Direct Observation of Nanoparticle Embedding into the Surface of a

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Langmuir 2007, 23, 13169-13173

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Direct Observation of Nanoparticle Embedding into the Surface of a Polymer Melt Ranjan D. Deshmukh and Russell J. Composto* Department of Materials Science and Engineering and Laboratory for Research on the Structure of Matter, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104-6272 ReceiVed August 17, 2007. In Final Form: October 4, 2007 Direct embedding of metal nanoparticles (NPs) into the surface of a polymer melt is observed by TEM and a new embedding mechanism proposed. Upon annealing above the glass transition temperature of polystyrene (PS), NPs (20 nm gold) are rapidly covered by a thin PS wetting layer, h* ∼ 1.3-1.8 nm (i.e., about two or three monomers). Because it creates capillary pressure on a NP, this “universal” wetting layer is proposed to be responsible for NP embedding. The value of h* is independent of the molecular weight of PS and constant during the embedding process. The value of h* is found to be similar to the equilibrium wetting layer thickness of a polymer melt spreading on a metal substrate. Using a model that includes the spreading coefficient, long-range van der Waals interactions, and a chain-stretching penalty, h* is shown to be independent of the molecular weight of the polymer. Using this model and the measured value of h*, the interfacial energy between Au NP and PS is estimated to be 8.7 J/m2.

Introduction Nanoparticles (NPs) positioned on polymer surfaces are of great recent interest because these devices can have unique electrical,1,2 mechanical,3 optical sensing,4 catalytic sensing,5 and antimicrobial6 properties that can be tuned by varying the size, type, and surface functionality of NPs. To position NPs on or near a polymer surface, ion implantation2,7 and evaporation1,4 methods have been utilized. For example, ion implantation was employed to create silver NPs in the near surface region of poly(methyl methacrylate) (PMMA). In another example, thermal evaporation of different metals like Ag, Au, In, Pb, Sn, and Bi was used to create metal NP arrays and nanowires on the PS or PMMA domains of poly(styrene-b-MMA), (PS-b-PMMA) having a cylindrical morphology.1,8 Thermal decomposition of organometallic precursors has also been utilized to produce Ag NPs that surface segregate, resulting in reflective and/or conducting polymer surfaces.9-12 In order to modify the polymer surface, NPs have also been deposited from a solution directly onto a polymer surface.13-16 NPs located near the surface not only affect * To whom correspondence should be addressed. Telephone: 215-8984451. Fax: 215-573-2128. E-mail: [email protected]. (1) Lopes, W. A.; Jaeger, H. M. Nature 2001, 414 (6865), 735-738. (2) Heilmann, A.; Kiesow, A.; Gruner, M.; Kreibig, U. Thin Solid Films 1999, 344, 175-178. (3) Taylor, L. T. Recent AdVances in Polyimide Science and Technology; Mid-Hudson Chapter SPE: New York, 1987. (4) Tokareva, I.; Minko, S.; Fendler, J. H.; Hutter, E. J. Am. Chem. Soc. 2004, 126 (49), 15950-15951. (5) Jaramillo, T. F.; Baeck, S. H.; Cuenya, B. R.; McFarland, E. W. J. Am. Chem. Soc. 2003, 125 (24), 7148-7149. (6) Kim, J. W.; Lee, J. E.; Kim, S. J.; Lee, J. S.; Ryu, J. H.; Kim, J.; Han, S. H.; Chang, I. S.; Suh, K. D. Polymer 2004, 45 (14), 4741-4747. (7) Stepanov, A. L.; Khaibullin, R. I. ReV. AdV. Mater. Sci. 2004, 7, 108-125. (8) Darling, S. B.; Hoffmann, A. J. Vac. Sci. Technol. A 2007, 25 (4), 10481051. (9) Rubira, A. F.; Rancourt, J. D.; Taylor, L. T.; Stoakley, D. M.; Clair, A. K. S. J. Macromol. Sci. Pure 1998, A35 (4), 621-636. (10) Southward, R. E.; Thompson, D. W. AdV. Mater. 1999, 11 (12), 10431047. (11) Southward, R. E.; Thompson, D. W. Chem. Mater. 2004, 16, (7), 12771284. (12) Deshmukh, R. D.; Composto, R. J. Chem. Mater. 2007, 19, (4), 745-754. (13) Darling, S. B.; Yufa, N. A.; Cisse, A. L.; Bader, S. D.; Sibener, S. J. AdV. Mater. 2005, 17 (20), 2446-2450. (14) Zhang, Q. L.; Gupta, S.; Emrick, T.; Russell, T. P. J. Am. Chem. Soc. 2006, 128 (12), 3898-3899.

