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Langmuir 1998, 14, 6974-6979
Anisotropy of Diffusion in a Lamellar Styrene-Isoprene Block Copolymer Mark W. Hamersky,‡,§ Matthew Tirrell,‡ and Timothy P. Lodge*,†,‡ Departments of Chemical Engineering & Materials Science and Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 Received February 5, 1998. In Final Form: September 6, 1998 The self-diffusion properties of a poly(styrene-b-isoprene) diblock copolymer (MPS ) 10000, MPI ) 13000) in a lamellar microstructure have been determined by forced Rayleigh scattering. Diffusion coefficients along the lamellar interface (Dpar) and through the layers (Dperp) were resolved. The lamellae were macroscopically oriented using large amplitude oscillatory shear; small-angle X-ray scattering and transmission electron microscopy confirmed a high degree of alignment. The measured anisotropy of mobility was surprisingly large at 90 °C: Dpar/Dperp ≈ 40. However, at 110 °C the anisotropy decreased by an order of magnitude. This reduction is only partly attributable to the approaching order-disorder transition (at 160 °C); the strong temperature dependence of the styrene monomeric friction factor in styrene-rich domains is also implicated. Further measurements were made on a copolymer with half the total molecular weight (MPS ) 5000, MPI ) 6500), which was in the disordered state over the temperature range of interest. These data confirm the importance of the composition and temperature dependences of the monomeric friction factors, coupled with the spatial homogeneity/heterogeneity of the average composition. The results are discussed in terms of proposed mechanisms of diffusion in block copolymer microstructures.
Introduction Block copolymers are macromolecular amphiphiles, and the interactions between dissimilar A and B monomers in the two blocks are usually effectively repulsive. Consequently, block copolymers in the bulk state selfassemble into microstructures that minimize A-B contacts, such as lamellae, hexagonally packed rods, and cubic arrays of spheres.1 These morphologies are analogous to the bilayers (LR or smectic A phase), wormlike micelles, and spherical micelles, respectively, commonly found in low-molecular-weight amphiphiles such as lipids and surfactants.2 However, the copolymer microdomain dimensions are determined by the block molecular weights and are typically in the 100-1000 Å range, about an order of magnitude larger than those of small molecule microstructures. Such mesoscopic length scales are of great interest in materials chemistry and “soft” materials science. Furthermore, block copolymers can exploit the obvious advantages that polymeric materials enjoy (e.g., in mechanical properties). For these reasons and more, an understanding of the dynamic properties of microstructured block copolymers, such as diffusion and viscoelasticity, is of considerable importance.3 Consider a lamellar block copolymer microstructure, illustrated schematically in Figure 1. From the point of view of molecular motion, the key feature is the possibility that the mobility along the interface differs significantly from that perpendicular to the layers. Furthermore, either * Corresponding author. ‡ Department of Chemical Engineering & Materials Science. † Department of Chemistry. § Current address: The Procter & Gamble Company, Miami Valley Laboratories, Cincinnati, OH 45247 (1) See, for example, Bates, F. S. Science 1991, 251, 898 and references therein. (2) See, for example, Micelles, Membranes, Microemulsions, and Monolayers; Gelbart, W. M., Ben-Shaul, A., Roux, D., Eds.; Springer: New York, 1994 and references therein. (3) See, for example, Fredrickson, G. H.; Bates, F. S. Annu. Rev. Mater. Sci. 1996, 26, 503 and references therein.
Figure 1. Schematic illustration of an oriented lamellar block copolymer. The inset indicates that the average chain resides with the junction point between the two blocks confined to an interfacial region. However, at finite temperatures the composition profile is not a step function in the z-direction and the interface is not infinitely sharp. Rather, the profile evolves from a weak sine wave near the order-disorder transition toward a step function, as either the degree of polymerization, N, or the interaction parameter, χ, is increased.
