Unexpected PDMS Behavior in Segregated ... - ACS Publications

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Unexpected PDMS Behavior in Segregated Cylindrical and Spherical Nanophases of PS−PDMS Asymmetric Diblock Copolymers Lourdes del Valle-Carrandi,†,‡ Angel Alegría,*,†,‡ Arantxa Arbe,‡ and Juan Colmenero†,‡,§ †

Departamento de Física de Materiales, Universidad del País Vasco (UPV/EHU), Apartado 1072, 20080 San Sebastián, Spain Materials Physics Center (MPC), Centro de Física de Materiales (CSIC-UPV/EHU), Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain § Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain ‡

ABSTRACT: The structure and dynamics of the poly(dimethylsiloxane) (PDMS) segregated nanophase in block copolymers with polystyrene (PS) has been analyzed in detail by combining wide- and small-angle X-ray diffraction, infrared absorption, differential scanning calorimetry, and dielectric relaxation spectroscopy. In particular, we have investigated PS-rich PS−PDMS diblocks where the minority PDMS phase is segregated into cylindrical and spherical regions with diameter in the range 10−20 nm and compared the results with those previously reported on symmetric diblocks with lamellar phases of similar size. It is found that in these highly segregated cylindrical and spherical regions in the copolymers PDMS presents a rather unexpected behavior as probed by X-ray diffraction, infrared absorption, differential scanning calorimetry, and dielectric relaxation spectroscopy. Structural techniques indicate poor packing of the PDMS segments, whereas calorimetric experiments evidence both strong suppression of PDMS crystallization and significant reduction of the glass transition temperature range. Connected with that, the dielectric relaxation probing the PDMS segmental dynamics is much more heterogeneous and markedly faster not only than that observed for PDMS in lamellar nanophases but more strikingly than that of PDMS melt.

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INTRODUCTION Block copolymers offer an attractive route to generate new nanostructured materials because the large variety of structural arrangements they give rise by spontaneous self-assembly into a diversity of mesophases.1−4 Both the structure and size of the domains can be in principle carefully tuned by controlling the molecular weight of each of the blocks and the specific interactions between them and with the substrate. These ordered structures range from spherical, cylindrical, lamellar, to bicontinuous geometries.2,3 For symmetric block copolymers, i.e., when the fraction of the two blocks is similar, the lamellar structure is commonly preferred. However, by decreasing the fraction of one of the blocks, highly curved surfaces are favored, leading to segregated phases of cylindrical or spherical shape where the chains of that block are restricted in two or three dimensions, respectively. Despite the evident interest of the impact of this confinement on the dynamics, most of the attention on the diblock copolymer systems has been focused on the structural features. In addition to the applied interest, the structural arrangements of diblock copolymers can also provide a way to investigate the properties of the components in circumstances that can be very different from those of the bulk material. In particular, the nanometer size of these structures might cause the emergence of confinement-related effects.5,6 Moreover, the interfacial effects7,8 can become prominent because the strong © 2011 American Chemical Society

increase of the surface-to-volume ratio. Results in the literature report on the confinement-related effects on the component chain dynamics.9−21 Particularly, it has been found that the chain dynamics of polyisoprene (PI) in lamellar mesophases formed by PS−PI−PS (PS: polystyrene) triblock is dramatically disturbed.22 On the other hand, the PI chain dynamics in diblocks PI−PDMS (PDMS: polydimethylsiloxane) with micelle-like structures resulted to be speeded-up with respect to that of bulk PI and significantly more heterogeneous.23 In both cases, the fluctuations at the interfaces seemed to play a major role. When considering the segmental dynamics, the number of reported results is also rather limited.11,13,14,16−19,21,24−26 In general, all these studies reported a relatively minor effect of the nanostructure on the component segmental dynamics. This is the case even when the size of the segregated phase is reduced to tens of nanometers. In fact, most of the results have been interpreted as a consequence of the presence of the interface. For example, for triblock PS−PI−PS and diblock PS−PI a small slowing down of the PI segmental dynamics has been detected.22,25 Contrarily, in the PI−PDMS micellar structures it was evident that the PI segmental dynamics is significantly faster than that of the bulk state.23 This latter effect was Received: September 16, 2011 Revised: November 24, 2011 Published: December 12, 2011 491

dx.doi.org/10.1021/ma202107m | Macromolecules 2012, 45, 491−502

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rationalized quantitatively as induced by the high mobility of the fast-moving PDMS chain surrounding the PI micelle core coupled with the presence of interfacial capillary waves. The linear block copolymers based on PS and PDMS chains have been considered as good candidates for both technological applications and model systems.27,28 In this particular system, the two components are highly immiscible and the Flory− Huggins interaction parameter increases on cooling. Thus, the strong segregation limit can be achieved even with moderately molar mass blocks as evidenced in ref 27. The segmental dynamics of PDMS in symmetric diblocks and triblocks with PS was investigated in the past showing a noticeable effect of the nanostructure.16 In particular, it was reported that the PDMS segments attached to the interface present a distinct slower dynamics and there was a gradient of increasing mobility to the bulklike behavior. More recently, molecular dynamics simulations showed that this gradient of mobility occurs essentially at the interface.21 One of the particularities of the PS−PDMS system is the extremely large difference in chain flexibility of the blocks, PDMS being one of the most flexible polymers whereas PS is a relatively stiff one. Although this feature seems to have no remarkable effects in the behavior of PDMS nanosegregated in lamellar phase as in symmetric diblock PS−PDMS copolymers,16 the situation could be different in asymmetric diblocks where the segregated and highly flexible PDMS phase would be completely surrounded by a relatively rigid matrix. In that situation the combination of interfacial tension and packing frustration could imply a higher degree of constrains and therefore might have a profound impact in the segregated PDMS behavior. Noticeably, preliminary results evidenced that in these asymmetric diblocks with highly segregated PDMS phase PDMS crystallization seems to be strongly suppressed.19 In this work, we present new results on the effect of the nanostructure in the PDMS behavior in highly segregated nanophases of PS−PDMS diblock copolymers presenting different mesophase geometries. Particularly, we have investigated PS-rich PS−PDMS diblocks where the minority PDMS phase is segregated into cylindrical and spherical regions with diameters in the range 10−20 nm. It is found that in these highly segregated copolymers PDMS presents a rather unexpected behavior as probed by wide- and small-angle X-ray scattering (WAXS and SAXS), infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), and broadband dielectric relaxation spectroscopy (BDS). In addition to a strong suppression of PDMS crystallization, confirmed by DSC, FTIR, and WAXS, the PDMS segments present a dynamics that is markedly different from that of the bulk melt and much more heterogeneous. Furthermore, the PDMS segments at the interface of these segregated phases seem to be highly constrained, as it was already reported for the symmetric PS−PDMS diblock in lamellar mesophase. These results are interpreted as mainly originated by the packing frustration of the segregated PDMS segments.

