Synthesize Multiblock Copolymers via Complex Formations between Î²

Article pubs.acs.org/JPCB

Synthesize Multiblock Copolymers via Complex Formations between β‑Cyclodextrin and Adamantane Groups Terminated at Diblock Copolymer Ends: A Brownian Dynamics Simulation Study Wei Wang, You-Liang Zhu, Hu-Jun Qian,* and Zhong-Yuan Lu* Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun 130023, China S Supporting Information *

ABSTRACT: Coarse-grained models for β-cyclodextrin (β-CD) and adamantane (ADA) are proposed by fitting to their experimental host−guest complex equilibrium constant in solution. By using Brownian dynamics simulations, we suggest a simple supramolecular route for synthesizing multiblock copolymers (MBCs) via forming complexes between β-CD and ADA groups terminated at the chain ends of diblock copolymers (DBCs). The chain length distribution of the resulted MBC is found to follow the statistics of Flory formula for typical linear condensation polymerization process. Therefore, the proposed supramolecular route can be viewed as a novel linear condensation polymerization process with DBCs as reactive monomers. Due to the complex formations between head and tail (β-CD and ADA), ringshaped MBCs are also observed in our simulations, which will reduce the yield of the MBC. Because we are using a generic model for DBC, the proposed route of building MBCs are applicable for all synthetic DBCs with two ends terminated by either β-CD or ADA groups.

1. INTRODUCTION Among many bottom-up strategies for the structuring of complex materials, hierarchical self-assembly was proven to be an outstanding method.1 In recent years, block copolymers have received intense research interests due to their ability to self-assemble at length scales spanning from a few nanometers to micrometers.2−6 As a family member, MBCs are often used to fabricate special materials applied in the fields of biochemistry,7,8 electrochemistry,9,10 etc. Recently, Zhang et al. proposed a route to fabricate patchy particles from the collapse of MBCs in dilute solution.11 Such patchy particles possess the ability to pack into more complicated ordered structures at higher level through a hierarchical self-assembly process.12,13 There are many ways of synthesizing block copolymers. In early times, people preferred to use techniques of living anionic polymerization,14,15 ring-opening polymerization,16,17 cationic polymerization,18,19 or condensation polymerization.20 However, most of them do not tolerate even extremely low levels of impurities and are compatible only with a limited number of monomers. With the development of controlled free-radical techniques, many other ways had been developed, such as nitroxide-mediated polymerization,21 atom transfer radical polymerization (ATRP),22−24 reversible addition−fragmentation chain transfer (RAFT),25−27 and some other novel ways like combining ATRP and RAFT,28,29 Cu(0)-mediated radical polymerization,30,31 etc. Recently, “click chemistry” was also developed for the synthesis of MBCs.32−34 Alternatively, MBCs can also be fabricated by using supramolecular techniques.35−38 One simple way is to borrow © 2013 American Chemical Society

the idea from the concepts of host−guest interactions: the host molecule normally has a good affinity toward the guest molecule, as a consequence the host molecule will catch the guest molecule when they are approaching each other. Therefore, when the covalent bonds that hold the monomeric units together in a macromolecule are replaced by such highly directional noncovalent interactions, supramolecular polymer structures can also be achieved.39,40 In this respect, βcyclodextrin (β-CD) is a good candidate for a host molecule with quite outstanding properties. It consists of seven Dglucopyranose residues, linked by R-1,4 glycosidic bonds into a macrocycle.41 The relatively hydrophobic interior and hydrophilic exterior of the molecular pockets make them suitable and fascinating hosts for small hydrophobic molecules with compatible sizes to the interior pockets.42−47 Among various host−guest pairs, the inclusion complex between β-CD and adamantane (ADA) in aqueous solution had been mostly investigated due to its high binding ability.47−51 With β-CD and ADA as binding groups, several supramolecular methods had been proposed to obtain an amount of interesting polymer architectures connected through noncovalent attractive host− guest binding associations between various building blocks.52 Therefore, it is quite interesting to examine the possibility of synthesizing MBCs via host−guest coupling interactions between the β-CD and ADA groups terminated at the DBC chain ends. In such a way, the MBC chain length can be Received: July 23, 2013 Revised: October 20, 2013 Published: November 21, 2013 16283

