Dissipative Particle Dynamics Simulation on the Nanocomposite

Article pubs.acs.org/IECR

Dissipative Particle Dynamics Simulation on the Nanocomposite Delivery System of Quantum Dots and Poly(styrene‑b‑ethylene oxide) Copolymer Pihui Pi,† Dongxia Qin,† Jia-ling Lan,† Zhiqi Cai,‡ Xianxia Yuan,§ Shou-ping Xu,*,† Lijuan Zhang,† Yu Qian,† and Xiufang Wen*,† †

The School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, People’s Republic of China 510640 ‡ Shaoguan Institute, Jinan University, Shaoguan City, People’s Republic of China 512026 § Department of Chemical Engineering, Shanghai Jiao Tong University, Shanghai, People’s Republic of China 200240 S Supporting Information *

ABSTRACT: Dissipative particle dynamics (DPD) simulation was used to investigate the self-assembling dynamics process of poly(styrene-b-ethylene oxide) (PS-b-PEO) block copolymer and quantum dots (QDs) in an aqueous solution. The effects of molecular weight (MW) and segment construction of a PS−PEO block copolymer on the structure and size of the self-assembled micelles were discussed. The structural properties of micelles were characterized by a radial distribution function. The simulation results are qualitatively consistent with those of previous experiments and show that there are only small QD clusters. The hydrophobic PS chains form the micelle core, while the hydrophilic PEO chains form the shell. The size of the self-assembled PS−PEO/QDs micelle increases with the MW of PS-b-PEO block copolymer and the lengths of PEO and PS segments. The simulation results indicate that the assembling process includes four sequential transient stages: (1) the random distribution of all components in aqueous solution; (2) formation of small clusters with polymer chains and QDs; (3) crashing together of small spheres and the formation of larger aggregates; (4) stabilization of assembled micelles. The simulation reveals the physical insights of the QD loading mechanism of the PEG micelle at the mesoscopic scale, indicating the DPD simulation can be used as an adjunct to provide other valuable information for experiments. structure of the molecule. Ruan and co-workers26found that PS−PEO block copolymer with MWs of 3800-b-6500 Da and 9500-b-18 000 Da could form CNPs with diameters of 25 and 40 nm, respectively. However, the QD loading mechanism of this PEO−PS block polymer is not clear yet. Dissipative particle dynamics (DPD) simulation can reveal the mesoscopic-level information in the formation of PEO/ nanoparticles, such as the self-assembling structure and the encapsulation mechanism. Huang and co-workers used the DPD method to investigate the response of the nanoparticle aggregation to a continuous increase of double-hydrophilic block copolymer concentration (DHBC).27 DPD had been used to simulate different nanoparticle systems, including gold nanoparticles in PEO−PPO−PEO block copolymer micelles28 and binary nanoparticle mixtures in lamellar diblock copolymers.29 In our early work, DPD simulation was employed to investigate the micelle behaviors of cross-linked block fluorinated copolymer in different solvents, where the simulation results agreed satisfactorily with the experiment results.30 In this work, DPD simulation and coarse-grained models were coupled to study the self-assembling dynamics process of

1. INTRODUCTION Nanoparticles have shown great potential in biomedical applications including diagnosis, treating, and imaging of diseases.1−7 In particular, single-component nanomaterials, such as quantum dots (QDs) and carbon nanotubes, have shown great potential for in vivo applications.8−13 However, these nanomaterials are limited due to nonspecific adsorption and aggregation when they are used as biomarkers in vivo,14,15 e.g., fluorescence in situ hybridization.16 To solve this problem, these nanomaterials have been modified with different surfaces so as to improve their biocompatibility and biodistribution in vivo. Poly(ethylene oxide) (PEO) and its derivatives have been widely used for biomemic surface modification of nanoparticles because PEO is poorly immunogenic and antigenic and can act as an excellent repellent for biomolecules.17−23 Ruan and co-workers24 studied a novel class of composite nanoparticles (CNPs) based on QDs exhibiting near-continuous, alternating-color fluorescence which permits aggregation status discrimination by observable color changes even during motion across the focal plane, and QDs with different emission wavelengths were modified with polystyrene (PS)−PEO block copolymer (molecular weight of 3800-b-6500 Da) micelles. Dubertret and co-workers25 encapsulated individual nanocrystals in phospholipid block−copolymer micelles and demonstrated in vitro and in vivo imaging. In this particle they mentioned, the core/shell thickness of the micelle will increase with the length of hydrophobic/hydrophilic segment in the © 2015 American Chemical Society

