Unraveling the Mechanism of Nanoscale Mechanical Reinforcement

May 20, 2016 - The mechanical reinforcement of polymer nanocomposites (PNCs) above the glass transition temperature, Tg, has been extensively studied...
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Letter pubs.acs.org/NanoLett

Unraveling the Mechanism of Nanoscale Mechanical Reinforcement in Glassy Polymer Nanocomposites Shiwang Cheng,*,† Vera Bocharova,*,† Alex Belianinov,‡,§ Shaomin Xiong,⊥ Alexander Kisliuk,† Suhas Somnath,‡,§ Adam P. Holt,¶ Olga S. Ovchinnikova,‡,§ Stephen Jesse,‡,§ Halie Martin,∥ Thusitha Etampawala,∥ Mark Dadmun,∥ and Alexei P. Sokolov†,¶,∥ †

Chemical Sciences Division, ‡The Institute for Functional Imaging of Materials, and §Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ⊥ Department of Mechanical Engineering, University of California Berkeley, Berkeley, California 94720, United States ¶ Department of Physics and Astronomy and ∥Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States S Supporting Information *

ABSTRACT: The mechanical reinforcement of polymer nanocomposites (PNCs) above the glass transition temperature, Tg, has been extensively studied. However, not much is known about the origin of this effect below Tg. In this Letter, we unravel the mechanism of PNC reinforcement within the glassy state by directly probing nanoscale mechanical properties with atomic force microscopy and macroscopic properties with Brillouin light scattering. Our results unambiguously show that the “glassy” Young’s modulus in the interfacial polymer layer of PNCs is two-times higher than in the bulk polymer, which results in significant reinforcement below Tg. We ascribe this phenomenon to a high stretching of the chains within the interfacial layer. Since the interfacial chain packing is essentially temperature independent, these findings provide a new insight into the mechanical reinforcement of PNCs also above Tg. KEYWORDS: Polymer nanocomposites, mechanical reinforcement, interfacial layer, band excited atomic force microscopy, Brillouin light scattering

P

achieve optimal mechanical performance. Therefore, there is an obvious discrepancy between the currently proposed mechanisms of reinforcement for rubbery PNCs and their applicability to glassy counterparts. The modification of mechanical properties in the so-called interfacial layer between the polymer matrix and the nanoparticles has been proposed to explain the mechanical reinforcement of PNCs in both the glassy and rubbery or melt states.10,21,22 For rubbery PNCs, the interfacial layer has been assumed to have a modulus 102−103-times higher than the neat polymer,12,23 that is, can have a glassy modulus, whose thickness is typically estimated to be identical to a length scale where a significant suppression of segmental dynamics in the interface (i.e., a “glassy” or “dead” layer) is found.12,15−17 Although the assumption that the interfacial layer has a significantly higher modulus than the neat polymer has been proven by scanning probe microscopy (SPM),2,24,25 there is still no validation that the thickness of this layer with enhanced

olymer nanocomposites (PNCs) have become one of the most important functional materials for various modern technologies due to their wide tunable properties and significant mechanical reinforcement.1−5 Despite decades of intensive study, the microscopic origin of the enhancement in PNCs’ mechanical properties, in both the rubbery or melt state and the vitrified or glassy state, remains actively debated.6−17 For rubbery PNCs, which exhibit desirable viscoelastic properties above the glass transition temperature, Tg, several mechanisms, such as particle jamming, strain field distortion around the nanoparticle (NP),14 NP induced dynamic change of the polymer matrix,15,16 and the formation of bridges between NPs,16,17 have been proposed to explain the increase in the mechanical moduli. Furthermore, glassy PNCs with prominent applications,18,19 used as acrylic windows, gaspermeable membranes, and ion conductors, have not been studied as intensively as the rubbery PNCs, and the origin of their mechanical reinforcement remains an open question. Macroscopically, the optimal mechanical performance for rubbery PNCs occurs when particles form a continuous network through either jamming or aggregation,20 while in glassy PNCs, the NPs must be well dispersed in the matrix20 to © 2016 American Chemical Society

Received: February 22, 2016 Revised: May 11, 2016 Published: May 20, 2016 3630

DOI: 10.1021/acs.nanolett.6b00766 Nano Lett. 2016, 16, 3630−3637

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Nano Letters Table 1. Characterizations of PVAc/SiO2 Nanocomposites samples

