Constrained and Heterogeneous Dynamics in the Mobile and the

Article pubs.acs.org/Macromolecules

Constrained and Heterogeneous Dynamics in the Mobile and the Rigid Amorphous Fractions of Poly(dimethylsiloxane): A Multifrequency High-Field Electron Paramagnetic Resonance Study Carlo Andrea Massa,† Silvia Pizzanelli,‡ Vasile Bercu,§ Luca Pardi,† and Dino Leporini*,∥,† †

Istituto per i Processi Chimico-Fisici-Consiglio Nazionale delle Ricerche (IPCF-CNR), via G. Moruzzi 1, 56124 Pisa, Italy Istituto di Chimica dei Composti OrganoMetallici-Consiglio Nazionale delle Ricerche (ICCOM-CNR), via G. Moruzzi 1, 56124 Pisa, Italy § Department of Physics, University of Bucharest, Str. Atomistilor 405, Ilfov, RO-077125, Romania ∥ Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy ‡

ABSTRACT: The reorientation of TEMPO spin probe in semicrystalline poly(dimethylsiloxane) (PDMS) is investigated in the temperature range from the glassy region (below 147 K) up to the melt (above about 230 K) by high-field electron paramagnetic resonance (HF-EPR) spectroscopy at two different Larmor frequencies (190 and 285 GHz). The spin probe is confined in the disordered phase. Accurate numerical simulations evidence that the spin probe undergoes activated jump reorientation overcoming an exponential distribution of barrier heightscharacteristic of highly constrained systemsand resulting in a power-law distribution of the reorientation times. Below 180 K the spin probe is coupled to local relaxations and does not sense the glass transition. A strong narrowing of the distribution of the reorientation times and a sudden drop of the mean value are observed at ≃213 K, above the onset of the melting at ≃209 K. Strikingly, it is found that the faster fraction of the spin probes does not sense the melting and couples to the segmental motion of the bulk amorphous PDMS from about 200 K onward. Our findings support the conclusion that the faster and the slower TEMPO molecules are located in (or very close to) the mobile (MAF) and the rigid (RAF) amorphous fractions of PDMS, respectively. The results suggest that MAF is negligible close to the glass transition but it is present above about 200 K, whereas RAF at about 211 K is reduced to about 8% and softens above 213 K, well below the melting transition (≃230 K). Similarities between the disordered phase of semicrystalline PDMS and the PDMS layers in poly(styrene)−PDMS diblock are discussed.

1. INTRODUCTION In a semicrystalline polymer (SCP) the macromolecules pack together in ordered regions called crystallites which are separated by disordered noncrystalline regions.1,2 In fact, due to the severe constraints of the connectivity, ordering in SCPs is often far from complete. The disordered domains are amorphous solids below the glass transition temperature Tg, whereas on heating and crossing Tg, they gain increased mobility and transform into rubbers or viscoelastic liquids. By further heating, crystallites melt. Melting first involves the smallest crystallites, whereas thicker and more ordered ones become unstable at higher temperatures. Above the melting temperature, if the polymeric chains are not cross-linked, molecular flow is possible. Semicrystalline homopolymers are not in equilibrium. This is evidenced by the existence of two phases over a range of temperatures at constant pressure in that in a one-component system, according to the phase rule, the equilibrium between liquid and crystal occurs only at the melting temperature Tm. In the past years it has become clearer that the elementary two-phase modelcrystallites embedded in disordered surroundingsis too crude, and an intermediate interfacial region must be also considered.1,3,4 The presence of an extended © XXXX American Chemical Society

interfacial region is ascribed to the large contour length of the polymer chain (1 μm−1 mm) which may participate in multiple nanophases. Then, macromolecules belonging to the crystallites are anticipated to have also portions in the noncrystalline region, i.e., free ends or inner parts grafted to the same crystallite or joining different ones. The interfacial region is a disordered constrained environment usually referred to as rigid-amorphous fraction (RAF).3 The rest of the noncrystalline region other than RAF is expected to exhibit properties like the completely amorphous bulk polymers and is usually termed as mobile amorphous fraction (MAF). Differently from MAF, RAF does not become liquid-like above Tg. Because of the small density changes between RAF and MAF (expected in disordered structures5), X-ray scattering experiments are little informative about the former, whereas more insight is provided by techniques sensitive to mobility variations like NMR, measurements of the solubility of a gas, and temperature-modulated calorimetry, recently reviewed in ref 4. Polymers which show a RAF are often the stiffer chain Received: August 1, 2014 Revised: September 16, 2014

