A Simulation Study of Phase Behavior of Double-Hydrophilic Block

Dec 4, 2015 - ACS eBooks; C&EN Global Enterprise .... A Simulation Study of Phase Behavior of Double-Hydrophilic Block Copolymers in Aqueous Solutions...
0 downloads 0 Views 4MB Size
Download PDF
Article pubs.acs.org/Macromolecules

A Simulation Study of Phase Behavior of Double-Hydrophilic Block Copolymers in Aqueous Solutions Jiaping Wu, Zheng Wang, Yuhua Yin, Run Jiang, and Baohui Li* School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Nankai University, Tianjin 300071, China

An-Chang Shi Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada ABSTRACT: The phase behavior of double-hydrophilic AB diblock copolymers in concentrated aqueous solutions is investigated using a simulated annealing technique. Phase diagrams of the system are constructed as a function of the volume fraction and concentration of the copolymer (Φ) as well as the hydrophilicity difference between the two blocks. Rich phase transition sequences, especially reentrant phase transitions, such as lamellae → gyroid → hexagonally packed cylinders → gyroid → lamellae → disorder, are observed for a given copolymer with decreasing Φ. By analyzing the variations of the average contact numbers between the A or B monomers and solvents, and of the effective volume fractions, the mechanisms of the reentrant, the order−order, and the order−disorder transitions are elucidated. The difference in hydrophilicity or in volume fraction can be used to tune the degree of swelling of the two blocks, resulting in a nonmonotonic variation of the effective volume fraction of the A (or B)-rich domain with the decrease of Φ, thus inducing the reentrant transitions. Our results are compared with those from available experiments, theory, and simulation and also with the simulation result of an amphiphilic diblock copolymer.

■

given block copolymer.18−22 Furthermore, in dilute solutions, various micelles or aggregates can be observed.23−26 Another interesting class of block copolymers is the double-hydrophilic BCP, which are composed of two hydrophilic blocks, albeit with different degree of hydrophilicities. Compared with the amphiphilic BCPs, the aqueous solution phase behaviors of double-hydrophilic BCPs are less well-understood.27−29 In the present work, we investigate the self-assembly of doublehydrophilic BCPs in concentrated aqueous solutions. It should be emphasized that in a double-hydrophilic BCP all of the blocks are hydrophilic, and there is no hydrophobic components in the polymers, whereas an amphiphilic BCP has at least one hydrophobic block. For the phase behavior of permanently double-hydrophilic BCPs in concentrated aqueous solutions, we are aware of two reported experimental studies. Meier and co-workers first reported the phase behavior of a single double-hydrophilic BCP [PEO113−PMOXA85] in concentrated aqueous solutions.27 They observed that at low temperatures a lamellar lyotropic mesophase occurs above a polymer concentration of ∼60 wt %, while another mesophase, which they assumed as hexagonal

INTRODUCTION Block copolymers (BCPs) have attracted much scientific attention because their self-assembly has been proved to be one of the bottom-up strategies for creating mesoscopic ordered structures with potential applications in various areas.1−3 For the simplest BCPs, i.e., the AB diblock copolymers, typical ordered phases including lamellae, hexagonally packed cylinders, body-centered-cubic spheres, and gyroid have been identified both experimentally and theoretically.4−7 Besides these phases, a narrow window of close-packed spherical phase was predicted,6 and recently, a narrow window of the Fddd (O70) phase was also predicted theoretically8 and later observed experimentally.9−11 All these phases were summarized in the up-to-date phase diagram for AB diblock copolymer melts more recently.12 A phase diagram has also been constructed from Monte Carlo simulations,13 and it contains most of the typical phases. The solution selfassembly, particularly aqueous self-assembly, of BCPs may provide important biological insights and open up the possibility of biomedical applications.14−17 The solution selfassembly of amphiphilic BCPs, i.e., hydrophilic−hydrophobic BCPs, has been extensively investigated.14−26 Previous studies have demonstrated that the use of solvents of different selectivity, and the temperature dependence of the selectivity, can provide access to several different ordered phases for a © XXXX American Chemical Society

Received: September 10, 2015 Revised: November 5, 2015

A

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

variations of the average contact number between A or B monomers and solvent molecules and of the effective volume fractions.

cylindrical phase, is sometimes observed at lower concentration. At high temperatures, a transition to isotropic phase occurs.27 They suggested that microphase separation in their sample is driven by the incompatibility of the two polymer blocks rather than the hydrophilic−hydrophobic repulsion. A recent study by Armes and co-workers found that for a series of doublehydrophilic BCP samples poly(ethylene oxide)−poly(2(methacryloyloxy)ethylphosphorylcholine) [PEOm−PMPCn] in concentrated aqueous solutions, well-defined and highly hydrated phases, including body-centered- cubic spheres (S), hexagonal packed cylinders (C), and lamellar (L) phases, were observed.28 They suggested that the self-assembly in their samples is driven by the configuration entropy of the two blocks rather than by hydrophobic interactions. Furthermore, for the lamella-forming PEO114−PMPC23 sample, phase transitions with sequence L → C(PEO) → L → disorder were observed upon decreasing the copolymer concentration.28 Such reentrant phase transitions have never been observed for amphiphilic BCPs. The phase behavior and the mechanisms of phase transitions, especially reentrant phase transitions in double-hydrophilic BCP system, however, remain to be explored. On the theoretical or simulation front, to the best of our knowledge, there are virtually no systematical studies of the phase behavior of double-hydrophilic BCPs in concentrated aqueous solutions. However, there have been a few studies of double-hydrophilic BCPs or related systems. Using dissipative particle dynamics (DPD) simulation, Huang and Wang investigated double-hydrophilic BCP-directed mineralization.30,31 For a two-component system composed of doublehydrophilic BCPs and solvents, they found that microphase separation occurs when the copolymer (A3B3) concentration (CP) exceeds 0.8, and a lamellar structure is observed for CP = 0.9.30 In a related study using random phase approximation (RPA) and self-consistent field theory (SCFT) calculations, Zhou and Shi found that diblock copolymer/homopolymer blends with three miscible binary pairs, A/B, B/C, and C/A can undergo microphase separation and form different ordered structures.32 This blend system is similar to double-hydrophilic BCP solutions, but no reentrant phase transitions were observed there. For the phase behavior of double-hydrophilic BCPs in dilute aqueous solutions, we are aware of a few reported studies. A recent study by Schlaad and co-workers found that for a double-hydrophilic BCP differences in hydrophilicity between the blocks are sufficient to drive polymer aggregation.29 The self-assembly of stimulus-responsive AB diblock copolymers that can be classified as a category of double-hydrophilic BCPs in highly dilute aqueous solution has been investigated.33−37 Studies of double-hydrophilic model networks have also been carried out.38,39 In the present work, we use a simulated annealing technique to explore the phase behavior of double-hydrophilic BCPs in concentrated aqueous solutions. Compared with experiments, theory and simulation are much less expensive in both economy and time. We obtain a variety of phase diagrams by varying the volume fraction and concentration of the copolymer as well as the differences in hydrophilicity between the two blocks. Rich phase transitions, especially reentrant transitions, are predicted for a given copolymer with the decrease of the copolymer concentration. The mechanisms of the reentrant phase transitions, the order−order and the order−disorder transitions, are elucidated by analyzing the

