J. Phys. Chem. B 2007, 111, 13675-13682
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Multicompartment Micelles from Star and Linear Triblock Copolymer Blends Jing Xin, Dahuan Liu, and Chongli Zhong* Department of Chemical Engineering and the Key Lab for Nanomaterials of Ministry of Education, Beijing UniVersity of Chemical Technology, Beijing 100029, China ReceiVed: April 24, 2007; In Final Form: September 24, 2007
Dissipative particle dynamics simulations were performed on multicompartment micelles formed by blending star and linear triblock copolymers, in which the influences of blending options and blending ratio as well as copolymer chain compositions were studied systematically. The results show that blending of copolymers with different architectures is a promising strategy to control the morphology and structure of multicompartment micelles. This work revealed several new morphologies of multicompartment micelles by blending star and linear triblock copolymers, and the dynamic processes were elucidated at the molecular level by tracing the motions of copolymer chains. The results of this work provide deep insight into micro/mesoscopic details of the underlying mechanisms, contributing to a more complete understanding of multicompartment micelle formation and structural control.
1. Introduction Synthesis and identification of multicompartment micelles with novel morphology is an ongoing hot topic in the area of colloid science.1-9 The concept of multicompartment micelles was originally inspired by biological systems in which a single cell, with many different subunits, can perform a series of different functions.4,8,9 So far, the commonly used method for preparing multicompartment micelles is the self-assembly of amphiphilic multiblock, particularly triblock, copolymers in a selective solvent,5,9 while blending of block copolymers is considered a promising strategy to tune multicompartment micellar structure very recently. The first investigation into control of the structure of multicompartment micelles by mixing star triblock copolymers with diblock copolymers was performed by Hillmyer and Lodge experimentally,8 and the observations were reproduced by selfconsistent field theory (SCFT) calculation later.10 Although the studies show that this is a promising strategy to produce novel multicompartment micelles, the knowledge of mixed multicompartment micelles, particularly of their exact inner structure and formation process is very limited to date. In the meantime, the structures of mixed multicompartment micelles are more complicated, and thus are more difficult to be assessed experimentally. By performing systematic molecular-level simulations, deep insight into the underlying mechanisms may be revealed, leading to a microscopic understanding of such complicated micelles. In addition, the parameter space that affects the morphology and structure of mixed multicompartment micelles is very large, leading to a difficult or even impossible task to explore in the whole parameter space experimentally. Therefore, a prescreening by theoretical investigations, such as SCFT calculation and dissipative particle dynamics (DPD) simulation, is very helpful that may provide valuable and systematic information to guide further experimental studies. In this work, using DPD simulation, multicompartment micelles formed by blending star and linear triblock copolymers * Corresponding author. E-mail:
[email protected].
TABLE 1: DPD Repulsion Parameters aij (in DPD units) Used in This Work A B C S
A
B
C
S
25 45 75 50
45 25 90 27
75 90 25 120
50 27 120 25
were studied systematically. The dynamic processes of micelle formation with different mixing options were elucidated at the molecular level, and the influences of blending ratio and copolymer composition were also discussed. 2. Method and Simulation Details 2.1. Dissipative Particle Dynamics Method. As a particlebased mesoscopic simulation technique, the dissipative particle dynamics (DPD) method was originally developed by Hoogerbrugge and Koelman11,12 which is particularly suitable for complex fluids over larger length and time scales than classical molecular dynamics and Monte Carlo simulations. It has been successfully used to study microstructures and properties of polymers in the bulk state and in solvent.13-21 In this method, a series of soft particles are considered to interact with each other and each particle represents a small volume of fluid containing many atoms. Details of the DPD method are given elsewhere,14, 22 and only a brief introduction is given here. In the DPD method, the force acting on a particle contains three parts, each of which is pairwise additive22
Fi )
(FCij + FDij + FRij ) ∑ j*i
(1)
where the sum runs over all other particles within a certain cutoff radius rc. The conservative force is a soft repulsion acting along the line of centers and is given by
FCij )
{
aij(1 - rij/rc)rˆij (rij < rc) (rij grc) 0
10.1021/jp073173k CCC: $37.00 © 2007 American Chemical Society Published on Web 11/15/2007
(2)
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Figure 1. Morphologies of micelles obtained by DPD simulations (B blocks and solvent were omitted for clarity; A, red; C, green): (a) spherical micelles formed from diblock copolymers; (b) wormlike multicompartment micelles formed from star triblock copolymers; (c) “hamburger” multicompartment micelles formed by blending star triblock and diblock copolymers.
