Architecture-Induced Microphase Separation in Nonfrustrated A–B–C

Apr 15, 2013 - Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States. Macromolecules ...
0 downloads 0 Views 3MB Size
Article pubs.acs.org/Macromolecules

Architecture-Induced Microphase Separation in Nonfrustrated A−B−C Triblock Copolymers Bryan S. Beckingham and Richard A. Register* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: The extent of block microphase separation in nonfrustrated A−B−C triblock copolymers forming a “threedomain, four-layer” lamellar morphology is examined. Specifically, the extent of separation between the B and C blocks is probed, for the case where the B and C blocks are sufficiently compatible that they would not be microphaseseparated if they were connected as a diblock. However, attachment of the A block, and consequent localization of the A−B block junction to the A−B lamellar interface, induces extensive separation between the B and C blocks. This separation is revealed both through the small-angle X-ray scattering pattern in the melt, and by distinct glass transitions observed in the solid state for the B block at low B−C segregation strengths, and for both the B and C blocks at higher segregation strengths. The particular polymers studied here have polyethylene as the A block; except for the most weakly segregated triblock, upon cooling from the melt, crystallization of the polyethylene block is confined within the lamellar structure established in the melt, with the polyethylene crystals stacking orthogonally to the microdomain lamellae.



INTRODUCTION A−B−C triblock copolymersblock copolymers with three chemically dissimilar blocksare of increasing interest due to their ability to form a far more diverse array of morphologies than diblock copolymers.1−17 In such materials, there are potentially two distinct types of interblock interfaces (A−B and B−C), such that A−B−C and A−C−B triblocks often form qualitatively different structures.8 Phase behavior is best understood18,19 for A−B−C triblocks with so-called “nonfrustrated” sequences, where the Flory interaction parameters χ (or alternatively, the interaction energy densities X ≡ χRT/Vref) obey the relations XA−C > XA−B and XA−C > XB−C. In such systems, A−C contacts are minimized to the extent possible; this is often achieved through “core−shell” variants of the familiar spheres, cylinders, gyroid, and lamellae exhibited by diblock copolymers, where a layer of B separates the A and C domains.3,4,7,8,12−14 Here, we probe the question of interblock segregation in such nonfrustrated triblocks forming a “three-domain, fourlayer” lamellar morphology.1,14 In the strong-segregation limit, the one-dimensional repeating unit in this morphology is an ...ABCB... stack, where the individual layers are nearly pure A, B, or C. However, the present work focuses on the weakly segregated case, in particular where the B and C blocks would be mixed (disordered) if connected simply as a B−C diblock. In this case, separation between the B and C blocks is induced by the attachment of the A block, or more precisely, by the localization of the A−B block junction to a lamellar interface, combined with the A−B−C block connectivity. We show that even when the analogous B−C diblocks would be far from the © XXXX American Chemical Society

order−disorder transition (ODT), the B and C domains in A− B−C triblocks can be extensively microphase-separated enough to show distinct glass transition temperatures (Tg) and for the separation between B and C blocks to strongly modulate the small-angle X-ray scattering (SAXS) pattern in the melt. The triblocks studied here have polyethylene (E) as the A block; hydrogenated medium-vinyl polyisoprene (hI), an amorphous rubber, as the B block; and a random copolymer of either styrene and hydrogenated isoprene (SrhI) or vinylcyclohexane and hydrogenated isoprene (VCHrhI) as the C block. SrhI and VCHrhI are amorphous and, at the compositions employed herein (≈50 wt % S or VCH), have T g values near or below room temperature. Previous studies20−22 of E-containing triblock copolymers have focused on the case where one of the other two blocks is glassy at the E freezing point, thereby confining E crystallization. Here, we show that E crystallization can also be confined by microphase separation in the melt, well above any block Tg, and even in polymers which are only moderately segregated; this confinement imparts a strong orientation to the E crystallites. The abrupt change in the electron density profile upon E block crystallization also produces dramatic changes in the intensities of the SAXS peaks from the lamellar domain structure. Received: February 24, 2013 Revised: April 5, 2013

