PS Revisited by

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Cite This: Macromolecules XXXX, XXX, XXX−XXX

Molecular Dynamics of the Asymmetric Blend PVME/PS Revisited by Broadband Dielectric and Specific Heat Spectroscopy: Evidence of Multiple Glassy Dynamics Paulina Szymoniak, Sherif Madkour, and Andreas Schönhals* Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany

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S Supporting Information *

ABSTRACT: The molecular mobility of the highly asymmetric miscible blend poly(vinyl methyl ether)/polystyrene was investigated by broadband dielectric (frequency range 10−1−109 Hz) and specific heat spectroscopy (frequency range 101−104 Hz). The dielectric spectra revealed a complex molecular dynamic behavior, where three different relaxation processes were observed. At temperatures below the glass transition temperature an α′-relaxation was found, with an Arrhenius-like temperature dependence of its relaxation rates. It is assigned to localized fluctuations of the confined PVME segments within a frozen glassy matrix dominated by PS. Above the thermal glass transition temperature two processes with a VFT behavior of their relaxation rates were detected called α1- and α2-relaxation, both originating from PVME dipoles fluctuating in PS-rich environments, however with diverse PS concentrations. The relevant length scales for the processes are assumed to be different, corresponding to the Kuhn segment length for the former relaxation and to the CRR for the latter one. The observed multiple glassy dynamics result from spatial local compositional heterogeneities on a microscopic level. Additionally, SHS investigations were performed for the first time for this system, proving an existence of a fourth relaxation process (α3relaxation) due to the cooperative fluctuations of both PS and PVME segments. The separation between the thermal α3relaxation and dielectric α2-relaxation increases dramatically with increasing polystyrene concentration, proving that the thermal response is dominated by PS.

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INTRODUCTION Because of the limited possibilities of synthesizing novel polymers, obtaining new polymeric systems by blending of two already commercialized polymers has been in the focus of extensive research for years. Creating tailor-made materials with unique properties, controlled by the characteristics of the used homopolymers, yet not achievable from the individual components, is important for applications.1,2 Nevertheless, an understanding of the effect of blending on a macroscopic and molecular level remains challenging. Macroscopically, the composition of a miscible binary polymer blend may appear to be homogeneous, which might be confirmed for instance by DSC measurements.3 Typically, for a miscible polymer blend only one broad glass transition region is observed, characterized by one thermal glass transition temperature Tg located in an intermediate temperature range between the glass transition temperatures of the both homopolymers. Investigations of the molecular dynamics could provide insight into the segmental dynamics of the both components, delivering information about the effect of blending on the homopolymers at the molecular level. In general, miscible polymer blends exhibit a complex behavior of the molecular mobility. For a miscible A/B blend the relaxation times of component A (τA) and component B (τB) are affected by the local compositional heterogeneity, present in binary systems on a microscopic level, regardless of the macroscopic homogeneity.4 Microscopic heterogeneity is expressed for polymer blends as © XXXX American Chemical Society

bimodal relaxation times distribution and broadening of the relaxation functions, which can be understood in terms of two theoretical schemes: the self-concentration approach (SC)5,6 and the thermally driven concentration fluctuations (TFC) model.7,8 On the one hand, the former approach assumes that due to chain connectivity the probability that a segment of component A is surrounded by segments of the same kind is higher than the probability that this segment is surrounded by segments of component B. This effect results in different effective local glass transition temperatures, giving rise to two different characteristic time scales for segmental dynamics.9−13 Because the self-concentration effect is related to the chain connectivity, the relevant length scale is the Kuhn segment length,14 which is only weakly temperature dependent. On the other hand, because of the thermally driven concentration fluctuations, polymer blends show a broadening of the relaxation time spectra with respect to that of the both pure homopolymers.15−19 Here, the overall relaxation function is a superposition of different relaxation modes, introduced by a distribution of local compositions. From a theoretical point of view, the TFC model can be understood in terms of the cooperativity model of the glass transition, pioneered by Adam and Gibbs, introducing the cooperatively rearranging region Received: December 20, 2018 Revised: January 22, 2019

A

DOI: 10.1021/acs.macromol.8b02697 Macromolecules XXXX, XXX, XXX−XXX

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polystyrene segments. As discussed below, because of the change in the apparent activation energy, the α′-relaxation exhibits faster dynamics compared to the temperature dependence of the segmental relaxation times of the pure homopolymer. The discussion of the underlying reason proposed by Green disagrees also with the work of the Colmenero group and with the small-angle neutron scattering investigations of Koizumi.43−45 Therefore, a detailed revision of the molecular mobility of the PVME/PS blend is needed. Moreover, a fraction of the data presented in the Supporting Information of ref 36 show a high degree of scatter for higher concentrations of PS and might be not completely reliable. Here, we will address the dissimilarities between the different interpretations available in the literature and provide a systematic study of a PVME/PS blend with seven different compositions, focusing on samples with a high PS content. The molecular dynamics of the blend is discussed covering 10 decades in frequency by dielectric spectroscopy together with a more quantitative data analysis. Moreover, the dielectric data will be compared in detail with results obtained by specific heat spectroscopy. This comparison provides new insights into the dynamical heterogeneity of the PVME/PS blend system.