■

MODEL AND METHOD Our simulations are carried out based on the simulated annealing method,40,41 which is a well-established procedure for obtaining the lowest-energy ground states in disordered systems. The block copolymers are modeled by the single-site bond fluctuation model proposed by Carmesin and Kremer and by Larson.42,43 The model and simulation algorithm are reviewed briefly in this section, and a detailed description can be found elsewhere.44 The model system is embedded in a simple cubic lattice of volume V = Lx × Ly × Lz. Periodic boundary conditions are applied in all three directions. The system is composed of two components: AB diblock copolymers and solvents (S). The diblock copolymer chain used in the simulation is of the type AnBN−n, where N is the total number of monomers and n is the number of A monomers. In our simulations, the number of monomers in each chain is fixed at N = 12. The bulk phase diagram of the diblock copolymers AnB12−n has been constructed previously. Specifically, hexagonally packed cylinders are formed for n = 2 and 3 and lamellae and gyroids are formed for n = 6, 5, and 4.45 The number of diblock copolymer chains in a system is denoted as NC. Thus, the copolymer concentration is specified by Φ = NCN/V. The copolymers are assumed to be self-avoiding; that is, no two monomers can occupy the same site simultaneously. The bond length is set to be 1 and √2 lattice spacing, so that each site has 18 nearestneighbor sites. In our simulations, the volume of the simulation box is fixed at V = 24 × 24 × 24 for all systems; however, larger simulation boxes with sizes 36 × 36 × 36, and 48 × 48 × 48, are also employed to examine the reproducibility of the structures in typical regions of a phase diagram. Furthermore, when a gyroid or a distorted continuous or perforated lamellar (PL) structure region is formed, the simulation box is varied continuously with Lx = Ly = Lz = L in the range of L = 24−52 to identify the morphology. The copolymer concentration Φ is changed from 0.2 to 0.95 with an interval of 0.1, for some regions, an interval of 0.05 is adopted, and the volume fraction of the B-blocks f B (= (12 − n)/12) is changed from 2/12 to 10/12 with an interval of 1/12, and the phase diagrams are constructed by scanning the parameter space discretely. In all the simulations, initial configurations are generated by first placing the copolymer chains, parallel with one of the axes, to the simulation box until the entire cubic lattice is filled (the maximum concentration is 100%). Then randomly chosen chains are taken away from the box until the desired concentration is reached. After the desired number of chains has been generated, each empty site represents a solvent molecule. Starting from an initial configuration, the ground state of the system is obtained by executing a set of Monte Carlo simulations at decreasing temperatures. Two types of trial moves are used in the simulations: the exchange movement and the chain overturn.44 In an exchange movement, a solvent molecule is selected first, and it can exchange with a monomer on one of its 18 nearest neighbors, or a monomer is selected first, and it can exchange with a solvent on one of its 18 nearest neighbors. If the exchange does not break the chain, it is allowed. If the exchange creates a single break in the chain, the solvent molecule will continue to exchange with subsequent B

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules monomer(s) along the broken chain until reconnection of the links occurs. If the exchange breaks the chain into more than two parts, it is not allowed. In a chain overturn, a chain is selected, and the A/B sequence of the chain is reversed. For example, a chain with a sequence of AAAABBBBBBBB is changed to BBBBBBBBAAAA. The acceptance or rejection of the attempted moves is further governed by the Metropolis rule. The energy of the system is the objective function in the simulated annealing. In the present paper only the 18 nearestneighbor interactions are considered. There are three types of effective pair interactions in the system, which are interactions of block A and block B, block A and solvent S, and block B and solvent S. These interactions are modeled by assigning an energy Eij = εijkBTref to each nearest-neighbor pair of unlike components i and j, where i, j = A, B, and S; εij is the reduced interaction energy, kB is the Boltzmann constant, and Tref is a reference temperature. For double-hydrophilic systems with incompatible blocks, we set εAB = 1.0 and εAS = −0.1 and vary the value of εBS as −0.1, −0.25, −0.5, −1.0, −1.5, and −2.0. Hence, A- and B-blocks are incompatible, and the hydrophilicity of B-block is equal to or stronger than that of A-block. For double-hydrophilic copolymers with compatible blocks, we set εAB = 0 or εAB = −1.0, and a large difference in hydrophilicity, i.e., εAS = 0 and εBS = −4.0. Furthermore, an amphiphilic system is also investigated, in which εAB and εAS are fixed as 1.0 and 0.1, respectively, and the value of εBS is varied. In all cases, it is assumed that εii = 0 with i = A, B, and S. The annealing procedure follows the commonly used linear schedule, Tj = f Tj−1, where Tj is the temperature used in the jth annealing step and f is a scaling factor. Starting at an initial temperature T1, The annealing is continued until the number of the annealing steps reaches a predetermined value. Specifically, the scaling factor f is taken as 0.92 or 0.95, depending on the difference of the average energies of the system at the previous two annealing steps; f = 0.92 is used when the difference of the average energies is small, and f = 0.95 is used when the average energy difference is large. The initial temperature is T1 = 100Tref, and 80 annealing steps are performed. At each annealing step, 25 000 Monte Carlo steps (MCS) are carried out. One MCS is defined as the time taken for on average, all the lattice sites to be visited for an attempted move. We have tested the choice of these parameters by carrying out simulations using larger annealing steps or MCS, and our results indicate that the parameters used in the computations are adequate.