A

dx.doi.org/10.1021/ma400397h | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules



Article

Morphological Characterization. Differential scanning calorimetry (DSC) measurements were made on ≈10 mg specimens, using a PerkinElmer DSC 7 equipped with a Type II intracooler, calibrated with indium and tin. Specimens were simply cooled from the melt at 10 °C/min to −70 °C, held for 5 min, and data recorded upon heating at 10 °C/min. Small- and wide-angle X-ray scattering (SAXS and WAXS) patterns were obtained on three different instruments, all employing PANalytical PW3830 generators with long fine focus Cu Xray tubes to yield Cu Kα radiation (λ = 0.154 18 nm). Data were collected in transmission, both at room temperature and at elevated temperature using hot stages. One-dimensional (1D) SAXS patterns were collected with an Anton-Paar compact Kratky camera and an MBraun OED-50 M position-sensitive detector. Data were corrected for detector sensitivity and positional linearity, empty beam scattering, sample thickness, and transmittance, placed on an absolute intensity scale via a polyethylene standard, and desmeared for slit length.27 Absolute SAXS intensities (I/IeV) are plotted against the magnitude of the momentum transfer vector q = (4π/λ) sin θ, where θ is half the scattering angle; calibration was via silver behenate (d = 5.838 nm).28 Intensities were multiplied by q2 to approximately correct for the form factor of lamellae.29 For two-dimensional (2D) SAXS and WAXS measurements, oriented specimens were prepared by planar extensional flow in a lubricated channel die.30,31 2D SAXS measurements employed a custom-designed point-collimation system of the “DuMond geometry”32 which uses two bent Si (111) triangular crystals to focus the X-ray beam in the vertical and horizontal directions (Molecular Metrology). Scattered X-rays are collected by a Molecular Metrology 2D argon-filled Gabriel-type33 multiwire detector situated 1.5 m downstream from the sample position. The sample chamber and optical train are evacuated to minimize scattering and absorption by air; transmitted X-ray intensity is monitored by a photodiode in the beamstop. Data were corrected for detector sensitivity, empty beam scattering, sample transmittance, and specimen thickness, with the scattering angle and absolute intensity calibrated as for the 1D SAXS system. 2D WAXS measurements employed a Statton pinhole camera system previously described,34 using Kodak image plates read by a GE Biosciences Storm 820 scanner.

EXPERIMENTAL SECTION

Polymerization. A glass reactor was flamed out under vacuum and rinsed with tert-butyllithium (t-BuLi) and subsequently with cyclohexane (CH) prior to charging with t-BuLi as the initiator in a nitrogen-filled glovebox. Both CH and triethylamine (TEA) were stirred over diphenylhexyllithium (adduct of s-BuLi and 1,1-diphenylethylene) and degassed via freeze−pump−thaw (FPT) cycles. After initiator charging, degassed CH was vacuum-transferred directly into the reactor. Butadiene (Bd) was condensed in a trap containing n-BuLi and submersed in liquid nitrogen; the trap was equilibrated with an ice−water bath prior to vacuum-transferring the Bd into the reactor. Following the Bd polymerization, TEA was vacuum-transferred into the reactor prior to addition of the isoprene (I) monomer, in equal volume to the original CH solvent charge. TEA is an effective randomizer for styrene−isoprene (SrI) copolymerization as discussed elsewhere.23 I monomer was stirred over n-BuLi, degassed via FPT cycles, and vacuum-transferred directly into the reactor. For the statistical copolymer block, S and I monomers were mixed, stirred over dibutylmagnesium, degassed via FPT cycles, and vacuum transferred into the reactor. The Bd and I blocks were polymerized at 60 °C, while the SrI block was polymerized at 30 °C. Aliquots of the reaction mixture were collected immediately prior to the second and third monomer charges to permit characterization of the first block (Bd) and the Bd−I diblock. Hydrogenation. Subsequent to polymerization, the polymers were catalytically hydrogenated using one of two catalyst systems. Both saturations were performed in a stirred 2 L Parr batch reactor with 4− 6 g/L polymer in cyclohexane at 100 °C and 400−500 psi of H2. The extent of hydrogenation was monitored with infrared spectroscopy on samples taken from the reactor, and upon completion (>99% of the desired units saturated, corresponding to the detectability limit), the catalyst was removed and the polymer precipitated into methanol. A homogeneous Ni/Al catalyst24,25 was used to selectively saturate the Bd and I units while retaining the S aromaticity. Undesired S saturation using this catalyst was quantified using an SrI random copolymer via comparison of the aliphatic and aromatic regions of the 1 H NMR spectrum and found to be zero within experimental error ( 0 would only exacerbate the discrepancy. This point was already noted in Figures 3b and 4, where the second-order peak intensity is much greater than one would observe for a near-symmetric diblock. Thus, we next consider a three-domain lamellar structure (four-layer, ...ABCB... repeat), for which a representative electron density profile is shown as the dashed curve in Figure 8b. For the sharp-interface case and an isotropic specimen, the peak intensities are given by

