ARTICLE pubs.acs.org/JPCC
Self-Assembled Superstructures of Polymer-Grafted Nanoparticles: Effects of Particle Shape and Matrix Polymer Yung-Lung Lin,† Chi-Shiang Chiou,† Sanat K. Kumar,‡ Jiang-Jen Lin,§ Yu-Jane Sheng,*,†,§ and Heng-Kwong Tsao*,||,^ †
Department of Chemical Engineering, National Taiwan University, Taipei 106 Taiwan Department of Chemical Engineering, Columbia University, New York, New York 10027, United States § Institute of Polymer Science and Engineering, National Taiwan University, Taipei 10617, Taiwan Department of Chemical and Materials Engineering, National Central University, Jhongli, 320 Taiwan ^ Department of Physics, National Central University, Jhongli, 320 Taiwan
)
‡
ABSTRACT: The incorporation of nanoparticles into polymer matrices increases reinforcement and leads to stronger plastics. However, controlling the spatial distribution of nanoparticles within polymer matrices is a challenge in improving the properties of polymer nanocomposite. Dissipative particle dynamics simulations are employed to investigate the self-assembly of nanoparticles into a variety of anisotropic superstructures. The shape of nanoparticle varies from hexagonal nanoplatelet to nanorod by changing the aspect ratio (S). A hexagonal particle with S ≈ 1 is spherelike. Depending on the grafted chain length and number of grafted chains, the self-assembled structure in the morphology diagram may be spherical aggregate, fillet, ribbon, or string, in addition to dispersed phase. In general, nanoplatelets tend to form string structure while nanorods have a tendency to pack as fillet or ribbon structure. The length of matrix polymer (Lm) changes the phase boundary separating different regions in the morphology diagram. As Lm is increased, the nanoparticle solvophobicity declines and thus results in smaller aggregates generally. Nonetheless, for weakly solvophilic grafted nanoplatelets, the string size grows with Lm due to depletion attraction.
’ INTRODUCTION Despite the fact that polymer systems are widely used due to their unique characteristics—light weight and ease of production— polymer materials have lower mechanical strength and thermal stability as compared to metal and ceramic materials. In order to enhance the properties of polymer materials, low concentrations of inorganic nanofillers are embedded into a polymer matrix to form composite materials. Using such an approach, material properties can be significantly improved while the characteristics of light weight and high workability are maintained.13 For instance, the dispersion of nanofillers in polymer matrix can improve the mechanical or thermal properties such as impact strength of epoxy,4 elongation at break of high-density polyethylene,5 heat release rate of nylon-6,6 heat deflection temperature of nylon-67 and poly(ether sulfone),8 and thermal conductivity of epoxy.9 In addition, the nanoparticles in polymer matrix may form into a variety of morphologies, and there are various applications for each type of morphology. For example, the self-assembly of nanoparticles into rodlike clusters in poly(3-hexylthiophene) matrix was widely used for polymer solar cells;10,11 sheetlike clusters formed by polyhedral oligomeric silsesquioxanes nanoparticles in polystyrene matrix were employed for improving the dewetting behavior of polymer thin film.12 r 2011 American Chemical Society
Since inorganic nanofillers are typically immiscible with an organic matrix, the nanoparticles often aggregate into spherical clusters instead of dispersing in polymer matrix. As a result, nanofillers do not bring about improvement to material properties. In order to control the dispersion or aggregate structure of nanoparticles in polymer matrix, various methods were adopted, such as adding dispersing agent into the nanocomposites8 and grafting polymer chains on nanoparticle surface.4 Also, a method like using ultramicrotome to shorten carbon nanotubes (CNTs) was found to improve dispersion without reducing their thermal conductivity.9 Since grafting chains are usually the same as the matrix polymer, they are able to shield nanoparticle surface from the immiscible solvent. However, the nanoparticle and grafted chains are immiscible as well but are constrained by chain connectivity. Therefore, nanoparticle core and grafted polymer layer attempt to phase separate and self-assembly of the nanoparticles is observed, analogous to “microphase separation” in surfactants and block copolymers. Controlling the spatial distribution of the inorganic nanoparticles within the polymer matrix is a challenge in achieving the Received: December 20, 2010 Revised: February 24, 2011 Published: March 15, 2011 5566
dx.doi.org/10.1021/jp112088x | J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
superior property associated with polymer nanocomposites. Selfassembly of particles has been used as a “bottom-up” route to material assembly. It is anticipated that anisotropic assemblies and complex structures useful for new materials can be created by anisotropically shaped particles or spherical particles with directional interactions. On the other hand, it was reported that the self-assembly morphology of spherical nanoparticles can be controlled by grafted polymer chain length and number of grafted chains.13 To gain theoretical insights, Monte Carlo (MC) simulations have been adopted to explore the self-assembly of spherical particles uniformly grafted with polymer chains in an implicit solvent. The theoretical predictions expressed by a “morphology diagram”, which depicts the variation of the assembly superstructure with the characteristics of grafted polymer brush, are in agreement with experimental observations. However, the experimental morphology diagram also shows the dependence on the ratio of grafted chain length to matrix chain length, which has not been considered in the simulation study. Evidently, the shape of nanoparticle and the length of matrix polymer play important roles in determining the self-assembled superstructure associated with the amphiphile-like behavior of grafted nanoparticles. Nonetheless, a theoretical understanding of how individual anisotropy dimensions conspire to generate the range of novel and complex structures useful for new materials is still lacking. In this paper, we adopt dissipative particle dynamics (DPD) simulations to explore the self-assembly of nanoparticles with grafted polymer chains into a variety of anisotropic superstructures. DPD takes into account the solvent explicitly and allow simulations on mesoscopic space and time scales beyond those available with molecular dynamics.14,15 The morphology diagrams are constructed for various particle shapes, which vary from hexagonal nanoplatelet to nanorod by changing the aspect ratio (S). Moreover, the effect of matrix polymer on the self-assembly is considered as well.
