, which is consistent with the experimental observations in recent literature. The kinetic study reveals that the increase of vesicle size is mainly caused by the mechanism of vesicle fusion at the early stage, and the evaporation-condensation mechanism cannot be neglected at the late stage. The fusion of vesicles is accompanied by translocation of chains from the outer monolayer to the inner monolayer. For mixed amphiphiles, the degree of segregation exhibits a size dependence of the vesicle. Compared to the chains with shorter hydrophilic blocks, those with longer hydrophilic blocks exhibit stronger trends to translocate from the outer monolayer to the inner one in vesicle self-adjustment, which leads to the quasi-equilibrium asymmetric distribution of the hydrophilic blocks in the post-fused vesicles.

I. Introduction Amphiphilic molecules can be self-assembled into various kinds of supermolecular structures, such as micelles, cylinders, and bilayers (lamella or vesicle). Among these structures, the vesicle is of special interest.1-12 A vesicle, an enclosed structure of the molecular bilayer, is believed to play an important role during the origination of life and is usually used to mimic cells. Vesicles also have potential applications in drug delivery systems, microreactors, etc. In recent years, it has been a hot topic to study vesicles composed of amphiphilic block copolymers.9-30 Poly* To whom correspondence should be addressed. E-mail: jdding1@ fudan.edu.cn. (1) Safran, S. A.; Pincus, P.; Andelman, D. Science 1990, 248, 354. (2) Lipowsky, R. Nature (London) 1991, 349, 475. (3) Luisi, P. L.; Walde, P.; Oberholzer, T. Curr. Opin. Colloid Interface Sci. 1999, 4, 33. (4) Wang, Y. J.; Winnik, F. M.; Clarke, R. J. Biophys. Chem. 2003, 104, 449. (5) Junquera, E.; del Burgo, P.; Arranz, R.; Llorca, O.; Aicart, E. Langmuir 2005, 21, 1795. (6) Nieh, M. P.; Raghunathan, V. A.; Kline, S. R.; Harroun, T. A.; Huang, C. Y.; Pencer, J.; Katsaras, J. Langmuir 2005, 21, 6656. (7) Yin, H. Q.; Huang, J. B.; Gao, Y. Q.; Fu, H. L. Langmuir 2005, 21, 2656. (8) Wang, J. F.; Guo, K. K.; Qiu, F.; Zhang, H. D.; Yang, Y. L. Phys. ReV. E 2005, 71. (9) Zhang, L. F.; Eisenberg, A. Science 1995, 268, 1728. (10) Zhang, L. F.; Yu, K.; Eisenberg, A. Science 1996, 272, 1777. (11) Discher, D. E.; Eisenberg, A. Science 2002, 297, 967. (12) Jain, S.; Bates, F. S. Science 2003, 300, 460. (13) Ding, J. F.; Liu, G. J. Macromolecules 1997, 30, 655. (14) Ding, J. F.; Liu, G. J. J. Phys. Chem. B 1998, 102, 6107. (15) Discher, B. M.; Won, Y. Y.; Ege, D. S.; Lee, J. C. M.; Bates, F. S.; Discher, D. E.; Hammer, D. A. Science 1999, 284, 1143. (16) Kukula, H.; Schlaad, H.; Antonietti, M.; Forster, S. J. Am. Chem. Soc. 2002, 124, 1658. (17) Liu, F. T.; Eisenberg, A. J. Am. Chem. Soc. 2003, 125, 15059. (18) Mu, M. F.; Ning, F. L.; Jiang, M.; Chen, D. Y. Langmuir 2003, 19, 9994. (19) Bermudez, H.; Brannan, A. K.; Hammer, D. A.; Bates, F. S.; Discher, D. E. Macromolecules 2002, 35, 8203. (20) Lee, J. C. M.; Santore, M.; Bates, F. S.; Discher, D. E. Macromolecules 2002, 35, 323. (21) Luo, L. B.; Eisenberg, A. J. Am. Chem. Soc. 2001, 123, 1012. (22) Luo, L. B.; Eisenberg, A. Langmuir 2001, 17, 6804. (23) Terreau, O.; Luo, L. B.; Eisenberg, A. Langmuir 2003, 19, 5601. (24) Terreau, O.; Bartels, C.; Eisenberg, A. Langmuir 2004, 20, 637. (25) Choucair, A. A.; Kycia, A. H.; Eisenberg, A. Langmuir 2003, 19, 1001. (26) Choucair, A.; Lavigueur, C.; Eisenberg, A. Langmuir 2004, 20, 3894. (27) Antonietti, M.; Forster, S. AdV. Mater. 2003, 15, 1323.