A

dx.doi.org/10.1021/ma501565z | Macromolecules XXXX, XXX, XXX−XXX

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polymers.6 Nonetheless, RAF has been observed also in one of the most flexible polymers known: poly(dimethylsiloxane) (PDMS).7−10 It was concluded that at the end of the crystallization process MAF disappears and RAF contains all of the uncrystallized chains in PDMS.10 Relaxation processes in SCPs are complicated.8,11−16 One issue concerns the assignment of the process to the amorphous, crystalline, or interfacial regions. From this respect, dielectric relaxation is able to single out the contribution coming from the disordered fraction because the relaxation of dipoles within the crystalline phase is strongly suppressed. However, the suppression reduces the dielectric loss and markedly broadens the dispersion, e.g. see refs 8, 9, and 11, so that the peak center (or αc relaxation time) is determined in highly crystalline polymers with more difficulty.15 In the case of neutron scattering experiments with fully protonated SCPs the total scattering cross section is affected by the strong elastic term due to the crystalline phase.17 In NMR, 1H spin−spin relaxation is often exploited to distinguish the disordered from the crystalline regions, together with 13C isotropic chemical shifts.18 Techniques correlating these shifts to motional-averaged anisotropic interactions, such as 1H−13C dipole−dipole coupling and 13C chemical shift anisotropy, are used to study local chain dynamics in each phase,19 whereas 13C exchange experiments are employed to provide indications of the chain diffusion across the interphase between the two regions.20 Recently, proton low-field NMR experiments based upon the spin diffusion effect suggested a complex arrangement of RAF.21 Transport properties, like diffusion and permeability, are markedly affected by the crystallinity degree of SCPs since the crystallites are very often impermeable even to small molecules which are expelled by the ordered regions during the crystallization.22−25 The confinement of small tracer molecules in the disordered fraction offers the possibility of selective studies of such regions in semicrystalline materials. One viable approach is provided by electron paramagnetic resonance (EPR) which is able to investigate the reorientation of spin probes, such as nitroxide molecules, dissolved in the host matrix of interest at very low concentration (≲1 mM).26 EPR investigations of polymeric materials by using spin probes are widely reported.12,13,27−33 Use of spin probes in semicrystalline materials is reported in ice−water mixtures34−39 whereas, as far as we know, are very sparse in SCPs.40−42 Building on the evidence by high-field electron paramagnetic resonance (HF-EPR) spectroscopy of the accelerated dynamics of the spin probe close to the PDMS melting,42 we investigate the disordered RAF and MAF fractions of well-annealed PDMS by means of HF-EPR spectroscopy at two different Larmor frequencies (190 and 285 GHz). A sketch of the expected location of the spin probes is given in Figure 1. We summarize our major novel results. No signature of the PDMS glass transition is found, thus suggesting thatat least around Tg RAF is larger than MAF, consistent with previous studies10 and in agreement with the calorimetric observation that in slowly cooled PDMS the glass transition is rather weak (e.g., see Figure 5.129 in ref 43). Clear evidence of the strong influence of the melting on the spin probes with slower reorientation is given. The faster spin probes are found to track the segmental motion of the unconstrained, amorphous PDMS from about 9 K below the onset of the melting onward across all the melting region, thus signaling the presence of MAF. Noticeably, our findings are perfectly complementary to what is observed in

Figure 1. Sketch of the location of TEMPO in the MAF (white region) and the RAF (light blue region) close to a crystallite (dark blue region).

polycrystalline ice, where spin probes confined in intergranular water are unable to detect ice melting but reveal the glass transition.37−39

2. HETEROGENEOUS DYNAMICS AND BARRIER DISTRIBUTION The dynamics of the amorphous PDMS between the crystallites is highly heterogeneous and constrained.8,10 In fact, the growth of the crystallites is associated with the transport to the surface of all noncrystallizable chain parts, such as short chain branches, end groups, and entanglements.1 Ideally, there is a mobility gradient from MAF to the more constrained RAF, also due to the intrinsic roughness of the lamellar surfaces.21 The spin probe reorientation in the amorphous PDMS is modeled as a series of activated angular jumps between traps separated by energy barriers with variable height. The distribution of the energy barriers leads to the distribution of the average reorientation times ρ(τ). Two limit forms of the distributions of the barrier heights are envisaged.44 In a liquid-like weakly constrained host, the activation energy may be thought as sum of uncorrelated contributions by the closer neighbors of the spin probe. In this case the central limit theorem ensures the Gaussian distribution of the activation energy. Gaussian barriers in viscous liquids45 and polymers29,46−48 are reported. On the other hand, in a solid-like strongly constrained host the rotation of the spin probes requires some degree of collective rearrangement of the surroundings, involving high energy barriers. The distribution of the highest energy barriers is an example of the so-called extreme-value distributions which are expected to be exponential on universal grounds,49,50 a conclusion supported by the experiments.51−54 In particular, thermoluminescence experiments show that shallow traps in glasses are separated by barriers with Gaussian distribution, whereas the distribution is exponential for deep traps.54 Consistent with the view that the escape process from shallow and deep traps involves Gaussian and exponential barrier distributions, respectively, is the finding that virtually identical spin probes exhibit a Gaussian distribution of the activation energies in the melt of poly(vinyl acetate)29 and an exponential distribution in rigid glassy polystyrene.31,33 The Gaussian and the exponential distributions of the energy barriers yield log-Gauss and power-law distributions of the B