’ MODEL AND SIMULATION METHOD The dissipative particle dynamics (DPD) method, introduced by Hoogerbrugge and Koelman in 1992,16 is a particle-based mesoscale simulation technique. This method combines some of the detailed description of the MD but allows the simulation of hydrodynamic behavior in much larger, complex systems, up to the microsecond range. In a DPD simulation, a bead with mass mi represents a block or cluster of atoms or molecules moving together in a coherent fashion. These DPD beads are subject to soft potentials and governed by predefined collision rules. Like MD, the DPD beads obey Newton’s equation of motion dri =dt ¼ vi ,
dv i =dt ¼ f i =mi
ð1Þ
where fi denotes the total forces acting on bead i. The interparticle force Fij exerted on bead i by bead j is made of a conservative term (FijC), a dissipative term (FijD), and a random term (FijR). Therefore, the total force acting on bead i is given by fi ¼
∑ðFij C þ Fij D þ FijR Þ
j6¼ i
ð2Þ
The sum acts over all beads within a cutoff radius rc = 1 beyond which the forces are neglected. Typically, the conservative force is represented by a soft-repulsive interaction Fij
C
¼ aij ð1 rij =rc Þrij ,
for rij e rc ;
0,
for rij > rc ð3Þ
where rij is the distance between the two beads and rij is the unit vector in the direction of the separation. The interaction parameter
aij represents the maximum repulsion between bead i and j, and the dissipative force is proportional to the relative velocity Fij D ¼ γωD ðrij 3 vij Þrij
ð4Þ
where γ is the friction coefficient, ωD is the weight function and vij is the velocity vector of bead i with respect to bead j. The random force is related to the temperature Fij R ¼ σωR rij θij rij
ð5Þ
where σ = (2γkBT)1/2 represents the noise amplitude, ωR is the weight function, and θij is the random number whose average number is zero. In the system, there are three different species of DPD beads, including solvents (S), solvophobic beads (A) for constructing nanoparticles, and solvophilic beads (B) for forming polymeric chains. The box size in our simulations was 65 65 65 with periodic boundary conditions in the x, y, and z directions. Note that we have performed the simulations for various box sizes. The comparison between 50 50 50 and 65 65 65 demonstrates that the morphological outcomes are essentially not affected by the cell size. System density was set as 3.17 The repulsive interactions between the same species are set as aSS = aAA = aBB = 25. We have chosen aAS = 45, aBS = 25, and aAB = 45. Note that if species i and j are fairly compatible, one has aij ≈ 25.17 As the incompatibility between i and j rises, aij increases. To connect the realistic grafted nanoparticle and our DPD model, the grafted nanoparticle used in ref 13 was taken as a template. In ref 13, the authors used 14 nm diameter spherical silica particles grafted with polystyrene chains and the polystyrene chains are with molecular weight (Mw) ranging from 25 to 160 kg/mol. From the work of Terao and Mays,18 the relations between radius of gyration of polystyrene and Mw in a good and theta solvents are given. The radii of gyration are estimated to be about 5 and 15 nm for polystyrenes with Mw = 25 kg/mol (∼240 repeat units) and 160 kg/mol (∼1500 repeat units), respectively. In our work, a DPD polymer bead is chosen to have a diameter of 5 nm containing a polystyrene segment with ∼300 repeat units, and the therefore polystyrene with 1500 repeat units roughly corresponds to model polymer with 45 DPD beads. Since the DPD nanoparticle bead is with relatively the same size as the DPD polymer bead, we estimated that a DPD nanoparticle bead contains about 4000 silica atoms. A nanoparticle is modeled by connecting beads with springs and the arrangement of DPD beads in a nanoparticle is shown in Figure 1a. In this study, nanoparticles were constructed with H layers of hexagon, which consists of DPD beads in a hexagonal arrangement. The radial span of a nanoparticle is defined as D, and therefore the number of beads along the diagonal line of the hexagon is D. The aspect ratio (S) of the nanoparticle is defined as the ratio of the height to the radial span of the nanoparticle, S = H/D. Different values of S correspond to different geometrical characteristics. As S e 0.4, the nanoparticle is plateletlike. For S g 1.2, a rodlike nanoparticle is obtained. S ≈ 1 indicates a spherelike nanoparticle. The volume fraction of nanoparticles in the system is defined as jnp ¼
Nnp Mnp total no: of beads in the systems
ð6Þ
where Nnp and Mnp represent the total number of nanoparticles in the system and total number of beads per nanoparticle, respectively. Note that Mnp does not include the solvophilic 5567
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
Table 1. Physical Parameters of the Nanoparticles Studied in This Worka H
D
S
Mnp
Nnp
Nmax
2
9
0.222
122
203
48
2 2
7 5
0.286 0.400
74 38
334 650
36 24
3
5
0.600
57
433
24
6
5
1.200
114
216
24
9
5
1.800
171
144
24
12
5
2.400
228
108
24
a
H is the number of hexagonal layers. D is the number of beads on the diagonal line of a hexagon layer. S = H/D is defined as the ratio of the maximum span to the height of the nanoparticle. Mnp is the total number of beads per nanoparticle. Nnp represents the total number of nanoparticles in the system. Nmax is the maximum number of sites on a nanoparticle for grafting.
The line spring force (FijLS) is the force between two beads separated by one bead in the axial direction. The face-to-face spring force (FijFS) represents the axial force between two beads located respectively on the top and bottom surfaces. The diagonal spring force (FijDS) denotes the force between two beads located respectively on the top and bottom surfaces along the diagonal line. They are expressed as follows:
L
Figure 1. (a) Schematic of the arrangement of DPD beads in a nanoparticle and the definition of axial span H and radial span D. In this case, H = 6 and D = 5. The green beads represent the sites which can be tethered with solvophilic chains. (b) The neighboring beads are connected through springs represented by red lines. (c) Three additional spring forces of nanoparticle: line spring force FijLS, face-to-face spring force FijFS, and diagonal spring force FijDS. (d) Schematic of grafted nanoparticles. (e) Schematic of face-to-face (string) packing. (f) Schematic of side-by-side (fillet, ribbon, and sheetlike) packing.
polymeric beads. In this work, jnp is set as 0.03. For example, for the nanoparticle depicted in Figure 1a with D = 5 and H = 6, one has Mnp = 114 and thus the number of nanoparticles is Nnp = 216. Table 1 lists the physical parameters (H, D, S, Mnp, Nnp, and Nmax) of the nanoparticles studied in this work. The neighboring beads of a nanoparticle are connected through springs (Figure 1b). Thus, spring forces FijS are needed for adjacent beads in a nanoparticle. The present work adopts a harmonic spring Fij S ¼ Cðrij req Þrij
ð7Þ
where the spring constant C = 100 and the equilibrium length req = 0.7. Note that eq 7 is used to impose connectness among beads of a nanoparticle, and the choice of C and req will not affect the qualitative behavior of the system studied in our work. To further stabilize the structure of a nanoparticle, three additional forces were also imposed in our simulations as shown in Figure 1c.