Figure 1. Morphology phase diagram in the Φ and εBS space for the double-hydrophilic BCP with f B = 5/12, εAS = −0.1, and εAB = 1.0 in aqueous solutions. In the legend, D presents disordered phase, C cylinder, G gyroid, and L lamellae. A phase labeled with “(A)” means that the phase is formed by the A-domain. Color scheme in the snapshots: A (yellow) and B (green). Snapshots (d) and (e) are for the same phase viewed in two perpendicular directions.

in double-hydrated lamellar phases is presented as a function of Φ (Figures 7 and 8). Simulation results for an amphiphilic BCP are reported (Figures 9 and 10) and compared with those for double-hydrophilic BCPs. Figure 1 presents phase diagram of the double-hydrophilic BCP with f B = 5/12 in aqueous solution, in the parameter space specified by εBS and the copolymer concentration Φ. It should be reminded that the bulk phase of the copolymer with f B = 5/12 is lamellar. As can be seen from Figure 1, when this lamella-forming diblock copolymer is dissolved in a solvent good for both blocks, the lamellar phase (L) remains in the ranges of Φ = 0.95−0.7 and Φ = 0.3; it finally transforms into a disordered phase when Φ ≤ 0.2. In these regions the phase behavior does not depend on the value of εBS. However, the solution phase in the region with 0.35 ≤ Φ ≤ 0.6 depends on εBS. As shown in Figure 1, with the increase of the value of |εBS|, phase transitions with sequences L → G(A), L → G(A) → C(A), and L → G(A) occur at Φ = 0.6, Φ = 0.5−0.4, and Φ = 0.35, respectively, where G(A) and C(A) are gyroid phase and hexagonally packed cylinders, respectively, formed by the Ablocks. For fixed values of |εBS|, it is worth noting that with the decrease of Φ, reentrant phase transitions with the sequence L → G(A) → C(A) → G(A) → L → disorder (in which both L and G(A) occur in two separated Φ regions), are obtained when |εBS| ≥ 1.0, whereas L → disorder occurs when |εBS| ≤ 0.5. We further investigate the phase behavior of doublehydrophilic BCPs with various volume fractions, and the phase diagrams in the Φ−εBS space are shown in Figure 2. More phase transitions including reentrant ones are observed in Figure 2. For example, upon decreasing the copolymer concentration, sequences C(B) → G(B) → L → G(B) → C(B) → disorder, G(B) → L → G(B) → disorder, and G(A) → C(A) → G(A) → disorder, are formed at |εBS| ≥ 0.5 in Figure 2a, at εBS = −0.1 in Figure 2c, and at εBS = −0.5 in Figure 2g, respectively. All these sequences contain reentrant phase transitions, indicating that the degree of swelling of Aand B-blocks may change with the copolymer concentration. From Figure 2, we can obtain some general features of the phase behavior. (1) When the copolymer concentration approaches 0.95, the phase is the same as the bulk one. However, there are exceptions. In Figure 2b, the bulk cylindrical phase is changed to a G phase at a high hydrophilicity difference, and in Figure 2i, the bulk cylindrical phase is changed to a spherical phase. (2) When the two blocks

■

RESULTS AND DISCUSSION In this section, simulation results of double-hydrophilic BCPs are presented in terms of phase diagrams as a function of the Bsolvent interaction and copolymer concentration Φ for copolymers with incompatible blocks and various volume fractions (Figures 1 and 2) as well as a function of the volume fraction and Φ for copolymers with compatible blocks and different A−B interactions (Figure 3). The mechanism of the phase transitions upon dilution is elucidated by analyzing the variations of the average contact numbers between different species (Figure 4), and of the effective volume fractions (Figure 5), along with discussions and comparisons with available results from experiments, theory, and simulations. The reproducibility and stability of the obtained structures are examined, and the dependence of typical snapshots on box size is presented in Figure 6. The distribution of solvent molecules C

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 2. Phase diagrams in the Φ and εBS space for double-hydrophilic BCPs in aqueous solutions with εAS = −0.1 and εAB = 1.0 but different volume fractions. (a) f B = 2/12; (b) f B = 3/12; (c) f B = 4/12; (d) f B = 5/12; (e) f B = 6/12; (f) f B = 7/12; (g) f B = 8/12; (h) f B = 9/12; (i) f B = 10/ 12. The “+” on the right side of some diagrams indicates the occurrence of reentrant phase transitions at the corresponding value of εBS.

have the same hydrophilicity (i.e., εBS = εAS = −0.1) and the copolymer is or is close to symmetric, the resulting ordered phase is usually similar to the corresponding bulk one regardless of the copolymer concentration, except that disorder phases occur at low polymer concentrations. (3) When the difference in hydrophilicity between the two blocks is large (|εBS| ≥ 0.5), a series of phase transitions occur with the decrease of Φ. For instance, as shown in Figure 2e for the lamella-forming copolymer with f B = 6/12, phase transitions with the sequence L → G(A) → C(A) occur when |εBS| ≥ 0.5. We have also carried out simulations for double-hydrophilic BCPs with miscible blocks. In this case, ordered phases can only be induced when the hydrophilicity difference between the

Figure 3. Phase diagrams in the Φ and f B space for double-hydrophilic BCPs with compatible blocks in aqueous solutions with εAS = 0, εBS = −4.0 and (a) εAB = 0, (b) εAB = −1.

Figure 4. Variation of the average contact numbers with Φ for various copolymers with εAS = −0.1 and εAB = 1.0 but different εBS and different volume fraction values. (a−c) εBS = −1.0; (d, e) εBS = −0.1. (a) f B = 2/12, (b) f B = 5/12, (c) f B = 9/12, (d) f B = 6/12, (e) f B = 4/12, and (f) f B = 2/ 12. The corresponding phases are labeled in the figure. D