dx.doi.org/10.1021/jp4073137 | J. Phys. Chem. B 2013, 117, 16283−16291

The Journal of Physical Chemistry B

Article

Figure 1. CG model for the PS-b-PMMA chain with functional terminals. Models on the upper left show the molecular structure and schematic shape of β-CD. The yellow bead represents the hydrophilic part, called the H bead, and the orange bead represents the hydrophobic part, called the P bead. Models on the upper right show the molecular structure and schematic shape of ADA. The gray bead represents the carboxyl acid group, naming N bead, and the red bead represents the methyl group, naming C bead. The green bead represents the PS unit, naming S bead, and the blue bead represents the PMMA unit, naming M bead.

2. MODEL AND SIMULATION METHOD Coarse-Grained Models. Compared with all-atom simulation models, coarse-grained (CG) models use reduced degrees of freedom and have a relatively smoother potential energy landscape; therefore, it can significantly accelerate the simulation and extend both the time and the length scales of simulated system.53 The essential of the coarse-graining is to make appropriate coarse-grain descriptions for given molecules by grouping several atoms into a single CG bead. Depending on particular phenomena of interest at different length/time scales, various CG models can be adopted with only important degrees of freedom kept in the system while some other unnecessary degrees of freedom are abandoned. Therefore, attentions must be paid to keep important degrees of freedom during a coarse-graining process; i.e., it is crucial in this study to make coarse-grained models for β-CD and ADA groups by keeping characteristics of host−guest interactions between them. Figure 1 shows the schematic DBC model with host β-CD (marked in yellow) and guest ADA (marked in red) molecules attached on both ends of a block copolymer chain ends. Here we use PS-b-PMMA, which is widely used in experiments, as our representative for incompatible DBCs. Experimentally, adding functional groups onto block copolymer chain ends can be achieved through several techniques.54,55 With these endfunctionalized DBCs distributed in dilute solution, inclusion of (red) ADA groups into pockets of (yellow) β-CD groups can be expected, as schematically illustrated in Figure 2. In such a

reversibly tailored by changing temperature or solvent condition, making the synthesis process practically easy and environmentally friendly. The aim of this study is to use computer simulations to elucidate the possibility of synthesizing MBCs via host−guest binding processes between β-CD and ADA terminal groups attached on DBCs. However, due to the limited capability of brute force atomistic molecular dynamics simulations, we instead propose coarse-grained models of β-CD, ADA and polymer chains. The association process between β-CD and ADA groups are simulated in a dilute solution by using Brownian dynamics. Effects of the concentration and the chain length of DBC precursors are evaluated. During the simulation, we do find MBC chain formations via the coupling between the two terminal groups belonging to different DBCs. Because a generic DBC chain model is used in our simulations, the proposed host−guest coupling “reactions” between β-CD and ADA groups can be in principle applied to all synthetic DBCs. Furthermore, the block sequence on target MBCs and volume fraction of different blocks can be easily tuned by varying the ratio of the two blocks in DBC precursors. This paper is organized as follows: In section 2, the coarsegrained models of DBC chain, β-CD and ADA groups are described. The details of Brownian dynamics simulations are given. Section 3 shows the main results and discussion. Final conclusions are presented in section 4. 16284



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copolymer model of S128M32. β-CD is attached at the end of PS block and ADA group at the end of PMMA block. Coarse-Grained Potentials. Bonded Forces. Both bonds and angles are described by harmonic potentials in our CG simulations,

way, the DBCs can be connected one-by-one, forming linear MBCs.

Ubond =

1 k bond(rij − rij ,0)2 2

(1)

Uangle =

1 kangle(θijk − θijk ,0)2 2

(2)

where Ubond and Uangle are bond and angle potentials, kbond and kangle are the force constants, rij and θijk are the instantaneous distance or angle between bonded CG beads, rij,0 and θijk,0 are the corresponding equilibrium values at the energy minima. The detailed definitions for different bonds and angles are shown in Figure 3.