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Table 1. Molecular Characteristics of the Copolymers Investigateda product ID

Mn PS (g/mol)

Mn PDMS (g/mol)

Mw/Mn

N

ϕPDMS

χN (room temp)

22PDMS7500 25PDMS4000

30 000 13 500

7500 4000

1.10 1.07

428 184

0.22 0.25

140 66

a

Number-average molecular weights (Mn), polydispersity index (Mw/ Mn), overall degree of polymerization (N), PDMS volume fraction (ϕPDMS),29 and the interblock segregation strength (χN).30

for 12 h in a vacuum oven before heating to 450 K for 2 h in order to allow the complete development of the preferred morphology. Finally, the sample was allowed to cool under vacuum at room temperature. Transmission Electron Microscopy. The measurements were carried out at room temperature by means of a JEOL JEM 1010 transmission electron microscope operating at an acceleration voltage of 100 kV. Samples were prepared on a copper grid (400 mesh) covered only with carbon (purchased from Fedelco). A drop of the previously prepared solutions was deposited, and the excess was removed in order to obtain a thin layer. Then, the thermal treatment mentioned previously was followed. Small-Angle X-ray Scattering (SAXS). For the SAXS characterization of the samples, the same copolymer solution was added drop by drop over Kapton. After that, the same thermal treatment mentioned above was followed, and finally the sample was separated carefully from the support. SAXS diffraction experiments were performed on a Rigaku PSAXS-L equipment operating at 45 kV and 0.88 mA. The MicroMax-002+ X-ray generator system is composed by a microfocus sealed tube source module and an integrated X-ray generator unit which produces Cu Kα transition photons of wavelength λ = 1.54 Å. The flight path and the sample chamber in this equipment are under vacuum. The scattered X-rays are detected on a two-dimensional multiwire detector (2D-200X) of 200 mm diameter active area with ca. 200 μm resolution and converted to onedimensional scattering curves by radial averaging. The scattered intensities are represented as a function of momentum transfer Q, Q = 4πλ−1 sin θ, where θ is half the scattering angle. Reciprocal space calibration was done using silver behenate as standard. The sample-todetector distance was 2 m, covering a Q range from 0.008 to 0.2 Å−1. The measurements as a function of temperature were performed by means of a Linkam Scientific Instruments THMS600 temperature controller. This setup allows measurements in the range from 77 to 873 K with a temperature stability of ±0.1 K. In our case, measurements from 100 to 450 K were carried out in steps of 25 K. The measuring time was 1 h at each temperature. The measurements were corrected (subtraction) for the very low-Q scattering tail likely due to voids and impurities in the samples. Wide-Angle X-ray Scattering (WAXS). The WAXS measurements of the copolymers were carried out by a Bruker D8 Advance diffractometer operating at 30 kV and 20 mA equipped with Cu Kα source and a Vantec-1 PSD detector. The Q range covered was between 0.36 and 2.1 Å−1. A MRI wide range low-temperature chamber was used in order to cover the temperature range from 110 to 300 K. In the case of the reference PDMS homopolymer, we used the Rigaku PSAXS-L equipment supplied with a WAXS image plate chamber. In this case a Q range from approximately 0.7 up to 5 Å−1 was covered. The same temperature control than in the case of the SAXS measurements was used. The PDMS homopolymer that is liquid at room temperature was placed in sealed boron-rich capillaries with an outside diameter of 1 mm and wall thickness of 0.01 mm. Fourier Transform Infrared Spectroscopy. Fourier transform infrared (FTIR) analysis was carried out by means of a JASCO 6500 spectrometer. The measurements were done by using a lowtemperature diamond ATR system (Golden Gate-Specac) purged with nitrogen. The high thermal conductivity provides rather rapid cooling and temperature stabilization. Spectra were obtained by using 50 scans with a 4 cm−1 resolution. The experiments were performed at

EXPERIMENTAL SECTION

Samples. The main characteristics of the copolymers investigated are shown in Table 1. For comparative reasons, measurements were also performed on PS and PDMS homopolymers with similar molecular weight than the respective component of the copolymers. The materials were all purchased from Polymer Source Inc. When preparing the samples for the different setups, the block copolymers and PS homopolymers were solved in toluene with a 4% weight concentration and deposited in the proper holder for each experiment. Then, the samples were heated to 390 K and maintained 492


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room temperature and at 140 K, which is the lowest temperature achieved with our setup. Differential Scanning Calorimetry. The samples were prepared from the copolymer−toluene solutions added drop by drop on a goldplated stainless steel electrode disk of 40 mm diameter used for further dielectric measurements. After the thermal treatment mentioned before, 5−10 mg of sample was taken and encapsulated in an aluminum pan. The DSC measurements were carried out using a Q2000 set up from TA Instruments with a liquid nitrogen cooling system (He gas was used for thermalization). The sample pan was inserted rapidly into the instrument sample holder after temperature stabilization at 100 K. In this way, the cooling rate from room temperature was higher than 100 K/min (sufficient to avoid possible PDMS melt crystallization). The calorimetric results were obtained using a rate of 3 K/min by temperature-modulated experiments, 60 s period and 0.5 K amplitude, during heating from 100 to 400 K, cooling back to 100 K at the same rate, and finally heating again to 400 K. Broadband Dielectric Spectroscopy. Measurements of the complex dielectric permittivity (ε* = ε′ − iε″) vs frequency were performed in the range 10−1−106 Hz, using a Novocontrol highresolution dielectric analyzer (Alpha-N analyzer). As was mentioned above, the sample preparation for calorimetric and dielectric measurements was done simultaneously. An upper electrode of 20 mm was placed on the previously prepared film over the goldcoated disk, and a separation of 100 μm between both electrodes was maintained by using a cross-shaped Teflon spacer of small area. Then, the sample cell was set in a cryostat, and its temperature was controlled via a nitrogen gas jet stream coupled with the Novocontrol Quatro controller. Before the dielectric measurements, the sample cell was quenched in liquid nitrogen to avoid possible crystallization of PDMS during the first cooling. The dielectric experiments were performed isothermally from 120 to 140 K in steps of 5 K, from 140 to 160 K in steps of 2.5 K, from 160 to 180 K in steps of 10 K, and from 180 to 270 K in steps of 10 K. Then, the sample was cooled back to 120 K at a rate of 3 K/min and finally heated again to 270 K with the same steps mentioned for the first heating program.