where aij is the maximum repulsion between particles i and j, and b rij ) b ri - b rj, rij ) |r bij|, and rˆij ) b rij/|r bij|. The dissipative force is given by
FDij ) - γωD(rij)(rˆij ‚V bij)rˆij
(3)
and the random force is given by
FRij ) σωR(rij)θijrˆij
(4)
where b Vij ) b Vi - b Vj , ωD and ωR are weight functions vanishing for r >rc , γ is the friction coefficient, σ is the noise amplitude, and θij is a randomly fluctuating variable with Gaussian statistics. The two weight functions can be taken simply as
ωD(r) ) [ωR(r)]2 )
{
(1 - rij/rc)2 (rij < rc) (rij grc) 0
σ2 ) 2γkBT
(5) (6)
To determine the conservative force FC, the repulsion parameter aij has to be known. In this work, the relationship between aij and the Flory-Huggins χ-parameter proposed by Groot and Warren is adopted22
{
a + 3.27 χ F ) 3 aij ) aii + 1.45 χij ii ij F ) 5
(7)
where F is the density and aii is the repulsion parameter between like particles, and its value is derived from the compressibility of pure component by
aii ) 75kBT/F
(8)
2.2. Model and Parameters. In our previous work,13 the selfassembly of ABC star triblock copolymers into multicompartment micelles in water was studied, and the DPD repulsion parameters between unlike species were determined by reproducing the experimental observations of Lodge and co-workers,4 in which A, B, and C mimic the weakly hydrophobic polyethylethylene, the hydrophilic poly(ethylene oxide), and the strongly hydrophobic poly(perfluoropropylene oxide) in experiments, respectively. In this work, star and linear ABC block copolymers were considered with the DPD repulsion parameters remaining unchanged as shown in Table 1. The systems studied in this work are composed of a binary copolymer blend and a selective solvent. The solvent molecule (S) was modeled as a
single DPD bead, while the star and linear copolymers were modeled as spring-bead chains denoted ANABNBCNC and BNBANACNC where Ni (i ) A, B, C) is the length of block i. 2.3. Simulation Details. The DPD simulations were performed in a cubic cell of size 30 × 30 × 30rc3 containing about 81 000 DPD beads. Periodic boundary conditions were applied, and the volume fraction of the copolymer blends was set to 0.15 to ensure formation of enough micelles in the system. For convenience, the cutoff radius rc, the particle mass m and kBT were all taken as unity. The time step ∆t was taken as 0.05, and adjacent particles in the polymer chain interact via a linear spring with the harmonic spring constant of 4.0. The bead density was set to 3.0, and thus the repulsion parameter between like particles was aii ) 25.0 according to Groot and coworkers.14,22 2-4 × 105 DPD steps were carried out for a DPD simulation to guarantee the stability of properties including the conservative energy and the root-mean-square radius of gyration of copolymer chains, which indicates equilibration of the system. 3. Results and Discussion Considering that the simulation box size is an important factor that may affect the results, comparative simulations were first performed with box dimensions varied from 25 to 35 to obtain an optimal box size. The results show that the copolymer blends formed similar morphologies with the box sizes larger than 30 × 30 × 30 rc3. Therefore, the box size 30 × 30 × 30 rc3 was adopted in this work to save computational efforts. 3.1. Validation of the DPD Method. Lodge and co-workers observed that “hamburger” micelles were formed by blending star triblock copolymers and diblock copolymers that formed wormlike and spherical micelles in water, respectively.8 Therefore, we first performed corresponding DPD simulations and compared with these experimental observations to validate the reliability of the DPD method for describing multicompartment micelles from copolymer blends, although it has been validated in our previous work for studying the formation of multicompartment micelles from star triblock copolymers in water.13 We constructed a model star triblock copolymer of A4B8C2 and a diblock copolymer of A4B8, with identical block compositions to the species adopted in ref 8, to mimic their experimental copolymers. Since the copolymer species remained unchanged in their experiments (only with different block ratio and/or length), the DPD parameters aij, obtained by reproducing their previous experimental observations, were kept unchanged also. The simulation results are shown in Figure 1. Obviously, the DPD simulations can reproduce the morphologies formed by both single and binary copolymer systems, demonstrating that
Multicompartment Micelles
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Figure 2. Morphologies of multicompartment micelles obtained from star A4B19C2 and linear B2A6C1 copolymer blends with different blending ratios of star triblock copolymers (the total volume fraction of the blend was fixed at 15%; B blocks and solvent were omitted for clarity; A, red; C, green). Views with and without A blocks were both given.