Figure 2. Illustration for the formation process of MBCs in aqueous solution induced by inclusions of ADA groups into the hollow pockets of β-CD groups.

In the following, we will show the details of CG models for block copolymers as well as the host and guest molecules. As has been discussed above, hydrophilic shell and hollow hydrophobic cavity are essential characteristics of β-CD. To keep these characteristic features and the shape of the molecule, we use two bead types in our CG model to represent the β-CD molecule, one represents the hydrophilic part and the other the hydrophobic part (as shown in Figure 1). The hydrophilic beads coarsely represent the hydroxymethyl and hydroxyl groups stretched outside the β-CD molecule, whereas the hydrophobic beads represent other atoms inside. A coarsegrained α-CD model proposed by Urakami and co-workers56,57 is utilized to build up our β-CD model by adding one more Dglucose structure in the cyclic amylose structure. The corresponding parameters are refined to better reproduce the structural properties of β-CD. To be consistent with experiments, we use the ADA derivative, 1-adamantananime hydrochloride (also abbreviated for ADA in the following text), in our simulations.58 In the coarse-grained ADA model, one bead is used to represent the −NH2HCl group, and four other beads represent −CH and −CH2 groups (as shown in Figure 1). The coarse-graining level of our models for β-CD and ADA is similar to that of the MARTINI force field;59−61 i.e., one CG bead represents 2−4 heavy atoms. As shown in Figure 1, the main part of ADA model is represented by four beads connected in a shape of tetrahedron, which can keep the symmetry of ADA molecule in Td point group. For the DBC chain in our simulations, we use one bead to represent either one PS or one PMMA monomer, respectively; therefore, we have two bead types in the DBC chain. A schematic mapping is shown in Figure 1 for illustration (green S beads represent PS monomers, whereas blue M beads for PMMA monomers). To be consistent with previous work,11 we also construct a DBC model containing 160 monomers with a ratio between PS and PMMA bead numbers (monomers) of 3:1; i.e., we have a block

Figure 3. Definition of bond and angle types in (a) β-CD molecule, (b) ADA molecule, and (c) PS or PMMA polymers.

The parameters of the bond and angle forces for β-CD are taken from refs 56 and 57. To reflect the geometric characteristics of β-CD, some parameters are slightly modified. Following the parametrization strategy in refs 56 and 57, the bond and angle force parameters for ADA are determined referring to the real shape and size of the molecule. Parameters for PS and PMMA blocks are taken directly from ref 11. The parameter values are listed in Table 1. Nonbonded forces. We use the Lennard-Jones (LJ) potential, Uij(r) = 4ε[(σ/r)12 − (σ/r)6], to describe the nonbonded interactions. LJ parameters ε and σ are energy and length units, respectively. As has been explained above, the most important part of our simulations is the host−guest interactions between β-CD and ADA. Their nonbonded interaction parameters should have the capability to reflect experimental host−guest complex characteristic, which can be represented by the equilibrium complex constant K, as defined by58

K=

[β ‐CD·ADA] [β ‐CD][ADA]

(3)

where [β-CD], [ADA], and [β-CD·ADA] represent the concentrations of the free β-CD and ADA molecules and the 16285



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interactions can guarantee the efficient inclusion of ADA into βCD pocket. By doing so, we can very well reproduce the experimental complex formation equilibrium constant K between β-CD and ADA in our simulations, as we have shown above. As for bonded parameters, the nonbonded LJ parameters used in ref 11 for PS and PMMA polymers are adopted directly in this work. The radius of gyration (Rg) of polymer chains in solution simulated with these parameters shows a chain length N dependence of Rg ∼ N0.455, which is non-Gaussian and a little contracted, implying a slightly bad solvent condition. To simplify our model, we use the same nonbonded parameters between M and M beads as those between S and S beads. To represent the incompatibility between S and M beads, we simply make the value of ε between S and M beads half that between S−S or M−M bead pairs. For the other unlike bead pairs, ε are calculated by using Lorentz−Berthelot mixing rules. All the nonbonded parameters are listed in Table 2.

