Effect of Chain Architecture on Self-Assembled Aggregates from Cyclic

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Effect of chain architecture on the self-assembled aggregates from cyclic AB diblock and linear ABA triblock copolymers in solution Yongbing Song, Teng Xie, Run Jiang, Zheng Wang, Yuhua Yin, Baohui Li, and An-Chang Shi Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00630 • Publication Date (Web): 15 Mar 2018 Downloaded from http://pubs.acs.org on March 19, 2018

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Effect of chain architecture on the self-assembled aggregates from cyclic AB diblock and linear ABA triblock copolymers in solution Yongbing Song†, Teng Xie†, Run Jiang†, Zheng Wang†, YuhuaYin†*, and Baohui Li†, †

School of Physics, Nankai University, Tianjin 300071, China

An-Chang Shi‡ ‡

Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada

Abstract: The self-assembly behaviors of two block copolymers with the same chain length but different chain architectures (cyclic AB, linear ABA) in B-selective solvents are investigated using Monte Carlo simulations. A morphological transition sequence, from spherical micelles to cylindrical micelles, to vesicles and then to multicompartment vesicles, is observed for both copolymer systems when the interaction between the solvophobic A-block and the solvent is increased. In particular, toroidal micelles could be formed in triblock systems due to the presence of the bridging chains at the parameter region between cylindrical micelles and vesicles whereas disk-like micelles are formed in cyclic systems. The simulation results demonstrated that the architecture of block copolymers could be used to regulate the structural characteristics and thermal stability of these self-assembled aggregates.

*

To whom correspondence should be addressed. E-mail: [email protected]

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Introduction The self-assembly of block copolymers in solutions has been extensively investigated for many decades and a large number of nano-morphologies have been observed.1,2 Previous extensive studies have revealed that the self-assembled morphologies include not only the basic structures such as spherical micelles, cylindrical micelles and bilayer vesicles, but also numerous novel structures such as toroidal micelles,3,4 tubules,5 large compound vesicles,6 multilamellar vesicles7 and multicompartment vesicles.8,9 Much attention have been paid to these aggregates due to their potential or practical applications in, e.g., catalytic nanoreactors,10 drug delivery vehicles,11,12 and molecular imaging agents.13,14 The formation of various morphologies of self-assembled block copolymer aggregates depends strongly on the copolymer block length, composition, concentration, and the solvent quality.1 In addition, the architecture of the block copolymer chains could also play an important role on their self-assembly behavior. In the past decades, a number of studies have been carried out to clarify the micellization behavior of block copolymers with different chain architectures. It has been demonstrated that the entropic penalty due to the conformational change from unimer state to micellar state is the key factor to explain the architectural effect on the micellization.15-21 For example, the micelle formation of linear ABA triblock copolymers in a solvent selective for the middle block is more difficult than that of linear AB diblock copolymers. 22 This difference in the micellization behavior arises from an additional entropy penalty associated with the formation of flower-like micelles in which the two end blocks must fold back into the core so that the ABA copolymer chain would assume a looping conformation. Compared to linear block copolymers, the self-assembled aggregates from cyclic 2


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copolymers exhibit unique properties because of the topological constraint due to the ring architecture.23 Booth and coworkers24,25 have compared the aggregation number and hydrodynamic radius of spherical micelles formed by cyclic diblock copolymers with that of their linear triblock and diblock analogues. They found that for ethylene oxide (EO) and 1,2-butylene oxide (BO) block copolymers of different architectures in EO-selective solvents, the micelles assembled from cyclic diblock copolymers (cyclic-PBO8-b-PEO42) were larger than that from the linear triblock copolymer PEO21-b-PBO8-b-PEO21, but smaller than that from linear diblock copolymer PBO8-b-PEO41. Iatrou et al.26 reported similar findings, where a significantly larger aggregation

number

and

hydrodynamic

radius

for

aggregates

of

linear

poly(styrene)-b-poly(butadiene) (PS-b-PBD) have been observed in a PS-selective solvent, in comparison to analogous cyclic PS-b-PBD and linear PS-b-PBD-b-PS. However, when the same copolymers were assembled in a PBD-selective solvent, the micelles of the linear PS-b-PBD-b-PS displayed the largest values of aggregation number and hydrodynamic radius. Additionally, Zhang et al. 27 have observed that the hydrodynamic diameter of cyclic diblock copolymer micelles was approximately half of the micellar diameter formed from the equivalent linear diblock copolymers. Yamamoto and Ree et al.28 have studied the structural differences between assemblies of cyclic poly (n-butyl acrylate-b-ethylene oxide) (PBA10-b-PEO69) and linear PBA5-b-PEO69-b-PBA5 in a PEO-solvent selective. They observed that the micelles formed by the cyclic block copolymers possess a more compact core and shell than the linear triblock copolymers. More recently, enhanced thermal and salt stability of the flower-like micelles formed by cyclic AB block copolymers has been obtained in comparison with the linear ABA counterparts in a B-selective solvent, although they showed comparable values of critical micelle concentrations (cmc) and hydrodynamic 3


