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Jul 14, 2016 - Multiscale Dynamics of Polymers in Particle-Rich Nanocomposites. Rahul Mangal, Yu Ho Wen, Snehashis Choudhury, and Lynden A. Archer*...
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Multiscale Dynamics of Polymers in Particle-Rich Nanocomposites Rahul Mangal, Yu Ho Wen, Snehashis Choudhury, and Lynden A. Archer* Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: We report on the dynamics of entangled polymers in polymer−nanoparticle composites (PNCs) with moderate and high particle loadings. Using composites comprised of poly(ethylene glycol) (PEG)-tethered silica (SiO 2 ) nanoparticles and poly(methyl methacrylate) (PMMA), we show by means of small-angle X-ray scattering (SAXS) analysis that the nanoparticles are uniformly dispersed over a range of particle concentrations. From oscillatory shear rheology measurements, we find that the time−temperature superposition (TTS) principle holds for these SiO2-PEG/ PMMA PNCs up to a particle concentration ϕG ≈ 11% where the materials begin to exhibit soft glassy rheological properties. At particle concentrations below ϕG, we take advantage of TTS to create dynamic maps for PNCs that span time scales ranging from fast segmental motions to slow terminal relaxation of polymer chains. These maps reveal that at low ϕ and depending on the host polymer (PMMA) molecular weight (Mw), hairy nanoparticles may either speed up or slow down terminal relaxation of the host. In contrast, at high ϕ, nanoparticles slow down polymer dynamics on intermediate and long time scales, irrespective of the host polymer Mw. The slowdown coincides with particle concentrations at which the mean interparticle spacing lies below the equilibrium tube diameter of the entangled PMMA host and is thought to reflect the onset of confinement dynamics of polymer chains in PNCs. Studies of PNCs in the conf inement regime reveal important analogies between glassy attributes of 3D-confined polymer chains in nanocomposites with those of polymer thin films supported on attractive substrates.

1. INTRODUCTION Homogeneous blends of inorganic nanoparticles and organic polymers provide pathways for engineering nanoparticle− polymer composite (nanocomposite) materials with explicit, desired properties, including enhanced mechanical strength,1,2 thermal stability,2,3 gas barrier properties,4,5 dimensional stability,1 wear resistance,6 and selective ion transport behaviors.7 From a fundamental point of view, model nanocomposites comprised of polymer-tethered nanoparticles with well-defined particle size, grafted polymer chemistry, molecular weight, and grafting density, uniformly dispersed in polymer matrices of well-defined molecular weight provide as important opportunities for understanding how the constituents in nanomaterials influence overall material relaxation and rheology. By analogy to miscible star/linear polymer blend systems,8,9 one might expect that a general understanding of such materials will require isolation and investigation of the hierarchy of dynamics that govern relaxation of the free and tethered polymer components and their associated nanoparticle cores. We also expect such materials to emerge as crucial for identifying the molecular origins of the hierarchy of transport anomalies recently reported in soft materials. Recent theoretical10 and experimental works11−13 are instructive about how enthalpic and entropic interactions between particle-tethered and free polymer molecules may be used to uniformly distribute nanoparticles in polymer matrices. © XXXX American Chemical Society

At the same time, theories for motions of nanosized tracer particles in polymer matrices have started to emerge.14−16 Here, we take advantage of both developments to create model nanocomposite materials in which nanoparticles are well dispersed in polymers at low and high loadings to study the hierarchical dynamics of nanocomposites at elevated particle concentrationsa regime where essentially nothing is known. This regime is important for a variety of reasons, including access to novel material properties, as dynamics of polymers between particle surfaces dominate material flow properties and physical contacts between particles provide transport mechanisms for momentum, ions, and charges not possible in dilute nanoparticle−polymer composites. All battery electrodes,17−19 including emerging semisolid electrodes20,21 are, for example, designed to be in this regime to simultaneously maximize active material content in the electrode and to ensure access to electrons generated by electrochemical processes in the electrode. Polymer and particle dynamics in such materials is expected to become even richer if the dimensions of particle and polymer mesh are comparable, wherein long-range particle and polymer motions are simultaneously hindered by particle cages and by entangled polymer networks. Received: March 8, 2016 Revised: July 4, 2016

A

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range of rates studied (see Figure 3). An overshoot, although slight, in the heat flow curves was observed at low particle loadings in which case Tg is generally not the same as the fictive temperature (Tf) obtained from the inflection point. Hence, the Moynihan integral method (Figure 4) was also used for these composites to obtain a more accurate estimate of Tg.