the surface properties but also the morphology of block copolymers. For example, because of their low surface energy, CdSe NPs segregated to the surface of P2VP domains of poly(styrene-b-2-vinylpyridine) (PS-b-P2VP) films and induced a change in orientation of P2VP cylinders from parallel to perpendicular with respect to the silicon substrate.17 More recently, surface-segregated Ag NPs were found to slow down the transition from perpendicular to parallel lamellae near the surface of a PS-b-PMMA film.18 In most of these studies, the surface properties as well as the morphology of the block copolymer depends on the exact location of NPs, which can be either partially exposed at the surface or embedded below the surface. To precisely control the surface properties of polymer nanocomposite films, it is essential to understand how NPs interact with the surface of a melt and how they become embedded into and below the surface. In addition to their technological interest, polymer nanocomposite films are model systems for exploring the fundamental thermodynamic principles that govern NP embedding into a surface. Kovacs et al.19,20 showed that complete embedding of a NP into a polymer melt is expected if γ1 > γ2 + γ12, where γ1 and γ2 are the surface energies of the NP and polymer, respectively, and γ12 is the NP-polymer interfacial energy. This condition is usually satisfied for metal NPs on a polymer and thus complete embedding is expected.19,20 However, this condition may not be satisfied for inorganic NPs on a polymer, resulting in partial wetting or exposed NPs.19,20 Using scanning electron microscopy (SEM), Rimai et al.21 observed the rate of engulfment of soda-lime glass particles (8 µm) in a plasticized polystyrene (PS) surface and found that the particles were partially exposed (15) Zehner, R. W.; Lopes, W. A.; Morkved, T. L.; Jaeger, H.; Sita, L. R. Langmuir 1998, 14 (2), 241-244. (16) Zehner, R. W.; Sita, L. R. Langmuir 1999, 15 (19), 6139-6141. (17) Lin, Y.; Boker, A.; He, J. B.; Sill, K.; Xiang, H. Q.; Abetz, C.; Li, X. F.; Wang, J.; Emrick, T.; Long, S.; Wang, Q.; Balazs, A.; Russell, T. P. Nature 2005, 434 (7029), 55-59. (18) Deshmukh, R. D.; Buxton, G. A.; Clarke, N.; Composto, R. J. Macromolecules 2007, 40 (17), 6316-6324. (19) Kovacs, G. J.; Vincett, P. S. J. Colloid Interface Sci. 1982, 90 (2), 335351. (20) Kovacs, G. J.; Vincett, P. S. Thin Solid Films 1984, 111, 65. (21) Rimai, D. S.; Schaefer, D. M.; Bowen, R. C.; Quesnel, D. J. Langmuir 2002, 18 (12), 4592-4597.

10.1021/la7025544 CCC: $37.00 © 2007 American Chemical Society Published on Web 11/17/2007