mobility may differ from the value found in the isotropic, disordered phase. An understanding of these differences will ultimately underlie any successful molecular theory of the collective dynamics of block copolymers (i.e., the rheological properties). Let Dpar, Dperp, and D0 denote the diffusivity of an individual copolymer along the interface, through the layers, and in the disordered phase, respectively. One anticipates that Dperp < Dpar because, in order to move through the layers, block A must pass through
10.1021/la980140a CCC: $15.00 © 1998 American Chemical Society Published on Web 10/30/1998
Diffusion in a Lamellar PS-PI Block Copolymer
the B-rich microdomain, and vice versa. In doing so, it should encounter a thermodynamic barrier that increases with the dimensionless product χN, where χ (∼T-1) is the Flory-Huggins interaction parameter between A and B monomers and N is the degree of polymerization. Conversely, chains may be able to move along the interface without significant mixing of A and B blocks, in which case Dpar ≈ D0. Previous experiments on diffusion in lamellar block copolymers suggest that an additional, strictly polymeric feature plays a crucial role: the degree of entanglement.4,5 In a molten homopolymer, when N is below a critical value, Nc, (typically 150-300), the diffusivity scales as D ∼ N-1 and the viscosity as η ∼ N, but when N . Nc, D ∼ N-2 and η ∼ N3.4. The high N exponents are ascribed to the mutual intertwining of different chains, or “entanglements”, that severely retard chain motion over distances greater than the average chain size.6 Such topological constraints are pictured as forcing individual chains to move primarily along their own contours (i.e., to “reptate”).6,7 Conversely, the low N, “unentangled” scaling relations reflect a simple linear increase in chain friction with increasing chain length, the so-called “Rouse” dynamics. For lamellar copolymers with N/Nc > 5, measurements revealed very little anisotropy of motion: Dperp was within a factor of 3 of Dpar.8 However, Dpar itself was substantially less than D0, by as much as 2 orders of magnitude, and Dpar/D0 followed an exponential dependence on χN.5 This was attributed to the “pinning” of the chains by the entanglements; a copolymer could not even reptate along the interface without pulling the A block into the B-rich microdomain, and vice versa. The resulting mechanism was dubbed “activated reptation”. If this picture is correct, an unentangled copolymer should show quite different behavior. In particular, motion along the interface should be essentially unimpeded, such that Dpar ≈ D0, but Dperp should still feel a strong barrier; consequently, one expects Dperp , Dpar. Heretofore, there has not been any direct determination of Dpar and Dperp in an unentangled lamellar copolymer, although there is some indirect experimental evidence that the anisotropy of motion is at least greater than that in the entangled case.9,10 In this paper we report direct measurements of Dpar and Dperp in an unentangled copolymer and find a substantial anisotropy of motion. Experimental Section Materials. A poly(styrene-b-isoprene) (PS-PI) diblock copolymer was synthesized by sequential living anionic polymerization, as previously described.11 The resulting block molecular weights were 10 000 and 13 000 g/mol for the PS and PI components, with an overall polydispersity index (Mw/Mn) < 1.06, and the sample is designated SI(10-13).12 This copolymer adopts a lamellar morphology with a period L ≈ 190 Å, below the order(4) Dalvi, M. C.; Eastman, C. E.; Lodge, T. P. Phys. Rev. Lett. 1993, 71, 2591. (5) Lodge, T. P.; Dalvi, M. C. Phys. Rev. Lett. 1995, 75, 657. (6) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics, 2nd ed.; Oxford University Press: Oxford, 1988. (7) de Gennes, P. G. J. Chem. Phys. 1971, 55, 572. (8) Dalvi, M. C.; Lodge, T. P. Macromolecules 1993, 26, 859. (9) Ehlich, D.; Takenaka, M.; Okamoto, S.; Hashimoto, T. Macromolecules 1993, 26, 189. (10) Ehlich, D.; Takenaka, M.; Hashimoto, T. Macromolecules 1993, 26, 492. (11) Hamersky, M. W.; Tirrell, M.; Lodge, T. P. J. Polym. Sci., Polym. Phys. Ed. 1996, 34, 2899. (12) The value of Nc is ca. 300 for PS and ca. 150 for PI. It is not immediately clear how to construct Nc for a block copolymer from the values for its homopolymer constituents, but it should lie between these two limits. For this copolymer, therefore, N is presumed to be close to Nc, which justifies its classification as “unentangled”; it is not until N/Nc > 2-5 that clear evidence of entanglements would appear.