In this study we create model nanocomposites by covalently tethering poly(ethylene glycol) (PEG) chains to silica (SiO2) nanoparticles of well-defined size and dispersing the hairy particles in poly(methyl methacrylate) (PMMA). As the tethered PEG chains interact favorably with the PMMA host chains due to a negative Flory−Huggins interaction parameter, this design allows for better nanoparticle (NP) dispersion even in highly entangled hosts.12 We take advantage of materials created in this manner to prepare a series of SiO2-PEG/PMMA nanocomposites with silica core particle volume fractions ϕ ranging from 0 to an upper limit ϕ = ϕmax, where the particles form self-suspended suspensions (i.e., ϕPMMA = 0). The glass transition temperatures of the studied PNCs are in a convenient range (Tg ∼ 60−105 °C), which makes it possible to combine dynamic shear rheological measurements and time−temperature superposition (TTS) to create master curves spanning a broad range of time scales. By means of TTS we develop dynamic maps of the materials that capture dynamics ranging from segmental-scale motions of polymer chains, to particle motions in relaxing polymer melts, and ultimately to terminal relaxation of the host polymer.

3. RESULTS AND DISCUSSION 3.1. Structural Characterization Composites Using SAXS. Figure 1 reports SAXS intensity profiles for entangled

2. EXPERIMENTAL SECTION 2.1. Material Synthesis. Silica (SiO2) nanoparticles (NPs) with average size davg = 10.84 nm and standard deviation σ ∼ 2.5% (Supporting Information Figure 1S) were densely grafted (Σ ∼ 1.5−2 chains/nm2), with linear PEG chains of Mw = 2000 g mol−1 using previously reported procedures.22 Polymer nanocomposites (PNCs) comprised of these hairy NPs in linear atactic PMMA chains of Mw ∼ 55 and 280 kDa were created using chloroform as a cosolvent. Removal of the cosolvent followed by thermal annealing in vacuum yields a library of nanoparticle fluids with varying silica core volume fractions (ϕ) from neat PMMA melt (ϕ = 0%) to a PMMA-free nanoparticle fluid (ϕ = 16%). 2.2. Small-Amplitude Oscillatory Shear (SAOS) Flow. Oscillatory shear measurements were performed at different temperatures, using a Rheometrics ARES rheometer outfitted with a 3 mm diameter parallel plate fixture. Measurements were performed in the linear viscoelastic regime at frequencies in the range ω = 1−100 s−1. The obtained frequency-dependent rheological maps were shifted horizontally and vertically, with respect to a reference temperature (here we choose it to be the Tg for PNCs with low nanoparticle content and 70 °C for PNCs with high particle content), to obtain time−temperature superposition (TTS) master curves. An advantage of this shifting procedure is that it eliminates the trivial plasticization effect caused by the increase in free volume resulting from addition of nanoparticles. 2.3. Small-Angle X-ray Scattering (SAXS). To investigate particle dispersion in the as-prepared PNCs, small-angle X-ray scattering (SAXS) measurements were performed at Sector 12-ID-B of the Advanced Photon Source at the Argonne National Laboratory. A point-collimated monochromated beam with energy 7.9−14 keV was used. Measurements were carried out at fixed temperatures ranging from 80 to 130 °C. Scattering data were averaged over five consecutive exposures, 0.5−1 s each, and no radiation damage was found after repeated measurements. The scattering intensity of NPs in the PNCs is obtained by subtracting that of particle-free polymer host. 2.4. Differential Scanning Calorimetry (DSC). The glass transition temperatures (Tg) for the SiO2-PEG2k/PMMA composites and particle-free (neat) PMMA were measured using differential scanning calorimetry (DSC). DSC measurements were carried out at a range of temperature ramp rates of 5, 10, 15, and 20 K/min in a nitrogen environment using a TA Instruments DSC Q2000. Tg values were obtained from the infection point in heat flow versus temperature plots, shown in Figure 2S. Thus, obtained Tg values were observed to increase with increased scan rate at low particle loading; however, at high particle loadings Tg exhibited no dependence on scan rate for the

Figure 1. SAXS intensity profiles of PEG-tethered silica nanoparticles in PMMA 55K host, with 0.5% ≤ ϕ ≤ 16%. The curves are displaced vertically for clarity of presentation.

polymer composites with silica core volume fractions ranging from ϕ = 0.5% to ϕ = 16%. An important goal of the study is to synthesize entangled polymer−nanoparticle composites with uniform particle dispersion. It is evident from Figure 1 that the measured scattered intensity I(q) exhibits a power law scaling, I(q) ∼ q−4, at qR ≫1, which is the expected result for an ideal two-phase model scatter for spheres.23 As significant is the fact that at low q (qR ≪1) the I(q) profiles typically reach a plateau; evidence that the materials do phase-separate with particle-rich clusters, except for ϕ = 16%. For ϕ > 7%, a power law scattering in the intermediate q range is evident, and the data do not plateau until at very low q, with the plateau regime being shifted toward progressively lower q values with increasing ϕ. This scattering feature indicates that at high particle content long-range particle correlations, likely due to the excluded volume and van der Waals (vdW) interactions between tethered PEG chains, exist in the materials and that the correlated domain size increases with increasing ϕ (>7%). Fitting the I(q) data with the unified Beacuage equation (Figure 5S), we find that the correlated domains (at low q) are more or less uniformly distributed and have a power law (I(q) ∼ q−2) at intermediate q. Absence of any additional structure at intermediate to high q confirms that within these domains particles are well separated and do not form compact aggregates. The observed trend suggests that for ϕ = 16% the size of the correlated domain falls outside of the q range explored in the SAXS experiments. The ratio of the degree of polymerization of the polymer host (P) to that of the particle-tethered chains (N) has been used in the literature to develop state diagrams for the phase stability of hairy nanoparticle/polymer blends24 where a P/N value above 5 has been reported to demarcate the transition B