meric vesicles or polymersomes not only have the advantage of superior stability and toughness, but in addition offer numerous possibilities of tailoring vesicle properties by variation of the properties of block copolymers, such as molecular weight, ratio of different block length, and reactivity. Synthetic block copolymers are more or less polydispersed, and are thus mixtures of block copolymers with possibly similar but not identical molecular weights. Eisenberg and coworkers11,21-24 have carried out a series of researches to investigate the effect of polydispersity on spontaneous vesicle formation. After various poly(styrene)-b-poly(acrylic acid) (PS-PAA) block copolymers with narrow molecular weight (MW) distributions were synthesized, different block copolymers were mixed together to artificially broaden the molecular weight distribution. When mixed PS-PAA block copolymers self-assemble into vesicles, the polymer with longer PAA chains prefers to segregate into the outer monolayer of the vesicle. (In their studies, the PS block is insoluble in the solvent used.) This segregation is believed to be helpful for stabilizing the vesicles.21 It was found experimentally that the driving force of the segregation seemed size dependent; i.e., the larger vesicle size, the smaller degree of segregation.22 Today, computer simulation of computer experiments has been regarded as the third research approach besides theory and experiment. Drouffe et al.31 simulated the formation of vesicles in 1991. In their model, the lipids are modeled as single particles with anisotropic pair interactions and a multibody hydrophobic interaction. So far, different simulation techniques, such as lattice Monte Carlo (MC) simulation,32,33 dissipative particle dynamics (DPD) simulation,34,35 molecular dynamics (MD) simulations,36,37 (28) Zhu, J. T.; Jiang, Y.; Liang, H. J.; Jiang, W. J. Phys. Chem. B 2005, 109, 8619. (29) Kesselman, E.; Talmon, Y.; Bang, J.; Abbas, S.; Li, Z. B.; Lodge, T. P. Macromolecules 2005, 38, 6779. (30) Wang, R.; Tang, P.; Qiu, F.; Yang, Y. L. J. Phys. Chem. B 2005, 109, 17120. (31) Drouffe, J. M.; Maggs, A. C.; Leibler, S. Science 1991, 254, 1353. (32) Bernardes, A. T. Langmuir 1996, 12, 5763. (33) Bernardes, A. T. J. Phys. II 1996, 6, 169. (34) Yamamoto, S.; Maruyama, Y.; Hyodo, S. J. Chem. Phys. 2002, 116, 5842.