Langmuir, Vol. 14, No. 24, 1998 6975 disorder transition (ODT) temperature of 160 °C. A second copolymer with block molecular weights of 5000 and 6500 g/mol for the PS and PI components was also synthesized and designated SI(5-6.5). Due to the reduced degree of polymerization, this polymer is in the disordered state over the temperature range of interest and provides a reference for estimating D0. A portion of each living copolymer was terminated with p-dichloroxylene, to permit labeling by reaction with the Cs+ salt form of the photochromic dye 4′-(N,N-dimethylamino)-2nitrostilbene-4-carboxylic acid. Labeled samples were subjected to additional purification steps, to remove unreacted dye and the small portion of coupled, unlabeled chains. Samples for forced Rayleigh scattering measurements incorporated approximately 10% labeled chains; the measured D is independent of the fraction of labeled chains, up to at least 25%.11 Forced Rayleigh Scattering. Diffusion measurements were performed by forced Rayleigh scattering (FRS), a transient optical grating technique.8,13,14 The sample is exposed to crossed beams from an Ar+ laser operating at λ ) 488 nm, for an interval of 50-100 ms. The resulting interference pattern is recorded as a volume grating in the sample by the photoinduced isomerization of a suitable dye; the period of the grating, d, is given by λ/2sin(θ/2), where θ is the crossing angle between the incident beams. The subsequent state of the grating is probed by diffraction of one of the original beams (attenuated by a factor of 104); the diffracted intensity decays in time, as diffusion of the two forms of the dye randomizes their spatial distribution. It is important to note that the experiment is inherently uniaxial; only diffusion along the grating normal contributes to the intensity decay. In the simplest case, the diffracted intensity decays exponentially in time, with the decay time τ given by d2/4π2D. Shear Orientation. To resolve Dpar and Dperp, it is necessary to prepare samples with a high degree of orientation over millimeter length scales. This is achieved through the imposition of large-amplitude, low-frequency oscillatory shear. After annealing at 110 °C for 12 h, a 14-mm diameter, 1.0-mm thick specimen of SI(10-13) was subjected to a strain amplitude of 100% at a frequency of 1 rad/s for 12 h, with the sample maintained under nitrogen at 138 °C. This results in the socalled “perpendicular” alignment, with the lamellar normal lying along the vorticity axis.3 In the coordinate system of Figure 1, the shear direction was x and the vorticity axis was z. This is favorable for the FRS measurements, as the laser beams are subsequently directed along the thin dimension of the sample (y), the grating axis lies in the x-z plane, and both Dpar and Dperp can be determined following appropriate rotation of the sample about y. The mechanism(s) of block copolymer orientation under flow is a topic of great current interest;3 we were guided in the choice of conditions by previous results on styrene-isoprene diblocks.15-17 Small-Angle X-ray Scattering. X-ray scattering experiments were carried out with Cu KR radiation (λ ) 1.54 Å) from a Rigaku RU-200BVH rotating anode generator equipped with an 0.2 mm × 0.2 mm microfocus cathode and Franks mirror optics. Two-dimensional SAXS patterns were recorded on a 1024 × 1024 pixel multiwire detector (Siemens) located at the end of a 1.0-m evacuated flight tube. Samples were placed inside an evacuated chamber, where the temperature was maintained to within (0.1 °C by resistive heaters mounted in a water-cooled brass block. After the selected temperature was reached, 10 min was allowed for annealing prior to collecting scattering data for a 15-min period. All SAXS data were corrected for detector response prior to analysis. Transmission Electron Microscopy. Portions of the shearaligned copolymer used in the FRS experiments were examined by TEM. Ultrathin sections (ca. 70 nm) were prepared with a Reichert Utracut S equipped with a diamond knife. Microtoming (13) Hervet, H.; Urbach, W.; Rondelez, F. J. Chem. Phys. 1978, 68, 2725. (14) Lodge, T. P.; Chapman, B. R. Trends Polym. Sci. 1997, 5, 122. (15) Patel, S. S.; Larson, R. G.; Winey, K. I.; Watanabe, H. Macromolecules 1995, 28, 4313. (16) Gupta, V. K.; Krishnamoorti, R.; Kornfield, J. A.; Smith, S. D. Macromolecules 1995, 28, 4464. (17) Zhang, Y.; Wiesner, U.; Yang, Y.; Pakula, T.; Spiess, H. Macromolecules 1996, 29, 5427.