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similar systems.10,62,64,65 The sample was kept about 1 h at each temperature before the measurement. TEMPO has one unpaired electron with spin S = 1/2 subject to hyperfine coupling to 14N nucleus with spin I = 1. For the calculation of the line shapes we used numerical routines described elsewhere.66 Because of the simple isotropic reorientation of TEMPO, the routines are numerically quite efficient even if more advanced simulation techniques are reported.55 The g and hyperfine A tensor interactions were assumed to have the same principal axes. The x-axis is parallel to the N−O bond, the z-axis is parallel to the nitrogen and oxygen 2π orbitals, and the y-axis is perpendicular to the other two. The principal components of the two tensors (gxx, gyy, gzz, Axx, Ayy, and Azz) are input parameters to calculate the EPR line shape. They were carefully measured by simulating the ”powder” spectrum, i.e., that recorded at very low temperature where the line shape is not influenced by the tracer reorientation, and resorting to the constraint 1/3(Axx + Ayy + Azz) = Aiso, with Aiso being the hyperfine splitting of TEMPO in highly mobile PDMS melt at 280 K. Within the uncertainties one finds Axx = Ayy. The best fit magnetic parameters are gxx = 2.0095, gyy = 2.0058, gzz = 2.0017, Axx = 0.47 mT, Ayy = 0.47 mT, and Azz = 3.40 mT. The tracer rotation is assumed to occur by sudden jumps of angular width ϵ0 around isotropically distributed rotation axes after a mean residence time τ* in each orientation. The corresponding average reorientation time τ (the area below the correlation function of the spherical harmonic Y2,0) is τ*/[1 − sin(5ϵ0/2)/(5 sin(ϵ0/2))].67−69 In the presence of jump dynamics, τ* and τ do not differ too much; hence, τ may be identified with the average waiting time before an activated jump takes place.68,69 The theoretical line shape was convoluted with a Gaussian function with a width of 0.1 mT to account for the inhomogeneous broadening. The spectra expected when a distribution of reorientation times ρ(τ) occurs were calculated summing up about 150 spectra characterized by reorientation times in the range 0.003−1000 ns, each spectrum being weighted according to the distribution parameters. The best-fit parameters and related uncertainties were obtained by routine procedures. Only two parameters were adjusted at most, as it will be detailed below.

average reorientation times, respectively. They will be discussed in detail in section 4.2. HF-EPR is more well-suited than the usual X-band EPR to discriminate between different distributions of reorientation times of the spin probes, and therefore of the energy barriers that they overcome. The point is elucidated in the Appendix. Moreover, the resonating magnetic fields in HF-EPR are distributed over a range 1 decade larger than in X-band EPR, allowing a much better resolution of the details of the rotational dynamics.55,56

3. EXPERIMENTAL SECTION 3.1. Sample. PDMS and the paramagnetic tracer 2,2,6,6tetramethyl-1-piperidinyloxy (TEMPO) were purchased from Aldrich and used as received. The choice of TEMPO as spin probe was motivated by several interesting features, namely the small size limiting the host perturbation, the structural stiffness ensuring that the reorientation of the N−O bond tracks the molecular one, and the nearly spherical shape decreasing the number of adjustable parameters accounting for the rotational dynamics with respect to nonspherical radicals. Other spin probes dissolved in PDMS are reported.57 The weight-average molecular weight Mw of PDMS was 90 200 g/mol, and polydispersity, Mw/Mn, was 1.96. The sample was prepared by dissolving TEMPO and PDMS in chloroform according to the solution method.58 Then the solution was heated at about 330 K for 24 h, and no residual chloroform was detected by NMR. TEMPO concentration was less than 0.04 wt %. The sample (about 0.5 cm3) was put in a Teflon holder, which was then placed in a single-pass probe cell. Differential scanning calorimetry (DSC), performed on a Seiko SII ExstarDSC7020 calorimeter at a heating rate of 3 K/min after a cooling scan at the same rate (see Figure 2), gave the following