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even after several months. Using scanning probe microscopy (SPM), Forrest et al.22,23 showed that the embedding of Au NPs (diameters ) 10, 20 nm) can be used to probe the glass transition temperature (Tg) near the surface of PS and found that the “surface” Tg is lower than that of the bulk. However, McKenna et al.24 showed that the rate of Au NP embedding in the PS surface may be explained by viscoelastic contact mechanics without invoking a depression of the surface Tg. Other research groups have used X-ray reflectivity25,26 and X-ray photoelectron spectroscopy27,28 to study the embedding of metal nanoclusters on polymer surfaces and, thereby, the surface Tg. Whereas some studies show complete embedding,19,20,26,27 others show only partial embedding22,23 of metal NPs, resulting in exposed NPs on polymer surfaces. Because the embedding of a metal NP depends on “chain mobility”, partial or no embedding can be expected at temperatures below Tg of the polymer, whereas at high temperatures complete NP embedding is observed.27 NP embedding can also be induced by exposing the film to a saturated solvent vapor, commonly known as solvent annealing.19 Although some studies of NP embedding have been performed using a variety of techniques, the embedding mechanism of NPs remains largely unknown. By investigating how Au NPs embed in PS having a range of molecular weights, this paper shows that NP penetration can be attributed to capillary forces from a wetting layer that rapidly engulfs the NPs. Using transmission electron microscopy (TEM), individual Au NP embedding in a PS melt is directly observed. Compared to SEM and SPM techniques used in earlier studies,21-23 TEM has an excellent spatial resolution and is able to resolve the nanoscopic region surrounding the NPs. We show that the NPs near the polymer surface are completely covered by a thin wetting layer, 1.3-1.8 nm. This wetting layer thickness (h*) did not change significantly as the molecular weight of the melt was increased from 5.78 to 900 kg/mol. A new mechanism for NP embedding is proposed. Specifically, the capillary pressure that results from the curvature of the wetting layer drives a NP to completely embed into the polymer. Further, the value of h* corresponds to the equilibrium film thickness for a spreading polymer melt on a metal substrate. A thermodynamic model that incorporates the spreading coefficient, long-range interactions, and entropic chain stretching terms can account for h* and its molecular weight independence. We also show that by utilizing this model and the measured value of h*, the interfacial energy between Au NP and PS can be estimated. Experimental Section Polystyrene with three different molecular weights, (a) PS6 (Mw ) 5.78 kg/mol, PDI ) 1.05), (b) PS152 (Mw ) 152 kg/mol, PDI ) 1.05), and (c) PS900 (Mw ) 900 kg/mol, PDI ) 1.06), was acquired from Pressure Chemical Co. Gold colloid (mean diameter 20 nm, coefficient of variation from mean diameter < 8 %, concentration ∼ 7.0 × 1011 NPs/mL, Ted Pella Inc.) and toluene (Sigma Aldrich) were used without any purification. The gold colloid is commonly synthesized by reduction of HAuCl4 in presence of trisodium (22) Sharp, J. S.; Teichroeb, J. H.; Forrest, J. A. Eur. Phys. J. E 2004, 15, 473-487. (23) Teichroeb, J. H.; Forrest, J. A. Phys. ReV. Lett. 2003, 91 (1), 016104. (24) Hutcheson, S. A.; McKenna, G. B. Phys. ReV. Lett. 2005, 94 (7), 076103. (25) Weber, R.; Zimmermann, K. M.; Tolan, M.; Stettner, J.; Press, W.; Seeck, O. H.; Erichsen, J.; Zaporojtchenko, V.; Strunskus, T.; Faupel, F. Phys. ReV. E 2001, 64, 061508. (26) Weber, R.; Grotkopp, I.; Stettner, J.; Tolan, M.; Press, W. Macromolecules 2003, 36 (24), 9100-9106. (27) Erichsen, J.; Kanzow, J.; Schurmann, U.; Dolgner, K.; Gunther-Schade, K.; Strunskus, T.; Zaporojtchenko, V.; Faupel, F. Macromolecules 2004, 37 (5), 1831-1838. (28) Zaporojtchenko, V.; Strunskus, T.; Erichsen, J.; Faupel, F. Macromolecules 2001, 34 (5), 1125-1127.

Deshmukh and Composto Table 1. Characteristics of Polystyrene Used: Molecular Weight (M), Radius of Gyration (Rg), Glass Transition Temperature (Tg), Annealing Temperature (T), Temperature above Tg (T - Tg) and Wetting Layer Thickness (h*) of Polymer on NP M (kg/mol)

Rg (nm)

Tg (°C)

T (°C)

T - Tg (°C)

h* (nm)