SiO2 (vol %)

core radius (nm)

shell thickness (nm)

SLD (shell) (10−5 Å−2)

SLD (matrix) (10−5 Å−2)

neat PVAc PVAc-6% PVAc-11.8% PVAc-20.5% PVAc-23% PVAc-31.9% silicaa

0 6.11 11.8 20.5 23.0 31.9 100

8.98 9.07 9.10 8.91 8.90

2.10 2.14 2.32 2.43 2.30

0.652 0.739 0.890 0.913 0.913

1.295 1.391 1.395 1.400 1.430

density (g/cm3)

dIPS (nm)

Tg (oC)

± ± ± ± ± ± ±

29.60 18.85 11.47 10.11 6.48

40.6 41.4 41.6 41.7 41.6 41.8

1.2058 1.2702 1.3384 1.4379 1.4573 1.5315 2.4057

0.0018 0.0018 0.0020 0.0024 0.0012 0.0015 0.0019

a Note: The density of silica nanoparticles varies from 2.00−2.65 g/cm3 depending on the synthesis.30 The mass density of commerical Nissan Chemical nanoparticle (MEK-AC-4101) is found to be 2.1606 ± 0.0013 g/cm3 from pycnometry, which is lower than the density of our homemade silica nanoparticles (for details, see Supporting Information).

Figure 1. (a) SAXS data (symbols) for nanocomposites with the volume fractions of 6%, 11.8%, 20.5%, 23%, and 31.9% (from top to bottom) at T = 293.15 K. The solid black lines are the fits to a polydispersed core−shell model with parameters shown in Table 1. The y-axis is arbitrarily shifted for ρ −ρ φ PNC clarity. Inset shows the TEM images of PVAc-23%. (b) Normalized matrix density, ρmatrix = PNC1 − φNP NP , of the PNCs with various loadings where ̅ NP

ρneat PVAc, ρPNC, and ρNP are the densities of neat polymer, PNCs, and NPs, respectively. Here, we assume the mass conservation before and after mixing and the density of silica nanoparticles remains unchanged. The horizontal line presents ρneat PVAc. The inset shows the total mass density of the PNCs from the pycnometry (symbols); the black solid line is a prediction from a simple mixing rules by assuming the volume conservation during the mixing: ρPNC = ρNPφNP + ρneat PVAc(1 − φNP).

layer of ∼2−3 nm from BE AFM, consistent with SAXS measurements and previous dielectric spectroscopy measurements.29 The value for Young’s modulus derived from force− distance measurements of this layer is ∼2.3-times higher than that of the neat polymer, in good agreement with BLS measurements. Detailed analysis suggests that the chain stretching in the interfacial layer provides the observed significant increase in the modulus. Figure 1, panel a shows the SAXS curves of five PNCs with different NP volume fractions and their fit to a polydispersed core−shell model (for details, see Supporting Information). The description of the samples and fit parameters are presented in Table 1, where the core, shell, and matrix represent the NP, the interfacial layer, and the bulk polymer, respectively. The scattering length density (SLD) of the core is fixed to 2.1123 × 10−5 Å−2, corresponding to a mass density of 2.4057 g/cm3 of silica nanoparticles measured directly by pycnometry. We note that density of our nanoparticles is higher than density of silica nanoparticles from Nissan Chemical, apparently due to different synthetic routes (for details, see Supporting Information).30 The analysis estimates the shell thickness, ls, to be (2.3 ± 0.2) nm, which is slightly smaller than the results from previous dielectric spectroscopy measurements.29 For all PNCs, the dIPS is larger than 2ls (Table 1), indicating the condition of optimal mechanical performance20 with nonoverlapping interfacial layers. The excellent dispersion of the NPs in polymer matrix is confirmed by the low scattering intensity in the low q range (q < 0.02 Å−1)31,32 of the SAXS

