Amphiphilic Block Copolymer Aided Design of Hybrid Assemblies of

Article pubs.acs.org/Macromolecules

Amphiphilic Block Copolymer Aided Design of Hybrid Assemblies of Nanoparticles: Nanowire, Nanoring, and Nanocluster Shiying Ma,†,‡ Yi Hu,† and Rong Wang*,† †

Key Laboratory of High Performance Polymer Materials and Technology of Ministry of Education, Department of Polymer Science and Engineering, State Key Laboratory of Coordination Chemistry and Collaborative Innovation Center of Chemistry for Life Sciences, School of Chemistry and Chemical Engineering, Nanjing National Laboratory of Microstructures, Nanjing University, Nanjing 210093, China ‡ College of Chemistry and Chemical Engineering, Taishan University, Taian 271021, China ABSTRACT: We investigate the self-assembly and aggregation behaviors of nanoparticles in hybrid assemblies made from amphiphilic block copolymer tethered nanoparticles using the dissipative particle dynamics (DPD) approach. By varying the arm number of the tethered amphiphilic block copolymers, hydrophobic block chain length, and interaction parameter between nanoparticle and hydrophobic block, different morphological hybrid aggregates are obtained, including branching rod-like micelles, ring-like micelles, disk-like micelles, and vesicles. Most importantly, the nanoparticles aggregate in the various micelles and form nanowires, nanorings, and nanoclusters. Only using amphiphilic block copolymer tethered nanoparticles, hybrid vesicles including patchy vesicles and heterogeneous vesicles are obtained. Moreover, nanoclusters with distinct number of nanoparticles in hybrid disk-like micelles and vesicles are fabricated through controlling the interaction parameter between nanoparticle and hydrophobic block.

1. INTRODUCTION Hybrid assemblies made from nanoparticles and block copolymers can exhibit collective properties that are different from those of individual nanoparticles. Collective properties of the hybrid assemblies depend on the spatial organization and alignment of nanoparticles as well as the properties of individual building blocks. Hybrid assemblies of nanoparticles display unique electronic, optical, and magnetic properties as a result of coupling and exchange phenomena and have significant potential applications in the fields of biotechnology, biomedicine, and electronics, among others.1−3 Self-assembly of nanoparticles with block copolymers in solution has emerged as a powerful bottom-up method not only for controlling the structures and properties of hybrid assemblies of nanoparticles but also for allowing for selective localization of nanoparticles in different domains of block copolymers aggregates of various morphologies.4−6 The distribution, orientation, and localization of nanoparticles within the aggregates may critically influence the resulting properties and applications of the polymer nanocomposites. For example, locating quantum dots (QDs) in the micellar cores not only can preserve the unique optoelectronic properties of QDs but also can enhance the water solubility, prevent aggregation, extend circulation time, and reduce toxicity to animal body.7,8 Encapsulation of magnetic nanoparticles inside block copolymer aggregates can not only lead to high particle loading but also improve the detection sensitivity in magnetic resonance imaging.9,10 Precise localization of nanoparticles in micellar core or vesicle © XXXX American Chemical Society

membrane can control drug release through an oscillating magnetic field producing local hyperthermia in the magnetic nanoparticles loaded portion of the aggregates.11,12 Therefore, the selective localization of nanoparticles in block copolymer aggregates has been extensively investigated in recent years. Many strategies have been used to precisely localize nanoparticles in different domains of aggregate. For example, Hickey et al.13,14 investigated how to control the distribution of magnetic nanoparticles in micellar core or vesicle wall through changing nanoparticle size or modifying the relative volume ratio between the hydrophobic block and the hydrophilic block. Liu et al.15 obtained unique hybrid Janus-like vesicles with different shapes, patchy vesicles, and heterogeneous vesicles by coassembling molecular amphiphiles of block copolymers and nanoparticle amphiphiles comprising inorganic nanoparticles tethered with amphiphilic block copolymers. The theoretical simulation research may provide valuable microscopic insights and complement the deficiency of experimental studies on the self-assembly of amphiphilic block copolymer tethered nanoparticles.16,17 Glotzer et al.18−23 have systematically studied the effect of building block shape, the polydispersity of nanoparticle, etc., on the selfassembled behaviors of polymer tethered nanoparticles using Brownian dynamics simulation. Jayaraman and co-workers24−30 Received: December 27, 2015 Revised: April 2, 2016