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Figure 2. Tg values vs particle core content (ϕSi) for (a) PNCs based on PMMA 55K (b) PNCs based on PMMA 280K. Dashed line denotes the values estimated from the Fox mixing rule, and solid line shows the fit obtained from the Lu−Weiss equation.

Figure 3. (a) Surface-to-surface distance (ds−s) vs particle volume fraction in PNCs compared to the tube diameter (ae) for neat PMMA. (b) ΔT vs h for PNCs with PMMA 55K as host. Inset shows ΔT vs h for PNCs based on PMMA 280K as host. Solid line represents the fit to the empirical relation proposed by Keddie et al.37

to understand how these interactions cause Tg to deviate from the mixing rule. Lu and Weiss29 extended Couchman’s analysis to quantitatively correlate Tg deviations with the Flory− Huggins interaction parameter (χ). The authors proposed the expression

from well-dispersed to phase-separated mixtures of hairy nanoparticles in polymers. The results in Figure 1 show that even for P/N as high as 32 the fluids exist as homogeneous materials. As shown in our previous study,12 this enhanced ability of PMMA to disperse PEG-tethered nanoparticles originates from enthaplic interactions (χ < 0) between the tethered PEG chains and host PMMA, which promotes mixing. 3.2. Dynamic Behavior. Figure 2 reports Tg values obtained from DSC measurements and compares the measured values with expectations based on the Fox mixing rule.25 A comparison of Tg values obtained using the inflection point method and Moynihan’s integral method26 has also been included at low particle loadings. A good agreement between Tg values obtained from the two approaches is observed, likely due to the inconsequential contribution from the overshoot in the heat flow curve. It is apparent that the measured Tg are consistently lower than expected values from the Fox mixing rule for particle concentrations in the range (0 ≤ ϕ ≤ 4%), where a stronger decrease in Tg with increasing particle content is observed. These observations therefore cannot be simply explained in terms of equal contributions of the components to the overall Tg, which emphasizes the need to account for the role of interactions between them. Equations proposed by Gordon− Taylor27 and Couchman28 are commonly used in the literature

Tg,m =

w1Tg,1 + kw2Tg,2 w1kw2 +

Aw1w2 (w1 + kw2)(w1 + bw2)(w1 + cw2)2

with A=

−χR(Tg,1 − Tg,2)c M1Δcp ,1

and

k=

Δcp ,2 Δcp ,1

Here, R is the gas constant, χ is the Flory−Huggins interaction parameter, Δcp,i is the change in the specific heat of polymer i at Tg,i, c = ρ1/ρ2, b = M2/M1, ρi is the density of polymer i, and Mi is the molar mass per chain segment of component i. We used the Lu−Weiss expression to fit the measured Tg for SiO2-PEG/PMMA PNCs in the low particle content regime, as shown in Figure 2, with i = 1 as PEG 2K and i = 2 as PMMA 55K or PMMA 280K. k values used in the analysis were obtained from the Δcp values of the respective components C

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Figure 4. TTS master curves obtained from small amplitude oscillatory shear measurements for PNCs based on PMMA 55K host for (a) 0 ≤ ϕ ≤ 1%, (b) 1.25 ≤ ϕ ≤ 3%, (c) 4 ≤ ϕ ≤ 9%, and (d) 11 ≤ ϕ ≤ 16%. Master curves at different particle concentrations are shifted vertically for clarity, and shift factors have been reported in the figure legends.

able to have on PMMA. Geometric confinement of PMMA chains between the SiO2-PEG particles could explain these observations.36 We note that at the highest particle volume fractions studied (11 ≤ ϕ ≤ 16%) no discernible slope change is apparent from the heat loss data (Figure S2), and hence Tg could not be deduced from DSC measurements. The surface-to-surface distance (ds−s = dp−p − D) between the nanoparticles can be estimated from the interparticle distance (dp−p = D(0.63/ϕ)1/3), i.e., ignoring any expansion of the particle diameter due to the tethered PEG chains. However, the PEG brush on the nanoparticles is expected to increase the effective particle diameter and hence the apparent (to the PMMA chains) particle content in the nanocomposites. For the densely grafted SiO2-PEG nanoparticles used in the present study, the spacing between neighboring PEG chains on the surface ∼1/√Σ = 0.72 nm; this value increases quickly as one moves away from the particle surface due to the strong curvature of the particles. We estimate an effective PEG stem