In/I1 which are all larger than the observed values in Table 4, which indicates an additional damping of the peak intensities. To account for this damping, we employ the same exponential correction as in eq 1: In ,4L ∼ n−4{ρA sin(nπϕA ) − ρB sin(nπ (1 − ϕB)) + ρC [sin(nπ(1 − ϕB)) − sin(nπϕA )]}2 e−kn

2

(3)

Since there are two dissimilar types of interface (A−B, B−C), using a single-exponential factor is clearly an approximation; however, since the present triblocks typically show only one (n = 2) or at most two (n = 2, 3) higher-order peaks with measurable intensity, there is no experimental basis for further refinement of the model. Moreover, there is relatively little electron density contrast between the A (E) and B (hI) blocks in the melt; at 112 °C, (ρhI − ρE) = 1.1 e−/nm3, while (ρSrhI − ρhI) = 22.2 e−/nm3 and (ρVCHrhI − ρhI) = 19.0 e−/nm3. This small contrast is shown graphically in Figure 8b, where the dashed curve corresponds to the electron density profile for E− hI−(SrhI)50-60 at 112 °C in the limit of perfect phase separation between all three blocks. Thus, the measured k for the molten triblocks can be reasonably associated with the B−C interface, and interpreted as an (apparent) thickness t = d(k/ 2π)1/2 of the B−C interface. The values of k and apparent t are listed in Table 4, calculated via eq 3 by adjusting k to match I2/I1. For E−hI−

In,4L,sharp ∼ n−4{ρA sin(nπϕA ) − ρB sin(nπ (1 − ϕB)) + ρC [sin(nπ(1 − ϕB)) − sin(nπϕA )]}2 (2)

Values of ρA, ρB, ρC, ϕA, and ϕB were set using the specific volumes for the various blocks as functions of temperature (see Supporting Information), coupled with the measured polymer compositions. For all three triblocks, eq 2 predicts values of H

dx.doi.org/10.1021/ma400397h | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