Table 1. Equilibrium Bond Lengths and Angles of β-CD, ADA, and PS (PMMA)a bond lengths (Å) kbond = 1000 (kbond = 5000)

bond angles (deg) kangle = 500 (kangle = 656)

r1 = 0.640 r2 = 0.689 r3 = 1.39 r4 = 1.39 r5 = 1.13 r6 = 1.13 r7 = 0.647 θ1 = 0.122 θ2 = 1.01 θ3 = 0.192 θ4 = 1.09 θ5 = 1.60 θ6 = 1.57 θ7 = 1.53 θ8 = 1.57 θ9 = 1.05 θ10 = 2.53 θ11 = 2.04

Table 2. Parameters of Lennard-Jones Potential between Beads of β-CD, ADA, PS, and PMMAa

a

kbond and kangle represent the strength of harmonic bond force and angle force, respectively. The kbond and kangle values in the brackets are the parameters for PS and PMMA. All the parameters are in reduced units with ε = 0.5 kJ/mol and σ = 0.38 nm.

εHH = 2.0 εHP = 0.2 εHC = 6.0 εHN = 6.5 εPP = 2.0 εPC = 0.6 εPN = 0.6 εCC = 1.0 εCN = 0.7 εNN = 1.6 εSS = 0.4 εMM = 0.4 εSM = 0.2

complex between them in equilibrium, respectively. The value of the constant K actually represents the complex strength between this host−guest pair. For a system with the initial concentration of ADA group smaller than that of β-CD, the formula can be rewritten as K = p/[([β-CD] − [ADA]p)(1 − p)], where p is the reaction probability. Therefore, for a given experimental system58 with [β-CD] = 10 mmol/L, [ADA] = 0.67 mmol/L, and the equilibrium constant K = 8396 L/mmol, we can directly estimate the reaction probability p = 0.987. To refine and validate the LJ parameters for both β-CD and ADA molecules adopted in this work, we have constructed a system containing 4747 β-CD molecules and 320 ADA molecules in a simulation box with a size of (31.5 nm)3. The concentrations of the two molecules are comparable to the available experimental system.58 Two different initial conditions are set with all 320 ADA molecules either fully separated from or well included in the β-CD pockets. Ten parallel Brownian dynamics simulations started from these two different conditions lead to an almost identical equilibrium state with ∼10.6 isolated ADA molecules and 309.4 ADA·CD complexes on average in the system, resulting in an reaction probability of p = 0.967, which is very close to the experimental value of p = 0.987.58 Note that by directly taking the CG parameters of α-CD from refs 56 and 57, we construct a CG β-CD model in our simulations. All the bead types have the same size as in the αCD model, which can effectively make the simulation setup simpler and speed up the simulations. On the other hand, the incorporation of the ADA into β-CD is the most important issue in our system and it is mainly determined by the interactions between ADA and β-CD atoms instead of the atom sizes in the ADA and β-CD molecules, because the shape and the size of the ADA can match the interior of the β-CD pocket very well. Most importantly, the overall interaction between ADA and the β-CD pocket is attractive. Therefore, we adjust the interactions between the hydrophilic beads of the β-CD and the beads of ADA also to be attractive. Such attractive

σ σ σ σ σ σ σ σ σ σ σ σ σ

= = = = = = = = = = = = =

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

H and P represent the hydrophilic and hydrophobic beads of β-CD, respectively, N represents the −NH2HCl group of ADA, C represents the methyl groups of ADA, S represents the bead of PS monomer, M represents the bead of PMMA monomer. All in reduced units, ε = 0.5 kJ/mol and σ = 0.38 nm. a

Simulation Method. We use Brownian dynamics in our simulations, which has been proven to be very efficient for the simulations of polymers in solution,62 where an additional force Fadd is introduced to represent the effect of the solvents: Fadd = −γ ·v + Frand

