Glassy Dynamics of an All-Polymer Nanocomposite Based on

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Glassy Dynamics of an All-Polymer Nanocomposite Based on Polystyrene Single-Chain Nanoparticles Beatriz Robles-Hernań dez,†,‡,# Xavier Monnier,§,# Jose A. Pomposo,∥,†,‡ Marina Gonzalez-Burgos,‡ Daniele Cangialosi,*,‡,§ and Angel Alegría†,‡ †

Departamento de Física de Materiales, University of the Basque Country (UPV/EHU), Apartado 1072, 20080 San Sebastián, Spain Centro de Física de Materiales, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain § Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain ∥ IKERBASQUE-Basque Foundation for Science, María Díaz de Haro 3, E-48013 Bilbao, Spain

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‡

ABSTRACT: We employ broadband dielectric spectroscopy (BDS) and fast scanning calorimetry (FSC) to provide insights on the glassy dynamics of an all-polymer nanocomposite made of linear poly(vinyl methyl ether) (PVME) with dispersed single-chain nanoparticles (SCNPs) based on polystyrene (PS). In doing so we obtain information on both the molecular mobility and the way equilibrium is recovered in the glassy state, the so-called physical aging. Our results show the presence of a PVME matrix with glassy dynamics identical to that of bulk PVME. However, the PVME/SCNPs mixture presents physical aging effects at considerably higher temperatures, as high as 80 K above the glass transition temperature (Tg) of PVME. The connection of these effects with a slow relaxational component detected by BDS, originating from SCNPs enriched by PVME, is highlighted. Accordingly, we conclude that the PVME/SCNPs mixture gives rise to a nanocomposite where the fillers behave similarly to PS-rich blends with PVME. Altogether our results highlight the hybrid nature, between that of a conventional nanocomposite and that of a miscible polymer blend, of the investigated system.

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INTRODUCTION Formulation of polymeric composites1 is a very useful approach to tune material properties starting from already existing materials. In the case of polymer nanocomposites, this approach is often limited by the tendency of the filler nanoparticles to segregate from the polymer matrix. To face this problem, surface treatment of the inorganic fillers is often conducted. In such a way it is possible to obtain satisfactory nanoparticle dispersion into the polymer matrix.2 As a result, a fine-tuning of the resulting material properties can be achieved.3 Concerning the molecular dynamics responsible for the glass transition, the so-called α relaxation, polymer nanocomposites usually present a relatively slow contribution, which has been generally interpreted as originating from polymer chain segments in direct contact with the nanoparticles’ surface.4−14 In addition to this slower component, a main component with properties nearly indistinguishable from those of the neat polymer is generally detected.15,16 Other properties of polymer nanocomposites are very different from those of the neat polymer.17,18 Of particular interest from the application viewpoint is the change in the mechanical behavior of the material provoked by the presence of a relatively small fraction of filler nanoparticles.15 Despite the relatively minor changes in the segmental scale molecular dynamics, also the physical aging behavior,19 that is, the way equilibrium is recovered in the glassy state, of polymer nanocomposites can © XXXX American Chemical Society

be dramatically different from that of the corresponding polymer matrix.20 In particular, for nanocomposites exhibiting strongly interacting polymer/nanoparticles, resulting in a slowdown of segmental dynamics,21,22 the rate of physical aging is found to decrease with increasing nanofiller concentration.21−27 The opposite is observed for nanocomposites with neutral or repulsive polymer/nanofiller interactions,28 though, in such a case, the polymer segmental mobility may be bulklike.29−34 In this case, despite the unchanged segmental dynamics, the presence of noninteracting nanofiller generally manifests in an accelerated physical aging behavior, which has been attributed to the additional surface generated in the system easily accessible for free volume migration.35,36 In recent years, significant effort has been devoted toward the synthesis of what is commonly referred to as single-chain polymer nanoparticles (SCNPs).37 These are polymeric objects obtained through the folding/collapse of individual polymer chains. This generally requires starting from highly diluted linear polymer solutions (below the overlap concentration). By inducing intrachain cross-linking reactions of these linear polymers, one ends up with a system composed by unimolecular entities that can be identified as SCNPs.38−41 For Received: June 18, 2019 Revised: July 26, 2019

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DOI: 10.1021/acs.macromol.9b01257 Macromolecules XXXX, XXX, XXX−XXX