(SrhI)50-60 in the melt (112 °C), three SAXS peaks were observed, with I2/I1 = 0.055 and I3/I1 × 103 = 1.2; thus, values of k could be obtained from either I2/I1 (yielding k = 0.62 and I3/I1 × 103 = 2.1, top line in Table 4) or I3/I1 (yielding k = 0.69 and I2/I1 = 0.044, second line in Table 4). These results indicate the robustness of the model (eq 3) to errors in the determination of integrated peak intensities (due largely to the choice of baseline in peak integration), as both methods give t = 16.5 ± 0.5 nm. For E−hI−(VCHrhI)50-60, only one higherorder peak was obtained (n = 2), yielding k = 0.78 and t = 17.3 nm; sensitivity analysis in the model indicated dt/d ln(I2/I1) = −3.8 nm and dt/dϕC = +16 nm, where ϕC is the volume fraction of the C (random copolymer) block, so again the results are robust to the experimental errors present (≈20% relative error in I2/I1, ≈2% absolute error in ϕC). The value of t for the VCH derivative (17.3 nm) is scarcely larger than for the S derivative, despite the ≈3× difference in XB−C in the two cases (see Table 2). A similar value of t (16.6 nm) is also obtained for E−hI−(SrhI)51-38 (with the sensitivity analysis yielding dt/d ln(I2/I1) = −2.4 nm and dt/dϕC = +10 nm). Though the values of t for the triblocks are much larger than for the related near-symmetric microphase-separated diblocks (t values in Supporting Information), they still indicate substantial separation between the B and C blocks, despite the fact that none of the constituent B−C sequences from the A−B−C triblocks would form a microphase-separated diblock at these temperatures (Table 2). This is consistent with the DSC results in Figure 7b, which indicated good segregation between B and C for all of the triblocks following E block crystallization. Finally, Figure 8c illustrates the idealized electron density profile (perfect phase separation between the blocks) for E−hI−(SrhI)50-60 at room temperature, where the electron density of A is weighted over both crystalline and amorphous E (with wx = 0.28, as in Table 3); this corresponds to a stacking of the E crystallites perpendicular to the A−B−C lamellar stacking, which will be shown to be true in the next section. Calculations using eq 3, either with k = 0 or with the melt value of k = 0.65, reveal that this electron density profile predicts I2/I1 > 1, as experimentally observed for E−hI− (SrhI)50-60 at room temperature (Figure 3a). Crystal Orientation. Microphase separation in the melt can impart strong orientation to crystals which form within the preexisting domain structure.55 For polyethylene crystallization confined within lamellar microdomains, both the b-axis (fast growth direction) and the c-axis lie preferentially in the plane of the lamellae, resulting in the orthorhombic PE unit cell orienting with its a-axis parallel to the lamellar normal.45,46,55,56 To examine the orientation of E crystals within the four-layer lamellar morphology, specimens of both hydrogenated derivatives were aligned in planar extensional flow using a lubricated channel die.30,31 In this arrangement the extensional axis is the “flow direction” (FD), the compression axis is the “load direction” (LD), and the neutral direction is denoted the “constraint direction” (CD). We use these principal axes to indicate the direction of the incident X-ray beam; i.e., the “LD view” has the X-ray beam parallel to LD. Typically lamellar block copolymers aligned in this manner orient with their lamellar normal parallel to the LD.31,56,57 Similar results were obtained for both of the higher molecular weight triblocks; those for E−hI−(VCHrhI)50-60 are shown in Figure 9, while an analogous figure for E−hI−(SrhI)50-60 is provided in the Supporting Information.

As expected for lamellae with their normals lying along LD, no microdomain scattering is visible in the LD view (Figure 9a,b); only isotropic crystallite scattering is present (Figure 9c). The distinct spots at q* and 2q* on the meridian in the CDview SAXS pattern (Figure 9d−f) correspond to the microdomain spacing d, confirming that the lamellae align with their normals parallel to LD, as anticipated and illustrated in Figure 9j. Retention of the melt microstructure in the 2D SAXS data for these polymers indicates that E crystallization is restricted to within the pre-existing microdomains, despite the relatively weak segregation and the fact that both amorphous blocks are well above their Tg at the E freezing point.45,55 The azimuthal positions of the indexed WAXS reflections from Figure 9g−i are used to determine the crystal orientation within the lamellar microdomains. All observed reflections correspond to the usual orthorhombic E unit cell. Based on these reflections, the crystals are oriented as schematized in Figure 9k, with the fast growth direction (b-axis) along the flow direction and free rotation around the a-axis. The azimuthal split angles across the equator for the (110) reflection, ∼65° and 66° for E−hI−(SrhI)50-60 and E−hI−(VCHrhI)50-60, respectively, are slightly below the expected split angle of 68.8° based on the known E unit cell and may reflect some tilt of the crystal stems with respect to the lamellar interfaces (around the b-axis, see Figure 9k).56 This observed crystal orientation within the four-layer lamellar structure matches that of previously studied E-containing diblocks wherein E crystallization is confined by the (two-layer) lamellar structure.45,46,55,56 In the lower molecular weight triblocks (data not shown), E−hI−(SrhI)51-38 exhibited similar 2D SAXS and WAXS patterns as E−hI−(VCHrhI)50-60 and E−hI−(SrhI)50-60. By contrast, E−hI−(VCHrhI)51-38 showed no orientation in channel-die-processed specimens, by either SAXS or WAXS. This is characteristic of “breakout” crystallization58,59 and is not surprising given the weakly segregated nature of this material (TODT = 153 °C).



