Temperature-Dependent Suppression of Polymer Diffusion in Polymer

May 27, 2016 - The polymer center-of-mass tracer diffusion coefficient in athermal ... The polymer tracer diffusion coefficient in the PNC relative to...
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Temperature-Dependent Suppression of Polymer Diffusion in Polymer Nanocomposites Wei-Shao Tung,†,∥ Philip J. Griffin,†,∥ Jeffrey S. Meth,‡ Nigel Clarke,§ Russell J. Composto,† and Karen I. Winey*,† †

Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19803, United States Central Research and Development, DuPont Co., Wilmington, Delaware 19803, United States § Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom ‡

S Supporting Information *

ABSTRACT: The polymer center-of-mass tracer diffusion coefficient in athermal polymer nanocomposites (PNCs) composed of polystyrene and phenyl-capped, spherical silica nanoparticles was measured over a range of temperatures and nanoparticle concentrations using elastic recoil detection. The polymer tracer diffusion coefficient in the PNC relative to the bulk decreases with increasing nanoparticle concentration and is unexpectedly more strongly reduced at higher temperatures. This unusual temperature dependence of polymer diffusion in PNCs cannot be explained by the reptation model or a modified version incorporating an effective tube diameter. Instead we show that our results are consistent with a mechanism based on nanoparticle-imposed configurational entropy barriers.

M

while parallel to the surface it remains relatively unperturbed.15−18 Perturbations of the polymer radius of gyration have also been observed experimentally in polymer nanocomposites,19,20 although contradictory results exist.21 It has been proposed that such perturbations to the polymer structure produce entropic barriers restricting polymer motion on the chain scale, while leaving local segmental dynamics comparatively unchanged.22,23 In this letter, we report measurements of the polymer tracer diffusion coefficient in athermal polymer nanocomposites comprising polystyrene and phenyl-capped colloidal silica NPs over a wide range of temperatures and NP concentrations using elastic recoil detection. We find that not only does polymer diffusion slow down with increasing NP concentration, but also it becomes increasingly slower (relative to the bulk) as the temperature of the nanocomposite increases. We show that nanoparticle-imposed excess entropic free energy barriers are the primary mechanism slowing polymer diffusion in athermal nanocomposites. Polymer nanocomposites (PNCs) were prepared by mixing monodisperse spherical, phenyl-capped silica NPs (2RNP = 28.5 ± 0.3 nm, determined via dynamic light scattering) dissolved in dimethylacetamide with the necessary amount of polystyrene (PS) (M W = 650 kg/mol, PDI = 1.1) dissolved in dimethylformamide to produce matrix films of varying NP concentration (0−50 vol. %). Matrix films were prepared by

acromolecular diffusion in crowded environments is a process fundamental to a range of physical and biological phenomena such as the rheology of polymer nanocomposite melts,1−3 polymer translocation through nanopores, 4,5 and the regulation of intracellular biological processes.6,7 Generally, diffusion in crowded environments is significantly modified relative to the uncrowded state. It has been demonstrated experimentally that polymer diffusion (D) in nanocomposites becomes slower with increasing spherical nanoparticle (NP) concentration at a fixed temperature regardless of the particle size, polymer molecular weight, or nature of the interactions between the particles and polymer chains.8−10 In these studies, the magnitude of diffusion reduction reported as a normalized diffusion coefficient (D/ Do) depends on the average interparticle distance normalized by the size of the polymer chain (ID/2Rg), suggesting that NPinduced confinement plays a key role in the diffusion process. This correlation also applies for NPs functionalized with polymer chains, where an effective interparticle distance is employed to account for the molecular-weight-dependent penetration of the polymer brush.11 To date, however, the temperature dependence of the D/Do versus ID/2Rg relationship in PNCs has yet to be explored. These observed modifications of center-of-mass diffusion occur regardless of changes (or lack thereof) in the glass transition temperature of the polymer,10,12−14 implying that the influence of NPs on the diffusive polymer motions may be significantly different from how NPs affect local segmental mobility. Simulations of nanoconfined polymers generally indicate that in the vicinity of an impenetrable surface the polymer radius of gyration normal to the surface is compressed, © XXXX American Chemical Society

Received: April 16, 2016 Accepted: May 25, 2016

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DOI: 10.1021/acsmacrolett.6b00294 ACS Macro Lett. 2016, 5, 735−739

