Effect of Matrix Molecular Weight on the Coarsening Mechanism of

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Effect of Matrix Molecular Weight on the Coarsening Mechanism of Polymer-Grafted Gold Nanocrystals Xiaolong Jia,†, Jessica Listak,‡ Velencia Witherspoon,§ E. Eric Kalu,§ Xiaoping Yang,† and Michael R. Bockstaller*,‡

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† The Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology, Beijing 100029, PR China, ‡Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, and § Department of Chemical Engineering, Florida A & M University, Tallahassee, Florida 32307. Current address: Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213

Received February 26, 2010. Revised Manuscript Received June 9, 2010 A systematic evaluation of the effect of polymer matrix molecular weight on the coarsening kinetics of uniformly dispersed polystyrene-grafted gold nanoparticles is presented. Particle coarsening is found to proceed via three stages (i.e., atomic-diffusion-based Ostwald ripening (OR), particle-migration-based collision-coalescence, and the subsequent reshaping of particle assemblies). The relative significance of each stage and hence the evolution of particle size and shape have been found to depend sensitively upon time, temperature, and the molecular weight of the host polymer. At temperatures close to the matrix glass-transition temperature, Ostwald ripening has been observed to be dominant on all experimental timescales. With increasing annealing temperature, collision coalescence becomes the dominant mode of coarsening, leading to rapid particle growth. The onset of the latter process is found to be increasingly delayed with increasing molecular weight of the polymer host. Particle coalescence is observed to proceed via two fundamental modes (i.e., diffusion-limited aggregation and growth resulting in the formation of fractal particle clusters and the subsequent recrystallization into more spherical monolithic aggregate structures). Interestingly, particle coarsening in highmolecular-weight matrix polymers is found to proceed significantly faster than predicted on the basis of the bulk polymer viscosity; this acceleration is interpreted to be a consequence of the network characteristics of high-molecularweight polymers by analogy to the phenomenon of nanoviscosity that has been reported in the context of nanoparticle diffusion within high-molecular-weight polymers.

Introduction Research in polymer nanocomposites is driven by the opportunity to enhance specific property characteristics (such as optical, thermal, and transport properties) of a polymer matrix by means of the dispersion of inorganic filler particles.1-5 In general, the effect of particle addition on the properties of the composite material is intimately linked to the dispersion state of the particle filler, and thus significant research has focused on developing synthetic and processing conditions that enable the formation of stable particle dispersions within polymer matrices.6-9 In this context, particular interest has been placed on polymer-grafted nanoparticles (in which graft and matrix polymer are chemically analogous), and multiple studies have been performed in order to understand the interrelationship between particle architecture and dispersion morphology. The more recent application of microphase-separating block copolymers as embedding materials has further expanded the opportunities of polymer/particle (1) Sardar, R.; Funston, A. M.; Mulvaney, P.; Murray, R. W. Langmuir 2009, 25, 13840–13851. (2) Link, S.; El-Sayed, M. A. Annu. Rev. Phys. Chem. 2003, 54, 331–366. (3) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, 1025–1102. (4) Burda, C.; Chen, X.; Narayanan, R.; Xia, Y.; Halas, N. J. MRS Bull. 2005, 30, 338–348. (5) Li, M.; Schnablegger, H.; Mann, S. Nature 1999, 402, 393–395. (6) Mackay, M. E.; Tuteja, A.; Duxbury, P. M.; Hawker, C. J.; Van Horn, B.; Guan, Z.; Chen, G.; Krishnan, R. S. Science 2006, 311, 1740–1743. (7) Xu, J. Q.; Bartels, J. W.; Bohnsack, D. A.; Tseng, T. C.; Mackay, M. E.; Wooley, K. L. Adv. Funct. Mater. 2008, 18, 2733–2744. (8) Chen, X.; Ohno, K.; Ladmiral, V.; Composto, R. J. Polymer 2008, 49, 3568– 3577. (9) Oh, H.; Green, P. F. Nat. Mater. 2009, 8, 139–143.