mechanical properties is comparable to the thickness of the interfacial layer with distinguishing dynamics.12,17 For glassy PNCs, the analysis of the interfacial layer presents additional challenge because both the interfacial layer and bulk polymer are vitrified, and their dynamics are experimentally inaccessible. Moreover, because of the limited contrast between the glassy mechanical moduli of the bulk polymer and the interfacial layer, current SPM measurements are usually not conclusive.26,27 Thus, a useful method of characterizing the mechanical properties of the interfacial layer in glassy PNCs is highly desirable, and direct probing the interfacial layer below Tg remains an important and challenging experimental task. In this Letter, by combining small-angle X-ray scattering (SAXS), Brillouin light scattering (BLS), and a novel band excited (BE) atomic force microscopy (AFM), we provide direct experimental evidences of the interfacial layer modulus gradient in model PNCs, poly(vinyl acetate)/silica (PVAc/ SiO2), below their Tg, and address its role in the overall mechanical properties. Details of the sample preparations and the measurements are presented in the Supporting Information. Relevant sample characterizations are summarized in Table 1, where the radius of NP is RNP = 12.5 nm, and the average interparticle surface-to-surface distance, dIPS, is calculated by assuming a random NP distribution:28 ⎛ 16 1/3 ⎞ dIPS = RNP⎜ πφ − 2⎟ with φNP the volume fraction of NP ⎝ ⎠ nanoparticles. All the measurements were carried out at least 20 °C below Tg of the PNC. We directly visualize an interfacial

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Figure 2. (a) A sketch of the right angle symmetric geometry used in BLS. Here, the incident beam (along the direction of the red line) has a 90° angle with the direction to the detector (along the direction of the blue line). ki⃗ and ks⃗ are the wave vectors of the incident light and the scattered light; q⃗ is the scattering vector. (b) Representative depolarized (VH polarized) BLS spectra (symbols) of neat PVAc and PVAc-23% at T = 213.15 K. The orange (black, inset) solid lines are the fits to the damped harmonic oscillator model that estimates the characteristic frequency of the longitudinal (transverse, inset) phonons. (c) Shear modulus, G, and bulk modulus (inset), K, for PNCs with different loadings estimated from the BLS data. The lines are fits to continuum mechanics based on Woods’ law, a two-phase model (TPM), an interfacial layer model (ILM), and the dashed-orange lines are predictions by a simulation of finite element analysis (FEA) with an interfacial layer.

this geometry, the material’s refractive index, n, is canceled out.37 Depolarized (VH polarized) light scattering spectra were measured at T = 213.15 K using tandem Fabry-Pérot interferometer (JRS instrument) with the distance between mirrors of 7 mm and laser wavelength λlaser = 532 nm. Figure 2, panel b shows representative spectra of the neat PVAc and the PVAc-23% with well resolved longitudinal (LM) and transverse modes (TM, inset). The spectra are fit to the damped harmonic oscillator function to estimate the characteristic frequencies (νT,L) of the acoustic sound waves, and sound velocities

data (Figure 1a) and the ability to resolve individual particles on the transmission electron microscopy (TEM) image (inset in Figure 1a). From the SAXS fits, the SLD of the shell (the interfacial layer) is found to be significantly smaller than that of the bulk matrix, independent of the NP loadings. This suggests a presence of a low density interface in PNCs. Such low density is further confirmed by direct mass density measurements as shown in both the relative mass density of the matrix (Figure 1b) and the overall PNC density in comparison to the prediction of a simple two phase mixing rule (inset Figure 1b). Notably, these results of a reduced matrix density in PNCs are consistent with previous PALS measurements33 and specific volume data34 reported by different groups. In a recent publication,29 we studied the role of molecular weight in composites with a fixed loading of nanoparticles. We found the interfacial layer thickness, the average slowing down of segmental relaxation in the interfacial layer, and the mass density of polymer matrix decrease with increasing molecular weight. At high molecular weight, especially when dIPS < 2Rg (Rg is the polymer radius of gyration), the average mass density of the matrix appears to be lower than the density of the neat polymer. On the basis of these experimental observations, we suggested that the reduction in mass density of the high molecular weight PNCs is caused by the screening effect of the absorbed loops, which frustrates chain packing in the interfacial layer.29 To study the mechanical properties of PNCs in glassy state, we apply BLS, a noninvasive technique with a pure linear response.35,36 We apply right angle scattering with the samples placed in symmetric scattering geometry (Figure 2a). Under