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Figure 2. (a) Small-angle X-ray scattering pattern with the incident beam directed along the y-axis of Figure 1. Three orders of reflection at q*, 2q*, and 3q* are clearly evident along qz, where q is the usual scattering wavevector: |q| ) (4π/λ) sin(θ/2). The sample was not perfectly aligned in the sample holder, which accounts for the slight tilt between the principal reflections and the qz-axis. (b) Intensity as a function of azimuthal angle (around y) at |q| ) q*. (c) Small-angle X-ray scattering pattern with the incident beam directed along the z-axis of Figure 1. (d) Intensity as a function of the azimuthal angle (around z) at |q| ) q*; intensity scale is the same as that in (b). was performed at -100 °C at cutting speeds of 0.8-1.0 mm/s. Sections were collected and placed onto 400-mesh copper grids and exposed to the vapor above a 2% aqueous solution of osmium tetraoxide for 6-7 h to create adequate TEM contrast. This procedure selectively stains the PI domains of the ordered block copolymer, rendering them dark. The PS regions are unaffected during this exposure time and thus appear light in the images. TEM was carried out with a JEOL 1210 electron microscope operating in bright field mode at 120 kV.
Results and Discussion Degree of Orientation. Quantifying the degree of orientation is crucial, as a substantial population of defects in the desired “single-crystal-like” specimen would compromise the extraction of Dpar and Dperp. Figure 2a shows a two-dimensional small-angle X-ray scattering (SAXS) pattern obtained by directing the X-rays along the same axis as the FRS laser (y). A very high degree of orientation is evident, with intense spots at q* ()2π/L) and clear arcs at 2q* and 3q*, along the axis corresponding to the lamellar normal (z). There is a faint ring of intensity at q*, indicating some misaligned lamellae, but the intensity around this ring is highly concentrated along the lamellar normal axis, as shown by the azimuthal plot in Figure 2b. SAXS patterns obtained by directing the X-rays along the lamellar normal (z) (Figures 2c and 2d) gave peak intensities less than 1% of those indicated in Figure 2, also suggesting the overwhelming predominance of the desired alignment. Scattering patterns alone are not sufficient to establish the degree of perfection in the aligned sample, as defective regions need not provide a strong scattering signature. Accordingly, transmission electron microscopy (TEM) was used to obtain real-space (albeit two-dimensional) images of the sample. A series of images were taken over a 30µm2 area of the sample. All indicated a substantial degree
of orientation; examples of nearly perfect (Figure 3a) and partially defective (Figure 3b) alignment are shown. The majority of the images taken resembled Figure 3a rather than 3b. Each image corresponds to a 1 µm × 1 µm area of material, a (linear) dimension which is comparable to a typical value of d; thus, it is reasonable to anticipate that a significant fraction of chains will diffuse one grating period within nearly perfectly oriented domains. Diffusion in Shear-Oriented SI(10-13). FRS measurements were taken at 90 °C on the shear-aligned sample; this temperature is well-below the ODT, but sufficiently far above the styrene block glass-transition temperature (78 °C by differential scanning calorimetry) that measurement times were practical. Four orientation angles were used, φ ) 0°, 30°, 60°, and 90°, where φ is the angle between the grating normal and the shear direction; thus measurements at 0° (90°) would provide Dpar (Dperp) in a perfectly oriented material. For each orientation decays were recorded at four different grating spacings: 0.7, 1, 1.4, and 2 µm. The resulting decays were all welldescribed by a sum of two exponentials, with one exponential contributing approximately 80% of the diffracted intensity. For φ ) 0°, 30°, and 60° the faster decay process dominated the signal, but at 90° the slower decay was more prominent. The two decay times consistently differed by approximately 1 order of magnitude, and both fast and slow decay times scaled linearly with d2, indicating that the underlying relaxation processes are diffusive. A typical decay for φ ) 0° is shown in Figure 4a, and the corresponding plots of τ versus d2 for the fast and slow processes are shown in Figure 4b. The resulting values of “Dfast” and “Dslow”, obtained from the slopes of τ versus d2, are shown as a function of φ in Figure 5. We interpret these results as follows. The larger amplitude decay is attributed to diffusion in essentially
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Figure 4. (a) FRS decay for the sample oriented at φ ) 0° and d ) 1 µm, and the fit to a sum of two exponentials. Note that the intensity axis is logarithmic. (b) Fast and slow decay times as a function of squared grating spacing for the sample oriented at φ ) 0°. Dfast and Dslow are obtained from the slopes of the linear regression fits. Figure 3. Transmission electron micrographs of 70-nm thick sections of oriented SI(10-13); the isoprene-rich microdomains appear dark due to the OsO4 stain. Each image corresponds to a roughly 1 µm × 1 µm area of the sample. The image in (a) indicates near perfect alignment, whereas that in (b) shows defective regions. A series of micrographs taken over tens of µm2 tended to resemble (a) more than (b).
