Glass Transition Temperature of Polymer–Nanoparticle Composites

Article pubs.acs.org/Macromolecules

Glass Transition Temperature of Polymer−Nanoparticle Composites: Effect of Polymer−Particle Interfacial Energy F. Chen,† A. Clough,† B. M. Reinhard,‡,§ M. W. Grinstaff,‡,§ N. Jiang,∥ T. Koga,∥,⊥ and O. K. C. Tsui*,†,§ †

Department of Physics, Boston University, Boston, Massachusetts 02215, United States Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States § Division of Materials Science & Engineering, Boston University, Boston, Massachusetts 02215, United States ∥ Department of Materials Science & Engineering, Stony Brook University, Stony Brook, New York 11794-2275, United States ⊥ Depertment of Chemistry, Stony Brook University, Stony Brook, New York 11794-3400, United States ‡

ABSTRACT: Numerous studies have shown that the glass transition temperature, Tg, of polymers may change visibly upon addition of even small amounts of nanoparticles. In this study, we examine the effect of polymer−nanoparticle interfacial energy on this phenomenon in nanocomposite films containing polystyrene-grafted nanoparticles mixed with polystyrene homopolymer at low particle loadings. A previous experiment showed that the interfacial energy of this system modulates with the grafting density of the grafted polymer and the molecular weight ratio of the matrix and grafted polymers. We find that the changes in Tg vary with both parameters in manners that quantitatively agree with the interfacial energy. matrix to grafted polymer molecular weight, Mmatrix/Mgraft.31−35 We find that the change in Tg of our nanocomposites varies systematically with both σ and Mmatrix/Mgraft. Importantly, those variations display quantitative agreement with the published values of the interfacial energy.35 While the majority of the measurements are performed on thin films with thicknesses between ∼40 and ∼90 nm, comparison between the results of some thin films and their bulk counterparts shows that the change in Tg found in the two cases exhibit similar dependences on Mmatrix/Mgraft and hence the polymer−nanoparticle interfacial energy, except for a small shift that is attributable to segregation of the nanoparticles to the film surface.

I. INTRODUCTION Incorporating nanofillers into a polymer has become a common strategy to improve the functionality of the polymer for a wide range of applications.1−6 Impressive enhancements in material properties including mechanical,7−10 rheological,4,11,12 electrical,4,13 optical,1 thermal,4,8,14 glass transition,15−21 dewetting,22−25 self-healing,26 and flame retardation2,27 have been demonstrated with this approach. Many of these improvements are attributable to the alterations to the properties of the polymer in the vicinity of the particles due to the polymer− filler interactions, which generally differ from the polymer− polymer interactions.28−30 Because this effect increases in proportion to the filler’s surface-area-to-volume ratio, which varies as one over the filler size, the effect gets amplified when the filler size is decreased, especially to the nanometer range. The main interest of this investigation is to study how the glass transition temperature, Tg, of a polymer may be modulated by loading it with nanoparticles with tunable polymer−nanoparticle interactions. According to computer simulations, attractive polymer−nanoparticle interfacial interactions cause the local dynamics of the polymer to slow down28−30 and thereby an increase in the Tg,28 but repulsive interactions produce the opposite effects. Experiments15−18,20,21 have demonstrated consistency with this prediction, but only qualitative corroboration has been made. In this experiment, we measure the Tg of nanocomposites consisted of a mixture of polystyrene-grafted nanoparticles and a polystyrene homopolymer. Previous studies showed that the polymer−nanoparticle interfacial energy of this system was adjustable through the grafting density of the grafted polymer, σ, and the ratio of the © XXXX American Chemical Society