5.78 152 900

2.0 10.5 25.4

82.7 99.3 99.9

130 165 165

47.3 65.7 65.1

1.3 ( 0.1 1.4 ( 0.1 1.8 ( 0.2

citrate.29,30 The surface of the gold NPs has a negative charge due to adsorbed citrate species, which is balanced by Na+ counterions. The gold NPs are stabilized from aggregation because of the electric double layer.31 Polyetherimide (PEI) substrates were purchased from Westlake Companies. The PEI substrates were coated with a 10-20 nm layer of Au-Pd by a sputter coater (Cressington sputter coater). To produce ∼500700 nm thick films, a solution of 10.5 wt % PS6, 6.5 wt % PS152, or 5 wt % PS900 in toluene was spin-coated (2000 rpm) on the metal-coated PEI substrates. The films were dried overnight at room temperature in a fume hood and then preannealed in vacuum at 105 °C for a day to remove residual solvent. The original gold colloid was diluted 10 times with ultrapure Millipore water. A few drops of this solution were deposited on the polymer films and dried overnight at room temperature. Because it has a lower Tg, films of PS6 (82.7 °C, Table 1) were annealed at 130 °C for 4320 min (3 d) in argon. PS152 (Tg ) 99.3 °C) and PS900 (Tg ) 99.9 °C) films were annealed at 165 °C for 3 d in argon (cf. Table 1). The “bulk” Tg was calculated from Tg(M) ) 373 - 105/M (K), where M is the molecular weight.32 PS900 films were also annealed for shorter times, 1 and 45 min. The NPs were imaged at 80 kV by transmission electron microscopy (TEM, Phillips 2010). The point-to-point resolution of this TEM was 0.3 nm. The cross sections (∼50-70 nm) for TEM were prepared by ultramicrotomy (Richtheart Jung Ultramicrotome) of the annealed polymer films deposited on the PEI substrate.

Results and Discussion The wetting and subsequent embedding of NPs into a polymer melt surface were investigated by TEM. Figure 1a-c shows representative images of individual Au NPs at different stages of embedding (i.e., partial, nearly complete, and complete) near the surface of PS6 films after annealing for 3 d at 130 °C. Figure 1a shows a partially embedded spherical NP that is completely wet by a polymer layer. Moving from point a to b, the wetting layer contour follows the local curvature of the underlying NP (i.e., convex profile). Point b represents the inflection point where the curvature of the polymer surface changes sign. Between point b and c, the polymer surface profile is concave and eventually the surface flattens near c. For the same PS6 sample imaged at a different location, Figure 1b shows a NP that is nearly completely embedded, protruding only about 3 nm above the plane of the surface. A wetting layer still covers the NP with a curvature defined by the protruding section of the NP. The wetting layer thickness, h*, averaged over ∼25 NPs was found to be 1.3 ( 0.1 nm. This thickness was found to be independent of embedding stage (cf. Figure 1, part a vs part b). In our previous study, for silver NPs that segregated to the surface of PMMA, a wetting layer of comparable thickness to the Au/PS system was observed.12 This similarity is particularly surprising given that (29) Slot, J. W.; Geuze, H. J. Eur. J. Cell. Biol. 1985, 38 (1), 87-93. (30) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday. Soc. 1951, (11), 55-75. (31) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (32) Bandrup, J.; Immergut, E. H.; Grulke, E. A. Polymer Handbook, 4th ed.; Wiley-Interscience : New York, 1999.

Nanoparticle Embedding into a Polymer Melt

Figure 1. TEM images of gold NP embedding into a polymer melt (PS6) surface upon annealing for 3 d at 130 °C. Images show (a) a partially embedded NP covered by a wetting layer of polymer, (b) a nearly completely embedded NP near the surface (indicated by the arrow), (c) a completely embedded NP diffused below the surface, and (d) a partially embedded cluster containing six to eight NPs and covered by a wetting layer. The dotted lines in b, c, and d are a guide to the eye to denote the polymer surface.

the silver NPs were prepared in situ and migrated to the surface, whereas the Au NPs were initially located at the surface and then embedded into the polymer melt. Thus, these experiments suggest that the formation of a polymer wetting layer around a NP is a general phenomena and plays a critical role in NP embedding. Figure 1c shows a NP that has diffused more than 17 nm (∼ NP diameter) below the surface and become completely embedded. Note that the polymer surface is now completely flat. Whereas Figure 1a-c focuses on individual NPs, Figure 1d shows a cluster containing about six to eight NPs that is also covered by a wetting layer (∼1.5 nm). This finding suggests that the size of the NP, at least in 10-40 nm range, does not greatly influence the value of h*. The radius of gyration, Rg, of the PS chain relative to the NP diameter (2R) and the NP-polymer interaction determine how the polymer chains stretch or contract in the vicinity of a NP.33 The polymer chain conformation in the vicinity of a NP would in turn affect h*. Thus, to understand the wetting behavior at the molecular level, the effect of Rg (or M) on h* should be considered. Table 1 shows the chain size, annealing conditions, and h* for PS6, PS152, and PS900 films. To prevent dewetting of PS6 films on the PEI substrate, PS6 films were annealed at a lower T - Tg ∼ 47 °C as compared to the T - Tg ∼ 65 °C for PS152 and PS900. Even though Rg increases by an order of magnitude, from 2.0 nm (2R) for PS6 and PS900 films, the value of h* varies from only 1.3 to 1.8 nm, respectively, as shown in Table 1. Given the uncertainty in the measurements due to instrumental resolution and sample tilting, no conclusions can be drawn from the insignificant change in h*. To observe the very early stages of NP embedding, PS900 films were also annealed for short times, 1 min and 45 min. For the 1 min sample, the diamond knife removed many NPs, because they did not have enough time to penetrate deep into the surface. For the 45 (33) Mackay, M. E.; Tuteja, A.; Duxbury, P. M.; Hawker, C. J.; Van Horn, B.; Guan, Z. B.; Chen, G. H.; Krishnan, R. S. Science 2006, 311 (5768), 17401743.

