Article pubs.acs.org/Macromolecules
In Situ SAXS Studies of Structural Relaxation of an Ordered Block Copolymer Melt Following Cessation of Uniaxial Extensional Flow Erica M. McCready and Wesley R. Burghardt* Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States ABSTRACT: A hexagonally ordered styrene−ethylene-co-butylene− styrene triblock copolymer melt is studied during and immediately following uniaxial extensional flow using small-angle X-ray scattering. Strips of polymer melt are stretched between counter-rotating drums inside an oven designed for in situ synchrotron studies. Previous study of this sample demonstrated deformation and reorientation of PS microdomains and identified a critical Hencky strain ∼0.2 at which the structure is dramatically disrupted. To further probe microstructural dynamics, we study relaxation behavior of structure and stress in samples stretched in the melt to various Hencky strains. Upon cessation of stretching below the critical strain, structural relaxation is strongly retarded; stretching to higher strain leads to more rapid relaxation. At all strains, microdomain orientation relaxation following flow is slower than relaxation of flow-induced deformation and mechanical stress. The extension rate dependence of the sample’s response is also explored; higher rates result in faster relaxation of both stress and structure.
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INTRODUCTION The ability of shear flows to affect microphase-separated structures in block copolymer melts has been well documented using in situ methods.1−8 The application of shear flow can cause microdomains to reorient1−9 or change morphology10 and can affect the transition from a disordered to an ordered phase.11,12 However, there have been relatively few studies of block copolymer melts undergoing uniaxial extensional flow. Many of the existing studies have exploited advances in extensional rheometry methods in order to study nonlinearities in the mechanical behavior, with any analysis of structural changes limited to ex situ studies of samples quenched after flow.13−17 A few studies have been performed using in situ birefringence during the flow combined with ex situ small-angle X-ray scattering (SAXS), which provides some amount of structural information about these materials.18−21 In all cases, there has been a conspicuous absence of studies of either mechanical or structural properties following the cessation of extensional flow. In a recent study22 we have applied uniaxial extensional flow to a styrene−ethylene butylene−styrene (SEBS) triblock copolymer melt exhibiting a hexagonally packed cylindrical morphology. Structural changes, including deformation and reorientation of microphase-separated PS domains, were measured using in situ SAXS, while mechanical data were collected via offline transient extensional viscosity measurements. This in situ study employed a custom built convection oven housing a Sentmanat extensional rheometer (SER),23,24 described in more detail below. The ability to collect structural information both during and immediately following flow is extremely advantageous. First, it allows for observation of structural changes at all time points during flow, free from concerns of any structural relaxation during sample quenching. © XXXX American Chemical Society
In addition, it allows for the direct monitoring of structural relaxation following flow cessation. This initial study revealed a complex structural response to extensional flow, including deformation of the microphase-separated morphology (characterized by anisotropic flow-induced changes in d-spacing), and a reorientation process by which elongated PS microdomains progressively rotate and align toward the stretching direction. This reorientation proceeds through a complex intermediate state exhibiting a characteristic “four point” SAXS pattern.25−27 A critical Hencky strain εH ≈ 0.2 was identified, where dspacings in the parallel and perpendicular directions deviate from an initially affine deformation and the extensional viscosity deviates from linear viscoelastic predictions. Interestingly, there is no discernible manifestation of this critical strain on the domain orientation, which reaches a maximum value at a larger Hencky strain, εH ≈ 1, after which anisotropy in SAXS patterns decreases. Upon flow cessation after prolonged stretching, relaxation of both d-spacing and flow-induced orientation was observed, with the former much faster than the latter. Although extension rate seemed to have little effect on the quantitative measures of deformation and orientation under the conditions studied, a clear rate dependence was observed in the qualitative characteristics of SAXS patterns collected during the reorientation process, attributed to the competing effects of the applied flow and microscopic structural relaxation. Clear evidence of significant structural relaxation, together with the observation of complex intermediate morphological states during flow, has prompted the experiments that are the focus in this work. Here, uniaxial extensional flow is applied to a Received: August 7, 2014 Revised: November 10, 2014
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dx.doi.org/10.1021/ma501633f | Macromolecules XXXX, XXX, XXX−XXX
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separated morphology, SAXS patterns were collected on solid samples at room temperature using a Rayonix CCD detector at an energy E = 9.4 keV (λ = 1.32 Å) and sample-to-detector distance of 7.50 m. These patterns were analyzed to extract intensity as a function of scattering vector, I(q) (Figure 1). Samples annealed in the melt at 130 °C after
range of intermediate Hencky strains, chosen based on qualitatively and quantitatively distinctive points along the trajectory of flow-induced structural states. These include one value below the critical strain (εH = 0.15), two values where the “four point” features are most pronounced (εH = 0.4 and 0.7), and strains near the maximum in microdomain orientation (εH = 0.7 and 1.0). Studying the nature of relaxation from these diverse structural states provides deeper insights into the response of this polymer to extensional flow. In addition, we consider a wider range of extension rates in this work than in our previous study. As in our earlier study, in situ SAXS data are complemented by offline extensional viscosity measurements.