II. EXPERIMENTAL SECTION Polystyrene (PS) homopolymers with weight-average molecular weights Mw = 1.1−1600 kg/mol and polydispersity index PDI ≤ 1.17 are purchased from Scientific Polymer Products (Ontario, NY) and Polymer Source (Montreal, Canada). The grafting polymers, thiolterminated PS (PS-SH with Mw = 1.4, PDI = 1.4 and 53 kg/mol, PDI = 1.06) and carboxy-terminated PS (PS-COOH with Mw = 2.4 kg/mol and PDI = 1.2) are purchased from Polymer Source (Montreal, Canada). The other chemicals are purchased from Sigma-Aldrich. We use the grafting-to approach to graft the grafting polymers to the nanoparticles. A major advantage of this approach is a more monodisperse chain length distribution one typically attains, which may help reduce the uncertainty in the interfacial properties due to variations in the chain length distribution.36,37 While it is more difficult to control the grafting density or attain a very high grafting density Received: January 6, 2013 Revised: May 8, 2013

A

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with the grafting-to approach, we find that it is adequate in here where the main goal is to examine the effect of favorable versus unfavorable interfacial interactions on the Tg of polymer nanocomposites. As seen below, for the range of grafting density attained by the grafting-to approach, we have been able to produce both types of interfacial behaviors by adjusting the Mmatrix/Mgraft ratio. Gold nanoparticles grafted with the PS-SH ligands (labeled as Au@ PS1K and Au@PS53K) are synthesized by using the two-phase arrested precipitation method as reported in ref 38, except that the thiolterminated ligands therein are replaced by the PS-SH. Figures 1a and

scattering measurements at the X27C beamline of the National Synchrotron Light Source (NSLS, Brookhaven National Laboratory) on a < 1 wt % toluene solution of the nanoparticles, and an identical value was found for d. To determine the ligand grafting density, σ, the weight loss of a specimen taken from each nanoparticle species is monitored upon heating at a rate of 20 °C/min, from room temperature to 600 °C in a TA Instruments TGA 2050 thermogravimetric analyzer (TGA). The determined values of σ are shown in Table 1.

Table 1. Characteristics of the Nanoparticles Used in This Study

Au@PS1K Au@PS53K Si@APTS [email protected]

Au or Si core diameter, d (nm)

grafting density of the surfactant and/or ligands, σ (nm−2)

normalized grafting density,a σ′

vol % at 3 wt %

± ± ± ±

3.3 0.2 3 0.4

2.5 0.9 NA 0.5

1 1.7 1 2.1

4.6 3.9 6.5 6.5

1.2 0.8 1 1

σ′ = σN1/2a−1ρ0−1, where N is the degree of polymerization of the ligand chains, a is the statistical length, and ρ0−1 is the pervasive volume of a segment. Essentially, the thickness of a grafted layer scales as N1/2a while the volume of a grafted chain scales as Nρ0−1. So, the scale for the area of a grafted chain is the ratio of the latter to the former. a

To graft the PS−COOH ligands onto the silica nanoparticles (nominal diameter = 6.5 nm), the nanoparticles are mixed with (3aminopropyl)trimethoxysilane (APTS) in toluene and refluxed at 110 °C for 24 h in a N2 atmosphere. The resulting particles (labeled as Si@ APTS) are washed in abundant toluene and acetone in turn and precipitated by centrifugation. Analysis with TGA shows that the grafting density of APTS is 3 nm−2, corresponding to a ∼81% coverage. Next, the Si@APTS particles are allowed to react with the PS−COOH ligands by esterification for 24 h. Afterward, the reaction product is centrifuged, and the precipitate is redispersed in THF by ultrasonication and then extracted with THF followed by toluene to remove the unreacted PS−COOH. The final product is dried in a vacuum at 30 °C until no further weight loss is detectable. For the nanocomposite films, silicon (100) wafers covered with a 102 ± 5 nm thick thermal oxide layer and cut into 1 × 1 cm2 slides are used as the substrates. Prior to use, the slides are cleaned in a piranha solution (H2SO4:H2O2 in 7:3 volume ratio) at 140 °C for 20 min followed by thorough rinsing with deionized water and then drying with 99.99% nitrogen. Afterward, they are further cleaned in an oxygen plasma for 25 min. Nanocomposite films are prepared by spin-coating solutions containing 1.0−2.5 wt % of the PS−nanoparticle mixtures in toluene. The film thickness, as determined by ellipsometry, is about 40 nm for the gold nanocomposites and 90 nm for the silica nanocomposites. Prior to Tg measurement, the films are annealed at 75 °C for 48 h, except for those with Mmatrix < 5K g/mol. For these low-Mmatrix nanocomposites, the annealing temperature is 35 °C. The use of such low annealing temperatures prevents coarsening of the Au nanoparticles39,40 and may help reduce aggregation of the nanoparticles within the nanocomposites in general.21 Unless otherwise stated, the samples used in the study are thin films. To examine if bulk samples may give different results, we measure the Tg of the [email protected] nanocomposites in both thin film and bulk forms and compare the results. To make the samples in bulk form, we follow the method of Mackay et al.,12 who reported the particles dispersed well in the nanocomposites even at large nanoparticle loadings up to 50 wt %. In their method, blends of the nanoparticles and host polymer are codissolved in THF and then rapidly precipitated with methanol. This is followed by drying in a vacuum at 40 °C for at least a week to remove the solvent. The powder is then molded under vacuum into ∼1 cm radius by ∼1 mm thick disks for differential scanning calorimetry (DSC) measurement. We have used