Received: Revised: Accepted: Published: 6123

December 15, 2014 May 15, 2015 May 21, 2015 May 21, 2015 DOI: 10.1021/acs.iecr.5b00912 Ind. Eng. Chem. Res. 2015, 54, 6123−6134

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Industrial & Engineering Chemistry Research PS-b-PEO block copolymer and QDs in an aqueous solution, which had been experimentally examined by Ruan and Dubertret et al. The radial distribution function g(r) was also used to analyze the structural properties of micelle microspheres. The effects of segment construction of different segments, the lengths of the PEO segment and the PS segment, and the MW of PS−PEO block copolymer on the structures and size of the self-assembled micelles was studied. The formation process of CNPs and distribution of QDs in the matrixes of PEG micelle were investigated. It helps to reveal the QD loading mechanism of PS−PEO micelle from a mesoscopic point of view.

ωR (rij) = 1 − rij/rc

(7)

ωD(rij) = [ωR (rij)]2 = (1 − rij/rc)2

(8)

where T is the absolute temperature of the system and kB is the Boltzmann constant. The value of kBT is set as 1 in our simulation. In addition, a spring force, FSi , is introduced into the simulation to describe the constraint between the bonded consecutive beads within one molecule. The spring force acting on the beads of a chain is given by

FiS =

∑ Crij j

2. SIMULATION DETAILS 2.1. DPD Method. The DPD is a method for modeling complex multiphase materials, which was first introduced by Hoogerbrugge and Koelman in 1992 and subsequently modified by Groot et al.31−33 In our DPD simulation, the molecules are divided into a set of DPD soft beads, each of which represents a group of atoms or a volume of fluid. The evolution of the positions and impulses of all interacting beads over time is governed by Newton’s second law, as given in eq 1: dri = vi dt

mi

dvi = Fi dt

(9)

where C is the spring constant and the sum runs over all particles to which particle i is connected.35 2.2. Simulation System and Parameters. The system simulated in this work is composed of water, PS−PEO block copolymer, and quantum dots (QDs). All species involved in this multicomponent system are transformed into representative coarse-grained models,37 as shown in Figure 1. Since

(1)

where ri, vi, and mi denote the position vector, velocity, and mass of bead i, respectively. Fi represents the total force exerted on bead i. For simplicity of presentation, the masses of all beads are set as 1 DPD unit.34 The total force exerted on bead i contains three parts, each of which is pairwise additive. Fi =

∑ (FijC + FijD + FijR ) j≠i

(2)

where FCij is the conservative force and linear in the bead−bead separation; FDij is the dissipative force and proportional to the relative velocities of bead i and its neighboring bead j; FRij is the random force between bead i and bead j. All forces are short-range with a fixed cutoff radius rc = 1, set as the length scale of the system. The expressions of the three types of forces are given by FijC

⎡ aij(1 − rij)riĵ (rij ≤ 1)⎤ ⎥ =⎢ ⎢0 ⎥ > ( r 1) ij ⎣ ⎦

(3)

FijD = [−γωD(rij)(vijriĵ )riĵ ]

(4)

FijR = [σωR (rij)ξijriĵ ]

(5) Figure 1. Coarse-grained models of (a, b) QDs, (c, d) PS−PEO block copolymer, and (e, f) water.