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Figure 1. TEM micrographs from 22PDMS7500 (upper frame) and 25PDMS4000 (bottom frame). The dark areas correspond to the PDMS-rich phase.

contrary to the TEM case where extremely thin films are imaged, the sample thickness used for these experiments is of the same order than that used afterward for further investigation. The results obtained at 175 K for 22PDMS7500 and 25PDMS4000 samples are shown in Figure 2 as a

RESULTS

TEM. In order to characterize the morphology/nanostructure of the diblock copolymers, we have combined TEM and SAXS measurements. We will start describing TEM results. Figure 1 shows representative images obtained by TEM at room temperature after the thermal treatment of the samples described in the previous section. Patterns typical of phasesegregated block copolymer domains can be clearly seen for both copolymer systems, with dark areas corresponding to PDMS rich regions due to the higher electronic density of the silicon atoms. According to the theoretical phase diagram, from the PDMS volume fractions and the segregation strengths (see Table 1) we would expect cylindrical PDMS phases for both copolymers. However, in the case of the 22PDMS7500 samplethe lowest PDMS volume fractionthe pattern suggests a nanostructure of PDMS spheres, with radii of about 10 nm, embedded in a PS matrix. This result, which will be confirmed by SAXS, is in line with the reported strong skewed toward low styrene volume fractions of the PS−PDMS experimentally determined phase diagram.31 These spheres seem to be ordered in a BCC (bodycentered cubic)-like disturbed lattice. In the case of the 25PDMS4000 sample, the TEM image seems to be more compatible with the expected cylindrical PDMS regions with radii of about 5 nm. SAXS. A better insight into the nanostructure of our diblock copolymers can be obtained by SAXS experiments. Note that

Figure 2. SAXS intensities as a function of the scattering vector for the two diblock copolymers studied here: 22PDMS7500 (red) and 25PDMS4000 (green) at 175 K. The solid lines represent the proposed fits.

representative example. The SAXS intensity of both samples shows both primary and secondary defined peaks at low Q, suggesting ordered structures. A quantitative analysis of the SAXS profiles at the different temperatures was carried out by fitting the experimental curves to analytical expressions for the scattering functions, which contain contributions from both structure and form factors.32 The calculations were done by using the Scatter software developed by S. Förster and L. Apostol [http://www.chemie.uni-hamburg.de/pc/polymer/ software.html].33,34 493


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Figure 3. Fitting parameters, radius (left) and its distribution σ (right), for SAXS experimental data: upper frames 25PDMS4000 and lower frames 22PDMS7500. Insets in (c) and (d) show the temperature variation of the domain size and lattice constant obtained for the 22PDMS7500 copolymer. The vertical bars correspond to the typical estimated uncertainty. The lines are only guides for the eyes.

copolymers. Whereas the radius of the cylinders increases rather moderately and monotonously, the radius of the spheres presents an important increase in a relatively narrow range and becomes essentially constant above room temperature. Noticeably, as far as the average radius increases with temperature, the width of the distribution diminishes accordingly for both copolymers. WAXS. Figure 4a shows the X-ray intensity scattered by the two reference homopolymers, namely PS (Mn = 33 000 g/mol and Mw/Mn = 1.06) coded PS33000 and PDMS (Mn = 7000 g/mol and Mw/Mn = 1.14) coded PDMS7000. In the case of PDMS7000 at 250 K, only one broad peak is mainly visible, centered at about 0.85 Å−1. Based on MD simulations, this peak has been attributed to PDMS intermacromolecular correlations in the liquidlike state with an average interchain distance of z8.4 Å.35 Such an interpretation is supported by the observation of a shift of this peak toward lower Q values with increasing temperature (see the arrow in Figure 4a). At 110 K, sharp peaks evidence the crystalline structure of this sample. In the case of the PS33000 homopolymer, the diffraction pattern reveals a broad peak centered at around 1.4 Å−1. The position of this peak does not vary with temperature, hinting its intramolecular character. MD simulations point also to this origin and show that it is predominantly controlled by the relative position of phenyl rings.36−38 The increasing intensity at low Q of the PS33000 diffraction pattern is due to the presence of a low-Q peak centered at Qmax ≈ 0.5 Å−1, likely reflecting intermolecular distances either between phenyl rings or main-chain atoms.37 The WAXS intensities corresponding to the two copolymers are shown in Figure 4b,c. At room temperature two main peaks are evident for the two copolymers. By direct comparison with the homopolymer intensities (Figure 4a), we can attribute the peak at Q ∼ 0.85 Å−1 in the copolymers to the intermolecular correlations of PDMS in the segregated PDMS phases. It appears at the same Q value as the corresponding peak of pure PDMS, and in addition, the PS X-ray diffraction curve does not

In the case of the 22PDMS7500 copolymer, the best simple model results to be a nanostructure of PDMS spheres ordered in a BCC lattice, in agreement with TEM observations. The SAXS data corresponding to the sample 25PDMS4000 were well described with a simple model of cylinders of PDMS in a HCP (hexagonally close packing) lattice, also in agreement with the features observed by TEM. The disorder scattering was taken into account by considering a Gaussian displacement from the ideal lattice point distribution33 with zero average and relative mean-squared value of 2 nm. The fitting curves corresponding to 175 K are shown in Figure 2 as an example. The temperature dependence of the parameters characterizing the PDMS nanosegregated phase, namely the radius of the sphere/cylinder and its relative standard deviation, σ, are depicted in Figure 3a−d. When fitting the SAXS patterns for the 25PDMS4000, it was possible to keep constant the domain size (90 nm), length of the cylinders (300 nm), and lattice constant (22.9 nm) for the full range of temperatures investigated. Contrary, for the 22PDMS7500 copolymer, the required lattice constant and domain size are temperature dependent (see insets in Figure 3c,d). It is worthy of remark that the values of the radii obtained at room temperature (5.9 nm for 25PDMS4000 sample and 13 nm for 22PDMS7500 sample) agree rather well with those estimated from those TEM micrographs. Moreover, the rather pronounced distortion of the BCC lattice observed by TEM is also consistent with a relatively small domain size as obtained from SAXS in the case of the 22PDMS7500 sample. This feature becomes more pronounced at lower temperatures. Figure 3 shows that in the low-temperature range below about 200 K the main structural parameters corresponding to both copolymers tend to a plateau value, indicating that the nanostructural features are essentially temperature independent in this range. It is noteworthy that this is the range of the dynamics studies carried out by us (see below). However, at higher temperatures systematic changes are apparent in both 494