measured from the DSC experiments as shown in Figure 6S, and A was used as a fitting parameter. Values of all parameters used in the fits are provided in Table 1S. A values obtained from fits were used to determine χ. On the basis of the χ values thus determined, we conclude that −0.10 ≤ χPEG2K−PMMA55K ≤ 0.06 and −0.06 ≤ χPEG2K−PMMA280K ≤ 0.05, which is in the range of values reported for χPEG−PMMA in the literature,30−35 suggesting that as is often the case for miscible polymer blends, Tg values for SiO2-PEG/PMMA PNCs follow the mixing rule once the interactions between the components are properly considered. At intermediate SiO2 particle volume fractions (3 ≤ ϕ ≤ 9%), the measured Tg values are seen (Figure 2) to exhibit large positive deviations from the Lu−Weiss expression, and the experimental Tg values display at most a weak dependence on ϕ. This behavior is important; it means that at these concentrations other physics in the composites are able to compensate for the extra plasticization effect PEO chains are D

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Keddie et al.37,44 proposed an empirical relation Tg(h) = Tg,Bulk[1 − (A/h)δ)], where A represents a characteristic length and δ is the exponent, to fit the decreasing Tg values with decreasing thickness for poly(styrene) and PMMA films on nonattractive substrates. The authors suggested that on the surface of the glassy film, a liquidlike layer exists, which causes on overall reduction in the Tg(h). The empirical expression for Tg of a thin polymer film proposed by Keddie et al. has received significant support from many previous studies. Here we use a simple variant of this expression, Tg(h) = Tg,Lu−Weiss[1 + (A/ h)δ] to capture the positive deviation in Tg. As shown in Figure 3b, a good fit was obtained using A ∼ 0.3 nm and δ ∼ 1.4 for h = ds−s and using A ∼ 0.7 nm and δ ∼ 1.3 for h = heff. The presence of a relatively immobile layer at the polymer− nanoparticle interface due to the attractive interactions is believed to increase the Tg with respect to the expected values. Also, the fact that the sign of the Tg deviation upon confinement is qualitatively consistent with expectations for polymer thin films near attractive surfaces confirms the importance of the attractive enthalpic attractions between the tethered PEG and the host PMMA chains in regulating segmental scale motion of PMMA. The inset to Figure 3b shows similar results for ΔT vs h data for the PNCs based on PMMA 280K host. Figure 4 reports master curves obtained from frequencydependent oscillatory shear measurements for entangled nanoparticle composites with particle content (0 ≤ ϕ ≤ 16%). Measurements were performed at multiple discrete temperatures, T > Tg, and shifted with respect to the measured Tg values for the respective material; Tg values for composites with 11% ≤ ϕ ≤ 16% could not be obtained from the DSC measurements, and TTS master curves for these materials were shifted with respect to 70 °C. In Figure 7S, we show that irrespective of the particle content, TTS works well at temperatures T > Tg but that overlap among the shifted moduli becomes worse as the temperature approaches Tg. Several features of the TTS master curves stand out: (i) For low particle volume fractions (0.25% ≤ ϕ < 4%) the linear viscoelastic moduli are of comparable magnitude and are superimposable with the dynamic moduli of the particle-free neat PMMA melt for the entire frequency range. (ii) For moderate particle contents (4% ≤ ϕ ≤ 11%) G′ dominates G″ in the high frequency range with effect becoming stronger with increasing ϕ. For these composites, a clear terminal regime is not visible from oscillatory shear. (iii) For high particle content (13% ≤ ϕ ≤ 16%), G′ not only dominates G″ in the highfrequency range and the terminal regime is not accessible, and the rheological responses resemble those reported previously for soft-glassy materials45 (iv) Successive addition of NPs shifts the frequency-dependent dynamic moduli for the composites toward lower frequency, especially for low particle content after which this effect gets weaker. This slowing down of relaxation times with addition of particles is expected from the strong enthalpic attraction between the tethered PEG chains and host PMMA chains which is thought to couple motions of the host polymer chains and particles in the PNCs.12 To gain further insights into topological confinement/tube constraints on the host polymer relaxation in PNCs from their rheological response, we quantified the fundamental time scales typically associated with entangled polymer viscoelastic behaviorthe entanglement relaxation time (τe) and the terminal relaxation time (τt), estimated from the crossover of G′ and G″.46 For low particle content both the crossovers are

