In Situ Rheodielectric, ex Situ 2D-SAXS, and Fourier Transform

Article pubs.acs.org/Macromolecules

In Situ Rheodielectric, ex Situ 2D-SAXS, and Fourier Transform Rheology Investigations of the Shear-Induced Alignment of Poly(styrene‑b‑1,4-isoprene) Diblock Copolymer Melts T. Meins, N. Dingenouts, J. Kübel, and M. Wilhelm* Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology (KIT), Engesserstrasse 18, 76128 Karlsruhe, Germany ABSTRACT: A highly sensitive rheodielectric experimental setup was used to investigate the macroscopic alignment of symmetric poly(styrene-b-1,4-isoprene) (SI) diblock copolymers under large-amplitude oscillatory shear (LAOS). The dielectric normal-mode of the 1,4-cis-polyisoprene chains in the diblock copolymer was chosen to probe in situ the macroscopic orientation process. It was shown that the development of the overall orientation of the lamellar microstructure can be followed in situ using the time progression of the dielectric loss modulus ε″(t). The dielectric loss ε″(t) correlates directly with the nonlinear mechanical response I3/1(t) of the sample as determined via Fourier transform rheology (FT-rheology). In addition to these two dynamic methods, small-angle X-ray scattering was used to ascertain the degree and type of the macroscopic orientation as a function of the applied shear conditions. Evidence presented here showed that a decrease in ε″(t) relative to the initial value of ε″(t = 0 s) for a macroscopically isotropic sample melt was indicative of a macroscopic parallel orientation while an increase in ε″(t) corresponded to an overall perpendicular alignment. These phenomena are explained on a molecular level by the anisotropic diffusion of the confined polymer chains, resulting in a higher mobility of the dielectrically active end-to-end vector parallel to the interface, which can be detected via dielectric spectroscopy.

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INTRODUCTION Block copolymers consist of two or more distinct polymers which are covalently bonded to each other. In the case of thermodynamic repulsions between the different monomers of the constituent blocks, block copolymers can undergo a order− disorder transition (ODT) into different self-assembled nanoscaled three-dimensional structures.1,2 Self-assembly usually leads to a polydomain structure with locally anisotropic ordered domains (grains) that are randomly orientated throughout the whole sample,3,4 which results in a macroscopically isotropic material. These microphase separated domains exhibit a variety of different symmetries,5 depending on the degree of polymerization N, the monomer−monomer interaction described by the Flory−Huggins parameter χFH, and the volume fraction of the polymer blocks.6 As hierarchically structured materials, block copolymers have been of growing interest in the fields of polymer and material science. For example, they can be used as a template to generate organic−inorganic hybrid materials.7−9 By applying an external stimulus10 (e.g., electrical11,12 or mechanical13,14), the randomly orientated microdomains can be macroscopically aligned, resulting in long-range order of the hierarchically ordered structures. As most advanced applications require the nanostructured materials to be macroscopically aligned,15 probing the mechanism and underlying processes of macroscopic block copolymer alignment especially for shear-induced macroscopic orientation was investigated in numerous scientific contributions.16−22 For macroscopic orientation of symmetric block copolymers, large-amplitude oscillatory shear (LAOS) was shown to be the © 2012 American Chemical Society

preferred method because it allows for different orientations of the unit normal of the lamellae.14 However, detailed knowledge of the underlying processes occurring in mechanical alignment of block copolymer melts during LAOS is still a challenging task in the field of polymer science. In recent years different techniques have been developed to examine in situ flow effects on the dynamics and structural changes in block copolymer melts. For example, a rheo-optical technique using birefringence measurements could monitor online the macroscopic alignment process with a high time resolution.19,23 Dichroism measurements provided information on the time-dependent changes in orientation anisotropy, but had, in general, insufficient spatial resolution on the length scale corresponding to the spacing of the self-assembled structures. In contrast, small-angle X-ray scattering methods have the benefit of good spatial information, but are usually limited in their time resolution.24−26 However, a newly developed combined rheo-SAXS method described by Struth et al.27,28 appeared to overcome this drawback with time resolutions for the orientation process in the range of seconds.27 Nevertheless, the above-described techniques do not give direct access to the local dynamics of the polymer chains. Therefore, we suggest rheodielectric techniques as an important complementary tool to other in situ methods.29 Adachi et al.30 introduced one of the first rheodielectric experimental setups published in the literature. The published Received: January 17, 2012 Revised: July 3, 2012 Published: August 20, 2012 7206

dx.doi.org/10.1021/ma300124b | Macromolecules 2012, 45, 7206−7219

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setup consisted of a custom-made, coaxial cylinder-type rheometer equipped with an automatic capacitance bridge. Because of the inadequate heating system, this approach was limited to concentrated polymer solutions, polymers with glass transition temperatures Tg below room temperature or emulsions and suspensions. Crawshaw et al.31 described a simple setup to measure the effect of shear on the electrical conductivity in pipe flow for conductive colloidal systems. Peng et al.32 studied the influence of various processing conditions on the injection molding of polymer melts using a specially designed plate mold geometry equipped with a three-element sensor rosette. However, as both of these setups are limited to steady shear flow experiments, they are not suitable for performing LAOS experiments. A first approach to combining a commercially available rheometer with dielectric measurement techniques was reported by Sato et al.33 This rheodielectric combination was based on a modified rheometer to induce a mercury contact point, which enabled rheodielectric measurements without mechanical disturbance of the electrical contacts.29 However, the mercury contact was unfortunately limited to experimental temperatures that were generally lower than those needed to probe the shear-induced alignment of block copolymer melts.14 The highly sensitive rheodielectric setup34 used in this work enabled simultaneous and precise rheological and dielectric measurements at temperatures between −70 and 250 °C. A detailed description of this technique on a homopolymer melt was provided in a previous publication by Hyun et al.35 In the work presented here, the efficiency of this highly sensitive rheodielectric approach and its capability to study the effect of large-amplitude oscillatory shear on SI diblock copolymer melts is presented. As polyisoprene is a typical type A polymer36,37 with a nonvanishing dipole moment pointing, along the polymer backbone dielectric spectroscopy enabled the observation of large scale chain motions, the so-called normal mode. This mode is directly correlated to fluctuations of the end-to-end vector and has been the subject of numerous studies.38−46 Thus, rheodielectric techniques were able to characterize polymer chain dynamics under mechanical flow35,47−49 and provided new insights into the shear-induced macroscopic orientation of SI diblock copolymer melts. It is important to note that the dielectric response of SI diblock copolymers has been the subject of several scientific publications.50,51 However, for the first time, we present evidence that the overall orientation process of the lamellae can be followed and the relative orientation of the lamellar microstructure distinguished by the dielectric response of the sample melt. Additionally, the nonlinear mechanical response during LAOS obtained via Fourier transform rheology52−54 (FT-rheology) was compared with the time evolution of the dielectric loss modulus ε″(t). The macroscopic orientations before and after the mechanical shear treatment were identified via ex situ 2D-SAXS measurements to quantify the orientation states as they are essential for the interpretation. Both mechanical and dielectrical in situ measurements showed significant correlation and were attributed to a rotational mechanism of locally anisotropic ordered lamellar microdomains, which is consistent with our recently published results obtained on SI diblock copolymers with an unique and newly developed in situ rheo-SAXS setup.28

Article

EXPERIMENTAL SECTION

Materials and Sample Preparation. The polystyrene and polyisoprene homopolymers as well as the poly(styrene-b-1,4isoprene) (SI) diblock copolymers were synthesized via anionic polymerization under high vacuum at room temperature using toluene as the solvent and sec-butyllithium as the initiator. A detailed description of the polymerization procedure is described in ref 55. The poly(styrene-b-1,4-butadiene) (SB) diblock copolymer and the linear polystyrene homopolymer PS-100 were obtained from BASF SE. The investigated samples and their relevant physical and chemical properties are listed in Table 1.