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METHODS
The material used in this study is a styrene−ethylene-co-butylene− styrene (SEBS) triblock copolymer donated in pellet form by Kraton. The sample has a reported MW = 87 kg/mol with a 13 wt % styrene content. This material is very similar to a polymer studied extensively by Modi and co-workers,28 who reported an order−disorder transition (ODT) at approximately 190 °C and an order−order transition (OOT) at 140 °C. The microphase-separated structure was found to depend on the thermal history of the sample. Hexagonally packed PS cylinders are formed when the sample is quenched from high temperature to below the OOT. Heating above the OOT will then induce a slow transition in the structure to form a spherical morphology with BCC ordering. We were able to replicate both the ODT (189 °C in our sample)22 and, as described further below, the order−order transition from cylindrical to spherical morphology found in their results. Samples were prepared by first dissolving the pellets in toluene, casting into a sheet via solvent evaporation, and then ensuring the removal of any remaining solvent by holding the material in a vacuum oven at elevated temperature overnight. This erases the orientation induced by production of the pellets. This material is compression molded in sheet form at 200 °C for 20 min to disorder the microphase-separated structure and then annealed at 130 °C for 8 h to ensure the cylindrical phase-separated structure is achieved. Because of the prior thermal clearing, this sample preparation should lead to an initially random orientation distribution of cylindrically ordered “grains”. These sheets are cut into rectangular strips (22 mm × 9 mm × 0.75 mm) for use in both X-ray scattering and transient extensional viscosity studies. Extensional viscosity measurements were performed using a Sentmanat extensional rheometer fixture (SER-HV-A01) in a Rheometrics Scientific ARES-LS controlled strain rheometer. More information on the SER’s operation can be found in other publications.23,24 Samples were subjected to an extension rate ranging from 0.01 to 0.2 s−1 to final Hencky strains in the range 0.15−2.5, followed by a period of relaxation for 5 min following flow cessation. While there have been reports and analyses of necking failure after cessation of drum rotation in SER testing of entangled polymers,29 we have seen no indications of this phenomenon in these samples. All tests were performed at 130 °C. As indicated in our previous work on this material,22 although the sample undergoes uniaxial deformation (equal reduction in width and thickness with increasing strain), for Hencky strains of ∼1 and above the actual strain experienced is somewhat greater than the nominal applied strain. This introduces uncertainty into calculation of extensional viscosity through positive deviation of extension rate and negative deviation of sample crosssectional area (although these errors may cancel to some extent in the data reduction). This may reflect inhomogeneous deformation associated with the nearly constant extensional viscosity observed throughout most of the experiments. Nevertheless, we have found that samples are generally not prone to overt necking failure under the conditions studied here. All SAXS measurements were performed at the Advanced Photon Source at Argonne National Laboratory, at the DND-CAT Sector 5IDD beamline. To verify the impact of thermal history on microphase-
Figure 1. Intensity as a function of scattering vector q measured at room temperature for samples annealed at 130 °C (dashed line) and 150 °C (solid line). Peak locations expected for, respectively, hexagonally packed cylinders and BCC spheres are indicated by the arrows. thermally clearing at 200 °C yielded diffraction peaks that may be indexed to hexagonally packed cylinders (peaks at q*, √3q*, and √4q*). Diffraction peaks in such samples are broad, indicative of relatively poor long-range order, consistent with TEM and SANS data reported by Modi et al.28 If such a sample is subsequently annealed for a prolonged time at 150 °C, a growth of storage modulus is observed, attributed by Modi et al.,28 to an order−order transition from hexagonally packed cylinders to BCC ordering of spherical microdomains. SAXS data in Figure 1 confirm that the polymer studied here transforms to BCC ordering upon annealing at 150 °C, indicated by peaks at q*, √2q*, √3q*, and √4q*. In contrast to SANS data reported by Modi et