CONCLUSIONS The present work illuminates aspects of the interblock segregation in A−B−C triblock copolymers, specifically those of the “nonfrustrated” type, where XA−C > XA−B and XA−C > XB−C. Even when the B and C blocks might naively be expected to mixwhen the B−C “diblock combination” has χN ≪ (χN)ODTextensive separation between the B and C blocks is observed. Attaching a well-segregated A block to the hypothetical B−C diblock induces a localization of the A−B block junction to the A−B interface, producing a situation analogous to end-grafted B−C diblock brushes, wherein there is always some stratification of the B and C blocks, even when XB−C = 0. Only when the entire triblock is close to its ODT, as in E−hI− (VCHrhI)51-38, do the B and C blocks mix extensively, approaching the “two-domain” limitbut in this case there is extensive mixing between all three blocks. For triblocks not close to their ODT, segregation between the B and C blocks in the melt is evident in the relative intensities of the higher-order SAXS peaks, and in the increased lamellar d spacing relative to analogous A−B diblocks, while segregation in the solid state (below the E block freezing point) is evident through the observation of distinct glass transitions corresponding to domains of nearly pure B (or, for the more-segregated E− hI−SrhI diblocks, distinct glass transitions for separate domains of nearly pure B and C). In the weakly segregated E−hI− (VCHrhI)51-38, crystallization of the E block destroys the melt I

dx.doi.org/10.1021/ma400397h | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