F
Fij LS ¼ CL ðrij req L Þrij
ð8Þ
Fij FS ¼ CF ðrij req F Þrij
ð9Þ
Fij DS ¼ CD ðrij req D Þrij
ð10Þ
D
= 100, reqL = 1.4, reqF = 0.7(H 1), and reqD = 2 1/2
where C = C = C 0.7[(H 1)2 þ (D 1) ] . Newton’s equation of motion was integrated using the modified velocity-Verlet algorithm. The DPD time step was set at a relatively small value Δt = 0.02 to avoid divergence of the simulation, and the total DPD steps are 1 1062 106. The surface modification of nanoparticles involves solvophilic polymer chains grafted onto the solvophobic nanoparticles. In this work, we assume that only beads situated on the outer rims of the nanoparticles can be grafted. This is consistent with the concept that the functional groups for polymer grafting are generally the defects located at the edges. Therefore, the maximum number of sites (Nmax) for grafting (shown as the green beads of Figure 1a) varies with D. For example, one has Nmax = 24 for D = 5 as listed in Table 1. Grafted polymers with the chain length depicted by L beads were tethered onto the edged beads of nanoparticle randomly and each site can have only one tethered chain (Figure 1d). The nanoparticles can self-assemble into a variety of superstructures, which can be characterized by the radial distribution function g(r). The radial distribution function (RDF) (or pair correlation function) g(r) describes how the nanoparticle density varies as a function of the distance from one particular nanoparticle. The g(r) is defined as gðrÞ ¼
dnðrÞ NP 2 4πr V
ð11Þ
where dn(r) is the number of nanoparticles at a distance between r and r þ dr from a given nanoparticle. NP represents the total 5568
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
number of nanoparticle, and V is the model volume. Note that the distance between two nanoparticles is defined as the distance between the centers of masses between two nanoparticles. Moreover, in order to describe the size of the self-assembly, we adopt the z-average aggregation number, ÆPæz hP iz ¼
∑i Ni Pi 3= ∑i Ni Pi 2
ð12Þ
where Pi represents the aggregation number of ith cluster and Ni is the number of clusters with aggregation number, Pi. Note that one can also use such a size definition to investigate a specific substructure within an aggregate, for example, the string structure within a spherical aggregate. Note that a grafted nanoparticle belongs to a face-to-face stacking structure if the distance from its surface center to the neighboring one is less than a value of d and to a side-by-side stacking structure if the distances from two of its edged beads to the neighboring ones are less than a value of d as illustrated in Figure 1e,f. Here, we choose d = 1.4.
’ RESULTS AND DISCUSSION The superstructures formed by solvophobic nanoparticles with grafted, solvophilic polymers are investigated by DPD simulations. We focus on the effect of shape anisotropy of nanoparticle on the morphology of the self-assembled superstructures. The anisotropic characteristics of nanoparticles are realized by varying the aspect ratio of the hexagonal cylinder. Note that the aspect ratio is defined as the ratio of the height to the radial span of the nanoparticle, S = H/D. The self-assembly of four types of nanoparticles are considered. One is that the aggregation of bare nanoparticles is studied as reference states. Second, by changing the length and number of grafted polymer chains, the morphology diagram of grafted plateletlike nanoparticles (S e 0.4) is obtained. Third, the self-assembly morphology of grafted rodlike nanoparticles (S g 1.8) is presented as well. Fourthly, grafted spherelike nanoparticles (S ≈ 1) are considered. The results are compared to those reported previously by MC simulations.13 Finally, the influence of the length of matrix polymer on the morphology diagram is discussed as well. Bare Anisotropic Nanoparticles. Experimental studies show that inorganic nanoparticles often aggregate into clusters rather than disperse in polymer matrix. This fact indicates the solvophobic nature associated with the nanoparticles. In our simulations, we consider bare hexagonal nanoparticles with the radial span D = 5 and the height H = 29. Because of the immiscibility between nanoparticles and solvents, nanoparticles are prone to cluster together in order to reduce the interfacial contact. Among all surfaces enclosing a given volume, spheres have the smallest surface area. Therefore, the shape of all aggregates tend to be spherelike as shown in Figure 2a for H = 2, in agreement with the previous study.13 Note that nanoparticles are depicted by the yellow color and solvent beads were omitted for clarity. As the height of the nanoparticle is increased from 2 to 3, 6, and 9, the number of aggregates declines from 16 to 13, 7, and 2, as depicted in Figure 2ad. Nonetheless, the averaged DPD beads per aggregate corresponding to the snapshots of Figure 2 grows from 1544 to 1899, 3518, and 12 312. Note that in this work we have fixed the total numbers of nanoparticle beads at about 24 700, and as a consequence the total numbers of nanoparticles decrease as H increases. By doing so, the weight fractions of the various nanoparticles in the systems are kept constant. An increase in H with fixed D results in the increase of
Figure 2. Morphologies of bare nanoparticles with D = 5 in polymer matrix: (a) H = 2, (b) H = 3, (c) H = 6, and (d) H = 9. Only aggregates of nanoparticles are shown. Solvent beads are omitted for clarity.