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DOI: 10.1021/acs.macromol.5b02778 Macromolecules XXXX, XXX, XXX−XXX

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have extensively investigated the effects of the nanoparticle diameter, grafted chain length, and grafting density, etc., on the self-assembly of polymer grafted nanoparticle in dense solutions and melts of homopolymer using Monte Carlo simulation or polymer reference interaction site model (PRISM) theory. In our previous research, we investigated the self-assembly of AB diblock copolymer tethered nanoparticles in dilute solution by fixing the number of polymer arms and hydrophobic chain length.31 The interaction parameter between nanoparticle and block copolymers has a significant impact on the overall micellar morphologies and distribution of nanoparticles within the aggregates.31 Nevertheless, many questions are not answered, and detailed investigations about these questions are still needed, such as: How does the number of tethered amphiphilic copolymer affect the overall self-assembled morphologies? How does the interaction between nanoparticle and copolymer affect the aggregation behaviors of nanoparticles within the same shape of aggregate? In this paper, we systematically investigate the self-assembly of amphiphilic copolymer tethered nanoparticle. The number of tethered polymer arms and hydrophobic chain length mostly affect the self-assembled phase behaviors in selective solvents. The self-assembled aggregates exhibit a rich variety of morphological structures, such as branching rod-like micelles, ring-like micelles, vesicles and disk-like micelles. Most importantly, the nanoparticles can form nanowires within the rod-like micelles, nanorings within ring-like or disk-like micelles, and nanoclusters within vesicles or disk-like micelles. Furthermore, we investigate the effect of interaction between nanoparticle and hydrophobic beads and hydrophobic chain length on the aggregation behaviors of nanoparticles within different morphological aggregates. Simulation results show that the nanoparticles gradually aggregate with the increase of interaction between the nanoparticle and hydrophobic bead in vesicles or disk-like micelles. Most importantly, we find that only three or four nanoparticles aggregate to form nanoclusters as the interaction parameter is larger.

Fij⃗ = aijω(rij)riĵ D

Fij⃗ = −γω 2(rij)(riĵ ·vij⃗ )riĵ

f⃗ dvi⃗ = i dt mi

R

fi ⃗ =

∑

+

D Fij⃗

Figure 1. Model of amphiphilic diblock copolymer tethered nanoparticle. The blue bead, red beads, and green beads represent the nanoparticle (P), hydrophobic block (B), and hydrophilic block (A), respectively.

no extra angle force between the copolymer arms. Therefore, the copolymer arms are free to move around the surface of the nanoparticle. There are four different types of DPD particles, including nanoparticle beads (P), hydrophobic beads (B), hydrophilic beads (A), and solvent beads (S), in our simulation system. The concentration of block polymers with nanoparticles P(BmA1)n in the solution (φ) is defined as φ=

+

Npc × Vpc + Nn × Vn Npc × Vpc + Nn × Vn + Ns × Vs

(6)

where Npc, Nn, and Ns are the number of beads of polymer chains, nanoparticle beads, and solvent beads, respectively; Vpc, Vn, and Vs are the volume of one bead of polymer chains, nanoparticle, and solvent, respectively. The concentration of block copolymer tethered nanoparticles (φ) is 0.10 unless otherwise stated in our simulation. The finitely extensible nonlinear elastic (FENE) potential is added between the consecutive particles to bind the connected beads of the diblock copolymer tethered nanoparticle.34

(1)

⎧ 2⎤ ⎡ ⎪− 1 kR 2 ln⎢1 − ⎛⎜ rij ⎞⎟ ⎥ r < R ⎪ 0 ij 0 ⎢⎣ ⎝ R 0 ⎠ ⎥⎦ VFENE(rij) = ⎨ 2 ⎪ ⎪∞ rij ≥ R 0 ⎩

