Copyright 2008 by the American Chemical Society
VOLUME 112, NUMBER 22, JUNE 5, 2008
ARTICLES Dissipative Particle Dynamics Simulation on a Ternary System with Nanoparticles, Double-Hydrophilic Block Copolymers, and Solvent Jianhua Huang,*,† Mengbo Luo,‡ and Yongmei Wang§ Department of Chemistry, Zhejiang Sci-Tech UniVersity, Hangzhou 310018, China, Department of Physics, Zhejiang UniVersity, Hangzhou 310027, China, and Department of Chemistry, The UniVersity of Memphis, Memphis, Tennessee 38152 ReceiVed: NoVember 2, 2007; ReVised Manuscript ReceiVed: February 27, 2008
Dissipative particle dynamics (DPD) simulations are performed to study the aggregation of hydrophobic nanoparticles in the presence of double-hydrophilic block copolymer (DHBC). A single compact spherical nanoparticle aggregate is formed in the absence of DHBC. The response of the aggregate to a continuous increase in the concentration of DHBC has been investigated in detail. We observe the evolvement from single spherical aggregate, through single ellipsoidal aggregate, single platelike aggregate, single long and curly rod, dispersed aggregates, then to hexagonally packed cylinders, and ultimately to ordered lamellar structures upon slow addition of DHBC chains. However, when nanoparticles and DHBCs are added into the system simultaneously at the beginning of simulation, we only obtain single spherical aggregate, dispersed aggregates, hexagonally packed cylinders, and ordered lamellar structures at different concentrations of DHBC. Phase diagrams of structures against concentration of DHBC are presented for these two methods, and the stabilities of structures obtained with the two methods are compared. 1. Introduction Biominerals found in nature, such as seashell, pearl, bones, etc., exhibit remarkably intricate structures with patterns organized from nanoscale to macroscale. These hierarchical structures can be further sculpted into complex forms, such as spheroids, spirals, and skeletons, leading to unique mechanical and optical properties. These natural systems provide inspirations to synthetic chemists trying to produce biomimetic systems and/ or nanostructured inorganic materials.1 The synthesis of inorganic materials with controlled size and morphology are of †
Zhejiang Sci-Tech University. Zhejiang University. § The University of Memphis. ‡
interest to fields as diverse as catalysis, medicine, electronics, and cosmetics. In experiments, amphiphilic copolymers and double-hydrophilic block copolymers (DHBCs) have been used as templates to direct mineral formation, resulting in hierarchical structures. Amphiphilic copolymers can self-organize into micelles, vesicles, and foams at different conditions, and these self-assembled templates can be replicated into inorganic structures, such as the reported hollow silica tubes,2 iron oxide cylinders,3 and helical strings of gold crystal.4 DHBCs consist of two hydrophilic blocks, for example, poly(ethylene oxide)-block-(polystyrene sulfonic acid); both blocks are soluble in water but have different interaction strengths with inorganic minerals or surfaces. DHBCs cannot self-assemble into ordered structures at low concentration, but they are very effective in controlling
10.1021/jp710567f CCC: $40.75 2008 American Chemical Society Published on Web 05/10/2008
6736 J. Phys. Chem. B, Vol. 112, No. 22, 2008 the crystallization of inorganic particles.5 The key factors in achieving hierarchical structures are the interactions between the inorganic materials and DHBCs.1 For instance, DHBCcontrolled or -directed formation of CaCO3 pancakes,6 aggregated BaCrO4 fiber bundles,7 peanutlike calcite particles,3 and unconventional crystal superstructures of BaSO48 has been reported. The approach relies on synergistic coassembly of DHBCs with inorganic crystals, as opposed to replication of stable, preorganized, self-assembled organic templates. Recently, we made a first attempt to model the DHBCdirected mineralization process.9 The mineralization process is approximated by aggregation of hydrophobic nanoparticles precipitated from solution. DHBC is modeled as a copolymer chain: Two blocks are hydrophilic in the solvent with different attractive strengths, but they repel against each other. We studied the effect of DHBC concentration on the aggregation of nanoparticles. In the previous study, nanoparticles, DHBC chains, and solvents were simultaneously put into a simulation box at the beginning of simulation. The system was then allowed to evolve until the final structure showed no obvious change upon further equilibration. With this approach (called method A in the following), we observed a single sphere with adsorbed DHBC chains on the surface only at a low concentration of DHBC, Cp (i.e., Cp rc, where rc is the cutoff radius. DPD particles move according to Hamilton’s equations:
∂ri ) vi, dt
mi
∂vi ) fi dt
(5)