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dispersions to encompass multifunctional hybrid materials in which novel property combinations are derived from the hierarchical arrangement of the polymer and particle constituents as well as novel lithographic techniques.10-13 To establish a fundamental understanding of the interrelationship between particle architecture and dispersion morphology, the gold-thiol system has attained particular significance. This is because of both the accessibility of a wide range of surface chemistries as well as the particular characteristics of gold such as high electron density, plasmon absorbance, and biocompatibility that render gold an attractive material system for a wide range of analytical and technological applications. However, a common problem encountered in gold-thiol nanocomposites is the partial (or complete) desorption of ligands during thermal annealing, a process that convolutes the analysis of the structure-formation process in polymer/particle systems with an unknown time dependence of particle-particle and particle-polymer interactions as well as particle coarsening.14-16 Particle coarsening in polymer matrices is therefore of dual interest, first, because of the ramifications of (10) Bockstaller, M. R.; Lapetnikov, Y.; Margel, S.; Thomas, E. L. J. Am. Chem. Soc. 2003, 125, 5276–5277. (11) Bockstaller, M. R.; Kolb, R.; Thomas, E. L. Adv. Mater. 2001, 13, 1783– 1786. (12) Bockstaller, M. R.; Mickiewicz, R. A.; Thomas, E. L. Adv. Mater. 2005, 17, 1331–1349. (13) Bockstaller, M. R.; Thomas, E. L. Phys. Rev. Lett. 2004, 93, 166106. (14) Listak, J.; Hakem, I. F.; Ryu, H. J.; Rangou, S.; Politakos, N.; Misichronis, K.; Avgeropoulos, A.; Bockstaller, M. R. Macromolecules 2009, 42, 5766–5773. Listak, J.; Bockstaller, M. R. Macromolecules 2006, 39, 5820–5825. (15) Srisombat, L.; Zhang, S. H.; Lee, T. R. Langmuir 2010, 26, 41–46. (16) Guo, Q.; Sun, X.; Palmer, R. E. Phys. Rev. B 2005, 71, 0354061–0354065.

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particle growth on the properties of nanocomposite materials and, second, because the complex microscopic environment presented by polymer matrices is expected to result in a richer parameter space that determines particle coarsening as compared to low-molecular-weight embedding media. Several mechanisms have been discussed in the context of particle coarsening dependent on the dominating process of material transport (i.e., Ostwald ripening and particle coalescence).17-24 Although in both mechanisms the driving force is associated with the decrease in chemical potential due to the reduction of interfacial area, the difference is in the dominant process of mass transport that is fundamental to the growth process. In particular, Ostwald ripening (OR) is caused by the diffusion of atoms through the matrix leading to the growth of larger particles at the expense of smaller ones, whereas coalescence involves the collision of migrating particles and subsequent recrystallization and reshaping of aggregates. Note that both mechanisms differ in the temperature dependence of the dominant mass-transfer process (i.e., although atomic diffusion can occur in solid embedding media, particle migration requires a mobile environment). Thus, diffusion-driven aggregation and coalescence are expected only at temperatures above the softening temperature of the embedding medium. To date, the coarsening characteristics of polymer-embedded nanocrystals has been vigorously studied for the case of pristine nanocrystals (typically fabricated by the sputtering of metal clusters onto polymer films), and it was shown that because of the low softening temperatures of polymer materials both coarsening mechanisms are active during particle growth. Interestingly, the interaction of nanocrystals with the polymer matrix was also shown to impart a subtle influence of the molecular weight of the embedding media on particle diffusivity and aggregation.25-27 Although pristine nanocrystals offer an intriguing model system for studying particle coarsening, the blending of surface-functionalized nanoparticles into polymer matrices (by solution or melt processing) represents the technologically predominant approach to the preparation of nanocomposites. Because surface-bound ligands affect polymer-particle interactions, different coarsening characteristics are expected as a function of ligand and matrix composition as well as ligand-particle bond strength. For example, Green and co-workers recently studied the coarsening behavior of aliphatically modified gold particles within poly(methyl methacrylate) above the polymer’s glass-transition temperature and reported coarsening to proceed initially through concurrent OR and collision-coalescence, followed by predominant collision-coalescence in the later stages of coarsening.28 Understanding the governing parameters that determine the time dependence of the coarsening process will be of significant relevance to the further development and study of polymer nanocomposite materials. In this contribution we present a systematic evaluation of the effect of polymer matrix molecular weight on the (17) Kirchner, H. O. K. Metall. Trans. 1971, 2, 2861–2864. (18) Speight, M. V. Acta Metall. 1968, 16, 133–135. (19) Smoluchowski, M. V. Phys. Z. 1916, 17, 585–599. (20) Kang, K.; Redner, S.; Meakin, P.; Leyvraz, F. Phys. Rev. A 1986, 33, 1171– 1182. (21) Sholl, D. S.; Skodje, R. T. Physica A 1996, 231, 631–647. (22) Pai, W. W.; Swan, A. K.; Zhang, Z.; Wendelken, J. F. Phys. Rev. Lett. 1997, 79, 3210–3213. (23) Huang, F.; Zhang, H. Z.; Banfield, J. F. Nano Lett. 2003, 3, 373–378. (24) Lo, A.; Skodje, R. T. J. Chem. Phys. 2000, 112, 1966–1974. (25) Cole, D. H.; Shull, K. R.; Baldo, P.; Rehn, L. Macromolecules 1999, 32, 771–779. (26) Cole, D. H.; Shull, K. R.; Rehn, L.; Baldo, P. Phys. Rev. Lett. 1997, 78, 5006–5009. (27) Shull, K. R.; Kellock, A. J. J. Polym. Sci., Part B 1995, 1417–1422. (28) Meli, L.; Green, P. F. ACS Nano 2008, 2, 1305–1312.