(4)

where γ is the friction coefficient, v is the velocity of the CG bead, and Frand is a random force with magnitude being chosen according to fluctuation−dissipation theorem at given friction (γ) and temperature (T). In our simulations, systems containing various β-CD-S4xMxADA (x = 8, 16, 24, and 32) block copolymer precursors are considered. We use a time step of 2.0 fs, and the total simulation time is 2.0 μs for each sample. Ten parallel simulations are performed for each system. The bead coordinates are recorded every 25 ns for each parallel run during the last 1.0 μs for data analysis. All the results are averaged over 10 parallel runs. HOOMD-0.10.1 package63 is used in our simulations. 16286



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Figure 4. Distribution of resulted MBC chain lengths in simulation boxes with different lengths (NDBC) of DBC chains and box sizes (L): (a) NDBC = 160, L = 31.5 nm; (b) NDBC = 120, L = 29.2 nm; (c) NDBC = 80, L = 26.4 nm; (d) NDBC = 40, L = 22.8 nm. Solid circles represent the simulation results, averaged from 10 parallel simulations for each system. The insets show the examples of MBC formed from 6 DBCs.

Figure 5. Number of formed ring molecules in the systems with different chain lengths of DBC precursors. (a) The chain lengths of DBC precursors and simulation box sizes are referred to in Figure 3. (b) The simulation box is fixed at L = 31.5 nm. The solid squares, circles, up triangles, and down triangles represent the results for the systems with diblock chain lengths of NDBC = 160, 120, 80, and 40, respectively.

3. RESULTS AND DISCUSSION

which the host and guest molecules can be viewed as two reactive groups.12 Thus we can apply the Flory formula of linear condensation polymerization to theoretically estimate the MBC chain length distribution in our simulations,

In our simulations, we indeed find that MBCs can be obtained by forming host−guest complexes between terminal groups of DBCs. But these MBCs (especially for those long chains composed of over 10 DBCs) are not very stable; they can easily deassemble into shorter multiblock or even isolated DBC chains. Apparently, it indicates that such a MBC formation process is reversible, which is a characteristic of the host−guest complex formation process. This reversible complex process for generating MBCs is quite similar to the linear condensation polymerization process, for

Nn = n0(1 − p)2 pn − 1

(5)

where n0 is the number of DBCs, Nn is the number of the MBCs composed of n repeated DBCs, and p is the reaction probability that depends on the equilibrium complex constant K defined in eq 3. In the first simulated system, we have 200 initially homogeneously distributed β-CD-S128M32-ADA block copoly16287



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mers in a simulation box with a size of (31.5 nm)3. After a 2.0 μs simulation, a statistic distribution (P(n)) of formed MBCs with different chain lengths (in the number of DBC chains, n) can be obtained by averaging over different snapshots in parallel runs of the last 1.0 μs. The result is shown in Figure 4a. In this system, we finally obtain ∼115.4 β-CD·ADA complexes (except the ones in ring shape) on average, which results in a reaction probability of p = 115.4/200 = 0.577. The value is smaller than that for a pure β-CD and ADA complex system, where p = 0.967. The reason can be attributed to the fact that the diblock polymer chains connecting the two reactive ends will reduce the mobility of reactive β-CD and ADA groups and therefore will reduce the reaction probability. Using the value of p = 0.577, the theoretical prediction from eq 5 is also shown in Figure 4a for comparison. We find that the simulated distribution can be well described by the Flory theory. Most of the MBC chains are short and the population decays rapidly with the increase of the MBC chain length. The resulted MBCs may serve as candidates for further self-assembly: collapse of such MBCs in bad solvent might be used for fabricating patchy particles.11 The influences of the chain length are also evaluated. To deal with this issue, we choose three different chain lengths. Besides the model of S128M32, DBCs composed of 120 beads (S96M24), 80 beads (S64M16), and 40 beads (S32M8) are also simulated. In simulations for all these systems, we also have 200 chains in the simulation box while keeping the number of density constant at 1.235 nm−3 by changing the volume of the simulation box. The box size is set at (29.2 nm)3, (26.4 nm)3, and (22.8 nm)3, for systems containing polymers with chain lengths of 120, 80, and 40, respectively. The results are given in Figure 4b−d. From these figures, we can see that the reaction probability will decease with the decrease in the chain length of the DBC precursors. Moreover, with the chain length decreasing in the DBC precursors, more ring-shaped molecules are found in the system, which will reduce the yield of the linear multiblock chains. Figure 5a shows the number of ring molecules in the four systems. We can see that once the diblock chain is getting shorter, more ring molecules are found in the system. Because most of the ring molecules contain only one DBC, we have not observed any interlocked rings and therefore only count these single DBC rings in Figure 5. The relationship between the number of ring molecules and the chain length can be estimated with the following formula:

Pring = p

N (r ≤rinclusion) N0

To evaluate the effect of the DBC concentration, we have also simulated the last three systems with 200 chains with lengths of 120, 80, and 40 in a simulation box with fixed size of (31.5 nm)3, so that we have a more dilute concentration for shorter diblock chains. Figure 5b shows the number of ring molecules in these systems. We can see that even more ring molecules are found in these diluted systems. It can be easily understood if we consider the diffusive nature of the inclusion reactions between β-CD and ADA groups. In a diluted system, the β-CD and ADA groups belonging to different DBCs have a much smaller chance to react with each other than those groups connected to the same molecule. As more ring molecules appear in the system, there will be less active end groups available for chain propagation. Therefore, to get more multiblock polymer chains, one should use relatively long DBC precursors in relatively high concentration solutions. To further understand the influence of the concentration, we then define the yield of multiblock chains as rmulti = (ntotal − nring − nsingle)/ntotal (here ntotal is the total number of diblock chains, nring is the number of ring molecules, and nsingle is the number of free diblock chains). For all the simulated systems with different chain lengths, we expand the simulated box to 1.5Vi, 2.0Vi, and 2.5Vi, where Vi = (31.5 nm)3 is the initial size of the simulation box. The results are shown in Figure 6 (the distributions of

Figure 6. Yield of MBCs of the four systems with different DBC precursor chain lengths. The solid squares, circles, up triangles, and down triangles represent the results for the systems of DBC chain lengths of NDBC = 160, 120, 80, and 40, respectively. The size of the simulation box is varied from Vi = (31.5 nm)3 to 1.5 Vi, 2.0 Vi, and 2.5 Vi for each system.

MBC chain lengths in these cases are provided in the Supporting Information). We can see that with the increase of box size, the yield of multiblock chains will decrease in all systems, which suggests that dilute solutions should be avoided for the purpose of achieving high yield of multiblock chains. Although the yield will be reduced at lower concentrations, the distribution of the multiblock chain length can be always described by the Flory theory, which in return reflects the robustness of our model. To investigate the MBC formation kinetics, we plot in Figure 7a−d the time evolution of the MBC chain length distributions in the 160-mer, 120-mer, 80-mer, and 60-mer systems, respectively. There are initially 200 isolated DBCs in a simulation box with fixed size of (31.5 nm)3, and the number of DBCs belonging to different MBCs is indicated by vertical color bars at a time interval of 25 ns. As we can see from these

(6)

Pring represents the probability of forming ring-shaped molecules, and p is the reaction probability. rinclusion is a threshold distance, within which the two ends of the DBC are considered to be close enough to react with each other and form an inclusion complex. N(r≤rinclusion) is the number of DBCs with end-to-end distance smaller than rinclusion, and N0 is the total number of MBCs. As the rinclusion is mainly related to the shape and chemical characteristics of β-CD and ADA molecules, it remains a constant when the lengths of the DBC chains change. With the reduction of the chain length from 160 to 40, more chains with end-to-end distance smaller than rinclusion are expected to be found in the system. Thus more ring molecules will form in the system with shorter DBC chains, as shown in Figure 5a. 16288