10.1021/la0525067 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/03/2005

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and Brownian dynamics simulations38 have been carried out to study the formation of vesicles on more realistic levels. All simulations prove that proper amphiphilic molecules can selfassemble into vesicles under appropriate conditions. The mechanism of vesicle formation does not appear to be very model dependent.39 Most relevant simulations of vesicles are performed for just mono-MW amphiphiles. To better understand the segregation of mixed block copolymers observed in the experiments of Eisenberg et al.,21-23 this paper performs a lattice MC simulation to investigate the formation of vesicles from a mixture of coarsegrained chains and focuses upon the asymmetric distribution of chains with different hydrophilic block lengths (if reproduced). This paper also examines the mechanism of vesicle formation. The paper is organized as follows. In section II, the lattice model is described. In section III, the Results and Discussion are given in four parts: the first part describes the self-assemblies of mono-MW amphiphiles, and discusses the properties of vesicles formed by mono-MW amphiphiles; the second part shows the vesicle properties formed by mixed amphiphiles; the third part examines the mechanisms of vesicle formation; and the fourth part studies the chain translocation in vesicle self-adjustment. A brief conclusion is given in section IV. II. Model and Method MC simulation is a widely used stochastic modeling method. Lattice MC simulation is especially efficient as far as the computing cost is concerned,40 and it has been applied in many fields such as modeling the microphase separation of block copolymers.41-51 For this paper, the simulation of self-avoiding chains was carried out in a simple cubic lattice system with 40 × 40 × 40 sites. The periodic boundary condition was applied in all three directions. A Larsontype bond fluctuation model with the permitted bond length of 1 or x2 was used.41,42 Each lattice site was occupied by either a bead or a vacancy (a solvent). Two beads cannot occupy the same site simultaneously. The partial-reptation algorithm51-54 has been applied in our simulation. This algorithm enhances the efficiency of the simulation by introducing a cooperative motion of beads, and has been proved suitable to study the dynamic process.54 The microrelaxation modes are defined as follows: 1. A bead is randomly chosen to exchange with one of its 18 nearest and next-nearest neighbors. If the neighbor is a vacancy, exchange with the bead is attempted. 2. If the exchange does not break the chain, it is allowed to do so. This process constitutes a single movement (Figure 1a).

Ji and Ding

Figure 1. Schematic presentation of microrelaxation modes in the simulation. (a) A single bead movement, in which the exchange between bead and vacancy does not break the chain; (b) an illegal movement, in which the exchange breaks two bond connections; (c) a multiple-bead movement as a partial reptation, in which the exchange breaks just one bond connection and the vacancy continues to exchange with subsequent beads until reconnection of a bond. 3. If the exchange would break two chain connections, it is not allowed (Figure 1b). 4. If the exchange creates a single break in the chain, the vacancy will continue to exchange with subsequent beads along the chain until reconnection of a bond. This process constitutes a cooperative movement (Figure 1c). Beside the rules described above, bond crossing is forbidden in any elementary movement. The Fortran program was coded by us and run on a PC with a 2.8 GHz CPU. A very simple model of amphiphiles is chosen to study the effect of hydrophilic block length. The amphiphiles are presented as A3B1 or A3B2 in this study. Here, A and B refer to hydrophobic and hydrophilic segments, respectively, if the implicit solvent is thought to be water. The subscripts denote the number of beads or segments in each block. The total number of beads in the whole simulated system is fixed as 6000, corresponding to a volume fraction of 9.375%. There are 1500 A3B1 or 1200 A3B2 amphiphiles when the simulated system contains just one kind of amphiphile. When a mixture is simulated, the proportion is adjusted according to the set ratio. Pairwise nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions are considered for the amphiphile solution. Only AA attraction is considered, and the strength of one pair interaction is set as AA ) -kB (kB is the Boltzmann constant), while all other interactions are set to be zero. The inverse temperature 1/T is used and equals zero at the athermal state. Metropolis importance algorithm55 is employed in sampling. In this study the time t is measured in units of Monte Carlo step (MCS). One MCS means that on average every bead has attempted exchange once.