where rij = | ri ⃑ − rj⃑|, r ̂ = rij⃑ /rij , and ri and rj are the positions of bead i and bead j. vij = |vi⃑ − vj⃑|, where vi and vj are the velocities of bead i and bead j, respectively. αij is constant for the maximum repulsion between the interacting beads. ξij is the symmetric Gaussian random variable with zero mean and unit variance, chosen independently for each interacting pair of beads at each time step Δt. γ and σ represent the dissipation and noise strengths. Finally, ωD(rij) and ωR(rij) are weight functions of FDij and FRij forces, respectively. They can be determined using the following equations:35,36 σ=

2γkBT

quantum dots with different diameters will emit different wavelengths, diameters of the QDs (λem = 545 or 605 nm) used in our simulation are 3 and 4.1 nm according to Ruan’s research.24 The QD is composed of a semiconductor CdSe core and a trioctylphosphine oxide (TOPO) coating. TOPO is a capping ligand for the production of CdSe quantum dots. The P element in TOPO and the metal Cd in CdSe form the coordination bonds, so the CdSe and TOPO are taken as an ensemble of connected beads to simplify the simulation. Since the study of Chan and Král38 has demonstrated that specific

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DOI: 10.1021/acs.iecr.5b00912 Ind. Eng. Chem. Res. 2015, 54, 6123−6134

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Industrial & Engineering Chemistry Research

rescaling from molecular dynamics (MD) simulations (see the Supporting Information). The Flory−Huggins χ interaction parameter can be found in the literature or calculated from the solubility parameters by eq 11:40

geometric structure has insignificant influence on the physical and chemical properties of gold nanoparticles with a diameter about 1.6 nm, spherical structure is chosen for our QD model to simplify the simulation (Figure 2). In order to conform to

χij =

the Flory−Huggins theory, the basic assumption is that all bead types (each representing a single species) are of the same or similar volume.39 Herein, a bead’s volume is set to 320 Å3. Based on this basic assumption, the monomer number per bead of each species is calculated and listed in Table 1. As displayed Table 1. Parameters of Beads in the System monomer vol/ Å3

A B C D E W

55 252 217 161 65 30

monomer no. per bead solubility param δ/MPa0.5 6 1 1 2 5 10

kBT

(δi − δj)2

(11)

where Vij is the average molar volume of the beads; δi and δj are the solubility parameters of bead i and bead j, equal to the square roots of corresponding cohesive energy densities, respectively. The bead volume is set to 320 Å3 in our simulation. The Flory−Huggins parameter χij for PEO in H2O is set as 0.3, as widely adopted by others.41 The solubility parameters in Table 1 are calculated by molecular dynamics (MD) simulations using the Amorphous Cell module and the Discover module of the commercial software Materials Studio 5.0 with COMPASS force field (see the Supporting Information). This method has successfully been used to calculate the solubility parameters by Kaihang Shi and coworkers.42 So far, the estimation is based on solubility parameters following the “similarity and inter-miscibility principle”,43,44 which works well for nonpolar systems or those without specific interactions (e.g., protonation and hydrogen bonding). However, no consistent protocol has been established to determine the interaction parameters between solid particles and polymers in DPD simulation.45 Recently, a blend method, which combines a modified Flory−Huggins model and Monte Carlo simulation to directly calculate the χ parameters from the mixing energy between DPD beads, has been successfully applied in a gold nanoparticle DPD system.46,47 In this study, the bead−bead Flory−Huggins χ parameters were calculated by the Blends module of Materials Studio 5.0 with COMPASS force field at room temperature (298 K) for CdSe−TOPO, CdSe−PS, CdSe−PEO, CdSe−water, PS−water, and TOPO− water, respectively. Other Flory−Huggins χ interaction parameters were calculated using eq 11. The values of the interacting parameters αij at 298 K used in this study are listed in Table 2.