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radius of aggregates.29,30 The combination of reduced size and unique chain conformations of the cyclic copolymer micelles could be advantageous for applications such as potential drug delivery carriers. However, because of difficulties in the synthesis and purification of cyclic copolymers, only a few reports are available for a comparison of the characteristics of non-spherical micellar morphologies, such as vesicles, composed of equivalent cyclic and linear block copolymers.31,32 Nevertheless, experimental33 and simulation34 studies both demonstrated that the cyclization of a linear copolymer chain induces a remarkable change in the micellar morphology. Recent advancements in synthetic methodologies have allowed the fundamental properties and potential utilities of cyclic copolymers to be explored.35 Understanding the topology effects on various nanostructures will help to design the topology-based polymer material with novel properties and functions. 36 In our previous study, we have investigated the topology effects of cyclic AB diblock copolymers by comparing their self-assembly behavior with that of their linear AB diblock counterparts, focusing on the case where the dimension of the cyclic chains is much smaller than linear chains in self-assembled aggregates.34 In the present study, we focus on the topology effect on the copolymers with comparable chain dimensions in an aggregated state. Specifically, we examine the self-assembly behaviors of cyclic-AB diblock copolymer and its linear-ABA triblock counterparts in B-selective solvents using Monte Carlo simulations. In this case, both of cyclic and linear copolymers tend to form flower-like micelles in which the corona formed by looped hydrophilic blocks. However, different with the triblock copolymer, the cyclic copolymer lacks chain ends. It is therefore desirable to investigate the effect of the chain topology on the self-assembly behavior of the copolymers. 4


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Model and Methods Monte Carlo simulations of the self-assembly of model block copolymers are carried out using the simulated annealing method applied to the single-site bond fluctuation model.37,38 Detailed descriptions of the model and simulation algorithm have been given elsewhere. 39,40 In what follows only a brief account of the model and method is given for completeness. The model system is embedded in a simple cubic lattice of size

V = Lx × Ly × Lz with periodic boundary conditions applied in all three directions. In most of the simulations, a simulation box with Lx = Ly = LZ = L = 72 is used. In some cases a larger simulation box with Lx = Ly = LZ = L = 96 is employed to examine the reproducibility of typical structures. The block copolymers examined in the current study are cyclic diblock copolymers Am Bn or linear triblock copolymers

Am Bn Am , where m and n are the numbers of the A- and B-segments, respectively. For all the simulations reported in this paper, the chain length is fixed at N = 24 for both cyclic and linear systems. If not specified, two block copolymers, cyclic-A18B6, and linear-A9B6A9, with cyclic and linear architectures are simulated in this study. The copolymer concentration is defined by cP = nc N / V , where nc is the number of copolymer chains in the system. To study the transition from spherical micelles to other self-assembled morphologies, the copolymer concentration in our simulation systems is kept at a relatively high value of c p = 0.06 . The copolymers are assumed to be self-avoiding, i.e. two or more segments cannot occupy the same lattice site at the same time. Within one copolymer chain, two consecutive segments are connected by 5


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bonds that could adopt the length of 1 and 2 . Therefore, each lattice site has 18 nearest neighbor sites. To avoid chain self-knoting and concatenation, the initial configuration of the simulations is generated by placing an array of copolymer chains onto the lattice such that they are parallel to the z-axis in the form of once-folded linear chains. This initial configuration is the same as that used in our previous study.34 After the desired number of chains has been generated, the remaining empty sites were assigned to solvent molecules. The trial move used in the simulations includes the exchange between segments and solvent molecules. The partial-reptation movement41,42 is also included to accelerate the relaxation process of the chains. Bond crossing is always forbidden during the relaxation. The acceptance or rejection of the attempted move is further governed by the Metropolis rules.43 The energy of the system is the objective function of the simulated annealing procedure. In the simulations, the interaction between segments are described by the 18 nearest-neighbor interactions. There are three types of effective pairwise interactions in the system, which are interactions of block A and block B, block A and solvent, block B and solvent. These interactions are modeled by assigning an energy

Eij = ε ij k BTref to each nearest-neighbor pair of unlike species i and j, where i, j = A, B, and S (solvent). Here ε ij is the reduced interaction energy, k B is the Boltzmann constant, and Tref is a reference temperature. In our simulations, we set ε AB = 1.0 to ensure the immiscibility between the A- and B-segments, whereas we set ε BS = −1.0 6


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to model the selectivity of the solvents. The value of ε AS is varied from 0.3 to 7.0. These parameters are chosen so that the solvent is a poor -solvent for the A-blocks but a good one for the B-blocks. In all cases, ε ii = 0 with i = A, B, and S. Staring from the initial state, we apply a linear annealing schedule, T j = fT j −1 , is used, where Tj is the temperature used in the jth annealing step and f is a scaling factor. The annealing was continued until the annealing steps reached a predetermined value. In all the simulations f = 0.94 is used. The initial temperature is set at T1 = 70Tref and 70 annealing steps are performed. At each annealing step, 500000

Monte Carlo steps (MCS) are carried out. One MCS is defined as the average number of moves required for all the polymer segments to be visited once.

Results and Discussion In this section, we present simulation results on various aggregates formed from linear-A9B6A9 and cyclic-A18B6 in a B-selective solvent. Figure 1 shows snapshots of typical morphologies formed from the two block copolymers as a function of the repulsive interaction between the solvophobic A-block and the solvent ( ε AS ). The effects of chain topology on the structural characteristics of these aggregates including spherical micelles, cylindrical micelles, vesicles and multicompartment vesicles (MCV) will be discussed, followed by an examination of the effects of chain topology on the thermal stability of spherical micelles and vesicles.