the nanoparticle surface and the unfavorable interactions between the nanoparticles and the solvents go up accordingly. Since the solvophobicity of the nanoparticle is increased with increasing height at a fixed D, the clustering tendency is increased with H and the number of clusters declines, in agreement with the colloid chemistry concept that particles with a large specific surface agglomerate easily compared to those with smaller specific surface.9 Although the morphologies tend to be still spherical for various heights, the surface of the cluster becomes increasingly rough as the size of the nanoparticle (H) is increased. Superstructures Formed by Grafted Nanoplatelets (S e 0.4). The hexagonal nanoparticle with D = 5 and H = 2 is disklike and can be regarded as nanoplatelet. There are 650 nanoplatelets in the system, and they contain about 3% of the overall DPD beads in the system. The solvophilic polymer chains are randomly grafted on the edges of the top and bottom faces of the nanoparticle. Depending on the number (N) and length (L) of grafted polymer chains, three types of self-assembly morphologies are observed: spherical aggregates, strings, and dispersed phases as shown in Figure 3. The influence of the number of polymer chain (N) is examined first by fixing the chain length at L = 1. Note that the maximum grafting number is Nmax = 24 for D = 5. As the number of polymer chains is small, N = 28, nanoparticles gather into spherelike clusters, as shown in Figure 3a. The radial distribution function g(r) of the spherical cluster shows two distinct peaks at r ≈ 1.4 and 3, as depicted in Figure 4a. The results clearly suggest that there is a short-ranged packing order within the aggregates. The first peak locates at r = 1.4, revealing that two nanoplatelets often stack together in a face-to-face fashion. The second peak locates at about r = 3, but the peak width is apparently much broader than that of the first peak. This peak is the result of short-ranged packings, such as three stacking nanoplatelets with r = 2 1.4 and side-by-side packing with r = 3.13. The corresponding packing patterns are 5569
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
Figure 3. Three types of morphologies formed by grafted disklike nanoparticles (D = 5, H = 2) in polymer matrix: (a) spherical aggregation (N = 4, L = 1); (b) string (N = 16, L = 1); (c) dispersion (N = 24, L = 1).
shown on the right. The short strings and side-by-side packing of the short strings formed within the aggregate can be clearly observed by the enlarged illustration in Figure 4a. Besides the first two peaks, other peaks are not clear, and this implies the absence of long-ranged order within the aggregates. Note that the aggregate structures of the disk discussed in Figure 4a seems very reminiscent of the tactoid structure discussed in polymer clay nanocomposites. In our study, an attractive interaction between the platelets is present; the summation of such an attractive interaction over the large platelet surfaces may give rise to a formation of tactoids of parallel platelets.19 As a consequence, ordered tactoids can been found to be embedded in larger, amorphous aggregate structure for small N and L. Since the surface of the platelet increases as the radial span D increases, the above-mentioned nested structures become more evident and can been observed directly as the spherical aggregate for
ARTICLE
nanoparticles with D = 9 and H = 2 grafted with polymers with N = 4 and L = 1 shown in Figure 6b. The arrangement of nanoplatelets inside spherical aggregates can be further examined by the size of the stacking configuration. It is found that ÆPffæz is around 7. Note that ÆPffæz does not correspond to the z-average aggregation number of the overall spherical aggregates, but it denotes only the short-ranged face-toface stacking structures within the aggregates. Nanoplatelet belongs to a stacking structure if the distance from its surface center to the neighboring one is less than 1.4 (see Figure 1e). In this system, we found that ÆPffæz ≈ 7. This result suggests that face-to-face stacking of the nanoplatelets does take place inside the spherical aggregates and is consistent with the long tail of the second peak in the radial distribution function, which can extend to r = 9. For small grafted number, the shield of solvophobic nanoplatelets against solvents by solvophilic chains is weak and the spherical shape of the aggregate can reduce the particle solvent contacts. However, as the number of grafted polymers is increased, the height of the first peak of g(r) grows but that of the second peak declines accordingly, indicating that the packing order rises with increasing N (see Figure 4a). When the grafting number becomes large, N = 1022, nanoplatelets with L = 1 aggregate into stringlike clusters. As illustrated in Figure 3b, nanoplatelets tend to stack regularly in a face-to-face manner, like coin stacking. In these cases, the radial distribution function g(r) exhibits periodic peaks (Figure 4b). The peak located at r = 1.4 corresponds to the two contact nanoplatelets, and the peak at r = 2.8 corresponds to the two nanoplatelets separated by one nanoplatelet. Similarly, the peaks at r = 4.2 or 1.4 m denote the two nanoplatelets separated by two or (m 1) nanoplatelets. Figure 4b also shows that the peak value decrease with increasing the number of grafted chains. As N = 22, only the first three peaks exist clearly. This consequence originates from the increment of the affinity between solvent and nanoplatelet due to solvophilic polymer chains. When N = 24, nanoplatelets are able to disperse in solvent, as illustrated in Figure 3c, because of their high solvent affinity and the steric repulsion between nanoplatelets provided by grafted chains. In addition to the morphology depicted by the radial distribution function, the size of the self-assembly can be characterized by the z-average aggregation number ÆPstæz for stringlike structures. Figure 5 shows the variation of the aggregation number with the grafted number of polymer for L = 1, 2, and 3. Take L = 1, for example, as the morphology becomes stringlike, ÆPstæz grows rapidly and reaches a maximum at N = 14. Further increase of the grafted number leads to a continuous decrease of the aggregation number. When ÆPstæz < 3, the system can be regarded as the dispersed phase. These results indicate that for L = 1 the string structure can be formed for nanoplatelets with high enough grafted number (N = 1022) because the solvophilic polymers are able to protect the long sides of the string. However, the evident existence of the maximum ÆPstæz at N = 14 reveals the competition between the shielding capability around the long side of the string by grafted polymers and the solvophilicity associated with grafted nanoplatelet. As N is increased, both the shielding capability of the grafted polymers and solvophilicity of the grafted nanoplatelet grow. However, the former encourages the string formation but the latter leads to dispersion. As we can see, solvophilicity of the nanoplatelet becomes dominant for N > 14. Such an effect, together with particle entropy, results in the size reduction of the self-assembled string and eventually the nanoplatelet dispersion appears as N = 24. 5570
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
Figure 4. Radial distribution function of spherical aggregate and string for nanoplatelets with H = 2 and D = 5 grafted with solvophilic polymer chains of (a) L = 1 and N = 28 and (b) L = 1 and N = 1422. The corresponding packing patterns of the first few peaks are also shown.