al., here we find sharp diffraction peaks indicative of high quality long-range ordering of spherical PS microdomains. The origin of this difference is unclear. Like Modi et al., we find that q* in the spherical phase (0.0263 Å−1) is higher than in the cylindrical phase (0.0248 Å−1), indicating somewhat smaller d-spacing. However, the relative difference in d-spacing (∼6%) is somewhat smaller in our case. In the remainder of this paper, we only consider samples prepared by annealing at 130 °C and studied in the melt at 130 °C and hence in the hexagonally packed cylinder phase. For in situ extensional flow tests at 130 °C, SAXS images were collected with a Mar CCD detector at a resolution of 1024 × 1024 pixels using X-rays with E = 9 keV (λ = 1.378 Å) and a sample-todetector distance of 2.42 m. Images were collected every 5 s using a 1 s exposure. Several frames were collected prior to flow in order to confirm the initial cylindrical morphology and to assess the structural state in the initial condition of each sample. The experimental setup included the SER fixture housed in a custom-built oven with a stepper motor to drive the fixture. The X-ray beam travels into the oven, between the two drums of the SER, through the center of the sample, while scattered X-rays leave out the backside of the oven to the detector. Experiments were performed at 130 °C at extension rates of 0.01−0.2 s−1 to final Hencky strain values of 0.15−2.5, followed by a 5 min period of relaxation following flow cessation. Two primary types of analysis are performed on X-ray scattering images (Figure 2a). Intensity as a function of scattering vector is extracted in 10° wide sectors of the image parallel (azimuthal angle 175°−195°) and perpendicular (85°−95°) to the flow direction using the program Fit2D.30 I(q) plots reveal the microphase-separated morphology as well as characteristic domain spacing (d-spacing). The hexagonal cylindrical morphology is again confirmed in the melt at 130 B
dx.doi.org/10.1021/ma501633f | Macromolecules XXXX, XXX, XXX−XXX
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The azimuthal distribution of intensity is related to the orientation distribution of grains with hexagonally packed cylindrical microdomains. Given the nearly random initial condition (Figure 2a) and uniaxial symmetry of the applied flow, the orientation distribution itself should exhibit uniaxial symmetry, such that the degree of microdomain orientation may be quantified in terms of the Hermann’s orientation parameter, ⟨P2⟩. This is defined as the average of P2(cos φ) = 3/2(cos2 φ − 1), weighted by the uniaxial orientation probability distribution function f(φ). Since cylindrical microdomains diffract perpendicularly to their axes, I(φ) is not itself equal to f(φ), but is rather related to f(φ) via an Abel transformation.31 Nevertheless, the orientation parameter may be computed by first calculating an average of P2 weighted by I(φ), and then normalizing by the value (= −1/2) that would be realized for a perfectly oriented sample with intensity concentrated at φ = π/2.31 The resulting expression is π
⟨P2⟩ = − 2
∫0 P2(cos φ) sin φI(φ) dφ π
∫0 sin φI(φ) dφ
(2)
Defined in this way, ⟨P2⟩ = 0 for a random orientation and approaches a value of 1 for perfect orientation of microdomains along the stretching direction. In this work we measure relaxation of several physical quantities: mechanical stress, X-ray orientation parameter, and d-spacing. To quantify and compactly represent the rates of these relaxation processes, we fit data using a multimode decaying exponential function: g (t ) =
∑ aie−t/ λi + b i
(3)
where g(t) represents relaxation data from a particular experiment and variable. This function includes a constant baseline term (b), since many of the quantities being studied here do not relax to a zero value. From such fits we calculated an average relaxation time according to λavg =
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Figure 2. Representative small-angle X-ray scattering images (a) prior to flow and (b) following flow cessation. Image in (a) shows the analysis regions for orientation parameter (dotted line) and d-spacing (solid lines). As described in the text, the q-range used to extract I(φ) is adjusted to conform to φ-dependent shifts in the diffraction peak location induced by flow. Images in (b) represent relaxation behavior (columns) from samples that were subjected to an extension rate ε̇ = 0.01 s−1 to various values of Hencky strain (εH) (top row).