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Figure 1. Snapshots of typical morphologies of aggregates formed from (a) linear-A9B6A9; (b) cyclic-A18B6 as a function of ε AS . The A-blocks are shown in red, B-blocks in green, and solvents inside the aggregates in blue, respectively.

In order to examine the robustness of the observed morphologies, we have carried out simulations using bigger simulation box (results are given in the supporting information). It is observed that the simulated morphologies for cyclic copolymers shown in Figure 1 do not depend strongly on the system size, indicating that the results obtained with a box size of L = 72 represent typical equilibrium morphologies of the system. We have also examined the influence of the annealing rate on the self-assembled morphologies using different annealing factor f (see the supporting information). The results with different values of f show that an annealing rate of f = 0.94 used in this study is a suitable annealing rate to obtain equilibrium states. Spherical micelles As seen in Figure 1, spherical micelles composed of A-core and B-shell are observed at small ε AS for both copolymers. In particular, a group of interconnecting micelles are formed by linear triblock copolymers due to some soluble middle blocks bridging between neighboring solvophobic cores, whereas only individual spherical micelles are formed by cyclic diblock copolymers. The fraction of bridging chains in 8


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the spherical micelles from A9B6A9 is small. For example, the fraction of bridging chains in the triblock system is about 8% at ε AS = 0.5 , where the total number of chains for system is 933 and the number of micelles is 26. Therefore, the average number of bridge chains is only about 3 per micelle. Thus, the influence of the bridge chains on the characteristics of micelles can be ignored in this triblock system. It is noted that in the following calculations, a micelle is defined as a group of two or more chains having multiple A-A interchain contacts.44 To examine the effect of chain architecture on micellar properties, geometrical characteristics of micelles are obtained (Table 1). Specifically, the micellar radius of gyration and the eccentricity (η ) given in Table 1 characterize the size and the shape of the micelles, respectively. Here, η is calculated from the equation,45

η = 1−

I min , I avg

(1)

where Imin is the smallest principal moments of inertia and Iavg is the average of the three principal components of the moment of inertia. The eccentricity is defined such that when the micelle is a perfect sphere, I min / I avg = 1 and η = 0 . As can be seen from table 1, the eccentricities of micelles formed by the two types of block copolymers are very small (η < 0.08 ), indicating that the micelles are nearly spherical. We find that the average size of the spherical micelle ( R = 3.96 ) and the solvophobic micellar core ( RC = 3.03 ) for the cyclic copolymers are both smaller than that for the linear triblock system ( R = 4.72 , and RC = 3.38 ). We have also calculated the corona thickness of spherical micelles according to the RS = R − RC , which is obviously smaller for cyclic diblock system (0.93) than that for linear triblock system (1.34). In addition, the average number of A-segments in a micelle (denoted by N A ), which is 9


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proportional to the average aggregation number, or number of copolymer chains, of the micelle ( N agg = N A 18 ), is 442 for the cyclic copolymer micelle and 646 for the linear copolymer micelle.

Table 1. Characteristics of the spherical micelles formed by linear-A9B6A9 and cyclic-A18B6 at ε AS = 0.5 Characteristics

Linear-A9B6A9

η

0.066

0.077

R

4.72

3.96

Rc

3.38

3.03

Rs

1.34

0.93

NA

646

442

Cyclic-A18B6

η : Eccentricity of the micelle; R: Radius of gyration of the micelle; Rc: Radius of gyration of the micellar core; Rs: Thickness of the micellar shell; NA: Average number of A-segments in a micelle.

To characterize the structure of such spherical micelles obtained in our simulations, the density profiles of the A, B-segments are calculated as a function of the distance from the micellar center of mass. The segment density profiles for the spherical micelles with the same number of A-segments ( N A = 468 ) from linear-A9B6A9 and cyclic-A18B6 are shown in Figure 2a. The density of the A-segments is 1.0 in the cores of the spherical micelles ( r ≤ 4 ) for both of the two block copolymers. In the interface region of the core-shell ( 4 < r < 5.5 ) the density of the A-segments is higher for the cyclic copolymers than that for linear triblock copolymers. In the shell of the spherical micelle ( 5.5 < r < 7.5 ), the density of the 10


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B-segments from cyclic copolymers is also higher than that from linear triblock copolymers. This observation indicates that the cyclic diblock copolymers form a denser core and shell than the corresponding linear triblock copolymers. We also investigated the density distributions of the end A-segments of the linear copolymers, the middle A-segments of cyclic copolymers and the junction A-segments of both copolymers as a function of the distance from the micelle center of mass. The results are shown in Figure 2b. The distribution of the junction A-segments is broader and its maximum lower for the linear triblock copolymers than that for the cyclic copolymers. Furthermore, the plot of Figure 2b shows that, for the case of linear triblock copolymers, there is no free end A-segments found at the center of the micellar core. These features of density distributions indicate that linear copolymers have looser chain packing structure in the core of the spherical micelles than that of the cyclic copolymers.

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Figure 2. Radial density distribution for spherical micelles with N A = 468 from linear-A9B6A9 and cyclic-A18B6: (a) total A and B segments; (b) the junction A-segment, and the end A-segments or the middle A-segments.