Table 1. Molecular Characteristics of the Investigated Polymer Melts sample SB-13-13 SI-13-13 SI-17-15 PS-17 PS-100 PI-20

Mw (PS-block) [g/mol]

Mw (PI/PB-block) [g/mol]

f PS [%]

PDI

13 000 13 500 16 700 17 300 108 500

13 400 13 000 15 100

49 51 53 100 100 0

1.04 1.12 1.03 1.04 1.07 1.04

19 500

TODT [K] 469 478 488

The SI sample and its precursor were characterized by a GPC equipped with a refractive index monitor and an UV detector using THF as the elution solvent. Calibration was performed with commercially available monodisperse PS and PI standards (Polymer Standard Service, Mainz, Germany). With the molecular weight of the precursor determined by GPC, the SI composition was calculated from 1 H NMR data. Additionally, the 1,4-cis PI content (≈90%) was calculated from the 1H NMR spectra of the BCPs. The resulting SI was freeze-dried from a cyclohexene solution (10 wt %) under high vacuum for 10 h. The purified block copolymer powder was hot pressed under vacuum at 140 °C into sample disks with diameters of 13 and 25 mm and thicknesses varying between 0.5 and 0.8 mm. The pressure applied to the block copolymer melt was adjusted to 3 bar. The obtained discs were used without a further annealing step. Rheological and Dielectric Setups. The FT-rheology and rheodielectric measurements were performed on a strain controlled ARES (TA Instruments) rheometer under oscillatory shear flow. For the rheodielectric measurements, the sample was placed between two custom-made INVAR steel parallel plate electrodes 25 mm in diameter and a spacing between 0.6 and 0.3 mm. Therefore, the capacitance of the empty cell was between 15 and 7 pF. The accuracy of the rheometer gap control, which defines the spacing between the electrodes, was in the order of ±0.5 μm. Dielectric measurements were carried out with an ALPHA analyzer (Novocontrol, Hundsangen, Germany) using a custom-made experimental setup described in detail elsewhere.34,35 The broadband dielectric measurements were carried out within the frequency range between 0.1 Hz and 1 MHz. The resolution of the setup in tan δ for the applied experimental conditions was approximately Δtan δ ≈ 10−5. FT-rheology was used to examine the time-dependent mechanical nonlinear response of the sample melts during LAOS where the time dependence of the ratio of the intensity of the third harmonic I(3ω1) over the fundamental I(ω1) was chosen to characterize and quantify the degree of nonlinearity. From here on, this ratio I(3ω1)/I(ω1) will be denoted as I3/1. The order−disorder transition temperature was detected by a drastic decrease in the temperature dependence of the low frequency (ω1/2π = 1 Hz) mechanical storage (G′) and loss (G″) moduli when applying a heating rate of 0.5 K/min. External SAXS Measurements. The morphology of the diblock copolymers was determined by ex situ 2D-SAXS measurements (Hecus S3-Micro X-ray system) using a point microfocus source, 2DX-ray mirrors, and a two-dimensional CCD detector from Photonic Science. In addition, a block collimator system was used to ensure low 7207


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background scattering. With this system, the detectable q⃗ vector varies from 0.08 to 4.7 nm−1. To examine ex-situ the state of orientation, the sample melts were rapidly cooled to room temperature (within 10 min) and the normal force was constantly adjusted to compensate for thermal shrinking until the state of orientation was frozen in by the glassy PS blocks. At this point, the sample was removed from the shear geometries. To quantify each state of orientation, the macroscopic orientation along each of the three major directions was determined at three points in the sample, i.e. at three different radii, which corresponded to local strain amplitudes γ0‑loc of γ0‑loc(a) = 0.85γ0, γ0‑loc(b) = 0.62γ0, and γ0‑loc(c) = 0.31γ0. Investigations at these three different positions revealed the influence of the strain gradient caused by the parallel plate geometry on the macroscopic orientation. Sample Loading and Experimental Procedure. The dielectric measurements were carried out before, during, and after the LAOS experiments. For this purpose, custom-made parallel-plate geometries were used which were made out of invar steel with a diameter of 25 mm. The parallel plate geometries were tempered at the measurement temperature for 1 h before the zero fixture was performed. The sample disk was then inserted between the plates and slightly squeezed until the whole geometry surface was covered with the polymer melt. Prior to each orientation experiment, the diblock copolymer melts were heated to 20 °C above their respective TODT and then annealed for at least 20 min to remove all previous thermal and deformation histories. The sample was then cooled to the desired measurement temperature while constantly adjusting the gap to control for thermal shrinkage of the sample and the sample geometries. To avoid squeeze flow induced orientation, a normal force of less than 0.05 N (∼100 Pa) was applied. At the measurement temperature, the samples were allowed to temper for another 20 min. Before and after each LAOS experiment, mechanical frequency sweeps in the linear regime were performed. For all rheodielectric measurements, a dielectric frequency sweep was performed both before and after each LAOS experiment. During the LAOS experiment, the dielectric response was followed at one specific dielectric frequency, which was chosen to correspond to the frequency range at which the normal-mode relaxation of the polyisoprene chains in the block copolymer occurs. To ensure the equilibrium state of the sample melt before LAOS was performed, three to five data points for ε″(t) were collected without subjecting the sample to any shear. This procedure guaranteed that the observed changes in the dielectric response could be attributed only to the external applied mechanical stimulus.

Figure 1. Frequency dependence of the dielectric loss ε″(ω) for the (a) SI-13-13 and (b) SI-17-15 diblock copolymers at six different temperatures ranging between 140 and 190 °C. The rapid increase in ε″ on the low-frequency side of the spectra was attributed to conduction contributions.

correlation between the PI chains, can be used assuming the PI block is built up by polyisoprene chains tethered to both sides of the confining polystyrene interfaces. This means specifically that the number densities of polyisoprene chains on both sides of the domain are equal. Therefore, the orientation of the cross-correlation of the PI chains cancels, and eq 2 can be replaced by the single chain expression for Φ(t):

Φ(t ) =

■

∫0

∞

dΦ(t ) sin ωt dt dt

(1)

with the dielectric strength Δε and the normalized dielectric relaxation function Φ(t) being given by Φ(t ) =

∑a , b ⟨Ra⃗ (t ) ·R⃗b(0)⟩ ∑a , b ⟨Ra⃗ (0) ·R⃗b(0)⟩

(3)

For the temperatures used here, the block copolymers were all below their TODT according to rheological measurements (see Table 1). In addition, three relaxation processes were visible in the investigated dielectric frequency range. Besides the strong increase in ε″(ω) at the low frequency side of the spectra attributed to conduction contributions, two separate relaxation processes at intermediate and high frequencies occurred. All three relaxation processes were shifted to higher frequency with increasing temperature, indicating that the processes were thermally activated. This behavior was observed for both copolymers with the only difference being that the formation of the slowest process for the SI-17-17 diblock copolymer was less pronounced compared to that for the SI-1313 diblock copolymer. However, based on previous measurements on symmetric SI diblock copolymer melts with different molecular weights and, therefore, different preparation conditions, the appearance of the slow relaxation process was shown to be strongly dependent on the sample history, which has also been stated by Karatasos et al.57 The underlying origin for this phenomenon is still under discussion in the literature and will be addressed here as part of the discussion on the observed dielectric response before and after the shear-induced alignment was performed. In contrast, the relaxation process at

RESULTS Static Measurements of Macroscopically Unorientated Samples. Figure 1 shows a double-logarithmic plot of the frequency dependence of the loss part of the dielectric permittivity ε″(ω) for the symmetric SI-13-13 and SI-17-15 diblock copolymer melts in the frequency range between 1 and 106 Hz at multiple temperatures well above the glass transition of the polystyrene block. Assuming the standard expression56 ε″(ω) = −Δε

⟨R⃗(t ) ·R⃗(0)⟩ ⟨R⃗(0) ·R⃗(0)⟩

(2)

where a and b specify the different end-to-end vector R⃗ of the polyisoprene chains in the PI block. However, it has to be noted that though in the SI diblock copolymer the PI chains cannot penetrate through the confining PS interface, the commonly used expression, which neglects the cross7208


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for the following discussion on the influence of shear-induced alignment on the dielectric response. For this reason, the ε″(ω) values obtained at different temperatures and frequencies were fitted with three Havrilliak−Negami61 (HN) relaxation processes and a conductive contribution:62

high frequencies can be identified as the superposition of the polyisoprene normal mode and the segmental mode of the polystyrene, which was proven by comparison with measurements on the corresponding homopolymers. To clearly assign and separate the different dielectric relaxation processes in the SI diblock copolymer melts, the dielectric loss spectra ε″(ω) for SI-13-13, SB-13-13, and the homopolymers PI-20 and PS-17 are shown in Figure 2.