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components at 250 K, properly weighted. A rather dramatic difference is observed when the diffraction curves measured for the two samples at the same temperature are compared with the so calculated ones. The peak maximum characteristic of the PDMS interchain distances is located at distinctly lower Q values for both copolymers. Furthermore, the peaks in the copolymers are poorly defined, which suggests that the PDMS local order in the copolymers is considerably lost. Noticeably, the PDMS peak intensity of the copolymer with cylindrical morphology (25PDMS4000) is smaller than that of the copolymer with spherical morphology despite the larger PDMS content. The WAXS results at 250 K can be interpreted as due to the fact that PDMS segments in the copolymers reach a poor packing level. At room temperature the maximum of this peak in all the samples, as well as in the reference one, is slightly shifted toward lower Q values without much change of intensity and shape, which would just be indicative of expansion on heating. At the lowest temperature (110 K), Figure 4b,c shows that no peak signature of crystalline PDMS is observed in the copolymers where the PDMS is nanosegregated in spheres or cylinders. Here the crystallization seems to be frustrated. Even at 110 K the broad peak characteristic of the amorphous state remains and is located at much smaller Q values than the crystalline diffraction peak of PDMS, which again indicates a poor packing level. Surprisingly, the peak position is not strongly affected by decreasing the temperature from 250 to 110 K (i.e., a 140 K jump). All this clearly evidences the presence of constraints imposed by the rigid PS matrix in the segregated PDMS spheres and cylinders that likely prevents the expected PDMS densification. FTIR. The vibrational properties of PDMS in the copolymers were studied by FTIR as a complementary technique. Analyzing both PS33000 and PDMS7000 homopolymers, we concluded that the region where the Si−O−Si asymmetric stretching bands are located (940−1140 cm−1) could be suitable for selectively characterize PDMS because only two weak bands from PS appear, namely around 1068 and 1028 cm−1 (see Figure 5a). Then, for the study of these PS−PDMS diblock copolymers the Si−O−Si asymmetric stretching bands will be analyzed in detail. In Figure 5b, the results obtained for the two diblock copolymers under study are depicted. The vertical lines represent the position of the two main peaks of the PDMS homopolymer at around 1011 and 1083 cm−1. At room temperature, the spectra observed in the 22PDMS7500 and 25PDMS4000 samples are rather similar to each other. The positions of the maxima of their absorption peaks match almost perfectly among them and are close to those observed in the PDMS homopolymer. Nevertheless, the shape of the whole band is different from that observed in the homopolymer; for example, the two prominent peaks present some kind of shoulder at around 1020 and 1065 cm−1 that, however, might be related to the contributions expected from weak PS vibration bands mentioned before. For PDMS homopolymer at low temperature, which has crystallized, the high wavenumber peak becomes better defined, without detectable changes in the two main peak frequencies. Contrarily, for the two copolymers the intensities of both peaks increase at low temperature, and both experience a noticeable red shift. The previous results can be more quantitatively examined by performing a band analysis based on a description in terms of a few sub-bands. By this approach the PS absorption is well accounted for with only two Gaussian sub-bands at 1068.8 and

Figure 4. WAXS curves for (a) PDMS7000 (solid line at 250 K, dotted line at 110 K) and PS33000 at 250 K (dashed line), (b) 25PDMS4000, and (c) 22PDMS7500. In (b) and (c) the experimental data are shown as a dashed line at room temperature, as a solid line at 250 K, and as a dotted line at 110 K. The vertical arrows represent the position of the peaks for the PDMS7000 homopolymer at 300 K (dashed arrows), 250 K (full arrows), and 110 K (dotted arrows). Dashed-dotted lines are the expected result of a simple superposition from the homopolymer WAXS curves at 250 K (shifted down vertically for clarity).

show any peak in this Q range. Just for comparison, and underlining the intermacromolecular character of this peak, we have included in Figure 4b,c as vertical lines, the position of the peak of pure PDMS for different temperatures. On the other hand, the main peak at about 1.4 Å−1 in the copolymers must be dominated by the intramolecular phenyl−phenyl correlations of the PS phase above-described, and the increasing intensity toward lower Q values can be assigned to the intermolecular PS low-Q peak. The dashed lines in Figure 4b,c correspond to the patterns obtained by simple addition of the diffraction curves of the two 495


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analysis of these features is out of the scope of the present work. When considering the output of the fitting procedure followed in the copolymers, at room temperature the obtained PDMS subbands positions for 22PDMS7500 and 25PDMS4000 are 1089.3, 1040.8, and 1009.9 cm−1, with relative areas around 25%, 53%, and 22%, respectively, and 1089.7, 1042.3, and 1010.8 cm−1, with relative areas around 23%, 55%, and 22%, respectively. By comparing these values with those from pure PDMS, a remarkable blue shift of the central (hidden) sub-band is very apparent. Furthermore, this sub-band is further blue-shifted to 1050 when fitting the low-temperature data. Noticeably, the shape of the whole band at low temperature is not much different from that at high temperature, which is in marked contrast with the evident changes associated with PDMS crystallization. This result is in agreement with the strong crystallization suppression detected by WAXS in the copolymers. Particularly, any significant narrowing of the sub-band centered around 1087 cm−1 is detected in the copolymers, this precise sub-band being clearly narrower in crystallized PDMS. DSC. DSC measurements provide insight into the thermodynamical behavior of the copolymers studied here. In Figure 6a,

Figure 5. FTIR spectra of the reference polymers (a) and copolymers (b): PDMS7000 (open squares at room temperature, solid squares at 140 K), PS33000 at room temperature (diamonds), 22PDMS7500 (open triangles at room temperature, filled triangles at 140 K), and 25PDMS4000 (open circles at room temperature, filled circles at 140 K). Intensities of the copolymers are scaled to match at 1100 cm−1. The vertical lines represent the peak position of the reference PDMS. The solid thin lines correspond to the fitting according with Gaussian subbands superposition. The dashed thin lines in (a) correspond to the Gaussian PDMS components at room temperature.

1027.4 cm−1 with relative areas of 35% and 65%, respectively. For PDMS, three Gaussian sub-bands at 1086.7, 1029.7, and 1008.0 cm−1 with relative areas of 26%. 55%, and 19% are required at room temperature. It is worth mentioning that the central sub-band is somehow hidden but accounts for most of the IR absorption. Upon crystallization, at the lowest temperature there are minor changes in relative areas and sub-band positions: namely, sub-bands move to 1085.7, 1025.4, and 1008.9 cm−1, respectively, with areas 29%, 57%, and 17%. Since the whole band transforms clearly, the changes in width of the sub-bands is the major effect, particularly the sub-band at around 1086 cm−1 becomes notably narrower. A rather good description of the absorption band is obtained for the two copolymers (see Figure 5b) by simply maintaining the characteristics of the two PS sub-bands and allowing those of PDMS to change. However, the resulting line is not able to capture the details, and particularly it does not account for the shoulders appearing close to the PS sub-band positions. All this suggests that these features are characteristics of the PDMS vibrations and particularly could be related with the chain segments anchorage to the PS interface. However, a more detail

Figure 6. DSC scans during (a) the cooling and (b) heating runs after being rapidly (solid lines) and slowly cooled (dashed lines) for the copolymers and the reference PDMS7000 homopolymer. The vertical lines correspond to the Tg values of linear PS39 with the same molecular weight than that of the PS blocks. The inset in (b) represents the nonreversing signal during the first heating run. 496