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ACS Macro Letters solvent casting onto a heated glass substrate, transferred to silicon substrates, and then annealed in a vacuum oven at 425 K for 3 days. As-prepared PS nanocomposite films exhibited homogeneous NP dispersion at all particle concentrations, as demonstrated previously (these PNC matrix films are a subset of those measured by Meth et al.,12 where the homogeneous dispersion of phenyl-capped silica NPs in 650k PS was demonstrated via transmission electron microscopy and X-ray scattering). Thin tracer films (20 nm, measured via ellipsometry) of deuterated polystyrene (dPS) (MW = 532 kg/mol, PDI = 1.04) were prepared by spin coating from toluene solutions onto silicon substrates and transferred onto the annealed PS nanocomposites. As-prepared dPS/PS nanocomposite diffusion couples were then annealed in a vacuum oven at select temperatures (416−470 K) for variable annealing times such that the diffusion lengths were ≈ 300−500 nm. Temperature-modulated differential scanning calorimetry (TMDSC) measurements were performed on the PNC matrix films to measure the segmental relaxations over a narrow range of time scales (τ = 100.5−101.5 s). Figure SI. 1 presents the glass transition temperatures (determined as the temperature where τ = 100 s), which vary only mildly with increasing NP concentration.12 Similarly, the fragility of segmental relaxation,24 mτ =

d log10(τ )

is also nominally independent of NP

Tg

dT

T = Tg

loading (Figure SI. 1). Depth profiles of dPS in the annealed diffusion couples were measured using elastic recoil detection (ERD), as previously described.25 In ERD, a He2+ ion beam is accelerated to 3 MeV and incident upon the sample in forward scattering geometry. The energy spectrum of forward-recoiled deuterium ions is collected at a 30° scattering angle using a solid-state detector. The dPS volume fraction depth profile is then calculated from this measured energy spectrum. Figure SI. 2 depicts the measured depth profile of dPS diffusing into the 5 vol. % PNC matrix at 453 K (Tg + 78 K). To extract the center-of-mass polymer tracer diffusion coefficients, the dPS depth profiles were fit using the solution to Fick’s second law26 describing the concentration profile of a finite source diffusing into a semiinfinite medium, convoluted with the Gaussian resolution profile (full width = 70 nm). The dPS tracer diffusion coefficient decreases with increasing NP concentration and decreasing temperature, as expected (Figure 1a).8 The tracer diffusion coefficients, normalized by their respective values in the bulk polymer, are also plotted as a function of NP concentration in Figure 1b and the confinement parameter ID/2Rg (the average interparticle distance normalized by the bulk polymer radius of gyration) in Figure 1c.8 One would not expect that D/Do in these PNCs should exhibit any significant temperature dependence because the glass transition temperatures and segmental fragilities vary only mildly with NP concentration (Figure SI. 1). However, the tracer diffusion coefficient is more strongly reduced by the presence of NPs at higher temperatures. At ∼ Tg + 100 K (470 K), the reduction in diffusion relative to the bulk melt is nearly a factor of 10 at the highest NP concentration (50 vol. %), while at ∼ Tg + 40 K (416 K) it is less than a factor of 2. Plotting the data of Figure 1 as a function of inverse temperature depicts the changes in temperature dependence of the tracer diffusion coefficient with increasing NP concentration (Figure 2a) (Figure SI. 3 shows the data at all NP concentrations). Not only is the magnitude of the diffusion

Figure 1. Deuterated polystyrene (dPS) tracer diffusion coefficients are shown plotted against NP volume percent at (a) all measured temperatures and (b) select temperatures normalized by the diffusion coefficient in the bulk (0 vol. % NP) polymer matrix. (c) Normalized dPS tracer diffusion coefficient are plotted against ID/2Rg, the ratio of the interparticle distance and the bulk polymer radius of gyration.

coefficient reduced with increasing NP concentration (the expected result) but also, importantly, the curvature of the temperature dependence of the diffusion coefficient decreases. This change in the temperature dependence of diffusion can be quantified by the fragility index, mD =

d log10(1 / D)

.

Tg

dT

T = Tg

Fragility provides an empirical way to quantify the curvature of a dynamical quantity with temperature, whether that dynamical quantity is the polymer diffusion coefficient or the segmental relaxation time. When there is no curvature, m ≈ 16, and the temperature dependence is strictly Arrhenius. To calculate mD, we have fit the temperature-dependent diffusion coefficient using the Vogel−Fulcher−Tammann (VFT)

( ) and extrapolated the measured

function D = D0 exp

−B T − T0

diffusion coefficients to Tg.27,28 Literature data29 for the temperature-dependent terminal shift factor of entangled polystyrene (scaled by a multiplicative constant to match with the measured 0 vol. % diffusion data) were fit using the VFT function, and the obtained divergence temperature (T0 = 736

DOI: 10.1021/acsmacrolett.6b00294 ACS Macro Lett. 2016, 5, 735−739

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R ∼ Rg.19 More importantly, the polymer Rg is expected to be nominally independent of temperature.33 Therefore, changes in RPNC are unlikely to account for the strong temperature R bulk

dependence of

DPNC(T ) , D bulk (T )

especially at large NP concentrations.