Figure 2. Number-average diameters of simulated beads in different size boxes after 50 000 simulated time steps.

bead

Vij

− 16.8 15.1 19.5 20.7 47.8

Table 2. Interaction Parameters in DPD Simulation in Figure 1, six CdSe molecules are defined as one bead (bead A). The molecular structure of TOPO is comprised of two types of beads (Figure 1, beads B and C). The bond strength (15.0 kcal·mol−1) and the bead A−A−A angle (120°, 2.988 kcal·mol−1), are chosen for a rigid core.38 Two S (styrene) segments are defined as one bead (bead D), while five EO segments form one bead (bead E). Water molecules are all simplified as one type of bead (bead W), each of which contains 10 water molecules, as shown in Figure 1. To simulate the nanocomposite system, the set of interacting parameters αij between beads must be first determined according to their linear relation with Flory−Huggins χ parameters35 by αij ≈ αii + 3.50χij

(ρ = 3)

A B C D E W

A

B

C

D

E

W

25 25.6a 27.1a 19.7a 22.5a 36.8a

25 25.9 26.9 29.1 282.4

25 30.3 33.7 312.9

25 25.4 58a

25 26.05b

25

The DPD interaction parameters αii were calculated by the Blends method. bInteraction parameters were found from the literature;41 others were gained from the solubility theory. a

Scocchi et al.48 also introduced a method bridging the gap between atomistic and mesoscopic simulations for polymer− clay nanocomposite, which can be used to calculate interaction parameters for DPD simulations. We also used Scocchi’s method to calculate some of interaction parameters and compared them with the corresponding interaction parameters in Table 2. Details are given in the Supporting Information.

(10)

where αii is the repulsion parameter for the same type beads. The species in the simulation are compatible, namely χij ≈ 0, and water can represent a large group of incompressible material including the monomers in this simulation; therefore αii is set to 25. This value was confirmed qualitatively by 6125


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Industrial & Engineering Chemistry Research The DPD simulation was performed in a cubic box with periodic boundary conditions. To avoid the finite size effects, DPD simulations were performed in 15 × 15 × 15, 20 × 20 × 20, 25 × 25 × 25, 30 × 30 × 30, and 35 × 35 × 35 cubic boxes with 50 000 time steps. All the systems in our work were composed of 2.5% QDs (3 nm), 0.5% QDs (4.1 nm), 12.5% PS−PEO block copolymers, and 84.5% water. The numberaverage diameters of the simulated particles in different box sizes are shown in Figure 2. We can find that the average diameter of simulated particles increases with the box size when a small box was adopted. However, the particle sizes achieved the maximum and remained the same in 25 × 25 × 25, 30 × 30 × 30, and 35 × 35 × 35 cubic boxes, indicating that a box of 25 × 25 × 25 is large enough to avoid the finite size effects. Thus, a 30 × 30 × 30 cubic box was used in this work. As described previously, the radius and the density of the beads were defined as 1 and 3, respectively. Beads comprised of the same molecules were connected by a harmonic spring with the spring constant C = 4.34 The simulations were performed using the DPD program with the commercial software Materials Studio 5.0 (Accelrys). The DPD simulations run 50 000 steps with a time step of 0.05 ns.