(CRR) as the smallest spatial region, which can change its configurations independently from its neighbors.20 The size of a CRR grows if temperature is decreased toward the glass transition. In the framework of the fluctuation approach to the glass transition21,22 Donth later showed that the correlation length defining the CRR is larger than the Kuhn segment length (see for instance ref 23). Historically, Katana et al. estimated the size of a CRR first from dielectric measurements on blends.7 It should be noted that a substantial progress in the TFC model was reported in ref 24. It is worth to note that neither the self-concentration nor the TFC model can describe all effects of blending on the molecular dynamics of the blends.4 For instance, the SC approach cannot describe the broadening of the relaxation time spectra, whereas the TFC models results in values that are too large for the size of the CRR at the thermal glass transition temperature. Therefore, attempts have been made to combine both models.32,25 More recently, the self-concentration approach was combined with the theory of Adam and Gibbs.26 This approach was further extended by Cangialosi et al.,27 and the estimated sizes of CRR were found in the range 1−3 nm for a variety of polymers. These values are in agreement with the fluctuation approach to the glass transition by Donth21−28 as well as with more recent theories using approximations of higher order correlation functions.29,30 The dynamic heterogeneity of miscible polymer blends was investigated widely in the literature;4,31−38 however, a complete understanding of the behavior of polymer blends is still missing.4 Here, the highly asymmetric poly(vinyl methyl ether) (PVME)/polystyrene (PS) blend with different concentration ratios of the both components is studied by dielectric and thermal spectroscopy. The asymmetry in the investigated system arises first from the significant differences in the thermal glass transition temperatures of the both homopolymers (ΔTg = 130 K). Second, because of the much higher dipole moment of PVME compared to that of PS, it is possible to study the segmental dynamics of PVME, as it is affected by the PS segments4,15 by dielectric spectroscopy. The PVME/PS blend has been an object of extensive studies4,15,32−41 where the obtained results were sometimes discussed controversially. Recently for this system Green et al. reported by dielectric investigations three distinct relaxation processes, α-, α′-, and α0-relaxation, governed by different local compositions and relaxation mechanisms.35,36 The α-relaxation was related to the glassy dynamics in this system (“typical αrelaxation”). With decreasing temperature, close to the thermal glass transition temperature of the blend, the temperature dependence of the relaxation rates of the α-relaxation seems to change from a one with a higher apparent activation energy to a one with a lower apparent activation energy. This relaxation process is then assigned as α′-relaxation. The α0-relaxation has a stronger temperature dependence of its relaxation rates than the α-process. The molecular origin of the α0-relaxation is not further discussed by Green et al.36 At the first glance these results seem to be in disagreement with the comprehensive studies of Colmenero et al.,4,15,32,33,39,41,42 where only α- and α′-relaxations were found. The assignment of the detected molecular processes differs in the two studies as well. Nevertheless, also a transition in the temperature dependence of relaxation times of the α-relaxation was reported.4,15 This was discussed as a transition of glass-like to confined dynamics due to the immobilization of PVME segments taking place at the thermal glass transition of the blend dominated by

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EXPERIMENTAL SECTION

Materials. Both homopolymers were purchased from Aldrich Inc. PS has a molecular weight (Mw) of 524 kg/mol and a polydispersity index (PI) of 1.04. PVME was obtained as an aqueous solution (50 wt %) with a Mw of 10.455 kg/mol, which is below the entanglement Mw for this material, and a PI of 3. The employed polymers exhibit a large disparity in the molecular weights (1:50-fold). PVME was dried in an oil-free vacuum at 303 K for 72 h and further at 323 K for 96 h. PVME/PS solutions with the compositions of 70/30, 50/50, 40/60, 30/70, 25/75, 15/85, and 10/90 wt % were obtained by dissolving the both homopolymers in toluene (≥99.9%). Sample films were prepared by casting from the solutions in a Petri dish. The samples were dried in an oil-free vacuum for 72 h at 313 K. The blends were further annealed for 72 h at T = Tg,Fox + 45 K in an oil-free vacuum to remove residual solvent. For this annealing procedure a glass transition temperature was estimated according to the Fox equation (Tg,Fox).46 The thermal glass transition temperatures of pure PS, PVME, and the blends were measured by DSC (10 K/min, second heating run) and estimated from the midstep temperature of the heat flow curve in the glass transition region. Values of the obtained glass transition temperatures are given in Table S1 of the Supporting Information. Methods. Broadband Dielectric Spectroscopy (BDS). The complex dielectric function ε*(f) = ε′(f) − iε″(f) was measured in a broad frequency range (10−1−109 Hz). Here, ε′ and ε″ are the real and imaginary (loss) part of the complex dielectric function, f is the frequency, and i = − 1 symbolizes the imaginary unit. In the frequency range from 10−1 to 106 Hz the measurements were performed with a Novocontrol high-resolution dielectric Alpha analyzer with an active sample cell. In the frequency range from 106 to 109 Hz the measurements were performed by a coaxial reflectometer as described in detail in ref 47. In this case the sample is modeled as an integral part of the internal transmission line. An Agilent E4991A RF analyzer was employed as a measuring device. All measurements were performed in parallel plate geometry, where the sample diameters were 20 nm (low-frequency range) and 10 nm (high-frequency range). The capacitors were prepared by melting the sample between the electrodes. The sample thickness was controlled by fused silica spacers with a diameter of 50 μm. For both dielectric setups a Quatro cryosystem (Novocontrol) was used to control the sample temperature, with nitrogen as a heating agent, providing a temperature stability better than 0.1 K. All the measurements were performed in a dry nitrogen atmosphere. It is known that the PVME/PS blend undergoes a phase separation B