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WAXS or FTIR experiments. Furthermore, SAXS patterns did not show any additional reflections when decreasing temperature as it is actually found in crystallized PDMS.42 On the other hand, the quantification of the Cp jump at Tg could provide additional insights. When the value from amorphous PDMS is considered and the “dilution effect” is taken into account, the comparison with the Cp jump in the copolymers evidence a reduction of about 7% for the 22PDMS7500 copolymer and of about 22% for 25PDMS4000. This detectable Cp jump reduction would be due, at least in part, to the significant reduction of the rotational degrees of freedom of the PDMS segments anchorage to the PS interface. The larger reduction found in the 25PDMS4000 copolymer would be naturally explained by the shorter PDMS chains. The fact that the Cp jump remains essentially the same for the samples quenched into liquid nitrogen and those cooled down at a moderate rate again indicates that, if any, the possible crystallinity in the PDMS segregated phase has to be small. Broadband Dielectric Spectroscopy. The dielectric relaxation techniques allowed studying selectively the PDMS segmental dynamics within the diblock PS−PDMS copolymers since PDMS is the component contributing more to the dielectric relaxation, the PS relaxation strength being very weak. Furthermore, the contribution of PS to the dielectric losses in the temperature range relevant for PDMS is completely negligible. On the other hand, close to the Tg of the PS phase, the sample conductivity prevents a detailed analysis of the weak dielectric relaxation associated with PS. The dielectric behavior of the corresponding PDMS homopolymer with a chain length similar to that of the PDMS sequence in the diblocks will also be considered. In PDMS dielectric loss spectra, only the segmental motions (α-process) are observed, and no significant secondary relaxation processes can be detected.42 The dielectric experiments on the copolymers after being fast cooled to the lowest temperature showed time-dependent results (mainly for 25PDMS4000) which, together to what was shown in the DSC scans of Figure 6b, suggest that the copolymer samples are in a highly unstable state when fast cooled. This was not the case for the samples cooled down at 3 K/min where well reproducible results were obtained. So we considered more reliable to analyze the dielectric loss of the copolymers in this latter situation. Moreover, this is the structural state characterized by SAXS, WAXS, and FTIR. Figure 7 shows the dielectric losses as recorded isothermally on the copolymers after being cooled at a rate of 3 K/min in the dielectric cell. For comparative reasons we have also included previously reported results from a symmetric PS−PDMS diblock copolymer with a lamellar nanostructure,16 here coded 53PDMS11600 (Figure 7c). All ε″ values were normalized according to the high-frequency permittivity ε∞ (around 2.7 for all samples), which was taken as the value of the ε′ component at high frequency (1 MHz) and low temperature (120 K). In this way, the effect of small uncertainties in sample geometry on the signal (loss intensity) is minimized. In Figure 7a−c a prominent relaxation process is observed within the probed frequency window at temperatures between 145 and 160 K, which is straightforwardly related to the segmental mobility of PDMS component. The dielectric losses in the copolymers are broader than those observed in amorphous PDMS. However, this effect is much more dramatic for the two copolymers with cylindrical and spherical PDMS nanophases than that previously reported for the symmetric copolymer with PDMS lamellar nanophase.

we present the heat flow during a cooling run at 3 K/min. The step at high temperatures in the data of the copolymers corresponds to the glass-transition temperature Tg of the PS phase. In both cases this Tg step is very visibledue to the high weight content of the PS componentand located at distinctly lower temperatures than linear PS with the same molecular mass than the PS block (see vertical lines39), in agreement with earlier literature results.40 This suggests that the presence of the PDMS segregated phase in the copolymer causes a small plasticization effect on the PS matrix. The presence of a large interface associated with the segregated PDMS phase could also play a significant role.41 One additional remarkable feature observed in this cooling run is the presence of exothermic peaks. In pure PDMS a very prominent exothermic peak in the range 200−215 K reflects the PDMS crystallization, taking place during cooling at moderate rates. The copolymers present a rather small exothermic peak, taking place at about 230 K for 22PDMS7500 and at about 160 K for 25PDMS4000. These features might be attributed to a crystallization process in the PDMS phase, but considering the WAXS and FTIR results mentioned before where no signatures of PDMS crystallization were present, the situation is unclear. By quantifying the energy of the exothermic peaks, it is clear that PDMS crystallization, if any, is strongly suppressed in the copolymers, the energetic reduction with respect to pure PDMS being 65% for 25PDMS4000 and 85% for 22PDMS7500. In Figure 6b, we depict two heating runs at 3 K/min after a fast (solid line) and a slow (dashed line) cooling rate, of about 100 and 3 K/min, respectively, for the two copolymers and pure PDMS as a reference. Pure PDMS is completely amorphous at the beginning of the first run,42 and consequently it shows a sharp increase of Cp at the glass transition temperature (147 K) followed by a cold crystallization occurring at around 170 K, resulting in a strong reduction of Cp. Increasing temperature further, a complex melting process is detectable in the range 220−240 K. Contrarily in the second run, PDMS has crystallized during cooling and presents a weak and broad Cp step in the range 150−200 K characteristic of a semicrystalline polymer, followed by a rather sharp melting event at around 230 K. All this is in perfect agreement with previous results.42 When the thermal behavior of the 22PDMS7500 and 25PDMS4000 copolymers during the heating runs is considered, both present a prominent but broader Tg feature, detectable at much lower temperatures than that of the corresponding PDMS homopolymer. This decrease of Tg is a very surprising result taking into account that in the copolymers the PDMS segments are anchored to the frozen PS chains, and if any, one could more easily expect a shift of Tg to higher temperatures. It is also noticeable that the Cp jump during the second heating runs of the copolymers is not reduced (but slightly shifted to high temperatures, particularly for 25PDMS4000), which again indicates that PDMS crystallization is strongly suppressed in these copolymers. The nonreversing signal during the first heating run from the copolymers in this T range (see inset in Figure 6b) shows no detectable events for 22PDMS7500 and a weak feature just above the glass transition range for 25PDMS4000. By increasing temperature further, both copolymers evidence endothermic events in the reversing signal with nearly no effect of the cooling rate used before the heating run. These results again evidence that the conventional PDMS crystallization is inhibited in the strongly segregated copolymers. In fact, no changes around these temperatures were detectable in 497


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empirical Havriliak−Negami (HN) equation:43

⎡ ⎤ −1 ε″(ω) = Δε Im⎢ ⎥ ⎣ (1 + [i ω/ωc]α )γ ⎦

(1)