perfectly aligned regions of the sample, such as that shown in Figure 3a. Thus, Dfast(φ ) 0°) ) 3.2 × 10-12 cm2/s corresponds to Dpar, and Dslow(φ ) 90°) ) 8.5 × 10-14 cm2/s corresponds to Dperp. The dashed line in the figure denotes Dpar cos2 φ + Dperp sin2 φ (i.e., what one would expect to measure for a perfectly oriented sample as a function of φ). The agreement with Dfast at φ ) 30° and 60° is excellent and lends support to this interpretation. In addition, we previously reported measurements of D for the same copolymer but in a quenched (i.e., totally unaligned) sample.11 According to theory this isotropic average 〈D〉 should be given by18
〈D〉 ) (2/3)Dpar + (1/3)Dperp
(1)
or 2.1 × 10-12 cm2/s based on the results in Figure 5; the measured value was actually 2.3 ( 0.4 × 10-12 cm2/s, which is identical within the experimental uncertainty. The smaller amplitude decay is ascribed to diffusion in regions of the sample with defective orientations, as in Figure 3b. Quite reasonably, the diffusivity in such regions falls between Dpar and Dperp. Close examination of the FRS decays reveals that whereas the dominant mode is single-exponential, the lesser mode could correspond well to a distribution of exponentials, with a mean decay time close to that assigned by the two-exponental fit. Thus, we cannot yet assign any significance to the apparent variation of the diffusivity in the defective regions with φ, although it is conceivable that the misaligned regions are anisotropic. These measurements provide the first quantitative determination of Dperp in an unentangled lamellar co(18) Fredrickson, G. H. Acta Polym. 1993, 44, 78.
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Figure 5. Dfast and Dslow as a function of rotation angle. The dashed line indicates the expected projections of Dpar and Dperp. The four points close to this curve typically corresponded to 80% of the diffracted intensity.
polymer, and in this instance it is approximately 40 times less than Dpar. This anisotropy is at least an order of magnitude greater than that obtained for oriented, entangled lamellar copolymers under similar thermodynamic conditions,5,8 and provides direct evidence for a fundamental difference in the way microstructure affects the mobility of entangled and unentangled copolymers. This observation is also consistent with the factor of 80 recently reported for the anisotropy of diffusion in shearoriented, unentangled poly(ethyleneoxide)-poly(ethylethylene) cylinders.19 The consequences of this difference have been implicated in the linear viscoelastic properties of block copolymers both above and below the ODT.3 For example, the low-frequency elastic modulus (G′) of entangled copolymers shows a strong signature of pretransitional composition fluctuations, whereas G′ of unentangled copolymers apparently does not. This result is counter to the thermodynamic expectation that such fluctuations should be stronger for lower N polymers, but may now be understood as reflecting the relative ease with which low N copolymers can move along an interface. It is interesting to estimate the magnitude of the anisotropy that one might expect for this material. From previous work, we take χ as -0.0228 + 33/T ) 0.068 and N as 241 (referenced to the styrene segment volume), and thus χN ≈ 16.4.20 Barrat and Fredrickson simulated the diffusion of symmetric, unentangled copolymers through periodic potentials.21 To compare their results to the experiment, we use self-consistent mean-field theory to estimate that the first harmonic of the composition profile has an amplitude of 0.3;22 this gives a predicted ratio Dpar/ Dperp ≈ 6, which is significantly less than that observed. However, it is well-known that copolymer composition profiles are rarely pure sine waves, and contributions from additional harmonics could act to further reduce Dperp (i.e., through sharper, steeper interfaces). Alternatively, Lodge and Dalvi found the empirical relation Dperp/D0 ≈ exp{(19) Hamersky, M. W.; Hillmyer, M. A.; Tirrell, M.; Bates, F. S.; Lodge, T. P. Macromolecules 1998, 31, 5363. (20) Lodge, T. P.; Pan, C.; Jin, X.; Liu, Z.; Zhao, J.; Maurer, W. W.; Bates, F. S. J. Polym. Sci., Polym. Phys. Ed. 1995, 33, 2289. (21) Barrat, J.-L.; Fredrickson, G. H. Macromolecules 1991, 24, 6378. (22) Shull, K. R. Macromolecules 1992, 25, 2122.