4. RESULTS AND DISCUSSION 4.1. EPR Line Shapes. Figure 3 shows selected firstderivative HF-EPR spectra of TEMPO in PDMS at 190 and 285 GHz. The spectra markedly change with the temperature above Tg = 147 K, also at temperatures below the melting onset at about 209 K. This is anticipated being TEMPO dissolved in the disordered fraction of PDMS which unfreezes above Tg. As the temperature is increased above Tg, the difference between the resonating magnetic field of the most distant peaks ΔB at 285 GHz decreases and the line width of the peaks increases (see Figure 3), until the features reminding those of the “powder” sample are lost around 210 K. Above that temperature, the motional narrowing of the EPR line shape becomes strong, and a triplet structure starts appearing which sharpens as the temperature is increased. It is observed that the EPR line shape at 190 GHz recorded at 207 K, and more clearly at 210 K, shows a signature of the three-peak structure mentioned above. Differently, the line shape at 285 GHz, even if recorded at the higher temperature 211 K, does not show any hint of the same structure. This is expected in that the higher the frequency, the lesser the motional sensitivity. Instead, at 213 K the line shape at 190 GHz shows a clearer hint of the three-line pattern, and the line shape recorded at 214 K and 285 GHz shows a more marked three-line pattern at the center of the line shape. This is evidence that an abrupt change of the rotational dynamics is occurring around 213 K. 4.2. Dynamical Heterogeneity of the Tracer Reorientation. To gain quantitative information on the spin probe reorientation, we adopt the jump model described in section

Figure 2. DSC thermogram of the PDMS sample.

transitions: glass transition (Tg) at 147 K, cold crystallization at 183 K, and melting onset at about 209 K with endothermic peaks at 228 and 234 K and ΔHm = 32.5 J/g. We remind that cold crystallization is the crystallization occurring above the glass transition upon heating polymers,43 including PDMS.59 By using the literature value of 61.3 J/ g as the perfect heat of fusion for PDMS,60,61 one finds a crystallinity fraction of 0.53. Other studies reported a crystallinity fraction 0.3− 0.4.10,62 3.2. High-Frequency EPR: Experimental and Data Analysis. The EPR experiments were carried out on an ultrawide-band EPR spectrometer, equipped with a phase-locked Gunn-effect diode source, a 12 T maximum-field superconducting magnet, and an enhanced hotelectron bolometer (InSb) as detector operating at liquid helium. More details are given elsewhere.63 The spectrometer frequencies used were 190 and 285 GHz. The sample was cooled in situ from room temperature to 124 K at an average rate of 1 K/min, and spectra were recorded stepwise at increasing temperatures. In these conditions, when the glass transition is reached, crystallization should be complete, according to the crystallization rates reported in the literature for C


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Figure 3. Selected HF-EPR spectra of TEMPO in PDMS at different temperatures using the irradiating frequencies of 285 GHz (left-hand side) and 190 GHz (right-hand side). ΔB is the difference between the resonating magnetic fields of the outermost peaks observed at lower temperatures at 285 GHz.

temperature (not shown) rules out that the jump angle size ϵ0 is large.32 On this basis, with the purpose of limiting the number of adjustable parameters, ϵ0 = 10° is set at all the temperatures at both 285 and 190 GHz. Above Tg the SRT model is poor. This is seen in Figure 5 where the best fit with the SRT model is compared with the experimental HF-EPR line shapes at 285 and 190 GHz. The failure of the SRT model is anticipated in that it misses any detail on the heterogeneous dynamics occurring in the disordered region between the crystallites (see section 2). To improve the SRT model, we considered the HF-EPR line shape L(B0) as a weighted superposition of contributions:

3.2, which depends on the adjustable parameters ϵ0, the jump angular width, and τ, the reorientation time. Initially, dynamical homogeneity is assumed, namely the reorientation of all the TEMPO molecules is accounted for by a single reorientation time. This will be referred to as single reorientation time (SRT) model. The spectra below Tg ∼ 150 K were successfully simulated using the SRT model with jump size ϵ0 = 10°; e.g. see Figure 4 (the small discrepancy between the simulation and the peak at low magnetic field was already noted33). The effectiveness of the SRT model is consistent with the single relaxation process detected by dielectric spectroscopy below 155 K in PDMS.9 On the other hand, at higher temperatures the change of ΔB with

L(B0 ) =

∫0

∞

L(B0 , τ )ρ(τ ) dτ

(1)

where L(B0,τ) is the HF-EPR line shape, τ is the reorientation time, and ρ(τ) is the corresponding distribution. In the presence of dynamical heterogeneity a proper account of the reorientation of TEMPO is provided by the average reorientation time ⟨τ⟩: ⟨τ ⟩ =

∫0

∞

τρ(τ ) dτ

(2)

To avoid numerical issues, the upper limit of the integrals in eqs 1 and 2 has been conveniently set to 1 μs. Motivated by the discussion in section 2, we first considered the log-Gauss distribution (LGD):

Figure 4. Experimental (black line) and simulated (blue short dot line) HF-EPR spectra of TEMPO in PDMS at 124 K and an irradiating frequency of 285 GHz. The simulation was performed using a single reorientation time (SRT model), with dynamic parameters ϵ0 = 10° and τSRT = 165 ns.