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

similar phase transition trend with the variation of Φ. Hence, all these phase transitions should have the same origin. To elucidate the mechanism of the phase transitions, we calculate the average contact numbers between different species and the effective volume fraction of B domain (feB). There are three species in contact with each monomer: A monomer, B monomer, and solvent (S). The total contact number for each monomer should be the same as the number of the nearest neighbors which is 18 in our model. The average contact number for each A monomer with solvent is defined as NAS. Similarly, the average contact number for each B monomer with solvent is defined as NBS. Since there are two bonded monomers (the chain end monomer has one bonded monomer) for each monomer, hence ∼16 is the maximum value that NAS and NBS can reach theoretically. Figure 4 shows the variations of NAS and NBS with Φ for copolymers with different εBS and different volume fractions. It is noted that in a strongly B-hydrophilic solvent the overall shape of the NAS and NBS curves in each plot of Figures 4a−c looks like a closed or nearly closed leaf. Similar trends are observed for NAS and NBS curves in all cases with |εBS| ≥ 0.5. In this case, NBS increases rapidly at the beginning of dilution, and its value is much larger than that of NAS at a given Φ, regardless whether the copolymer is symmetric or not. With a further dilution, NBS increases slowly, reaches its maximum value of ∼16 at a Φ value depending on f B, and finally keeps the maximum value. For example, the maximum values of NBS occur at Φ ≈ 40%, 30%, and 20% for copolymers with f B = 2/ 12, 5/12, and 9/12, respectively. NAS increases slowly at the beginning of dilution. At the later stage of dilution, however, NAS increases rapidly, and at a quite dilute stage of Φ ∼ 0.2, NAS reaches its maximum value which is nearly the same as the maximum of NBS, that is the theoretical maximum value for both of them. Comparing the curves shown in Figures 4a and 4c, it is noted that the rapid increase stage of NAS is postponed to lower Φ regions with the increase of f B. The curves shown in Figures 4a and 4c indicate that the solvent molecules mainly swell the B-block first, presumably due to the stronger hydrophilicity of the B-blocks. This may lead to an increase of feB and correspondingly a decrease of feA as feA = 1 − feB. At the later stage of dilution, the rapid increase of NAS in Figures 4a and 4c indicates an increase of feA with the decrease of Φ. This may result in an inverse change of feB. When the two blocks have the same hydrophilicity, the variation trend of the NAS and NBS curves in each plot looks similar to each other as shown in Figures 4d−f where εBS = −0.1. Figure 4d shows that the two curves of NAS and NBS present perfect coincident due to the symmetry of the copolymer (f B = 6/12), indicating that the solvent swells both blocks of the copolymer equally. On the other hand, Figures 4e,f show that there is a small deviation between the two curves of NAS and NBS due to the asymmetry of the copolymer, and the deviation increases with the decrease of f B. The curves in Figures 4e,f indicate that the solvent may slightly swells the short B-block at the beginning of dilution, which may be due to the entropy effect. The effective volume fraction of B-domain ( feB) is defined as the ratio of the number of the lattice sites occupied by Bdomain (NB‑d) to the total number of lattice sites. NB‑d is equal to the sum of the number of B monomers and the number of solvent molecules that belong to the B-domain, since that all Bmonomers are in the B-domain. For a given solvent molecule, it may belong to the A- or B-domain depending on the species of

Figure 5. Variation of the effective volume fractions of B-domain ( feB) with Φ for various copolymers with εAS = −0.1 and εAB = 1.0 but different εBS. (a) εBS = −1.0 and (b) εBS = −0.1. The corresponding phases are labeled in the figure.

Figure 6. Dependence of typical snapshots on box size. All morphologies are obtained at εAS = εBS = −0.1 and Φ = 0.85 but for copolymers with different volume fractions. f B = 6/12 for lamella, 4/12 for gyroid, and 3/12 for cylinder. V is the volume of the simulation box.

two blocks is large enough. The phase diagrams in the Φ−f B space for systems with εAS = 0 and εBS = −4.0 are shown in Figure 3. It is noted that disordered phase also occurs in high Φ regions besides in low Φ regions. Reentrant phase transitions C(B) → G(B) → L → G(B) → L→ disorder and disorder→ G(B) → L → G(B) → L → G (A) → disorder occur with the decrease of Φ at f B = 0.167−0.25 in Figure 3a and Figure 3b, respectively. The transition sequence at f B = 0.167 shown in Figure 3a or Figure 3b is similar to that shown in Figure 2a when εBS = −1.0 to −2.0. In these two cases, the BCPs are of the same volume fractions, but different B/S and A/B interactions. This comparison indicates that double-hydrophilic BCPs with both incompatible and compatible blocks have E

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Figure 7. Snapshots obtained with aqueous dilution of the copolymer with f B = 5/12, εBS = −0.5, and different copolymer concentrations. (a) Φ = 0.95; (b) Φ = 0.85; (c) Φ = 0.6; (d) Φ = 0.5; (e) Φ = 0.4; (f) Φ = 0.3; (g) Φ = 0.2. Phases are lamellar in snapshots (a−f) and disorder in (g). Color scheme: A (yellow), B (green), S (blue). In the top row, solvent molecules are not shown for clarity.

Figure 8. Density profiles (ρ) of monomers and solvent in phases obtained for the copolymer with f B = 5/12, εBS = −0.5, and (a) Φ = 0.4, (b) Φ = 0.3, and (c) Φ = 0.2. The direction is normal to the layers of the lamellae in (a) and (b) and is an axis direction in (c). R is the distance to the reference layer. The volume of the simulation box is V = 32 × 32 × 32 in (a) and V = 24 × 24 × 24 in (b) and (c).

the hydrophilicities of the two blocks. The solvent is defined as belonging to B-domain if B-block has stronger hydrophilicity. On the other hand, when the two blocks have the same hydrophilicity, the solvent contributes 1/2 to both A and B domains. (4) For the case nSA = 0 and nSB = 0, i.e., the solvent is totally surrounded by other solvent molecules, its species is defined based on which domain those surrounding solvent molecules belonging to the judgment follows the three steps mentioned above. Finally, the value of NB‑d can be calculated and the value of feB can be obtained. The value feA can be calculated in a similar way, and the fact that feA + feB = 1 is satisfied. Figure 5 shows the variation of feB with Φ for copolymers with different volume fractions in the two typical solvent cases. It is noted that in a strongly B-hydrophilic solvent (εBS = −1.0) case shown in Figure 5a each curve increases first, reaches a maximum value, and then decreases with the decrease of Φ. That is an inverse change of feB occurs at the later stage of dilution. This result proves the conclusion inferred from the NAS and NBS curves shown in Figures 4a−c. For copolymers with f B = 2/12−3/12 and f B = 4/12, the increase of feB with the decrease of Φ at relatively higher Φ regions results in sequences C(B) → G(B) → L and G(B) → L, respectively, as shown in Figures 2a−c when εBS = −1.0. For these three copolymers, the maximum values of feB are 0.442, 0.562, and 0.646, which occur at Φ = 50%, 50%, and 40%, respectively. These Φ values correspond to the positions where the corresponding NAS curve increases rapidly, as shown in Figure 4a. From the feB curves shown in Figure 5a, it is noted that in the inverse change region L phase remains when the decrease of feB is too small to span different phase regimes. This is the case shown in Figures 2b,c ( f B = 3/12, 4/12). However, when the decrease of feB is large enough to span different phase regimes, G(B) reoccurs at a lower Φ region next to the L phase.

Figure 9. Phase diagram in the εBS and Φ space for the amphiphilic copolymer with f B = 1/4, εAB = 1.0, and εAS = 0.1.