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compared to the corresponding behavior of other nanocomposites. Moreover, we also compare the results obtained for the mixture PVME/SCNPs with those corresponding to an equivalent mixture of PVME with the linear polymer precursor of the SCNP.

their construction, intramolecular cross-linking techniques based on (i) noncovalent, (ii) covalent, and (iii) dynamic covalent bonds have been developed.42−45 These folded/ collapsed soft nano-objects present very promising applications in different fields, including catalysis,39,46,47 sensing,39,48,49 and nanomedicine,39,50−54 among other applications. Obtaining all-polymer nanocomposites by mixing conventional linear polymer chains with SCNPs is one of the recently explored applications of SCNPs. All-polymer nanocomposites consist of materials obtained by incorporating polymeric fillers with nanometric size into a polymer matrix. Examples of this kind of material are those using as filler small polymeric crystals or glassy star-shaped polymers.55−58 All-polymer nanocomposites based on SCNPs were first reported by Mackay and Hawker and their co-workers.59−61 By means of small-angle neutron scattering (SANS) it was shown that the dispersion degree of polystyrene (PS) nanoparticles of different sizes dispersed in linear PS matrices of varying molecular weight was highly satisfactory in the resulting allpolymer nanocomposite. Furthermore, PS-SCNPs were found to be effective in shifting to higher temperatures the phase separation of homogeneous PS/PVME [poly(vinyl methyl ether)] blends.62 More recently, the microscopic dynamics of SCNPs-based nanocomposites have been investigated by neutron spin echo (NSE) experiments. Particularly, nanocomposites formed by mixing single-chain poly(methyl methacrylate) nanoparticles with linear poly(ethylene oxide) showed a spectacular disentanglement of PEO chain motions for the all-polymer nanocomposite containing 25% SCNPs.63−66 Despite these efforts on the microscopic characterization of SCNPs, when they are incorporated as fillers in all-polymer nanocomposites, no systematic study of the specific properties of the resulting materials has been pursued so far. In a very recent work some of us explored the segmental dynamics behavior of mixtures of linear polymer PVME with PS-based SCNPs for various PVME concentrations (75/25, 50/50 and 25/75 wt %).67 The results obtained in this system evidenced profound differences with respect to equivalent mixtures of PVME with the linear precursors of the SCNPs, confirming that the mixtures of linear polymers with SCNPs constitute a new family of materials with properties somehow intermediate between those of polymer blends on the one hand and polymer nanocomposites on the other hand. Thus, a question that remains to be answered is how physical aging in this new kind of nanocomposite compares with that observed in more conventional nanocomposites prepared using inorganic hard nanofillers. In this work, we have addressed this question by investigating the glassy dynamics around the glass transition of a nanocomposite prepared by mixing the linear PVME with 10% wt PS-based SCNPs. To this end we have employed a combination of broadband dielectric spectrosocopy (BDS)68 and fast scanning calorimetry (FSC).69 The former technique allows characterization of the molecular motions of PVME segments in the system with negligible contributions from the SCNPs, since the dielectric relaxation of PS is extremely weak.70 On the other hand, FSC, which is sensitive to both components of the mixture, provides both the time scale of the molecular motions responsible for the glass-transition phenomenon, the so-called α relaxation, and the kinetics of equilibrium recovery of the system during physical aging.19,20 The comparison of both sets of data allowed us to identify the major peculiarities of this all-polymer nanocomposite as