1+δ
∫1−δ
I(qr , φ) dqr
(4)
RESULTS AND DISCUSSION SAXS patterns collected in the melt (Figure 2a) reveal a nearly isotropic initial condition, indicating random orientation of hexagonally packed PS cylindrical microdomains. Figure 2b presents representative SAXS images collected during the flow (top row, ε̇ = 0.01 s−1) and following flow cessation after various intermediate strains (columns) at 30, 120, and 300 s from the time the flow is stopped. Images along the top row of Figure 2b demonstrate the multiple modes of structural response during flow identified in our earlier work.22 Upon flow inception there is an elongation of the initially circular pattern perpendicular to the flow direction together with a compression of the pattern parallel to the flow, indicating anisotropic deformation of the microphase-separated morphology. Reorientation of microdomains is revealed by the progressive azimuthal redistribution of scattered intensity. At intermediate strains (εH = 0.4 in Figure 2b), the pattern exhibits a symmetrical four-peak feature; with further increase in strain the peaks migrate toward the direction perpendicular to flow and eventually merge. This change in intensity distribution corresponds to reorientation of PS microdomains such that their axes ultimately point along the flow direction. Patterns remain qualitatively similar for the remainder of the flow, although quantitative analysis reveals continued structural evolution at higher Hencky strains. When the flow is stopped at intermediate strains, X-ray patterns collected following flow cessation reveal relaxation of
°C by the 1:√3:√4 spacing between peaks (I(q) scans in the melt were presented in our earlier work).22 Flow-induced changes in primary peak location (q*) both parallel and perpendicular to the flow direction are determined from polynomial fits of data near the primary diffraction peak, allowing extraction of corresponding d-spacing values according to d = 2π/q*. Intensity is extracted as a function of azimuthal angle φ over a q range that spans the primary diffraction peak, focusing on the top half of the image (φ = 0−180°) to avoid the shadow from the beam stop holder in the bottom of the image. Under flow, the diffraction peak location is dependent on azimuthal angle. To ensure consistency in extraction of azimuthal scans under these conditions, the azimuthal scan I(φ) is computed according to
I(φ) =
∑ aiλi ∑ ai
(1)
where qr = q/q*(φ). Thus, the range of q used in computing I(φ) (depicted as circular in Figure 2a) is made to conform to the elliptical distortion of the primary diffraction peak in the 2D scattering images. In our analyses, δ is set equal to 0.35. C
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both flow-induced deformation and microdomain orientation (Figure 2b). The primary diffraction peak relaxes from the elongated shapes measured during the flow back toward its original circular shape. Following flow cessation, diffracted intensity progressively redistributes azimuthally toward a more isotropic distribution. At strains for which diffraction patterns exhibit distinct four-peak features, the pair of peaks on each side of the stretching direction tends to blur together to form a single broader peak. At higher strains where multiple peaks have already merged together, these peaks spread out azimuthally. The significant relaxation processes revealed in these patterns highlight the advantages of in situ methods and the risk of possible structural relaxation during quenching when relying on ex situ characterization methods. The orientation parameter can be calculated for every data frame collected during the experiments from which images in Figure 2 were selected and is plotted as a function of time in Figure 3. Despite some small variation in the initial value
Figure 4. Normalized domain spacing as a function of time during flow (closed) and following flow cessation (open) in 10° slices in the parallel (>1) and perpendicular (1) and perpendicular (