To further understand the effects of chain architecture on the density profiles observed in Figure 2, we analyzed the probability distributions of loop angles of the B-blocks for the cyclic and linear chains (Figure 3). The loop angle ϕ is defined as the angle between the two vectors from the position of the central segment of the solvophilic B-block to the positions of the two junction segments,21

cos(ϕ ) =

(rj1 − rc ).(rj 2 − rc ) rj1 − rc rj 2 − rc

,

(2)

where r is the position vector and the subscripts j1, j2, c indicate the two junction segments and the central segment, respectively. Considering the number of the segments in the solvophilic block of the chains is even in our simulations, the average position of the two segments in the middle of the solvophilic chain is used as the position of central segment in the original definition. As shown in Figure 3, most of the chains take tightly folded conformations with cosϕ > 0 ( ϕ < 900 ) for both two systems. The fraction of linear copolymers is found to be smaller than that of the 12


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0

cyclic copolymers in the region of folded conformations with cosϕ > 0.1 ( ϕ < 85 ), whereas the ordering of the fractions is reversed in the region of open conformations with cosφ < 0.1. This feature indicates that the linear copolymers in the micelles prefer open conformations with their end A-segments distributed at the opposite regions on the spherical micelles. This behavior arises from the fact that there is no topological constraint on these two free ends of linear triblock copolymer molecules. In particular, the linear topology of the ABA copolymers explains the observation that the end A-segments for the linear triblock copolymers vanishes at the center of spherical micelles (Figure 2b).

Figure 3. Probability distributions of the loop angle of hydrophilic B-block for spherical micelles with N A = 468 formed from linear-A9B6A9 and cyclic-A18B6.

Our simulation results for the spherical micelles could be compared with available experimental studies. Iatrou et al. 26 reported that the aggregation number, core radius, and corona thickness ( N agg = 400, Rc = 17.2nm, Rs = 10.8nm ) for aggregates of linear PS14-b-PBd22-PS14 in a PBd-selective solvent (n-decane), are significantly larger than their corresponding values for micelles formed from the 13


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cyclic PS28-b-PBd22 ( N agg = 210, Rc = 14.5nm, Rs = 9.5nm ). Our simulation results are consistent with these results. Yamamoto and Ree28 have performed a detailed small angle X-ray scattering (SAXS) investigation on the structural differences between assemblies of cyclic PBA10-b-PEO69 and linear PBA5-PEO69-PBA5. They found that the cyclic block copolymer micelle formed a more compact and denser PBA core ( Rc = 1.69 − 1.78nm ) and a thinner and denser PEO shell ( Rs = 4.13 − 4.27nm ), compared to that of the corresponding linear block copolymer micelle ( Rc = 1.85 − 1.94nm, Rs = 4.62 − 4.65nm ). These observations also agree with our simulation results. However, in their experiment the aggregation number determined from the SCM analysis for the micelle composed of the cyclic block copolymer ( N agg = 10.02 ) was just slightly smaller than that for the micelle composed of the linear block copolymer ( N agg = 11.61 ), while in our simulation, this difference is more significant, that is N agg = N A / 18 = 25 for the cyclic block copolymers and

N agg = N A / 18 = 36 for the linear block copolymers. This discrepancy could be due to the much longer solvophobic A-block used in our simulations ( f A = 0.75 ). To confirm this point, we performed additional simulations for block copolymers with

f A = 0.25 , i.e., linear-A3B18A3 and cyclic-A6B18. The results show that N agg = 90 / 18 = 5 for the cyclic block copolymers, which is slightly smaller than that for the linear block copolymer ( N agg = 110 / 18 = 6.1 ). Therefore, the composition of the block copolymers also influences the topology effect.

Cylindrical micelles

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As shown in Figure 1, with the increase of ε AS , the morphology of the aggregates changes from spherical micelles to a mixture of spherical and short rod-like micelles. The structure transition occurs for the linear triblock copolymers at

ε AS = 0.9 , whereas this transition happens at ε AS = 1.6 for the cyclic diblock copolymers. This difference could be attribute to the stronger stretching of the solvophobic blocks in the larger core of the spherical micelles, quantified by the

Rc listed in table 1, formed from the linear triblock copolymers. Similar to the case of spherical micelles formed by the linear triblock copolymers, there exists a small fraction (about 4% for triblock copolymer chains at ε AS = 1.0 ) of bridging chains with one end A-block in the rod-like micelle core and the other end A-block in another spherical micelle or rod-like micelle. For both cases, the rod-like micelles exhibit a relatively narrow distribution of solvophobic core diameters, but a broader distribution of rod lengths. Similar to the observations from the spherical micelles, the average solvophobic core diameter of the rod-like micelles formed by the cyclic block copolymers is much smaller than that of the linear copolymer micelles. With further increasing of ε AS , the fusion of some short rods and spheres for the cyclic diblock copolymers could occur, resulting in a long cylindrical micelle (Figure 1b). Because of the presence of bridging chains for the case of linear triblock copolymers, the situation becomes more complicated. The spherical micelles prefer to merge into neighboring rod-like micelles to form a threefold “Y-like” junction (Figure

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1a). Similar structure has been reported in several simulation and experimental studies on the self-assembly of triblock copolymers. 46-48 Disk-like and toroidal-like micelles

Figure 4. Typical toroidal micelles for linear- A9B6A9 at ε AS = 1.5 .