ρLGD (τ ) = D

2⎤ ⎡ τ ⎞ ⎥1 1 ⎛ ⎢ exp − 2 ⎜ln ⎟ ⎢⎣ 2σ ⎝ τLGD ⎠ ⎥⎦ τ 2πσ 2

1

(3)


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Figure 5. Experimental HF-EPR spectra at 285 GHz (top) and 190 GHz (bottom) of TEMPO in PDMS at 189 K (black line). The bestfit spectra calculated by using SRT (blue short dot line), LGD (blue short dashed line), and PD (red solid line) models are superimposed. The best-fit parameters at 285 GHz (190 GHz) are τSRT = 12 (15) ns, τLGD = 1.0 (2.1) ns, σ = 1.3 (1.3), and τPD = 0.14 (0.30) ns and x = 0.45 (0.49).

which depends on the two adjustable parameters τLGD and σ. The LGD distribution follows from a Gaussian distribution of barrier heights (see section 2). Figure 5 compares the HF-EPR spectra recorded at 190 and 285 GHz with the best-fit curves in terms of the LGD distribution. The line width of the three outermost lines at high field is overestimated, and deviations are also observed at about 6.782 and 10.172 T at 190 and 285 GHz, respectively. Finally, we considered the power-law distribution (PD): ⎧ 0 if τ < τPD ⎪ ρPD (τ ) = ⎨ ⎪ x −(x + 1) if τ ≥ τPD ⎩ xτPD τ

Figure 6. Experimental (black line) and simulated (red line) HF-EPR spectra of TEMPO in PDMS at different temperatures using an irradiating frequency of 285 GHz (left) and 190 GHz (right). The simulations were performed using PD or SRT model with the following parametes. At 285 GHz starting from 189 up to 259 K, x = 0.45 and τPD = 0.14 ns; x = 0.63 and τPD = 0.10 ns; x = 0.70 and τPD = 0.10 ns; x = 0.75 and τPD = 0.08 ns; τSRT = 0.065 ns; τSRT = 0.007 ns. At 190 GHz starting from 189 up to 259 K, x = 0.49 and τPD = 0.30 ns; x = 0.68 and τPD = 0.20 ns; x = 0.82 and τPD = 0.19 ns; x = 0.86 and τPD = 0.16 ns; x = 0.90 and τPD = 0.15 ns; τSRT = 0.018 ns.

⟨τ⟩ as drawn by the HF-EPR data sets recorded at 190 and 285 GHz by using the PD model. The values of ⟨τ⟩ depend little on the frequency, signaling that the whole distribution of reorientation times is collected by both frequencies. This is confirmed by the missing frequency dependence of the width parameter (Figure 8 b). ⟨τ⟩ decreases slowly as the temperature is increased. For temperatures below 180 K, the TEMPO reorientation is accounted for by the Arrhenius law, with an activation energy of 4.36 ± 0.3 kJ/mol (Figure 8a). A close value, 4.6 kJ/mol, was found for PDMS investigated by quasi-elastic neutron scattering in the range 100−200 K and attributed to CH3 reorientation.47 This suggests a good coupling between the probe and local motions rather than the structural relaxation around Tg, as also evidenced elsewhere.29 No signatures of both the glass transition and the cold crystallization are found. This is in harmony with the calorimetric observation that in slowly cooled PDMS the glass transition is rather weak and cold crystallization is missing (e.g., see Figure 5.129 in ref 43) as well

(4)

with τPD and x indicating the shortest reorientation time and a width parameter, respectively. ρPD follows from an exponential distribution of activation energies (see section 2). Notice that the PD model reduces to the SRT model if x ≫ 1. The PD distribution significantly improves the simulation with respect to the SRT and LGD ones, as shown in Figure 5. A nice agreement was found at other temperatures as well (Figure 6) and led us to the conclusion to adopt the PD model with τPD and x as adjustable parameters of the best-fit procedure. The use of the SRT model at higher temperatures in Figure 6 follows by the fact that ρ(τ) narrows by increasing the temperature. The decreasing difference between the PD and SRT models on increasing the temperature is shown in Figure 7. 4.3. Temperature Dependence of the Average Reorientation Time ⟨τ⟩ and the Distribution Width Parameter. Figure 8a shows the temperature dependence of E