ε″(ω) =

σ0 + ε0ωs

3

∑ n=1

Δεn (1 + (iωτn)αn )βn

(4)

where Δε is the dielectric strength, ω is the angular frequency, τ is the characteristic relaxation time, the exponents α and β account for the symmetric and asymmetric broadening of the relaxation peak, respectively, σ0 is the dc conductivity, ε0 is the permittivity of free space and the exponent s characterizes the type of conductivity, where s = 1 denotes pure direct conductivity.56 The relaxation mode for the SI diblock copolymer melts at high frequencies, which corresponded to a superposition of the normal mode of the polyisoprene and the segmental mode of the polystyrene (see Figure 3), was described by two HNFigure 2. Frequency dependence of the dielectric loss ε″(ω) for SI-1313 (open symbols), SB-13-13 (filled symbols), and the homopolymers PS-17 (open symbols with center cross) and PI-20 (half filled symbols) at T = 120 °C (circles) and 150 °C (squares). It can be seen that the segmental mode of the PS-block and the normal mode of the PI-block superimpose as both processes occur in the same frequency region in the investigated temperature range. However, the segmental mode of the polystyrene in the diblock copolymer was significantly broadened and accelerated compared to the neat homopolymer. The solid line represents the best fit obtained by a superposition of three Havriliak−Negami relaxation processes and a conductive contribution for the SI-13-13 at T = 150 °C. Figure 3. Dielectric loss ε″(ω) for the SI-13-13 lamellar diblock copolymer at 120 °C. The dielectric loss data (typically 63 data points) were analyzed using three HN functions plus a conductive contribution. In the spectrum presented here, the decomposition of the data into the main three relaxation processes, which are assigned in the plot, is shown where the high-frequency relaxation peak is attributed to a superposition of the polystyrene segmental mode and the polyisoprene normal mode (see Table 2 for numerical values).

Comparison of ε″(ω) at different temperatures for SI-13-13 and SB-13-13, where the latter has no dielectric active normal mode relaxation process, revealed that SB-13-13 did not have a slow relaxation process as was observed for SI-13-13 (see Figure 2). This finding is consistent with the assumption stated by Karatasos et al.57 that the slow mode relaxation process is caused by conformal motion of the interfacial plane perpendicular to the interface, which involves motion of the entire polymer chain. Therefore, the slow dielectric relaxation mode of the interface should only be detected by dielectric spectroscopy if the block copolymer possesses a type A polymer with a nonvanishing dipole moment along the polymer backbone, such as poly(1,4-cis-isoprene). On the other hand, the dielectric spectra of the SB-13-13 diblock copolymer and the PS-17 homopolymer support the hypothesis that the segmental mode of the polystyrene block and the normal mode of the polyisoprene block superimpose in the investigated temperature range. However, in contrast to the segmental mode of the linear PS-17 homopolymer, the segmental relaxation process of the polystyrene chain segments in the SB-13-13 diblock copolymer was significantly broadened, which can be explained by the heterogeneity of the segmental dynamics caused by their confinement in the lamellar phase.58 The shift to higher frequencies for the polystyrene segmental mode in the block copolymer melt was likely caused by the higher mobility induced by the very mobile polyisoprene chains near the interface.59,60 The exact separation of the different dielectric relaxation processes in the SI diblock copolymers is of major importance

relaxation processes. For this purpose, the parameters for the segmental relaxation of the polystyrene block, which were obtained from the SB-13-13 dielectric spectrum, were taken to be equal to the parameters for the segmental relaxation process of the polystyrene block in the SI sample melts under isothermal conditions. Because of the limited experimental frequency window (ωmax/2π ≤ 106 Hz), the full segmental relaxation process could unfortunately not be followed. Therefore, the exponent β was set equal to the mean value of β obtained from the linear polystyrene homopolymer PS-17. The values for the temperature averaged parameters α and β were obtained from the best fits for the different relaxation processes of each polymer and are given in Table 2. As already discussed in the literature,63 the empirical HN function shows a physically impossible behavior at frequencies small compared to the peak frequencies due to the infinitely long terminal relaxation time that is not realistic for relaxation processes completed in finite time scales. In Figure 3, the tail of the PS segmental mode is higher than the tail of the PI normal mode, resulting in a slower segmental relaxation of PS than the 7209


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Table 2. Havriliak−Negami Shape Parameters for the Relaxation Processes of Different Block Copolymers (BCPs) and Homopolymersa slow process

a

PI normal mode (BCP)

PS segmental mode (BCP)

samples

α

β

α

β

α

β

SI-13-13 SI-17-15 SB-13-13 PS-17 PS-100 PI-20

0.87 (±0.10) 0.88 (±0.08)

0.77 (±0.21) 0.87 (±0.20)

0.76 (±0.11) 0.79 (±0.09)

0.35 (±0.11) 0.31 (±0.14)

0.56 0.56 0.56 (±0.05) 0.81 (±0.04) 0.89 (±0.06)

0.34 0.34 0.34 0.34 (±0.04) 0.33 (±0.08)

0.93 (±0.07)

0.55 (±0.14)

The values given were averaged over the investigated temperature.

normal relaxation of PI. Other descriptions avoid this physically impossible behavior, as, for example, an equation often used in the literature that is the physically based Kohlrausch− Williams−Watts (KWW) equation,56,64 and another possibility is the empirical Davidson−Cole equation.65 In spite of this limitation in the empirical HN function, we decided to use this numerically more simple equation for two reasons: First, the terminal relaxation tail of the segmental mode is never accessible in our data because the dielectric loss contains up to four different contributions (see above). Second, the contribution of the tail far away from the peak position to the total dielectric loss function is always extremely small, so that this limitation in the equation never influences our results. It can be seen that the shape parameters corresponding to the segmental relaxation of the PS-17 and PS-100 homopolymers and the α parameter for the polystyrene segmental relaxation process in SB-13-13 were nearly independent of temperature. However, while the shape parameters for the normal mode and the slow relaxation process varied more strongly with temperature, there was no obvious trend in the dependence of the polyisoprene normal mode shape parameters (α, β) on the temperature. Figure 4 depicts the relaxation times τmax corresponding to the peak maximum as a function of the inverse temperature for the different relaxation processes. These relaxation times were calculated from the characteristic relaxation time τ (τ = τn of eq 1) obtained from the HN function according to44 1/ α −1/ α ⎛ ⎛ αβπ ⎞ απ ⎞ τmax = τ ⎜sin ⎟ ⎜sin ⎟ 2(1 + β) ⎠ 2(1 + β) ⎠ ⎝ ⎝

Figure 4. Arrhenius plot of the relaxation times for SI-13-13 (open symbols) and SI-17-15 (open symbols with cross) for the slow relaxation process (stars), the normal mode relaxation of the polyisoprene chains (circles), and the segmental relaxation of the polystyrene block (squares). The segmental mode of the polystyrene block is only shown once, as its value was kept fixed for both SI diblock copolymers. For the analysis of the polystyrene block segmental process see the text. Additionally, the relaxation times for the segmental relaxation of PS-100 (squares), PS-17 (triangles), and the normal mode of PI-20 (circles) are shown. From the temperature dependence of the relaxation times, a clear assignment for the normal mode of the polyisoprene block can be derived. The dotted line represents the temperature below which the relaxation process at high frequencies is described by a superposition of the normal mode of the polyisoprene and the segmental mode of the polystyrene block. Above this temperature, the segmental mode of the polystyrene block is shifted out of the investigated frequency range.