III. Results and Discussion (35) Yamamoto, S.; Hyodo, S. J. Chem. Phys. 2003, 118, 7937. (36) Marrink, S. J.; Mark, A. E. J. Am. Chem. Soc. 2003, 125, 15233. (37) de Vries, A. H.; Mark, A. E.; Marrink, S. J. J. Am. Chem. Soc. 2004, 126, 4488. (38) Noguchi, H.; Takasu, M. Phys. ReV. E 2001, 64, 41913. (39) Marrink, S. J.; Mark, A. E. J. Am. Chem. Soc. 2003, 125, 11144. (40) Binder, K.; Heermann, D. W. Monte Carlo Simulation in Statistical Physics; Springer-Verlag: Berlin, 1988. (41) Larson, R. G.; Scriven, L. E.; Davis, H. T. J. Chem. Phys. 1985, 83, 2411. (42) Larson, R. G. J. Chem. Phys. 1988, 89, 1642. (43) Fried, H.; Binder, K. J. Chem. Phys. 1991, 94, 8349. (44) Larson, R. G. J. Chem. Phys. 1992, 96, 7904. (45) Yang, Y. L.; Lu, J. M.; Yan, D.; Ding, J. D. Macromol. Theory Simul. 1994, 3, 731. (46) Viduna, D.; Milchev, A.; Binder, K. Macromol. Theory Simul. 1998, 7, 649. (47) Geisinger, T.; Muller, M.; Binder, K. J. Chem. Phys. 1999, 111, 5241. (48) Zaldivar, M.; Larson, R. G. Langmuir 2003, 19, 10434. (49) Kenward, M.; Whitmore, M. D. J. Chem. Phys. 2002, 116, 3455. (50) Ji, S. C.; Ding, J. D. J. Chem. Phys. 2005, 122, 164901. (51) Ding, J.; Carver, T. J.; Windle, A. H. Comput. Theor. Polym. Sci. 2001, 11, 483. (52) Hu, W. B. J. Chem. Phys. 1998, 109, 3686. (53) Haire, K. R.; Windle, A. H. Comput. Theor. Polym. Sci. 2001, 11, 227. (54) Haire, K. R.; Carver, T. J.; Windle, A. H. Comput. Theor. Polym. Sci. 2001, 11, 17.

1. Simulation of Mono-MW Amphiphiles and Characterization of Vesicles. The aggregation structures of A3B1 or A3B2 amphiphiles are shown in Figure 2. The systems have been quenched to low temperatures from the athermal state, and relaxed for an adequately long time. A vesicle was formed for A3B1 amphiphiles (Figure 2, top), while a bilayered micelle (Figure 2, bottom) was observed for A3B2 amphiphiles with longer hydrophilic blocks. The following discussion will focus on the vesicle. The above visualized vesicle was quantitatively characterized by us. The inner and outer monolayers of vesicles were distinguished according to the following criterion. Assuming the vesicle is shaped as an ideal sphere and all of the tailed hydrophobic beads A1 locate at the midplane of the bilayer, the radius of gyration of A1 to the mass center of the vesicle, R0, was calculated, which refers to the position of the midline of the (55) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. J. Chem. Phys. 1953, 21, 1087.

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Figure 3. Indicated density profiles as a function of distance to the mass center of the vesicle composed of A3B1 amphiphiles.

There is just one vesicle in Figure 2a considering the periodic boundary condition. This vesicle contains 1500 amphiphiles. In the inner monolayer 502 amphiphiles were located, while 998 amphiphiles were located in the outer monolayer (Table 1). The fraction of chains in the inner monolayer is defined as

fin )

Figure 2. Schematic presentation of simulated A3B1 and A3B2 amphiphilic chains, and aggregation structures after microphase separation. The hydrophobic and hydrophilic parts (A and B) are displayed in red and green spheres, respectively, while the solvents are not shown. The temperature is 1/T ) 0.8. The systems relaxed for 30 million MCS after quenching from the athermal state. The vesicle and bilayered structures were observed for A3B1 and A3B2 amphiphiles, respectively.

bilayer. Then the distance R of the headed hydrophilic bead B1 (or B2 for A3B2 molecules) of each chain to the vesicle center was calculated. If R e R0, this amphiphile resides in the inner monolayer; If R > R0, the amphiphile locates in the outer monolayer. Similarly, the number of the encapsulated solvent (vacant sites) can be obtained. The above criterion works only for those vesicles with a nearly spherical external shape.

ninner ninner + nouter

(1)

where ninner and nouter refer to the number of chains in the inner and outer monolayers, respectively. For an ideal symmetric chain distribution, fin ) 0.5. For this vesicle, fin ≈ 0.33. The observed location of chains is thus asymmetric. It might be accounted for considering that the inner monolayer with a smaller radius can accommodate fewer chains. Such an asymmetric distribution at different monolayers has also been observed in other simulation of mono-MW vesicles38 and is believed to decrease the bending rigidity by which to benefit the formation of vesicles. The number of encapsulated solvents is around 730, and exhibits some fluctuation during simulation to a certain degree. The radius of gyration R0 is 9.35. From the tensor of the squared radius of gyration, the shape of the vesicle can be analyzed according to the relative sizes along different dimensions.49,50,56,57 The radii of the vesicle along three Cartesian coordinate dimensions (Rx: Ry:Rz) are 5.23, 5.39, and 5.56, which confirms that this vesicle is a nearly perfect sphere. The straightforward statistical evidence of a vesicle structure instead of a micelle comes from the density profile calculation. The densities of the beads and solvents at a distance R to the mass center of the vesicle are shown in Figure 3. The solvent’s density profile indicates that the self-assembly is a “hollow” vesicle rather than a micelle. For a graphical interpretation, the