following VT,L =

2πνT,L q

, where q =

2π 2 λlaser

is the scattering vector

for the right angle symmetric geometry (Figure 2a). The longitudinal modulus, M, and shear modulus, G, can be obtained through M = ρVL2 and G = ρVT2,38 where ρ is the mass density of the PNCs. A significant blue shift is found for both the TM and LM of PNCs (Figure 2b), indicating a more rigid medium with a higher modulus. The BLS data demonstrate a significant increase in both 4 shear modulus, G, and bulk modulus, K = M − 3 G, with the increase in NPs loading (Figure 2c). Although such trend can be anticipated from the hydrodynamic effect of the hard nanoparticles, more detailed analyses are required to extract any possible changes to the mechanical properties of polymer matrix. Several models, including Wood’s law,36 a two-phase model (TPM),39−41 and an interfacial layer model (ILM)42,43 (details of these models can be found in the Supporting Information), have been developed to account for the hydrodynamic effect of the NPs on the moduli. As shown in Figure 2, panel c, both Wood’s law and the TPM model predict significantly lower modulus than experiments, indicating the 3632

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Figure 3. AFM images of the PNC with 23 vol % silica. (a) Contact AFM topography image of the surface of the composite; (b) resonance frequency shift (Δf) map of the surface; (c) Q-factor (the bandwidth of the resonance peak) of the cantilever map of the surface. (d) The spatial Δf and Q profile for a single nanoparticle framed by the black boxes in panels b and c. The gradient profile presented as a function of the distance, r, from the center of the nanoparticle along the directions 1 and 2 indicated by the black arrows in panels b and c. The inset shows schematic positioning of the nanoparticle in the polymer matrix and demonstrates three regions associated with different changes in Δf and Q.

cant increase in the interfacial elastic constant in both TM and LM modes has been reported.46 To directly probe the mechanical properties of the interfacial layer, we turn to BE AFM for contact resonance measurements in conjunction with force−distance mapping on a grid for a quantitative assessment of Young’s modulus on the nanoscale.47 This novel technique allows direct measurements of the frequency shift and energy dissipation with sensitivity close to the thermo-mechanical limit.47−50 More details of the BE AFM technique can be found elsewhere47 and in the Supporting Information. In this study, the shift in the contact resonance frequency and the Q-factor (the resonance peak width) is used to spatially characterize the changes in mechanical properties of the glassy PNC.51 The results of AFM topography mapping and BE measurements for PVAc-23% with dIPS ≈ 10 nm are presented in Figure 3, panels a−c. Three regions can be visualized from the BE AFM measurements. In Figure 3, panel b, the red/yellow islands with a contact resonance shift on average of about −10 kHz correspond to an increase in material stiffness where the energy dissipation is also minimized, as corroborated by the change in Q-factor map (Q < 40) (Figure 3c). Compared with the topography image (Figure 3a), the stiff regions coincide with the elevated topographical features associated with silica nanoparticles, which are roughly 25 nm in size. In the text below, we will refer to this region as Region I. We note that the resonance frequency shift (Δf) and Q-factor (Q) within Region I are not constant. For instance, Δf changes from −20 to 0 kHz. We expect that nanoparticles are partially immersed in polymer matrix and hence covered by a layer of

presence of an additional mechanical enhancement other than the hydrodynamic effect from the NPs. We associate this enhancement with the formation of the interfacial layer, which has different mechanical properties than the neat polymer matrix.8 The interfacial layer is typically described as a layer with distinct properties, such as a reduced segmental mobility17,44 or a modified mass density,29 with thickness about 3−5 nm.44,45 Following our earlier study on the same samples,29 we set the interfacial layer thickness to be 3 nm, which is confirmed by the AFM measurements below. By using this interfacial layer thickness, the ILM model shows excellent agreement with the experiments (Figure 2c), including both G and K, for all five loadings that were studied. Moreover, a simulation of finite element analysis (FEA) (dashed-orange, for details, see Supporting Information) based on the same geometry as the ILM also produces good agreement with experimental observations. Both methods yield a shear modulus in the interfacial layer of Gint = 4.79 GPa and a bulk modulus of Kint = 7.86 GPa. Note that these values are significantly higher than Gneat = 1.89 GPa and Kneat = 5.76 GPa of neat PVAc. The Young’s modulus values of the interfacial layer and the neat polymer are estimated as Eint = 11.9 GPa and Eneat = 5.1 GPa, 3K − 2G using E = 2G(1 + σ), where σ = 2(3K + G) is the Poisson’s ratio. Thus, the Young’s modulus is about 2.3-times higher in the interfacial layer than in the bulk. We want to emphasize that our findings are in a good agreement with the recent BLS experiments of polymer-grafted-nanoparticles, where a signifi3633