R Fij⃗ )

j≠i

(5)

where aij is the repulsive interaction parameter between particles i and j, rij⃗ = ri ⃗ − rj⃗ , rij = | rij⃗ |, riĵ = rij⃗ /rij , and vij⃗ = vi⃗ − vj⃗ . γ is the friction coefficient governing the magnitude of the dissipative force, σ is the noise amplitude that controls the intensity of the random force, and θij is a randomly fluctuating variable with zero mean and unit variance. The combined effect of the dissipative and random force is that of a thermostat, leading to σ2 = 2γkBT.33 The weight function ω(rij) provides the range of interaction for DPD particle with a commonly used choice: ω(rij) = 1 − rij/rC for rij ≤ rC and ω(rij) = 0 for rij > rC, where rC is the cutoff radius.33 Model. In this work, we focus on the model of amphiphilic diblock copolymer tethered nanoparticle P(BmA1)n, where m is the number of hydrophobic block bead and n represents the number of the copolymer arms, as shown in Figure 1. There is

where ri ⃗ , vi⃗ , mi, and f ⃗ denote the position, velocity, mass of the ith particle, and the acting force on it, respectively. The total force on the ith particle, f i, is the sum of all pairwise interactions as C (Fij⃗

(4)

Fij⃗ = σω(rij)θijriĵ

2. METHOD AND MODEL Method. The dissipative particle dynamics (DPD) method, introduced by Hoogerbrugge and Koelman32 in 1992, is a coarse-grained particle based mesoscopic simulation technique that allows the simulation of hydrodynamic behavior in much larger, complex systems, up to the microsecond range compared to the molecular dynamics (MD) simulations. In a DPD simulation, the coarse-grained DPD particles interact with each other via pairwise interaction that contains conservative force FC, random force FR, and dissipative force FD. All the DPD particles obey Newton’s equation of motion:33 d ri ⃗ = vi⃗ , dt

(3)

(2)

The three pairwise forces are given by B

(7)


Article

Macromolecules We choose k = 30 and the finite extensibility of the FENE spring R0 = 1.5rC.35 The radius of a nanoparticle bead is 2 times that of copolymer bead or solvent bead.36 Solvent beads are included explicitly in the simulation; however, they are not shown in the following figures for clarity. On the basis of the model of the amphiphilic diblock copolymer tethered nanoparticle, we performed the dynamics of total 81 000 DPD beads in a cubic box (303) under the periodic boundary conditions. The number density of all beads in the system is set to 3. In the present simulations, all the block copolymer and solvent beads are of the same mass as m = 1. The interaction cutoff radius for block copolymer and solvent particles is set to rC = 1 as the unit of length, and energy scale kBT = 1. Here, kB is the Boltzmann constant and T is the temperature. The time unit τ is defined as τ = (mrC2/kBT)1/2. Newton’s equation of motion was integrated using modified velocity-Verlet algorithm with λ = 0.65. The DPD step was set as Δt = 0.03 to avoid divergence of the simulation, and the amplitude of random noise is set as σ = 3.0. DPD simulation utilizes soft-repulsive potentials; the systems studied are allowed to evolve much faster than the molecular dynamics. Therefore, a typical DPD simulation requires only about 105 steps to equilibrate.33,37 In our simulation, each simulation takes at least 1.2 × 106 steps, and the last 2 × 105 steps are for statistics. The morphology of aggregate at equilibrium is independent of the initial conditions. The different size of boxes does not affect the formation of aggregations except the number of aggregates in the boxes after equilibrium.37 The repulsive interaction parameters chosen are shown by a symmetric matrix ⎛ ⎜ ⎜P aij = ⎜ B ⎜ ⎜A ⎜ ⎝S

B A S ⎞ ⎟ aPB 65 150 ⎟ aPB 25 50 75 ⎟ ⎟ 65 50 25 25 ⎟ ⎟ 150 75 25 25 ⎠

3. RESULTS AND DISCUSSION Morphological Diagram of Aggregates Formed by Diblock Copolymers Tethered Nanoparticles. In this

P 25

Figure 2. (a) Morphological phase diagram of aggregates formed by model polymer as a function of tethered arm number and hydrophobic chain length. (b) Characteristic morphological snapshots illustrated for various tethered arm number and hydrophobic chain length. (The arrow points to the cross-sectional slice of the aggregate, and the blue beads represent nanoparticles.)