Figure 10. Variations of (a) the average contact number and (b) feB with Φ for the amphiphilic diblock copolymer with f B = 1/4, εAB = 1.0, εAS = 0.1, and εBS = −1.

its nearest-neighbor sites. The contact number for a given solvent molecule S with A monomers is defined as nSA, and similarly, the contact number of the S with B monomers is defined as nSB. The given solvent should be in one of the following four cases. (1) If nSA = 0 and nSB > 0, then the solvent is defined as belonging to B-domain. (2) If nSB = 0 and nSA > 0, then the solvent is defined as belonging to A-domain. (3) If nSA > 0 and nSB > 0, the solvent locates on the boundary of A- and B-domains and its species is defined depending on F

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

copolymers with f B ≤ 4/12 each feB curve increases first, reaches a maximum value, and then decreases with the decrease of Φ. That is an inverse change of feB occurs at the later stage of dilution, which is similar to the case in a strongly B-hydrophilic solvent, but with a much smaller variation range. This result indicates that the solvent indeed slightly swells the short Bblock at the beginning of dilution. For the copolymer with f B = 4/12, feB value increases from 0.339 to 0.355 as Φ decreases from 0.95 to 0.7, which results in the transition G(B) → L, as shown in Figure 2c when εBS = −0.1. L phase remains during 0.4 ≤ Φ ≤ 0.7. When Φ < 0.4, the decrease of feB results in the reoccurrence of the continuous phase G(B). This is the case in Figure 2c where reentrant transition with the sequence G(B) → L → G(B) occurs at εBS = −0.1. The same mechanism induces the reentrant transition in Figure 2g at εBS = −0.1, where the Ablock is the shorter one. It should be mentioned that the variation of feB in the whole Φ range is small for the copolymer with f B = 4/12. One essential reason for the occurrence of the reentrant phase transition for this copolymer is that the f B value is near the boundary between G and L regimes; a small change in feB can induce the phase transition. For copolymers with much smaller or much larger f B ( f B ≤ 3/12 or f B ≥ 9/12), the change of feB with the decrease of Φ is too small to span both C and G regimes; as in this case, f B is far from the G window. Hence in this case phase transitions, not to mention reentrant ones, cannot be induced when εBS = −0.1. We can also elucidate the mechanism of a double-hydrophilic BCP transitioning into a disordered phase at a lower Φ region by analyzing the variation of the average contact numbers. In Figure 4, it is noted that in all cases both of NAS and NBS curves increase to the maximum value of about 16 at Φ ≈ 0.2. In this case, the monomers A and B are totally surrounded by solvent molecules except the bonded monomer(s). Hence, phase separation cannot be induced even when the two blocks are incompatible. This leads to the formation of disordered phases in which the A- and B-chains are completely loose and in dispersion. It is interesting to compare the predicted phase diagrams with available experimental, theoretical, and simulation results. Recently, Armes and co-workers carried out experimental studies for double-hydrophilic BCPs PEOm−PMPCn.28 First of all, they found that for sample PEO114−PMPC23 with PEO weight fractions (XPEO) = 0.42 in aqueous solution, rich phase transitions with sequence L → C(PEO) → L → disorder were observed upon decreasing the copolymer concentration.28 It is noticed that the continuous structure of G did not appear in their experiments, which is possibly due to the narrow window of G phase in the diagram.5,6,46 Taking this into consideration, the predicted phase transitions with sequence L → G(A) → C(A) → G(A) → L → disorder in Figure 2d for the copolymer with f B = 5/12 have the same trend with those observed in their experiments. Second, body-centered-cubic nanostructures were observed for copolymer PEO45−PMPCn with XPEO ranging from 0.12 to 0.24 at a concentration of 70% (w/w) in Armes and co-workers’ experiments.28 In our study, it is found that spherical phases are obtained for copolymers with f B = 0.75− 0.83 (Figures 2h,i). Finally, phases of body-centered-cubic spheres, cylinders, and lamellae were observed for copolymers PEO114−PMPCn with PEO weight fractions of XPEO = 0.15, 0.26, and 0.42, respectively, at a concentration of 50% (w/w) in their experiments, where 50% (w/w) is order−disorder transition (ODT) concentration.28 In our simulations, the ODT concentration is around Φ = 0.2, and at Φ = 0.3,

This is the case in Figure 2a (f B = 2/12) where reentrant transitions occur at |εBS| ≥ 0.5. It is the large volume fraction of A-blocks of the copolymer with f B = 2/12 that makes the inverse change of the effective volume fractions more efficient. It is interesting to notice that a further inverse change of the effective volume fractions leads to the reoccurrence of C(B) at a low concentration of Φ = 40% for copolymer with f B = 2/12. A similar mechanism induces the phase transitions in Figures 2d−f when |εBS| ≥ 1.0. For the lamella-forming copolymers with f B = 5/12, 6/12, and 7/12, transitions L → G(A) → C(A) are obtained (Figures 2d−f) at relatively higher Φ regions as a result of the increase of feB, as shown in Figure 5a, since that the solvent molecules mainly swell the B-domain then. The curves in Figure 5a show that the maximum values of feB are located at Φ = 40% and 30% for copolymers with f B = 5/12−6/12 and 7/ 12, respectively, which also correspond to the positions where the corresponding NAS curve increases rapidly, as shown in Figure 4b. At the later stage of dilution when each feB curve decreases with the decrease of Φ, transitions C(A) → G(A) → L occur at lower Φ regions when the decrease of feB is large enough to span different phase regimes, where G(A) and L are reentrant phases. This is the case in Figure 2d for the copolymers with f B = 5/12 when |εBS| ≥ 1.0. However, when the decrease of feB is not large enough to span different phase regimes, C(A) remains. This is the case in Figures 2e and 2f for copolymers with f B = 6/12 and 7/12 when |εBS| ≥ 1.0. It is also the larger volume fraction of A-blocks in the copolymer with f B = 5/12, which makes the reentrant transition possible. For copolymers with f B = 8/12, 9/12, and 10/12, the concentration positions at which the maximum values of feB occur are postponed to Φ = 30% as shown in Figure 5a. This is because the B-domain can accommodate more solvent molecules due to the large volume fraction of B-block, so that the position where the corresponding NAS curve increases rapidly is postponed to lower polymer concentrations, as shown in Figure 4c. On the other hand, the A-domain can only accommodate much less amount of solvent molecules to cause NAS approaches to its maximum value due to the small volume fraction of A-blocks. These facts make the occurrence of reentrant phase transitions impossible in these systems when |εBS| ≥ 1.0, as shown in Figures 2g−i. From Figure 5a, it is also noted that the phases C(B), G(B), L, G(A), C(A), and S(A) locate at feB ranges of 0.20−0.31, 0.31−0.36, 0.36−0.65, 0.65−0.70, 0.70−0.87, and 0.84−0.87, respectively, indicating that the resulting feB value of a system largely defines its structure. This result is quantitatively in agreement with that obtained from Monte Carlo simulations in the stronger segregation regime.13 The conclusion inferred from the NAS and NBS curves for the case when the two blocks have the same hydrophilicity (εBS = −0.1) is confirmed in Figure 5b. The nearly flat line in Figure 5b proves that the solvent swells both blocks of the copolymer equally in the copolymer with f B = 6/12. This result is also approximately true when the copolymer is close to symmetric, as demonstrated by the nearly flat line in Figure 5b for copolymer with f B = 5/12. This is the reason that when the copolymer is symmetric or close to symmetric and the two blocks have the same hydrophilicity, the resulting ordered solution phase is usually similar to that in the bulk except that disorder phases occur at low polymer concentrations, as mentioned above. Therefore, ordered phase transitions cannot be induced in these systems, as shown in Figures 2d−f when εAS = εBS = −0.1. On the other hand, Figure 5b shows that for G