In this equation, α (γ) denotes the symmetric (asymmetric) broadening of the relaxation peak (0 < α, γ < 1); Δε is its dielectric strength, and ωc is a characteristic frequency related to the peak relaxation time τ by the equation

⎡ ⎛ γαπ ⎞⎤1/ α ⎡ ⎛ απ ⎞⎤1/ α −1 ⎥ ⎢sin⎜ ωc⎢sin⎜ = τ ⎟⎥ ⎟ ⎣ ⎝ 2γ + 2 ⎠⎦ ⎣ ⎝ 2γ + 2 ⎠⎦

(2)

This empirical description also allows to characterize the loss peak width by the full width at half-maximum (fwhm) that can be approximately calculated from the shape fitting parameters (α and γ) by means of the empirical equation44 fwhm(α , γ) = −0.516 +

1.058 0.039 0.563 + + α γ αγ

(3)

For the copolymer samples 22PDMS7500 and 25PDMS4000, depicting both rather symmetric loss peaks, the parameter γ was fixed to 1 (Cole−Cole relaxation function) in order to reduce the coupling among fitting parameters. Representative fitting curves are shown as dashed lines in Figure 7. Although some discrepancies are apparent in the tails, at this point we consider the fitting satisfactory enough to be used for the comparison among the different systems. First, in Figure 8a we can see the temperature dependence of the PDMS relaxation time as determined from the loss peak frequency. For a detailed comparison the trivial differences associated with changes in molecular weight of the PDMS blocks have to be considered, so the Tg values obtained from DSC on the corresponding homopolymers have been used for normalization of the temperature scale. While in the lamellar nanophase the PDMS segmental dynamics is slowed down with respect to that in the homopolymer, in the copolymers nanosegregated in spheres and cylinders we observe faster motions of the PDMS segments. As already mentioned, this behavior is completely unexpected a priori due to the presence of the essentially frozen PS component. The dielectric strength obtained from the fits is represented in Figure 8b also as a function of Tg,PDMS/T, where the Δε values have been normalized to the PDMS fraction to remove the trivial dilution effect. For all copolymers the obtained values are lower than those of the pure PDMS, the difference being relatively small for the lamellar nanophase (ca. 90%). This discrepancy can be rationalized by a more detailed analysis16 of the low-frequency background (see below). However, for the other two copolymers the difference is dramatic, ∼50%, and can hardly be explained in a similar way. Moreover, for these two samples the temperature dependence of Δε is also markedly weaker. Finally, in Figure 8c the width of the loss peak (fwhm) as a function of temperature for the different samples is compared. For the homopolymer and the copolymer with lamellar nanophase, this parameter shows a quite similar behavior, in the latter case being larger by less than half a decade. On the other hand, once again the behavior of the 22PDMS7500 and the 25PDMS4000 is clearly different, showing much larger values of fwhm, which could be anticipated from the direct inspection of the dielectric loss curves. Moreover, in these two copolymers a further sudden increase of the width at the lowest

Figure 7. (a, b) Dielectric loss vs frequency for the two asymmetric diblock copolymers studied here at different temperatures. (c) Previously reported measurements on a symmetric diblock copolymer.16 The vertical arrows show the position of the peak maximum of the corresponding PDMS homopolymers at 150, 155 and 160 K. Dashed lines correspond to HN fits according to eq 1. The solid lines present the description obtained for 145, 150, 155, and 160 K with a single distribution of the fragility parameter (see text for details).

It is worth mentioning that in the case of the cylindrical and spherical PDMS copolymers the loss peaks are also rather symmetric. In addition, and likely related with the Tgdepression detected by DSC, the dielectric relaxation in these two copolymers is notably faster than that in the corresponding PDMS homopolymers (see arrows in Figure 7). These results suggest a markedly different molecular environment of PDMS segments in the two copolymers with cylindrical and spherical PDMS nanophase. Note that for example in Figure 7b, contrary to the homopolymer and the 53PDMS11600 copolymer case (Figure 7c), the loss peak corresponding to 145 K already enters in the probed frequency window. Nevertheless, the three copolymers, irrespective of the phase morphology, share a low-frequency tail-like contribution in the dielectric losses indicative of the presence of a fraction of slowly moving PDMS segments, likely influenced by the PS rigid phase. The main part of the dielectric losses from the copolymers (including 53PDMS11600) was fitted according to the 498


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segmental degrees of freedom typical of a polymer melt remain active, as evidenced by the fact that the jump in Cp at Tg is relatively large, and it does not change noticeably when directly comparing the data from both runs, after quenching and after slow cooling, on the same sample. The subsequent discussion will be mainly focused on the dynamical behavior of PDMS at low temperatures (ca. T < 200 K) where the nanostructural features of the systems are essentially temperature independent. All the previous results on the PDMS properties evidence that both structure and dynamics are considerably perturbed with respect to the usual PDMS melt when the cylindrical and spherical segregated phases are considered, the effects being qualitatively different and more pronounced than in the previously reported lamellar segregated phases. As the characteristic sizes of the different segregated phases are similar, the observed effects cannot straightforwardly be attributed to finite size effects. Noteworthy, the sphere diameter (∼18 nm) is larger than the lamella thickness (∼10 nm). As was already mentioned in the Introduction, in copolymers with lamellar segregated phases the properties of the PDMS block do not differ much from those of the corresponding homopolymer, most of the detected differences being ascribed to the PS−PDMS interfaces.16 Furthermore, simulations on symmetric diblocks with components of distinct mobility17 have recently confirmed this result. Taking this into account, the origin of the observed effects could be related with the balance between the degree of chain stretching, packing frustration, and interface curvature,3 the latter being absent in lamellar phases. Because the high flexibility of PDMS blocks the preferred local structure in the bulk, it could not be the most favorable one in the segregated phase with large interfacial curvature. In addition, in these segregated phases the PDMS regions can become easily isolated and completely surrounded by the majority component forming the matrix. When considering such a situation with a matrix of high Tg, as is the case of PS, as soon as the sample temperature decreases and the matrix becomes frozen, the segregated phase is forced to fill the space as dictated by the thermal contraction of the matrix, which is rather limited. This would result in the emergence of stresses mainly at the interface and eventually to a “negative pressure” in the still very mobile segregated phase. This picture could explain the deep changes observed in the segregated PDMS phases of the copolymers 22PDMS7500 and the 25PDMS4000 both in the local structure and in the dynamical behavior. The WAXS patterns evidence the significant difference between the local order of PDMS in the curved segregated phases with respect to that of bulk PDMS, the packing in the asymmetric diblock system being relatively poor. This is also reflected in the noticeable changes of the PDMS vibrational modes as observed by ATR-FTIR, particularly the chain stretching could explain the blue shift of the central PDMS sub-band which is even stronger at lower temperatures. In addition to that, on cooling below the glass transition temperature of PS, strong stresses at the interfaces and negative pressure in the segregated PDMS phase could be expected. All this would explain the strong suppression of the PDMS phase crystallization at low temperature. Moreover, as a consequence of these structural changes the PDMS glass transition temperature would become lower and broader than that of the pure polymer. These effects are clearly reflected in the PDMS segmental dynamics as detected by the dielectric relaxation experiments, where the loss peak is extremely broad and presents its maximum at frequencies considerably higher