The positions and velocities of the particles are solved using a modified velocity-Verlet algorithm proposed by Groot and Warren.17 In simulation, we set rc ) 1, energy scale kBT ) 1, all DPD particles have the same mass m ) 1, and σ ) 3. All results are in reduced DPD units, i.e, length in rc, energy in kBT, mass in m, and one time unit is defined as τ ) (mrc2/ kBT)1/2 ) 1. The integration time step ∆t is 0.02τ. Our simulations are performed in a cubic simulation box with size Lx × Ly × Lz ) 20 × 20 × 20. The simulation box contains four types of DPD particles: solvent (s), nanoparticle (n), and A and B segments of DHBC chains. One nanoparticle is represented by a DPD particle. Each DHBC chain consists of three A segments and three B segments connected via a finitely extensible nonlinear elastic (FENE) potential:18 FENE Ui,i+1 )
{
[ (
kF ri,i+1 - req - (rmax - req)2 ln 1 2 rmax - req ∞
)] 2
for ri,i+1 < rmax for ri,i+1 g rmax (6)
where the equilibrium bond length req ) 0.7, the maximum bond length rmax ) 2.0, and the elastic coefficient kF ) 40. The FENE spring model is a more realistic model of polymers. In this model, the spring force is linear at small extensions, but the spring becomes stiffer at large extensions. This therefore places a maximum bond length allowed during its extension. The FENE potential is widely used in modeling polymer chains with Monte Carlo (MC) and molecular dynamics (MD) simulations, as well as in DPD simulations.19–21 The hydrophilic properties of DHBC and the hydrophobic property of nanoparticle, as well as the interaction between polymer segments with nanoparticle, emerge from the relative interaction strength aij, which are shown below:
(
DPD Simulation on a Ternary System
A aij ) B s n
A 25 30 20 25
B 30 25 25 15
s 20 25 25 50
n 25 15 50 25
)
J. Phys. Chem. B, Vol. 112, No. 22, 2008 6737
(7)
These interaction parameters are the same as those we used in our previous paper. 2.2. Detailed Simulation Procedure. The overall DPD particle density is defined as F ) N/V; here, V ) Lx × Ly × Lz is the volume of the simulation box and N is the total DPD particles, which is the sum of solvent particles Ns, DHBC segments 6Np, and nanoparticles Nn, i.e., N ) Ns + 6Np + Nn. Here, Np is the number of DHBC chains. Following refs, 22–24 F is set at 6 in the present work. For a simulation box size of 20 × 20 × 20, the total DPD number is 48000. Concentrations of DHBC, Cp, and nanoparticles, Cn, are defined as Cp ) 6Np/N and Cn ) Nn/N, respectively. The concentration of nanoparticles is fixed at Cn ) 0.06, which means Nn ) 2880. With method B, 2880 nanoparticles and 45 120 solvent particles are first put in the simulation box and equilibrate for 4000τ. Then, the concentration of DHBC slowly increases from 0 to 0.9 by adding 50 DHBC chains after a fixed time interval of t ) 4000τ. These 50 DHBC chains are randomly put into the box to replace 300 solvent particles; thus, the total DPD particle concentration is kept constant. The incremental change of the DHBC concentration is 0.006 25 at every step. We focus on how the morphology of nanoparticle aggregate changes upon the continuous slow increase of DHBC chains in the box. The equilibration time 4000τ between each interval is found to be sufficient, since we do not find any obvious structural difference in the systems when we use 8000τ at several concentrations of Cp compared with those obtained at 4000τ. In section 3, we will give a short summary of our main results from our previous paper where method A was used.9 Then, in section 4, results obtained in the current study by method B will be presented. Different structures are observed when DHBC chains are added into the system using two different methods. In section 5, we try to give a comparison of the structures obtained from these two methods and discuss the implication on the kinetics of the aggregation process. 3. Structures Obtained with Method A With method A, 2880 nanoparticles, a specified amount of DHBC chains (specified by the DHBC concentration Cp) and solvents were simultaneously put into a simulation box at the beginning of the simulation; then, the system was allowed to equilibrate for time interval 5000τ. We define nanoparticles forming an aggregate if the two particles are within distance rmin, which is set to be 1.0 in the study. Figure 1a-e presents the final structures formed at various Cp values at the end of the simulations. A single spherical aggregate wrapped by DHBC chains was formed only at a low concentration of DHBC, such as Cp ) 0.02; see Figure 1a. When the concentration of DHBC reached 0.025, two smaller spherical aggregates were formed, as shown in Figure 1b. The two aggregates did not merge into one as the simulation continued. The number of aggregates formed increased with Cp, accompanied by a decrease in the aggregate size (see Figure 1c and d). Hexagonally packed cylinders (HPCs) were formed at Cp ) 0.5 (Figure 1e). We found that such an ordered cylindrical structure only formed in a very narrow region of Cp ≈ 0.5. A lamellar structure emerged at high Cp ) 0.9, as shown in Figure 1f. Between these two ordered structures, disordered structures are formed in a wide range of concentration.