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Figure 1. Dielectric loss spectra of the bulk PVME homopolymer (A) and the PVME/PS blend with the composition 25/75 wt % (B) as a function of frequency and temperature, represented in a 3D plot. process at higher temperatures. Therefore, the maximum temperature of the measurements was restricted to a temperature value below the phase separation temperature. Specific Heat Spectroscopy (SHS). SHS was employed in a form of ac-chip calorimetry,48 using the nanocalorimeter chip sensor (XEN 39390, Xensor integrations). The chip consists of a free-standing SiN membrane (thickness 1 μm), supported by a Si frame. In the centrally located heated area of about 30 × 30 μm2 a six-couple thermopile and two four-wire heaters are integrated. A SiO2 layer (thickness 0.5−1 μm) protects the heated area and the thermopile.49 The heat capacity of the empty chip sensor contributes to the measured signal. To minimize this contribution, a differential approach is applied.48 In the approximation of thin films, the heat capacity of the sample Cs is given by

Cs =

iωC̅ 2(ΔU − ΔU0) SP0

the composition of 25/75 wt % is discussed in detail, whereas in the second part the concentration dependence of the relaxation processes is considered. PVME/PS 25/75 wt % as a Showcase. Figure 1A,B represents the dielectric loss spectra as a function of frequency and temperature in a form of a 3D plot for the PVME/PS blend with the composition of 25/75 wt %, in comparison to pure PVME. Figure 1A shows the dielectric response of pure PVME. As expected, one relaxation process is observed corresponding to the α-relaxation or the dynamic glass transition, related to the segmental dynamics of PVME. At lower temperatures the β-relaxation takes place due to localized fluctuations. It is known that this process is not affected by blending.15,42 Therefore, this process is not discussed further here. At higher temperatures than characteristic for the α-relaxation a conductivity contribution is observed as an increase of the dielectric loss with decreasing frequency. Examples for spectra measured in the highfrequency range are given in the Supporting Information (see Figure S1A). As known from the literature, the dielectric behavior of the blend system is quite different from that of homopolymers. First, as depicted in Figure 1B, several relaxation processes are observed, in accordance with literature data.36,39−41,50−55 In the glassy state a broad relaxation process takes place, which shifts to higher frequencies with increasing temperatures. According to the notation of Colmenero et al.,42 it will be called α′-relaxation. Above the thermal glass transition temperature, a main relaxation process becomes active. In difference to pure PVME its intensity increases strongly with increasing temperature. In addition, this peak has a pronounced low-temperature tail. This is further represented in Figure 2, where the dielectric loss of the blend is compared to that of pure PVME at a temperature where both processes have the same maximum position. The relaxation peak observed for the blend has a strong low-frequency tail with an increased relative dielectric loss, in comparison to pure PVME. According to the fluctuation dissipation theorem this increased loss level corresponds to additional molecular fluctuations with lower relaxation rates in the blend, in comparison to pure PVME, due to the spatial heterogeneity in the blend. Interestingly, also a broadening at the highfrequency side of the spectrum is observed, indicating the

(1)

where C̅ = C0 + G/iω describes the effective heat capacity of an empty sensor C0 and G models the heat loss through the surrounding atmosphere. S is the sensitivity of the thermopile, P0 is the applied heating power, ΔU is the complex differential thermopile signal for a sensor with a sample and an empty sensor, and ΔU0 is the complex differential voltage measured of the two empty sensors. Absolute values of Cs can be deduced using calibration techniques. The experiments were performed in the temperature scan mode, where the material response was measured at a fixed frequency with a heating rate of 2 K/min to ensure stationary conditions. The power for temperature modulation was kept constant at ∼25 μW, which ensures the maximum amplitude of the temperature oscillation to be smaller than 0.25 K and thus a linear regime.48 The measurements were performed in a frequency range from 10 to 104 Hz. The samples were placed on the chip sensors under an optical microscope and annealed for 72 h at T = Tg,Fox + 45 K. For the measurements, relatively thick samples are prepared (ca. 1 μm). This means that the influence of preferential adoption effects known for thin films37,38 can be excluded. The maximum temperature of the measurements was restricted to a temperature value below the phase separation temperature.

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RESULTS AND DISCUSSION By dielectric spectroscopy the molecular dynamics is probed by measuring the relaxation times of fluctuating dipoles within the sample as a function of temperature. As discussed above, the dipole moment of PS is much weaker than that of PVME. Therefore, the measured dielectric response is due to fluctuations of PVME segments as affected by PS. The paper is structured in following way: first the PVME/PS blend with C


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single HN equation, as incorrectly stated in ref 36. In that reference the fit was probably accomplished by obtaining unrealistic values for the exponent of the conductivity contribution. For that reason, the values obtained for the relaxation strength Δε should be regarded only as lower bound approximations. To analyze the data in more detail, the spectra are considered in both the frequency domain (dielectric loss versus frequency at constant temperature, isothermal scan) and the temperature domain (dielectric loss versus temperature at constant frequency, isochronal scan) (Figure 3A,B). A similar methodology has been considered in refs 35, 36, and 57. It is worth noting that for homopolymers an identical temperature dependence of the relaxation rates is obtained, regardless whether the analysis of the dielectric spectra is performed in the frequency domain or in the temperature domain.58 This is also true for blends with a low polystyrene content (see Figure S2). Therefore, in most cases the analysis of the dielectric αrelaxation of homopolymers was performed only in the frequency domain. As shown in Figure 3A,B and also in refs 35 and 36 for the PVME/PS blends with higher polystyrene contents the situation is more complex. In cases where multiple processes coexist in the same range of temperatures or frequencies, a combined isothermal and isochronal analysis of the dielectric spectra could provide complementary views on the underlying molecular dynamics. The analysis in the temperature domain amplifies the relaxation process, where relaxation rates have a stronger temperature dependence. Consequently, in the temperature domain slower processes can be detected and separated from faster processes. On the contrary, in the frequency domain, processes with faster relaxation rates are observed. Therefore, a slower process could be submerged or hidden at the low-frequency side of the frequency domain.35,36 It is further worth to note that as discussed in ref 58, the maximum temperature estimated in the temperature domain might also be influenced by the temperature dependence of the dielectric strength. However, keeping in mind that the temperature dependence of the