height (Δ) as the distance from the nanoparticle surface beyond which the interchain spacing becomes comparable to the Kuhn step length of PMMA (bPMMA ∼ 1.1 nm) as l ∼ (D/ 2)(bPMMA√Σ − 1) ∼ 4.4 nm. This estimate is justified by the fact that it would be entropically unfavorable for the PMMA chains to penetrate the PEG stem, where the interchain spacing is 5−6 nm, it is apparent that ΔT ∼ 0. This result is expected because at these particle loadings the PMMA chains do not feel particleimposed confinement as shown in Figure 3a. At smaller surface separations (h ≤ 5 nm), chains are confined (h < ae ∼ 7 nm), and we observe a large positive deviation in ΔT as shown in Figure 3b. These length scales for the onset of polymer confinement are evidently smaller than what has been reported for free-standing or supported polymer films (e.g., 30−150 nm). This difference is thought to originate from the large curvature of nanoparticles. Molecular simulations by Ganesan et al.42 reported that much smaller surface-to-surface distances between nanoparticles are needed in PNCs to produce quantitatively similar effects on Tg as in polymer thin films, which is consistent with our findings. A more concrete understanding of this point is possible by using an analogy to fluid flow in porous particle beds to compute the effective separation between flat plates, heff = (Deff/3)[(1 − ϕeff)/ϕeff],43 required to achieve the same flow resistance. Here Deff and ϕeff are the nanoparticle diameter and volume fraction, including the polymer brush height (Δ), respectively. Figure 3b compares ΔT vs heff with ΔT vs h, where it is seen that the heff values for polymer confinement effects to become noticeable (30−50 nm) are generally larger and closer to the length scales typically reported in thin film studies. The critical heff values also fall within the limit of 20Rg of the host polymer suggested by recent computer simulations.43 E

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Figure 5. (a) TTS master curve for PMMA55K (ϕ = 0%) (b) G* and δ (= tan−1(G″/G′)) vs aTω for PMMA55K. (b) TTS master curve for SiO2− PEG/PMMA55K (ϕ = 7%) (d) G* and δ (= tan−1(G″/G′)) vs aTω for SiO2-PEG/PMMA55K (ϕ = 7%). In (a) and (c) relaxation times (τ0, τe, τt) were directly obtained from the crossover of G′ and G″ curves. In (b) and (d) τe is obtained from the frequency at which G* changes slope. This point is identified from the intersection of the tangents (blue solid lines) drawn on the G* curve at points where δ shows an extremum as shown. (e) Relaxation times (τ0, τe, τt) vs particle content for SiO2-PEG2K/PMMA55K. Closed symbols represent data obtained from actual crossovers in G′ and G″ curves. Open symbols represent the data obtained from the crossover points of tangents drawn on G* curve. Numerical values are also given in Table 2S.

readily accessible. For intermediate particle content (7% ≤ ϕ ≤ 9%), however, only the terminal crossover was observed. This necessitated a second approach, wherein τe was estimated from the frequency at which a slope change in G* (see Figure 5b,d) is observed. The characteristic τe values obtained using the two approaches are compared in Figure 5e, where good agreement is seen in the low-particle concentration regime where both methods can be used. At the highest particle loadings (13% < ϕ ≤ 16%) τe values could not be estimated using either approach. For low particle content composites (0 ≤ ϕ ≤ 4%), we also obtained the segmental relaxation time (τ0) from the high frequency crossover of G′ and G″. The time scales shown in Figure 5e can be used to calculate dimensionless groups β = (τt/τe)1/3 ∼ N/Ne and ξ = (N/β)1/2 ∼ ae/b where ae is the tube diameter and b is the Kuhn length of the host polymer, N is the number of Kuhn segments in the entire chain of molecular weight Mw, and Ne is the number of Kuhn segments in molecular weight of an entanglement strand of the host polymer. Hence, the value ξ can be thought to characterize the importance of topological confinement/tube

constraints on the host polymer relaxation, whereas β quantifies the effective number of entanglements experienced by polymer host chains during their terminal/reptation relaxation. Another estimate of polymer tube confinement can be obtained by calculating dimensionless group α = (τe/τ0)1/4 ∼ ae/b; however, α values were only obtained for low particle content composites where τ0 values could be obtained from the crossover of G′ and G″ in the high frequency regime. It is understood that our calculations thus far inherently assume the rheological response of the materials is dominated by the host polymer, which is unlikely at moderate to high particle content where particles and tethered chains will also contribute significantly to the measured viscoelastic response of the materials. Figure 6a shows the variation in α/αneat and ξ/ξneat with respect to particle content in PNCs. It is apparent that at low particle content (ϕ ≤ 2%) the polymer tube diameter remains unperturbed by addition of SiO2-PEG to PMMA 55K. At particle volume fractions above 2%, both α and ξ values are observed to drop sharply, meaning that the PMMA chains in the PNC’s are more topologically constrained than in the neat F