Figure 1. Final structures formed with method A for a fixed nanoparticle concentration Cn ) 0.06 in the presence of different concentrations of DHBC: Cp ) 0.02 (a); 0.025 (b); 0.05625 (c); 0.11875 (d); 0.5 (e); 0.9 (f). For clarity, solvent particles are not shown. Grey beads represent nanoparticles. Red and blue rods represent A and B blocks of copolymer, respectively. The same symbols are used in the following figures.
4. Structures Obtained with Method B With method B, the concentration of DHBC is slowly increased from 0 to 0.9, while that of nanoparticle Cn ) 0.06 is fixed. As we mention in section 2, nanoparticles are hydrophobic to solvent (ans ) 50, ass ) ann ) 25), so in the absence of DHBC, they aggregate into a big spherical aggregate to avoid solvent contact. As DHBC is incrementally added into the system, the aggregate changes its shape and forms a structure that in many cases is different from that obtained with method A. The first difference is observed when the DHBC concentration is increased to Cp ) 0.025. At this concentration, the final structure formed with method A (see Figure 1b) has two small, nearly spherical aggregates. These two small aggregates do not merge into one large aggregate even if the simulation is continued for a much longer time. However, with method B, the aggregate remains as one when Cp increases from 0 to 0.12. Figure 2 depicts the final structures obtained with method B at several Cp values up to 0.12. As DHBC is slowly added, the single aggregate first remains nearly spherical and then changes to ellipsoidal, and further transforms into a platelike aggregate. The change of the aggregate can be characterized by an increase in the surface area that would thus allow more DHBC chains to be adsorbed onto the surface. For example, an ellipsoidal aggregate has more surface area than a sphere.
6738 J. Phys. Chem. B, Vol. 112, No. 22, 2008
Huang et al.
Figure 2. Final structures formed using method B for a fixed nanoparticle concentration Cn ) 0.06 in the presence of different concentrations of DHBC: Cp ) 0.025 (a); 0.05625 (b); 0.11875 (c).