Figure 2. Dielectric loss versus frequency for pure PVME and the blend with the composition PVME/PS 25/75 wt % at temperatures corresponding to the same maximum position: squares, PVME at 291 K; circles, PVME/PS at 311 K.

existence of faster fluctuations in the blend as well, as compared to pure PVME. In general, dielectric data are analyzed by fitting the Havriliak−Negami (HN) function to the spectra.47,56 The HN function is given by * (ω) = ε∞ + εHN

Δε (1 + (iωτHN)β )γ

(2)

where β and γ are shape parameters (0 < β ≤ 1 and 0 < βγ ≤ 1) describing the symmetric and asymmetric broadening of the dielectric spectra in comparison to the Debye function, Δε denotes the dielectric strength, and τHN is the characteristic relaxation time, related to the maximum position of the dielectric loss spectra (relaxation rate f p = 1/(2πτ). With regard to the data depicted for the blend in Figure 2 one has to note that these spectra cannot be completely described by a

Figure 3. Dielectric loss spectra of PVME/PS 25/75 wt % sample as a function of (A) frequency at fixed temperatures of 243 and 293 K (frequency domain) and (B) temperature at fixed frequencies of log(f p [Hz]) = 1.91 and log( f p [Hz]) = 3.92 (temperature domain). D


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of the PVME homopolymer does not overlap with the processes detected for the blend, even though dielectric measurements are sensitive only to the dipole fluctuations of PVME in the system. The change of the relaxation processes of the blend compared to the pure PVME homopolymer results first from constraining of PVME segments in the blend, when PS segments are present.15,17,60,61 Second, with increasing PS concentration the PVME segments become more and more localized. As discussed above, a variety of processes are observed. Because of the fact that the processes have different position in frequency and temperature domain, they are denoted by different names. As discussed below, currently it is not clear if they are completely independent from each other. For each of them the relaxation rates have a specific temperature dependence. All these processes are related to the spatial heterogeneity of the composition at the nanoscale in the blend system. For further discussion, first we focus on the process observed in the temperature domain (isochronal analysis). Green and co-workers called this process as α0,36 whereas Colmenero et al. assigned it as the α-relaxation.42 For a reason which will become clear below here this process is called α2relaxation. At high temperatures the temperature dependence of the relaxation rates of the α2-relaxation is curved when plotted versus 1/T. In general, such a temperature dependence of the relaxation rates f p is described by the Vogel−Fulcher− Tammann (VFT) equation,62−64 which reads

relaxation takes place at an exponential scale, while that of the dielectric strength is linear, the influence of the latter is of second order. In the isothermal scans (Figure 3A) the relaxation spectra show a single peak. In contrast, isochronal scans (Figure 3B) show one main peak with a shoulder at lower frequencies. As known from the literature,36,57 the peak positions obtained for both domains are different. It is worth to note that the process observed in the frequency domain seems to correspond to the shoulder found in the temperature domain, but it could not be analyzed unambiguously. In principle, the isothermal spectra could be analyzed by fitting a sum of HN functions to the data. Because of the fact that the data show no clear second peak or even a shoulder, such a procedure would lead to highly scattered relaxation rates for the low-frequency process, from which no conclusion can be drawn unambiguously. Alternatively, the complete spectra could be also analyzed by a sum of Debye functions in terms of a spectrum analysis, as discussed in ref 59, which gives probably the most accurate description. In the focus of the following discussion is the estimation of the temperature of the maximum frequency of the relaxation process in the frequency domain, which is hardly influenced by the employed analysis method. To obtain the relaxation rates of the main process in the frequency domain in a simplified way, here the HN function was fitted to the symmetrical part of the peak (γ = 1) including a contribution to the dielectric loss to model the conductivity εcond″ = σ/(ωsε0). For examples of the fit of the HN function to the data, see Figure S1. In the temperature domain a Gaussian was fitted to the data to obtain the maximum temperature of the peak. It should be noted that also a Lorentzian function or a parabola could be used to analyze the isochronal data. However, the concrete employed function is not sensitive to the estimated maximum temperature of the peak. From the obtained relaxation rates f p in frequency domain and from the maximum temperature for the given measurement frequency in temperature domain a relaxation map can be constructed, as shown in Figure 4. As known, the α-process

log fp = log f∞ −

ln(10)DT0 A = log f∞ − T − T0 T − T0

(3)

where f∞ is a pre-exponential factor, A is a constant, and T0 is the so-called Vogel or ideal glass transition temperature, which is found for conventional glass-forming systems below the thermal glass transition temperature. D is the so-called fragility parameter or fragility strength. The fragility parameter can be used to classify glass-forming systems.65 A glass-forming material is called fragile if the temperature dependence is close to the VFT behavior, while a glass-former is classified as strong if the temperature dependence of the relaxations rates is closer to an Arrhenius dependence which is defined as ÄÅ É Å E ÑÑ fp = f∞ expÅÅÅÅ− A ÑÑÑÑ ÅÅÇ RT ÑÑÖ (4) Here, EA symbolizes the activation energy and R is the general gas constant. Close to the glass transition temperature the temperature dependence of the relaxation rates of the α2relaxation changes, and they seem to become independent of temperature. This is not an artifact of the analysis (see Figure S2). A similar behavior can be deduced from the figures given in ref 36. Nevertheless, this change in the temperature dependence is not discussed further there. A derivative method can be used to characterize the temperature dependence of the relaxation rate irrespective of the prefactor.66 For a VFT dependence one obtains ÅÄÅ d log f ÑÉÑ−1/2 ÅÅ pÑ ÑÑ ÅÅ = A−1/2 (T − T0) ÅÅ ÑÑÑ ÅÅÇ dT ÑÑÖ (5) VFT ÅÄÅ d log fp ÑÉÑ−1/2 This means when plotting ÅÅÅÅ dT ÑÑÑÑ versus T, one obtains a ÅÇ ÑÖVFT straight line. From the intersection with zero at the