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Figure 6. Effect of particle concentration on (a) ξ/ξneat and α/αneat and (b) β/βneat for SiO2-PEG2K/PMMA55K composites with respect to the particle-free polymer melt. Insets to (a) and (b) show similar results for SiO2-PEG2K/PMMA280K. Circles represent the data points where τe values are obtained from the tangent method, and crosses represent data points where τe values are obtained from the actual crossovers of G′ and G″ curves. (c) Power law exponent n vs ϕ extracted from the Rouse regime of the TTS master curves in Figure 4.

melts. This finding in turn means that the PMMA chains discover the tube sooner, leading to an early onset of reptation dynamics because the PEG-tethered nanoparticles impose additional topological constraints to the reptative motion of the free PMMA host chains. The computed values for β = (τt/ τe)1/3 ∼ Mw/Me ∼ Z provide additional insights about the PMMA chain motions as the particle content increases. Figure 6b shows that at a similar particle concentration (≈2%) at which the confinement effect is observed, β increases. This result also follows from the discussion in the previous section because the PMMA host chains become more entangled, and their chain motions in the tube are more restricted due to the tube shrinkage by particle confinement, as already pointed out in Figure 3a. Thus, the structural information inferred from the dimensionless groups at different length scales are consistent.12 Also, the particle-induced tube confinement at ϕ ≈ 2% (ϕeff ∼ 15%), deduced from drop in ξ/ξneat in Figure 6a is consistent with results reported in Figure 3a. Our finding that particles can provide topological constraints on the host polymer is consistent with computer simulations47,48 and theory.49 Careful inspection of Figure 6 gives additional insight into the dynamics of SiO2-PEG/PMMA nanocomposites at high particle concentrations. It is seen that ξ/ξneat decreases monotonically until ϕ ≈ 4−5%, followed by the appearance of a plateau up to ϕ ≈ 9%. The plateau is followed by a regime of sharply decreasing ξ/ξneat up to ϕ ∼ 13%. Based on the discussion in the previous sections, the apparent number of entanglements (β/βneat) would be expected to increase monotonically with ϕ, if the stress response in the SAOS experiment arose entirely from the PMMA host polymer. Figure 6b shows that β/βneat follows these expectations up to a polymer volume fraction ϕ ≈ 4−5% and thereafter plateaus up to ϕ ≈ 9%. For ϕ > 9% a large increase in β/βneat (Figure 6b) is

observed, which in a host-polymer centered analysis would suggest that the number of entanglements diverges. The observed behavior may, however, also arise from contributions to the stress from particle−particle interactions. In particular, at high particle loadings, confinement of NPs in cages created by their neighbors and/or by interdigitation of the tethered PEG chains will lead to a transition to a jammed, glass-like rheological regime where elastic stresses produced by a particle network make a large contribution to the measured rheology. This view is supported by the fact that at a concentration ϕ = ϕG ≈ 15% the terminal regime is inaccessible, and both G′ and G″ become frequency-independent (Figure 4d). Nevertheless, the disappearance of a crossover in G′ and G″ between the high-frequency segmental regime and the intermediatefrequency (Rouse-like) regime at ϕ ≈ 7% evident in Figure 4c likely means that an elastic stress contribution due to the particle network is present at concentrations well below ϕG. Similar findings for a higher host polymer with Mw = 280K were also observed. Insets to Figures 6a and 6b report similar increases in the apparent confinement (ξ or α) and in the effective number of entanglements (β) with increased particle loading. The anomalous decrease in Z, observed at low ϕ, however was earlier explained12 on the basis of faster movement of NPs providing constraint release behavior for the host chains. More information about polymer motions leading up to the transition can be obtained by fitting the storage modulus to a power-law function, G′ ∼ ωn, in the intermediate frequency regime. The power-law exponents obtained from the fits are plotted in Figure 6c. It is seen that for ϕ ≤ 3% n is around 0.7, typical for unconfined polymer solutions exhibiting Zimm-like chain dynamics. For ϕ > 3%, the power-law exponent decreases continuously and eventually for ϕ = 16%, n ≈ 0 for the entire G

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Figure 7. Horizontal shift factor (aT) vs temperature difference (T − Tr) for SiO2-PEG2K/PMMA55K at different particle loadings (ϕ). In (a) solid line represents the corresponding WLF fit, and in (b) the dashed lines represent the Arrhenius fit.