(15) Wang, C.; Lee, D. H.; Hexemer, A.; Kim, M. I.; Zhao, W.; Hasegawa, H.; Ade, H.; Russell, T. P. Nano Lett. 2011, 11, 3906−3911. (16) Meuler, A. J.; Hillmyer, M. A.; Bates, F. S. Macromolecules 2009, 42, 7221−7250. (17) Bates, F. S.; Hillmyer, M. A.; Lodge, T. P.; Bates, C. M.; Delaney, K. T.; Fredrickson, G. H. Science 2012, 336, 434−440. (18) Tyler, C. A.; Qin, J.; Bates, F. S.; Morse, D. C. Macromolecules 2007, 40, 4653−4668. (19) Qin, J.; Bates, F. S.; Morse, D. C. Macromolecules 2010, 43, 5128−5136. (20) Park, C.; De Rosa, C.; Fetters, L. J.; Thomas, E. L. Macromolecules 2000, 33, 7931−7938. (21) Schmalz, H.; Böker, A.; Lange, R.; Krausch, G.; Abetz, V. Macromolecules 2001, 34, 8720−8729. (22) Mahanthappa, M. K.; Lim, L. S.; Hillmyer, M. A.; Bates, F. S. Macromolecules 2007, 40, 1585−1593. (23) Beckingham, B. S.; Register, R. A. Macromolecules 2011, 44, 4313−4319. (24) Hahn, S. F. J. Polym. Sci., Part A: Polym. Chem. 1992, 30, 397− 408. (25) Adams, J. L.; Quiram, D. J.; Graessley, W. W.; Register, R. A.; Marchand, G. R. Macromolecules 1998, 31, 201−204. (26) Sebastian, J. M.; Register, R. A. J. Appl. Polym. Sci. 2001, 82, 2056−2069. (27) Register, R. A.; Bell, T. R. J. Polym. Sci., Part B: Polym. Phys. 1992, 30, 569−575. (28) Huang, T. C.; Toraya, H.; Blanton, T. N.; Wu, Y. J. Appl. Crystallogr. 1993, 26, 180−184. (29) Russell, T. P. In Handbook on Synchrotron Radiation; Brown, G. S., Moncton, D. E., Eds.; North-Holland: New York, 1991; Vol. 3, Chapter 11, pp 379−469. (30) Scott, D. B.; Waddon, A. J.; Lin, Y.-G.; Karasz, F. E.; Winter, H. H. Macromolecules 1992, 25, 4175−4181. (31) Lee, H. H.; Register, R. A.; Hajduk, D. A.; Gruner, S. M. Polym. Eng. Sci. 1996, 36, 1414−1424. (32) Shenfil, L.; Danielson, W. E.; DuMond, J. W. M. J. Appl. Phys. 1952, 23, 854−859. (33) Gabriel, A.; Dauvergne, F. Nucl. Instrum. Methods 1982, 201, 223−224. (34) Dean, D. M.; Rebenfeld, L.; Register, R. A.; Hsiao, B. S. J. Mater. Sci. 1998, 33, 4797−4812. (35) Beckingham, B. S.; Register, R. A. Macromolecules 2013, DOI: http://dx.doi.org/10.1021/ma4002512. (36) Beckingham, B. S.; Burns, A. B.; Register, R. A. Macromolecules 2013, DOI: http://dx.doi.org/10.1021/ma400311p. (37) Leibler, L. Macromolecules 1980, 13, 1602−1617. (38) Matsen, M. W.; Griffiths, G. H. Eur. Phys. J. E 2009, 29, 219− 227. (39) Li, W.; Shi, A.-C. Macromolecules 2009, 42, 811−819. (40) Torikai, N.; Noda, I.; Karim, A.; Satija, S. K.; Han, C. C.; Matsushita, Y.; Kawakatsu, T. Macromolecules 1997, 30, 2907−2914. (41) Loo, Y.-L.; Register, R. A.; Ryan, A. J.; Dee, G. T. Macromolecules 2001, 34, 8968−8977. (42) Hashimoto, T.; Shibayama, M.; Kawai, H. Macromolecules 1980, 13, 1237−1247. (43) Winey, K. I.; Gobran, D. A.; Xu, Z.; Fetters, L. J.; Thomas, E. L. Macromolecules 1994, 27, 2392−2397. (44) Semenov, A. N. Zh. Exsp. Teor. Fiz. 1985, 88, 1242−1256. (45) Hamley, I. W.; Fairclough, J. P. A.; Terrill, N. J.; Ryan, A. J.; Lipic, P. M.; Bates, F. S.; Towns-Andrews, E. Macromolecules 1996, 29, 8835−8843. (46) Koo, C. M.; Wu, L. F.; Lim, L. S.; Mahanthappa, M. K.; Hillmyer, M. A.; Bates, F. S. Macromolecules 2005, 38, 6090−6098. (47) Rangarajan, P.; Register, R. A.; Adamson, D. H.; Fetters, L. J.; Bras, W.; Naylor, S.; Ryan, A. J. Macromolecules 1995, 28, 1422−1428. (48) Wunderlich, B.; Dole, M. J. Polym. Sci. 1957, 24, 201−213. (49) Koberstein, J. T.; Morra, B.; Stein, R. S. J. Appl. Crystallogr. 1980, 13, 34−45. (50) Ruland, W. J. Appl. Crystallogr. 1971, 4, 70−73.

lamellar structure, but for the other three triblocks, E crystallization is effectively confined by the melt structure, leading to an orientation wherein the E crystallites stack orthogonally to the lamellar microdomains, as observed previously in E-containing diblock copolymers exhibiting confined crystallization.



ASSOCIATED CONTENT

S Supporting Information *

Detailed procedures for determining the true molecular weights of the Bd, I, and SrI blocks by GPC; specific volumes V as functions of T for the constituent homopolymers; comparison of Tg values for SrhI and VCHrhI random copolymers with the Fox equation; fits of eq 1 to the SAXS peak intensities for related near-symmetric diblocks; 2D SAXS/WAXS characterization of E−hI−(SrhI)50-60. This material is available free of charge via the Internet at http://pubs.acs.org.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was generously supported by the National Science Foundation (NSF) Polymers Program (DMR-1003942). Acquisition of the 2D SAXS instrument was made possible by the NSF Instrumentation for Materials Research Program (DMR-0215578), while the acquisition of the image plate scanner used for the 2D WAXS patterns, and components of the GPC system, was supported by the NSF Materials Research Science and Engineering Center Program through the Princeton Center for Complex Materials (DMR-0213706 and DMR0819860).