The microscopic Rouse relaxation times in similar athermal PNCs are also nominally unaffected by NP concentration,34−36 and as such τbulk likely does not account for the measured τPNC

temperature dependence of diffusion. Our measurements of the segmental relaxation times via TMDSC verify that the temperature dependence of the microscopic dynamics is essentially unaffected by the presence of NPs (Figure SI. 1). N The ratio e−PNC also likely does not account for the observed Ne − bulk

temperature-dependent reduction of

Instead, confine-

ment of polymer chains in athermal PNCs (and in other confining geometries) actually increases Ne,15,34 which leads to faster polymer diffusion in the reptation model. Richter et al. have suggested that NPs can act as effective entanglements in a modified version of the reptation model, which they invoke to account for the observed slowing of chainscale polymer dynamics in PNCs comprising poly(ethylene-altpropylene) and phenyl-capped SiO2 NPs studied via neutron spin echo spectroscopy.36 More recently, Mangal et al. also invoked this concept to describe their rheology studies of PEOgrafted silica/PMMA nanocomposites.37 In both cases, the proposed effective tube diameter arises from the static network of topological constraints imposed by NPs on polymer chains, which is unlikely to exhibit significant temperature dependence over the measured temperature range. In contrast, our results would require a nearly 10-fold reduction in the effective tube diameter over a ∼60 K temperature increasei.e., an unphysical decrease for polystyrene from ∼8 to 0.8 nm. Thus, to the first approximation, the reptation model even with a modified tube diameter cannot completely describe the observed temperature dependence of the polymer diffusion coefficient in these PNCs. Alternatively, we consider how NPs may influence chain diffusion directly. We consider the process of polymer diffusion in PNCs to be perturbed relative to the bulk, where the NPs impose an excess free energy barrier ΔFNP on the diffusing polymer chain such that

Figure 2. (a) Measured dPS tracer diffusion coefficients (circles) versus inverse temperature for select nanocomposite (PNC) compositions. The solid line depicts literature data for the terminal creep compliance shift factor (scaled by a constant) in entangled polystyrene,29 and dashed lines are Vogel−Fulcher−Tammann (VFT) fits to the experimental data. (b) The fragility of chain diffusion mD calculated from the VFT fits to the temperature-dependent diffusion coefficients for all PNCs.

316 K) was fixed during fitting of all measured diffusion data a necessary approximation due to the limited dynamic range of diffusion measurements (10−12−10−16 cm2/s). As is seen in Figure 2a, the constrained VFT functions fit the measured data well, and furthermore the scaled literature rheology data match the measured 0 vol. % diffusion coefficients nearly identically. The fragility of chain diffusion decreases by approximately 30% with increasing NP concentration in this athermal PNC (Figure 2b), in contrast to the fragility of segmental relaxation which remains constant at all NP concentrations (Figure SI. 1). This result indicates that polymer center of mass diffusion is not directly coupled to polymer segmental relaxation in these PNCs. Recent simulations of both attractive and repulsive PNCs by Betancourt et al. have also demonstrated that fragility of polymer chain diffusion decreases with increasing NP concentration, regardless of the respective changes in segmental fragility.30 According to the reptation model,31,32 the ratio of the polymer diffusion coefficient in the nanocomposite relative to the neat melt depends on three factors 2 DPNC(T ) ⎛ RPNC ⎞ ⎛ Ne − PNC ⎞⎛ τbulk ⎞ =⎜ ⎟⎜ ⎟⎜ ⎟ D bulk (T ) ⎝ R bulk ⎠ ⎝ Ne − bulk ⎠⎝ τPNC ⎠

DPNC(T ) . D bulk (T )

⎛ ΔF ⎞ DPNC(T ) = D bulk (T )exp⎜ − NP ⎟ ⎝ kBT ⎠

(2)

We have calculated ΔFNP using the data in Figure 1, and it is seen that ΔFNP increases strongly with NP concentration and, importantly, with increasing temperature (Figure 3a). This observation provides quantitative evidence for the temperaturedependent reduction of polymer diffusion in PNCs being entropic in nature.32 Polymer diffusion modified by entropic barriers has been demonstrated both for single-chain translocation through short, bottleneck-shaped pores38 and for star polymers in the melt.39 Significant enthalpic contributions to ΔFNP would likely appear either as temperature-independent additive constants in Figure 3a or, alternatively, as contributions that increase with decreasing temperature (in the case of hydrogen bonding or dipole−dipole interactions). Instead it is observed that ΔFNP extrapolates to zero at temperatures above the glass transition (∼376 K), indicating that enthalpic