In order to quantitatively investigate the structural change of nanoparticle aggregate with the addition of DHBC, the asphericity parameter A and the square radius of gyration S2, which are generally used to characterize the shape and size of a polymer chain, are adopted to analyze the shape and size of nanoparticle aggregate. Following the concept used in polymer science, the asphericity parameter A is defined as25,26 3
A )
∑ (Li
(∑ ) 3
2
- Lj ) /2 2 2
i>j
2
2
Li
(8)
i)1
in three dimensions; L12, L22, and L32 (L12 e L22 e L32) are referred to as the momentums of the three principle axes of the ellipsoid, respectively. The value of the asphericity parameter A ranges from zero for spherically symmetric aggregate to 1 for rod-shaped aggregate. L12, L22, and L32 are three eigenvalues of the radius of gyration tensor S:
S )
(
Sxx Sxy Sxz Nn 1 sk · sTk ) Sxy Syy Syz Nn k)1 Sxz Syz Szz
∑
)
(9)
Here, Nn is the number of nanoparticles in an aggregate and columnar matrix sk ) col(xk,yk,zk) is the position vector of nanoparticle k in an aggregate with its origin at the center of mass. sTk ) (xk,yk,zk) is a transposed matrix of sk. The square radius of gyration is S2 ) L12 + L22 + L32. Figure 3 shows the dependence of the asphericity parameter A and the three momentums L12, L22, and L32 on the concentration of DHBC Cp in the range from 0 to 0.12. In this concentration region, there is only one single aggregate in the system. When Cp < 0.031, A is close to zero, suggesting that a nearly spherical aggregate is formed and the addition of DHBC has little effect on the aggregation of nanoparticles. Afterward, A increases with Cp, indicating that the aggregate deviates from spherical shape and an ellipsoidal aggregate forms. From Figure 3a, we find A goes up abruptly around Cp ∼ 0.06. Combining with the snapshots shown in Figure 2, we conclude that it is caused by the transformation from the ellipsoidal aggregate to the platelike aggregate. The change in the shape of nanoparticle aggregate can also be explained by the variances of the three momentums L12, L22, and L32 plotted in Figure 3b. L12, L22, and L32 nearly have equal values at a low concentration of DHBC, suggesting that the aggregate is nearly spherical. When Cp > 0.031, with the increase of Cp, L12 decreases and L22 and L32 increase, indicating the shape of the aggregate deviates from spherical. Three regions representing nearly spherical, ellipsoidal, and platelike are indicated in Figure 3. Figure 4 presents the dependence of the square radius of gyration S2 on the concentration of DHBC. S2 increases slowly
Figure 3. Dependence of the asphericity A (a) and three momentums L12, L22, and L32 (b) on the concentration of DHBC in the range 0-0.12, respectively. Three regions are divided: (I) nearly spherical; (II) ellipsoidal; (III) platelike.
Figure 4. Dependence of the square radius of gyration S2 on the concentration of DHBC in the range 0-0.12. Three different regions are indicated: (I) nearly spherical; (II) ellipsoidal; (III) platelike.
with Cp at the low Cp region where spherical aggregate and ellipsoidal aggregate forms. Then, it goes up quickly when Cp is bigger than 0.06 and platelike aggregate forms. With the further increase of the concentration of DHBC, the size of nanoparticle aggregate now exceeds the simulation box size. Long and curly rods are formed when the concentration
DPD Simulation on a Ternary System
Figure 5. Final structures formed in the presence of DHBC: Cp ) 0.125 (a) and 0.2 (b) with method B.
Figure 6. Structures formed in the presence of DHBC at Cp ) 0.3125 (a) and 0.4375 (b) with method B.
J. Phys. Chem. B, Vol. 112, No. 22, 2008 6739
Figure 8. Cylindrical structure formed at Cp ) 0.5 using method B (a) and the corresponding structure factors (b). The unit of wave vector k is 2π/rc (rc ) 1).
Figure 9. Lamellar structure formed at Cp ) 0.8 using method B (a) and the corresponding structure factor (b). The unit of wave vector k is 2π/rc (rc ) 1).
cylindrical structure, we have calculated two-dimensional (2D) structure factor which is defined as23,27
|
Nn
∑
|
1 S(k b) ) exp(ik b ·b rj) Nn j)1
Figure 7. Change of the number of nanoparticle aggregates Nagg with the concentration of DHBC.