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

further solvent addition results in a uniform distribution of the solvent molecules on the interfaces and inside the B-rich layers at Φ = 0.85. With a further solvent addition, the B-rich layers are nearly full of solvent molecules, and there are a small amount of solvent molecules getting into the A-rich layers at Φ = 0.6. A large number of solvent molecules are distributed in both of the A-rich and B-rich layers when Φ ⩽ 0.4. We can observe the quantitative distributions of solvent molecules in phases obtained at Φ = 0.4−0.2 from the density profile (ρ) curves shown in Figure 8. Since there are only three species in our model systems, the sum of ρ(A), ρ(B), and ρ(S) should be 1.0. In Figures 8a,b, the peaks of ρ(A) and ρ(B) curves alternate, indicating that the A-rich and B-rich layers alternate in a lamellar phase. The ρ(S) value inside B-rich layers is higher than that inside A-rich layers. The range of ρ(S) is between 0.3 and 0.7 at Φ = 0.4 in Figure 8a, while it is between 0.6 and 0.8 at Φ = 0.3 in Figure 8b. This result indicates that due to the rapid increase of solvent molecules inside the A-rich layers upon dilution, the fluctuation of ρ(S) between the two domains becomes smaller in the case with Φ = 0.3 than that in the case with Φ = 0.4. On the other hand, it is noted that the peaks of ρ(A) or ρ(B) curve in Figure 8b are not as sharp as those in Figure 8a, indicating that there are wider interfaces in the case with Φ = 0.3 than that in the case with Φ = 0.4. This result is consistent with that shown in the snapshots in Figures 7e,f. A further dilution leads to three almost horizontal curves of ρ(A), ρ(B), and ρ(S) in Figure 8c in the case with Φ = 0.2, which corresponds to the disordered phase shown in Figure 7g. In this case the density profile curves in any directions are the same, indicating that solvent molecules are distributed almost uniformly in the whole phase. The distribution patterns of solvent molecules shown in Figures 7 and 8 are consistent with the variations of the average contact numbers shown in Figure 4b and of feB shown in Figure 5a. When solvent addition is large enough (specifically, when Φ ≤ 0.6 in our study), lamellae formed by double-hydrophilic BCPs are double-hydrated structures. This result is consistent with that observed experimentally by Meier and co-workers, and they proposed “layers of solvent molecules stacked on top of one another without a hydrophobic interlayer”.27 The high content of solvent molecules in double-hydrated lamellar structures is attractive for precipitation of inorganics with a well-defined morphology and high inorganic fraction.27 We have also investigated the phase behavior of an amphiphilic diblock copolymer with f B = 3/12 in order to make a comparison with that of double-hydrophilic systems, and the phase diagram is shown in Figure 9. The only difference between the two systems in parameters is that εAS = 0.1 in an amphiphilic system whereas εAS = −0.1 in a doublehydrophilic system. The phase diagram shown in Figure 9 is consistent with that obtained experimentally for a cylinderforming diblock copolymer dissolved in a solvent strongly selective to the short block.20 A comparison between the double-hydrophilic and the amphiphilic systems reveals the following three different aspects. (1) The concentration range of ordered phases in a double-hydrophilic system is narrower than that in the amphiphilic system. (2) Reentrant phase transitions can occur in a double-hydrophilic system, whereas “inverted” phase transitions occur in an amphiphilic system. In the sequence C(B) → G(B) → L → G(A) → C(A) observed in Figure 9 with the decrease of Φ, G(A) and C(A) are formed by A-blocks whereas G(B) and C(B) are formed by B-blocks, and they are the so-called “inverted” phases.22

structures of spheres, cylinders, and lamellae are obtained in Figures 2g−i, 2e,f, and 2b−d, respectively. In the other experimental study, Meier and co-workers observed a transition from a lamellar lyotropic mesophase to an assumed hexagonal cylindrical phase with decreasing the polymer concentration for a single double-hydrophilic BCP [PEO113−PMOXA85] in concentrated aqueous solution.27 Taking this into the narrow window of G phase in the diagram, the predicted phase transitions with sequence L → G(A) → C(A) in Figures 2d−f for the copolymer with symmetric or close to symmetric component have the same trend with the observation of Meier and co-workers. All these comparisons indicate that our simulation results are qualitatively consistent with the experiments.27,28 Using DPD simulation, Huang and Wang found that microphase separation occurs when the concentration CP > 0.8 for model double-hydrophilic BCP A3B3, and only a lamellar structure was observed for CP = 0.9.30 The difference between their results and ours may be due to the difference in interaction parameters. By using the RPA and SCFT calculations, transitions between various ordered structures were predicted for diblock copolymer/homopolymer blends with three miscible binary pairs of interactions.32 However, no re-entrant transitions were observed. This may be due to the difference in entropy between homopolymer and solvent molecules. It should be pointed out that from a large number of testing runs with different simulation boxes good reproducibility has been obtained of the morphologies shown in the phase diagrams 1−3, except the gyroid phase. Phases such as sphere, hexagonally packed cylinder, and lamellar structures could form in all the boxes used. However, the gyroid structures could only form when the box size is close to an integer multiple of the period of the structure; otherwise, distorted continuous or PL morphologies in simulations were obtained if the size of box does not match the period of this phase, as shown in Figure 6. This behavior is consistent with what obtained earlier.13,21 It is noted that the PL morphologies were also observed in place of gyroid phases in pervious off-lattice moleculardynamics simulations,47 lattice Monte Carlo simulations,48 and lattice simulated annealing study.21 The occurrence of PL was ascribed as finite-size effect.48 Furthermore, a more recent study13 of AB diblock copolymer melts, using Monte Carlo simulations with parallel tempering algorithm, revealed that the gyroid morphology spontaneously forms in place of the PL phase identified in the earlier study, adding to the evidence that G is more stable than PL. However, there was still a small region in the phase diagram, where PL phase appears to be stable.13 As the PL window is small in the phase diagram, we do not distinguish PL and G in the present study. The quantized dependence of the resulting morphology (G or PL) on the box size observed here and previously21,13 indicates that the occurrence of PL is not due to the finite-size effect alone. Another deciding factor is the commensurability of the box with the structure, similar to that in the case of block copolymers under spatial confinement.49 The double-hydrated lamellar phases mentioned in the experiments27 are also observed in our simulations. To understand how the solvent molecules are distributed in the double-hydrated structures, we choose the simplest phase of lamellae formed by the copolymer with f B = 5/12 and εBS = −0.5 (Figure 2d) as an example. From the snapshots shown in Figure 7, it is noted that solvent molecules are only distributed at the interfaces between A-rich and B-rich layers at Φ = 0.95. A H