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mechanism and time dependence of coarsening of polystyrenefunctionalized gold nanoparticles embedded in polystyrene. This experimental system expands previous work in two respects. First, the absence of enthalpic ligand-matrix interactions allows for the identification of more subtle effects related to particle diffusion in polymer networks and, second, the systems’ capability to form stable particle dispersions is representative of technologically relevant nanocomposite materials. In agreement with previous reports,28 we observe that initial OR is followed by migrationdriven particle coalescence. The onset of the latter process is found to be increasingly delayed with increasing molecular weight of the polymer host. Particle coalescence is observed to proceed via two fundamental modes (i.e., diffusion-limited aggregation and the growth of fractal particle clusters and subsequent recrystallization into nearly spherical monolithic clusters). Different geometric shapes of coarsened particles are observed and interpreted as a consequence of the kinetic competition between diffusion-limited aggregation and crystal reshaping. Interestingly, particle coarsening in high-molecular-weight matrix polymers is observed to proceed significantly faster than predicted on the basis of the bulk polymer viscosity; this acceleration is interpreted to be a consequence of the network characteristics of high-molecularweight polymers and is similar to the phenomenon of nanoviscosity that has been reported by several authors in the context of particle diffusion within polymer-embedding media.29-33

Experimental Section Chemicals. Materials used in our study are composed of polystyrene-grafted gold nanoparticles (AuSPS) and polystyrene (PS) homopolymers (atactic) with three different numberaveraged molecular weights of 35 (PS35, PDI = 1.18), 300 (PS300, PDI = 1.20), and 1100 kg/mol (PS1100, PDI = 1.15). The PS homopolymers were obtained from Polymer Source Inc. Preparation of Gold Nanoparticles and Films. PS-grafted gold nanoparticles with an average core diameter of 2.91 nm were synthesized by using the phase-transfer method developed by Brust et al.34 Great care was taken to remove residual ligands quantitatively from the particle product (by repeated washing of the particle precipitate with 4/1 EtOH/THF). The synthesis of thiol-terminated oligomeric styrene ligands with a degree of polymerization DP of ∼10 (equal to a molecular weight of Mn = 1.04 kg/mol) and a degree of polydispersity PDI of ∼1.04 as well as details of particle purification and characterization has been described in ref 11. The composite solutions with a polymer concentration of 5 wt % were formed by mixing gold nanoparticles and respective PS homopolymer in toluene. The composite films with a thickness of about 1 mm were prepared by casting the solution, and the final weight fraction of gold nanoparticles in the films was about 1 wt %. The obtained films were annealed in a saturated toluene atmosphere for 72 h at 50 C before being dried in a vacuum at room temperature for 24 h to remove excess solvent. The resulting films were annealed in vacuum at 120 or 170 C for a given time period and subsequently quenched to room temperature. Characterization of Gold Nanoparticles. The morphology characterization of gold nanoparticles within polymer films was carried out by using a JEOL 2000 FX transmission electron microscope (TEM). The TEM samples were prepared by (29) Narayanan, S.; Lee, D. R.; Hagman, A.; Li, X. F.; Wang, J. Phys. Rev. Lett. 2007, 98, 185506. (30) Liu, J.; Cao, D. P.; Zhang, L. Q. J. Phys. Chem. C 2008, 112, 6653–6661. (31) Brochard-Wyart, F.; deGennes, P. G. Eur. Phys. J. E 2000, 1, 93–97. (32) Mackay, M. E.; Dao, T. T.; Tuteja, A.; Ho, D. L.; Horn, B. V.; Kim, H. C.; Hawker, C. J. Nat. Mater. 2003, 2, 762–766. (33) Ye., X.; Tong, P.; Fetters, L. J. Macromolecules 1998, 31, 5785. (34) Brust, M.; Bethell, M. W. D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, 801.

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microsectioning the final films at -110 C using a LEICA EM FCS cryo-ultramicrotome, and the TEM images were acquired from different regions of the samples. The average diameter Æd æ, shape factor Sf, and number density N of gold nanoparticles and particle aggregates in PS films were calculated with TEM images by using ImageJ software to measure at least 1000 particles in each thermal annealing period. The projected areas A of the particles and particle aggregates as well as the maximum lengths L of the projected areas were also determined from TEM images using ImageJ.