(5)

polystyrene homopolymers. From the Arrhenius behavior and the good agreement with the temperature dependence of the normal mode of the homopolymer PI-20, it can be seen that assuming the fast relaxation process is a superposition of the relaxation processes for a segmental mode attributed to polystyrene and a normal mode attributed to the polyisoprene block is a valid assumption. Besides these two high-frequency relaxation processes, the temperature dependence of the slow relaxation process showed no correlation with either the segmental mode of the polystyrene chains or with the normal mode of the polyisoprene chains. Nevertheless, the pronounced temperature dependence of the slow relaxation process and the related shape parameters (α, β) indicate they are connected to a global chain motion of the polyisoprene block that is several decades slower than the observed normal mode of the polyisoprene chains. It is important to note that after the shear induced macroscopic alignment the relaxation times τmax of the normal mode of the polyisoprene chains (not shown here) only changed slightly by a factor between 1.2 and 1.5,

To clearly assign the different relaxation processes, the characteristic temperature dependence of the three relaxation modes (the conductive contribution was not considered) were analyzed using an Arrhenius type diagram. Additionally, the relaxation times of the dielectrically active modes of the homopolymers are included. At elevated temperatures where the maximum of the polystyrene segmental mode was shifted out of the investigated temperature range (T > 150 °C), τmax was calculated assuming an Arrhenius-like temperature dependence. It can be seen that the relaxation times for both the normal mode of the PI-20 homopolymer and the resolved relaxation process at high frequency for the SI diblock copolymers, which was identified as the normal mode of the polyisoprene block, possessed the same temperature dependence. For temperatures above 160 °C, the relaxation process for the segmental mode of the polystyrene block was shifted outside the investigated frequency range (vertical dotted line in Figure 4), which was confirmed by the ε″(ω) spectra of SB-13-13 and the 7210


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which we regard as sufficiently small to be neglected on a logarithmic time scale. In the literature, the splitting of the normal mode into a slow and fast relaxation process was already observed by Yao et al.66 The authors assigned the slow process to an end-to-end vector fluctuation while the fast process appears below the ODT, and they then introduced a new relaxation process attributed to the SI junction point fluctuation in the interphase. However, dielectric measurements combined with additional computer simulations performed by Karatasos et al.57 instead presented evidence that the fast process was caused by the normal mode of the polyisoprene chains, which is consistent with the results presented here. Furthermore, the authors claimed57 that the slow mode corresponded to conformal motion of the interfacial plane perpendicular to the interface, which requires the motion of the whole chain. This led to the apparent molecular weight dependence seen in the data, which was also observed in Figure 4. Nevertheless, a publication by Jensczyk et al.67 reported that the observed slow relaxation motion was instead caused by the segmental motion of the polystyrene block. However, the results presented here do not support this assumption. In the Discussion, it is shown that the origin of the slow relaxation process can be more likely attributed to vibration or undulation of the normal vector of the interfacial plane affecting both the block and chain end-to-end vectors.57 Perpendicularly Aligned Sample Melts (Static Measurements). In this section, the influence of large-amplitude oscillatory shear (LAOS) on the dielectric response is investigated. The data were analyzed by comparing the frequency dependence of the dielectric loss ε″(ω) both before and after the LAOS experiments. During the dielectric frequency sweeps, no mechanical stimulus was applied to the investigated sample melts. The applied LAOS conditions were deliberately chosen to shear-induce either a macroscopically perpendicular or parallel alignment, which was additionally examined by ex situ 2D-SAXS measurements. Figure 5 depicts the frequency dependence of the dielectric loss ε″(ω) for the symmetric SI-13-13 and SI-17-15 diblock copolymer melts before and after LAOS was applied. The LAOS experiments were carried out at 150 °C using a shear frequency of f LAOS = 1 Hz and a strain amplitude γ0 between 1 and 0.5 and a mechanical excitation duration between 5000 and 8000 s. The insets in Figure 5 depict the ex situ determined azimuthally averaged 2D-SAXS patterns for the sample after the shear-induced macroscopic orientation was applied. A strongly anisotropic scattering intensity observed when the sample was aligned in the normal direction to the beam in combination with the low isotropic scattering intensity in the radial direction indicated that a well-aligned macroscopically perpendicular orientation was achieved; opposite results for the intensity were seen for the parallel alignment. Clear differences were observed in the dielectric loss spectra before and after the macroscopic alignment. In the frequency region where the dielectric normal mode of the polyisoprene chains occurs, LAOS caused an increase in ε″(ω), while for the relaxation process at lower frequencies, ε″(ω) decreased after LAOS. It is important to note that the conductive contribution was apparently not affected by the macroscopically perpendicular orientation of the lamellar morphology. The differences in ε″(ω) between the initial and final macroscopically aligned state were largest at the peak maximum of the corresponding relaxation process. In addition, the magnitude of the changes in ε″(ω) between the initial unoriented and the final aligned state

Figure 5. ε″(ω) for SI-13-13 before (open triangles) and after (open squares) LAOS (T = 150 °C, f LAOS = 1 Hz) for (a) γ0 = 1 and (b) γ0 = 0.5 and (c) SI-17-15 for γ0 = 1. The insets represent the azimuthally averaged ex situ 2D-SAXS patterns obtained along the normal (filled symbols) and radial (open symbols) direction after the LAOS experiments. σSAXS denotes the standard deviation in χ and is a measure for the quality of the macroscopic orientation. It can be seen that, in the frequency range corresponding to the normal mode relaxation of the polyisoprene chains, ε″(ω) increased after the shearinduced macroscopic perpendicular alignment while the relaxation process at lower frequencies decreased. The solid lines represent the fit to the data.

was on the order of Δε″ ≈ 0.001 for both the normal mode relaxation at high frequencies and the slow relaxation process at lower frequencies. Interestingly, ε″(ω) was more strongly affected at higher strain amplitudes as indicated by the measurements for SI-13-13 with γ0 = 1 and γ0 = 0.5. For the SI-17-15 diblock copolymer, the slow relaxation process was less pronounced than that for SI-13-13. As was already suggested in ref 57, this relaxation process may be influenced by the sample preparation procedure. It is important to note that changes in the normal mode relaxation when the sample is undergoing steady or oscillatory shear flow as described in the literature34,38 were detected; however, the frequency-dependent spectra of ε″(ω) presented here were measured before and after LAOS, i.e., when the sample was not subjected simultaneously to any shear. This shows evidence that the LAOS-induced dielectric changes 7211