By further increasing ε AS , the cylinders formed by the cyclic diblock copolymers transform into bilayers in the form of disk-like micelles to reduce the stretching of the chains. This is consistent with previous experimental and theoretical studies of crew-cut micelles formed from linear diblock copolymers in solution. 49,50 It should be mentioned that, in our simulations, the disk-like micelles formed by the cyclic diblock copolymers is a stable structure.34 For the linear triblock copolymers, toroidal micelles, instead of the disk-like micelles, are formed from the Y-like junctions to reduce contact, induced by the free end caps, between the solvophobic blocks and the solvents. All of the toroidal micelles are constructed by Y-junctions, spherical end caps and cylindrical loops, and the cylindrical parts of these toroidal structures have a uniform diameter. However, the morphologies of the toroidal micelles are different from independent simulations with different random number seeds at the same ε AS . There are at least four types of toroidal micelles formed from the triblock copolymers at ε AS = 1.5 as shown in Figure 4: a three dimensional looped structure with protruding tails and no end caps (Figure 16


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4a), one end cap (Figure 4b), two end caps (Figure 4c), and without protruding tails and end caps (Figure 4d). When periodic boundary conditions are considered in this case, the first type of toroidal micelles form an extended cage-network structure.51 The existence of closed ring structures at different positions of cylindrical micelles and the complex multi-ring structure may indicate that the end-to-end cylinder connection cannot be the exclusive toroidal structure-forming mechanism in this system, in agreement with the prediction by Pochan et al..3 Experimentally, toroidal micelles have been observed in AB diblock, ABA or ABC

triblock

copolymer

solutions.52-54

In

the

experiments

of

poly

(1,2-butadiene-b-ethylene oxide) (PB-PEO) diblock copolymers with high molecular weight PB blocks, Bates et al.52 demonstrated the formation of “Y-junctions”, which assemble into a three-dimensional network in water at compositions between those associated with vesicle and wormlike micelle morphologies. This observation is in agreement with our simulation results for the linear-A9B6A9 triblock copolymers. Especially, complex micelles similar to the last three types of structures shown in Figure 4 have also been observed in their experiments. Their small-angle x-ray scattering patterns, taken from the network phase, indicated that the local domain curvature remains nearly cylindrical. This feature is also observed in the toroidal or cage-like morphologies formed by the triblock copolymers in our simulations. Vesicles

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Figure 5. Two possible morphological transition sequences from toroidal micelles to vesicles for linear- A9B6A9.

Vesicular aggregates could be formed from both of the two types of block copolymers with further increasing ε AS . However, as mentioned above, the transition sequences from cylindrical micelles to vesicles are quite different for the different chain architectures. For the cyclic diblock copolymers, the transition from cylinders to disk-like micelles, and then to vesicles is observed, while for the linear triblock copolymers, the transition from cylinders to Y-junctions, then to toroidal micelles, and finally to vesicles is observed. For the case of triblock copolymers, two typical morphological sequences from toroidal micelles to vesicles could occur (Figure 5). For the morphological sequence (a), with increasing ε AS , the cage-like micelles are constructed from toroidal micelles and then more and more holes appear in the cage-like micelles, at the same time the cylindrical struts of the cage become flattened to form a shell, finally to form a vesicle. For the morphological sequence (b), the evolution of the toroidal structure is similar to the morphological sequence (a) except

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that the toroidal micelles and vesicles are connected by rods to form a necklace-like structure when the periodic boundary conditions are taken into account. Similar net-cage micelles have also been experimentally observed in amphiphilic multiblock copolymers in aqueous solution,55,56 and their formation has been investigated by computer simulation study of diblock copolymer solution after a quench from a homogenous state.4 The simulation results showed that such micelles might form in the vicinity of the critical micelle concentration via the nucleation, growth, and subsequent breakup of vesicles. In our computer simulations the transition from cage micelles or toroidal structures to vesicles is observed from the linear triblock copolymers. To examine the structural details of the vesicles from the two copolymers, we plot the radical density distribution of A, B segments as a function of the distance from the center of mass at ε AS = 4.0 (Figure 6). The thickness of the solvophobic wall could be obtained by calculating the width at half maximum of the peak of the A segment distribution curve. It is found from figure 6a that the thickness of the solvophobic wall in the vesicle formed by the cyclic diblock copolymers is a little thinner than that of the linear triblock copolymers. From Figure 6b, the density profile of the solvophilic B-segments display two peaks corresponding to the two solvophilic B-rich layers at the outer surface and inner surface of the solvophobic wall, respectively. It can be clearly seen that the density of the B-segments at the outer surface is lower than that at the inner surface for both copolymers, which is a typical feature for simple vesicle structure. Comparing with the position of the peaks of the 19


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B-segment density at the inner surface for the two copolymers, we find that the peak of the cyclic copolymers shifts slightly to the direction of increasing r, indicating a slightly bigger aqueous core of vesicles formed by the cyclic copolymers than that of the linear copolymers. Furthermore, we also notice that the peak value of B-segment density at the outer surface of the vesicle from the linear triblock copolymers is higher than that from the cyclic copolymers. The difference of the peak values could be understood based on the fact that eliminating the free ends from the cyclic chains compared with the triblock chains leads to a more restricted conformation at the interface.