3. RESULTS AND DISCUSSION 3.1. QD Loading and Distribution in Micelles. Ruan et al.24 has presented a novel class of composite nanoparticles (CNPs) based on QDs. In his study, CNPs were formed by the encapsulation of QDs with different emission wavelengths (Invitrogen, λemission = 545 nm (green) and 605 nm (red), respectively) into polymeric PS−PEO block copolymer (MW 3800-b-6500) micelles. Based on the experiment of Ruan and his co-workers,24 a system composed of 2.5% QDs1 (λemission = 545 nm), 0.5% QDs2 (λemission = 605 nm), 12.5% PS−PEO block copolymer, and 84.5% water was constructed and then simulated by DPD. Figure 3 shows the dynamics process of QDs loading in one DPD simulation. In order to exhibit the aggregate morphologies clearly, water molecules are not displayed in Figure 3. As shown in Figure 3a, all components are randomly distributed in aqueous solution at the beginning. With the increase of simulated steps, polymer chains and QDs assemble to small clusters (Figure 3b). At the simulated steps of 10 000, some spheres crash and form four larger aggregates (Figure 3c). Following that, the four aggregates move closer to each other and form a large cluster (Figure 3d). During the simulated steps between 30 000 and 40 000, the larger cluster (Figure 3d) first transforms to a rodlike aggregate (Figure 3e) and then forms a spherical micelle (Figure 3f). No discernible change of the micelle morphology is observed as the simulation step increases (Figure 3f−h), indicating that the simulation has reached an equilibrium at 40 000 simulated steps. To observe the distribution of QDs in PS−PEO block copolymer micelles more distinctly, a sectional view of QD-loaded micelle at simulated steps of 50 000 is shown in Figure 4a. As expected, the clear assembly morphologies, in which the quantum dots coated by the hydrophobic PS chains form the micelle core and the hydrophilic PEO chains form the shell, can be seen. Also, QDs with two different emission wavelengths are loaded into the micelle core. Figure 5 is three sectional views of QD-loaded micelle. It can be seen from Figure 5 that each CNP is comprised of seven QDs, existing in the form of a very small QD cluster; there is no large QD aggregation when the MW of PS−PEO block copolymer is 3800-b-6500. In Ruan’s research, it is difficult to determine from transmission electron

Figure 3. Dynamic process of QD-loaded PS−PEO block copolymer assembly at different simulated steps: (a) 0, (b) 5000, (c) 10 000, (d) 20 000, (e) 30 000, (f) 40 000, (g) 50 000, and (h) 100 000 steps.

microscopy (TEM) the exact numbers of QDs in each micelle and it is estimated that the CNP contains four green QDs and two red QDs.24 Comparing them with the simulation result, the numbers of QDs between experiment and simulation are approximate. Those demonstrate that DPD simulation results are in agreement with those in the experiments not only on the micelle morphologies (Figure 4b,c) but also in the numbers of QDs in the micelle. CdSe nanoparticles are coated by TOPO (hydrophobic ligand), which forms a hydrophobic shell and isolates the CdSe core from the other components in the simulation system.49 Thus, the interaction between CdSe and the other components can be ignored, and the effect of QDs with different emission wavelengths is the same in simulation. As shown in Table 2, values of the interaction parameter αij of TOPO−water, PS− 6126


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Figure 4. (a) Sectional view of a self-assembled nanocomposite micelle at the simulated step of 50 000. (b) Schematic of composite nanoparticles (CNPs) formed via micelle encapsulation.24 (c) TEM image with negative staining for a typical CNP preparation. QDs and the polymer micelle are indicated by left and right arrows, respectively. Scale bar (red): 25 nm.24

Figure 5. Three sectional views of QD-loaded micelle.

good compatibility with water (αij(PEO−water) < αij(PS− water). 3.2. Effects of PS MWs of PS−PEO Block Copolymer on the Morphology of Self-Assembled Micelles. Dubertret et al.25 have found that micelle size could be affected by the constituent amphiphilic molecule employed. The longer the hydrophobic/hydrophilic segment in the structure of the molecule, the larger/thicker the core/shell of the micelle. Herein, we investigated the effects of different PS MWs of PS− PEO block copolymer on the morphology of the self-assembled micelles. In this work, we set the MW of the PEO segment of PS−PEO block copolymer at 6500 Da, and then changed the molecular weight of the PS segment as required. Figure 6 shows

water, PEO−water, TOPO−PS, and TOPO−PEO are 282.4− 312.9, 58, 35, 26.9−30.3, and 29.1−33.7, respectively. According to a study published in 2004,50 a system with an αij significantly larger than 25 tends to have high aggregation degree driven by the reduction of the total energy of the system, whereas the components i and j in a system always display great compatibility when the value of αij is close to 25. Therefore, QDs and the PS block of PS−PEO copolymer tend to aggregate in aqueous solution because of their poor compatibilities with water (large αij) and the good compatibility between TOPO and PS blocks (αij between 25 and 30). Therefore, QDs were encapsulated by PS segments in the micelle core, while PEO blocks formed the micelle shell for its 6127