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Figure 7. Experimental (black) and simulated (red solid line and red dashed line for PD and SRT model, respectively) spectra in the region of melting at 285 GHz (left) and 190 GHz (right). Simulation parameters at 285 GHz: at 214 K, τSRT = 0.065 ns; at 211 K, τSRT = 0.15 ns and τPD = 0.08 ns, x = 0.75; at 206 K, τSRT = 0.15 ns and τPD = 0.10 ns, x = 0.70. Simulation parameters at 190 GHz: at 213 K, τSRT = 0.25 ns and τPD = 0.15 ns, x = 0.90; at 210 K, τSRT = 0.25 ns and τPD = 0.16 ns, x = 0.86; at 207 K, τSRT = 0.3 ns and τPD = 0.19 ns, x = 0.82.

as the conclusion that MAF is small around Tg in well-annealed PDMS.10 Note that the absence of signatures of the glass transition cannot be ascribed to the decoupling between the spin probe and the structural relaxation at Tg in that counterexamples are reported68,70,71 which are well understood in terms of the coupling between structural relaxation and the fast dynamics.14,72−74 As anticipated by Figure 3 and the discussion in section 4.1, Figure 8a shows that a steep decrease of ⟨τ⟩ by about 1 order of magnitude takes place at about 213 K, i.e., 4 K above the melting onset. The finding strongly suggests that a significant part of TEMPO molecules is located in or, within a few nanometers, very close to RAF which softens above 213 K. Note that softening occurs well below the melting transition (≃230 K). The temperature dependence of ⟨τ⟩ of TEMPO in PDMS melt is described by an Arrhenius law with activation energy 18.8 ± 0.9 kJ/mol, which is in good agreement with the previous estimate 19.2 kJ/mol gathered by X-band EPR.13 The activation energy is comparable to the one of the PDMS segmental dynamics (14.6 kJ/mol47); i.e., TEMPO is more coupled to the structural relaxation above the melting temperature than around Tg.29 This aspect will be investigated in detail in section 4.4. The temperature dependence of the width parameter x, as drawn by the best-fit procedure, is shown in Figure 8b. The frequency dependence is negligible which suggests that HFEPR at both 190 and 285 GHz gathers information on the overall distribution of reorientation time. The smooth increase of x with the temperature is in qualitative agreement with simple models leading to the PD distribution (eq 4).31,75 Above

Figure 8. Temperature dependence of the average reorientation time ⟨τ⟩ (a) and the width parameter x of the PD distribution (b) of TEMPO in PDMS. The dashed vertical lines mark the glass (≃147 K) and the melting transitions (≃230 K). The gray region highlighths the range of the onset of the PDMS melting (≃209 K). The lowtemperature and the high-temperature straight lines in the upper panel are Arrhenius fits with activation energies 4.36 ± 0.3 and 18.8 ± 0.9 kJ/mol, respectively. Note the large jump of ⟨τ⟩ between 213 and 214 K. For T > 213 K the PD distribution narrows dramatically and reduces to the SRT one. For comparison, the lower panel also plots the width parameter of the distribution of the relaxation times of the PDMS segments within the inner lamellae of the PS−PDMS diblock.9

213 K the width parameter x is large enough that the PD model approaches the SRT limit. 4.4. Localization of TEMPO in PDMS Amorphous Fractions. Representative plots of the PD distribution of the reorientation time ρPD(τ) at different temperatures, as drawn from the best-fit of the HF-EPR line shapes at 285 GHz, are shown in Figure 9. As already noted in Figure 8b, the distribution narrows by increasing the temperature. One interesting feature of Figure 9 is the fact that, even if the width of ρPD(τ) vanishes abruptly at about 214 K, the shortest reorientation time of the distribution τPD approaches smoothly the single reorientation time found at 214 K. Figure 10 characterizes this behavior by plotting the temperature dependence of the shortest reorientation time of the PD distribution. One reminds that the data are collected on heating. On increasing the temperature in the glass transition region, τPD decreases weakly. In this range TEMPO exhibits F