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EXPERIMENTAL SECTION

Materials and Methods. The SCNPs were obtained through intrachain cross-linking of individual polymeric chains (precursors) upon microwave-assisted azide decomposition in DMF solution, following the procedure reported in ref 71. As precursors, linear random copolymers of styrene and 4-(azidomethyl)styrene (AMS), namely, P(S0.7-ran-AMS0.3), were used. The molecular weight (Mw) was 275 kDa with a polydispersity (Mw/Mn) of 1.3. The glasstransition temperature (Tg) of the precursor PS linear chains (Prec) was 366 K, as obtained by differential scanning calorimetry (DSC) on cooling at 10 K/min. PVME with Mw = 60 kDa, Mw/Mn = 1.3 (determined by size-exclusion chromatography, Agilent 1200 GPCSEC) and Tg = 250 K was obtained from Aldrich Chemicals. The investigated nanocomposite containing 10% SCNPs was prepared starting from a dilute solution of the two components in tetrahydrofuran (THF), followed by solution casting to remove THF. Complete solvent evaporation was attained by maintaining the film at 333 K under vacuum conditions for 48 h. This sample is addressed as “90PVME/SCNP” throughout the paper. A sample containing the same composition but with linear precursor chains instead of SCNPs was prepared and investigated in parallel. This blend will be denoted as “90PVME/Prec”. The good dispersion of the SCNP fillers was confirmed by means of atomic force microscopy (AFM). The analysis of the AFM images yielded a typical SCNP size of about 20 nm, in good agreement with results obtained from dilute solutions and in crowded environments.65,72 Here, it is worth noting that, in the range of temperature and for the concentration used in the present work, PVME and PS are miscible.73−75 Furthermore, the presence of SCNPs enhances PVME/PS miscibility.62 Thereby, the presence of a significant amount of PVME in SCNPs must be expected. This is actually the case, as reported in ref 67 and discussed in detail in the Results section. Broadband Dielectric Spectroscopy (BDS). BDS experiments were carried out by using an Alpha-A Novocontrol dielectric analyzer to determine the complex dielectric permittivity [ε*(ω) = ε′(ω) − iε″(ω)] over a frequency range f = (ω/2π) from 10−2 to 106 Hz. Samples were placed between two flat gold-plated electrodes (20 mm diameter) forming a parallel plate capacitor with a 0.1 mm thick spacer of Teflon with negligible area. The temperature was controlled by a nitrogen-jet stream (Novocontrol Quatro temperature controller). Frequency sweeps were performed at constant temperature with a stability better than 0.05 K. The temperature range investigated was 120−350 K. BDS is sensitive to polar moieties, which, in the case of our study, are located in PVME. Furthermore, it is worth noticing that PS-based SCNPs actually contain some minor amounts of polar groups arising from the cross-linking reaction.71 However, as shown in ref 71, this only resulted in the presence of a secondary process, which was attributed to the motion of benzaldehyde pendants. The cross-linking polar group is located in a constrained environment, which prevents the cooperative α process from taking place. Fast Scanning Calorimetry (FSC). FSC experiments were carried out by using the Flash DSC 1 of Mettler Toledo, equipped with an intracooler, allowing temperature control between 183 and 723 K. Samples were directly placed onto the sensitive area of a MultiSTAR UFS 1 MEMS chip sensor with masses ranging from 200 to 350 ng. Prior to use, the calorimetric chips were conditioned and corrected according to standardized procedures. During measurements, a nitrogen flow of 20 mL min−1 was continuously flushed into the cell. Satisfactory thermal contact was ensured thanks to the good wettability of the samples on the chip. Thermal lag correction and temperature calibration were estimated, as described in a previous B


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Macromolecules work,76 resulting in an error of Tf within ±2 K when heating at 1000 K s−1. FSC was exploited to characterize both the molecular mobility and the kinetics of equilibrium recovery in the glassy state. Information regarding the former aspect was attained by determining the frequency (ω)-dependent complex specific heat capacity, Cp* = Cp′ − iCp″or equivalently its modulus, that is, the reversing specific heat, Cp,rev = [(C′p)2 + (C″p )2]0.5employing the step response analysis.77,78 Our protocol for such analysis consists of down-jumps of 2 K at cooling rates of 20, 200, or 2000 K s−1 followed by an isothermal step of duration tp. Prior to the application of such a protocol, the thermal history was erased by holding samples at 413 K for 0.1 s. Finally, the frequency dependence of the complex specific heat capacity is obtained by the ratio of the Fourier transformation of the instantaneous heat flow rate (HF) and the instantaneous cooling rate (βc): t

C*p (ω) =

∫0 p HF(t )e−iωt dt t

∫0 p βc(t )e−iωt dt

(1)

By changing the duration tp, using 0.05, 0.1, 0.5, 1, and 5 s, and accessing higher harmonics, the explored frequency range was between 0.2 and 200 Hz. The kinetics of equilibrium recovery in the glassy state, that is, the so-called “physical aging”,19,20 was investigated by employing the following protocol: (i) the previous thermal history was first erased by holding samples at 413 K for 0.1 s, and (ii) subsequently, samples were cooled down at 1000 K s−1 to a specific aging temperature and held at such a temperature for selected aging times ranging from 10−2 s up to 105 s. Finally, samples were cooled down to 183 K before heating to 413 at 1000 K s−1 for data collection. Reference scans for unaged samples were obtained using the same thermal protocol except for the isothermal step, which in this case was omitted.