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Figure 2. Schematic showing (a) partial, (b) nearly complete, and (c) complete embedding of a spherical NP of radius R, driven by a wetting layer of thickness h*. φ is the angle between the air/ polymer wetting layer and planar surface. In c, the squiggly lines represent the polymer chains. In this study, 2Rg varies from ∼4 to 50.8 nm and R ) 10 nm. Thus, this schematic represents the PS6/Au system.

min sample, partial, nearly complete, and complete penetration were observed as previously shown in Figure 1, and the value of h* was consistent with Table 1. These studies suggest that the wetting layer forms very rapidly, within tens of minutes. The h* value, 1.3-1.8 nm, provides insight into the molecular structure of the polymer chain confined between air and the NP. Initially, the gold colloid was deposited on top of a glassy PS film. Upon annealing above Tg, a polymer wetting layer rapidly engulfs the previously exposed NP (Figure 1a). The value of h* is only 2-3 times the statistical segment length of PS, ao ) 0.67 nm.34 Because they are confined between the air/polymer and polymer/NP interfaces, the polymer chains in the wetting layer must be highly stretched parallel to the surface as compared to an unperturbed Gaussian chain in the bulk (cf. Rg in Table 1). These experiments suggest that NP embedding into a polymer melt surface is driven by the formation of a thin wetting layer. Figure 2a-c shows a schematic of partial, nearly complete, and complete embedding of a NP driven by a wetting layer. We propose that the curvature of the polymer wetting layer causes a capillary pressure difference35 acting on the NP ∼ (γ2/(R + h*)) + (γ12/R). The second term can be ignored, because the pressure due to the curvature of the polymer/NP interface, γ12/R, produces a zero net force due to symmetry of a spherical NP. Thus a “net” capillary pressure [γ2/(R + h*)] acts on the particle and drives the NP below the polymer surface, as shown in Figures 1a,b and 2a,b. As the NP embeds deeper, the excess surface area of the polymer capping layer is reduced by 1 - cos φ, where φ is the angle between the air/polymer wetting layer and planar surface, as shown in Figure 2b. Once the NP is completely embedded, the polymer surface becomes flat, as shown in Figure 2c. The polymer chains near the surface (sketched in Figure 2c) (34) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Macromolecules 1994, 27 (17), 4639-4647. (35) Daoud, M.; Williams, C. E. Soft Matter Physics; Springer-Verlag: Heidelberg, 1999.

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Deshmukh and Composto

begin to relax as the NP diffuses further below the surface, as captured in Figure 1c. Why does a wetting layer form in the first place? The wetting behavior of a liquid (L) deposited on a solid (S) can be explained in terms of the spreading coefficient

S ) γS - γLS - γL

(1)

