Synthesize Multiblock Copolymers via Complex Formations betweenβ‑Cyclodextrin and Adamantane Groups Terminated at DiblockCopolymer Ends: A Brownian Dynamics Simulation StudyWei 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, Changchun130023, China

*S Supporting Information

ABSTRACT: Coarse-grained models for β-cyclodextrin (β-CD) and adamantane (ADA) areproposed by fitting to their experimental host−guest complex equilibrium constant insolution. By using Brownian dynamics simulations, we suggest a simple supramolecular routefor synthesizing multiblock copolymers (MBCs) via forming complexes between β-CD andADA groups terminated at the chain ends of diblock copolymers (DBCs). The chain lengthdistribution of the resulted MBC is found to follow the statistics of Flory formula for typicallinear condensation polymerization process. Therefore, the proposed supramolecular routecan be viewed as a novel linear condensation polymerization process with DBCs as reactivemonomers. Due to the complex formations between head and tail (β-CD and ADA), ring-shaped 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 areapplicable 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 ofcomplex materials, hierarchical self-assembly was proven to bean outstanding method.1 In recent years, block copolymershave received intense research interests due to their ability toself-assemble at length scales spanning from a few nanometersto micrometers.2−6 As a family member, MBCs are often usedto fabricate special materials applied in the fields ofbiochemistry,7,8 electrochemistry,9,10 etc. Recently, Zhang etal. proposed a route to fabricate patchy particles from thecollapse of MBCs in dilute solution.11 Such patchy particlespossess the ability to pack into more complicated orderedstructures at higher level through a hierarchical self-assemblyprocess.12,13

There are many ways of synthesizing block copolymers. Inearly times, people preferred to use techniques of living anionicpolymerization,14,15 ring-opening polymerization,16,17 cationicpolymerization,18,19 or condensation polymerization.20 How-ever, most of them do not tolerate even extremely low levels ofimpurities and are compatible only with a limited number ofmonomers. With the development of controlled free-radicaltechniques, many other ways had been developed, such asnitroxide-mediated polymerization,21 atom transfer radicalpolymerization (ATRP),22−24 reversible addition−fragmenta-tion chain transfer (RAFT),25−27 and some other novel wayslike combining ATRP and RAFT,28,29 Cu(0)-mediated radicalpolymerization,30,31 etc. Recently, “click chemistry” was alsodeveloped for the synthesis of MBCs.32−34

Alternatively, MBCs can also be fabricated by usingsupramolecular techniques.35−38 One simple way is to borrow

the idea from the concepts of host−guest interactions: the hostmolecule normally has a good affinity toward the guestmolecule, as a consequence the host molecule will catch theguest molecule when they are approaching each other.Therefore, when the covalent bonds that hold the monomericunits together in a macromolecule are replaced by such highlydirectional noncovalent interactions, supramolecular polymerstructures can also be achieved.39,40 In this respect, β-cyclodextrin (β-CD) is a good candidate for a host moleculewith quite outstanding properties. It consists of seven D-glucopyranose residues, linked by R-1,4 glycosidic bonds into amacrocycle.41 The relatively hydrophobic interior and hydro-philic exterior of the molecular pockets make them suitable andfascinating hosts for small hydrophobic molecules withcompatible sizes to the interior pockets.42−47 Among varioushost−guest pairs, the inclusion complex between β-CD andadamantane (ADA) in aqueous solution had been mostlyinvestigated due to its high binding ability.47−51 With β-CD andADA as binding groups, several supramolecular methods hadbeen proposed to obtain an amount of interesting polymerarchitectures connected through noncovalent attractive host−guest binding associations between various building blocks.52

Therefore, it is quite interesting to examine the possibility ofsynthesizing MBCs via host−guest coupling interactionsbetween the β-CD and ADA groups terminated at the DBCchain ends. In such a way, the MBC chain length can be

Received: July 23, 2013Revised: October 20, 2013Published: November 21, 2013

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reversibly tailored by changing temperature or solventcondition, making the synthesis process practically easy andenvironmentally friendly.The aim of this study is to use computer simulations to

elucidate the possibility of synthesizing MBCs via host−guestbinding processes between β-CD and ADA terminal groupsattached on DBCs. However, due to the limited capability ofbrute force atomistic molecular dynamics simulations, weinstead propose coarse-grained models of β-CD, ADA andpolymer chains. The association process between β-CD andADA groups are simulated in a dilute solution by usingBrownian dynamics. Effects of the concentration and the chainlength of DBC precursors are evaluated. During the simulation,we do find MBC chain formations via the coupling between thetwo terminal groups belonging to different DBCs. Because ageneric DBC chain model is used in our simulations, theproposed host−guest coupling “reactions” between β-CD andADA groups can be in principle applied to all synthetic DBCs.Furthermore, the block sequence on target MBCs and volumefraction of different blocks can be easily tuned by varying theratio of the two blocks in DBC precursors.This paper is organized as follows: In section 2, the coarse-

grained models of DBC chain, β-CD and ADA groups aredescribed. The details of Brownian dynamics simulations aregiven. Section 3 shows the main results and discussion. Finalconclusions are presented in section 4.