Figure 3. Root-mean-square radius of gyration of the two block copolymers in mixed micelles as a function of volume fraction of linear copolymers.
the DPD method can also be used to study the formation of multicompartment micelles from copolymer blends. Therefore, with this set of parameters, we can continue to study the effects of blending ratio and copolymer chain composition on the morphology of micelles, as well as the evolution processes of micelle formation. 3.2. Effects of Blending Ratio. First, the effects of the blending ratio were investigated, since it is a dominant parameter in controlling morphology of the mixed micelles formed for a
given binary copolymer blend. For this purpose, star A4B19C2 copolymer and linear B2A6C1 copolymer were chosen, since they can form representative morphologies of “hamburger” micelles (Figure 2a)13 and toroidal multidomain micelles (Figure 2h), respectively. A series of DPD simulations with volume fraction of star copolymers fstar varied from 15% to 0% were performed, with the total volume fraction of copolymer blends fixed as 15%. Some typical results are shown in Figure 2. The simulations show that discrete “hamburger” or spherical multicompartment micelles were formed when the star copolymer is predominant (Figure 2a,b). With the increase of the fraction of linear copolymer, disklike and rodlike micelles appeared (Figure 2c-e). With further increase of the fraction of the linear copolymer, novel toroidal multicompartment micelles with ring/cogwheel cores were formed as shown in Figure 2f,g, in which the core shows a ringlike morphology with a cogwheel-like C-block domain incorporated in the ringlike A-block domain (Figure 2f), leading to new multicompartment micelles with interesting core structure. This intriguing structure, different from those formed by the two pure copolymers, may have potential application in the drug controlledrelease field, since the cogs of the cogwheel-like domain may be used as release channels for the particles loaded in the C domains, and the unique core structure may lead to special release modes.
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Figure 4. Evolution of a toroidal multicompartment micelle with a ring/cogwheel core obtained by premixing (B blocks and solvent were omitted for clarity; A blocks, red; C blocks of linear copolymers, green; C blocks of star copolymesr, blue. Views with and without A blocks were both given).
The above simulations show that blending of block copolymers with different architectures is a promising strategy for controlling or fine-tuning the morphology of multicompartment micelles as well as their inner structure, and the blending ratio is an important influencing factor. Intermediate or even new morphologies and structures can be formed; thus, such investigations should be enhanced, for which DPD simulation is a powerful tool. To quantitatively understand the structural differences of the micelles with different blending ratios, the root-mean-square radius of gyration (Rg) of the two copolymers in the mixed micelles were calculated. The results are shown in Figure 3 as a function of the fraction of linear copolymer. As can be seen from Figure 3, the Rg of star copolymers remained nearly constant for the mixed micelles with different blending ratios, while for linear copolymers, this value increases gradually. To find out the underlying mechanisms, we traced the distributions of both star and linear copolymers in the mixed micelles, and found that the star copolymers mainly distributed on the outer space of core, such as the cogs of cogwheel-like domain, leading to approximately constant Rg. This provides interesting information on the evolution of mixed micelles and will be discussed in detail in the following paragraphs. 3.3. Evolution Dynamics of a Ring/Cogwheel Multicompartment Micelle. The dynamic process of evolution is important for understanding the formation of a micelle that may lead to useful information for structural control and tuning. For multicompartment micelles with complicated inner structures, it is difficult to give insight into molecular-level details of the evolution process experimentally, for which computer simulations such as the DPD technique is a powerful tool. Particularly, for mixed multicompartment micelles formed by blending block copolymers with different architectures, an understanding of the dynamic process of evolution can also help to reveal the motions of different copolymers during self-assembly, leading to deep insight into the underlying mechanisms. In this work, the evolution of the novel toroidal multicompartment micelle with a ring/cogwheel core formed by blending star triblock copolymer A4B19C2 (5%) with linear triblock copolymer B2A6C1 (10%) was studied by DPD simulations. Three series of simulations were performed: (1) the two kinds of block copolymers were mixed at the molecular level prior to micellization; (2) toroidal micelles formed from linear