Figure 1. (a) TEM micrograph of the Au@PS1K nanoparticles. The magnification is 60K. (b) TEM micrograph of the Au@PS53K nanoparticles. The magnification is 200K. (c) Size distribution of the nanoparticles based on 100 particles randomly picked from TEM micrographs as those shown in (a) and (b). 1b show the transmission electron micrographs (TEM) of the synthesized Au@PS1K and Au@PS53K nanoparticles, respectively, acquired by a JEOL 2010 Advanced High Performance TEM (JEOL, Japan). By analyzing 100 nanoparticles randomly picked from the micrographs (Figure 1c), we deduce the diameters of the gold core, d, to be 4.6 ± 1.2 and 3.9 ± 0.8 nm, respectively. The former has been cross-checked with synchrotron small-angle X-ray B

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So, in layered specimens where the ρ-contrast between layers is low, it is difficult to identify the layer interfaces. To circumvent this difficulty, Seeck et al.43 proposed to look at the Fourier transformation (FT) of I(qz), which is related to the corresponding one-dimensional Patterson function:

SAXS to characterize the structure of the nanoparticle dispersions in four [email protected] nanocomposites with various Mmatrix/Mgraft (i.e., ratio of the matrix to grafted polymer molecular weights) between 0.46 and 390 but a fixed particle fraction of 3 wt %. The result, plotted as scattering intensity vs q upon subtracting the corresponding data from a similarly prepared pure matrix polymer, is shown in Figure 2 (here, q

∫q

F(h , qz) ∼ |

qmax

min

qz 4I(qz) exp(− iqzh) dqz|2

(2)

Here, h is the film thickness, and qmin and qmax are the lower and upper limit of the integral and set here to be 0.52 and 5.5 nm−1, respectively. For polymer nanocomposite films with segregation of the nanoparticles to the air surface, for instance, the FT is expected to show two small peaks corresponding to the polymer/polymer and polymer/air interfaces, along with a main peak corresponding to the whole film. In this study, we determine the thicknesses of individual layers from the locations of the small peaks. Then these thicknesses are used to build a layered model to which the Parrat analysis44 is applied to fit the XR data.

III. RESULTS AND DISCUSSION We first compare the change in Tg of the nanocomposite films made of the Au@PS1K and Au@PS53K nanoparticles dispersed in a PS homopolymer with Mw = 5K g/mol. (We shall label these nanocomposites as Au@PS1K/PS5K and Au@PS53K/ PS5K below and use a similar naming scheme for all the other nanocomposites.) As the data of Figure 3 show, the change in