Figure 4. Relaxation map for pure PVME and PVME/PS 25/75 wt %: α-process of bulk PVME (up-sided triangles), α1- and α-processes (stars), α2-process (squares), and α3-process (circles) of PVME/PS 25/75 wt %. Dashed and dash-dotted lines represent VFT fits to the data, and the solid line indicates an Arrhenius fit to the data. E


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Macromolecules temperature axis the Vogel temperature T0 can be estimated. For the Arrhenius equation also a linear relationship is obtained as well but going to the point of origin ÄÅ É −1/2 ÅÅ d log fp ÑÑÑ−1/2 ij ln(10)R yz ÅÅ ÑÑ zz ÅÅ ÑÑ T = jjj zz j E ÅÅ dT ÑÑ A { ÇÅ ÖÑArrhenius k (6)

there is one process with a low dielectric strength and a low apparent activation energy and a second process at higher temperatures with a higher dielectric strength and higher apparent activation energy. The kink is then produced by the moving in of the second process in the considered frequency window. The observed transition behavior seems to support this latter scenario. The α1-process is assigned to PVME segments relaxing in a PS-rich environment but with a lower PS concentration than process α2. The α1-process has a higher relaxation rate than the α2-relaxation at the same temperature. In a simple scaling picture, it might be concluded the spatial length scale relevant for the α1-process is smaller than that for the α2-process. In a somewhat speculative way the associated length scale for the α1-process might correspond to the Kuhn segment length rather than to the CRR. The inset of Figure 5 compares the VFT dependencies of the α1- and α2-processes. The estimated Vogel temperatures for both processes are different by 16 K, where the value of T0 for the α2-process is higher than that for the α1-relaxation. This is a significant difference and cannot be assigned to the uncertainty of analysis. This proves that molecular origin of both processes is different due to the different spatial heterogeneity involved. Moreover, at high temperatures both processes approach each other (see Figure 4). In the model of thermally driven concentration fluctuations the spatial heterogeneity should become small at high temperatures, and both processes should merge, as is observed. Finally, the apparent activation energy of the α′-relaxation is estimated to be ∼60 kJ/mol. This points to a rather localized process. As discussed by Colemero et al.,42 localization here is due to confining of the PVME segments within the glassy frozen matrix dominated by PS segments. Currently, it is not clear if there is a relationship of α′-process with the α1relaxation or if both processes are completely independent from each other. Figure 6 depicts the temperature dependence of the dielectric strength for the process investigated by isothermal analysis. A complicated temperature dependence of Δεisotherm is observed. At low temperatures below Tg, Δεisotherm(T) increases with increasing temperatures but with different dependencies. At higher temperatures above the glass

The inset of Figure 5 gives the derivative for the α2-relaxation. Indeed, for temperatures above the glass transition temper-

Figure 5. Derivative {d log f isotherm/dT}−1/2 versus temperature for the process obtained by the isothermal analysis. The inset compares the VFT behavior of the α1-process (stars) and the α2-process (squares). Lines are linear regressions to the data.

ature the temperature dependence of the relaxation rates of the α2-process follows the VFT behavior, indicating glassy dynamics. This process is assigned to PVME dipoles fluctuating in an environment with a high PS concentration. The relevant spatial length scale should correspond rather to a kind of CRR than to the Kuhn length. At the thermal glass transition of the blend, the temperature dependence of f p,α2 changes. As discussed above, f p,α 2 seems to become independent of temperature. This behavior cannot be understood in a simple physical manner. The derivative technique is also applied to the relaxation rates of the process observed by isothermal analysis (see Figure 5). From high temperatures down to approximately the glass transition temperature, the data follow the VFT dependence, whereas at low temperatures an Arrhenius-like temperature dependence of the relaxation rates is observed. In the temperature range in between these distinct temperature dependencies, a complicated transition behavior takes place. This change does not look like a simple transition from one temperature dependence to another one, as it is observed for polymers confined in nanoporous glasses67 and polymer segments embed between liquid crystalline structures.68 Here the question arises whether the α′- and the α1-processes are due to the same molecular process, which changes its relaxation rate, as discussed by Colmenero et al.,42 or if the α′- and α1-processes have different molecular origins, as discussed in ref 36. In the latter case, the change in the temperature dependence was considered as an artifact of the fitting procedure arising from the fact that at low temperature

Figure 6. Dielectric strength of the process investigated by isothermal analysis Δεisothern versus temperature. Lines are guides to the eyes. The inset gives the temperature dependence of the shape parameter β. F


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Macromolecules transition temperatures Δεisotherm(T) decreases with further increase of the temperature. It should be noted that generally for low molecular and polymeric glass-formers Δε decreases with increasing temperature for an α-relaxation. In the Debye theory of dielectric relaxation, later modified by Onsager and Kirkwood, the dielectric strength Δε is given by47 Δε =