of DHBC is in the region from 0.125 to 0.22. Figure 5 shows the final structures formed at Cp ) 0.125 and 0.2, respectively. When Cp exceeds 0.22, long, rodlike aggregate disappears and dispersed aggregates form. We find the number of dispersed aggregates increases with Cp, while the corresponding size of the aggregates decreases with the continual addition of DHBC. Parts a and b of Figure 6 depict two final structures at Cp ) 0.3125 and 0.4375, respectively. There are fewer dispersed aggregates at Cp ) 0.3125 than those at Cp ) 0.4375. Figure 7 presents the dependence of the number of nanoparticle aggregates Nagg on Cp using method A and method B, respectively. With method A, Nagg increases roughly monotonously with Cp when Cp < 0.24, and then, it reaches a stable value of about 40 for Cp > 0.24. With method B, however, Nagg ) 1 for Cp below 0.22; then, it increases with Cp until it reaches a stable value of about 38 when Cp is bigger than 0.4. It is clear that, at this concentration of DHBC, the Nagg value of method A is still slightly bigger than that of method B. With a further increase of Cp to 0.5, nanoparticles form cylinders and a hexagonal structure appears. Figure 8 shows the HPC structure at Cp ) 0.5. To quantitatively analyze the
2
(10)
where b rj is the position vector of the jth nanoparticle, Nn is the total number of nanoparticles used in the calculation, and the wave vector b k is two-dimensional (2D). Here, only nanoparticles are taken into account. A bright spot means its structure factor b) is large. Here, the structure factor is normalized at k ) 0, S(k i.e., S(0) ) 1. The 2D structure factors correspond to patterns obtained in small-angle X-ray scattering experiments. b k is chosen to lie on a surface that is the most perpendicular to the direction of the cylinders. There are six bright spots at the first six reciprocal vectors in the structure factor shown in Figure 8b, implying a hexagonal structure exists at Cp ) 0.5. Further study shows that there is a relatively wide region of Cp (from about 0.5 to about 0.63) for the formation of the ordered cylindrical structure with method B. At Cp ) 0.6625, the HPC structure transforms into a disordered structure. When the concentration of DHBC reaches 0.6875 with method B, lamellar structure appears. Figure 9a shows the lamellar structure at Cp ) 0.8. Nanoparticles are buried in B block layers. The lamellar structure can be characterized by two bright spots in the 2D structure factor, as shown in Figure 9b. In the calculation of the structure factor, only nanoparticles are taken into account. The two bright spots correspond to two reciprocal vectors of the lamellar structure. The average value of the structure factor at the two reciprocal vectors, S1 ) 1/ ∑S(k ), is also calculated at different concentrations of DHBC. 2 h Figure 10 presents the dependence of S1 on Cp. We find that S1 at first increases with Cp for Cp < 0.8; then, it decreases slowly with Cp. There are two effects of DHBC on the lamellar structure: (1) the lamellar structure becomes better with the increase of Cp; (2) the thickness of B block layers increases
6740 J. Phys. Chem. B, Vol. 112, No. 22, 2008
Figure 10. Dependence of the average value of structure factor near the first two reciprocal vectors S1 on the concentration of DHBC.
Figure 11. Phase diagrams of the morphology of nanoparticle aggregate varying with the concentration of DHBC Cp for method A and method B.
with Cp. The first effect increases the S1 value, while the second effect decreases S1 because nanoparticles buried in B blocks become more dispersing in the perpendicular direction. Therefore, a peak of S1 is found. 5. Phase Diagrams for Methods A and B From sections 3 and 4, we have seen that the structures of nanoparticle aggregate formed in the simulations significantly depend on how the DHBC chains are added into the simulation box. The dependence of the structures on the concentration of DHBC Cp is summarized in Figure 11 for these two methods. With method A, we find a single sphere only at extremely low Cp, followed by a wide range of concentration where dispersed aggregates are formed. Hexagonally packed cylinders appear at moderate Cp. At high Cp, lamellar structures are formed. The concentration regions where HPC and lamellar structures formed are narrow with method A. It is especially difficult to find HPC structure because it only appears in the Cp region from about 0.49 to 0.52. In contrast, with method B, the concentration regions to find HPC and lamellar structure are much wider than those in method A. In addition, we also find ellipsoidal, platelike, and rodlike single aggregate at low Cp with method B but not with method A. We find that these structures formed with method A and method B do not change with prolonged simulation time. That likely indicates that these structures are at least in local free energy minima. There is a free energy barrier that prevents the transformation from one structure to another.
Huang et al.
Figure 12. Dependence of the energy difference ∆E ) EB - EA between two simulation methods on the concentration of DHBC. At three marked points (R, β, and γ), both simulation methods obtain the same structures. The error bars indicate the energy fluctuations in the system.