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

qualitatively consistent with that observed in recent experiments. Reentrant phase transitions are predicted for four copolymers with incompatible blocks. When the difference in hydrophilicity between the two blocks is large, solvent mainly swells the more hydrophilic block in the first stage of dilution, and mainly swells the less hydrophilic block in the late stage. Thus, the efficient volume fraction of the more hydrophilic block domain increases first and then decreases with the further decrease of Φ, resulting in the reentrant phase transitions. When the two blocks have the same hydrophilicity, reentrant phase transitions are observed in asymmetric copolymer systems. In this case, solvent slightly swells the short block in the first stage of dilution due to entropy effect and swells the longer block in the late stage; hence, the efficient volume fraction of the short block domain increases first and then decreases with the further decrease of Φ, resulting in the reentrant phase transitions. Reentrant phase transitions are also observed for copolymers with compatible blocks, and their trends are similar to those observed in copolymers with incompatible blocks. In an amphiphilic BCP system, the efficient volume fraction of the hydrophilic domain always increases with the decrease of Φ, resulting in the “inverted” phase transitions. The simulation results are consistent with available experimental and theoretical studies on doublehydrophilic BCPs in solutions. Furthermore, the predicted reentrant phase transitions and the proposed transition mechanism provide a good understanding of controlled selfassembly of double-hydrophilic BCPs.

The average contact number and the effective volume fraction curves in the amphiphilic system are shown in Figures 10a and 10b, respectively. Figure 10a shows that upon decreasing the copolymer concentration, NBS increases rapidly while NAS increases slowly, and the value of NBS is always much larger than that of NAS at a given value of Φ. At low Φ region, both of NBS and NAS reach a steady value. The maximum value of NBS is close to 16, the maximum value predicted theoretically, whereas the maximum value of NAS is much smaller than 16. The curves shown in Figure 10a have a totally different behavior with those shown in Figures 4a−c for a double-hydrophilic system with the same εBS values. Apparently, this difference can be attributed to the different behavior of NAS in the two types of systems. NAS keeps a small value in the whole Φ range in the amphiphilic system. Hence, feB increases monotonically from 0.288 to 0.824 with the decrease of Φ from 95% to 20%, as shown in Figure 10b. These data indicate that almost all solvent molecules are inside the hydrophilic domain, which results in the appearance of the “inverted” phases at lower copolymer concentrations. Ordered phases remain even at Φ = 0.2, where the hydrophobic Bblocks remain phase separated with the hydrophilic domain because the solvent does not swell the B-blocks. However, in a double-hydrophilic system, NAS keeps a small value only at high copolymer concentrations, it increases slowly and then rapidly with a further solvent addition, and at low Φ region NAS reaches a maximum value which is nearly the same as that for NBS. Hence, feB increases first and then decreases with the further decrease of Φ. This nonmonotonic variation of the effective volume fraction of A (or B)-rich domain with decreasing Φ is the reason that reentrant transitions may appear in a double-hydrophilic system. The different behavior between the two types of BCP systems is due to the solvent property. In an amphiphilic system, the solvent molecules are attractive to one block and repulsive to the other block, whereas in a double-hydrophilic system, the solvent molecules are attractive to both A- and Bblocks. In an amphiphilic system, the efficient volume fraction of the hydrophilic domain always increases with the decrease of Φ, resulting in the “inverted” phase transitions. In a doublehydrophilic system, solvent swells the more hydrophilic block in the first stage of solvent addition and then swells the other block in the late stage; hence, the efficient volume fraction of the more hydrophilic block domain increases first and then decreases with the further decrease of Φ, resulting in the reentrant phase transitions.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (B.L.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

This work is supported by the National Natural Science Foundation of China (21574071, 20925414, and 91227121), by the PCSIRT (IRT1257), and by the 111 Project. J. Wu gratefully acknowledges the supports from the National Science Fund for Talent Training in Basic Sciences under Grant J1103208. A.-C. Shi gratefully acknowledges the support from the Natural Sciences and Engineering Research Council (NSERC) of Canada.

■

CONCLUSION We have systematically investigated the self-assembly of doublehydrophilic BCPs in aqueous solutions using a simulated annealing method applied to a lattice model of BCPs. Phase diagrams for copolymers with both incompatible and compatible blocks are constructed by varying the copolymer volume fraction, copolymer concentration, and the difference in hydrophilicity between the two blocks. Rich phase transition sequences, such as with the sequence L → G(A) → C(A) → G(A) → L → disorder, are observed for a single copolymer upon diluting the solution. The mechanisms of phase transitions are elucidated based on the variations of the average contact numbers between the monomers and solvent and of the effective volume fraction. The distributions of solvent molecules in double-hydrated lamellar phases are unveiled as a function of Φ. The trend of the predicted phase transitions is

(1) Abetz, V.; Simon, F. W. Adv. Polym. Sci. 2005, 189, 125−212. (2) Bates, F. S.; Fredrickson, G. H. Phys. Today 1999, 52 (2), 32−38. (3) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, UK, 1998; p viii. (4) Khandpur, A. K.; Forster, S.; Bates, F. S.; Hamley, I. W.; Ryan, A. J.; Bras, W.; Almdal, K.; Mortensen, K. Macromolecules 1995, 28, 8796−8806. (5) Matsen, M. W.; Schick, M. Phys. Rev. Lett. 1994, 72, 2660−2663. (6) Matsen, M. W.; Bates, F. S. Macromolecules 1996, 29, 1091−1098. (7) Laradji, M.; Shi, A.-C.; Noolandi, J.; Desai, R. C. Macromolecules 1997, 30, 3242−3255. (8) Tyler, C. A.; Morse, D. C. Phys. Rev. Lett. 2005, 94, 208302. (9) Takenaka, M.; Wakada, T.; Akasaka, S.; Nishitsuji, S.; Saijo, K.; Shimizu, H.; Kim, M. I.; Hasegawa, H. Macromolecules 2007, 40, 4399−4402. I