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Figure 6. continued

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Figure 6. Sectional views and relative concentration profiles of self-assembled micelles with different PS MWs. The MWs of PS/PEO segments are (a1 and a2) 800/6500, (b1 and b2) 1800/6500, (c1 and c2) 3800/6500, (d1 and d2) 5000/6500, and (e1 and e2) 8000/6500 Da, respectively.

the sectional views and the relative concentration profiles of the self-assembled micelles with different PS MWs. The MWs of PS/PEO segments are (a) 800/6500, (b) 1800/6500, (c) 3800/6500, (d) 5000/6500, and (e) 8000/6500 Da, respectively. Size is a primary parameter of micelles and can be determined by calculating the mean radii of gyration of the micelles (rg) and the micelle cores (rg,c). The whole simulation box was first divided into a number of small cubic cells of equal size. According to the positions of beads of the block copolymer molecules, we could find out whether there are PS−PEO block copolymer molecules in each cubic cell. There must be no DPD beads belonging to the block copolymer in some cells which are located between different micelles. Therefore, we can determine which block copolymer beads belong to the same micelles, and then calculate the total number of micelles. Finally, we calculate the radius of gyration of each micelle with the positions of block copolymer beads.

The mean radius of gyration of the micelles can be obtained by averaging the radius of gyration of each micelle. Since the occupied volume associated with each bead is 320 Å3 and the number density is ρrc3 = 3, a cube of rc3 corresponds to a volume of 960 Å3. Thus, a natural length scale in the simulations can be obtained using the following equation:41,50 rcut =

3

960 Å = 9.8 Å

(12)

Accordingly, the average radii of the PS cores with different PS MWs are r(g,c)b = 6.2rcut, r(g,c)c = 6.9rcut, r(g,c)d = 7.3rcut, and r(g,c)e = 9.2rcut (Figure 7). When the MW of the PS/PEO segment is 800/6500 Da, as shown in Figure 6a, the relative concentration profile of PS segments fluctuates between 0 and 6 randomly, which demonstrates that the PS segments could not form an integrated hydrophobic core. Instead, the QDs were encapsulated directly by PEO segments, failing to form core−shell structure micelles, which led to a relatively low loading capacity of QDs. With the increase of the MW of the 6129


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Figure 7. Changes of diameter of PS core and thickness of PEO shell at different PS molecular weights: (A) diameter of PS core; (B) thickness of PEO shell.

compact. As shown in Figure 8b, the g(r) value of PS−PEO pairs (intermolecular) decreases with increase in PS MW. The g(r) value of the intermolecular PS−PEO pairs could indicate the adjacent interactions between PS chains and PEO chains.51 When the MW of PS is 800, the adjacent interactions between PS chains and PEO chains are the strongest among the five systems because PS segments are dispersed in the PEO layer directly (as shown in Figure 6a1). When the MW of PS increased from 3800 to 8000 Da, a core−shell structure micelle formed, which means that the PS segments and PEO segments were in two layers. Thus, the g(r) value of PS−PEO pairs of 3800/6500, 5000/6500, and 8000/6500 Da copolymer systems is smaller than that of the block copolymers systems (800-b6500 and 1800-b-6500 Da). Figure 8c shows the g(r) values of PEO−PEO pairs for the self-assembled micelles with different PS molecular weight ratios. The difference of g(r) for the five systems is very small for the reason that the MW of PEO is set to 6500 Da and remains unchanged. An increase in the length of the core-forming block had been found to cause an increase in the core size per micelle, which, in turn, results in an increased loading capacity.52 However, to ensure the stability as well as maintain the core−shell structure of the micelles, the thickness of the PEO shell should be optimized for the encapsulation of the hydrophobic core.25 As a result, the micelles with MWs of PS/PEO at 800/6500 and 1800/6500 Da had low loading capacity but good stability, whereas those with MW of PS/PEO at 8000/6500 Da had good loading capacity but poor stability. Ideally, the micelles with MW of PS/PEO at 3800/6500 Da can form a compact core−shell structure with a good loading capacity and stability in water. 3.3. Effects of PEO MWs of PS−PEO Block Copolymer on the Morphology of Self-Assembled Micelles. PEO is the hydrophilic segment in PS−PEO block copolymer, which could form the micelle shell and prevent the hydrophobic core from being exposed to water directly. The effects of different