Figure 1. Dielectric loss curves at several temperatures above Tg for (a) 90PVME/Prec and (b) 90PVME/SCNP samples.

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RESULTS BDS Characterization. Figure 1 shows a comparison between the dielectric relaxation behavior of 90PVME/Prec (panel a) and 90PVME/SCNP (panel b) mixtures above Tg. We can observe a main loss peak at low frequencies, which corresponds to segmental dynamics (α-relaxation), shifting to higher frequencies with increasing temperature. A qualitative inspection of Figure 1 indicates that, at a given temperature, the maximum of ε″ is located at higher frequencies for the 90PVME/SCNP system than for 90PVME/Prec blend. This indicates that in the former system PVME exhibits faster average segmental dynamics than in the latter. This difference in molecular dynamics is highlighted in Figure 2, which shows a detailed comparison of the dielectric losses at T = 275 K of pure PVME and of the mixtures with the precursor and with the SCNPs, respectively. We can observe clear differences between the two mixtures. The 90PVME/ Prec mixture behaves in a very similar way as the widely studied PVME/PS blends do:70 the segmental dynamics of PVME is clearly affected by blending, the main loss maxima being shifted toward lower frequencies. This indicates an overall slowing down of PVME dynamics induced by the presence of the more rigid precursor chains. Moreover, there is a temperature-dependent symmetric broadening of the peak with respect to PVME homopolymer α-relaxation (see Figure 1a). In contrast, the spectra of the 90PVME/SCNP mixture strongly resembles that of pure PVME, as the width and the position of the maxima of the main loss peak remain essentially unaltered. However, the loss curve of 90PVME/SCNP shows an obvious slower component, as indicated by the presence of excess dielectric loss at frequencies ∼1 Hz. As already reported,

Figure 2. Dielectric spectra at T = 275 K of PVME (red), 90PVME/ Prec (yellow), and 90PVME/SCNP (blue). The dashed line is the fitting curve corresponding to the α-relaxation of pure PVME. The solid black line is the fitting curve obtained by the addition of αrelaxation (blue), an additional slow mode (green), and DC contribution (gray) in the 90PVME/SCNP sample.

the relevance of this component increased for mixtures with higher SCNPs concentration.67 To quantify differences among spectra, we analyzed the BDS data using the Havriliak− Negami equation68 1 Φ*HN(ω) = [1 + (iωτHN)α ]γ (2) where τHN is a characteristic relaxation time, the shape parameters α and γ characterize, respectively, the symmetric and asymmetric broadening of the complex dielectric function, C


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Macromolecules and the condition 0 < α, αβ ≤ 1 holds. We restricted ourselves to the HN-family functions that describe well79 the Laplace transform of the time domain Kohlrausch−Williams−Watts (KWW) functions, which reads as ÄÅ É βÑ ÅÅ ÑÑ t Å ÑÑ. In these cases, the HN and ϕKWW (t ) = expÅÅÅ− τ ÑÑ KWW ÅÇÅ ÑÖÑ KWW shape parameters are related by the following equations:79,80

( )

αγ = β1.23 ÄÅ É ÅÅ τ ÑÑÑ logÅÅÅÅ HN ÑÑÑÑ = 2.6(1 − β )0.5 exp(3β) ÅÅÇ τKWW ÑÑÖ

(3a)

(3b)

The best correspondence between the HN and KWW descriptions is obtained when the following relation between the HN parameters holds: γ ≈ 1 − 0.8121(1 − α)0.387

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Figure 3. Inverse temperature dependence of the characteristic relaxation time for the 90PVME/SCNP sample obtained by BDS (blue and green circles) and by step response analysis in FSC (blue triangle); and for 90PVME/Prec blend obained by BDS (yellow circles) and by FSC (yellow triangles). The solid line corresponds to a description of the data of pure PVME by means of the VFT equation.70