Morphology Phase Diagram of Grafted Nanoplatelets (S e 0.4). In addition to the grafted number, the morphology
of self-assembly is also influenced by the grafted polymer length (L). Note that a soft DPD polymer bead represents a block of monomer units. As shown in Figure 5 for nanoplatelets, the variation of the z-average aggregation number with the grafted number is considerably altered by varying the chain length. The peak value of ÆPstæz drops as L is increased from 1 to 3. The position of the ÆPstæz peak also shifts from N = 14 for L = 1, to N = 10 for L = 2, and then to N = 8 for L = 3. Moreover, the grafted number leading to the nanoplatelet dispersion is lowered from N = 24 for L = 1, to N = 17 for L = 2, and then to N = 14 for L = 3. These results clearly indicate that increasing the chain length of grafted polymers raises the solvophilicity of the nanoplatelet and promotes the steric repulsion between nanoplatelets. Consequently, the size of the string is significantly reduced and the dispersion can occur at relatively low grafted number, as the chain length is increased at a given N. By varying the grafted number between 0 and 24 and polymer chain length between 1 and 3, the morphology phase diagram for nanoplatelets with D = 5 and H = 2 can be constructed by summarizing the superstructures observed in DPD simulations. As shown in Figure 6a, each data point depicts the self-assembly morphology for 3% volume fraction of nanoparticles. In general,
Figure 5. ÆPstæz versus N for D = 5 and H = 2 nanoplatelets tethered with solvophilic polymer chains of N = 224 and L = 13.
as the grafted number and polymer chain length are increased, the self-assembly morphology changes from spherical aggregate, to string, and then to dispersion owing to solvophilicity increment and steric repulsion enhancement. 5571
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
Figure 7. Morphologies of nanords (D = 5 and H = 9) tethered with polymer chains of various N and L: (a) spherical aggregates (N = 2 and L = 1); (b) fillet (N = 20 and L = 1); (c) ribbon (N = 16 and L = 4); (d) dispersion (N = 24 and L = 4).
Figure 6. Morphology phase diagram of nanoplatlets (D = 5 and H = 2) tethered with polymer chains of N = 224 and L = 13. (b) Superimposed morphology phase diagram of three polymer-grafted nanoplatlets with fixed H and various D. The lines separating the different regions are merely guides to the eye.
Although both the grafted polymer number (N) and chain length (L) play important roles in determining the morphology of the superstructure, they have different degrees of influences. This difference may be manifested by considering nanoplatelets grafted with the same amount of solvophilic units but different grafted numbers. A constant value of N L means the same amount of solvophilic units. For N L = 24, the self-assembly morphology of nanoplatelets with N = 12 and L = 2 is strings with ÆPstæz = 11, but it becomes a dispersed phase for those with N = 24 and L = 1. These results indicate that when the same amount of solvophilic units is attached, a nanoplatelet with larger grafted number is more solvophilic than that with longer chain length. That is, solvophilic units attached directly to the surface is more effective than those away from the surface in protecting the solvophobic nanoparticle from the solvent. The more uniform the grafted sites are, the more solvophilic the nanoplatelets become. In addition to N and L, the self-assembly morphology is also a function of the nanoplatelet shape in terms of the aspect ratio (S). Without loss of generality, the height of the nanoplatelet is fixed at H = 2, and we consider two radial spans, D = 7 and 9, in addition to D = 5. Similar to the case of D = 5, the morphology diagrams of D = 7 and 9 can be constructed from simulations and still consist of three kinds of morphologies: spherical aggregate, string, and dispersion. However, the solvophobicity of the nanoplatelet grows with increasing the radial span due to the increment of the surface area. As a result, nanoplatelets with different radial spans may have different morphologies at the same amount of grafted polymers. For example, for N = 10 and
L = 1, nanoplatelets of D = 5 self-assemble into strings while nanoplatelets of D = 7 form spherical aggregates. However, the amount of grafted polymers along the edges of the faces can be significantly increased to improve solvophilicity of nanoplatelets with larger radial spans due to the increment of Nmax. The maximum grafted numbers are given as Nmax = 24, 36, and 48 for D = 5, 7, and 9, respectively, as listed in Table 1. In order to understand the influence of the radial span (D), we compare the three morphology diagrams by normalizing the grafted number with Nmax. As shown in Figure 6b, it is interesting to find that the three morphology diagrams essentially collapse into one with superimposed boundaries. This consequence indicates that the solvophobic effect of larger surface area associated with the nanoplatelet can be reduced by the attachment of more solvophilic polymers and the superstructure morphology can be described by the diagram of grafted ratio (N/Nmax) versus chain length (L). Self-Assembly Formed by Grafted Nanorods (S g 1.8). When the height is significantly greater than the radial span, the shape of the nanoparticle is rodlike. Superstructures formed by grafted hexagonal nanorods exhibit the side-by-side packing formats, which are quite different from the face-to-face packing arrangements of nanoplatelets mentioned previously. For nanorods with D = 5 and H = 9 tethered with polymer chains of various N and L, four types of aggregates are observed: spherical, filletlike, ribbonlike, and dispersed structures as shown in Figure 7. With increasing grafted number and chain length, the packing patterns change from spherical packing to side-by-side packing such as ribbonlike and filletlike aggregations. Finally, as N and L are large enough, dispersed states are observed for nanorods. As the number of polymer chain is small and chain length is short, N = 2 and L = 1, the nanoparticles gather into spherelike clusters, as shown in Figure 7a. The radial distribution function g(r) of the spherical cluster shows two distinct peaks, as depicted in Figure 8a. The results clearly suggest that there is also a shortranged packing order within the aggregates. The first peak locates at r = 3.1, revealing that two nanoplatelets often stack together in 5572
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
Figure 8. Radial distribution function of spherical aggregation and fillet for nanorods of H = 9, D = 5 tethered with chains with (a) L = 1 and N = 4 and (b) L = 1 and N = 20 and 24. The corresponding packing patterns of the first few peaks are also shown.