Results and Discussion Particle coarsening was monitored both in the vicinity and well above the glass-transition temperature of the polymer host (Tg,PS ≈ 110 C) in order to assess the relevance of microscopic dynamics on the coarsening process. Note that both temperatures are above the expected stability limit of gold-thiol bonds based on prior studies of ligand-grafted gold nanocrystals in solution.35,36 Particle Coarsening at T=120 C. Figure 1 shows the TEM image of gold nanoparticles embedded in the low-molecularweight PS35 film before thermal annealing, revealing that gold nanoparticles are uniformly dispersed in the film, with a spherical shape and a calculated average diameter of 2.90 nm; similar particle dispersions were observed for higher matrix molecular weight, but the results are not shown here.37 From the total number density of particles within the film, the average particle distance can be estimated to be ÆLPæ = (V/N)1/3 = 52 nm. Because this distance significantly exceeds the range of dispersion interactions, we will neglect particle interactions in the following discussion. For all matrix molecular weights, particle size was found to increase only slightly during thermal annealing for 120 h at T = 120 C. As shown in Figure 2a for the case of PS35, both the particle diameter and number density as well as the particle shape remain unchanged (within experimental error). The average diameter Æd æ of the particles is found to increase slightly from 2.90 to 3.28 nm; similar trends were also observed for PS300 and PS1100 films, but the results are not shown here. We interpret the slow particle growth as well as the approximately spherical geometry as a consequence of particle growth being predominantly due to atomic-diffusion-driven coarsening (OR). Ostwald ripening is commonly described on the basis of the theory of Lifshitz, Slyozov, and Wagner (LSW), who showed the growth rate of particle volume VP to be of the form ΔVP(t) = KLSWt, where KLSW is a kinetic growth constant that depends on the atomic volume, the atomic diffusion coefficient, and the temperature.38 Using LSW theory, it has been shown that the OR mechanism results in asymmetric particle size distributions with negative skewness (i.e., with a median that is less than the average value of the particle size). The inspection of the particle size distributions before (inset of Figure 1) and after (inset Figure 2) thermal annealing reveals a decrease in the skewness coefficient R from 0.52 to 0.36, where R is defined as R = 3(Æd æ - dm), Æd æ is the average, dm is the median, and σ is the standard deviation of the particle diameter. Although a change in the skewness of the (35) Garg, N.; Carrasquillo-Molina, E.; Lee, T. R. Langmuir 2002, 18, 2717– 2726. (36) Shon, Y. S.; Lee, T. R. J. Phys. Chem. B 2000, 104, 8192–8200. (37) The uniform particle dispersion that is observed in our experiments is in agreement with previous reports on polymer/gold nanocrystal blend composites and is likely due to the small particle diameter that is significantly less than the radius of gyration of the matrix (Rg = 5.07, 14.84, and 28.41 nm for 35K, 300K, and 1100K PS, respectively). (38) Heilmann, A. Polymer Films with Embedded Metal Nanoparticles; Springer: Augustusburg, Germany, 2002.

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Figure 1. Electron micrograph of gold nanoparticles in a PS35 film at room temperature before thermal annealing. The inset shows the particle size distribution (υ denotes the frequency) and average diameter Æd æ of the particles.

Figure 2. (a) Electron micrograph of gold nanoparticles in a PS35 film after thermal annealing for 120 h at 120 C. The inset shows the particle size distribution (υ denotes the frequency) and average diameter Ædæ of the particles. (b) Time dependence of the average diameter Ædæ of gold nanoparticles in a 35K PS film at 120 C. The inset shows the time dependence of the particle number density N in a PS35 film during thermal annealing at 120 C.

distribution provides only a qualitative measure for the T = 120 C annealed samples (because of the initial positive skewness of the as-synthesized particle size distribution as well as the rather minor changes in particle size), the decrease of R is in agreement with the suggested preeminence of OR. The relevance of OR is further supported by the observed stability of ligand bonding during thermal annealing at T = 120 C. Langmuir 2010, 26(14), 12190–12197

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Figure 3. Morphology evolution of gold nanoparticles in a PS35 film during thermal annealing at 170 C for various time periods: (a) 5, (b) 6, (c) 24, and (d) 120 h. The insets show the particle size distribution (υ denotes the frequency) and average diameter Ædæ of the particles after each increment of thermal annealing.

To assess the stability of ligand-particle bonds, films were redissolved after thermal annealing and the morphology of particle monolayers was analyzed using TEM and compared to that of preannealed systems. As shown in the Supporting Information (Figure S1a), the particle size and the center-to-center distance remained virtually unchanged after annealing at T = 120 C, indicating the stability of the polystyrene shell. We note that the observed stability of thiol-bonded ligands is surprising because in solution debonding has been reported at temperatures exceeding about 80 C.39 Because the effective strength of ligand-surface bonds is not expected to depend significantly on the nature of the embedding medium and because the analogous chemical composition of ligand and matrix alleviates the relevance of enthalpic contributions, we rationalize the apparent increase in stability as a consequence of the reduced dynamics of polymeric ligands within the embedding polymer melt (at temperatures close to Tg) that results in the trapping of debonded ligands in the vicinity of the particle surface and therefore facilitates rapid restabilization during dissolution of the film. We note that this interpretation is somewhat speculative in nature. In particular, whereas thermogravimetric analysis of heat-treated particle solutions in DIBP confirms the rapid debonding of ligands at elevated temperatures (Figure S2), the postulation of a long-lived transient shell of (39) Dong, H. C.; Zhu, M. Z.; Yoon, J. A.; Gao, H. F.; Jin, R. C.; Matyjaszewski, K. J. Am. Chem. Soc. 2008, 130, 12852–12853. (40) An alternative explanation for the increased effective particle stability could be that a reduced number of polymer ligands are necessary to stabilize particles in polymeric embedding media as compared to low-molecular-weight solvents. A detailed understanding of this processes will require a more systematic analysis of the surface chemistry of embedded gold particle systems (or gold model surfaces) as a function of thermal processing using techniques such as XPS. This is beyond the scope of the present work.