Figure 2. Small-angle X-ray scattering intensity versus wave vector of the 3 wt % [email protected] bulk nanocomposites with Mmatrix/Mgraft = 0.46, 2.7, 7.8, and 390. = (2π/λ) sin(θ/2), with λ and θ being the wavelength of the incident beam and scattering angle, respectively). As seen, the data of all the samples show an upturn in the low-q region, with the same scaling of q−2.8±0.05 down to 0.06 nm−1. This suggests that the particles aggregate into fractal-mass objects with a fractal dimension of 2.8 ± 0.05 and a size of at least 2π/(0.06 nm−1) = 104 nm.41 We use a single-wavelength (633 nm) Stokes ellipsometer by Gaertner Scientific Corp. (Skokie, IL) to measure the Tg of the films. To initiate the measurement, we place the specimen onto the ellipsometer stage, preheated to 140 °C, and let the temperature equilibrate for 10 min. Then we start the measurement as the temperature is decreased at a rate of 1 °C/min to 36 °C. During the measurement, the ellipsometric angles, Δ and Ψ, of the laser beam reflected from the specimen are monitored at 2 °C temperature intervals. An average of 30 measurements taken over a period of 30 s at each measurement temperature, T, is used for statistical averaging. For small changes in the film thickness, the changes in Δ and Ψ are proportional to the thickness change. By using the fact that the thermal expansivity of a material exhibits a discontinuous change at the glass transition, the Tg is determined to be the midpoint temperature where a plot of dΔ/dT or dΨ/dT vs T shows a qualitative jump.42 Differential scanning calorimetry (DSC) is carried out in a TA4000 system thermal analyzer by Mettler Toledo (Columbus, OH). The sample is first heated from 20 to 160 °C at a rate of 10 °C/min to erase the thermomechanical history. Then it is quenched rapidly back to 20 °C at 100 °C/min. Immediately afterward, heat flow measurement is initiated as the sample temperature is increased at a rate of 10 °C/min to 160 °C. The Tg is determined as the location of a step change in the baseline of the DSC signal. X-ray reflectivity (XR) is used to determine the segregation of the nanoparticles, if any, in the films. The measurements are performed at the beamline X10B of the NSLS. The optics is set up as such to deliver an X-ray beam with a wavelength, λ, of 0.087 nm. Specular XR curves are obtained in the θ−2θ geometry as a function of the normal wave vector, qz (= 4π/λ sin θ) up to 5.5 nm−1. In the X-ray spectral regime, the complex refractive index of a material deviates slightly from 1 and is usually written as n = 1 − δ + iβ, where δ and β are the dispersion and absorption component, respectively. In the standard Born approximation, the reflected intensity, I(qz), is given by

I(qz) ∼

1 qz 4

∫ dρd(zz) exp(−iqzz) dz

Figure 3. Change in Tg of the Mw = 5K g/mol PS homopolymer upon loading with the Au@PS1K (●) and Au@PS53K (▲) nanoparticles plotted versus the loading concentration. The dotted and dashed lines are calculations using eq 3 on a homogeneous mixture of the 5K PS and ligand PS.

Tg of the Au@PS53K/PS5K nanocomposites is always positive, and the magnitude of change increases with increasing nanoparticle content. For the Au@PS1K/PS5K nanocomposites, on the other hand, the change in Tg is always negative, and its magnitude increases with increasing particle concentration, ϕ, initially, but becomes saturated for ϕ > ∼0.5 wt %. These findings are similar to those reported by Oh and Green on the same systems but in bulk form.21 The workers correlated the saturation in the Tg change of the Au@PS1K/PS5K nanocomposites at large particle loadings to the onset of particle aggregation near ϕ = 0.5 wt % as observed by scanning TEM. To assess if our observations may arise from a plasticization or antiplasticization effect of the grafted polymer on the matrix polymer, we estimate the Tg of a homogeneous blend composed of the matrix and grafting polymers by using the Gordon−Taylor equation, which presumes free-volume additivity:45

2

(1)

where ρ(z) is the electron density profile in the direction normal to the film. As eq 1 shows, I(qz) is determined by the gradient of ρ(z). C

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(3)