Table 1. Structural Characteristics of the Vesicles for Statistics time

(106

MCS)

vesicle

no. of chains total bilayer inner monolayer

no. of encapsulated solvent

fin (%)

gin,long (%)

gout,long (%)

4.3 4.3 3.2 3.9 6.4 11.7 9.5

17.2 21.3 21.9 20.9 20.8 17.7 20.0

Pure (1500 A3B1) 12.23 30 6 10 30

1 2 1′

624 876 1500

168 254 502

64 257 730

26.9 29.0 33.5

1 2 3 1 2′ 1 2′

592 (90 A3B2) 413 (72 A3B2) 435 (78 A3B2) 613 (102 A3B2) 827 (138 A3B2) 685 (110 A3B2) 755 (130 A3B2)

Mixed (1200 A3B1 + 240 A3B2) 92 (4 A3B2) 92 93 (4 A3B2) 24 93 (3 A3B2) 21 153 (6 A3B2) 61 236 (15 A3B2) 188 188 (22 A3B2) 119 201 (19 A3B2) 136

15.5 22.5 21.4 25.6 29.3 27.4 26.6

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Figure 4. Orientational order parameter P2 of bonds of the A3B1 amphiphiles in the bilayers of the vesicle. Table 2. Self-Assembly Structures of Mixed Amphiphiles at 1/T ) 0.8a A3B2:A3B1

v/v

mol/mol

vesicle

0:1500 240:1200 400:1000 500:750 667:666 800:500 1200:0

0:1 1:4 1:2 1:1 5:4 2:1 1:0

0:1 1:5 2:5 5:7 1:1 8:5 1:0

Y Y Y Y Y* N N

a “Y”, eventual formation of vesicles; “Y*”, eventual vesicles in two out of four independent runs; “N”, without vesicles but with micelles.

density profiles of the inner and outer monolayers exhibit separated peaks. The vesicle thus constitutes a typical bilayer shell. In the vesicle bilayer, the amphiphiles might take a preferred orientation. The degree of orientation could be quantitatively described by an order parameter defined as

1 P2 ) (3 cos2 θ - 1) 2

(2)

where θ is the angle between the bond vector and the vector from the mass center of the vesicle to the center of the associated bond. A perfect radial alignment of a bond in an amphiphile with the radial axis of the vesicle is indicated by P2 ) 1, whereas a perfect tangential alignment is indicated by P2 ) -0.5 and a random orientation is indicated by P2 ) 0. Figure 4 shows the calculated order parameters P2 of the bonds from our simulation. According to Figure 4, the hydrophobic tails around the midplane of the bilayer are basically randomly oriented, while the bonds nearest the boundary of hydrophilic and hydrophobic segments exhibit significant orientation parallel with the radius direction or normal to the vesicle surface. 2. Vesicles of Mixed Amphiphiles. Though pure A3B2 chains seemed not to self-assemble into vesicles at the examined temperature, vesicles were observed when A3B2 amphiphiles were mixed with A3B1 at proper ratios, as seen from Table 2. Vesicle formation was available until the molar fraction of A3B2 in the mixture was as high as 50%. In this study, we focus on the system of A3B2 mixed with A3B1 at a ratio of 1:5 (mol/mol), which predominantly led to vesicles. Starting from the athermal state (Figure 5a), two vesicles were observed at 30 million MCS at this ratio (A3B2:A3B1 ) 1:5) (Figure 5b) in the given trajectory. No further fusion between the vesicles has been observed even in the following 60 million MCS. Since just one vesicle was observed in the case of mono(56) Chen, Y. T.; Zhang, Q.; Ding, J. D. J. Chem. Phys. 2004, 120, 3467. (57) Xu, G. Q.; Ding, J. D.; Yang, Y. L. J. Chem. Phys. 1997, 107, 4070.