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debonded ligands is hypothetical and motivated by the experimentally observed increase in stability of PS-coated gold particles in polymer matrices as compared to that of small molecular solvent media.40 However, although accurate data on the change in the absolute number of ligands are difficult to obtain, our result indicates that the effective stability of ligand-grafted gold nanocrystals is a complex quantity that depends not only on thermodynamic considerations such as ligand-particle, ligand-matrix, and particle-matrix interactions but also on dynamic processes such as ligand diffusion within the matrix. Additional stabilization processes, for example, by means of the exchange reaction of ligand and matrix chain segments have been reported previously by Shull and co-workers.26 Particle Coarsening at T = 170 C. Very different particle growth characteristics are observed during thermal annealing at T = 170 C. Figure 3 depicts the morphology evolution of gold nanoparticles in PS35 film with the thermal annealing time at 170 C, revealing a significant change in both particle size and shape at annealing times exceeding t = 5 h. In particular, the initial formation of aggregates with a fractal shape is observed after 5 h of thermal annealing, indicating particle coarsening through diffusion-limited aggregation and growth. (See discussion below.) The fractal aggregate structures are subsequently found to reshape to form more globular structures of average diameter Æd æ = 49.2 nm after 120 h of thermal annealing as well as increasingly positively skewed aggregate size distributions. With increasing molecular weight of the embedding polymer, the tendency for fractal formation during particle coarsening is found to be reduced. For example, Figures 4 and 5 depict the evolution of particle morphology in PS300 and PS1100 films at DOI: 10.1021/la100840a

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Figure 4. Morphology evolution of gold nanoparticles in a PS300 film during thermal annealing at 170 C for various time periods: (a) 7, (b) 8, (c) 24, and (d) 120 h. The insets show the particle size distribution (υ denotes the frequency) and average diameter Ædæ of the particles after each increment of thermal annealing.

170 C, respectively. With increasing molecular weight, more globular aggregate structures are observed that indicate both migration-driven coalescence as the fundamental coarsening mechanism and a more subtle dependence of the resulting aggregate morphology on the molecular weight of the embedding polymer. Further insights into the mechanism of particle coarsening are gained by the analysis of the time dependence of the structural characteristics of the particle fillers during thermal annealing. Dissolution experiments of annealed particle-filled films revealed almost complete aggregation after about 30 min of thermal annealing (Figure S1b), confirming rapid ligand debonding at T = 170 C. Figure 6 shows the time evolution of aggregate size (Figure 6a) as well as particle skewness coefficients (Figure 6b) for the respective matrix molecular weights, revealing that three major growth stages can be distinguished during the coarsening process. The initial stage is characterized by small growth rates and decreasing skewness coefficients of the respective particle size distribution, both indicating coarsening by OR. After an induction period of tcrit (corresponding to 5, 7, and 11 h for PS35, PS300, and PS1100, respectively), a rapid increase in both the average particle size and the skewness coefficient are observed, indicating the onset of the second stage of particle coarsening through migration and collision-coalescence. Following this argument, the threshold time tcrit for the onset of stage 2 can be interpreted as a measure of the minimum time needed for particles to diffuse the average particle distance. (See the discussion below.) We note that the determination of the respective first and third moments of the particle size distribution as well as the coarsening exponent of the power-law time dependence of particle size 12194 DOI: 10.1021/la100840a