a side-by-side manner. The second peak locates at about r = 5 with a relatively broad peak width as compared to the first peak. This peak is the result of short-ranged packings, such as three stacking nanoplatelets with r = 5.4 and face-by-side packing with r = 4.7. The arrangement of nanorods inside spherical aggregates can be further examined by the size of the side-by-side configuration, i.e., ÆPssæz. Here ÆPssæz corresponds to the z-average aggregation number of the side-by-side stacking structure within the aggregates. Nanorods belong to a side-by-side stacking structure if the distances from its beads at the corners to the neighboring ones are less than 1.4 (Figure 1f). We found that ÆPssæz is around 12, which suggests that short-ranged side-by-side stacking of the nanorods exist inside the spherical aggregates and is consistent with the long tail of the second peak in the radial distribution function, which can extend to 10. When the grafting number becomes large, N = 1424, nanorods with L = 1 aggregate into filletlike clusters. As illustrated in Figure 7b, nanorods tend to stack in a long-ranged side-by-side manner. The packing pattern of the filletlike aggregation is hexagonal packing, i.e., one nanoparticle is surrounded by six nanoparticles, like planar beehives. Figure 8b shows that the radial distribution function of filletlike aggregates has periodic peaks. The first four distinct peaks are at r ≈ 3.1, 5.4, 6.2, and 8.3, and the corresponding packing patterns are shown on the right. Figure 8b
also shows that the heights of the peaks decrease with increasing the number of grafted chains. For N = 24, the height of the first peak is significantly lower than that of N = 20. As mentioned earlier, this consequence originates from the increment of the affinity between solvent and nanoparticle due to solvophilic polymer chains. When N = 24, grafted nanorods should be more dispersive in solvents because of their high solvent affinity and the steric repulsion between nanorods provided by grafted chains. When one increases the chain length of the solvophilic tethered polymers, e.g., L = 4, nanorods with sufficient number of tethered polymers self-assemble into ribbonlike aggregates as shown in Figure 7c. Once more this result originates from the increased solvophilicity and excluded volume effect between nanorods offered by the grafted chains. Consequently, the grafted nanorods are unable to form large-sized filletlike aggregates; however, the side-by-side stacking is still a preferred layout, and therefore the ribbonlike structure is formed. As N is further increased, the entropic effect dominates over the energetic shielding and grafted nanorods tend to disperse in the solution as shown in Figure 7d. In addition to the morphology depicted by the radial distribution function, the size of the self-assembly can be characterized by the z-average aggregation number ÆPflæz for filletlike structures. Figure 9 shows the variation of the aggregation number with the 5573
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
ARTICLE
Figure 9. ÆPflæz versus N for nanorods of D = 5 and H = 9 tethered with chains with L = 1 3.
grafted number for L = 1, 2, and 3. As the morphology becomes filletlike, ÆPflæz for L = 1 grows rapidly and reaches a maximum at N = 20. Further increase of the grafted number leads to a continuous decrease of the aggregation number. This consequence indicates that for short chain length (L = 1) the filletlike structure can be formed for nanorods with high enough grafted number (N = 1224) because the solvophilic polymers are able to protect the upper and lower faces of the fillets. However, the existence of the maximum ÆPflæz at N = 20 reveals that the solvophilicity of the grafted nanorod grows and becomes dominant for N > 20. As a result, the size reduction of the self-assembly is observed. Morphology Phase Diagram of Grafted Nanorods (S g 1.8). Evidently, the morphology of nanorod self-assembly is also a function of the grafted polymer length (L) and the grafted number (N). As shown in Figure 9, the variation of the z-average aggregation number with the grafted number is considerably altered by varying the chain length. The peak value of ÆPflæz drops as L is increased from 1 to 3. The position of the ÆPflæz peak also shifts from N = 20 for L = 1, to N = 16 for L = 2, and N = 10 for L = 3. These results reveal that, similar to nanoplatelets, an increase in the chain length improves the solvophilicity of the nanorods and enhances the steric repulsion between nanorods. By varying the grafted number between 0 and 24 and polymer chain length between 1 and 4, the morphology phase diagram for nanorods with D = 5 and H = 9 (S = 1.8) can be constructed by summarizing the superstructures observed in DPD simulations. As shown in Figure 10a, in general, as the grafted number and chain length are increased, the self-assembly morphology changes from spherical aggregate to filletlike, ribbonlike, and then dispersion owing to solvophilicity increment and steric repulsion enhancement. In addition to N and L, the self-assembly morphology is also a function of the aspect ratio (S). Besides S = 1.8, we consider nanorods with the height H = 12 but the radial span remains at D = 5. That is, S = 2.4. Similar to the case of H = 9, the morphology diagram of H = 12 still consists of four kinds of morphologies: spherical aggregate, filletlike, ribbonlike, and dispersion as displayed in Figure 10b. The solvophobicity of the nanorod grows with increasing the height due to the increment of the surface area. As a result, at the same amount of grafted polymers,
Figure 10. Morphology phase diagram of grafted nanorods of D = 5: (a) H = 9 and (b) H = 12. The lines separating the different regions are merely guides to the eye.
nanorods with different heights may have different morphologies. For example, for N = 16 and L = 3, nanorods of H = 9 selfassemble into ribbons while those of H = 12 form filletlike aggregates. Note that as the radial span is fixed, the maximum amount of grafted polymers along the edges of the faces, Nmax, is the same for all heights. In order to realize the influence of the aspect ratio (S), we compare the two morphology diagrams of H = 9 and 12. It is interesting to find that as H or S grows, the filletlike region expands but the dispersion region shrinks. This consequence indicates that with increasing H the surface area of the nanorod increases and the solvophobic effect of the nanorod dominates over the solvophilic contribution from the grafted chains. Thereby, an expansion in the self-assembly state and shrinkage in the dispersive state are observed. In general, the influences of N and L on the aggregative behavior are similar for both nanoplatelets and nanorods. Evidently, the self-assembly morphologies of nanorods (S g 1.8) are different from those of nanoplatelets (S e 0.4). The former possess ribbon- or filletlike aggregates while the latter has stringlike aggregates. Note that the area of the hexagonal side is much greater than that of the face for nanorods, but the situation is reverse for nanoplatelets. In order to reduce particlesolvent contacts, nanorods tend to have multiple side-to-side contacts, forming fillets for high solvophobicity, and double side-to-side contacts, yielding ribbons for low solvophobicity. However, nanoplatelets mainly have face-to-face contacts and the side-toside contact is not favorable at all. That is, the shape change from high to low aspect ratio leads to the disappearance of the filletlike morphology. 5574
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
Figure 11. (a) Schematic of grafted nanoparticles in matrix polymers with Lm = 4. (b) Morphology phase diagram for nanoparticles of H = 2 and D = 5 mixed with matrix polymers with Lm = 4. The lines separating the different regions are merely guides to the eye.