μ2 N 1 Fg 3ε0 kBT V

Besides dielectric spectroscopy, a complementary technique, SHS, was used to investigate the segmental dynamics of the blend system. One should keep in mind that SHS is sensitive to entropy fluctuations, which result from mobile segments of both PS and PVME, whereas BDS senses dipole fluctuations only of PVME segments. In other words, SHS probes a mean relaxation rate of cooperatively fluctuating PS and PVME segments, while BDS measures relaxation rates of PVME, as it is affected by blending with PS. Consequently, different perspectives of the α-relaxation are accessible by a combination of the two techniques. SHS data for pure PVME measured by ac-chip calorimetry can be found in ref 71, where data for PS are given in ref 72 for instance. Figure 7 depicts the

(7)

where μ2 is the mean-squared dipole moment involved, N/V is the number density of the contributing dipoles, ε0 is the permittivity of a vacuum, and kB is the Boltzmann constant. F is the so-called Onsager factor modeling internal field effects. The Onsager factor is an unspecific parameter and is not further considered in the discussion. g is the Kirkwood/ Frö hlich interaction factor describing static correlation between dipoles. Runt et al.69 derived an equation to model the effect of blending on the g factor in comparison to the unblended state. Experimentally, it was found that the g factor is only weakly affected by blending.69,70 In ref 36, the temperature dependence Δεisotherm is discussed assuming a strong temperature dependence of the g parameter. In light of the experimental results available in the literature (see refs 69 and 70) and also presented here this interpretation seems to be unlikely and probably misleading. It should be recalled that the parameter g was introduced to describe static correlations between dipoles. It is not explained or discussed in ref 36 how blending will lead to an increase of the correlation of the PVME dipoles, where in fact their dilution and isolation is expected, which is more coherent. The dielectric strength of α′-relaxation increases slightly with increasing temperature, as it is expected for a localized process. A similar dependence is also observed for confined polymers.71 For the α1-relaxation the dielectric strength increases strongly with increasing temperature. As discussed above, the α1-relaxation is assigned to PVME segments fluctuation in a PS-rich environment. The PS segments create constraints to the fluctuations of PVME segments or can even cause an immobilization of a part of it (confinement effect). With increasing temperature these constraints and immobilizations will be reduced or removed, leading to an increase in the number density of fluctuating dipoles or to an increase of their fluctuation angle. This release of the confinement leads to the increase of the dielectric strength of the α1-process. At high temperatures, where the spatial heterogeneity becomes small or even negligible, a decrease of Δε1 with further increasing temperature is observed, as it is expected for unconstrained glassy dynamics. The inset of Figure 6 depicts the temperature dependence of the shape parameter βisotherm estimated for the process investigated by isothermal analysis. In the temperature range of the α′-relaxation βisotherm increases slightly with increasing temperature, as it is expected for a localized process. With further temperature increase, in the temperature range of the α1-relaxation, βisotherm increases strongly with temperature. In the sense of a distribution of relaxation times resulting from a distribution of different environments of PVME dipoles due to the dynamic heterogeneity, the increase of the β corresponds to the fact that the dynamic heterogeneity decreases with increasing temperatures as it is expected from the model of thermally driven concentration fluctuations.

Figure 7. Thick black line is the real part UR of the complex differential voltage versus temperature for PVME/PS 25/75 wt % at a frequency of f = 320 Hz. The red line is a sigmoidal fit to the data, and the thin black line corresponds to the first derivative of the fit with respect to temperature.

temperature dependence of the real part of the measured complex differential voltage (f = 320 Hz), which displays a steplike change in the glass transition region. A glass transition temperature can be taken as the temperature of the half stepheight of the UR. To perform an unambiguous analysis, the raw data were fitted with a sigmoidal function, which was further differentiated with respect to temperature, resulting in a peak in dUR/dT. The maxima of this peak correspond to the glass transition temperature at the given frequency. First, it should be noted that the data estimated by SHS are consistent with the DSC measurements where besides the single glass transition temperature the whole width of the heat flow curve is considered, characterized by an onset and endset temperature value (see Figure S11). Second, the estimated data are included in Figure 4 and called α3-relaxation. The α3relaxation is shifted by more than 90 K to higher temperatures in comparison to the dielectric data. This is a further evidence of the spatial and dynamical heterogeneity of the blend system. For the PVME/PS blend system with the composition 25/75 wt % three relaxation processes having a VFT-like temperature dependence, indicating glassy dynamics are observed. This indicates a kind of multiplicity of the glassy dynamics in the considered blend system. Concentration Dependence of the Relaxation Processes. The temperature dependence of the dielectric loss was compared for different compositions of the PVME/PS blend in G