(Supporting Information Figures S3 and S4) further supports the interpretation of the second stage of particle coarsening being dominated by migration and collision-coalescence.24,41 Interestingly, the morphological evolution of particle aggregates reveals separate stages that are involved in the collision coalescence process. Figure 7 shows the time dependence of the shape factor Sf (Figure 7a) and 3D fractal dimension D3 (Figure 7b) of the particle aggregates. The shape factor Sf is a measure of the relative circularity of the planar projected particle image (Sf = 1 for circle shape), and the fractal dimension Di (i = 2 and 3 for 2D and 3D structures, respectively) is an evaluation of the efficiency of space filling of the aggregate structures (where D2 (D3) assumes a limiting value of 2 (3) for regularly shaped objects in 2D (3D)).42,43 Both parameters have been determined using literature definitions as Sf = 4πA/P2, A  LD2, and M  RgD3, where A is the projected area of the object, P is the perimeter of the projected area of the object, L is the maximum length of the projected area of the object, M is the mass of the object, and Rg is the radius of gyration of the object.42-45 The values of A, P, and L can be directly acquired from the TEM images using ImageJ software. By plotting log A versus log L, the values of D2 can be obtained from the slope of the curve as shown in the inset of Figure 7b. Then, we use the relationship D3 = 1.391 þ 0.01e2.164D2 given by Kramer45 to attain the values of D3. (41) Pich, J.; Friedlander, S. K.; Lai, F. S. J. Aerosol. Sci. 1970, 1, 115–126. (42) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. A. Particle Deposition and Aggregation; Butterworth-Heinemann: Woburn, MA, 1998. (43) Daoud, M., Williams, C. E., Eds. Soft Matter Physics; Springer-Verlag: Berlin, 1999. (44) Ehrl, L.; Soos, M.; Lattuada, M. J. Phys. Chem. B 2009, 113, 10587–10599. (45) Lee, L.; Kramer, T. A. Adv. Colloid Interfac. 2004, 112, 49–57.

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Figure 5. Morphology evolution of gold nanoparticles in a PS1100 film during thermal annealing at 170 C for various time periods: (a) 11, (b) 12, (c) 24, and (d) 120 h. The insets show the particle size distribution (υ denotes the frequency) and average diameter Ædæ of the particles after each increment of thermal annealing.

As shown in Figure 7a, Sf with values of approximate 0.79 in the first stage is consistent with the nearly spherical shape of the particles as observed in Figures 3a, 4a, and 5a, which is characteristic of OR-based growth.46 After a time tcrit, the Sf of particles in the PS35 film sharply decreases to 0.34 in the second stage, indicating the formation of loose particle aggregate structures through diffusion-limited aggregation and growth. In fact, the fractal dimension D3 determined using the algorithm described above ranges between 1.70 and 1.99, which is close to the D3 value that has been predicted and measured for diffusionlimited aggregation and growth processes.47-49 Similar but less pronounced transitions in fractal dimensions are observed for matrix polymers PS300 and PS1100 for which more globular aggregate structures are observed. We interpret the dependence of aggregate morphology on the molecular weight of the embedding polymer to be a consequence of the kinetic balance of two competing processes (i.e., diffusion-limited aggregation and growth, resulting in loose aggregate structures, and reshaping and densification, resulting in globular monolithic aggregates). Note that whereas migration-collision-based aggregate growth is expected to depend strongly on the particle density in the matrix, the reshaping of aggregates involves more local transport processes that will (to a first approximation) not depend on the concentration of particles. We thus propose that stage 2 coarsening proceeds (46) Huang, F.; Zhang, H. Z.; Banfield, J. F. J. Phys. Chem. B 2003, 107, 10470– 10475. (47) Witten, T. A.; Sander, L. M. Phys. Rev. Lett. 1981, 47, 1400–1403. (48) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360–362. (49) Hoekstra, L. L.; Vreeker, R.; Agterof, W. G. M. J. Colloid Interface Sci. 1992, 151, 17–25.

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by initial diffusion-limited aggregation and growth of (ligandfree) particles associated with the formation of fractal aggregate morphologies. As the collision-aggregation proceeds, the average number of free particles is continuously reduced, thus decreasing the aggregate growth rate. The final stage of coarsening (stage 3) involves the reshaping of aggregates into more globular monolithic structures and is driven by the thermodynamically favorable minimization of the free interfacial area. Stage 3 coarsening is thus associated with an increase in the fractal dimension for which a limiting value of D3 = 3 is expected. Because for lower-molecularweight polymer matrices particle migration is expected to be accelerated (see the discussion below), the formation of fractal aggregate structures is expected to occur more rapidly in PS35 than in the higher-molecular-weight analogs and therefore more loose aggregate structures are observed. Figure 8 illustrates the proposed coalescence process during particle coarsening. The above discussion has highlighted the relevance of particle diffusion in the evolution of particle morphology. To elucidate the relevance of the microscopic environment constituted by the entangled matrix chains, a more detailed evaluation of the experimental coarsening kinetics against the continuum-based Stokes-Einstein (SE) model will be presented in the following. Diffusion in homogeneous low-molecular-weight media is typically described by the SE model that relates the particle selfdiffusion coefficient Ds to the particle radius R, the melt viscosity η, and the temperature T by Ds = κBT(6πηR)-1. Approximate values for the polymer melt viscosity of the samples in our study can be derived by considering the molecular weight dependence of the melt viscosity η of PS homopolymers as log η = C log Mw - k, where Mw is the weight-average molecular weight and C and k DOI: 10.1021/la100840a