For the analysis of the 90PVME/SCNP data, the functional form and the characteristic time of the main contribution of the α-process can be fixed to those determined from the neatPVME data fitting. Moreover, an additional Cole−Cole function81 (eq 2, γ = 1) is considered to account for the slower relaxation component. Therefore, the loss curve of the 90PVME/SCNP mixtures was fitted using the following equation ε″(ω) = ΔεαϕPVME[xaIm{Φ*α (ω)} + (1 − xa) σ Im{Φ*CC(ω)}] + DC ω

temperature behavior as that of pure PVME. In contrast, the time scale of the slow component is about 3 decades slower over the whole explored temperature range. This behavior is also different from that observed in conventional PVME/PS blends.70 In the case of the blend, the relaxation times corresponding to the components tend to merge as the temperature increases, leading to a narrower loss peak at higher temperatures. This is also the case for the 90PVME/Prec blend of the present work, as can be observed in Figure 3. Fast Scanning Calorimetry. Figure 4 displays a comparison between the normalized reversing specific heat, Norm Cp,rev , of PVME, 90PVME/Prec, and 90PVME/SCNP obtained at 2 Hz by FSC employing the step response

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where ϕPVME = 0.9 is the weight fraction of PVME in the mixture; as a reasonable assumption, the dielectric relaxation strength is fixed to that determined for PVME homopolymer; σDC corresponds to the conductivity; and xa would represent the fraction of PVME segments barely affected by the presence of SCNPs. Solid lines in Figure 2 correspond to the different contributions. The slower component accounts for the relaxation of about 3% of the whole orientational polarization. Considering the content of PS in the all-polymer nanocomposite (10%), this results in a mixture of SCNPs with a PVME weight fraction of ∼30%, as already systematically characterized in a recent publication.67 Thus, the lowerfrequency process observed in the 90PVME/SCNP mixture would be related to the α-relaxation process coming from that 13% of the sample, that is, a mixture rich in SCNPs. The broadening of this slower component is found to increase at higher temperatures, which is contrary to the usual narrowing of the loss peak generally observed in polymer mixtures and, more particularly, in conventional polymer blends, as is also the case here for the 90PVME/Prec blend. The slower relaxation peak broadening on increasing temperature could suggest that there exists a gradient of PVME segments when moving from the SCNP core to the PVME matrix and that this increases at higher temperatures due to a higher SCNPs penetrability. The Arrhenius plot of τmax, that is, that corresponding to the maximum of Φα″ and ΦCC ″ components of the 90PVME/SCNP mixture, is shown in Figure 3, along with the temperature dependence for the PVME homopolymer obtained from ref 70. In line with the ε″ plots shown in Figure 2, the relaxation time of the main process of 90PVME/SCNP exhibits the same

Figure 4. Normalized reversing specific heat as a function of temperature obtained from step response analysis at 2 Hz by FSC for PVME (red), 90PVME/Prec (yellow), and 90PVME/SCNP (blue). The inset shows the normalized reversing specific heat for 90PVME/ SCNP at different frequencies from 0.2 up to 200 Hz. D