where γS and γL are the surface energies of solid and liquid and γLS is the interfacial energy between solid and liquid.36,37 For a planar substrate, S g 0 and S < 0 represent complete and partial wetting cases, respectively. Young’s equation describes the macroscopic equilibrium condition for a drop of liquid on a planar substrate, γS ) γLS + γL cos θ, where θ is the contact angle between the liquid and the substrate. Namely, θ ) 0 and θ > 0 represent complete and partial wetting, respectively. For a polymer melt on a metal surface, complete wetting is expected because metals have a much higher surface energy than polymers.36 For example, assuming only dispersion forces, Kovacs et al. determined that S > 0 for PS melt on Se, Sn, Ag, and Fe surfaces.19 This macroscopic description of wetting can be refined by including long-range interactions. The contour of a “spreading” polymer melt droplet on a planar substrate displays three distinct regions, (a) a spherical cap (which describes the bulk of the polymer drop), (b) a macroscopic foot (thickness less than 60 µm for PS), and (c) a precursor film (thickness ∼ tens of angstroms), extended over a finite region.36,38 During spreading, Hardy et al.39 showed that a precursor film develops as a halo that surrounds the macroscopic droplet. At the nanoscale, the precursor film profile is governed by the long-range van der Waals forces, which vanish at macroscopic length scales and, thus, do not affect the macroscopic contact angle.36 In our studies, polymer spreading (i.e., wetting layer) on a curved substrate with a diameter of 20 nm should also be governed by long-range interactions. We observe that the polymer wetting layer that covers the NPs has a characteristic thickness that remains constant during embedding (compare parts a and b of Figure 1) and does not depend on molecular weight. Previous studies, however, show that thin films of PS dewet planar gold substrates.40 In our experiments, the value of h* is only 1.3-1.8 nm, which is much smaller than the PS film thickness (40 nm) in the dewetting studies on Au.40 Our results are supported by studies of Seeman et al.,41 who observed an equilibrium film thickness of PS after the spinodal dewetting of a PS film on a silicon substrate covered with a thick oxide layer. X-ray reflectivity experiments inside the holes of the dewetted films showed that the silicon oxide substrate is not exposed but rather wet by a PS film of thickness 1.3 nm.41 This thickness is strikingly similar to the h* (1.3-1.8 nm) of PS covering the gold NPs in the present study. Following the work of de Gennes36 and Zhao,42 we propose a thermodynamic model to describe the free energy of an equilibrium wetting layer of a polymer melt on a substrate. Further, this model predicts that this thickness is independent of molecular weight of the polymer. For complete spreading, the final equilibrium thickness is expected to be a monomolecular layer (36) Degennes, P. G. ReV. Mod. Phys. 1985, 57 (3), 827-863. (37) Leger, L.; Joanny, J. F. Rep. Prog. Phys. 1992, 55 (4), 431-486. (38) Cazabat, A. M. Contemp. Phys. 1987, 28 (4), 347-364. (39) Hardy, H. W. Philos. Mag. 1919, 38, 49. (40) Karapanagiotis, I.; Evans, D. F.; Gerberich, W. W. Colloids Surf. A 2002, 207 (1-3), 59-67. (41) Seemann, R.; Herminghaus, S.; Jacobs, K. Phys. ReV. Lett. 2001, 86 (24), 5534-5537. (42) Zhao, W.; Rafailovich, M. H.; Sokolov, J.; Fetters, L. J.; Plano, R.; Sanyal, M. K.; Sinha, S. K.; Sauer, B. B. Phys. ReV. Lett. 1993, 70 (10), 1453-1456.

of liquid over a surface. Contrarily, de Gennes showed that the equilibrium thickness is greater than a monolayer (for small molecules) because of the stabilizing effects of van der Waals forces.36 Let us consider a wetting layer of thickness h on a planar substrate with a constraint of constant volume (h∆ ) constant), where ∆ is the area over which the liquid has spread. The free energy of the liquid film is given by

[

∆F ) -S - A/12πh2 +

[( ) ]]

Ro 2 π2 kBTn -1 ∆ 6 h

(2)

where n ) FNAh/NMo and Ro2 ) ao2N. Here, A is the Hamaker constant calculated by the Lifshitzs theory, which utilizes dielectric constants and refractive indices for the trilayered system air/PS/gold.43 Here, n is the number of chains per unit area and Ro2 is the mean square end-to-end distance of a Gaussian chain. kB, F, NA, N and Mo are the Boltzmann constant, the density of polymer at temperature T, Avogadro’s number, the degree of polymerization, and molecular weight of a monomeric unit of the polymer, respectively. In eq 2, the first and the second terms represent the spreading coefficient S defined in eq 1 and longrange van der Waals interactions, respectively.36 The third term takes into account the entropic penalty for stretching n polymer chains per unit area.42 Because a planar substrate is assumed, eq 2 does not include entropy loss of chains due to the curvature of the substrate. Minimization of eq 2, -d(∆F(h))/d∆ ) 0, at h ) h* leads to

S+

[]

π2kBTFNA ao2 A )0 3Mo h* 4πh*2

(3)