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Figure 4. Surface topography and mechanical properties of PVAc-6%. (a) AFM image of the topography acquired in tapping mode; black box indicates the area over which the force−distance curves were collected. (b) Oliver-Pharr model calculation of Young’s modulus extracted from the force−distance curves (Figure S2 in Supporting Information). Position of nanoparticles contoured by lines. (c) Force of adhesion map extracted from the force−distance data for the same region indicated by the black box in panel a, showing a much higher adhesion force between the AFM probe and polymer than the probe and silica nanoparticles.

higher hardness, shown in yellow around the particles in Figure 4, panel b. The adhesion map in Figure 4, panel c independently confirms the unusual material properties in the interfacial region. The calculated Young’s modulus for the interfacial areas is ∼12−14 GPa, and that of the neat polymer is ∼5−7 GPa. Although the absolute values of the Young’s modulus from AFM measurements depend on the consistency of the tip area throughout the measurement, the relative change of the Young’s modulus between the interfacial layer and the pure polymer is reliably reproducible for different nanoparticles in the same sample. Therefore, from AFM measurements, the interfacial layer has a modulus that is ∼2.0−2.8-times higher than that of the neat polymer, which is in good agreement with the ∼2.3-times increase in modulus found from the BLS analysis. Our observations, corroborated by three independent experimental techniques, illustrate the existence of an interfacial layer with the thickness of ∼2−3 nm. Interestingly, the thickness of the interfacial layer as measured by AFM is indeed comparable to that obtained from the dynamic measurements like the dielectric spectroscopy measurements.29 To the best of our knowledge, these results provide the first direct justification to support the prevailing assumption that the thickness of the interfacial layer with enhanced mechanical properties is comparable to the interfacial layer thickness obtained from the dynamic measurements.12,16,17,53 Notably, the spatial distribution of the mechanical properties from BE AFM exhibits many interesting features at relatively high NP loadings. For instance, the white arrows in Figure 3, panels b and c indicate the presence of domains that bridge neighboring NPs. Since these domains show up at a place where the interparticle surface-to-surface distance is twice larger than the thickness of the interfacial layer, they can be treated as a direct evidence of polymer bridges in PNCs. More importantly, these bridges have a slightly higher stiffness as evidenced by a smaller shift in frequency (Δf ≈ 5−10 kHz) (Figure 3b) and a low change in Q-factor (Q ≈ 40−60) (Figure 3c) relative to Δf > 20 and Q > 140 for the neat polymer, and they typically show up in a plane that crosses the centers of bridged nanoparticles. These observations provide direct justification to the recent speculations15,16,54 that in the presence of the interfacial layer and bridges, the threshold of the mechanical enhancement in rubbery PNCs starts at a much lower nanoparticle loading than a loading required for the nanoparticles to jam. These peculiar structural features also provide a solid background for future investigations of the role of polymer bridging in the overall mechanical properties of PNCs. Moreover, we want to emphasize that although our model analysis on BLS data does not take into account the