Here, ϕ1,2 and Tg,1,2 denote the volume fraction and Tg of individual components in the blend, respectively. The result from the estimation is shown by the dashed and dotted lines. Clearly, they display much weaker variations than the experimental data do, showing that the observed change in Tg cannot be accounted for by the mere fact that the grafted polymer has a different Tg than the matrix polymer. The divergent behaviors exhibited by the Tg of the Au@ PS1K/PS5K and Au@PS53K/PS5K nanocomposites are commensurate with the opposite interactions the nanoparticles expected to have with the PS5K matrix. In athermal systems where the grafted and matrix polymers are chemically identical, two factors affect the interaction between the grafted and matrix polymer chains. The increase in the translational entropy of the matrix chains upon migration into the grafted chains promotes favorable interactions and hence miscibility between the nanoparticles and the matrix. On the other hand, the migration may cause the grafted chains to stretch, resulting in unfavorable interactions. Various workers have studied the miscibility phase boundary and found that the net effect depends on the normalized grafting density, σ′, and degree of polymerization, N, of the grafted chains. (The conversion between σ and σ′ and the origin are discussed in the footnote of Table 1.) In both the screened wet brush regime (where 1/N0.5 < σ′ ≤ ∼1 and valid here (Table 1)) and stretched brush regime (σ′ > 1),31,33 theoretical studies show that miscibility or net favorable interaction ensues when σ′ < (P/N)−1/2, where P is the degree of polymerization of the matrix chains.31,33,34 Given the typical experimental σ′ to be on the order of 1, the crossover between favorable and unfavorable interaction is anticipated near P/N (≡ Mmatrix/Mgraft) ≈ 1. Good consistency has been found between this prediction and experiment.46−48 It should be mentioned that when the grafting surface is curved, miscibility is improved because the crowdedness of the grafted chains decreases with increasing distance from the surface.32,47,48 But this effect has been found to be small. In surfaces with nanometer radius of curvature, the miscibility boundary was only mildly adjusted from P/N = 1 to ∼4.44,45 Therefore, the present finding that the change in Tg changes from positive to negative values as Mmatrix/Mgraft is increased past 1 is consistent with the oft-quoted notion that the Tg of a nanocomposite should be enhanced/suppressed upon particle loading if the polymer−nanoparticle interactions are favorable/ unfavorable.15−21,28 To elucidate the effect of polymer−nanoparticle interfacial interactions, we study the change in Tg of these nanocomposites with a fixed nanoparticle content of 3 wt % but different matrix Mw, Mmatrix, from 1.1 to 212 kg/mol. The results from the Au@PS1K/PS and Au@PS53K/PS nanocomposites are shown in Figure 4a by the solid circles and solid triangles, respectively. The open circles and open triangles, respectively, represent the prediction by using eq 3 for the respective system. As seen, the change in Tg of the Au@ PS1K/PS nanocomposites is always negative; at the same time, its magnitude grows with increasing Mmatrix initially but begins to flatten within experimental uncertainty near Mmatrix ≈ 5 kg/ mol. For the Au@PS53K/PS nanocomposites, on the other hand, the change in Tg first stays relatively constant at a value of about +7 K. But near Mmatrix ≈ 5 kg/mol, it begins to decrease steadily as Mmatrix increases and crosses over to negative values

Figure 4. (a) Change in Tg of PS homopolymers upon loading with 3 wt % Au@PS1K (●) and Au@PS53K (▲) plotted versus the homopolymer Mw. (b) The same plot as in (a), except that the abscissa is normalized by the Mw of the ligand PS. The open symbols denote calculations obtained using eq 3 on homogeneous mixtures of the matrix and ligand PS.

at around Mmatrix ≈ 62 kg/mol. To gain further insight, we normalize the abscissa by the ligand Mw, Mgraft, and display the result in Figure 4b. The new plot clearly shows that the Tg of the nanocomposites is bigger (smaller) than the matrix Tg when Mmatrix/Mgraft is 1) and so reinforces the afore-stated notion about the effect of polymer−nanoparticle interfacial interactions on the Tg of polymer nanocomposites. To further confirm that this observation pertains to an interfacial effect, we repeat the measurements by using the PSgrafted silica nanoparticles, [email protected], with a similar core diameter of 6.5 nm (cf. those of the gold nanoparticles discussed above are 3.8 and 4.6 nm, Table 1). The result (shown by solid circles), together with the data reproduced from Figure 4b of the gold nanoparticle composites (shown by solid stars), is displayed in Figure 5. As one can see, the two data exhibit the same trend, albeit the data of the [email protected] nanocomposites demonstrate a weaker effect. We shall return to this point later. The gray triangles in the same plot display the change in Tg of the nanocomposites made of the Si@APTS nanoparticles, which contain no grafted polymer. Constancy of this data with Mmatrix confirms the significance of the PS-grafted interfacial layer on the variations exhibited by the other nanocomposites. As noted above (Figure 2), the morphology of the particle aggregates in the nanocomposites is the same for Mmatrix/Mgraft between 0.46 and 390, up to a length scale of at D