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for low concentrations of polystyrene than for higher ones. From 50 to 75 wt % PS the shift in Tmax,α2 is only 6 K (see also Figure S3). For the PVME/PS samples with compositions 15/ 85 and 10/90 wt % the peak maximum shifts back to lower temperatures, indicating faster dynamics of PVME segments in these systems in comparison to blends with higher PVME concentrations. The whole concentration dependence of Tmax,α2 can be understood as a competition of the slowing down of the fluctuations of the PVME segments by PS and its localization or confinement. For low concentrations of PS (high PVME concentration) the dominating effect is the slowing down, whereas for high concentrations of PS the localization of the PVME segments wins (see also Figure S3). The decreased values of Tmax,α 2 for the both highest concentrations of PS can be regarded as direct manifestation of the localization effect. For all considered compositions the data were analyzed in the same way as described for the sample with the composition PVME/PS 25/75 wt %. The relaxation maps for all compositions are given in the Supporting Information (see Figures S5−S10). For all samples with high PS concentrations (CPVME > 50 wt %) a similar behavior is observed. At low temperatures the α′-relaxation is observed with an Arrheniuslike temperature dependence of its relaxation rates. The apparent activation of this process is between 50 and 60 kJ/ mol and more or less similar for all composition as also discussed in ref 42. This points to an identical molecular origin of this relaxation process. Interestingly the change from the α′to α1-process takes place approximately in the same frequency range. This observation supports the conclusion that the transition from the Arrhenius-like process (α′-process) to the VFT-like temperature dependence of the relaxation rate (α1process) is not due to a confinement effect but probably due to the appearance of the α1-relaxation as a new separate process. For all considered compositions of the blends the temperature dependence of the α1-process follows the VFT equation, as proved by the derivative approach discussed above. Figure 9 depicts the estimated T0,α1 versus the PVME concentration. T0,α2 increases with increasing polystyrene concentration until 50 wt %. This increase is due to the above-discussed immobilization effect. With further increase of the polystyrene concentration T0,α1 decreases moderately until the composition PVME/PS 25/75 wt %. This can be understood in terms of the localization of confinement effect. Above it was discussed that the α1-relaxation corresponds to more localized fluctuation than the α2-process. This line of argumentation agrees with the moderate decrease of T0,α1, while Tmax,α2 of the α2-process still increases (Figure 9) because a less cooperative process should be influenced by the further localization stronger than the more cooperative one. For the two highest concentrations of PS (lowest PVME concentrations) the corresponding T0,α1 values are strongly decreased and do not follow the concentration dependence observed for the higher concentrations of PVME. Again, this is a consequence of the further localization of the PVME segments by PS. In the fragility picture to the glass transition65 this can be also discussed as a transition from a more fragile behavior to a strong one. Figure 10 gives the concentration dependence of the dielectric strength Δεα1 for the α1-process. Because the α1-

Figure 8 (α2-relaxation). Considering that the dynamic heterogeneity is more pronounced at low temperatures and

Figure 8. Dielectric loss spectra obtained from the isochronal scans at 1000 Hz of the pure PVME (black squaress) and PVME/PS blends with various concentrations: 70/30 wt % (red circles), 50/50 wt % (orange triangles), 40/60 wt % (olive stars), 30/70 wt % (green hexagons), 25/75 wt % (dark-blue pentagons), 15/85 wt % (purple rhombuses), and 10/90 wt % (pink down-sided triangles).

frequencies, the spectra for the different concentrations were compared at 1000 Hz. The α2-relaxation of the PVME segments is strongly affected by blending. Increasing PS concentration in the blend results in a decrease of the dielectric intensity of the spectra, as expected. Further, a broadening of the relaxation function due to the concentration fluctuations is observed. PS-richer blends exhibit a broader width of ε″, which is related to a broader distribution of the PVME relaxation times. Moreover, the peak position (Tmax,α2) shows a systematic shift toward higher temperatures up to the composition PVME/PS 25/75 wt %, as compared to the pure PVME, which might indicate only a slowing down of PVME segmental dynamics, due to the presence of PS (see the inset in Figure 9). It is interesting to note that the shift of the maximum temperature with increasing PS concentration is much stronger

Figure 9. Vogel temperature T0,α1 versus the concentration of PVME. Dashed lines are guides for the eyes. The inset shows the concentration dependence of the maximum temperature Tmax,α 2 obtained for 1000 Hz for the α2-process. Dashed lines are guides for the eyes. H


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Macromolecules

shift between the thermal and dielectric data, the difference of the maximum temperature of the α3- and α2-relaxations at 1000 Hz (ΔTα,1000Hz = Tα3 − Tα2) was calculated and plotted versus the concentration of PVME (see Figure 11). For the pure PVME and samples with low PVME contents the shift is in the range 1.4−15 K. However for PS-rich systems the ΔTα,1000Hz increases strongly, up to 120 K. This indicates that the thermal response is due to the combined fluctuations of PVME and PS segments and is dominated by PS for high polystyrene concentrations. This is different for the dielectric response, which is due to PVME segments which are localized for high PS concentrations (see the inset of Figure 9). The inset of Figure 11 depicts the concentration dependence of the maximum temperature of the α3-relaxation taken at 1000 Hz, where a more or less monotonous increase of Tα3 with decreasing PVME is observed. It resembles the concentration dependence of the thermal glass transition temperature.

Figure 10. Δεα1 versus PVME concentration. Lines are guides to the eyes.

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process depends on concentration, the concentration dependence of Δεα1 is not compared at the same temperature but at the same dynamical state, which means at the same relaxation rate. Here a relaxation rate of 104 Hz is selected. With increasing PS concentration Δεα1 decreases. According to eq 7, this behavior is discussed by a decreasing number density of fluctuating PVME dipoles. Like the concentration dependence of the Vogel temperature T0,α1, the concentration dependence of Δεα1 shows a transition in the same concentration range, indicating a change in underlying motional process. In the simplest case Δεα1 can be linearly extrapolated to zero, which reveals a finite concentration of ca. 5 wt %. This means that even at a frequency of 104 Hz maximum 5 wt % of the PVME segments does not contribute to the α1-process and are immobilized by the polystyrene segments. As discussed for PVME/PS with a composition 25/75 wt % only one process was detected by SHS, which is also the case for all other concentrations (α3-relaxation). Figure 11 shows that with increasing polystyrene concentration the separation between the dielectric data (α2-relaxation) and the thermal ones (α3-relaxation) increases dramatically. To quantify the