2. MODEL AND SIMULATION METHOD

Coarse-Grained Models. Compared with all-atom simu-lation models, coarse-grained (CG) models use reduceddegrees of freedom and have a relatively smoother potentialenergy landscape; therefore, it can significantly accelerate thesimulation and extend both the time and the length scales ofsimulated system.53 The essential of the coarse-graining is tomake appropriate coarse-grain descriptions for given moleculesby grouping several atoms into a single CG bead. Dependingon particular phenomena of interest at different length/timescales, various CG models can be adopted with only importantdegrees of freedom kept in the system while some otherunnecessary degrees of freedom are abandoned. Therefore,attentions must be paid to keep important degrees of freedomduring a coarse-graining process; i.e., it is crucial in this study tomake coarse-grained models for β-CD and ADA groups bykeeping characteristics of host−guest interactions betweenthem.Figure 1 shows the schematic DBC model with host β-CD

(marked in yellow) and guest ADA (marked in red) moleculesattached on both ends of a block copolymer chain ends. Herewe use PS-b-PMMA, which is widely used in experiments, asour representative for incompatible DBCs. Experimentally,adding functional groups onto block copolymer chain ends canbe achieved through several techniques.54,55 With these end-functionalized DBCs distributed in dilute solution, inclusion of(red) ADA groups into pockets of (yellow) β-CD groups canbe expected, as schematically illustrated in Figure 2. In such a

Figure 1. CG model for the PS-b-PMMA chain with functional terminals. Models on the upper left show the molecular structure and schematicshape of β-CD. The yellow bead represents the hydrophilic part, called the H bead, and the orange bead represents the hydrophobic part, called theP 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 bluebead represents the PMMA unit, naming M bead.

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

In the following, we will show the details of CG models forblock copolymers as well as the host and guest molecules. Ashas been discussed above, hydrophilic shell and hollowhydrophobic cavity are essential characteristics of β-CD. Tokeep these characteristic features and the shape of the molecule,we use two bead types in our CG model to represent the β-CDmolecule, one represents the hydrophilic part and the other thehydrophobic part (as shown in Figure 1). The hydrophilicbeads coarsely represent the hydroxymethyl and hydroxylgroups stretched outside the β-CD molecule, whereas thehydrophobic beads represent other atoms inside. A coarse-grained α-CD model proposed by Urakami and co-workers56,57

is utilized to build up our β-CD model by adding one more D-glucose structure in the cyclic amylose structure. Thecorresponding parameters are refined to better reproduce thestructural properties of β-CD. To be consistent with experi-ments, we use the ADA derivative, 1-adamantananimehydrochloride (also abbreviated for ADA in the followingtext), in our simulations.58 In the coarse-grained ADA model,one bead is used to represent the −NH2HCl group, and fourother beads represent −CH and −CH2 groups (as shown inFigure 1). The coarse-graining level of our models for β-CDand ADA is similar to that of the MARTINI force field;59−61

i.e., one CG bead represents 2−4 heavy atoms. As shown inFigure 1, the main part of ADA model is represented by fourbeads connected in a shape of tetrahedron, which can keep thesymmetry of ADA molecule in Td point group. For the DBCchain in our simulations, we use one bead to represent eitherone PS or one PMMA monomer, respectively; therefore, wehave two bead types in the DBC chain. A schematic mapping isshown in Figure 1 for illustration (green S beads represent PSmonomers, whereas blue M beads for PMMA monomers). Tobe consistent with previous work,11 we also construct a DBCmodel containing 160 monomers with a ratio between PS andPMMA bead numbers (monomers) of 3:1; i.e., we have a block

copolymer model of S128M32. β-CD is attached at the end of PSblock and ADA group at the end of PMMA block.