Hamersky et al.
0.422(χN - 9.1)} for diffusion in a well-entangled lamellar poly(ethylenepropylene)-poly(ethylethylene) copolymer.5 If one assumes that the barrier to diffusion through the layers is largely independent of the exact mechanism of motion (which is probably reasonable for samples in close proximity to the ODT), then this relation predicts an anisotropy of 22. Thus, the observed anisotropy is even greater than that estimated by either method. This is intriguing, as in general one expects the measured Dpar and Dperp to represent lower and upper bounds, respectively, to the “true” values, and thus the measured anisotropy to be less than or equal to the “true” anisotropy. The reason for this expectation is the inevitable finite degree of misalignment, and other defects, in the nominally “perfectly aligned” regions. Measurements of Dpar and Dperp were also conducted at 110 °C. Sample limitations precluded as extensive a series of measurements as those at 90 °C (i.e., varying both φ and d), so the measurements were restricted to φ ) 0° and 90°. Surprisingly, the anisotropy was significantly reduced: Dpar ≈ 1.5 × 10-11 cm2/s and Dperp ≈ 4.0 × 10-12 cm2/s, for an anisotropy of about a factor of 4. In addition, the FRS decays were reasonably well-approximated by single exponentials. These observations raise the possibility that upon heating the sample experiences enhanced composition fluctuations that degrade the degree of shear alignment to the extent that all chains experience defective regions during the erasure of the grating. However, upon returning to 90 °C, the two-exponential nature of the decays, and the relative magnitudes of the decay constants and amplitudes, were recovered. We therefore conclude that although fluctuations might assist diffusion through the layers at 110 °C, they are not so severe as to compromise the degree of alignment. The increase in temperature reduces χ, and thus the barrier to perpendicular motion, but using the relations given above, this decrease in χ should not attenuate the anisotropy by even as much as a factor of 2. Consequently, we are inclined to propose a “nonthermodynamic” explanation for these results; such an explanation will be outlined subsequently. It should be noted that the magnitude of the diffusional anisotropy at 110 °C is much more in accord with expectations based on the work of Barrat and Fredrickson21 than the data at 90 °C. Diffusion in Disordered SI(5-6.5). According to the physical picture summarized in the Introduction, for unentangled chains one expects Dpar ≈ D0. The latter quantity should be accessible from the self-diffusion coefficient of SI(5-6.5) as a function of temperature, after scaling for the difference in the molecular weight. This approach has been taken previously with polystyrenepolyvinylpyridine23 and poly(ethylenepropylene)-poly(ethylethylene)5,24 copolymers. For this disordered copolymer the FRS decays were single-exponential in all cases, and the decay constants linear with d2; the resulting diffusivities are shown as a function of temperature in Figure 6. Also shown are the data for SI(10-13) obtained in the quenched state, reported previously.11 Clearly 〈D〉 for SI(10-13) falls well below D for SI(5-6.5), even in the disordered state (i.e., above 160 °C), and scaling the former down by a factor of 2 (i.e., assuming Rouse dynamics) does not account for the difference. The mobility of SI(10-13) is therefore significantly retarded relative to the D0 thus estimated. The lower molecular weight of SI(5-6.5) does depress its glass-transition temperature relative to SI(10-13), and thus reduce its effective friction (23) Eastman, C. E.; Lodge, T. P. Macromolecules 1994, 27, 5591. (24) Dalvi, M. C.; Lodge, T. P. Macromolecules 1994, 27, 3487.
Diffusion in a Lamellar PS-PI Block Copolymer
Figure 6. Temperature dependence of diffusion in the disordered SI(5-6.5) and in the quenched SI(10-13) (the orderdisorder transition occurs at 160 °C). The measured values of Dpar and Dperp for SI(10-13) are also shown.