polymer. The differences in the immersion depth of nanoparticle can cause significant variance in the mechanical properties measured in Region I. In the second region (Region II), areas with relatively low resonance frequency shift (cyan in Figure 3b) are found to surround the Region I as the material transitions from the hard silica nanosphere to the much softer surrounding polymer matrix (Region III). The width of this transition region is estimated to be ∼3 nm, which is in line with the interfacial layer thickness obtained from dynamic measurements.29 Figure 3, panel d presents an example of the relative changes in the Δf and Q-factor for all three regions discussed above. The profile is taken for a single nanoparticle along directions 1 and 2 as indicated by the arrows in the black boxes in Figure 3, panels b and c. From the graph, the saturation of Δf and Q to the values characteristic for polymer matrix clearly extends to a distance noticeably larger than the size of the NP, implying a real mechanical enhancement in the interfacial layer. For convenience, we also present a sketch where we correlate position of the nanoparticle with the location of three aforementioned regions (inset of Figure 3d). To summarize, the BE AFM results demonstrate the existence of an interfacial layer with clear and distinct mechanical properties in glassy PNCs. To the best of our knowledge, this is the first real space visualization of the interfacial layer in glassy PNCs. The distinct contrast in resonance frequency shift, as well as the Q-factor variance, between different regions found in the PNC suggests that the interfacial layer has significantly higher modulus than the neat polymer. To quantify the mechanical properties of the interfacial layer, the Oliver-Pharr model52 was employed to analyze the force− distance curves that were collected on a 30 × 60 grid over a portion of an image, as shown by a black box in Figure 4, panel a. To accurately calculate the Young’s modulus, we extracted the actual area of the AFM tip by imaging a calibration grid. The cantilever stiffness was calibrated prior to the force distance measurements. The details of the calibration procedures are presented in the Supporting Information. To detect the influence of a single NP on the polymer matrix and avoid any interference between multiple NPs, a low loading of ∼6 vol % was used, where the NPs are well separated and isolated as shown in Figure 4. Figure 4, panel a shows the topography of the 150 × 150 nm2 area where a 30 × 60 grid of force distance curves was measured. Figure 4, panel b is the Young’s modulus map calculated from the force−distance curves (see Supporting Information) in the regions marked by a black box in Figure 4, panel a. As confirmed by the BE AFM measurements, the interface area is quite small, on the order of a few nanometers. Nonetheless, we were able to resolve these areas of noticeably 3634

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and the square of the Kuhn length. In a stretched chain with elongation ratio, μ, the effective Kuhn length can be viewed as increasing μ times. Assuming ls = 3 nm, the mass density reduction in the interfacial layer is ∼20% for PVAc-31.9% according to the data in Figure 1, panel b and Table 1. Thus, a total increase of the intramolecular part of the Young’s modulus of 1.802 × (1 − 0.2) ≈ 2.6-times is expected, which is slightly higher than the overall 2.3-times that is found from the AFM measurements and determined from the BLS measurements.

bridging effect, the clear visualization of an interfacial shell with a finite-thickness in the BE AFM image at ∼23 vol % validates the use of the ILM model analysis for the studies of PNC with high nanoparticle loadings. Surprisingly, the SAXS and pycnometry data demonstrate a reduction in the mass density in the interfacial layer, while BLS and AFM measurements show remarkable enhancement in the glassy modulus of the same interfacial layer. Since the glassy modulus is largely determined by the intersegmental interactions, such as van-der Waals interactions or intermolecular jamming, it is expected that higher mechanical modulus is only possible in the layer with a higher density. Contrary to this, our experiments demonstrate that a lower density interfacial layer also has a higher glassy modulus. The same phenomenon has also been observed in studies of well-dispersed poly(2vinylpyridine)/SiO2 nanocomposites (see Supporting Information), suggesting the universality of this effect in PNCs with attractive polymer−NP interactions. To understand this phenomenon, we turn to a more detailed analysis of the chain packing at the interface. Earlier theoretical work55−60 and recent experiments46 show that polymers physically adsorbed onto a solid surface can acquire a stretched conformation (pseudobrush) similar to that of a polymer brush covalently attached to a surface. In a pseudobrush, it is known that the height of the adsorbed chain is proportional to N0.83 (N is the number of segments) instead of N0.5 in the unperturbed melt state.61 Recent studies also show that the Young’s modulus can be significantly enhanced along the chain stretching direction.62,63 The degree of chain stretching, μ, near the surface of NPs can be calculated from the ratio of the average height of the pseudobrush, la, and the size of an unperturbed free chain, lb, with the same number of segments, nb, as the pseudobrush: μ = la/lb = la/(lk√nb), where lb = lk√nb, and lk is the Kuhn length of the polymer. According to the Scheutjens-Fleer’s theory (SFT), both la and nb can be calculated under the thermodynamic equilibrium limit (for details, see Supporting Information). For PVAc with a molecular weight of 40 kg/mol and lk = 1.7 nm, the calculation yields la = 8.96 nm and nb = 8.58, which give a strong stretching factor of μ = 1.80 in the adsorbed chains. Thus, it is highly possible that the stretched interfacial chains are the cause of the observed enhancement in mechanical modulus. It is nontrivial to quantitatively link the interfacial chain stretching with the enhanced glassy modulus, but some qualitative analysis may be possible. Below, we introduce one of these possibilities. The intramolecular part of the Young’s modulus due to the mode with wavelength, lw, can be written as Eintra ≈ kBTc(lk/lw)3,61 where kB is Boltzmann constant, T is the ρN l absolute temperature, and c ≈ M Al is the number density of