PS segment (from 1800 to 8000 Da), a hydrophobic core formed with an increased radius from 6.1 to 9.0 nm (see Figure 6b−e and Figure 7). In contrast, the diameter of the micelle remained at 18−19 nm (see Figure 6a2−e2), indicating the thickness of PEO shell decreases from 3.3 to 0.9 nm. The results of this simulation were qualitatively consistent with those reported by Dubertret et al.25 We further used the radial distribution function g(r) to analyze the structure properties of micelles formed by quantum dots and PS−PEO block copolymer. The g(r) represents the probability of finding a pair of beads at a distance r with respect to the bulk phase in a completely random distribution. It is defined as K

N

∑t = 1 ∑ j =AB1 ΔNAB(r → r + δr ) 1 gAB(r ) = NABK ρAB 4πr 2

(13)

where NAB is the total number of beads of A and B in the system, K is the number of time steps, δr is the distance interval, ΔNAB is the number of B (or A) beads between r and r + δr around an A (or a B) bead, and ρAB is the bulk density. Note that A and B could be the same type of beads.51 The g(r) of the intermolecular bead pairs (PS−PS, PS−PEO, and PEO−PEO) of the self-assembled micelles with different PS MWs was calculated by a DPD analytical tool. Figure 8a shows the g(r) of the PS−PS pair (intermolecular) for the selfassembled micelles with different PS molecular weights. For all five systems, there is a distinct peak at 7.8−8.6 Å and another peak at 12.2−13.9 Å. The g(r) values of block copolymer systems 1800-b-6500 and 3800-b-6500 Da are higher than those of the other block copolymer systems (800-b-6500, 5000b-6500, and 8000-b-6500 Da), which implies that the adjacent interactions between different PS chains in block copolymer systems 1800-b-6500 and 3800-b-6500 Da are stronger than the other (see Figure 8a). Thus, the formed PS core of block copolymers 1800-b-6500 and 3800-b-6500 Da is much more 6130


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Figure 9. Snapshots and sectional views of self-assembled micelles with different PEO MWs (the MW of PS in the block copolymer was set at 3800). The MWs of PS/PEO segments are (a1 and a2) 3800/ 2800, (b1 and b2) 3800/4500, (c1 and c2) 3800/8000, and (d1 and d2) 3800/15 000 Da.

shell increases with the MW of PEO segments (from 2800 to 15 000 Da). When the MWs of PEO segments were 2800 and 4500 Da, although most of the surface of the PS core was covered by PEO blocks, a small portion of PS blocks were still directly exposed to water (Figure 9a1,b1). This was mainly due to the low PEO MW in the copolymer and the resulting thin PEO shell (only 0.8 and 1 nm). When the thickness of the PEO shell was increased to 2.3 nm as the PEO MW increased to 6500 Da (Figures 6c and 7) and ∼8000 Da (Figure 9c), the surface of the PS core was completely covered by PEO blocks, forming a core−shell micelle (shown in Figure 9c). As the MW of the PEO segments further increased to 15 000 Da, a core− shell micelle with a 2.8 nm PEO shell was formed while some of the PEO blocks dispersed in water. Thus, the MW of PEO segments should be optimized to ensure the stability of the selfassembled micelles. The PS/PEO block copolymer with MWs at 3800/6500 and 3800/8000 Da could ideally form stable core−shell micelles. 3.4. Effects of the Construction of Segments with Different MWs on the Size of Self-Assembled Micelles. Overall CNP size can be controlled by choosing the segment

Figure 8. Radial distribution functions of PS−PS bead pairs, PS−PEO bead pairs, and PEO−PEO bead pairs for five different systems: (a) PS−PS bead pairs; (b) PS−PEO bead pairs; (c) PEO−PEO bead pairs.