Figure 5. Snapshots of mixed amphiphiles: (a) an initial random state and (b) two vesicles after quenching. There are 1200 A3B1 amphiphiles and 240 A3B2 amphiphiles in the system. 1/T ) 0.8; 30 million MCS. The hydrophobic parts (A) are displayed in red spheres. The hydrophilic parts (B) of A3B1 and A3B2 are displayed in green spheres and open circles, respectively.

MW A3B1 amphiphiles, the vesicle of the mixed amphiphiles is smaller than the A3B1 vesicles under similar conditions (concentration and temperature, etc.). (The vesicle size is roughly represented by the number of amphiphiles in a vesicle.) The relative amounts of A3B2 chains in different layers are of special interest to us, which are defined as

gin,long )

gout,long )

nA3B2,inner nA3B1,inner + nA3B2,inner nA3B2,outer nA3B1,outer + nA3B2,outer

(3)

(4)

Here, nA3B2,inner denotes the number of A3B2 chains in the inner monolayer, and other parameters are defined in a similar way. For both vesicles, the relative amounts of A3B2 chains in the inner monolayer gin,long (11.7% and 9.5%) are lower than those in the outer monolayer gout,long (17.7% and 20.0%). Figure 6 shows gin,long and gout,long of 12 vesicles from six independent runs. The results indicate that gin,long is smaller than gout,long for all vesicles. Our simulation did reproduce the experimental observation of the segregation of mixed block copolymers.21-23 The amphiphiles with a longer hydrophilic block

Formation of Vesicles from Mixed Amphiphiles

Figure 6. Relative amounts of A3B2 in the inner and outer monolayers in 12 vesicles from six independent runs. The dashed line denotes the fed molar percent of A3B2 chains (16.67%) in the mixture.

Figure 7. Aggregation kinetics of A3B1 vesicles.

(here A3B2) prefer to segregate to the outer surface, when the mixed amphiphiles self-assemble into vesicles. Such segregation can be explained by the reduction of the chain conformation entropy due to the spatial confinement. The inner monolayer with a smaller curvature radius might cause a larger reduction than the outer monolayer. When the mixed amphiphiles are considered, the longer the hydrophilic block length, the stronger reduction of the chain conformation entropy. As a result, the amphiphiles with longer hydrophilic blocks prefer to segregate to the outer layer to relieve the entropy induction. 3. Mechanisms of Vesicle Formation. Figure 7 shows the number and maximum size of clusters of A3B1 amphiphiles after quenching. A cluster is determined in our simulation as follows: when any hydrophobic beads from different chains are nearest neighbors, these chains form a cluster; a free chain is not a cluster. The number of chains in a cluster is defined as the cluster size. After quenching, the amphiphiles first aggregated to small clusters. There was a rapid decrease of the number of clusters and an increase of cluster size. Then, when those small clusters aggregated to larger clusters, a rearrangement was observed, leading to the formation of prevesicle aggregates (small doublelayer cluster with the inner heads compressed in the middle). When those aggregates came together, a new arrangement took place, leading to the formation of the vesicles. A large vesicle was observed by the gradual fusion of smaller vesicles. Fusion of vesicles is considered to be the main mechanism of the increase of vesicle size.22 Slices during the fusion of two A3B1 vesicles are shown in Figure 8. Two separated vesicles (Figure 8a) contacted each other and formed a stalk intermediate (Figure 8b). A center wall was observed in the intermediate