REFERENCES

(1) Mogi, Y.; Kotsuji, H.; Kaneko, Y.; Mori, K.; Matsushita, Y.; Noda, I. Macromolecules 1992, 25, 5408−5411. (2) Mogi, Y.; Mori, K.; Matsushita, Y.; Noda, I. Macromolecules 1992, 25, 5412−5415. (3) Mogi, Y.; Mori, K.; Kotsuji, H.; Matsushita, Y.; Noda, I.; Han, C. C. Macromolecules 1993, 26, 5169−5173. (4) Mogi, Y.; Nomura, M.; Kotsuji, H.; Ohnishi, K.; Matsushita, Y.; Noda, I. Macromolecules 1994, 27, 6755−6760. (5) Stadler, R.; Auschra, C.; Beckmann, J.; Krappe, U.; Voigt-Martin, I.; Leibler, L. Macromolecules 1995, 28, 3080−3097. (6) Krappe, U.; Stadler, R.; Voigt-Martin, I. Macromolecules 1995, 28, 4558−4561. (7) Hückstädt, H.; Goldacker, T.; Göpfert, A.; Abetz, V. Macromolecules 2000, 33, 3757−3761. (8) Hückstädt, H.; Göpfert, A.; Abetz, V. Polymer 2000, 41, 9089− 9094. (9) Bates, F. S.; Fredrickson, G. H. Phys. Today 1999, 52 (2), 32−38. (10) Shefelbine, T. A.; Vigild, M. E.; Matsen, M. W.; Hadjuk, D. A.; Hillmyer, M. A.; Cussler, E. L.; Bates, F. S. J. Am. Chem. Soc. 1999, 121, 8457−8465. (11) Bailey, T. S.; Pham, H. D.; Bates, F. S. Macromolecules 2001, 34, 6994−7008. (12) Bailey, T. S.; Hardy, C. M.; Epps, T. H., III; Bates, F. S. Macromolecules 2002, 35, 7007−7017. (13) Epps, T. H., III.; Cochran, E. W.; Bailey, T. S.; Waletzko, R. S.; Hardy, C. M.; Bates, F. S. Macromolecules 2004, 37, 8325−8341. (14) Chatterjee, J.; Jain, S.; Bates, F. S. Macromolecules 2007, 40, 2882−2896. J

dx.doi.org/10.1021/ma400397h | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

(51) Roe, R. J. J. Appl. Crystallogr. 1982, 15, 182−189. (52) Roe, R.-J. Methods of X-Ray and Neutron Scattering in Polymer Science; Oxford University Press: New York, 2000. (53) Anastasiadis, S. H.; Russell, T. P.; Satija, S. K.; Majkrzak, C. F. J. Chem. Phys. 1990, 92, 5677−5691. (54) Helfand, E.; Tagami, Y. J. Chem. Phys. 1972, 56, 3592−3601. (55) Douzinas, K. C.; Cohen, R. E. Macromolecules 1992, 25, 5030− 5035. (56) Myers, S. B.; Register, R. A. Macromolecules 2010, 43, 393−401. (57) Li, S.; Register, R. A.; Landes, B. G.; Hustad, P. D.; Weinhold, J. D. Macromolecules 2010, 43, 4761−4770. (58) Nojima, S.; Kato, K.; Yamamoto, S.; Ashida, T. Macromolecules 1992, 25, 2237−2242. (59) Rangarajan, P.; Register, R. A.; Fetters, L. J.; Bras, W.; Naylor, S.; Ryan, A. J. Macromolecules 1995, 28, 2932−4938.

K

dx.doi.org/10.1021/ma400397h | Macromolecules XXXX, XXX, XXX−XXX