This equation shows that h* is independent of N or, equivalently, the molecular weight (M ) MoN). Thus, this prediction is in agreement with our experimental observations (cf., Table 1) showing that molecular weight has an insignificant effect on h*. The fundamental interfacial parameters, S and γ12, can now be determined from eqs 3 and 1, respectively. Using h* ) 1.3 nm, AAu/PS/air ) -6.7 × 10-20 J,44 F ) 1 g/cm3 at T ) 403 K,32 and Mo ) 104 g/mol, the spreading coefficient, S, for a PS melt on a planar Au substrate is 0.0398 J/m2. To estimate the interfacial energy between PS and the Au NP, γ1 and γ2 are needed. For PS6, γ2 ) 0.0323 J/m2 at 130 °C.32 Unfortunately, the surface energy of the NP, γ1, is not well-known. Further, the surface energy of a metal NP is greater than that of the bulk metal.45,46 Whereas γ1 for bulk gold is 1.2-1.4 J/m2, the values for NPs range from 1.175 to 8.78 J/m2.46 The value of γ1 ) 8.78 J/m2 46 was chosen because it corresponds to NPs with diameters of 10-25 nm. Using eq 1 and the values for γ1 and γ2 (here 1 ) S and 2 ) L), the calculated value for γ12 is 8.7 J/m2. Note that short-range and nondispersive interactions, such as dipolar and hydrogen bonds, resulting from metal-polymer interactions, can strongly affect the free energy term in eq 2 and thus the calculated values of S and γ12. A detailed model that takes into account these interactions is beyond the scope of this paper. Nevertheless, the calculated value of γ12 is comparable to the interfacial energies of 6.3 and 6 J/m2 for Au and Pd NPs, respectively, in polymers.47,48 Because the exact value of γ1 for Au NP46 remains uncertain, (43) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, CA, 1991. (44) Sehgal, A.; Ferreiro, V.; Douglas, J. F.; Amis, E. J.; Karim, A. Langmuir 2002, 18 (18), 7041-7048. (45) Nanda, K. K.; Maisels, A.; Kruis, F. E.; Fissan, H.; Stappert, S. Phys. ReV. Lett. 2003, 91 (10), 106102. (46) Nanda, K. K. Appl. Phys. Lett. 2005, 87 (2), 021909.

Nanoparticle Embedding into a Polymer Melt

this agreement with the γ12 extracted by the embedding experiments is encouraging. To improve dispersion and prevent aggregation, the surfaces of NPs are commonly modified by surfactants and polymers. In this study, the NPs are stabilized by trisodium citrate, which can modify the surface and interfacial energy values. Note that these NPs have a limited solubility in organic solvents; therefore, nanocomposite films of citrate-modified NP and PS are difficult to prepare. Recent FTIR studies suggest that the three carboxylate groups coordinate with the Au surface to form a rather flattened structure.49 Further, the -OH group orients away from the surface, which explains how citrate adsorption leads to the solubility of Au NP in water. When citrate-stabilized Au NPs are incorporated into a polymer melt, the adsorbed citrate molecules might be displaced by PS chains. For PMMA containing Au NP modified with oleylamine, FTIR and XPS studies suggest that a ligandexchange process takes place with PMMA replacing the weakly adsorbed surfactant.50 In another example, because of its attraction to gold, pyridine has been found to displace the adsorbed citrate ions in a colloid.51 Similar studies are needed for citrate-modified Au blended with PS. Kunz et al.52 estimated that citrate groups covering the surface of a Au NP would only decrease the surface energy by 0.003 J/m2, which is a relatively small value compared to 8.78 J/m2. Thus, the contribution of citrate to the surface and interfacial energies of the Au NPs is not included in this study. In general, for polymer nanocomposites the moieties on the NP surface may not only affect the compatibility with the matrix but also the thermodynamics/dynamics of NP embedding. For example, one type of surfactant adsorbed to the NP surface can have unfavorable enthalpic interactions with the matrix and hinder the NP embedding, whereas a more compatible surfactant may promote NP embedding. For a polymer brush attached to a NP surface, the grafted chains may affect the kinetics of NP embedding, depending on how the matrix chains penetrate the brush. So far, only a thermodynamic description of NP embedding in a melt has been considered. However, the kinetics of NP embedding into a soft substrate might be important. Kinetically limited embedding may play a role, because the Tg of PS in the vicinity of a NP could change due to chain confinement and NP-chain interactions.53 Because a small increase in Tg will increase the effective viscosity of polymer surrounding the NP surface, the kinetics of wetting layer formation over a NP may be retarded and, therefore, NP embedding into the melt slowed down. This could possibly explain why some NPs are not completely embedded even after 3 d of annealing. Cole et al.54 showed that the Stokes-Einstein (SE) equation accurately (47) Lamber, R.; Wetjen, S.; Schulzekloff, G.; Baalmann, A. J. Phys. Chem. 1995, 99 (38), 13834-13838. (48) Lamber, R.; Wetjen, S.; Jaeger, N. I. Phys. ReV. B 1995, 51 (16), 1096810971. (49) Nichols, R. J.; Burgess, I.; Young K. L.; Zamlynny, V.; Lipkowsky, J. J. Electroanal. Chem. 2004, 563 (1) 33-39. (50) Abyaneh, M. K.; Pasricha, R.; Gosavi, S. W.; Kulkarni, S. K. Nanotechnology 2006, 17 (16), 4129-4134. (51) Weitz, D. A.; Oliveria, M. Phys. ReV. Lett. 1984, 52 (16), 1433-1436. (52) Kunz, M. S.; Shull, K. R.; Kellock, A. J. J. Colloid Interface Sci. 1993, 156 (1), 240-249. (53) Rittigstein, P.; Torkelson, J. M. J. Polym. Sci. Polym. Phys. 2006, 44 (20), 2935-2943.