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structure. When the center wall destabilized, a growing pore was observed, and a peanutlike vesicle was formed when the pore connected two cavities (from Figure 8c to 8e). In the end, this peanutlike vesicle relaxed to the final spherical vesicle (see, for instance, Figure 8f or 2a). The stalk model58-61 is widely used to understand the fusion of lipid membranes and vesicles. The simulated fusion process can also be described by the stalk model and follows the pore-opening process.39,62,63 Experimentally, it is not easy to continuously trace the fusion process of vesicles. Usually, the vesicle intermediates during fusion are identified by transmission electron microscopy (TEM) and then arranged in a reasonable sequence.11,22,25 Very recently, Zhou and Yan64 have reported a real-time fusion process of a giant polymersome. This fusion was very slow, and the real-time morphology was captured by optical microscopy. The fusion process in our simulation is rather consistent with that from their experiment (see Figure 1 in their paper). Our simulation further illustrates that the exterior morphology change and the interior pore opening are not in step during the fusion. No significant difference between Figure 8c′,e′ could be seen, although a significant difference of the interior is found in Figure 8c,e. Thus, to better understand the kinetics of vesicle fusion, it is very important to study both the interior and exterior changes, which is difficult to do so in an experiment but easy in a simulation (“computer experiment”). The aggregation kinetics of mixed amphiphiles is shown in Figure 9, which follows a way similar to that of mono-MW amphiphiles. It is rather interesting that an obvious fluctuation of the maximum vesicle size was seen at the late stage of the simulation. Since the number of vesicles remained unchanged during this period, such a fluctuation suggests an exchange of chains between two vesicles via a somewhat evaporationcondensation mechanism. A chain may detach from a vesicle and become a free chain. The free chain may attach to the original vesicle or other vesicles. The detachment causes a decrease of corresponding vesicle size, while the attachment causes an increase. The experiment of Luo and Eisenberg22 shows that the concentration of the free PS-PAA chain in solution is very low, and thus the single chain involvement is negligible in their experimental system. Our simulation confirms that the concentration of free chains is indeed very low. In many cases, there is no more than one free chain in the system after running for a long time. Only 18 free chains have been detected for all 1000 snapshots from 20 to 30 million MCS. Nevertheless, our simulation implies that the free chain involvement or the evaporation-condensation coarsening mechanism cannot be neglected at the late stage of vesicle formation, especially when the vesicle concentration is very low. The negligence of the single chain involvement suggested by Luo and Eisenberg22 is still justified because the number of vesicles in their experimental system was not very small. 4. Chain Translocation during and after Vesicle Fusion. As mentioned above, the location of chains at different layers is asymmetric. The fraction of chains in the inner monolayer fin is significantly smaller than 0.5 in the simulated vesicle. It is not hard to understand that, for an infinitely large vesicle, such an asymmetry must disappear and the asymptotic fin then equals 0.5. The asymmetric distribution of the amphiphile chains in (58) Markin, V. S.; Kozlov, M. M.; Borovjagin, V. L. Gen. Physiol. Biophys. 1984, 3, 361. (59) Siegel, D. P. Biophys. J. 1993, 65, 2124. (60) Siegel, D. P. Biophys. J. 1999, 76, 291. (61) Markin, V. S.; Albanesi, J. P. Biophys. J. 2002, 82, 693. (62) Noguchi, H.; Takasu, M. J. Chem. Phys. 2001, 115, 9547. (63) Noguchi, H. J. Chem. Phys. 2002, 117, 8130. (64) Zhou, Y. F.; Yan, D. Y. J. Am. Chem. Soc. 2005, 127, 10468.

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Figure 8. Sequential slice snapshots of the fusion of two A3B1 vesicles with indicated simulation time in units of million Monte Carlo steps (MCS). The hydrophobic and hydrophilic parts (A and B) are displayed in red and green spheres, respectively, while the solvents are not shown. (c′) and (e′) are the three-dimensional snapshots associated with the slices in (c) and (e).