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Macromolecules analysis. This was calculated as CNorm p,rev = (Cp,rev − Cp,rev,glass)/ (Cp,rev,melt − Cp,rev,glass), where Cp,rev,glass and Cp,rev,melt are the glass and melt specific heats, respectively, both varying with temperature in an approximately linear way. The inset of Figure 4 shows the same magnitude for 90PVME/SCNP as a showcase at different frequencies. As expected, a shift of the middle point of the CNorm p,rev step toward higher temperatures is observed when the frequency increases. Furthermore, observation of Figure 4 indicates an almost perfect match of Cp,rev of PVME/SCNPs systems with that of pure PVME, implying essentially identical segmental PVME mobility for the two systems, in agreement with the BDS results previously shown. In contrast, the PVME/Prec blend exhibits a ∼3 K shift of the middle point of the CNorm p,rev step, indicating an overall slower dynamics. This is also in line with the dielectric relaxation behavior described in the previous subsection above. However, differently from BDS, no evidence of a slow component of molecular motion is detected in Cp,rev vs temperature plots, likely as a result of its tiny contribution to the overall calorimetric response. Figure 3 shows the values of τ at the temperature of the half-step of CNorm p,rev for each investigated 1 frequency: τ = ω . This figure clearly shows that for neat PVME, FSC and BDS results well superimpose. Moreover, the slowing down of the PVME dynamics in the presence of the linear precursor is also confirmed, with a shift toward longer relaxation times. The overall coincidence in this blend between the dielectric response, basically originating from the more polar PVME component, and the calorimetric one, which also involves the nonpolar component, implies that the concentration of PS is too low to provide a clear difference between the two responses. This is different from what has been recently observed for PVME/PS blends rich in PS, which exhibit considerably slower calorimetric dynamic response with respect to the dielectric one.82 Figure 3 also shows the good agreement between τ values obtained by BDS and FSC regarding the prevalent contribution of PVME dynamics in the presence of the SCNPs. In both cases, such dynamics remains equal to that of pure PVME. The observed analogies between calorimetric results for 90PVME/SCNP and those for pure PVME indicate that thermal fluctuations from SCNP are weak, although they must be present at high temperatures. The presence of such fluctuations can be evidenced from enthalpy recovery experiments. An overview of these experiments is reported in Figure 5, where the calorimetric response at different aging times and temperatures is shown for pure PVME, 90PVME/Prec, and 90PVME/SCNP. Results in Figure 5 are shown in terms of the difference between heat flow rate scans of aged and unaged samples. Several common features can be evidenced: (i) all systems exhibit a main endothermic overshoot in proximity to PVME’s Tg at this high heating rate; (ii) as the aging time increases, the intensity of this peak increases until, at long aging times, all main endothermic peaks collapse on each others; (iii) a minor exothermic undershoot appears at temperatures lower than those relevant for the main endothermic overshoot, indicating that devitrification of aged samples begins at higher temperatures with respect to unaged samples; and (iv) at aging times longer than ∼1 s, the main endothermic peaks of all systems collapse on each other, indicating the achievement of equilibrium. Apart from these general observations, a specific feature is characteristic of 90PVME/SCNP, that is, the presence of a second, higher-

Figure 5. Heat flow rate subtraction curves (aged − unaged) obtained by FSC upon heating at 1000 K s−1 for (a) PVME, (b) 90PVME/ Prec, and (c) 90PVME/SCNP at various aging times for a given aging temperature below Tg.

temperature endothermic broad overshoot showing up after an aging temperature (tag) ∼10 s and exhibiting its maximum at ∼313 K. Such overshoot indicates the presence of glassy dynamics even above PVME’s Tg. This is not detected in standard heating/cooling ramps or in step response experiments as a step in total and reversing specific heat, respectively. Hence, this result shows the potentiality of aging experiments in unveiling glassy dynamics, otherwise undetectable by standard experiments. This potentiality has been recently exploited to characterize the glass transition of the mobile and rigid amorphous fraction in conjugated semicrystalline polymers.83,84 An overview of the amount of recovered enthalpy as a function of aging time is presented in Figure 6. The recovery of enthalpy manifests the following characteristics: (i) pure PVME and 90PVME/Prec show the standard single-step toward equilibrium recovery and (ii) 90PVME/SCNP depicts E


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Figure 7. Inverse temperature dependence of the characteristic equilibration time (τeq) obtained by FSC from physical aging experiments, for neat PVME (red, τeq1), 90PVME/Prec (yellow, τ eq1), and 90PVME/SCNP (blue and green, τ eq1 and τ eq2, respectively). The red solid line is the fit by means of the VFT equation to the τeq1 data of pure PVME. The green solid line is traced by shifting the red solid line by a factor C = 2.9, taken from the FKR equation relating the molecular mobility to nonequilibrium dynamics.

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DISCUSSION The previous section aimed to present a comprehensive study on the molecular mobility and kinetics of equilibrium recovery in the glassy state of an all-polymer nanocomposite of PVME with SCNP (based on PS) as compared with the behavior of pure PVME and that of a mixture of PVME with the linear chain precursor of the SCNP. Although these two aspects of glassy dynamics may be decoupled as, for instance, in some conditions of confinement,85 in the case of our study, we found that these two aspects of glassy dynamics are intimately connected. For the simplest investigated case, that is, pure PVME, both the temperature dependence of the relaxation time (see Figure 3) and that of the equilibration time (see Figure 7) exhibit super-Arrhenius behavior. This can be described by the Vogel−Fulcher−Tammann (VFT) equation86,87 B τ(T ) = τ∞ exp T − T0 (6)