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The best-fit procedure with eq 5 above 200 K is performed by setting the WLF parameters to the PDMS ones, c01 = 1.9, c02 = 222 K, T0 = 303 K,76 and adjusting τ∞ only. The results are in Figure 10. The strong coupling between the α relaxation and the reorientation of the fast fraction of TEMPO is confirmed by noting that at 250 K one finds τα ≃ 31.6 ps10 and the shortest GHz reorientation time of TEMPO is rather comparable (τ190 ≃ PD 285 GHz τα/1.4 and τPD ≃ τα/2.63). The interpretation of the results concerning ⟨τ⟩, the width parameter x (Figure 8), and τPD (Figure 10) is quite straightforward. Below 200 K the amorphous phase is largely constrainedmost probably largely contributed by RAF above Tgthe PDMS dynamics is exceedingly slow, and the TEMPO reorientation decouples from the structural relaxation. A similar decoupling has been already reported in amorphous polymers below ∼1.3Tg.29 On increasing the temperature, at about 200 K the fastest fraction of the spin probes couples to the PDMS segmental motion and reveals the presence of MAF, whereas the slowest fraction is assigned to TEMPO located in (or very close to) RAF (Figure 11). Note that MAF is evidenced about

Figure 9. Representative plots of the power-law distribution of the reorientation times ρPD(τ), eq 4, as drawn by HF-EPR at 285 GHz. The width parameter x and the shortest reorientation time τPD are (x = 0.24, τPD = 0.64 ns), (x = 0.45, τPD = 0.14 ns), and (x = 0.75, τPD = 0.08 ns) at 159, 189, and 211 K, respectively. The vertical dotted line represents the infinitely narrow distribution observed at 214 K, i.e., well above the onset of the PDMS melting at about 209 K. Note: (i) the progressive narrowing of the distribution on increasing the temperature and (ii) the approach of the shortest reorientation time of the distribution to the single reorientation time at 214 K.

Figure 11. Sketch of the power-law distribution of the reorientation times of TEMPO in PDMS between about 200 and 213 K. Above 213 K the width of the distribution vanishes (see Figure 9). Figure 10. Temperature dependence of the shortest reorientation time of the PD distribution τPD as drawn by HF-EPR at 190 and 285 GHz. Above 213 K the PD model is indistinguishable from the SRT model with single reorientation time τSRT. The gray region highlighths the range of the onset of the PDMS melting (∼209 K). The dashed vertical line marks the melting transitions (≃230 K). The red and the blue lines are the best-fit of the data at 190 and 285 GHz, respectively according to the Williams−Landel−Ferry (WLF) equation, eq 5. The WLF parameters are set to the ones of PDMS,76 and the curves are fitted to the data above about 200 K by a vertical shift.

9 K below the melting onset detected by DSC. Since HF-EPR signal is sensitive to the PDMS amorphous part only, whereas DSC thermograms are contributed by all the PDMS sample, it is tempting to ascribe the coupling to the melting of the thinnest lamellae releasing part of the constraints and facilitating the MAF dynamics. On further increasing the temperature above 200 K the fast fraction of TEMPO molecules in MAF accelerates without sensing the melting of PDMS, as expected (Figure 10). Differently, the slow fraction of TEMPO disappears abruptly above 213 K, signaling the softening of RAF. This results in the extreme narrowing of the distribution of reorientation times all collapsing to τPD ≃ τSRT (Figure 9). We stress once again that RAF softens well below the melting transition (≃230 K). It is rather interesting to compare the present results concerning the PDMS homopolymer with the ones concerning a poly(styrene)−poly(dimethylsiloxane) (PS−PDMS) diblock.9 One anticipates that below the glass transition of PS, at the scale of a few nanometers, PDMS segments close to glassy PS blocks and PDMS segments close to PDMS crystallites should not display great differences in their dynamics. In the PS−PDMS diblock in the temperature

activation energies close to the PDMS local motions largely decoupled by the structural relaxation (see section 4.3). Above about 200 K a new dynamical regime becomes apparent. Strikingly, it is seen that the faster fraction of TEMPO molecules tracks the segmental motion of the unconstrained, amorphous PDMS across all the melting region. This is seen by comparing τPD with the Williams−Landel−Ferry (WLF) equation: log

c 0(T − T0) τPD = − 01 τ∞ c 2 + T − T0

(5) G


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assessment of ρ(τ) relies on the accuracy of the best-fit of the line shape by varying the adjustable parameters of ρ(τ) and L(B0,τ). Using larger static magnetic fields improves the reliability of the fit procedure. To appreciate this, let us rewrite L(B0) as