Since K = −V

modulus K on density can be anticipated. This also qualitatively explains the much lower increase in the bulk modulus (∼1.36times) in the same region. A similar argument can be applied to explain the mechanical enhancement in similarly studied P2VP/ SiO2 PNCs as shown in the Supporting Information. Thus, we believe the above analysis of chain stretching captures, to a leading order, the origin of the interfacial mechanical enhancement, which is also in line with recent theoretical consideration on the effect of chain stretching to the enhancement in glassy modulus64 and consistent with recent observations on “hairy” nanoparticles.46 In conclusion, through a combination of SAXS, BLS, and AFM measurements, we provide the first direct visualization of the interfacial layer and present experimental evidence of polymer bridges between NPs in glassy PNCs. An interfacial layer of around ∼2−3 nm with significantly higher glassy modulus and a lower mass density is found in our measurements. We conclude that the strong chain stretching in the interfacial layer leads to a significant increase in the interfacial layer modulus, despite the less dense segmental packing. In a recent computer simulation,56 it was demonstrated that the strength of the attractive polymer−nanoparticle interactions does not affect the interfacial layer thickness, while it influences the slowing down of segmental dynamics. Therefore, the presented here results should be applicable to various types of glassy polymer nanocomposites. Moreover, since the interfacial chain packing will not change upon increasing temperatures and the stretched chains have intrinsically higher elastic spring constant also in the melt state,65−68 our findings could also provide insights into understanding the molecular mechanisms of reinforcement in rubbery PNCs.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b00766. Detailed procedures for sample preparations and characterizations; description of the polydispersed core−shell model; representative force−distance curves for nanoparticles, interfacial layer, and polymer matrix; detailed descriptions of mechanical models used in the paper; details of finite element analysis; supportive BLS and density data of poly(2-vinylpyridine)/silica nanocomposites; calculations by Scheutjens-Fleer’s theory; additional references (PDF)

0k

ρNAl M 0lk

×

lk 3 l

()

ASSOCIATED CONTENT

S Supporting Information *

Kuhn segments with M0 to be the reduced molar mass per bond, NA the Avogadro number, l the length of one bond, and ρ the mass density. For lw ≈ l, the Young’s modulus: E intra ≈ kBT ×

( ∂∂VP )T , a much stronger dependence of the bulk

≈ ρlk 2 . This relation can be

justified by estimating the Young’s modulus of the neat PVAc and neat P2VP (see Supporting Information). For neat PVAc at T = 213.15 K and neat P2VP at T = 291.15 K, this relation P2VP yields to EPVAc intra ≈ 5.4 GPa and Eintra ≈ 5.8 GPa, which are on the same order of magnitude of the values measured by BLS, EPVAc ≈ 5.1 GPa at T = 213.15 K and EP2VP ≈ 5.0 GPa at T = 291.15 K. Therefore, the intramolecular part of the Young’s modulus of a polymer glass is proportional to the mass density

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. 3635

DOI: 10.1021/acs.nanolett.6b00766 Nano Lett. 2016, 16, 3630−3637

Letter

Nano Letters Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Ken Schweizer for many helpful discussions and suggestions, and Dr. John Dunlap for the help with the TEM measurements. We thank Prof. Zawodzinski for permission to use the gas pycnometer. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. A.B., S.S., S.J., and O.S.O. thank the support from the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.

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DOI: 10.1021/acs.nanolett.6b00766 Nano Lett. 2016, 16, 3630−3637