Figure 8. Characteristic relaxation time, deduced from the frequency of the dielectric loss maximum (a), dielectric strength (b), and fwhm of the loss peak (c) as a function of Tg,PDMS/T: 22PDMS7500 (triangles), 25PDMS4000 (circles), 53PDMS11600 (diamonds), and PDMS7000 (+). Lines in (a) correspond to data fitting curves; see text for details. The values of Tg,PDMS were taken from ref 39.

temperatures is also apparent. Despite the similarities between these two copolymers, the sample 25PDMS4000 presents even larger values of fwhm, remaining very high (about 4.5 decades) even at the highest accessible temperatures.

■

DISCUSSION First, let us comment on the calorimetric features detected in the 22PDMS7500 and 25PDMS4000 copolymers. As already mentioned, these features seem to suggest some crystallization process. However, no indication of PDMS crystallinity was detectable at low temperatures by WAXS or FTIR. Neither, crystallinity-related reflections were observed by SAXS. All this suggests that likely there is some structural reorganization in the copolymers distinct from conventional PDMS crystallization. The extent of this structural reorganization is much smaller for 22PDMS7500, but in both cases the energy involved corresponds to a relatively small fraction than that expected for PDMS phase crystallization. This suggests the possibility of formation of a minor fraction of extremely little PDMS crystals or some other PDMS mesophase. In any case the PDMS 499


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than that in the homopolymer (see vertical arrows in Figure 3). Finally, the structural changes could also be at the origin of the markedly lower values of the dielectric strength of PDMS in these segregated phases. The suggested conformational and packing changes would also have consequences in the orientational correlation of neighboring dipole moments, modifying the Kirkwood correlation factor,43 which could account for the observed changes in the dielectric strength, at least in part, and mainly its temperature dependence. All these local packing perturbations are expected to be more relevant as the size of the segregated nanophase decreases (and the curvature of the interfaces increases), which seems to be the case as both structurally and dynamically the PDMS behavior in the diblock with the shortest PDMS blocks is the most striking. In this copolymer 25PDMS4000 the WAXS pattern features from PDMS are much weaker (even if the PDMS relative amount is larger than in the 22PDMS7500 copolymer), and the PDMS segmental dynamics is more speeded up with respect to the corresponding homopolymer. Furthermore, when comparing the fwhm of the dielectric loss peaks for the two copolymers 25PDMS4000 and 22PDMS7500, it is evident that the former is larger. This difference is likely related with the greater structural heterogeneity as revealed in the WAXS patterns but could be also associated with the structural modifications detected in the DSC scan as exothermic peaks during cooling, these features being much more prominent for 25PDMS4000 copolymer. In connection with the possible residual crystallinity in the two copolymers, the values of the dielectric relaxation strength obtained in the two copolymers are rather similar, questioning again the direct relationship between the features detected by DSC and the occurrence of conventional PDMS crystallization in the segregated phase. In spite of these differences between the PDMS behavior in the asymmetric PS−PDMS diblock copolymers here investigated and those previously reported for the lamellar case, some common features also exist. In all the PS−PDMS diblock copolymers the PDMS chains are anchored to rigid PS at the nanophase interface, and this fact has a noticeable impact in the dynamics of the neighboring PDMS segments. In our previous study of the symmetric PS−PDMS diblock copolymer with lamellar nanophase,42 there was a rather well-resolved feature in the dielectric loss spectrum that was attributed to the anchorage effects. Namely, the dielectric losses at low frequencies and relatively high temperatures do not decrease to zero as in the PDMS melt but seem to tend to a low loss plateau-like behavior (see Figure 6 in ref 16). This part of the response was conveniently described by a contribution with the same characteristics as that observed experimentally in the constrained amorphous phase (CAP) of semicrystalline PDMS. This result was interpreted as indicative that the PDMS segments affected by anchorage at the interface with rigid PS behave in a similar way as the PDMS segments in the amorphous phase anchored to the rigid PDMS crystallite surface. Note that also in this latter case the disordered PDMS phase is in a nanosegregated lamellar phase with typical thickness of a few nanometers. Although this approach would be less justified for cylindrical and spherical PDMS nanosegregation, we found that it is still compatible with the experimental data. This is illustrated in Figure 9, where it can be seen that the lowfrequency part of the data collected at 160 K in the two copolymers here investigated can be accounted for by the

Figure 9. Dielectric losses at 160 K for the two copolymers, 25PDMS4000 (a) and 22PDMS7500 (b), as compared with the dielectric losses measured at the same temperature in semicrystalline PDMS after proper rescaling (solid line).

type of response measured in semicrystalline PDMS, properly scaled. Moreover, this comparison also puts in evidence that the CAP-like response extends also toward high frequencies, indicating that at the interface slow and fast PDMS segments can coexist. This hypothesis has been very recently confirmed by simulation results on diblock copolymers in the lamellar phase with components showing different dynamical properties.17 The evaluation of this CAP-like background level for the different copolymers shows that, as it would be expected, it increases with the PDMS volume fraction. Nevertheless, the ratio of this signal to the PDMS volume fraction depends on the geometry of the nanosegregated phase, being the lowest for the spheres, whereas for the cylinders it is only marginally lower than for lamellas (with noncrystallized PDMS). Interestingly, the higher CAP-like background for the 25PDMS4000 would be directly related with the stronger reduction of the Cp jump at Tg detected by DSC. A possible explanation for the behavior of the CAP-like background can be found by considering that the effect of the anchorage to the interface extends to a limited distance from the interface, which could depend on geometry. Moreover, the shortest the PDMS chains the largest the fraction of affected segments would be. From previous estimations16 a layer of about 1 nm would be affected by anchorage in the lamella phase. Similar arguments using the present results yield a layer of about 0.5 nm thick for the cylindrical segregated PDMS phase and a layer of about 0.3 nm thick for the spherical segregated PDMS phase. These rough estimates clearly point to a strong effect of the interface curvature on the size of the highly constrain layer in the vicinity of the frozen interface. When comparing the PDMS segmental dynamics in the PS−PDMS diblock copolymers with that of the corresponding homopolymers, the values of the main relaxation times obtained from the loss peak maxima (see Figure 8a) were in qualitative agreement with the significant Tg reduction observed in the DSC traces. However, the difference in the temperature dependence of the relaxation times cannot be completely accounted for by the corresponding Tg change. 500