As the aspect ratio approaches unity like spheres, the area of side is essentially equal to that of the face. Consequently, it is anticipated that for S ≈ 1 the fillet structure can be regarded as the sheet morphology and the ribbon structure becomes essentially the same as the string structure. In our systems, nanoparticle with D = 5 and H = 6 can be regarded as being spherelike. Four types of self-assembly morphologies including spherical aggregates, fillets (sheets), ribbons (strings), and dispersed phases are observed. It is worth mentioning that the anisotropic superstructure formed by spherical polymer-grafted nanoparticles has been studied by MC simulations with implicit solvent. Spherical aggregates, short strings, sheetlike structures, and welldispersed particles were found.13 Clearly, our DPD results of anisotropic nanoparticles with S ≈ 1 are consistent with the MC simulation study of spherical nanoparticles. Effect of Matrix Polymer Length. Until now, the matrix polymer is modeled as a single DPD bead, but the length of the grafted polymer varies from one to four DPD beads. That is, the length of grafted polymer (L) is always equal to or greater than that of the matrix polymer (Lm), i.e., L g Lm. One may wonder whether the morphology of nanoparticle self-assembly changes or not if the matrix polymer length is greater than the grafted polymer length (Lm > L). The experimental work of ref 13 showed that particle dispersion is achieved when Lm e L, and composites with higher Lm (i.e., Lm > L) spontaneously self-assemble into highly
ARTICLE
Figure 12. (a) ÆPstæz versus N for nanoplateles of D = 5 and H = 2 tethered with chains with L = 1 in matrix polymers of Lm = 1 and Lm = 4. (b) ÆPstæz for nanoplateles of D = 5 and H = 2 tethered with chains with L = 1 and N = 22 in matrix polymers of Lm = 18.
anisotropic objects. Therefore, it is important to perform simulations to understand the effect of matrix polymer length on the morphology diagram. We will consider the matrix polymer with the length Lm > L for self-assembly of nanoplatelets and spherelike nanoparticles. The typical schematic is shown in Figure 11a. For nanoplatelets of D = 5 and H = 2 with L = 1 at various N in matrix polymer with the length Lm = 4, the morphological phase diagram is obtained as shown in Figure 11b, which is similar to the one with the Lm = 1 (Figure 6a). That is, there are three types of self-assembly morphologies: spherical aggregates, strings, and dispersed phases for both systems. However, the phase boundary and aggregative behavior associated with nanoplatelets differ for Lm =1 and Lm = 4. Figure 12a illustrates the effect of Lm by displaying the variation of the z-average aggregation number of strings with the number of grafted polymer (N) for nanoplatelet with D = 5 and H = 2. Evidently, the peak corresponding to the longest string structure occurs at N = 14 for Lm = 1 and N = 20 for Lm = 4. The two curves cross each other at about N = 18. As N < 18, the aggregate size of Lm = 1 is greater than that of Lm = 4. Note that the grafted nanoplatelets with N < 18 are quite solvophobic and tend to self-assemble for both systems. Nonetheless, the solvophobicity of nanoparticle is effectively reduced when they are within long-lengthed matrix polymers as compared 5575
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C
Figure 13. (a) ÆPshæz versus N for nanoparticles of D = 5 and H = 6 tethered with chains with L = 1 in matrix polymers of Lm = 1 and Lm = 4. (b) ÆPshæz for nanoparticles of D = 5 and H = 6 tethered with chains with L = 1 and N = 22 in matrix polymers of Lm = 18.
to the short-lengthed ones because the latter has more solventnanoparticle contacts. It may also be comprehended as that the increase in the length of the matrix polymer (Lm) disrupts the face-to-face packing of the nanoplatelets due to the steric hindrance effect. Thus, ÆPstæz of Lm = 4 is smaller than ÆPstæz of Lm = 1. On the other hand, as N > 18, the aggregate size of Lm = 1 is smaller than that of L = 4. The grafted nanoplatelets become weakly solvophilic and tend to be dispersive in the matrix. Nevertheless, it is known that a nanoplatelet with matrix polymers of Lm = 4 possesses more volume excluded to the polymers than that with Lm = 1. As the two nanoplatelets approach each other, the total excluded volume decreases due to the overlap of the excluded volumes. It is this increment in free volume that causes an entropic attraction: the so-called depletion force which induces the aggregative actions between nanoplatelets. As a consequence, ÆPstæz of Lm = 4 is greater than ÆPstæz of Lm = 1. This above result indicates that for weakly solvophilic nanoparticles the aggregation can be promoted due to the depletion attraction between nanoplatelets. In general, longer matrix polymers are larger in size and thereby easily depleted from the small space between two nanoparticles near contact. The uneven osmotic pressure around the nanoparticles pushes them toward each other. As a result, the string size grows with increasing the
ARTICLE
matrix polymer length, as depicted in Figure 12b for Lm = 14. Nonetheless, Figure 12b also demonstrates that the effect of Lm becomes insignificant for long enough matrix polymers, i.e., Lm > 4. It can be attributed to the slow increase in both polymer size and the solvophilicity of the nanoparticle, as Lm is large enough. The former tends to enhance aggregation while the latter leads to dispersion. Note that the classic picture of the depletion attraction involves solvent, polymers, and colloids. However, effective depletion attraction has been used to describe the interaction between two large particles in a colloidal mixture.20 Since our system also involve nanoparticles (large colloid) and polymers (small colloid), we can employ the same idea to describe the attraction. Our DPD simulation for grafted spherelike nanoparticle with H = 6 and D = 5 also shows that the self-assembled superstructures remain essentially the same irrespective of the length of matrix polymer (Lm). Four types of self-assembly morphologies can be seen: spherical aggregates, sheets, strings, and dispersed phases. As illustrated in Figure 13a, the plot of ÆPshæz for sheetlike structures versus N for Lm = 1 and 4 clearly demonstrates that the tendency of sheet formation is reduced by the decrease of solvophobic effect associated with the longlengthed matrix polymer. ÆPshæz for Lm = 4 is smaller than that of Lm = 1 for all N. The peak also shifts from N = 20 for Lm = 1 to N = 22 for Lm = 4. Since the solvophobicity of the nanoparticle declines with increasing the matrix polymer length, the size of the sheet decays accordingly for Lm = 14, as shown in Figure 13b. Again, the effect of Lm becomes insignificant for long enough matrix polymers, and ÆPshæz decreases slowly for Lm > 4. Note that in this case the depletion force does not come into effect because nanoparticles with D = 5 and H = 6 are significantly more solvophobic than nanoplatelets with D = 5 and H = 2, and they are still quite solvophobic even when N = Nmax = 24 at L = 1. One final note about the superstructures presented in this work is that it is believed that our systems are in equilibrium state. The snapshots of final configurations for nanoplatlets (H = 2 and D = 5) and nanorods (H = 9 and D = 5) grafted with various number of polymer chains have been shown in Figures 3 and 7. In all these snapshots, there are free grafted nanoparticles present within the systems. Just like typical micellar systems, the existence of the free nanoparticles indicates that there are exchanges of nanoparticles between aggregates (strings, sheets, or spherical aggregates). Even after equilibrium, we have continually observed frequent exchanges of nanoparticles between aggregates and the aggregates as a whole still move around and change shape continuously. The outcome of these direct observations guarantee true equilibrium.