frequency range accessed experimentally. This indicates that the transition to a glass-like regime is in fact continuous and begins at approximately the same particle concentration at which the interparticle spacing falls below the equilibrium tube diameter for the neat polymer melt. In Figure 7, we plot the TTS horizontal shift factor aT(T,Tr) used in constructing the master curves shown in Figure 4 against T − Tr, where Tr is the reference temperature. At low particle concentrations (0% ≤ ϕ < 4%) the temperaturedependent aT for the PNCs are superimposable with the corresponding results for the particle-free PMMA and follow the characteristic WLF equation (log aT = [−C1(T − Tr)]/[C2 + (T − Tr)]). This indicates that the segmental friction coefficient of the PMMA chains remains largely unaffected by the presence of the SiO2-PEG NPs. Further increases in particle concentration (4% ≤ ϕ ≤ 11%) leads to an obvious change in the shape of aT(T,Tr), and the results no longer conform to the WLF equation, particularly at low T. As illustrated in Figure 7b, the Arrhenius equation (log aT = (Ea/R)(1/T − 1/Tr)) provides better fits to the high-ϕ experimental data, indicative of extended glassy dynamics above Tg. At very high particle concentrations (13% ≤ ϕ ≤ 15%), the shift factors do not follow the WLF equation at all and instead obey the Arrhenius expression for almost the entire temperature range, indicating a completely different relaxation mechanism in these composites. The WLF and Arrhenius coefficients for the fits shown in Figure 7 are reported in Table 1. Angell and co-workers50 have proposed that the transition of temperature-dependent dynamics from WLF to Arrhenius indicates the transition in the dynamical behavior of a material from fragile to strong. This transition is believed to be a signature of less cooperative motions in glassy materials; polymer properties typically show Arrhenius thermal behavior below the glass transition temperature. However, such transition in polymer nanocomposites with increasing particle content to our knowledge has not been reported. Ultrathin polymer films, including free-standing and supported films have been reported to exhibit similar behavior once the film thickness falls below a certain threshold value associated with the onset of confinement effects.51,52 This behavior has been explained in terms of cooperativity rearrangement regions (CRRs), a notion first introduced by Adam and Gibbs.53 A

Table 1. Coefficients for WLF and Arrhenius Fit to the Horizontal Shift Factors’ (aT) Dependence on ΔT = T − Tr for PNCs Based on PMMA 55K Host WLF fit coeff

a

vol fraction (ϕ)

ref temp Tr (°C)

0 0.25 0.5 0.75 1 1.25 1.5 2 3 4 5 7 9 11 13 15 16

140 140 140 140 140 140 140 140 130 110 130 110 90 80 125 120 100

C1

C2 (°C)

17.5 18.0 17.2 19.3 19.2 17.2 17.9 17.8 19.9 29.1 18.8 24.1 26.0 30.6

83.5 90.4 87.0 93.3 93.7 91.7 91.1 95.0 89.7 97.8 96.8 113.8 56.4 119.5 NA

Arrhenius fit coeff Ea (kJ/mol)

NAa

245 196 191 284 202 89.4 59.5 57.3

NA: not applicable.

CRRs is defined as a subsystem, within which molecules are jammed and can rearrange their configuration cooperatively independent of their environment. In the case of bulk polymer films, as we decrease the temperature and approach Tg, CRRs grow in size, resulting in increased requirement of cooperative motion and hence increased activation energy for relaxation. This behavior is revealed in super-Arrhenius or WLF dependence of relaxation time. However, in ultrathin polymer films, due to nanoconfinement the macroscopic length scales approach the length scales of the CRRs, which reduces the requirement of increased cooperative movement of polymer segments and hence results in an activated motion. The activation energy however depends on film thickness and the type of interaction between the polymer chains and the support. As discussed earlier, increasing particle content can strongly confine the host polymer chains, which can produce similar effects to thin polymer films. Hence, this WLF to H

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Macromolecules Arrhenius transition with increasing particle content can be understood to stem from polymer nanoconfinement. Another key observation is that for moderate particle content (4% ≤ ϕ ≤ 11%), where polymer chains are moderately confined, the activation energy (Ea) of the Arrhenius fit fluctuates around 223.6 ± 40 kJ/mol, and for high particle content it decreases to almost 25% of the former value (Table 1). This drop in Ea suggests that for higher particle content, local relaxation of polymer chains occurs in a lower-friction environment than at the lower particle content. It is possible that this behavior arises from the increasing dominance of PEG chains in setting the local segment friction the PMMA chains experience at these high ϕ values. Similar behavior for PNCs based on PMMA 280K is shown in Figure 8S. Fragility is a key variable which reflects the structure and dynamics of a glassy polymer and determines the susceptibility to perturbations, in this case induced by particle confinement. The fragility index (m) is defined as m=

d log τ d(Tg /T )

= T = Tg

d log aT d(Tg /T )

decreases marking a fragile to strong transition. This decrease in fragility at higher particle loadings is also reflected in an increase in the glass transition width (ΔTg) as shown in the inset to Figure 8, which is consistent with the increase in ΔTg reported by Bansal et al.36 Thin polymer films are reported to exhibit a decrease in fragility with decreasing thickness due to reduced packing frustration and less cooperative−more activated dynamics (WLF to Arrhenius transition shown in Figure 7), which makes the films stronger.59−61 Reduced cooperativity in thin films has also been shown by molecular simulations, where reduction in the high-temperature activation energy is thought to produce a reduction in fragility.62 Hence, once again the framework of particle induced confinement of the host polymer chains can be used to draw an analogy with thin film behavior to explain the reduction in mr in our composites at moderate to high particle content as (see Figure 8). In agreement with simulations,62−64 a decreasing relative fragility from low to moderate particle loadings is consistent with the observed decreasing Tg values. At higher particle content, however, this proportionality breaks down and Tg remains virtually unchanged while relative fragility decreases continuously. This finding is consistent with simulation results of Hanakata et al. and Marvin et al.65,66 for ultrathin polymer films where interfacial effects dominate and release of packing frustration becomes more important under confinement at high particle loading, leading to nonproportional variation of mr and T g.