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Figure 6. (a) Time dependence of the average diameter Ædæ of gold nanoparticles in PS35, PS300, and PS1100 films during thermal annealing at 170 C. The inset shows the respective time dependence of particle number density N in PS35, PS300, and PS1100 films at 170 C. (b) Time dependence of the skewness coefficient R of the particle size distribution in PS35, PS300, and PS1100 films during thermal annealing at 170 C. (See the text for more details.) The inset illustrates generic size distribution functions with negative and positive skewness coefficients. In plots a and b, the markers represent different molecular weight PS films. Black squares, PS35; red circles, PS300; blue triangles, PS1100.

are constants. For atactic PS homopolymers (Mw g 38 000 kg/mol), C = 3.4 and k = 13.40 at 217 C. After obtaining the melt viscosity η217 at 217 C, the melt viscosity ηT of PS homopolymers at a given temperature can be calculated on the basis of the relationship log(ηT/η217) = 2.68  1016(1/T 6 - 1/4906)e-1330/Mw.50-54 Using the values for Ds, the critical timescale for the onset of collision-coalescence (stage 2) can be estimated as the characteristic time for particles undergoing Brownian motion to traverse a distance of ÆLPæ, that is, tSE = ÆLPæ2 (8Ds)-1.42,55 The results for Ds as well as the characteristic tSE of the respective matrix polymer systems are summarized in Table 1. The comparison of the experimental and predicted timescales for the onset of collision-coalescence reveals that tcrit/tSE =8.2103, 5.25, and 0.11 for PS35, PS300 and PS1100, respectively, indicating a more subtle relationship between the matrix molecular weight and coarsening kinetics that cannot fully be captured by continuum theories such as SE. We note that there will inevitably be an error in the estimated values due to the assumptions of the equations used. However, on the basis of uncertainties (50) Brandrup, J., Immergut, E. H., Grulke, H., Eds. Polymer Handbook; John Wiley & Sons: New York, 2005. (51) Fox, T. G.; Flory, P. J. J. Appl. Phys. 1950, 21, 581–591. (52) Fox, T. G.; Flory, P. J. J. Am. Chem. Soc. 1948, 70, 2384–2395. (53) Fox, T. G.; Flory, P. J. J. Polym. Sci. 1954, 14, 315–319. (54) Fox, T. G.; Flory, P. J. J. Phys. Chem. 1951, 55, 221–234. (55) Hiemenz, P. C. Polymer Chemistry; Marcel Dekker: New York, 1984.

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Figure 7. (a) Time dependence of shape factor Sf of gold nanoparticles in PS35, PS300, and PS1100 films during thermal annealing at 170 C. (b) Time dependence of the 3D fractal dimension D3 of gold nanoparticles in PS35, PS300, and PS1100 films during thermal annealing at 170 C. The inset shows a linear fit (correlation coefficient R = 0.98) of the experimental relationship curve of log A and log L in the PS35 film after thermal annealing for 120 h at 170 C. The slope of the curve is the 2D fractal dimension D2 of gold nanoparticles. The inset images show the morphology of the particles and particle aggregates in PS35 films at various thermal annealing times. In plots a and b, the markers represent different molecular weight PS films. Black squares, PS35; red circles, PS300; blue triangles, PS1100.

reported in the literature, we do not expect these to result in a deviation of the ratio tcrit/tSE in excess of 1 order of magnitude. Rather, we hypothesize that two primary competing mechanisms contribute to the order-of-magnitude variation in dynamic behavior. First, although we observe the debonding of ligands after only 1800 s of thermal annealing at 170 C, the particle is expected to interact strongly with the embedding polymer matrix because of the high surface energy of free metal surfaces resulting in dynamic adsorption and desorption of polymer chains. The transient shell of adsorbed chains will act to increase the particle’s effective radius and therefore result in a decrease in Ds. Similar results were reported by Shull and co-workers, who found that the mobility of gold nanoparticles in poly(t-butyl acrylate) (PTBA) was decreased by 2 to 3 orders of magnitude as compared to the prediction by SE theory due to the exchange kinetics of polymer segments at the polymer/metal interface.26 The range of interactions will approximately be on the order of one correlation length and therefore is expected to level off with increasing molecular weight. This is supported by our experimental observation that reveals a decrease in tcrit/tSE with increasing molecular weight. We rationalize this relative acceleration of collision coalescence with increasing molecular weight to be an implication of the microscopic environment provided by the matrix network structure Langmuir 2010, 26(14), 12190–12197

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Figure 8. Illustration of the coalescence process during particle coarsening. Initially, diffusion-limited aggregation and growth lead to the formation of fractal aggregate structures. Subsequently, reshaping and recrystallization lead to more globularly compacted structures. k1 and k2 are the rate constants of the two coarsening processes. Table 1. Calculated and Experimental Parameters Related to the Diffusion of Gold Nanoparticles in PS35, PS300, and PS1100 Films at 170 C PS 35K