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describes the diffusion of bare Au NP in poly(tert-butyl acrylate). The SE equation describes an isolated, rigid sphere moving in a continuum of viscosity η and is given by D ) kBT/6πηR, where R is the hydrodynamic radius of the particle.55 For Au NPs in PS6K, η ) 8.5 × 102 Pa s at T ) 130 °C56 and R ) 10 nm, if the hardcore NP radius is used. Thus after 3 d, the NPs should diffuse through the PS by the distance (Dt)1/2 ) 3 µm, which is much larger than experimental observations (Figure 1). Kovacs et al.19,20 have developed a modified diffusion equation that accounts for van der Waals forces between a NP and polymer as well as entropic effects due to NP incorporation in polymer. The penetration of a NP is given by

x5 tAAu/PS 4 3 x + x4 + ) 3 5 9πηR3

(4)

where x ) z/R is the distance of the NP from the polymer surface (z) normalized by NP radius, and AAu/PS is the Hamaker constant between Au and PS. Using AAu/PS ) (AAuAPS)1/2 ) 16.12 × 10-20 J, where AAu ) 40 × 10-20 J and APS ) 6.5 × 10-20 J are the Hamaker constants for Au and PS, respectively,43 NPs are expected to penetrate 235 nm, which is still much larger than the experimental results in Figure 1a-c. One complication of this kinetic model is that adsorption of polymer segments to the NPs could increase the SE radius, resulting in a smaller diffusion coefficient.52 A detailed study of the kinetics of NP embedding is beyond the scope of this paper.

Conclusion In conclusion, we have demonstrated that a metal NP can completely embed into a polymer melt surface. We have proposed a new and generic mechanism that describes the NP embedding process. A wetting layer covers the NP and creates a capillary pressure responsible for pushing the NP into the soft substrate until the NP is completely submerged. We have demonstrated that the wetting layer covering the NP is in fact the equilibrium wetting layer of a polymer melt spreading on a substrate. The wetting layer thickness, h*, 1.3-1.8 nm, was found to be independent of the molecular weight of the polymer. We have considered a model that includes the spreading coefficient, longrange interactions, and entropic chain stretching terms to account for h* and its molecular weight independence. Using this model and the measured value of h*, the interfacial energy between Au NP and PS, 8.7 J/m2, is estimated. Acknowledgment. This work was funded by the National Science Foundation Polymer (DMR05-49307), MRSEC (DMR0520020), and NSEC (DMR04-25780) programs, as well as the ACS/PRF program (43616-AC7). We gratefully acknowledge the use of the microtome in Prof. K. Winey’s laboratory at the University of Pennsylvania. LA7025544 (54) Cole, D. H.; Shull, K. R.; Baldo, P.; Rehn, L. Macromolecules 1999, 32 (3), 771-779. (55) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: New York 1997. (56) Kim, S. H.; Teymour, F.; Debling, J. A. J. Appl. Polym. Sci. 2007, 103 (4), 2597-2607.