Figure 6. Radial density distribution of (a) A-segments; (b) B-segments for vesicles formed by

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linear-A9B6A9 and cyclic-A18B6.

In our simulations, the vesicle structures are stable in a wide range of ε AS for the two copolymers investigated in the current study. That is, ε AS = 1.9 ~ 4.8 for the linear-A9B6A9, ε AS = 3.8 ~ 6.4 for the cyclic-A18B6, respectively. In Figure 7, we examine the effects of ε AS on the structure of vesicles formed by the two copolymers. First, from Figure 7a, it can be seen that the size of the vesicles (the radius of gyration of aggregate) decreases with increasing ε AS for both copolymers. But, the shrink of the vesicle structure from the triblock copolymers is clearly more evident than that from the cyclic diblock copolymers. For a given value of ε AS , (e.g. ε AS = 4.0 in Figure 7a), the size of the vesicle from the triblock copolymers is a little

smaller than that from the cyclic copolymers, which is contrast to the case of spherical micelles where the size of micelle for the linear triblock copolymers is larger. This is consistent with the experimental observations,32 where the size of vesicles formed by linear PS40-PEO48-PS40 and cyclic PS86-PEO48 is 109 nm and 112 nm recorded by dynamic light scattering, respectively. Second, from Figure 7b, an increasing thickness of the solvophobic wall could be seen by increasing the value of ε AS for both copolymers. The change in the thickness of the solvophobic wall is more sensitive to the increase of ε AS for the linear triblock copolymers than that for the cyclic diblock copolymers.

In addition, at the same value of ε AS , the vesicle

composed from the cyclic diblock copolymers possess the thinnest solvophobic wall when compared with the linear case. This is also shown in Figure 6a. Finally, a larger ε AS also results in a smaller fluidic core of vesicle for both systems, as shown in 21


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Figure 7c, where the number of solvent molecules located in the interior of vesicles decreases with ε AS . The increase of the ε AS results in an increase of the interfacial energy between the solvophobic wall and the solvents outside the wall. To minimize the total interfacial area so as to reduce the interfacial energy, there is a decrease in the vesicle size and the fluidic core size, at the same time an increase in the thickness of the solvophobic wall. This explains the observations from Figure 7. It should be noted that only one vesicle was observed in our simulation box for both copolymers. This is different from experimental studies, where the block copolymers can self-assemble into many vesicles under given parameters. As a result, to minimize the total interfacial energy, the vesicles will increase their size as suggested by Luo and Eisenberg in their experimental studies for linear diblock copolymer solutions57.

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Figure 7. Characteristics of the vesicles from two block copolymers with the increase of ε AS

: (a)

the size of vesicle; (b) the hydrophobic wall thickness; (c) the number of solvent molecules in the interior of vesicle. A dashed line is plotted to guide the eyes.

Multicompartment vesicles When the repulsive interaction between the solvophobic A-block and solvent is further increased to 4.9, the triblock copolymers self-assemble to form a multicompartment vesicle8,34 with two fluidic cores, as shown in Figure 1a. Simulation results show that further increase of ε AS could lead to an increase of the 23


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number of fluidic cores while the size of each fluidic core decreases. Similar morphology transition is also observed from the cyclic block copolymers at ε AS = 6.5 , as shown in Figure 1b. In Figure 8a, we plot the radial profiles of the center of mass of the copolymers for simple vesicles and multicompartment vesicles formed by the linear-A9B6A9 and cyclic-A18B6 copolymers. For these two copolymer cases, the self-assembled vesicle displays two distinctive peaks in the distribution of the chains, indicating that the block copolymers form a bilayer structure at

ε AS = 4.5 . When ε AS is increased to 7.0, some chains in the outer layer are pushed into the inner part to form multicompartment vesicle with more than one fluidic core. As a result, the peak in outer part drops and the peak in the inner part become blurred due to the increased number of fluidic cores as shown in Figure 8a. Similar features are observed in the vesicles and multicompartment vesicles formed from the cyclic block copolymers. On the base of the center of mass distributions shown in Figure 8a, for the simple vesicle and multicompartment vesicle, we could divide the chains into two parts: the inner and outer chains according to their locations. Information about the conformations of these chains is obtained by calculating the probability distribution of loop angles of the B-blocks in vesicles and multicompartment vesicles. For the two copolymers, i.e. the linear-A9B6A9 and cyclic-A18B6, the results are shown in Figure 8b1 and 8b2, respectively. For the case of linear copolymers shown in Figure 8b1, the distribution of the triblock 24


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chains has a high peak at cosφ ≈ 0 for both inner and outer chains. No significant difference in the conformations of the outer chains could be observed when the morphology changes from vesicle to multicompartment vesicle. This is because the overall shape of the vesicle and multicompartment vesicle is almost spherical. A similar observation is also made for the case of the cyclic block copolymers as shown in figure 8b2. For the inner chains, however, the situation is very different. As shown in Figure 8b1, the probability distribution of the loop angle for the inner chains of vesicle ( ε AS = 4.5 ) is higher than that of multicompartment vesicle ( ε AS = 7.0 ) for cosφ > 0 , whereas it is lower for

cosφ < 0 . This observation indicates that the linear triblock chains in the interior of the multicompartment vesicle have more open conformations which would reduce the conformation entropy loss when comparing with the case of the vesicle. However, for the case of cyclic copolymers shown in Figure 8b2, because of the topological constraint of the ring architecture, there is no significant change in the distribution of loop angles of the inner chains for the multicompatment vesicle when comparing with that of the vesicle, although the peak at cosφ ≈ 0 becomes higher for the case of the multicompatment vesicle. Therefore, it could be concluded that the formation of the multicompartment vesicle may be easier for linear triblock copolymers than for cyclic block copolymers due to the reduced entropic penalty associated with the presence of two free ends.