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mainly resulted from the macroscopic shear-orientation. For the polyisoprene homopolymer, only the conductive contribution and the normal mode were visible in the investigated frequency range, while a slow relaxation process as seen for the block copolymer melts could not be detected. It is important to note that the changes in the magnitude of the normal mode relaxation of ε″(ω) before and after the LAOS experiment were between 6% and more than 50% for the SI diblock copolymers while for the polyisoprene homopolymer the change in ε″(ω) was less than 1%. Parallel Aligned Sample Melts (Static Measurements). The ε″(ω) spectra before and after shear-induced alignment are shown in Figure 6 for LAOS experiments creating a

macroscopically parallel orientation. Figure 6 represents the results obtained for SI-13-13 at 120 °C, f LAOS = 5 Hz and either γ0 = 0.5 or γ0 = 0.2. For the SI-17-15 diblock copolymer (Figure 6c), the parallel orientation was achieved at 120 °C, f LAOS = 1 Hz and γ0 = 0.2. The insets in Figure 6 show the ex situ determined azimuthally averaged 2D-SAXS pattern for the aligned samples. Important differences in the frequency dependence of ε″(ω) before and after LAOS experiments were detected. In contrast to the macroscopically perpendicular orientation, the overall parallel alignment was characterized by a decrease in ε″ at frequencies where the fluctuation of the end-to-end vector of the polyisoprene chains in the block copolymer melt occurred. The magnitude of this decrease was largest in the vicinity of the peak maximum for the normal mode relaxation process. However, for the slow relaxation process, the macroscopically parallel orientation caused ε″(ω) to increase, but it is important to note that this relaxation process was less pronounced for the SI-17-15 diblock copolymer. Similar to the macroscopically perpendicular orientation, the conductive contribution at low frequencies appeared to be nearly unaffected by the alignment process. Additional investigations on SB-13-13 at 120 °C, f LAOS = 5 Hz, and γ0 = 0.5 were performed. From Figure 7 it can be seen

Figure 7. Dielectric loss ε″(ω) as a function of frequency for the lamellar SB-13-13 sample melt before (open triangle) and after (open squares) LAOS (T = 120 °C, f LAOS = 5 Hz, γ0 = 0.5, tLAOS = 5000 s). The LAOS conditions were chosen to generate a macroscopically parallel alignment. No significant influence of the shear-induced alignment on the dielectric loss was detected.

that SB-13-13, which does not possess a dipole moment parallel to the polymer chain backbone, was not significantly influenced by the macroscopic orientation of the lamellar microstructure. The results presented for the macroscopically perpendicular and parallel alignments indicate that the magnitude of the increase and decrease in the ε″(ω) values at around 70 (SI-1715) and 80 kHz (SI-13-13) and 20 (SI-17-15) and 40 kHz (SI13-13), respectively, are related to the peak maximum of the polyisoprene block normal mode relaxation process for the macroscopically aligned samples and correspond to the degree, or quality, of the overall orientated microstructure. As a measure of the quality of the macroscopic alignment, the peak width of the azimuthally averaged first-order reflection was used. For example, the peak width obtained from ex situ 2DSAXS measurements for the macroscopically perpendicular orientation (see insets Figure 5) was broader when the SI-13-13 was sheared at γ0 = 0.5 (σSAXS = 8.3°) instead of at γ0 = 1 (σSAXS

Figure 6. Frequency dependence of the dielectric loss ε″(ω) before (open triangles) and after (open squares) LAOS. (a) SI-13-13 LAOS: f LAOS = 5 Hz, γ0 = 0.5, T = 120 °C, tLAOS = 35 000 s; (b) SI-13-13 LAOS: f LAOS = 5 Hz, γ0 = 0.2, T = 120 °C, tLAOS = 25 000 s; and (c) SI-17-15 LAOS: f LAOS = 3 Hz, γ0 = 1, T = 130 °C, tLAOS = 11 000 s. For all LAOS experiments, a macroscopically parallel orientation was achieved, which was verified by additional 2D-SAXS measurements (see insets) along the normal (filled symbols) and radial (open symbols) directions. It can be seen that the parallel alignment causes a decrease in the dielectric loss ε″(ω) for the end-to-end vector relaxation process of the polyisoprene chains, while ε″(ω) for the slow relaxation mode increased. The solid lines represent the best fit to the data. 7212


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time-dependent dielectric loss ε″(t) increased over the course of the shear-induced orientation, where the shear resulted in a macroscopically perpendicular alignment. The magnitude of this increase was on the order of ε″(plateau) − ε″(initial) ≈ 0.001, indicating the need for a highly sensitive rheodielectric setup to accurately resolve this process. In contrast to the time progression of ε″(t), for the macroscopic parallel and perpendicular alignment, the nonlinear mechanical response I3/1(t) showed a stretched exponential decrease during LAOS, which finally led to a plateau value of approximately I3/1 = 0.16. In a recent publication,28 evidence utilizing both in situ and ex situ 2D-SAXS measurements was presented that proved I3/1(t) was directly related to the macroscopic orientation process, specifically that the minimum in I3/1(t) corresponded to the degree of macroscopic orientation. Consequently, ε″(t) also reached a stable plateau value as I3/1(t) reached its minimum. Examination of the time evolution of ε″(t) and I3/1(t) at LAOS conditions leading to a macroscopically parallel orientation revealed for both the dielectric and nonlinear mechanical response a stretched exponential decrease (see Figure 9). The results were obtained for SI-13-13 at 120 °C,

= 10.9°). Similar results were found for the macroscopically parallel orientation (compare insets in Figure 6). In Situ Rheodielectric Measurements (Dynamic Measurements). In this section, the macroscopic orientation process was monitored in situ. For this purpose, the dielectric active normal mode relaxation process of the polyisoprene chains, which are tethered on one side to the interface between the polystyrene and polyisoprene rich domains, was used to probe in situ the influence of shear-induced alignment on the dielectric response of the sample melts at one fixed dielectric measurement frequency f Diel. The dielectric measurement frequency was chosen to correspond approximately to the peak maximum of the normal mode. In addition to the dielectric response, the mechanical nonlinear response was detected and characterized via FT-rheology. The time dependence of the nonlinear mechanical response was quantitatively followed by the relative intensity of the third harmonic as a function of time, I3/1(t).20,68 It is important to note that under the strong mechanical excitation, as applied during the LAOS experiment, the expressions in eqs 1−3 are no longer valid. However, the observed changes in ε″(t), as described below, still reflect the end-to-end vector fluctuations of the dielectrically active normal mode of the polyisoprene chains and can be used to follow the macroscopic orientation process of the lamellar microdomains. Figure 8 shows the time-dependent dielectric loss ε″(t) and the time-dependent mechanical nonlinear response, repre-

Figure 9. In situ rheodielectric measurements of the dielectric (open squares) and the mechanical nonlinear response quantified by I3/1 (open circles) for the shear-induced macroscopically parallel alignment during LAOS at 120 °C for (a) SI-13-13 at a fixed dielectric frequency of f Diel = 40 kHz and a mechanical stimulation of f LAOS = 5 Hz, γ0 = 0.5 and for (b) SI-17-15 at a fixed dielectric frequency of f Diel = 20 kHz and a mechanical stimulation of f LAOS = 3 Hz, γ0 = 1. Figure 8. In situ rheodielectric measurements for the dielectric loss ε″(t) (open squares) and the mechanical nonlinear response as quantified by I3/1(t) (open circles) for the shear-induced macroscopically perpendicular alignment during LAOS at 150 °C, f LAOS = 1 Hz, and γ0 = 1 for (a) SI-13-13 at a fixed dielectric measurement frequency of f Diel = 80 kHz and (b) SI-17-15 at f Diel = 70 kHz.