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To illustrate this result, the relaxation time data in Figure 8a have been fitted by means of a Vogel−Fulcher−Tamman (VFT) equation:45

⎛ DT0 ⎞ τ(T ) = τ∞ exp⎜ ⎟ ⎝ T − T0 ⎠

As the loss peaks in Figure 7a,b look rather symmetric, we assumed a Gaussian distribution function g(D), i.e.

g (D) = (4)

∫0

∞

⎡ ⎤ −1 Im⎢ α γ ⎥g (D) dD ⎣ (1 + [i ω/ωc(D)] ) ⎦

(6)

with an average value Da equal to that obtained above for the corresponding copolymer. In this way, only the standard deviation of the distribution, σD, determines the temperaturedependent width of the dielectric losses from PDMS in the copolymer, whereas the other parameters are fixed. The result of such description is included in Figure 7a,b as solid lines, where the CAP-like background with the intensity determined from the comparison made in Figure 9 has been also added. The values used for σD were 0.64 and 0.56 for 25PDMS4000 and 22PDMS7500, respectively. Overall, this description captures fairly well most of the experimental features, taking into account the simplicity of this approach. The main discrepancies are detected at the lowest temperatures, suggesting the presence of even faster contributions that are not well accounted by the Gaussian distribution.

where T0 is the characteristic Vogel temperature, τ∞ is the high-temperature asymptotic value of the relaxation time, and D is the so-called fragility parameter. When the values of D and τ∞ are fixed to those obtained for pure amorphous PDMS according to ref 16 (D = 3.8 and τ∞ = 5.5 × 10−13 s), a change in Tg directly corresponds to an equivalent change in T0, assuming that the relaxation time at Tg remains the same. Dashed lines in Figure 8a represent the best possible fit of the data using this approach, i.e., with T0 as single free parameter. As was previously shown,16 this description works well for the PDMS in lamellar segregated phases, but the fits are not satisfactory for the two new diblocks considered here, mainly for 25PDMS4000. Remarkably, another simple approach that captures much better the experimental behavior is to fix the ratio T0/Tg to that found in pure PDMS (T0/Tg = 0.89) and use D as the single fitting parameter (see solid lines). The resulting values were D = 3.15 for 25PDMS4000 and D = 3.45 for 22PDMS7500. The values are significantly lower than that found in pure PDMS, and the difference is larger for the copolymer with shorter PDMS chains. This could be related to the larger perturbation of the PDMS properties expected as the size of the isolated nanophase becomes smaller. In the aboveproposed framework, this suggests that the fragility parameter D could be intimately related with the structural and conformational state of the PDMS in the segregated phase, particularly taking into account that D is not expected to be much influenced by density changes46,47 that might also exist. As aforementioned, the dielectric losses evidence a very heterogeneous PDMS segmental dynamics in the two copolymers here considered, whereas the heterogeneity in the symmetric PS−PDMS diblock with lamellar nanostructure was relatively small. In this latter case it was found that the temperature dependence of the dielectric loss shape is conveniently captured by considering the superposition of pure PDMS-like responses with the relaxation time distributions originated by a single distribution of T0 values in eq 4; i.e., the other parameters (D, τ∞) were fixed to the values used when describing PDMS bulk behavior. Thus, we can question whether an analogous approach would also be valid for the asymmetric copolymers with PDMS nanosegregated in cylinders and spheres. In these cases, we have found that the temperature dependence of the main relaxation time can be well captured by allowing only the parameter D in eq 4 to change, the other parameters taken from the corresponding pure PDMS behavior. Consequently, we have assumed that the main dielectric losses in these diblocks would result from a distribution of pure PDMS-like responses with relaxation time distributions originated by a single distribution of D values in eq 4, i.e. ε″(ω) = Δε

2⎤ ⎡ 1 1 ⎛ D − Da ⎞ ⎥ ⎢ exp − ⎜ ⎟ ⎢ 2π σD 2 ⎝ σD ⎠ ⎥⎦ ⎣

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CONCLUSIONS The segregated cylindrical and spherical PDMS nanophases formed by self-assembly of asymmetric diblock PS−PDMS copolymers evidence both structural and dynamical anomalies when compared not only with bulk PDMS but also with PDMS in lamellar nanophases. Because the typical sizes of the PDMS lamellae are similar to those of the cylindrical and spherical PDMS nanophases, the effect cannot be directly attributed to size effects by geometrical confinement. The reported results can be considered as a result of the poor packing of the PDMS segments originated by the balance between the degree of chain stretching, packing frustration, and interface curvature in the segregated phases of asymmetric diblocks. This poor packing is evidenced in the WAXS pattern and also is the detectable by important changes in the PDMS vibrational modes. Moreover, in these cylindrical and spherical PDMS nanophases PDMS crystallization is strongly suppressed, if not inhibited, and the glass transition temperature appears considerably reduced. In agreement with this latter finding, the dielectric loss peak associated with the PDMS segmental dynamics is located at higher frequencies and is much broader than that of bulk PDMS. The temperature dependence of the main dielectric relaxation times can be well described using a VFT equation similar to that describing the results in bulk PDMS, but with a quite lower value of the fragility parameter D. The temperaturedependent shape of the dielectric loss peaks can be semiquantitatively accounted by a T-independent distribution of D values leading to a distribution of relaxation processes with different times, each of the dielectric loss components having the shape of the segmental relaxation in PDMS melt. Regardless of these dramatic differences between PDMS nanosegregated in cylinders and spheres when compared with PDMS nanosegregated in lamellas, in all cases the effects of chain anchorage is reflected in the dielectric losses as a broad and slow contribution with the same characteristics as the dielectric relaxation produced by the constrained amorphous phase in semicrystalline bulk PDMS. It is noteworthy that the presence of this component was a main effect detected in the lamellar case and was interpreted as a signature of the dominant influence of the interface in that case. Although this feature also

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results relevant for PDMS nanosegregated in cylinders and spheres, the major cause for the most dramatic changes observed would be the poor local packing of the PDMS segments, likely as a result of the presence of a highly curved interface. A question that remains open is whether the results obtained depend on the chemical nature of the two polymer blocks here considered, or otherwise it is something that would be expected to occur to some extent in any strongly segregated block copolymer with highly curved interfaces. Work in this direction is currently in progress.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ACKNOWLEDGMENTS The authors acknowledge the University of the Basque Country and Basque Country Government (Ref. No. IT-436-07, Depto. Educación, Universidades e Investigación) and the Spanish Ministry of Science and Innovation (Grant No. MAT 200763681) for their support. We also thank SGIker UPV/EHU services for WAXS and TEM measurements and Silvia BarbosaFernandez (University of Vigo) for carrying out TEM measurements. L.V.C. particularly acknowledges the PhD grant support of the Basque Government.

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