T = Tg

where τ is the relaxation time.54,55 Hence, m can be obtained by calculating the slope of the log aT vs Tg/T plot as shown in Figure 9S. By calculating m, we can understand the relative rate at which structural relaxation changes with temperature. Very few reports have attempted to understand the change in fragility upon addition of nanoparticles to polymer melts. Experiments56,57 and simulations55,58 report an increase in fragility of the host polymer upon addition of attractive NPs and the opposite when repulsive particles are introduced to a polymer host. Uniformly distributed attractive NPs are expected to reduce the packing of the polymer chains leading to more fragile behavior and the opposite for repulsive NPs. However, these reports are limited to low particle content, where the host polymer is not confined and the dynamic response mainly reflects bulk polymer relaxation. In order to understand the role of nanoparticles induced confinement at high particle loading on the fragility of our SiO2-PEG/PMMA composites, we plot the relative fragility mr (= mPNC/mneat), with respect to the particle-free, neat polymer as a function of particle fraction in Figure 8. It is clear that mr increases very modestly at low particle content (ϕ < 2%), indicating a more fragile behavior. At higher particle content (ϕ > 2%), mr

4. CONCLUSIONS Multiscale polymer dynamics were investigated using a model polymer nanocomposite (PNC) system created by uniform dispersion of poly(ethylene glycol) (PEG) tethered silica nanoparticles in poly(methyl methacrylate) (PMMA) host polymer melts. PNCs with increasing nanoparticle loading were synthesized to systematically investigate the role of nanoparticle crowding on thermomechanical behavior of the host polymer chains and on rheology of PNCs with high particle loadings. Thermal investigation of the PNCs by means of differential scanning calorimetry (DSC) revealed that at low particle content (ϕ) Tg of SiO2-PEG/PMMA composites agree well with expectation based on mixing rules, provided interactions between the polymer components (PEG and PMMA) are appropriately considered using the Lu−Weiss formula. With increasing ϕ, the measured Tg values exhibit progressively larger positive deviations from respective values computed using the Lu−Weiss expression, indicative of a transition to a regime where confinement of PMMA between SiO2 particles in the PNCs play a significant role on the thermal behavior of PMMA. Rheological properties of PNCs were studied by means of oscillatory shear rheology measurements in an extended frequency range designed to report material response on all time scales. In PNCs with low particle content, the dynamic response (G′(aT ω) and G″(a T ω)) obtained from the composites showed typical features of entangled melts, including distinct transitions between dynamic regimes dominated by relaxations associated with segmental-scale motions, in-tube Rouse chain relaxation, and terminal tube escape. The horizontal shift factors (aT) used for creating time−temperature superposition master curves showed an expected WLF dependence on temperature (T). At moderate particle content, G′ begins to dominate G″ in the moderate to high frequency region and a clear transition from segmental to in-tube Rouse motion disappears. At high particle content a soft

Figure 8. Relative fragility mr (= mPNC/mneat) vs particle content (ϕ) for PNCs based on PMMA 55K as host. Inset shows the broadening of glass transition width with increasing particle content. I

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Macromolecules

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glassy response is observed with G′ dominating G″ in the entire frequency range, and no terminal relaxation is observed. These changes coincide with a transition of aT(T) from WLF to Arrhenius behavior with increasing particle content and a decrease in the relative fragility index. Thermal analysis of the SiO2-PEG/PMMA PNCs indicates that the transitions in rheological behavior with increased particle loading can be explained in terms of confinement of the host PMMA chains between attractive nanoparticle surfaces. By comparing our findings for PNCs at high particle loadings with those reported in the literature for polymer thin films, we illustrate that polymer chains under 3D confinement in PNCs provide good model systems for inferring confinement dynamics of polymer thin films from bulk measurements. To our knowledge, the experiments reported are the first to show that polymer chain dynamics in PNCs undergo a continuous transition from bulklike behavior at low particle contents to confinement behavior at intermediate particle loadings and ultimately to glassy behaviors at high particle content.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b00496. Figures 1S−9S; Tables 1S and 2S (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (L.A.A.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation, Award CBET-1512297. Use of the Advanced Photon Source, operated by Argonne National Laboratory, was supported by the U.S. DOE under Contract DE-AC02-06CH11357. We acknowledge Mr Xiaobing Zuo, Assistant Physicist, Argonne National Laboratory, for helpful discussions.

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