f LAOS = 5 Hz, and γ0 = 0.5 (Figure 9a) using a fixed dielectric measurement frequency of f Diel = 40 kHz and for SI-17-15 at 120 °C, f LAOS = 3 Hz and γ0 = 1 at a fixed f Diel = 20 kHz (Figure 10b). For the higher strain amplitudes, the mechanical excitation was stopped after tLAOS = 35 000 s and tLAOS = 1800 s, respectively, to exclude the possibility that the observed decrease in ε″(t) was caused solely by the mechanical shear flow orientating the polyisoprene chains along the shear direction as observed for linear polyisoprene homopolymers under LAOS.34,38 If this would be the case, ε″(t) would return to its initial value after the mechanical stimulus was switched off due to relaxation of the polymer chains. However, it can be

sented by I3/1(t), for the macroscopically perpendicular orientation of SI-13-13 and SI-17-15 at 150 °C, f LAOS = 1 Hz, and γ0 = 1. The dielectric measurement frequency was fixed at f Diel = 80 kHz for SI-13-13 and f Diel = 70 kHz for SI-17-15. Consistent with the static measurements introduced above, the 7213


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approximately ε′′ = 0.004. This clearly indicates that the observed changes in ε″(t) can be attributed to the overall alignment of the locally ordered lamellar microstructures even though after the mechanical stimulus is switched off, a small recovery of the dielectric response is observed. This recovery is attributed to the relaxation of the PI chains to their equilibrium state without any mechanical excitation. It is important to note that this effect is only about 10% of the total change in ε″(t) caused by the LAOS experiment, which strongly indicates that the governing effect of the macroscopic orientation is due to the shear-induced rotational orientation14,18 of the locally ordered lamellar microdomians as reported in our previous publication utilizing an unique in situ rheo-SAXS setup.28 It can also be seen that ε″(t) and the mechanical nonlinear response quantified by I3/1(t) have a similar time dependence. Furthermore, via recently published in situ rheo-SAXS measurements, a novel deordering process28 could be detected and was investigated via rheodielectric techniques. Our results showed for the first time that the achieved macroscopic orientation for the SI-13-13 diblock copolymer at 150 °C and deformation amplitudes higher than 1 (γ0 > 1) was not stable as the mechanical excitation continued above a certain length of time. Above this point, the state of orientation became less ordered under continuing mechanical stimulus, resulting in a biaxial distribution with approximately equal amounts of locally anisotropic lamellar ordered microdomains having either a preferentially parallel or perpendicular orientation. It is important to note that the above-described deordering process was also followed in situ using the time dependence of the mechanical nonlinearity as quantified by I3/1(t).28 This quantity was also investigated irrespective of whether the in situ dielectric response of the sample melt was capable of monitoring the deordering process.

Figure 10. In situ rheodielectric measurements of the dielectric loss ε″(t) (open squares) and the mechanical nonlinear response quantified by I3/1 (open circles) during LAOS for (a) SI-13-13 using a fixed dielectric measurement frequency f Diel = 80 kHz at 150 °C, f LAOS = 1 Hz, and γ0 = 2 and (b) SI-17-15 using a fixed dielectric measurement frequency f Diel = 90 kHz at 160 °C, f LAOS = 1 Hz, and γ0 = 2. The initial increase in ε″(t) indicates the development of a perpendicular orientation while the onset of the decrease in ε″(t) directly correlates with the beginning of the deordering process (vertical dotted line) as detected by the increase in I3/1(t).

clearly seen that only a small relaxation in ε″(t) occurred over the next 5000 s and that ε″(t) stayed nearly constant at

Figure 11. 2D-SAXS patterns of SI-17-15 after LAOS at T = 160 °C, f LAOS = 1 Hz, and γ0 = 2 along the normal (OX, OY) plane radial (OY, OZ) plane, and the tangential (OX, OZ) plane at three different positions with respect to the center of the sample disk: (a) r = 5.5 mm, (b) r = 4 mm, and (c) r = 2 mm. The anisotropic 2D-SAXS patterns at positions (a) and (b) indicate a biaxial orientation of the locally ordered lamellar microdomains, specifically one that is orientated both perpendicular and parallel with respect to the applied shear field. 7214


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Furthermore, the results presented here revealed that this deordering process was also found for the SI-17-15 diblock copolymer at 160 °C, f LAOS = 1 Hz and γ0 = 2. Figure 10 depicts the deordering experiments for SI-13-13 at 150 °C, f LAOS = 1 Hz and γ0 = 2, and for SI-17-15 under the mechanical conditions described above. The dielectric measurement frequency was fixed to f Diel = 80 kHz and f Diel = 90 kHz, respectively. The decrease in I3/1(t) and the increase in ε″(t) over the first time period of the LAOS experiment indicated the development of an overall perpendicular alignment of the lamellar microstructure. The measured quantities exhibited either a stretched exponential increase (ε″) or decrease (I3/1) leading to a maximum in ε″(t) and a minimum in I3/1(t), which corresponded to a well-aligned perpendicular orientation of the sample melt as probed by ex situ and in situ 2D-SAXS measurements.28 As the mechanical stimulus proceeded, I3/1(t) began to increase. This increase marks the onset of the deordering process as confirmed by additional ex situ 2D-SAXS measurements. It is important to note that the in situ determined timedependent dielectric loss was sensitive to both deordering and the development of a macroscopic biaxial structure. When looking at the time progression in Figure 11, the decrease in ε″(t) at the onset of the deordering correlated with the increase in the nonlinear mechanical response as indicated by the vertical dotted line. This decrease agreed with the abovedescribed time dependence of ε″(t) for the development of the macroscopically parallel orientation as shown in Figure 9. As the mechanical stimulus continued, more of the formerly perpendicularly aligned microdomains were orientated into a preferentially parallel alignment, which caused a continuing monotonic decrease in ε″(t) under the applied LAOS conditions. Finally, I3/1(t) and ε″(t) reached a stable minimum and maximum value associated with a stable biaxial orientation consisting of parallel and perpendicular fractions as confirmed by ex situ 2D-SAXS measurements for the SI-17-15 sample melt (see Figure 11). The anisotropic 2D-SAXS patterns along the normal and radial directions in Figure 12a,b reveal that the locally anisotropic ordered microdomains are preferentially ordered along both the parallel and perpendicular directions and also all orientations in between as indicated by the ringlike pattern along the tangential direction. It is important to note that the rearrangement towards a more biaxial alignment preferentially occurred at the two outermost positions of the analyzed sample disk where the local strain amplitudes were larger (γ0‑loc,a = 0.85γ0 and γ0‑loc,b = 0.65γ0). Closer to the center of the sample disk (γ0‑loc,c = 0.31γ0), the overall alignment of the microdomains remained mostly perpendicularly aligned.68 These findings were also reflected in the time dependence of ε″(t) for the SI-17-15 sample melt where the final plateau value for ε″(t = 20 000 s) was still greater than the initial value for ε″(t = 0 s), which corresponded to the macroscopically isotropic sample melt. The higher plateau value for ε″(t) suggests that the final sample contained a higher fraction of locally anisotropic lamellar microdomains that were preferentially orientated into the perpendicular direction. In contrast, the final plateau value of ε″(t) for SI-13-13 (Figure 10a) was approximately equal to the initial value of ε″(t = 0 s), indicating a roughly equal fraction of locally ordered microdomains with either a preferentially parallel or perpendicular orientation. Therefore, these results suggest that, in contrast to the nonlinear mechanical response

Figure 12. (a) Illustrations of the macroscopically parallel (left side) and perpendicular (right side) orientations and the experimental setup (middle). (b) A conceptual static figure of a polyisoprene chain confined by the polystyrene-rich lamellar region. The waveform of the interface between the polystyrene- and polyisoprene-rich regimes highlights the undulations at the interface, which occur well above the Tg of the polystyrene block as found by Willner et al.82 The chain in the confined lamellar system has an extension perpendicular to the interface, but the mobility perpendicular to the interface is strongly suppressed resulting in main mobility parallel to the interface.

I3/1(t), the dielectric response of the sample provides information on the preferential alignment of the locally ordered microdomains.