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the Tg reduction noted above. We notice that a multiplication factor of 4.6 is comparable to the ratio of the particle sizes used in the two experiments. Since the total particle surface area given the same wt % of the particle core varies as ∼1/d, we tentatively suggest the weaker Tg reduction Bansil et al. observed to the lower polymer−nanoparticle interfacial area present in their nanocomposites. All of the results reported so far are obtained from thin films with thickness 1. By applying this relation and assuming the high-Mmatrix value of γeff at σ′ = 0.84 to be 0.2 mJ/m2, we estimate 0.3 mJ/m2 for the corresponding value at σ′ = 2.5. Then we use the ratio between these two values to extrapolate the curve of γeff at σ′ = 2.5 and display it by ∗. This curve and that obtained for σ′ = 0.5 (denoted by ×) demonstrate excellent agreement with the observed changes in Tg. Given the large differences between the forms of the samples and natures of the measurements, the level of agreement is remarkable. Next, we discuss the issue of particle size. Bansal et al.18 had studied the Tg of Si@PS156 K/PS nanocomposites, where the silica diameter, d, was 14 nm (i.e., ∼3 times the diameter of the silica particles used here) and σ ∼ 0.57. They observed a qualitatively similar Mmatrix dependence of the Tg change as that seen here, but the magnitude was somewhat smaller. For instance, at the same SiO2 content employed here, the Tg reduction they saw in the high-Mmatrix limit was ∼1.6 K. Extrapolating from the result of Figure 5 that ΔTg/γΔeff ≈ −2 × 104 K m2/J, the projected value of −ΔTg given the σ′ value of their nanoparticles (estimated to 5.4) is 7.4 K, i.e., ∼4.6 times

Figure 6. (a) X-ray reflectivity (XR) curve of a 3 wt % Au@PS1K/ PS5K film and the Parratt algorithm calculation assuming the fourlayer (silicon oxide−PS−PS/Au−air) δ-profile depicted in the inset. (b) The Fourier transformation of the XR curves shown in (a). The major peak seen at z = 44.7 nm is due to the full thickness of the film. The two minor peaks, highlighted by the ↓ arrows, indicate there to be two thickness regions in the film with different scattering densities. In both panels, the experimental data are represented by open circles and calculation by the solid line. E

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segregation of the nanoparticles should cause the Tg reduction to be less than or equal to that observed otherwise. We examine this corollary by measuring the Tg of the [email protected]/PS nanocomposites in bulk by DSC. We also measure the Tg of the respective matrix polymer in bulk by DSC and determine the change in Tg by taking the difference between these measurements. The result, plotted as change in Tg vs Mmatrix/ Mgraft, is shown in Figure 7 (open circles). The data of the films

antiplasticizer on the matrix polymer. However, this possibility has been refuted by Oh et al.,21 who demonstrated that the dielectric relaxation spectra of the Au@PS53K/PS5K and Au@ PS1K/PS5K nanocomposites did not show any discernible change in fragility with nanoparticle loading. In another experiment, Bansal et al.17 found a quantitative equivalence between the Tg of polymer films and polymer nanocomposites, where the interparticle spacing, h, played the role of film thickness. In the present study, the average interparticle spacing is between 80 and 150 nm. But the onset of thickness dependence of the Tg in thin films is typically between 50 and 100 nm,52,53 implying that quantitative equivalence in Tg is unlikely to apply in our nanocomposites. By modeling the onset of glass transition by the percolation of slow, immobile domains through the system, Kropka et al.54 found that quantitative equivalence might be valid only when the interparticle spacing was much smaller than the particle radius, which is clearly not fulfilled here. Nonetheless, given the strong correlation seen between ΔTg and γeff in our data, and the observation of quantitative equivalence between the Tg of polymer films and nanocomposites at high nanoparticle loadings,17 we believe that the same physical process governs the changes in Tg of polymer films and nanocomposites alike. Based on the present result, γeff should be an important parameter.