Coarse-Grained Potentials. Bonded Forces. Both bondsand angles are described by harmonic potentials in our CGsimulations,

= −U k r r12

( )ij ijbond bond ,02

(1)

θ θ= −U k12

( )ijk ijkangle angle ,02

(2)

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

The parameters of the bond and angle forces for β-CD aretaken from refs 56 and 57. To reflect the geometriccharacteristics of β-CD, some parameters are slightly modified.Following the parametrization strategy in refs 56 and 57, thebond and angle force parameters for ADA are determinedreferring to the real shape and size of the molecule. Parametersfor PS and PMMA blocks are taken directly from ref 11. Theparameter 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 thenonbonded interactions. LJ parameters ε and σ are energy andlength units, respectively. As has been explained above, themost important part of our simulations is the host−guestinteractions between β-CD and ADA. Their nonbondedinteraction parameters should have the capability to reflectexperimental host−guest complex characteristic, which can berepresented by the equilibrium complex constant K, as definedby58

ββ

= ‐ ·‐

K[ CD ADA]

[ CD][ADA] (3)

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

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

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

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complex between them in equilibrium, respectively. The valueof the constant K actually represents the complex strengthbetween this host−guest pair. For a system with the initialconcentration of ADA group smaller than that of β-CD, theformula can be rewritten as K = p/[([β-CD] − [ADA]p)(1 −p)], where p is the reaction probability. Therefore, for a givenexperimental 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 asystem containing 4747 β-CD molecules and 320 ADAmolecules in a simulation box with a size of (31.5 nm)3. Theconcentrations of the two molecules are comparable to theavailable experimental system.58 Two different initial conditionsare set with all 320 ADA molecules either fully separated fromor well included in the β-CD pockets. Ten parallel Browniandynamics simulations started from these two differentconditions lead to an almost identical equilibrium state with∼10.6 isolated ADA molecules and 309.4 ADA·CD complexeson average in the system, resulting in an reaction probability ofp = 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-CDfrom refs 56 and 57, we construct a CG β-CD model in oursimulations. All the bead types have the same size as in the α-CD model, which can effectively make the simulation setupsimpler and speed up the simulations. On the other hand, theincorporation of the ADA into β-CD is the most importantissue in our system and it is mainly determined by theinteractions between ADA and β-CD atoms instead of the atomsizes in the ADA and β-CD molecules, because the shape andthe size of the ADA can match the interior of the β-CD pocketvery well. Most importantly, the overall interaction betweenADA and the β-CD pocket is attractive. Therefore, we adjustthe interactions between the hydrophilic beads of the β-CD andthe beads of ADA also to be attractive. Such attractive

interactions can guarantee the efficient inclusion of ADA into β-CD pocket. By doing so, we can very well reproduce theexperimental complex formation equilibrium constant Kbetween β-CD and ADA in our simulations, as we haveshown above.As for bonded parameters, the nonbonded LJ parameters

used in ref 11 for PS and PMMA polymers are adopted directlyin this work. The radius of gyration (Rg) of polymer chains insolution simulated with these parameters shows a chain lengthN dependence of Rg ∼ N0.455, which is non-Gaussian and a littlecontracted, implying a slightly bad solvent condition. Tosimplify our model, we use the same nonbonded parametersbetween M and M beads as those between S and S beads. Torepresent the incompatibility between S and M beads, wesimply make the value of ε between S and M beads half thatbetween S−S or M−M bead pairs. For the other unlike beadpairs, ε are calculated by using Lorentz−Berthelot mixing rules.All the nonbonded parameters are listed in Table 2.

Simulation Method. We use Brownian dynamics in oursimulations, which has been proven to be very efficient for thesimulations of polymers in solution,62 where an additional forceFadd is introduced to represent the effect of the solvents:

γ= − · +F v Fadd rand (4)

where γ is the friction coefficient, v is the velocity of the CGbead, and Frand is a random force with magnitude being chosenaccording to fluctuation−dissipation theorem at given friction(γ) and temperature (T).In our simulations, systems containing various β-CD-S4xMx-

ADA (x = 8, 16, 24, and 32) block copolymer precursors areconsidered. We use a time step of 2.0 fs, and the totalsimulation time is 2.0 μs for each sample. Ten parallelsimulations are performed for each system. The beadcoordinates are recorded every 25 ns for each parallel runduring the last 1.0 μs for data analysis. All the results areaveraged over 10 parallel runs. HOOMD-0.10.1 package63 isused in our simulations.