(8)

Typically, the pairwise repulsive interaction parameter between the same type of DPD particles is set as aii = 25 for density ρ = 3 to match the compressibility of water.33 The interaction parameter between different particles i and j can be estimated by the relationship between the aij and Flory−Huggins interaction parameter χij at ρ = 3 according to the relation33 aij ≈ aii + 3.27χij. The interaction parameters can be determined from the calculation of dimensionless compatibility. So the value of aij ≤ 25 corresponds to χij ≤ 0, which indicates that beads i and j are fairly compatible. As the incompatibility between i and j increases, aij rises from 25. The long polymer chains can be represented by short chains in DPD if the χ parameter increases at the same time because χN can be used to describe the interaction of diblock copolymers.33 Therefore, the long polymer chains on relatively small DPD chains with different interaction parameters can be actually simulated after applying these parameters.33,38 Here, since the nanoparticle and block B are hydrophobic, we choose aPS = 150 and aBS = 75. Note that the repulsive interaction between the nanoparticle and solvent is stronger than that between hydrophobic block B and solvent. The interaction parameter between hydrophilic block A and solvent is set as aAS = 25. The values of aPB is tunable in the simulation in order to examine the aggregation behavior of nanoparticles.

Figure 3. Morphological phase diagram of aggregates formed by eight arms tethered nanoparticle P(BnA1)8 as a function of interaction parameter aPB and hydrophobic chain length with fixed aPA = 65.

section, we intend to investigate the effects of the number of polymer arm and hydrophobic chain length on the selfassembled behaviors of the block copolymer tethered nanoparticles by constructing the morphological phase diagram. In this subsection, the interaction parameter between nanoparticle C


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Figure 4. Effects of the interaction parameter between nanoparticle and hydrophobic bead on the distribution of nanoparticle in vesicles formed by amphiphilic block copolymer tethered nanoparticle P(B4A1)8.

Figure 5. Radial distribution function g(r) of nanoparticles within the membrane of vesicles.

Figure 7. Radial distribution function g(r) of nanoparticles within the disk-like micelles.

and block copolymer is set as aPA = 65 and aPB = 75, respectively. Figure 2a shows the morphological phase diagram of model polymer as a function of the arm number of the copolymers and hydrophobic chain length. Four distinct types of aggregates are observed: branched rod-like micelles, ring-like micelles, disk-like micelles, and vesicles. In general, vesicles form for more polymer arms, and rod-like or ring-like micelles take shape for less polymer arms. The characteristic morphological snapshots are illustrated in Figure 2b (the arrow points to the cross-sectional slice of the aggregate). Compared with our previous studies,31 the branching rod-like micelles and ring-like micelles are observed; see the lower part of the phase diagram shown in Figure 2b. Branching probably

takes place because of polydispersity in size and shape of selfassembling micelle units.39 Because of the increase of the arm number and the hydrophobic chain length, as intermicellar interaction proceeds, the more arms or longer hydrophobic chain in the surface of aggregates have not enough time to adjust their positions before assembling into a growing rod-like micelle, which leads to two aggregates attaching and forming a branch. With further increasing the hydrophobic chain length (nB > 4), the branching rod-like micelles bend and close to form ring-like micelles. This is because the bending energy of rod-like micelles decreases with the increase of the hydrophobic chain length. The vesicles exist in the upper part (more polymer arms) of the phase diagram (Figure 2). The coverage

Figure 6. Effects of the interaction parameter between nanoparticle and hydrophobic bead on the distribution of nanoparticle in disk-like micelles formed by amphiphilic block copolymer tethered nanoparticle P(B8A1)8. D


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We also examine the distribution of nanoparticles in disk-like micelles. Figures 6 displays the distribution of nanoparticles in disk-like micelles formed by amphiphilic block copolymers tethered nanoparticle P(B8A1)8. The variation of radial distribution of nanoparticle in disk-like micelles is similar to that in the membrane of vesicles. With the increase of aPB, nanoparticles in disk-like micelles also gradually aggregate together (the arrow in Figure 7). Most interesting, we find that only three or four nanoparticles aggregate to form nanoclusters as aPB = 75. Furthermore, we analyze the radial distribution of nanoparticles as shown in Figure 7. The height of first highest peaks as aPB = 75 almost is 3 times that as aPB = 25, which also indicates that three or four nanoparticles aggregate to form nanoclusters. This may be because nanoparticles prefer to aggregate themselves as the repulsive interaction between the nanoparticle and hydrophobic beads in order to decrease the contact with hydrophobic beads. So, we can fabricate nanoclusters with distinct number of nanoparticles through controlling the interaction parameter between nanoparticle and hydrophobic block.