Figure 6. Time evolution of the recovered enthalpy measured at several aging temperatures below Tg for (a) PVME, (b) 90PVME/ Prec, and (c) 90PVME/SCNP. The dashed lines depicted in part c are linear fits to data in the time interval of variation as well as at the plateau. The intersection between both fits gives the equilibration time, τeq.

where τ can be either the α relaxation time (τmax) or the equilibration time (τeq), τ∞ is a pre-exponential factor, B is a material-specific energy constant, and T0 is the Vogel temperature. The red solid line in Figure 3 shows the previously reported VFT behavior describing the dielectric and calorimetric αrelaxation time of PVME, for which log10(τ∞/s) = −13.1, B = 1533 K, and T0 = 201 K. The fit of experimental values of τeq in PVME by the VFT equation (red line in Figure 7) delivers the same values of B and T0, but the pre-exponetial factor in this case is log10(τ∞/s) = −10.2. This result quantitatively demonstrates the intimate connection between the αrelaxation and the time scale to reach equilibrium in the glassy state in PVME and is in line with several reported results showing a one-to-one connection between vitrification kinetics and α-relaxation.88−91 The difference between the two time scales can be quantified from the ratio between τmax and τeq:

a two-step process. For a quantitative analysis of the enthalpy recovery data shown in Figure 6, it is possible to evaluate an equilibration time, τeq. This is done following the procedure schematized in Figure 6c for two particular cases. τeq can be defined as the time where the line marking the enthalpy plateau intersects the line describing the prior logarithmic variation. The so obtained results are shown in Figure 7 in an Arrhenius representation. Observation of the figure indicates that equilibrium for neat PVME is attained at the same time as the first decay of PVME/SCNP, whereas a shift to higher temperature (∼3 K) is observed for the equilibration time of 90PVME/Prec. The slower equilibration step for 90PVME/ SCNP requires a much larger time and its separation from the faster equilibration step increases with the annealing temperature. F


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ji τ (T ) zyz zz = C log10jjjj max j τeq(T ) zz k {

and ∼320 K, where the measured values of τeq only modestly depend on the annealing temperature. Overall, the results obtained along this work point toward the hybrid nature of the PVME/SCNP system, in the sense that this is in between what is typical of a miscible polymer blend and a polymer nanocomposite.55 The former characteristic is evidenced by the glassy dynamical behavior of the SCNP-rich domains, which is found to be intermediate between that of PS and PVME both in the molecular mobility and the kinetics of equilibrium recovery. The nanocomposite nature of PVME/SCNP is evidenced by the existence of welldefined glassy dynamics of PVME matrix basically exhibiting neat PVME behavior. This is a common behavior for polymer nanocomposites with weak interaction with inorganic nanoparticles.20,29,31,34,94 Another aspect that marks the hybrid nature of all-polymer nanocomposites based on SCNP is the presence of nonequilibrium dynamicsassociated with a slow component of segmental mobilitythe effects of which are visible in a temperature range well above the Tg of PVME. These results are indicative of a tremendous shift of the onset of the glass transition on cooling, intended as the onset of nonequilibrium effects,84,95,96 with respect to pure PVME. These are visible at temperatures as large as ∼333 K, whereby in pure PVME these effects disappear above 268 K (see panels a and c of Figure 6). In the context of the effect of nanofillers on glassy dynamics of polymers, this result is especially interesting if one considers that, in the all-polymer nanocomposite of the present study, the interaction between the two components of the nanocomposites is essentially neutral.75 A similar outcome has been shown by molecular dynamics simulations on PS/cross-linked PS all-polymer nanocomposites, which, in ways analogous to the present study, exhibited reduced segmental dynamics in the vicinity of cross-linked PS nanoparticles.97 Conversely, in conventional nanocomposites98−100 and other nanostructured systems with polymer/inorganic interface,101 to observe large positive Tg deviations, an essential requisite is the presence of strong interfacial interactions, such as hydrogen bonding or large degree or adsorption.101,102 When the physical aging results are considered in many polymer nanocomposites with weak interactions, it has been found that the equilibrium recovery kinetics in the nanocomposites presents an accelerated component, which is not present in the all-polymer nanocomposites considered here. This occurs without significant changes in the molecular dynamics of the matrix, something that it is also found here for the SCNP nanocomposite. This is additional evidence of the particular nature of this kind of nanocomposite material.