CONCLUSIONS The molecular dynamics of a highly asymmetric miscible PVME/PS polymer blend with different concentration ratios of the both components was investigated, employing a combination of broadband dielectric and specific heat spectroscopy. Generally miscible polymer blends exhibit a complex molecular dynamic behavior due to the effect of local spatial compositions in the range of nanometers, causing a dynamic heterogeneity. These effects can be discussed by the selfconcentration and thermally driven concentration fluctuation model. Here, the molecular dynamics of the PVME/PS blend with a composition of 25/75 wt % was discussed first as a show case. Considering that PS has a much weaker dipole moment compared to PVME, the molecular fluctuations of the segments of the latter component are probed by BDS. For homopolymers the dielectric loss spectra analyzed in frequency (isothermal) and temperature (isochronal) domain yields an identical temperature dependence of the relaxation rates. However, for PVME/PS blends with high PS content (>50 wt %) the combined isothermal and isochronal analysis provides complementary views on the molecular dynamics. As an example, for the PVME/PS with the composition 25/75 wt % multiple relaxation processes were observed by the dielectric investigations. First, in the temperature domain (isochronal scans) an α2-relaxation was found, which follows a VFT behavior of its relaxation rates, indicating glassy dynamics. This process results from PVME dipoles fluctuating in a PS-rich environment. The relevant length scale for this process is assumed to be rather that of the CRR. Moreover, this process becomes independent of temperature close to the thermal glass transition. Second, in the frequency domain (isothermal scans) a separate process was found, with a complicated temperature dependence of its relaxation rates. At temperatures below the glass transition temperature this process follows an Arrheniuslike behavior, and it is called α′-relaxation. With increasing temperature, approximately above Tg, the temperature dependence of the relaxation times at the first glance seems to change from the Arrhenius-like to a VFT-like. Here the process is called α1-relaxation. A derivative method, based on differentiating the relaxation rates with respect to temperature as well as a detailed analysis of the temperature dependence of the dielectric strength provides an evidence that α1- and α′relaxation are separate processes with probably different molecular origins. The change in the temperature dependence

Figure 11. Difference between the thermal and dielectric relaxation expressed by ΔTα,1000Hz = Tα3 − Tα2 taken at 1000 Hz versus the concentration of PVME. The line is a guide to the eyes. The inset gives the maximum temperature of the α3-relaxation at 1000 Hz versus the PMVE concentration. The solid line is a guide for the eyes where the dashed line is the prediction of the Fox/Flory equation. I


Article

Macromolecules from an Arrhenius to a VFT behavior is rather due to a fitting artifact than induced by a confinement. The α1-process is assigned to PVME segments relaxing in a PS-rich environment, however, with a lower PS content than α2-relaxation. The associated length scale might correspond to the Kuhn segment length rather than to a CRR. The α′-relaxation, with an apparent activation energy of ca. 60 kJ/mol, is a localized process related to the fluctuations of the confined PVME segments within a frozen glassy matrix, dominated by PS. The PVME/PS blend with the composition 25/75 wt % blend was further investigated by SHS, which is sensitive to entropy fluctuations within the system that results from mobile segments of the both components. SHS investigations proved the existence of an α3-relaxation, shifted by more than 90 K to higher temperatures, compared to the dielectric data. The process detected by the specific heat investigations follows a VFT behavior and is further evidence of the spatial and dynamic heterogeneity within the blend, which results in multiple glassy dynamics in the system. The concentration dependence of the relaxation processes was discussed for different compositions of the PVME/PS blend, concentrating on systems with high PS content. As expected, α2-relaxation is strongly affected by blending, showing a decrease of the dielectric loss intensity and broadening, related to a broader distribution of PVME relaxation times, as PS concentration increases. Moreover, the peak position shifts to higher temperatures up to the composition of 25/75 wt %, as compared to the pure PVME, indicating slowing down of the PVME segmental dynamics due to the presence of PS. For the samples with the highest PS content the peak maximum shifts back to lower temperatures, indicating faster dynamics of PVME segments in those systems, in comparison to blends with higher PVME concentrations. The concentration dependence of the α2relaxation is discussed as a competition of the slowing down of PVME segments by PS and their localization or confinement. The α′-relaxation for all samples with high PS content shows an Arrhenius-like temperature dependence with an apparent activation energy of ∼60 kJ/mol for all compositions, pointing to a similar molecular origin of the process. The α1-process shows a VFT-like temperature dependence of its relaxation rates for all considered compositions. Both the Vogel temperature and the dielectric strength dependencies of the α1-relaxation on the blend composition show a decrease with increasing PS content (CPVME < 50%), resulting from the localization or confinement effects on the fluctuations of the PVME segments by PS. SHS proved an existence of a separate process (α3-relaxation) for all considered compositions of the blend. The separation between the thermal α3-relaxation and dielectric α2-relaxation increases dramatically with increasing polystyrene concentration, proving that the thermal response is dominated by PS.

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loss peak maxima dependency on the PVME concentration of the α2-relaxation from the isochronal scans at 1000 Hz, analysis of the dielectric spectra for PVME/PS 70/30 wt % in frequency and temperature domain; relaxation maps for all considered concentrations (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel +49 30/8104-3384; Fax +49 30/8104-1617; e-mail [email protected]. ORCID

Sherif Madkour: 0000-0002-6086-7891 Andreas Schönhals: 0000-0003-4330-9107 Present Address

S.M.: BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We express our sincere gratitude to the German Science Foundation DFG (Grant SCHO 440/20-2 and Research Unit FOR 2021) for financial support.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02697. Glass transition temperatures estimated by DSC measurements, examples for measurements in the highfrequency range, dielectric loss versus temperature for PVME/PS 25/75 wt % at different frequencies, dielectric J


Article

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