In order to get a better understanding on the aggregation behavior of nanoparticles in the presence of DHBC obtained with two different methods, we compared the total energy of the systems obtained with the two methods. The total energy of a system contains the pairwise interaction energy between all DPD particles and the elastic bond energy of the DHBC chain. For the same structures obtained with methods A and B, such as a single spherical aggregate at Cp ) 0.01875, HPC structure at Cp ) 0.5, and lamellar structure at Cp ) 0.85, the corresponding system’s total energies are equal to each other; see the three marked points, R, β, and γ, in Figure 12. For Cp varying from about 0.02 to 0.2, where the structure formed with method B changes from an ellipsoid to a rod, systems equilibrated with method B have significantly lower energies than those equilibrated with method A. For Cp in the range from 0.5 to 0.85, ordered structures obtained in method B also have somewhat lower energies, but to a lesser extent, than the disordered structures obtained in method A. We note that the number of aggregates obtained with method B for Cp from 0.0 to 0.4 is smaller than that with method A (see Figure 7). More aggregates imply more translation entropy. However, in the range of Cp from 0.02 to 0.2, the translation entropy gained with more dispersed aggregates is unlikely to offset the energetic difference between methods A and B. Thus, we conclude that single aggregates formed with method B at Cp from 0.02 to 0.2 are more stable than dispersed aggregates formed with method A. This implies that dispersed aggregates obtained with method A are kinetically trapped. This is reasonable, since, in method A, nanoparticles first form small aggregates while at the same time DHBCs are adsorbed on the surface of these aggregates. These DHBC chains form a protective layer, preventing the small aggregates to further coalescence. The kinetic barrier is therefore produced by these DHBC chains. When Cp is in the range from 0.2 to 0.4, method B also gives the dispersed aggregates. However, these dispersed aggregates are formed by breaking up the earlier large aggregate. In this range of Cp, energies of structures obtained with method B become slightly higher than those obtained with method A. At even higher Cp concentration, the energies of systems obtained with the two methods are mostly the same, except at Cp ) 0.6 where method B gives HPC structure while method A leads to disordered cylinders. Overall, the energetic differences between the structures obtained with two methods at Cp from 0.2 to 0.8 are small and in many cases are within energy fluctuations displayed by the systems. We believe that the
DPD Simulation on a Ternary System stabilities of the systems obtained with the two methods in this range of Cp may be comparable with each other, but the structures may have hysteretic effects. We have tried to perturb the various configurations generated in methods A and B by imposing a vibration force F ) F0 cos(2πωt) on all DPD particles. Here, parameter F0 is chosen as 0.1, 0.2, or 0.4, and for each F0, three frequencies, ω ) 0.01, 0.1, and 1.0, are examined. We have not observed any obvious changes in the morphology of nanoparticle aggregate with the external force. At present, we therefore speculate that single aggregate and ordered structures formed with method B and dispersed aggregates formed with method A are both in local free energy minima. However, between them, there is an energy barrier that prevents the transformation from one structure to another. Our current study compares the structures obtained with two methods, method A, where DHBC chains/nanoparticles are added simultaneously at the beginning of simulations, and method B, where nanoparticles are first allowed to aggregate and DHBC chains are added incrementally. Method A likely leads to kinetically trapped systems, while method B allows us to observe the response of large aggregate to the addition of DHBC chains. If methods A and B produce the same structures, then this implies that structures formed under the corresponding conditions are controlled by thermodynamic equilibrium and will not be kinetically trapped. Ideally, we would like to increase DHBC concentrations as small as possible such that the structures observed in method B will not depend on the incremental concentration value chosen. Using the DHBC concentration increment 0.006 25, we obtain the phase diagram shown in Figure 11. We have checked our results with a smaller concentration increment 0.003 125 (half of 0.006 25) with a final DHBC concentration