Figure 9. Aggregation kinetics of mixed amphiphiles.

different monolayers is size-dependent: fin increases with the increase of vesicle size. Now a very interesting question arises of how to adjust the asymmetry during and after vesicle fusion. Quantitative characterization of the fusion process of A3B1 vesicles besides the morphological analysis was further performed. We compared the properties of vesicles before fusion and those of the final vesicles (Table 1). Eighty chains have

translocated from the outer monolayer to the inner monolayer after fusion (168 and 254 chains in the inner monolayer before fusion, and 502 chains in the inner monolayer of the final vesicle). The translocation of chains occurred during the fusion of vesicles and the relaxation of the post-fused vesicle. The driving force of translocation can be well understood on the basis of the curvature change. With the increase of the radius after fusion, more chains can locate at the inner monolayer, as demonstrated by experiment.22,25 The simulation also confirms that the encapsulated volume is not a constant during the fusion and the solvent number within the vesicles has been much increased (64 + 257 before fusion and 730 in the end; see also Table 1). One important feature of mixed vesicles is that the segregation of different chains is also size dependent.22,25 The value of gin,long in Table 1 reflects the degree of segregation: a smaller value in the inner monolayer or a larger deviation from the fed ratio refers to a higher degree of segregation. The larger the vesicle, the less significant the segregation of longer chains. Therefore, there must be an adjustment of the degree of segregation induced by the fusion of vesicles. Upon examination of the system at 6 and 10 million MCS, two vesicles (labeled “2” and “3”) were fused into a larger vesicle (labeled “2′”) (Table 1). The chain translocation was found as expected. It is interesting that the

Formation of Vesicles from Mixed Amphiphiles

translocation of chains, especially A3B2 chains, from the outer monolayer to the inner monolayer (increase of gin,long) is also rather significant during relaxation (from 10 to 30 million MCS) after vesicle fusion. It is not hard to understand that the chain translocation during fusion can only occur in the contact region and thus a rearrangement of chains between different layers seems necessary to stabilize the post-fused vesicle during the relaxation. Thermodynamically driven by chain conformational entropy, more A3B2 chains can reside in the inner monolayer with increasing vesicle size; thus the A3B2 chains show stronger trends than A3B1 chains to translocate to the inner monolayer during the relaxation of vesicles, and meanwhile, the A3B1 chains exhibit stronger trends to translocate to the outer monolayer after fusion.

IV. Conclusion This article employed dynamic MC simulation to study the self-assembly of mono-MW and dispersed-MW amphiphiles to better understand the segregation behaviors in mixed amphiphile vesicles observed in recent experiments. Under the proper conditions, amphiphiles can spontaneously form vesicles in our lattice MC simulation. The distribution of chains at the bilayer was found to be highly asymmetric with a smaller number of chains in the inner monolayer. The segregation of mixed vesicles has been reproduced: the amphiphiles with longer hydrophilic blocks prefer to aggregate onto the outer monolayer. The dynamic MC simulation also confirms that the increase of vesicle size is mainly caused by the mechanism of vesicle fusion. Meanwhile, the single chain involvement or the evaporation-condensation mechanism also works at the very late stage, especially when the vesicle concentration is low. The fusion

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process of vesicles qualitatively coincides with the stalk model. In both cases of mono-MW and dispersed-MW amphiphiles, the translocation of chains from the outer monolayer to the inner monolayer has been observed in vesicle self-adjustment, which is thermodynamically driven by the size dependence of the asymmetric distribution of amphiphiles between different monolayers. For mixed amphiphiles, the chains with longer hydrophilic lengths show stronger trends to translocate to the inner monolayer in vesicle self-adjustment, which results in a decrease of degree of segregation with the increase of vesicle size. In the present study, vesicles from mixed amphiphiles with an identical hydrophobic block have been studied. Our model can be extended to study vesicles from other systems, e.g., mixed amphiphiles with different hydrophobic and hydrophilic blocks or with repulsive interactions among multicomponent amphiphiles. Acknowledgment. The authors are grateful for financial support from NSF of China (Grants 20221402, 20374015, 50533010, and 20574013, and a Two-Base Grant), the Key Grant of Chinese Ministry of Education (Grant 305004), the Award Foundation for Young Teachers from Ministry of Education, Project 973, Project 863, and the Science and Technology Developing Foundation of Shanghai. Supporting Information Available: Details for obtaining the slice snapshots in Figure 8. This material is available free of charge via the Internet at http://pubs.acs.org. LA0525067