copolymers were blended with star copolymer chains; and (3) “hamburger” micelles formed from star copolymers were blended with linear copolymer chains. The corresponding snapshots of evolution processes are given in Figures 4-6 respectively, in which the last snapshot in each figure presents the morphology in the equilibrium state for which the time scale was selected to be similar for comparison. Obviously, toroidal multicompartment micelles with ring/ cogwheel cores were all formed finally in the three options; however, the formation processes were different. Figure 4 shows that, by premixing at molecular level, corporative self-assembly of the copolymer chains occurred, in which small spherical micelles were formed first that contain both kinds of copolymers, with C blocks of the linear copolymers in the inner core and C blocks of star copolymers distributed on the outer surface. The spherical micelles grew to larger cylindrical micelles with a centipede-like C domain by collision. The large cylindrical micelles finally closed up and formed toroidal multicompartment micelles with ring/cogwheel cores. This mechanism is common in the formation of toroidal micelles and vesicles.23,24 When two-compartment toroidal micelles formed from linear triblock copolymers were mixed with star triblock copolymer chains (Figure 5), the star copolymers assembled into dispersed small micelles first, then they fused onto the toroidal core of the linear copolymers and became the cogs of the induced cogwheel-like C domain. On the other hand, when “hamburger” micelles from star copolymers were mixed with linear copolymer chains (Figure 6), the linear copolymers aggregated into small disklike micelles first, then they grew up by collision to form large disklike micelles. The large disklike micelles were energetically unfavorable, and they self-organized into ringlike micelles to lower the energy. In the meantime, C blocks of the star copolymers fused onto the ringlike C domain of the linear copolymers to form a cogwheel-like C domain, leading to a toroidal multicompartment micelles with a ring/cogwheel core. Although a similar formation process had been observed for vesicles theoretically,24 additional simulations were performed with different initial configurations to confirm this mechanism. The results show that the same process was always obtained. It seems that this may be a possible pathway; however, a definite conclusion can be derived only when confirmed by future experimental observations.
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Figure 5. Evolution of a toroidal multicompartment micelle with a ring/cogwheel core obtained by mixing toroidal micelles from linear copolymer with star copolymer chains (B blocks and solvent were omitted for clarity; A blocks, red; C blocks of linear copolymers, green; C blocks of star copolymers, blue. Views with and without A blocks were both given).
Figure 6. Evolution of a toroidal multicompartment micelle with a ring/cogwheel core obtained by mixing “hamburger” micelles from star copolymers with linear copolymer chains (B blocks and solvent were omitted for clarity; A blocks, red; C blocks of linear copolymers, green; C blocks of star copolymers, blue. Views with and without A blocks were both given).
The above simulations show that, although the initial state of mixing can influence the pathway for micelle formation, the final morphology and structure are little affected; however, the size and the fine structure of micelles formed may be controlled by adopting different mixing options, leading to a useful strategy for fine control of micellar structures. On the other hand, the initial state largely influences the evolution speed. Our simulations show that option 1 is the slowest one to reach equilibration. The reasons may be that, although larger interfacial energy exists in this mixing option, the molecules are more dispersed and require more time to form the micelles. Therefore, in addition to the equilibrium structure, the effect of the mixing option on the kinetics of morphological evolution should be considered in future study. In order to further understand the formation process, the changes of energy estimated by the conservative interactions
Figure 7. Time evolution of the conservative energies corresponding to Figure 5.
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Figure 8. Morphologies of multicompartment micelles obtained by blending star copolymers (a,b,c) with linear copolymers (d,e,f) (B blocks and solvent were omitted for clarity; A, red; C, green).
in the evolution process described in Figure 5 were calculated, as an example, with the following equation:
(9)
while the conservative energy between copolymers increased to a constant. This illustrates that the toroidal multicompartment micelles with ring/cogwheel cores were formed through minimizing the interaction energy between the copolymers and solvent, similar to that for vesicles.25
The results are shown in Figure 7, where the conservative energies between copolymers, between copolymer and solvent, as well as the total are given respectively. Obviously, during the evolution process of the mixed micelles, both the conservative energy of the system (denoted “total”) and that between copolymers and solvent decreased with evolution to constants,
3.4. Effects of Copolymer Chain Compositions. For a given binary block copolymer system, the morphology and structure of the mixed micelles formed can be tuned by tailoring the blending ratio. On the other hand, they can also be controlled by changing the constituent copolymer chain compositions (by this way, the micelles formed by pure block copolymers can be changed). To give a crude preview of controlling micellar morphology and structure by changing the compositions of
VC )
1
aij(rc - rij)2 ∑ 2 i