300K

a

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1100K

1.30  10 6.20  10 8.43  10-22 Ds (m /s) ÆLpæ (nm)b 52.31 52.20 52.21 7.31  10-3 1.52 112.35 tSE (h)c 6 8 12 tcrit (h)d 8.20  103 5.25 0.11 tcrit/tSE a Ds is the calculated diffusion coefficient of gold nanoparticles in PS films at 170 C. b ÆLPæ is the average distance between adjacent gold particles in PS films. ctSE is the calculated duration time before the coalescence in which two primary gold nanoparticles diffuse over the average distance ÆLPæ in PS matrices at 170 C. dtcrit is the experimental duration time before the coalescence in which two primary gold nanoparticles diffuse in PS matrices at 170 C. 2

-20

on the local viscosity experienced by diffusing particle species. Several research groups have reported the self-diffusion coefficient of nanoparticles to accelerate in high-molecular-weight polymer hosts. For example, Mackay et al. recently reported that the diffusion of cadmium selenide nanoparticles (with a core radius of about 2 nm) in a melt of PS (M = 393 kg/mol) is approximately 200 times faster than predicted by the SE equation.21 Similarly, Berg and co-workers deduced from tracer diffusion experiments that the local viscosity experienced by nanoscopic inclusions within high-molecular-weight polyisobutylene and poly(dimethylsiloxane) is reduced by 3 to 4 orders of magnitudes as compared to the macroscopic melt viscosity.56,57 We hypothesize that for our systems the decrease in nanoviscosity offsets the increase in hydrodynamic radius for the PS300 and PS1100 systems, therefore resulting in net collision-coalescence kinetics similar to the SE prediction.

Conclusions The coarsening of uniformly dispersed polymer-thiol-functionalized gold nanoparticles in chemically analogous polymer media has been found to proceed via three stages (i.e., atomicdiffusion-based Ostwald ripening (OR), particle-migration-based collision-coalescence, and the subsequent reshaping of particle assemblies). The relative significance of each stage and hence the evolution of particle size and shape have been found to depend sensitively on time, temperature, and the molecular weight of the host polymer. At temperatures close to the matrix glass-transition (56) Somoza, M. M.; Sluch, M. I.; Berg, M. A. Macromolecules 2003, 36, 2721– 2732. (57) Sluch, M. I.; Somoza, M. M.; Berg, M. A. J. Phys. Chem. B 2002, 106, 7385– 7397.

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temperature, Ostwald ripening has been observed to be dominant for all experimental timescales. With increasing annealing temperature, collision coalescence becomes the dominant mode of coarsening, leading to rapid particle growth. The evolution of particle morphology during coalescence arises from the competition between the diffusion-limited aggregation and growth of particles to form fractal aggregate structures (favored for lowmolecular-weight matrix polymers, i.e., more rapid particle diffusion) and recrystallization processes that lead to globular monolithic aggregate structures (favored for high-molecular-weight host polymers). Although the coarsening kinetics follows the expected trend with molecular weight (i.e., more rapid coarsening with decreasing molecular weight of the host polymer), the analysis of the time dependence of aggregate growth reveals discrepancies as compared to a Stokes-Einstein-based diffusion model. In particular, our results point to the relevance of two competing effects (i.e., the formation of transient shells through the adsorption of the matrix polymer and the more rapid migration of nanoscopic fillers within high-molecular-weight matrix polymers, which is the nanoviscosity effect). Finally, we note that although we expect the presented results to be representative and suitable for categorizing the coarsening mechanism of polymer-functionalized gold nanoparticle fillers, the absolute values regarding coarsening should be considered with caution. This is because the coarsening of metal nanocrystals will depend sensitively on structural characteristics such as ligand molecular weight, grafting density, and particle core size that are difficult to control separately. In particular, the latter is expected to affect both the thermodynamic driving force for coarsening and particle diffusion significantly. Thus, more rapid coarsening is expected for smaller particle sizes. More detailed studies to elucidate the effect of particle characteristics on the coarsening process in polymer melts are underway. Acknowledgment. Financial support by the Petroleum Research Fund administered by the American Chemical Society as well as the National Science Foundation (PREM DMR-0351770, EEC-0836633, DMR-0706265) is gratefully acknowledged. X.J. is very pleased to acknowledge partial support received from the cofunding program of the Beijing Municipal Commission of Education and the Study Abroad Fund of Beijing University of Chemical Technology. Supporting Information Available: Electron micrographs of gold nanoparticles. Time dependence of the first moment μ1 and third moment μ3 of the particle size distribution in PS35, PS300, and PS1100 films during thermal annealing. Time dependence of the average diameter of the particles in a PS35 film. This material is available free of charge via the Internet at http://pubs.acs.org. DOI: 10.1021/la100840a

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