up to 0.3. No new phases are captured. Therefore, we believe 0.006 25 is small enough. Figure 11 shows that the sphere phase has the narrowest DHBC concentration range, which is about 0.03. We then find that the morphological changes roughly do not depend on the incremental concentration change as long as it is smaller than 0.03, such as 0.0125, 0.018 75, and 0.025. Otherwise, some phases, especially the sphere phase and ellipsoid phase, will not be observed. For example, with moderate increments 0.075 and 0.125, the final structures are plate and long curly rod, respectively. However, from the short-time dynamic evolution of the structures, we clearly observe the change from sphere, through ellipsoid, to plate, or even to long curly rod. We have also studied the evolution of structure at large concentration increments with method B. At increments of 0.55 and 0.7, HPC and lamellar structures are obtained, respectively. From the short-time evolution, we find the initial sphere quickly changes to dispersing aggregates and these then slowly form the ordered structures. However, in method A, disordered structures are obtained at these two concentrations of DHBC. 6. Conclusion We present a dissipative particle dynamic simulation on the structural change of hydrophobic nanoparticle aggregate in solution under the slow addition of double-hydrophilic block
J. Phys. Chem. B, Vol. 112, No. 22, 2008 6741 copolymer (DHBC). With the slow increase of the concentration of DHBC, Cp, the morphology of a single nanoparticle aggregate changes from nearly spherical, through ellipsoidal and platelike, and to long and curly rodlike. Such change in the shape and dimension of the single nanoparticle aggregate has been analyzed using the asphericity parameter A and the square radius of gyration S2. With the further addition of DHBC, single nanoparticle aggregate transforms into dispersed aggregates. When the concentration of DHBC reaches 0.5, HPC structure forms. HPC structure transforms into a disordered structure at Cp ) 0.6625. At last, when the concentration of DHBC reaches 0.6875, an ordered lamellar structure appears. A dynamic pathway for the evolution from a compact aggregate at low Cp to an ordered lamellae structure at high Cp is found. The results show that the interaction between nanoparticle and DHBC chain serves a driving force that changes the structure of nanoparticle aggregates. Acknowledgment. We acknowledge the financial support from the National Natural Science Foundation of China under Grant No. 20771092 and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. References and Notes (1) Mann, S.; Ozin, G. A. Nature 1996, 382, 313. (2) Baral, S.; Schoen, P. Chem. Mater. 1993, 5, 145. (3) Archibald, D. D.; Mann, S. Nature 1993, 364, 430. (4) Burkett, S. L.; Mann, S. Chem. Commun. 1996, 3, 321. (5) Yu, S. H.; Colfen, H. J. Mater. Chem. 2004, 14, 2124. (6) Chen, S. F.; Yu, S. H.; Wang, T. X.; Jiang, J.; Colfen, H.; Hu, B.; Yu, B. AdV. Mater. 2005, 17, 1461. (7) Yu, S. H.; Colfen, H.; Antonietti, M. Chem.sEur. J. 2002, 8, 2937. (8) Qi, L. M.; Colfen, H.; Antonietti, M. Angew Chem., Int. Ed. 2000, 39, 604. (9) Huang, J. H.; Wang, Y. M. J. Phys. Chem. B 2007, 111, 7735. (10) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Europhys. Lett. 1992, 19, 155. (11) Espanol, P. Europhys. Lett. 1997, 40, 631. (12) Laradji, M.; Hore, M. J. A. J. Chem. Phys. 2004, 121, 10641. (13) Liu, D. H.; Zhong, C. L. Macromol. Rapid Commun. 2006, 27, 458. (14) Wijmans, C. M.; Smit, B. Macromolecules 2002, 35, 7138. (15) Ripoll, M.; Ernst, M. H.; Espanol, P. J. Chem. Phys. 2001, 115, 7271. (16) Jiang, W. H.; Huang, J. H.; Wang, Y. M.; Laradji, M. J. Chem. Phys. 2007, 126, 044901. (17) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423. (18) Kremer, K.; Grest, G. S. J. Chem. Phys. 1990, 92, 5057. (19) Symeonidis, V.; Karniadakis, G. E.; Caswell, B. Phys. ReV. Lett. 2005, 95, 076001. (20) Chen, S.; Thien, N. P.; Fan, X. J.; Khoo, B. C. J. Non-Newtonian Fluid Mech. 2004, 118, 65. (21) Pan, G. A.; Manke, C. W. J. Rheol. 2002, 46, 1221. (22) Prisen, P.; Warren, P. B.; Michels, M. A. J. Phys. ReV. Lett. 2002, 89, 148302. (23) Jury, S.; Bladon, P.; Cates, M.; Krishna, S.; Hagen, M.; Ruddock, N.; Warren, P. Phys. Chem. Chem. Phys. 1999, 1, 2051. (24) Nakamura, H.; Tamura, Y. Comput. Phys. Commun. 2005, 169, 139. (25) Bishop, M.; Saltiel, C. J. J. Chem. Phys. 1988, 88, 3976. (26) Luo, M. B.; Huang, J. H. J. Chem. Phys. 2003, 119, 2439. (27) Matsen, M. W.; Griffiths, G. H.; Wickham, R. A.; Vassiliev, O. N. J. Chem. Phys. 2006, 124, 024904.
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