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DISCUSSION These results for ε″(t) and I3/1(t) show that the shear-induced macroscopic alignment process of SI diblock copolymers can be followed in situ by the time dependence of the dielectric response of the melts. For both macroscopic orientations, perpendicular and parallel, the time progression of the dielectric loss ε″(t) obeyed different trends. Starting from a macroscopically isotropic initial state, as confirmed by ex-situ 2D-SAXS studies, ε″(t) monotonically increased (perpendicular orientation) or decreased (parallel orientation) during the alignment process, leading to a plateau value or minimum (see Figures 9 and 10). These final states corresponded to either a macroscopically well-aligned perpendicular (increase in ε″) or parallel (decrease in ε″) aligned orientation as confirmed by ex situ 2D-SAXS measurements. Additionally, the nonlinear mechanical response followed and quantified by its time dependence of the nonlinear parameter I3/1(t) was significantly correlated with the time evolution of the dielectric response. Especially for the deordering process described above, a strong correlation between the onset of the deordering process as detected by I3/1(t) and ε″(t) was observed. Based on our recently published results,28 the time evolution of the mechanical nonlinear response was explained in terms of a rotational mechanism of the locally anisotropic ordered lamellar diblock copolymer microdomains accompanied by deformation of the microdomain interface. The assumption of the orientation process being mainly governed by a shearinduced rotation of the locally ordered lamellar microdomains is also supported by our results shown in Figure 11, where after the mechanical stimulus is switched off the recovery of the dielectric response is only 10% of its initial value which, as already suggested above, is attributed to the relaxation of the 7215


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Table 3. Dielectric Strength Δε Obtained from the HNRelaxation Model for the Normal Mode and the Slow Relaxation Mode before and after the LAOS Experiments (Eq 1)a

mechanically deformed polyisoprene chains to their undisturbed equilibrium state. In spite of this small recovery, the by far largest fraction of the observed change in the dielectric response does not recover to the initial value before the macroscopic orientation was performed and can therefore be assigned to the macroscopic alignment of the lamellar microdomains. Therefore, the following discussion on the changes observed in the dielectric response focus on this rotational mechanism, which governed the shear-induced macroscopic orientation process during LAOS. Note that the size of the locally ordered lamellar microdomains in the initial, macroscopically isotropic SI diblock copolymer was reported to be in the range of about 10 μm.69 From the analysis of the temperature dependence of the observed relaxation processes and their correlation to the normal and segmental modes of the respective homopolymers in Figure 4, the end-to-end vector fluctuations of the polyisoprene chains in the diblock copolymer melts were clearly assigned. Furthermore, a low-frequency relaxation process was observed and, based on the literature, attributed to global chain dynamics caused by vibrations or undulations of the interface.59 The results presented above indicate that this slow relaxation mode was dependent on the molecular weight of the polyisoprene block. Interestingly, LAOS had the opposite effect on the slow relaxation process compared to the normal mode relaxation of the polyisoprene; e.g., for the macroscopically parallel alignment, ε″ increased while for the normal mode (parallel alignment) ε″ decreased. As a first explanation, one could argue macroscopic alignment means perfectly separated phases with different dielectric properties; parallel alignment is equivalent to a serial connection of different materials while perpendicular alignment results in a parallel connection of the different materials. On a closer look, on the resulting differences are very small for the case under examination due to the fact that PS and PI are showing similar values for ε′ and ε″ that are small compared to ε′ for both materials. In addition, this model gives no explanation for the different behavior of the slow and fast relaxation process, i.e., ε″ for parallel orientation compared to the unoriented state is increased for the slow process, but decreased for the normal relaxation. From the HN-relaxation function used to describe these two distinct dielectric processes, the dielectric strength Δε of each process before and after alignment was obtained (see Table 3). The dielectric strength can be directly related to the number of dipole moments parallel to the applied electric field μ∥56 pointing along the normal vector of the plate−plate geometry. It should be mentioned that N and μ∥ in eq 6 includes only dipoles whose orientation can decay with time. If there are limiting factors such as extremely different mobilities in different directions or domain waviness that prohibit the full loss of the orientional memory, N is not equivalent to the total number of dipoles. For the system under consideration, it turns out that N and μ∥ are orientation dependent (see discussion later): Δε ∼

Nμ g kBT

f LAOS = 5 Hz, γ0 = 0.5, T = 120 °C

f LAOS = 5 Hz, γ0 = 0.2, T = 120 °C

SI-13-13 parallel

Δε (normal mode)

Δε (normal mode)

before after

0.0169 0.015

Δε (slow process)

0.0034 0.0137 0.0048 0.0095 0.0100 0.0068 f LAOS = 3 Hz, γ0 = 1, T = 130 °C Δε (normal mode)

SI-17-15 parallel before after f LAOS

Δε (slow process)

0.0168 0.0087 = 1 Hz, γ0 = 1, T = 150 °C

SI-13-13 perpendicular

Δε (slow process)

before after

0.0058 0.0034 f LAOS

Δε (slow process)

f LAOS

0.0045 0.0100 = 1 Hz, γ0 = 0.5, T = 150 °C

Δε (slow process) 0.0058 0.0052 = 1 Hz, γ0 = 1, T = 150 °C

SI-17-15 perpendicular

Δε (slow process)

before after

0.0056 0.0029

For the experiments performed at T = 150 °C, the Δε for the normal mode could not be determined accurately and are not included here; the accuracy of the Δε quantification for the normal mode was better than 1 × 10−3 while for the slow process it was better than 6 × 10−4.

a

between the PI chains vanishes as discussed in the beginning of the Results Section. In the confined system of a lamellar phase, the thermodynamic requirement of maintaining approximate uniform density requires motional cooperativity as already pointed out in literature from Watanabe et al.70 concerning the dielectric behavior of a Gaussian chain tethered to an impenetrable plane interface. In a lamellar SI system with fixed junction points, this motional cooperativitiy can occur only parallel to the interface as the PI chains cannot penetrate into the PS rich phase. This is one possible explanation for the experimental observed mobility and diffusion behavior in the directions parallel and perpendicular to the interface71−75 of the lamellar systems. From the differences between Δε in the macroscopically isotropic initial state and the final macroscopically anisotropic state, information was obtained about the orientation of the end-to-end vector mobility with respect to the applied electrical field. Since the dielectric tests were performed in the linearresponse regime, the measured dielectric strength Δε provides information about the fraction of dipoles and therefore the polyisoprene end-to-end vector parallel to the electric field that can decay with time. Therefore, in a macroscopically anisotropic system, the anisotropic diffusion process is equal to the fraction of rotatable dipoles and can be analyzed by the changes in the dielectric strength. It is important to note that for an accurate evaluation of Δε the total frequency behavior of the dielectric relaxation process is required. Therefore, only the values of Δε before and after LAOS obtained at lower temperatures for the macroscopically parallel orientation are discussed, while, for the slow relaxation process, the effect of the macroscopically perpendicular orientation could also be evaluated.