range 149−159 K it is found that9 (i) the inner part of the PDMS lamellae, i.e., the PDMS segments farther from the ones attached to the PS walls, exhibits a mobility gradient resulting in a power distribution of relaxation times and (ii) the minimum time of the distribution corresponds approximately to the relaxation time in pure PDMS. Both results are in close analogy with the TEMPO dynamics above about 200 K and support the conclusion that the rotational mobility of TEMPO correlates with the mobility of PDMS segments between the crystallites. We plotted in Figure 8 the width parameter of the distribution of the relaxation times of the PDMS segments within the inner part of the PDMS lamellae of the PS−PDMS diblock. The smaller width parameter of TEMPO close to Tg suggests that the spin probes experience stronger mobility gradient. This is consistent with our conclusion that a significant fraction of TEMPO molecules must be inside or very close to RAF also at higher temperatures in order to sense the melting. On this basis, if one assumes that the spin probes in RAF have reorientation times at least equal to the RAF relaxation time or longer, an estimate of RAF close to its softening may be given. To this aim, we evaluate the fraction of TEMPO molecules in RAF at 211 Kslightly below the abrupt increase of TEMPO mobility above 213 K (Figure 8)by considering the average 9 XRAF = ∫ ∞ τRAFρPD(τ) dτ with τRAF = 2.4 ns and other data from Figure 9. We find XRAF ≃ 8%.

L(B0 ) = Lf (B0 ) + Ls(B0 )

(6)

with Lf (B0 ) =

∫0

Ls(B0 ) =

∫τ

τ*

L(B0 , τ )ρ(τ ) dτ

(7)

∞

L(B0 , τ )ρ(τ ) dτ (8) * where τ* ≡ 10/γΔB with γ and ΔB the gyromagnetic ratio and the difference between the resonating magnetic fields of the outermost peaks observed at lower temperatures (see Figure 3 for the case of HF-EPR at 285 GHz), respectively. τ* is chosen to approximate L(B0,τ) in Ls(B0) with the “powder” line shape L(B0,∞) (section 3.2) to yield

L(B0 ) ≃ Lf (B0 ) + F∞L(B0 , ∞)

(9)

with F∞ =

∫τ

∞

ρ (τ ) d τ (10) * Equation 9 expresses the line shape as sum of two components, i.e., Lf(B0) and another term with nearly f ixed shape L(B0,∞) and variable amplitude F∞ given by the fraction of reorientation times exceeding τ*. Lf(B0) is restricted to the spin probes with faster reorientation times and contributes to the overall line shape in a narrower B0 range than L(B0,∞) due to the averaging effect of the reorientation (“motional narrowing”).39,55 HF-EPR has larger static magnetic field than Xband EPR. This has three consequences: (i) the B0 range spanned by L(B0,∞) is larger whereas the one of Lf(B0) nearly does not change; furthermore, since τ* shortens, (ii) F∞ increases and (iii) the component due to the slow fraction of spin probes is detectable at shorter reorientation times.55 As a result, the two components are more distinct, and the role of the broader component with f ixed shape increases. The clearer structure of the HF-EPR line shape guides the best-fit procedure and increases the accuracy to discriminate between different choices of ρ(τ). Notice that the approximation given by eq 9 is just presented for discussion and never used otherwise. In particular, the line shape was always calculated via the general expression given eq 1.

5. CONCLUSIONS The reorientation of TEMPO spin probe in semicrystalline PDMS has been investigated by means of HF-EPR spectroscopy at two different Larmor frequencies (190 and 285 GHz). The spin probe is confined in the disordered phase. Accurate numerical simulations evidence that the spin probe undergoes activated jump reorientation overcoming a distribution of barrier heights. An asymmetric, exponential distribution of activation energies is found to fit better the experimental data than a symmetric Gaussian distribution. The former is believed to be an universal feature of systems with highly constrained dynamics and leads to the PD distribution of the TEMPO reorientation times. Below 180 K the spin probe is coupled to local relaxations and does not sense the glass transition. On increasing the temperature, the onset of the melting transition is observed at ≃209 K, and a strong narrowing of the distribution of the TEMPO reorientation times together with a sudden drop of the average reorientation time is observed at ≃214 K. In spite of the abrupt change of the average rotational dynamics, it is found that the faster fraction of the spin probes does not sense the melting and couples to the segmental motion of the bulk amorphous PDMS from about 200 K onward. Our findings are consistent with the conclusion that MAF is negligible around Tg but is present at least above about 200 K, whereas RAF at about 211 K is reduced to about 8% and softens above 213 K. We confirm strong similarities between semicrystalline PDMS and the PDMS layers in PS−PDMS diblock.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Monica Bertoldo for the DSC characterization.

APPENDIX The Appendix discusses why, in the presence of heterogeneous dynamics, HF-EPR draws more accurate information about the distribution of the reorientation times ρ(τ) than the usual Xband EPR. The general expression of the line shape L(B0), eq 1, shows that it is not obvious how to single out ρ(τ) due to the nontrivial τ-dependence of the factor L(B0,τ). Then, the

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Constrained and Heterogeneous Dynamics in the Mobile and the

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