(1)

where DPNC and Dbulk are the temperature-dependent polymer chain diffusion coefficients; RPNC and Rbulk are the polymer radii of gyration; Ne‑PNC and Ne‑bulk are the degrees of polymerization between entanglements; and τPNC and τbulk are the microscopic Rouse relaxation times of the PNC and neat melt, respectively. Neutron scattering measurements of another athermal PNC comprising hydrophobically modified silica and poly(ethylenealt-propylene) have found that, on average, the polymer Rg was modestly reduced (by ∼10%) in the presence of NPs with size 737

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diffusion. Recent theoretical work has suggested that the entropy penalty for polymer chains confined between spherical particles should diverge as ∼ ID−6.41 While |ΔSNP| follows a power law dependence over the measured range of interparticle distances (Figure 3c), it diverges much more slowly (|ΔSNP| ∼ ID−0.5) as ID → 0 than this theoretical prediction. This observed deviation may be due to NP-induced excluded volume effects, which were recently shown to account for the sizable reduction in polymer diffusion at large interparticle distances.42 We speculate that these two mechanisms may occur simultaneously in the measured range of ID, potentially resulting in the observed weaker power law dependence. We plan to measure the temperature-dependent diffusion coefficients over a wide range of tracer and matrix polymer molecular weights to further explore this dependence of |ΔSNP| on ID. In conclusion, the polymer center-of-mass tracer diffusion coefficient in a model athermal PNC was measured over a wide range of temperatures and NP concentrations using elastic recoil detection. The tracer diffusion coefficients in the PNC relative to the bulk decrease with increasing nanoparticle concentration and are unexpectedly more strongly reduced at higher temperatures. In these athermal PNCs we conclude that nanoparticles impose entropic free energy barriers, and these barriers are the primary cause for slower polymer diffusion with increasing NP concentration. Furthermore, this finding implies that polymer diffusion in athermal PNCs is intimately connected to how NPs perturb polymer conformations. As a polymer chain traverses the PNC, it will eventually encounter a space between NPs through which it must pass to continue its diffusive path. As the chain traverses this space, it necessarily will contract in the direction normal to the NP surface. We hypothesize that this slow, entropically unfavorable reconfiguration is the structural manifestation of the entropic free energy barrier that impedes polymer diffusionespecially at higher temperaturesin athermal PNCs. Because the entropic barrier that is surmounted when a polymer chain traverses this space enters exponentially into the diffusion coefficient (eq 2), relatively small entropy penalties (e.g., low NP concentrations) arising from correspondingly small perturbations of the polymer conformation can significantly slow the diffusion process.

Figure 3. (a) Excess free energy barrier ΔFNP (eq 2) plotted as a function of temperature. Symbols depict ΔFNP calculated from measured D(T) data at all PNC compositions, and solid lines depict linear fits to the data. The magnitude of the excess entropic barrier |ΔSNP| is plotted against (b) NP concentration and (c) the average interparticle distance ID. The black line in (c) depicts a power-law fit.

contributions to ΔFNP are negligible relative to the entropic component. This observation is consistent with the nominally athermal interactions between phenyl-capped NPs and PS. As is seen in Figure 3a, ΔFNP varies approximately linearly with temperature in the measured range and notably exhibits a much stronger temperature dependence with increasing NP concentration. This calculated excess free energy barrier can be written as ΔFNP = ΔHNP − TΔSNP, so that the slopes in Figure 3a directly provide the magnitude of the excess entropic free energy barrier |ΔSNP| imposed by NPs (ΔSNP is negative). The magnitude of the excess entropic barrier |ΔSNP| monotonically increases 4-fold from 5 to 50 vol. % NP (Figure 3b). Figure 3c depicts |ΔSNP| plotted against the average interparticle distance ⎡ φ 1/3 ⎤ − 1 ID as given by ID = 2RNP⎢ RHS ⎥, where 2RNP is the ⎣ φ ⎦ nanoparticle diameter (28.5 nm); φ is the NP concentration; and φRHS = 0.638 is the maximum packing fraction for randomly distributed hard spheres.40 It is important to note that these PNCs contain a distribution of interparticle distances, and correspondingly, the tracer polymer molecules experience a variety of confining environments during the course of their center-of-mass diffusion. The |ΔSNP| increases as the interparticle distance decreases, suggestive of a confinement-induced configurational entropy barrier to polymer

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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/acsmacrolett.6b00294. Figures SI. 1−SI. 3 and Table SI. 1 (PDF)

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AUTHOR INFORMATION

Corresponding Author

( )

*E-mail: [email protected]. Author Contributions ∥

Co-first authors.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We gratefully acknowledge support from the NSF Materials World Network program (DMR − 1210379). ERD measurements were performed at the University of Pennsylvania’s 738

DOI: 10.1021/acsmacrolett.6b00294 ACS Macro Lett. 2016, 5, 735−739

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Nanoscale Characterization Facility, and we thank D. Yates for assistance with these measurements.

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DOI: 10.1021/acsmacrolett.6b00294 ACS Macro Lett. 2016, 5, 735−739