(6)

where N is the number of molecules possessing a parallel dipole moment, kB is the Boltzmann constant, and g is the Kirkwood− Fröhlich factor describing the motional cooperativity, which reduces to unity for our experiments because cross-correlation 7216


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stretches an already expanded polymer chain resulting in a thermodynamically unfavorable state. Next, as the dipole moment PA of the whole polyisoprene chain is given by56

It can be seen that for the macroscopically parallel orientation the final dielectric strength obtained for the normal mode relaxation of the symmetric SI diblock copolymer melts decreased relative to the initial state. The magnitude of this decrease appeared to correlate with the decrease in ε″(ω) detected during the in situ rheodielectric measurements (see Figures 8 and 9). As no reliable values for the dielectric strength Δε of the polyisoprene normal mode relaxation b at T = 150 °C before and after LAOS could be obtained, it is assumed that the increase in ε″(t) indicates that Δε would be larger for the final overall perpendicular state relative to the initial macroscopically isotropic state. However, for the slow relaxation process, ε″(ω) and Δε increased for the macroscopic parallel orientation and decreased for the overall perpendicular alignment relative to the randomly orientated initial state. At this point, the effect of shear-induced macroscopic alignment on the fast relaxation process attributed to the polyisoprene end-to-end vector fluctuations will be discussed, followed by an interpretation of the effects of LAOS on the slow relaxation process. The observed phenomena will be discussed with respect to the different orientations and dynamics of the end-to-end vector of the tethered polyisoprene chains. Hadziioannou et al.76 reported that the block copolymer chain was contracted along the parallel direction and Hasegawa et al. confirmed this result and reported an additional extension of the block copolymer chain along the perpendicular direction.77 These findings were confirmed by observations from Matsushita et al.78 The results from Meier showed that the requirement for maintaining uniform density in the lamellar domain invoked a relation between the domain size and chain dimension79 as given by 1/2

DK = 1.4αK⟨hK 2⟩0

PA⃗ = μP R⃗

(8)

where R⃗ is the end-to-end vector of the chain and μP is the component of the dipole moment of the monomer unit parallel to the polymer backbone, it can be seen that the dielectric normal mode reflects the fluctuations of the polyisoprene chain end-to-end vector (see Figure 12). Consequently, this anisotropy in the chain diffusion is also reflected in the differences observed for the dielectric normal mode of the macroscopically orientated anisotropic SI diblock copolymer melts with respect to their initial states and the relative overall alignment of the lamellar. For the macroscopically parallel alignment, diffusion of the free polymer chain ends mainly occurred in the X,Y-plane, resulting in a fluctuation of P⃗A parallel to the lamellar interface. The component of P⃗ A in the Zdirection is therefore independent of the main diffusion process; no contribution of these dipoles to the dielectric strength occurs (see eq 8 and discussion therein). Consequently, the dielectric loss decreased with respect to the initial state where the locally anisotropic lamellar ordered microdomains were randomly distributed throughout the whole sample. In contrast, the macroscopically perpendicular orientation led to an increase in the dielectric loss as fluctuations of the polymer chains in the X,Z-plane increased the contribution of dipoles to the dielectric strength. This was not possible in the parallel orientation, which corresponds to the direction of the applied electrical field. These interpretations are also supported by the investigation of the deordering process (see Figure 10) where a well-aligned macroscopically perpendicular orientation was first made and then deordered as the mechanical stimulus proceeded, resulting in a biaxial macroscopic orientation with preferentially parallel and perpendicular aligned fractions. From previous results,28 it was shown that this orientation process was mainly governed by a rotational mechanism while deformation of the microdomain interface affected the mechanical nonlinear response as measured by the time dependence of I3/1(t) obtained via FTrheology. Therefore, the time dependence of the dielectric loss of the polyisoprene normal mode was directly correlated with the nonlinear mechanical response and was sensitive to the relative orientation of the locally anisotropic ordered lamellar microdomains with respect to the direction of the applied electric field. The observed changes in the slow relaxation mode for the macroscopically aligned sample melts with respect to the initial state revealed an inverse trend as compared to Figure 12c. This can be explained by the origin of this relaxation process, which can be attributed to undulations and vibrational motions of the interface. As the measurements were performed at temperatures more than 20 °C above the Tg of the polystyrene block and at least 180 °C above the Tg of the polyisoprene block, the interface between the two polymers is considered to be flexible. Willner et al.82 presented evidence that these undulations occur with an amplitude of about 1 nm in hexagonally packed cylindrical poly(isoprene-b-dimethylsiloxane) diblock copolymer melts at a measurement temperature of 120 °C. Therefore, the fluctuation of the end-to-end vector for the polymer chains occurs in the X,Z-plane for the macroscopically parallel

(7)

where DK are the domain sizes for polymer block K, αK is the chain-expansion factor (along the lamellar normal) caused by the constraint-volume and volume filling effects, and ⟨hK2⟩0 is the unperturbed mean-square distance of the polymer K. Hashimoto et al.80 calculated that the ratio between the rootmean-square end-to-end distance ⟨h2⟩ of a polymer chain perpendicular (⟨hz2⟩) and parallel (⟨hx2⟩ = ⟨hy2⟩) to the lamellar interface is approximately ⟨hz2⟩/⟨hx2⟩ = 1.7. However, neutron reflection studies on lamellar poly(styrene-2-vinylpyridine) diblock copolymers performed by Torikai et al.,81 indicated that the free end group of the polymer chain was instead preferentially localized at the center of the lamellar microdomain, and its dimension parallel to the lamellar interface was then almost the same as that of an unperturbed chain with the same molecular weight. To understand the observed changes in the dielectric response during the alignment process, it is crucial to draw on previous work from which it is well-known that polymers tethered to an impenetrable, but flexible interface, such as block copolymers, have an anisotropic mobility and diffusion behavior in the directions parallel and perpendicular to the interface.71−75 The herein presented results and simulations support the conclusion that mobility of the confined polymer chains perpendicular to the lamellar is significantly suppressed compared to the mobility of the polymer chains parallel to the interface. This anisotropic mobility can be easily understood as diffusion in the perpendicular direction further 7217


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alignment and in the X,Y-plane for the macroscopically perpendicular orientation, which is opposite to the diffusion of the free chain ends. These undulations involve motion of the whole polymer chain by movement of the junction point located in the interface As a result, the orientation dependence of N and μ∥ in eq 6 and, consequently, of the dielectric strength is opposite to the fast relaxation process. Further investigations of SI diblock copolymers with different molecular weights and volume fractions of 1,4-cis-polyisoprene could reveal an even more detailed insight into the origin of these dynamic processes and their dependence on the macroscopic orientation of the sample.

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CONCLUSION

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AUTHOR INFORMATION

REFERENCES

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The macroscopic orientation process of poly(styrene-1,4-cisisoprene) (SI) diblock copolymer melts was studied in situ using both highly sensitive rheodielectric35 spectroscopy and FT-rheology52 under large-amplitude oscillatory shear (LAOS). The results clearly showed, for the first time, that the overall alignment of SI diblock copolymer melts can be followed in situ using the time progression of ε″(t) at a fixed dielectric measurement frequency that corresponds to the frequency range at which the normal mode relaxation of the polyisoprene chains occurs. By investigating the time dependence of ε″(t) and the dielectric strength Δε relative to the initial macroscopically isotropic state, the resulting macroscopic orientation of the lamellar microstructure both parallel and perpendicular to the applied shear field was investigated. The proposed explanations for the resulting dielectric phenomena were based on anisotropic diffusion of the free polyisoprene chain ends as detected by the dielectric normal mode and motions of the dielectrically active polyisoprene blocks perpendicular to the interface caused by undulations of the interface, thereby affecting the so-called slow relaxation process, which was itself attributed to global motions of the dielectrically active polyisoprene blocks. A recently observed deordering process28 occurring for continually applied shear and mechanical deformations could also be detected by the dielectric experiments. The observed time dependence of the dielectric loss ε″(t) further showed that the macroscopic alignment and deordering process occurred mainly via a rotational mechanism of the locally anisotropic lamellar ordered microdomains. The results presented here demonstrated that in situ monitoring of the orientation process for block copolymers containing a type A polymer leads to a better understanding of block copolymer dynamics and may find applications in the online monitoring of production processes for the fabrication of macroscopically anisotropic ordered functional materials.

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Article

ACKNOWLEDGMENTS

The authors thank Prof. Dr. Friedrich Kremer as well as Dr. Dirk Wilmer from Novocontrol for helpful and stimulating discussions. Furthermore, Prof. Dr. Kyu Hyun is acknowledged for a detailed introduction to the rheodielectric setup. 7218


Macromolecules

Article

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In Situ Rheodielectric, ex Situ 2D-SAXS, and Fourier Transform

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