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This approach is analogous to the so-called Frenkel− Kobeko−Reiner approach,90,92,93 which relates vitrification kinetics, in terms of the cooling-rate-dependent Tg, and the temperature-dependent relaxation time. The temperatureindependent parameter C, which quantifies the separation between τmax and τeq, is equal to 2.9 for PVME, implying almost 3 orders of magnitude separation between the two times scales. Obviously, the obtained value will depend on the particular choice for defining τeq. The same approach can be employed to analyze the data from PVME/Prec and PVME/SCNP. Regarding the former system, we found a behavior completely analogous to that of pure PVME, with the only difference being a slight shift of 0.2 decades toward larger values of both τmax and τeq, thus maintaining the same C value as that of pure PVME. Therefore, in this case the presence of the more rigid linear chains of precursor has an identical impact on both time scales (see Figures 3 and 7). This suggests that the shift factor C can be taken as a polymer-specific parameter. Regarding PVME/ SCNP, we consider the two resolved dielectric α-relaxation components and the two distinct steps observed in the kinetics of equilibrium recovery. The relatively fast dielectric relaxation basically exhibits identical behavior as that of pure PVME. When we apply the same shift factor (C = 2.9) to convert the time scale associated with this relaxation to that of equilibrium recovery, a good description of the fast step in the kinetics of equilibration is found. This allows associating the first equilibration to that part of PVME completely independent from the SCNPs. Concerning the slow dielectric relaxation component, as mentioned in the previous section, it should be attributed to PVME rotational motions taking place in an intimate mixture of PVME with essentially frozen SCNPs. Under this assumption, we can apply the PVME shift factor (C = 2.9) to convert the time scale associated with this relaxation to the corresponding equilibrium recovery time. In doing so, we obtain the green line in Figure 7, which is the VFT fit of data of Figure 3 (green circles) shifted by 2.9 orders of magnitude. Noticeably, such a line accurately describes the experimental τeq values of the slow equilibration step, but only at the three lowest investigated aging temperatures. Contrarily, τeq of the slow equilibration step at higher temperatures exhibits values orders of magnitude larger than those inferred from dielectric relaxation results. This result is not surprising, since dielectric results are not sensitive to the molecular motions in the SCNP except when they are coupled with the PVME units carrying the more significant dipole moment. Moreover, considering the existence of a broad distribution of PVME concentrations in the SNCP, as already discussed in our previous work, the value of the slow dielectric relaxation time is more representative of PVME-rich domains.67 Altogether these findings imply that the last equilibration step at the highest temperatures involves mainly the molecular motion of segments belonging to the SCNP that are not providing a direct dielectric signature. The transition from aging dominated by molecular motions in PVME-rich domains to aging dominated by molecular motions in PVME-poor ones is characterized by a broad crossover, localized between ∼270

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CONCLUSIONS The present work aims to investigate how glassy dynamics of a conventional linear polymer, that is, PVME, is modified by SCNPs based on PS. To do so, we have implemented a complementary approach based on BDS and FSC. Both techniques have been employed to study the molecular mobility in this system. However, while FSC provides information on the overall response of the system, the dielectric response is dominated by PVME, as a result of his much larger dipole moment with respect to PS. Apart from the characterization of the molecular mobility, FSC was also employed to characterize the physical aging of the PVME/ SCNP system in terms of the enthalpy recovered toward equilibrium. G


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Macromolecules

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Our results show the presence of two well-distinguished dynamics in the PVME/SCNP system. One of them exhibits all signatures of pure PVME, including the molecular mobility and the physical aging behavior. Apart from this, a slow component of molecular mobility is detected by BDS, which is attributed to the motion of PVME in intimate contact with the SCNPs. The presence of physical aging effects at temperatures well above PVME’s Tg is attributed to equilibrium recovery taking place in the dispersed phase made of SCNPs and PVME. The overall behavior of PVME/SCNP systems highlights the hybrid nature between those of conventional nanocomposites and miscible polymer blends.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +34 943018806. ORCID

Daniele Cangialosi: 0000-0002-5782-7725 Author Contributions #

B.R.-H. and X.M. contributed equally to this work and are joint first authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS ́ We thank Dr Daniel Martinez-Tong for the AFM studies. We acknowledge financial support from the project PGC2018094548-B-I00 (MICINN-Spain and FEDER-UE) and the project IT-1175-19 (Basque Government).

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