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host β-CD molecule pockets. At the end of the simulation, we obtain a mixture of MBCs with different chain lengthes. We also observe some ring-shaped molecules formations in the system due to the head-to-tail inclusions of ADA into β-CD belonging to the same DBC, which reduces the final yield of the linear MBCs. At a fixed volume fraction of DBCs, when the chain length of the DBC precursor increases, the system is found to form fewer ring molecules and hence a high yield of MBCs can be achieved. Furthermore, the chain length distribution of resulted MBCs and the reaction probability is found to be dependent on the DBC precursor chain length and it can be well described by the Flory formula for linear condensation polymerization. Therefore, the proposed route of synthesizing MBC via complex between ADA and β-CD molecules can be viewed as a linear condensation polymerization process with DBCs as reactive monomers. Because our coarse-graining strategy is general, different host−guest pairs can be used to replace the β-CD and ADA as the binding end groups. For example, we may choose pairs of βCD/ferrocene, β-CD/naproxen, etc. With the corresponding value of equilibrium constant K, which can be easily derived from experiments, we can directly predict the chain length distribution of the MBCs with those different host−guest pairs as connectors. Thus our method offers a simple way to synthesize MBCs via supramolecular host−guest complexes. Moreover, including the PS-b-PMMA DBCs we are using, the CG β-CD and ADA models can be readily attached to any other synthetic DBCs to synthesize MBCs from them.

Figure 7. Time evolution of the MBC chain length distribution in (a) 160-mer, (b) 120-mer, (c) 80-mer, and (d) 60-mer systems, respectively. Height of each color bar stands for the length (in the number of DBC chains) of each MBC chain in the system. The simulation box is fixed at (31.5 nm)3.

figures, longer MBCs begin to show up with the increase of simulation time, and the population of MBC reaches a steady level after 1000 ns. The stability of the MBC chain is also studied. To achieve this goal, we choose a relatively long MBC chain at 1000 ns, and trace the first DBC molecule as a label of the MBC chain. The number of DBC chains in this MBC chain is recorded during the simulation. As we can see in Figure 8, long MBC chains are not stable and will quickly break into shorter MBCs and quickly re-form into long chains as the time proceeds.

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ASSOCIATED CONTENT

S Supporting Information *

Figures of MBC chain length distribution and radius of gyration (Rg) of 120-mer DBC systems. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*H.-J. Qian: e-mail, [email protected]. *Z.-Y. Lu: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is subsidized by the National Basic Research Program of China (973 Program, 2012CB821500), and supported by National Science Foundation of China (21204029, 21025416, 50930001). Z.Y.L. thanks the finacial support from KITPC for his stay during the KIPTC event: “Advanced Simulation Methods in the Physical Sciences” in June 2013.

Figure 8. Time evolution of the length of a traced MBC chain (labeled by the first DBC in this MBC chain) that initially possesses 10 DBC chains. The simulation box is fixed at (31.5 nm)3.

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REFERENCES

(1) Groschel, A. H.; Schacher, F. H.; Schmalz, H.; Borisov, O. V.; Zhulina, E. B.; Walther, A.; Müller, A. H. Precise Hierarchical Selfassembly of Multicompartment Micelles. Nat. Commun. 2012, 3, 710. (2) Panyukov, S.; Potemkin, I. Phase Diagram of MicrophaseSeparated Multiblock Copolymers. Physica A 1998, 249, 321−326. (3) Hamley, I. W. Nanotechnologie mit Weichen Materialien. Angew. Chem. 2003, 115, 1730−1752. (4) Tsige, M.; Grest, G. S. Molecular Dynamics Study of the Evaporation Process in Polymer Films. Macromolecules 2004, 37, 4333−4335.

4. CONCLUSIONS In summary, we have proposed coarse-grained models for βcyclodextrin and adamantane molecules. The possibility of synthesizing MBCs via the complex formation process between β-CD and ADA groups attached at the synthetic DBC ends are investigated by using Brownian dynamics simulations. We find that at the current accessible simulation time scale, it is very easy for the guest ADA molecules to be included in the 16289



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Synthesize Multiblock Copolymers via Complex Formations between Î²

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