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

(46) Bate, F. D.; Schulz, M. F.; Khandpur, A. K.; et al. Faraday Discuss. 1994, 98, 7−18. (47) Schultz, A. J.; Hall, C. K.; Genzer, J. J. Chem. Phys. 2002, 117, 10329. (48) Matsen, M. W.; Griffiths, G. H.; Wickham, R. A.; Vassiliev, O. N. J. Chem. Phys. 2006, 124, 024904. (49) Shi, A. C.; Li, B. Soft Matter 2013, 9, 1398−1413.

(10) Kim, M. I.; Wakada, T.; Akasaka, S.; Nishitsuji, S.; Saijo, K.; Hasegawa, H.; Ito, K.; Takenaka, M. Macromolecules 2008, 41, 7667− 7670. (11) Kim, M. I.; Wakada, T.; Akasaka, S.; Nishitsuji, S.; Saijo, K.; Hasegawa, H.; Ito, K.; Takenaka, M. Macromolecules 2009, 42, 5266− 5271. (12) Masten, M. W. Macromolecules 2012, 45, 2161−2165. (13) Beardsleya, T. M.; Matsen, M. W. Eur. Phys. J. E: Soft Matter Biol. Phys. 2010, 32, 255. (14) Shuai, X. T.; Ai, H.; Nasongkla, N.; Kim, S.; Gao, J. M. J. Controlled Release 2004, 98, 415−426. (15) Lomas, H.; Canton, I.; MacNeil, S.; Du, J.; Armes, S. P.; Ryan, A. J.; Lewis, A. L.; Battaglia, G. Adv. Mater. 2007, 19, 4238. (16) Xiong, X. B.; Uludag, H.; Lavasanifar, A. Biomaterials 2009, 30, 242−253. (17) Blanazs, A.; Armes, S. P.; Ryan, A. J. Macromol. Rapid Commun. 2009, 30, 267−277. (18) Hanley, K. J.; Lodge, T. P.; Huang, C.-I. Macromolecules 2000, 33, 5918. (19) Lai, C.; Russel, W. B.; Register, R. A. Macromolecules 2002, 35, 841. (20) Lodge, T. P.; Pudil, B.; Hanley, K. J. Macromolecules 2002, 35, 4707. (21) Yu, B.; Li, B.; Sun, P.; Chen, T.; Jin, Q.; Ding, D.; Shi, A.-C. J. Chem. Phys. 2005, 123, 234902. (22) Suo, T.; Yan, D.; Yang, S.; Shi, A.-C. Macromolecules 2009, 42, 6791−6798. (23) Zhang, L. F.; Eisenberg, A. Science 1995, 268, 1728−1731. (24) Antonietti, M.; Forster, S. Adv. Mater. 2003, 15, 1323−1333. (25) Pochan, D. J.; Chen, Z. Y.; Cui, H. G.; Hales, K.; Qi, K.; Wooley, K. L. Science 2004, 306, 94−97. (26) Wang, X. S.; Guerin, G.; Wang, H.; Wang, Y. S.; Manners, I.; Winnik, M. A. Science 2007, 317, 644−647. (27) Taubert, A.; Furrer, E.; Meier, W. Chem. Commun. 2004, 2170− 2171. (28) Blanazs, A.; Warren, N. J.; Lewis, A. L.; Armes, S. P.; Ryan, A. J. Soft Matter 2011, 7, 6399−6403. (29) Casse, O.; Shkilnyy, A.; Linders, J.; Mayer, C.; Häussinger, D.; Völkel, A.; Thünemann, A. F.; Dimova, R.; Cölfen, H.; Meier, W.; Schlaad, H.; Taubert, A. Macromolecules 2012, 45, 4772−4777. (30) Huang, J.; Wang, Y. J. Phys. Chem. B 2007, 111, 7735−7741. (31) Huang, J.; Luo, M.; Wang, Y. J. Phys. Chem. B 2008, 112, 6735− 6741. (32) Zhou, J.; Shi, A.-C. J. Chem. Phys. 2009, 130, 234904. (33) Ke, F.; Mo, X.; Yang, R.; Wang, Y.; Liang, D. Macromolecules 2009, 42, 5339. (34) de las Heras Alarcon, C.; Pennadam, S.; Alexander, C. Chem. Soc. Rev. 2005, 34, 276. (35) Lazzari, M.; Liu, G.; Lecommandoux, S. Block Copolymers in Nanoscience; Wiley: New York, 2006. (36) Rodríguez-Hernandez, J.; Checot, F.; Gnanou, Y.; Lecommandoux, S. Prog. Polym. Sci. 2005, 30, 691. (37) Schmaljohann, D. Adv. Drug Delivery Rev. 2006, 58, 1655. (38) Voets, I. K.; de Keizer, A.; Leermakers, F. A. M.; Debuigne, A.; Jerome, R.; Detrembleur, C.; Stuart, M. A. C. Eur. Polym. J. 2009, 45, 2913−2925. (39) Loizou, E.; Triftaridou, A. I.; Georgiou, T. K.; Vamvakaki, M.; Patrickios, C. S. Biomacromolecules 2003, 4, 1150−1160. (40) Kirkpatrick, S.; Gelatt, C. D., Jr.; Vecchi, M. P. Science 1983, 220, 671. (41) Kirkpatrick, S. J. Stat. Phys. 1984, 34, 975. (42) Carmesin, I.; Kremer, K. Macromolecules 1988, 21, 2819. (43) Larson, R. G. J. Chem. Phys. 1989, 91, 2479; J. Chem. Phys. 1992, 96, 7904. (44) Sun, P.; Yin, Y.; Li, B.; Chen, T.; Jin, Q.; Ding, D.; Shi, A.-C. J. Chem. Phys. 2005, 122, 20490. (45) Yu, B.; Sun, P.; Chen, T.; Jin, Q.; Ding, D.; Li, B.; Shi, A.-C. Phys. Rev. Lett. 2006, 96, 138306. J

DOI: 10.1021/acs.macromol.5b01993 Macromolecules XXXX, XXX, XXX−XXX