PEO MWs on the morphology of the self-assembled micelles were investigated via DPD simulation. The MW of PS segments was set at 3800 Da, while the MW of PEO segments in PS−PEO block copolymer was increased from 2800 to 15 000 Da. Figure 9 shows the snapshots and sectional views of the morphology of the self-assembled micelles at different PEO MWs. As displayed in Figure 9a2−d2, the thickness of PEO 6131


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Figure 10. Snapshots of the self-assembled micelles of QD/PS−PEO block copolymer with different segment constructions. The MWs of PS/PEO were (a) 3800/6500, (b) 6650/11 400, and (c) 9500/18 000 Da.

construction of amphiphiles. Ruan et al.26 reported that PS− PEO block copolymer with MWs at 3800-b-6500 and 9500-b18000 Da could form CNPs with diameters of 25 and 40 nm, respectively. The effects of the segment construction of PS− PEO block copolymer on the morphology and size of the selfassembled micelles were investigated via DPD simulation. Figure 10 shows the snapshots of the self-assembled micelles of different segment constructions of PS−PEO block copolymer. When DPD simulations stabilized, the micelles with a core− shell structure were formed. The micelles with MWs of PS/ PEO at 3800/6500, 6650/11 400, and 9500/18 000 Da had particle diameters of 18.7, 19.6, and 21.0 nm, respectively. The particle diameter (D) was positively correlated to the block copolymer MW (i.e., D (3800‑b‑6500) < D (6650‑b‑11400) < D(9500‑b‑18000)). These results are in qualitative but not quantitative agreement with the experimental results.26 The deviation between the results of simulation and experiment might be attributed to the coarse-graining of components and the simplified method for the bonded interactions.53,54

segment is constant, the thickness of the micelle shell increases with PEO segment length. The size of the self-assembled micelle increases with the MW of the PS-b-PEO block copolymer. The simulation revealed the physical insights of the QD loading mechanism of PEG micelle at the mesoscopic scale, indicating DPD simulation can be used as an adjunct to provide other valuable information for experiments.

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ASSOCIATED CONTENT

S Supporting Information *

(1) Information about calculation of the solubility parameters in Material Studio. (2) Interaction parameters between the same type beads. (3) Discussion on self-assembled morphologies at different masses at bead A. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b00912.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86-20-87112057-804. Fax: +86-20-87112057-804. Email: [email protected] (S.X.). *E-mail: [email protected] (X.W.).

4. CONCLUSIONS Dissipative particle dynamics (DPD) simulation was performed to investigate the self-assembly dynamics process of PS-b-PEO block copolymer and QDs with different emission wavelengths in an aqueous solution. The structural properties of micelles were characterized by a radial distribution function. The simulation results were qualitatively consistent with previous experiments and showed that there are only small QD clusters. Four sequential transient stages were found during the formation process of CNPs: (1) all components are randomly distributed in an aqueous solution; (2) polymer chains and QDs assemble in small clusters; (3) crashing together of small spheres and the formation of larger aggregates; (4) stabilization of assembled micelles. As expected, the hydrophobic PS chains form the micelle core, while the hydrophilic PEO chains form the shell. QDs with two different emission wavelengths are loaded into the micelle core. The simulation results also showed that MW and segment construction of the PS−PEO block copolymer had significant effects on the structure and size of the self-assembled micelles. When the length of the PEO segment is constant, the diameter of the hydrophobic core increases with PS segment length. When the length of the PS

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful for the financial support from the National Natural Science Foundation of China (Grants 21176091 and 21376093), the Team project of Natural Science Foundation of Guangdong Province (Grant S2011030001366), and Fundamental Research Funds for the Central Universities 2013ZZ074.

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