’ CONCLUSION The incorporation of nanoparticles into polymer matrices increases reinforcement and leads to stronger plastics. However, controlling the spatial distribution of inorganic nanoparticles within organic polymer matrices is a challenge in improving the properties of polymer nanocomposite. In this paper, dissipative particle dynamics simulations are employed to investigate the self-assembly of solvophobic nanoparticles grafted with solvophilic polymers into a variety of anisotropic superstructures. The morphology diagrams are constructed. The influences of particle shape and matrix polymer length on the morphology of the aggregate are particularly focused on. 5576
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
The Journal of Physical Chemistry C The shape of the nanoparticle is defined by the aspect ratio of the hexagonal cylinder, i.e., height to radial span (S). By increasing the aspect ratio, the shape varies from plateletlike (S e 0.4), to spherelike (S ≈ 1), and rodlike (S g 1.8). For a specified shape, the self-assembled structure depends on the grafted polymer length (L) and number of grafted polymers (N). In general, the solvophilicity of the nanoparticle grows with increasing L and N. For nanoplatelets, the superstructure may be spherical aggregate, string, or dispersed phase. On the other hand, for nanorods, the superstructure contains spherical aggregate, fillet, ribbon, and dispersed phase. For spherelike nanoparticles, the fillet and ribbon structures become sheet and string, respectively. This result is consistent with the experimental finding and MC result. The morphology type of the self-assembly is not affected by the length of matrix polymer (Lm). Although the morphology diagrams are essentially similar for various values of Lm, the length of matrix polymer changes the phase boundary separating different regions. As Lm is increased, the solvophobicity of the nanoparticle declines and thus results in smaller aggregates in general. Nonetheless, for weakly solvophilic grafted nanoplatelets due to large amount of grafted polymers (N f Nmax), the size of the string may actually grow with increasing Lm because of the depletion attraction between nanoplatelets.
ARTICLE
(15) Huang, K. C.; Lin, C. M.; Tsao, H. K.; Sheng, Y. J. J. Chem. Phys. 2009, 130, 245101. (16) Hoogerbrugge, P. J.; Koelman, J. Europhys. Lett. 1992, 19, 155–160. (17) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423–4435. (18) Terao, K.; Mays, J. W. Eur. Polym. J. 2004, 40, 1623–1627. (19) Ren, J.; Silva, A. S.; Krishnamoorti, R. Macromolecules 2000, 33, 3739–3746. (20) Louis, A. A.; Allahyarov, E.; L€owen, H.; Roth, R. Phys. Rev. E 2002, 65, 061407.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (Y.-J.S.),
[email protected] (H.-K.T.).
’ ACKNOWLEDGMENT Y.-J.S. and H.-K.T. thank NSC of Taiwan for financial support. Computing time, provided by the National Taiwan University Computer and Information Networking Center for HighPerformance computing, is greatly acknowledged. ’ REFERENCES (1) Jordan, J.; Jacob, K. I.; Tannenbaum, R.; Sharaf, M. A.; Jasiuk, I. Mater. Sci. Eng., A 2005, 393, 1–11. (2) Hussain, F.; Hojjati, M.; Okamoto, M.; Gorga, R. E. J. Compos. Mater. 2006, 40, 1511–1575. (3) Choudalakis, G.; Gotsis, A. D. Eur. Polym. J. 2009, 45, 967–984. (4) Yang, K.; Gu, M. Polym. Eng. Sci. 2009, 49, 2158–2167. (5) Wang, L.; Chen, G. J. Appl. Polym. Sci. 2010, 116, 2029–2034. (6) Gilman, J. W. Appl. Clay Sci. 1999, 15, 31–49. (7) Usuki, A.; Kawasumi, M.; Kojima, Y.; Okada, A.; Kurauchi, T.; Kamigaito, O. J. Mater. Res. 1993, 8, 1185–1189. (8) Jana, S. C.; Jain, S. Polymer 2001, 42, 6897–6905. (9) Wang, S.; Liang, R.; Wang, B.; Zhang, C. Carbon 2009, 47, 53–57. (10) Huynh, W. U.; Dittmer, J. J.; Alivisatos, A. P. Science 2002, 295, 2425–2427. (11) Lu, G.; Li, L.; Yang, X. Small 2008, 5, 601–606. (12) Hosaka, N.; Otsuka, H.; Hino, M.; Takahara, A. Langmuir 2008, 24, 5766–5772. (13) Akcora, P.; Liu, H.; Kumar, S. K.; Moll, J.; Li, Y.; Benicewicz, B. C.; Schadler, L. S.; Acehin, D.; Panagiotopoulos, A. Z.; Pryamitsyn, V.; Ganesan, V.; Ilavsky, J.; Thiyagarajan, P.; Colby, R. H.; Douglas, J. F. Nature Mater. 2009, 8, 354–359. (14) Sheng, Y. J.; Wang, T. Y.; Chen, W. M.; Tsao, H. K. J. Phys. Chem. B 2007, 111, 10938–10945. 5577
dx.doi.org/10.1021/jp112088x |J. Phys. Chem. C 2011, 115, 5566–5577