factor, but this effect can only account for a small fraction of the discrepancy evident in Figure 6. The measured values of Dpar and Dperp at 90 and 110 °C are also plotted in Figure 6. At both temperatures (2/ 3)Dpar + (1/3)Dperp compares favorably with 〈D〉 measured on the quenched sample. Thus, there are only two features of these data that appear to be inconsistent with the picture discussed in the Introduction, namely Dpar ≈ 〈D〉 , D0 rather than Dpar ≈ 〈D〉 ≈ D0, and Dperp/Dpar increases more rapidly with decreasing temperature than anticipated. The additional factor that we suspect needs to be considered is the difference between the segmental friction factors, ζ, for the two blocks (D ∼ 1/ζ). As PS has a much higher glass transition temperature than PI (typically ca. 100 °C versus -70 °C), the individual friction factors (i.e., in pure homopolymers) can differ by several orders of magnitude at a given temperature. Little is known about the variation of ζ with composition in a blend or a copolymer, except that it is generally unpredictable and not necessarily monotonic.25-29 However, we have been investigating the composition and temperature dependence of ζ in disordered styrene-isoprene-styreneisoprene tetrablock copolymers and find that ζ is not strongly dependent on composition at a fixed temperature increment above the composition-dependent glass-transition temperature.30 Furthermore, ζ increases smoothly with increasing styrene content at a fixed temperature (25) Composto, R. J.; Kramer, E. J.; White, D. M. Polymer 1990, 31, 2320. (26) Lodge, T. P. J. Phys. Chem. 1993, 97, 1480. (27) Colby, R. H. Polymer 1989, 30, 1275. (28) Green, P. F.; Adolf, D. B.; Gilliom, L. R. Macromolecules 1991, 24, 3377. (29) Roovers, J.; Toporowski, P. M. Macromolecules 1992, 25, 1096, 3454. (30) Chapman, B. R.; Hamersky, M. W.; Milhaupt, J. M.; Kostelecky, C.; Lodge, T. P.; von Meerwall, E. D.; Smith, S. D. Macromolecules 1998, 31, 4562.
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and increases smoothly with a decreasing temperature at a fixed composition. Thus, we propose that the two discrepancies identified above can be reconciled as follows. In disordered SI(5-6.5), styrene and isoprene segments are homogeneously mixed, leading to an average effective ζ(T). In ordered SI(10-13), however, styrene (isoprene) segments move predominantly in styrene (isoprene)-rich regions, and the styrene-rich regions will have a higher effective ζ, even though the macroscopic average composition is the same as SI(5-6.5). Finally, when traversing the layers, all the styrene segments in a chain must pass through the most styrene-rich portion of the microdomain (i.e., the maximum of the styrene composition profile), whereas when moving along the layers, only the end-most segments are near the maximum of the profile. Consequently, Dperp experiences a larger (i.e., more styreneinfluenced) ζ(T) than does Dpar. Finally, for SI(10-13) in the disordered state, just above the ODT, the mobility remains below that of SI(5-6.5) suitably scaled. This may be attributed to the effect of composition fluctuations present in SI(10-13), leading to transient styrene-rich domains that have a greater than average ζ. Summary Forced Rayleigh scattering has been used to measure the diffusion parallel (Dpar) and perpendicular (Dperp) to the microdomain interfaces in a lamellar styrene-isoprene block copolymer SI(10-13). Application of large strain amplitude oscillatory shear was successful in producing a specimen with a high degree of orientation, as confirmed by small-angle X-ray scattering and transmission electron microscopy. The FRS signals were dominated by one single exponential, which was assigned to diffusion in nearly perfectly aligned regions of the sample, and the remaining, second exponential decay attributed to diffusion in regions with imperfect orientation. The resulting anisotropy of diffusion, Dpar/Dperp, was remarkably large, approximately 40 at 90 °C. However, it decreased to approximately 4 at 110 °C. The values of Dpar and Dperp were also consistent with previous measurements on the same material, but in a quenched (i.e., unoriented) state. The value of 40 is significantly larger than expected, either on the basis of theory or previous experiments on poly(ethylenepropylene)-poly(ethylethylene) copolymers. Measurements were also conducted on another copolymer of the same composition but half the molecular weight, SI(5-6.5), which was consequently disordered over the temperature range of interest. The mobility of this copolymer was considerably larger than that of SI(1013), even after accounting for the difference in molecular weight. This apparent discrepancy, and the unexpectedly strong anisotropy, can reasonably be attributed to the enhanced monomeric friction experienced by styrene segments moving in styrene-rich domains. Acknowledgment. This work was supported in part by the Center for Interfacial Engineering, an NSFsupported Engineering Research Center at the University of Minnesota, and by the NSF through Award DMR9528481 to T.P.L. We appreciate the assistance of Paul Lipic with the TEM measurements. LA980140A