degree of the nanoparticles increases with the increase of tethered polymer arms. Vesicles are developed due to the geometrical packing. Aggregation behaviors of nanoparticles in hybrid assemblies may critically affect their resulting properties and potential applications. We examined the aggregation behavior of nanoparticles in different morphological aggregates. Figure 2b shows the morphologies of aggregated nanoparticles in various micelles (the blue beads). Nanoparticles aggregate and form nanowires or nanorings in the center portion of rod-like micelles and ring-like micelles. However, nanoparticles take shape nanoclusters in disk-like micelles or vesicular membrane. This is because the surface of nanoparticle is covered by more polymer chains with the increase of the polymer arms and hydrophobic chain length. It is difficult for nanoparticles close enough to form linear or ring-like aggregates. This result shows that only few nanoparticles get together to form nanoclusters. Aggregation Behaviors of Nanoparticles in Hybrid Assemblies. As we have mentioned in the previous section, the aggregation behavior of nanoparticles is affected by polymer arm number and hydrophobic chain length, especially the aggregation of nanoparticles in disk-like micelles and vesicles. In order to illustrate the aggregation behaviors of nanoparticles in disk-like micelles and vesicles, we further investigate the effect of interaction parameter between nanoparticle and hydrophobic bead and hydrophobic chain length on aggregation behaviors of nanoparticle. First, we construct the morphological phase diagram for narm = 8 as a function of Bblock length and interaction parameter between nanoparticle and hydrophobic bead (aPB), as shown in Figure 3. Only three distinct aggregates are observed: vesicle, disk-like micelle, and spherical micelle. In general, vesicle forms for short B-block and disk-like micelle takes shape for long B-block length and large aPB. With the increase of the length of B-block, the morphology of aggregates changes from vesicle to disk-like micelle and further to spherical micelle. This may be because the bending energy of disk-like micelle increases with the increase of the Bblock length. Second, we mainly devote to studying the distribution of nanoparticle in vesicles and disk-like micelle. Figure 4 shows the distribution of nanoparticles in the half of vesicles formed by amphiphilic block copolymer tethered nanoparticle P(B4A1)8. From Figure 4, we can find that nanoparticles evenly distribute in the center of vesicular walls and form monolayer spherical shell as aPB = 25; that is, nanoparticle and B-block are compatible. With increasing of aPB, nanoparticles gradually aggregate and take shape patchy vesicles. Our simulation findings are consistent with the experimental observations.15,40,41 Most importantly, we present a new method to fabricate hybrid vesicles including patchy vesicles, and heterogeneous vesicles, only using amphiphilic block copolymers tethered nanoparticles. In the previous research, these hybrid vesicles are obtained by coassembling block copolymers and amphiphilic block copolymers tethered nanoparticles.15 To illustrate the distribution of nanoparticles in the membrane of vesicles, we calculate the radial distribution function g(r) of nanoparticles. Figure 5 displays the variation of g(r) of nanoparticles in the membrane of vesicles. It can be seen that the first highest peaks gradually move to the origin as the increase of aPB (the arrow in Figure 5), which indicates that the nanoparticles in the membrane of vesicles aggregate together gradually.

4. CONCLUSIONS In summary, we have employed dissipative particle dynamics (DPD) to study the aggregation behaviors of nanoparticles in hybrid assemblies made from amphiphilic block copolymers tethered nanoparticles in solutions, which can offer valuable microscopic insights and complement the deficiency of experimental studies on the self-assembly of nanoparticle amphiphiles. Through changing the arm number of the tethered amphiphilic block copolymers, the hydrophobic block chain length, and the interaction parameter between nanoparticle and hydrophobic block, we fabricate various hybrid aggregates, including branched rod-like micelles, disklike micelles, ring-like micelles, spherical micelles, and vesicles. Those hybrid aggregates have potential applications in sensing,42 bioimaging,43 drug delivery,44,45 nano- or microreactors,46 and optoelectronics.47 Most importantly, we present a new method to fabricate hybrid vesicles including patchy vesicles, and heterogeneous vesicles, only using amphiphilic block copolymers tethered nanoparticles. Furthermore, we can fabricate nanoclusters with distinct number of nanoparticles through controlling the interaction parameter between nanoparticle and hydrophobic block. Therefore, the simulation findings might be valuable for guiding the experimental studies to fabricate structurally complex functional materials with broad applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Grants 21474051, 21074053, and 51133002) and Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT). The numerical calculations in this paper have been done on the IBM Blade cluster system in the High Performance Computing Center (HPCC) of Nanjing University. E


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