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Figure 8. (a) Radial profile of center of mass of chains for simple vesicle ( ε AS = 4.5 ) and multicompartment vesicle ( ε AS = 7.0 ) formed by linear-A9B6A9 and cyclic-A18B6. A dashed line is plotted to distinguish between the inner and outer chains. And the corresponding probability distributions of loop angle of B-blocks for (b1) linear-A9B6A9; (b2) cyclic-A18B6.

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A similar morphological transition from vesicles to the multicompartment vesicles with the increase of the content of triblock copolymers in blends of diblock and triblock copolymers has been observed experimentally.8 The formation mechanism of compartmentalized vesicles was investigated using computer simulations by these authors. They suggested that the triblock copolymers prefer to distribute

inside

of

a

multicompartment

vesicle,

and

the

formation

of

multicompartment vesicles is due to the existence of the triblock copolymers. These observations are consistent with the results from the current study. Thermal stability To study the thermal stability of aggregates self-assembled from block copolymers with different chain architecture, we took spherical micelles obtained from the cyclic-A18B6, or linear-A9B6A9 at ε AS = 0.5 as the initial starting configuration and carried out simulations at increasing temperatures from T = Tref with a step of 0.5 Tref or 0.1 Tref (Figure S4). The average number of A-segments, N A , of one micelle is calculated. As shown in Figure 9a the N A of micelles from the linear-A9B6A9 and cyclic-A18B6 sharply decreases at T = 3.6Tref and T = 4.0Tref , respectively, indicating that the micelles become unstable at these temperatures. To understand this behavior, we analyze the changes of copolymer conformations, such as free, dangling, looping and bridging chains, in linear triblock system. The fraction of bridging and dangling chains began to increase with the temperature after T = 3.6Tref , at the same time, some free chains detached from the micelles were observed. The fraction of 27


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dangling chains increased faster than that of the bridging chains, which is consistent with the snapshot of the micelle at T = 4.0Tref and T = 4.5Tref where a large number of dangling chains could be seen (Figure S4). At T = 5.0Tref , the fraction of the looping chains is lower than 40%, implying the disintegration of the micelles. It is noted that topological effects on the thermal stability of spherical micelles have been observed by experimental studies, where the micelles from cyclic diblock copolymers were found to be much more stable than those form linear triblock copolymers. The lower thermal stability of the linear triblock aggregates was mainly attributed to the occurrence of intermicellar bridging via dangling chains, leading to agglomeration at lower temperatures. This effect is suppressed by the cyclic topology.29,30 The discrepancy between our simulation results and the experimental report could be explained by the much larger volume fraction of the solvophobic blocks used in our simulations and the larger aggregation number of micelle from linear-A9B6A9 than that from cyclic-A18B6 as mentioned previously. Because the larger enthalpic penalty associated with the chain end being pulled out from the core of the micelle, linear triblock copolymers with longer solvophobic blocks could enhance the stability of the micelles. In addition, the thermal stability of the vesicles from the linear-A9B6A9 and cyclic-A18B6 are also examined. The shape of vesicles is characterized by calculating the eccentricity (η ) of the aggregates (Figure 10a). The vesicles from the linear-A9B6A9 is generally spherical until T = 45Tref , indicated by the small 28


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value of η (less than 0.1) except a small peak at T = 27Tref . For vesicles from the cyclic-A18B6, the value of η starts to increase quickly (more than 0.3) at

T = 34Tref due to the deformation of the vesicle (see Figure S5). Furthermore, to monitor the change of the bilayer structure inside the vesicle, the radial density distributions of the chains is calculated. The radial density distribution function of typical bilayer structure is disturbed at T = 27Tref and

T = 33Tref for the linear-A9B6A9 and cyclic-A18B6, respectively. At this stage the solvents and the solvophilic segments appear at the solvophobic wall of the vesicle resulting in the increasing of the thickness of the wall as shown in Figure 10b and 10c. Then the solvophobic segments accumulated into the core of the aggregate, completely destroying the bilayer structure.

29


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Figure 9. Change of (a) the average number of the A segments in the spherical micelle from linear-A9B6A9 and cyclic-A18B6 respectively ; and (b) the fraction of each conformation

of the chains in linear-A9B6A9 solution, with increasing of the temperature.

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Figure 10. Change of (a) eccentricity; and the radial density distribution for vesicles from (b1) linear-A9B6A9 and (b2) cyclic-A18B6, with increasing of the temperature.

We notice that a higher thermal stability of vesicles from linear triblock copolymer than that from the cyclic counterpart has been observed in experiments, where the agglomeration of the disturbed vesicles appeared at 59oC for linear triblock copolymer and 52oC in the case of cyclic diblock copolymer.32 This is in agreement with our simulation results, when considering that the deformation of the spherical shape of whole aggregate occurs earlier for cyclic diblock copolymer than linear triblock copolymer. However, as we 31


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mentioned above, the bilayer structure inside the vesicle from linear triblock copolymer is destroyed at a temperature lower than that for cyclic diblock copolymers, due to the loosing of one of the chain ends from the inner layer of the wall of vesicle. From this viewpoint it could be conclude that the vesicle structure from cyclic copolymer is more stable than that from linear triblock copolymer.