Table 1. Equilibrium Bond Lengths and Angles of β-CD,ADA, and PS (PMMA)a

bond lengths (Å) r1 = 0.640kbond = 1000 r2 = 0.689(kbond = 5000) r3 = 1.39

r4 = 1.39r5 = 1.13r6 = 1.13r7 = 0.647

bond angles (deg) θ1 = 0.122kangle = 500 θ2 = 1.01(kangle = 656) θ3 = 0.192

θ4 = 1.09θ5 = 1.60θ6 = 1.57θ7 = 1.53θ8 = 1.57θ9 = 1.05θ10 = 2.53θ11 = 2.04

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

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

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

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

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3. RESULTS AND DISCUSSION

In our simulations, we indeed find that MBCs can be obtainedby forming host−guest complexes between terminal groups ofDBCs. But these MBCs (especially for those long chainscomposed of over 10 DBCs) are not very stable; they can easilydeassemble into shorter multiblock or even isolated DBCchains. Apparently, it indicates that such a MBC formationprocess is reversible, which is a characteristic of the host−guestcomplex formation process.This reversible complex process for generating MBCs is quite

similar to the linear condensation polymerization process, for

which the host and guest molecules can be viewed as tworeactive groups.12 Thus we can apply the Flory formula of linearcondensation polymerization to theoretically estimate the MBCchain length distribution in our simulations,

= − −N n p p(1 )nn

02 1

(5)

where n0 is the number of DBCs, Nn is the number of theMBCs composed of n repeated DBCs, and p is the reactionprobability that depends on the equilibrium complex constantK defined in eq 3.In the first simulated system, we have 200 initially

homogeneously distributed β-CD-S128M32-ADA block copoly-

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 simulationresults, 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 precursorsand 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 downtriangles represent the results for the systems with diblock chain lengths of NDBC = 160, 120, 80, and 40, respectively.

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mers in a simulation box with a size of (31.5 nm)3. After a 2.0μs simulation, a statistic distribution (P(n)) of formed MBCswith different chain lengths (in the number of DBC chains, n)can be obtained by averaging over different snapshots in parallelruns of the last 1.0 μs. The result is shown in Figure 4a. In thissystem, we finally obtain ∼115.4 β-CD·ADA complexes (exceptthe ones in ring shape) on average, which results in a reactionprobability of p = 115.4/200 = 0.577. The value is smaller thanthat for a pure β-CD and ADA complex system, where p =0.967. The reason can be attributed to the fact that the diblockpolymer chains connecting the two reactive ends will reducethe mobility of reactive β-CD and ADA groups and thereforewill reduce the reaction probability. Using the value of p =0.577, the theoretical prediction from eq 5 is also shown inFigure 4a for comparison. We find that the simulateddistribution can be well described by the Flory theory. Mostof the MBC chains are short and the population decays rapidlywith the increase of the MBC chain length. The resulted MBCsmay serve as candidates for further self-assembly: collapse ofsuch MBCs in bad solvent might be used for fabricating patchyparticles.11

The influences of the chain length are also evaluated. To dealwith this issue, we choose three different chain lengths. Besidesthe model of S128M32, DBCs composed of 120 beads (S96M24),80 beads (S64M16), and 40 beads (S32M8) are also simulated. Insimulations for all these systems, we also have 200 chains in thesimulation box while keeping the number of density constant at1.235 nm−3 by changing the volume of the simulation box. Thebox size is set at (29.2 nm)3, (26.4 nm)3, and (22.8 nm)3, forsystems containing polymers with chain lengths of 120, 80, and40, respectively. The results are given in Figure 4b−d. Fromthese figures, we can see that the reaction probability willdecease with the decrease in the chain length of the DBCprecursors.Moreover, with the chain length decreasing in the DBC

precursors, more ring-shaped molecules are found in thesystem, which will reduce the yield of the linear multiblockchains. Figure 5a shows the number of ring molecules in thefour systems. We can see that once the diblock chain is gettingshorter, more ring molecules are found in the system. Becausemost of the ring molecules contain only one DBC, we have notobserved any interlocked rings and therefore only count thesesingle DBC rings in Figure 5. The relationship between thenumber of ring molecules and the chain length can beestimated with the following formula:

=≤

P pN r r

N( )

ringinclusion

0 (6)

Pring represents the probability of forming ring-shapedmolecules, and p is the reaction probability. rinclusion is athreshold distance, within which the two ends of the DBC areconsidered to be close enough to react with each other andform an inclusion complex. N(r≤rinclusion) is the number ofDBCs with end-to-end distance smaller than rinclusion, and N0 isthe total number of MBCs. As the rinclusion is mainly related tothe shape and chemical characteristics of β-CD and ADAmolecules, it remains a constant when the lengths of the DBCchains change. With the reduction of the chain length from 160to 40, more chains with end-to-end distance smaller thanrinclusion are expected to be found in the system. Thus more ringmolecules will form in the system with shorter DBC chains, asshown in Figure 5a.