Figure 7. Comparison between the change in Tg found in thin films (●) and bulk samples (○) upon doping of 3 wt % [email protected] nanoparticles in PS homopolymers with various Mw. The data are plotted versus the ratio of the matrix Mw to that of the ligands, i.e., 2.4 kg/mol.

IV. CONCLUSION We have studied the change in Tg of polymer nanocomposite films containing PS-grafted nanoparticles blended with PS homopolymers with different molecular weights, Mmatrix, at low nanoparticle loadings. We found that the change in Tg was negative in cases where the grafted chains were shorter than the matrix chains or the polymer−nanoparticle interfacial energy, γeff, was positive, but the reverse was observed in the opposite cases. Importantly, for the former cases, where γeff was accessible by contact angle measurements, our result revealed a quantitative relation between the change in Tg and γeff, namely ΔTg/γΔeff ≈ −2 × 104 K m2/J. While X-ray reflectivity indicated there to be migration of the nanoparticles to the free surface, comparison with measurements of bulk specimens showed that the Tg reduction of the films followed the same Mmatrix dependence as the bulk, with the discrepancy accountable by a depletion of the nanoparticles from the main body of the films. Taken together, our result shows that the correlation seen between the changes in Tg and polymer− nanoparticle interfacial energy is intrinsic to the nanocomposites studied.

from Figure 5 are reproduced in the same plot (solid circles) for comparison. It is apparent that the two exhibit the same dependence on Mmatrix/Mgraft, although the magnitude of the Tg reduction exhibited by the bulk specimens is consistently bigger, in line with the above expectation supposing segregation of the nanoparticles from the main body of the films. A number of factors affect the mixing between the nanoparticles and matrix. A major factor comes from the interfacial energy, γeff, which, if positive, suppresses mixing, and this effect aggravates with increasing Mmatrix/Mgraft that is > ∼1. The fact that the difference between the data of the films and bulk specimens stays constant with Mmatrix/Mgraft for Mmatrix/Mgraft > 3 implies that the degree of segregation is not altered significantly or not enough to cause the Tg reduction to change in this range. Another factor affecting mixing is the total particle radius (core + ligands). When it is smaller than the unperturbed radius of gyration of the matrix polymer, the entropy of mixing promotes compatibility between the nanoparticles and matrix.49,50 In our system, this is expected to occur for Mmatrix/Mgraft > ∼20. The fact that the data of the films and bulk samples approach each other at Mmatrix/Mgraft ≈ 0.6 (which is nearer the Mmatrix/Mgraft = 1 threshold) and no qualitative change is seen in the thin film data near the Mmatrix/Mgraft = 20 threshold implies dominance of the interfacial effect on the segregation phenomenon seen here. Based on the foregoing discussions, the correlation seen in Figure 5 between the changes in Tg of the gold and silica nanocomposites and polymer−nanoparticle interfacial energy is intrinsic to the nanocomposites. The relation observed between the two, namely ΔTg/γΔeff ≈ −2 × 104 K m2/J, agrees within a factor of 2.4 to that found in an earlier experiment51 measuring the Tg of PS thin films supported by a grafted layer of random polystyrene−poly(methyl methacrylate) copolymer P(S-rMMA) brush. When the diameter of the nanoparticles is smaller than or equal to the radius of gyration of the matrix polymer, the nanoparticles as a whole may act as a plasticizer or

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (O.K.C.T.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Mr. Dongdong Peng and Mani Kuntal Sen for experimental assistance. O.K.C.T. is grateful to the support of the National Science Foundation through the projects DMR0908651 and DMR-1004648. T.K. acknowledges the financial support from NSF Grant CMMI-084626. Use of the National Synchrotron Light Source was supported by the U.S. DOE under Contract DE-AC02-98CH10886. F

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dx.doi.org/10.1021/ma4000368 | Macromolecules XXXX, XXX, XXX−XXX