Conclusions In this paper, we investigate the effects of chain architecture of block copolymers on the self-assembled morphologies and their thermal stability by using a simulated annealing method. The self-assembled morphologies of cyclic-AB and linear-ABA copolymers with the same chain length and same composition in B-selective solvents are investigated. Our simulation results show that a rich array of morphologies, such as spherical micelles, cylindrical micelles, vesicles, and multicompartment vesicles could be formed for both of the block copolymers with increasing the repulsive interaction between the hydrophobic blocks and solvent ( ε AS ).

In addition, toroidal

micelle is observed for the linear triblock system due to the presence of the bridging chains while the cyclic diblock systems tend to form disk-like micelles at the parameter region between cylindrical micelles and vesicles. The simulations also reveal that the architecture of copolymer chains plays an important role on their self-assembly behavior. In particular, to reduce chain conformational entropy loss due to the micellization, the triblock copolymers prefer to self-assemble into spherical micelles with larger size at small values of ε AS . 32


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In addition, because of the unique topological constraint of the ring architecture, the cyclic block copolymers form a more compact and denser hydrophobic core in micellar structure or a thinner and denser hydrophobic wall in vesicular structures, compared to that formed from linear triblock copolymers. This is consistent with previous experimental results. Furthermore, the thermal stability of these two morphologies is investigated. The spherical micelles and the bilayer structure from cyclic copolymer is more stable than that from linear copolymer due to the additional entropic penalty of folding the chains. A comparison of our simulation results and experimental reports indicates that the composition of the block copolymers could lead to a difference in the topological effect. The simulation results from the current studies provide insights for the effects of chain architecture on self-assembly behaviors and properties of copolymers. Hopefully, our simulation studies will stimulate the future experiments and help to design the topology-based polymer materials with novel properties and functions.

Author Information Corresponding Author ∗

Phone number: +86-022-23508403. E-mail: [email protected]

Notes The authors declare no competing financial interest.

Acknowledgments The research was financially supported by the National Natural Science Foundation of 33


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China (Grant Nos. 21674053, 20904027, and 21204040) and the Natural Science and Engineering Research Council (NSERC) of Canada.

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For Table of Contents Only

Effect of chain architecture on the self-assembled aggregates from cyclic AB diblock and linear ABA triblock copolymers in solution Yongbing Song, Teng Xie, Run Jiang, Zheng Wang, YuhuaYin*, Baohui Li, An-Chang Shi

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Figure1. Snapshots of typical morphologies of aggregates formed from (a) linear-A9B6A9; (b) cyclic-A18B6 as a function of εAS. The A-blocks are shown in red, B-blocks in green, and solvents inside the aggregates in blue, respectively. 46x14mm (300 x 300 DPI)


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Figure 2. Radial density distribution for spherical micelles with NA = 468 from linear-A9B6A9 and cyclicA18B6: (a) total A and B segments; (b) the junction A-segment, and the end A-segments or the middle Asegments. 123x183mm (300 x 300 DPI)


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Figure 3. Probability distributions of the loop angle of hydrophilic B-block for spherical micelles with NA=468 formed by cyclic-A18B6 and linear-A9B6A9. 58x41mm (300 x 300 DPI)


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Figure 4. Typical toroidal micelles for linear- A9B6A9 at εAS =1.5. 36x7mm (300 x 300 DPI)


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Figure 5. Two possible morphological transition sequences from toroidal micelles to vesicles for linearA9B6A9. 74x32mm (300 x 300 DPI)


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Figure 6. Radial density distribution of (a) A-segments; (b) B-segments for vesicles formed by linear-A9B6A9 and cyclic-A18B6. 121x177mm (300 x 300 DPI)


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Figure 7. Characteristics of the vesicles from two block copolymers with the increase of εAS : (a) the size of vesicle; (b) the hydrophobic wall thickness; (c) the number of solvent molecules in the interior of vesicle. A dashed line is plotted to guide the eyes. 159x306mm (300 x 300 DPI)


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Figure 8. (a) Radial profile of center of mass of chains for simple vesicle ( εAS = 4.5) and multicompartment vesicle ( εAS = 7.0) formed by linear-A9B6A9 and cyclic-A18B6. A dashed line is plotted to distinguish between the inner and outer chains. And the corresponding probability distributions of loop angle of B-blocks for (b1) linear-A9B6A9; (b2) cyclic-A18B6. 178x386mm (300 x 300 DPI)


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Figure 9. Change of (a) the average number of the A segments in the spherical micelle from linear-A9B6A9 and cyclic-A18B6 respectively; and (b) the fraction of each conformation of the chains in linear-A9B6A9 solution, with increasing of the temperature. 127x197mm (300 x 300 DPI)


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Figure 10. Change of (a) eccentricity; and the radial density distribution for vesicles from (b1) linear-A9B6A9 and (b2) cyclic-A18B6, with increasing of the temperature. 131x114mm (300 x 300 DPI)


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Effect of Chain Architecture on Self-Assembled Aggregates from Cyclic

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