To evaluate the effect of the DBC concentration, we havealso simulated the last three systems with 200 chains withlengths 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 forshorter diblock chains. Figure 5b shows the number of ringmolecules in these systems. We can see that even more ringmolecules are found in these diluted systems. It can be easilyunderstood if we consider the diffusive nature of the inclusionreactions between β-CD and ADA groups. In a diluted system,the β-CD and ADA groups belonging to different DBCs have amuch smaller chance to react with each other than those groupsconnected to the same molecule. As more ring moleculesappear in the system, there will be less active end groupsavailable for chain propagation. Therefore, to get moremultiblock polymer chains, one should use relatively longDBC precursors in relatively high concentration solutions. Tofurther understand the influence of the concentration, we thendefine 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 offree diblock chains). For all the simulated systems with differentchain lengths, we expand the simulated box to 1.5Vi, 2.0Vi, and2.5Vi, where Vi = (31.5 nm)3 is the initial size of the simulationbox. The results are shown in Figure 6 (the distributions of

MBC chain lengths in these cases are provided in theSupporting Information). We can see that with the increaseof box size, the yield of multiblock chains will decrease in allsystems, which suggests that dilute solutions should be avoidedfor the purpose of achieving high yield of multiblock chains.Although the yield will be reduced at lower concentrations, thedistribution of the multiblock chain length can be alwaysdescribed by the Flory theory, which in return reflects therobustness of our model.To investigate the MBC formation kinetics, we plot in Figure

7a−d the time evolution of the MBC chain length distributionsin the 160-mer, 120-mer, 80-mer, and 60-mer systems,respectively. There are initially 200 isolated DBCs in asimulation box with fixed size of (31.5 nm)3, and the numberof DBCs belonging to different MBCs is indicated by verticalcolor bars at a time interval of 25 ns. As we can see from these

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

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

4. CONCLUSIONSIn summary, we have proposed coarse-grained models for β-cyclodextrin and adamantane molecules. The possibility ofsynthesizing MBCs via the complex formation process betweenβ-CD and ADA groups attached at the synthetic DBC ends areinvestigated 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

host β-CD molecule pockets. At the end of the simulation, weobtain a mixture of MBCs with different chain lengthes. Wealso observe some ring-shaped molecules formations in thesystem due to the head-to-tail inclusions of ADA into β-CDbelonging to the same DBC, which reduces the final yield of thelinear MBCs. At a fixed volume fraction of DBCs, when thechain length of the DBC precursor increases, the system isfound to form fewer ring molecules and hence a high yield ofMBCs can be achieved. Furthermore, the chain lengthdistribution of resulted MBCs and the reaction probability isfound to be dependent on the DBC precursor chain length andit can be well described by the Flory formula for linearcondensation polymerization. Therefore, the proposed route ofsynthesizing MBC via complex between ADA and β-CDmolecules can be viewed as a linear condensation polymer-ization 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 asthe binding end groups. For example, we may choose pairs of β-CD/ferrocene, β-CD/naproxen, etc. With the correspondingvalue of equilibrium constant K, which can be easily derivedfrom experiments, we can directly predict the chain lengthdistribution of the MBCs with those different host−guest pairsas connectors. Thus our method offers a simple way tosynthesize MBCs via supramolecular host−guest complexes.Moreover, including the PS-b-PMMA DBCs we are using, theCG β-CD and ADA models can be readily attached to anyother synthetic DBCs to synthesize MBCs from them.

■ ASSOCIATED CONTENT*S Supporting InformationFigures of MBC chain length distribution and radius of gyration(Rg) of 120-mer DBC systems. This information is availablefree of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*H.-J. Qian: e-mail, hjqian@jlu.edu.cn.*Z.-Y. Lu: e-mail, luzhy@jlu.edu.cn.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work is subsidized by the National Basic ResearchProgram of China (973 Program, 2012CB821500), andsupported by National Science Foundation of China(21204029, 21025416, 50930001). Z.Y.L. thanks the finacialsupport from KITPC for his stay during the KIPTC event:“Advanced Simulation Methods in the Physical Sciences” inJune 2013.

■ REFERENCES(1) Groschel, A. H.; Schacher, F. H.; Schmalz, H.; Borisov, O. V.;Zhulina, E. B.; Walther, A.; Muller, A. H. Precise Hierarchical Self-assembly of Multicompartment Micelles. Nat. Commun. 2012, 3, 710.(2) Panyukov, S.; Potemkin, I. Phase Diagram of Microphase-Separated 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 theEvaporation Process in Polymer Films. Macromolecules 2004, 37,4333−4335.

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 thenumber of DBC chains) of each MBC chain in the system. Thesimulation box is fixed at (31.5 nm)3.

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

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