Uniaxial Extensional Behavior of (SIS)p-Type Multiblock Copolymer

Article pubs.acs.org/Macromolecules

Uniaxial Extensional Behavior of (SIS)p‑Type Multiblock Copolymer Systems: Structural Origin of High Extensibility Yumi Matsumiya and Hiroshi Watanabe* Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan

Atsushi Takano Department of Applied Chemistry, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

Yoshiaki Takahashi Institute for Materials Chemistry and Engineering, Kyushu University, 6-1 Kasugakoen, Fukuoka 816-8580, Japan S Supporting Information *

ABSTRACT: Rheological and structural behavior was examined for a series of symmetric styrene (S)−isoprene (I)−styrene (S) multiblock copolymers of (SIS)p-type (p = 1, 2, 3, and 5 corresponding to tri-, penta-, hepta-, and undecablock) in ntetradecane (C14), a selective solvent that dissolves the I block and precipitates (but swells) the S block. The molecular weights of respective blocks were almost identical for these copolymers (MI ≅ 40K for I block; MS ≅ 20K and 10K for inner and outer S blocks, respectively). At 20 °C, the (SIS)p/C14 systems with the copolymer concentration C = 30 wt % formed a bcc lattice of spherical S domains (with Tg,PS ≅ 38 °C) embedded in the I/C14 matrix. Under small shear and elongation in the linear regime, the systems exhibited gel-like elasticity sustained by the I blocks connecting the S domains. This linear elastic behavior, being associated with affine displacement of the S domains as revealed from small-angle X-ray scattering (SAXS) under small elongation, was very similar for all (SIS)p/C14 systems having the same C. In contrast, a remarkable difference was found for those systems under large (but slow) elongation: The maximum stretch ratio at rupture, λmax, significantly increased with the repeating number p of the SIS units, λmax ≅ 1.7, 2.2, 6.6, and ≥90 for p = 1, 2, 3, and 5, respectively. In particular, λmax ≥ 90 for p = 5 was much larger compared to the full-stretch ratio of the trapped entanglement strand (λfull‑ent ≅ 14) and even to the full-stretch ratio of the (SIS)5 copolymer chain as a whole (λfull‑copolymer ≅ 40). For investigation of the structural origin of such remarkably high extensibility of the undecablock system (p = 5), SAXS and rheological tests were made under elongation followed by reversal. The tests revealed affine stretching of the lattice (affine displacements of the S domains) and negligible stress−strain hysteresis on reversal of elongation from λrev < 3. In contrast, on reversal from larger λrev up to 60, nonaffine stretching of the lattice and the significant stress−strain hysteresis were observed. Thus, under large elongation, some of the S blocks were pulled out from their domains and transferred to the other S domains at 20 °C, the experimental temperature not significantly lower than Tg,PS (≅ 38 °C) of the swollen S domains, to allow the system to deform plasto-elastically. This deformation differed from unrecoverable plastic flow, as evidenced from spontaneous, full recovery of the size, shape, and SAXS profile of the (SIS)5/C14 specimen being kept at rest (without load) at 20 °C for a sufficiently long time after the elongation. This recovery strongly suggests that the material preserved some memory of initial connection between the (SIS)5 chains through the S domains, in particular in the direction perpendicular to the elongation, and the corresponding physical network still percolated the whole material even under large elongation. This argument in turn provides us with a clue for understanding the difference of λmax for the series of (SIS)p/C14 systems. The full percolation can survive and the material can stand with the elongation if at least two PS blocks, on average, remain intact (not pulled out) in each (SIS)p copolymer backbone. The probability of having such intact S blocks obviously increases with the repeating number p of the SIS units, which possibly resulted in the observed difference of λmax.

1. INTRODUCTION Properties of block copolymers have been extensively investigated from experimental and theoretical points of © 2013 American Chemical Society

Received: December 25, 2012 Revised: March 20, 2013 Published: March 29, 2013 2681

dx.doi.org/10.1021/ma3026404 | Macromolecules 2013, 46, 2681−2695

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Table 1. Characteristics of Multiblock Copolymer Samples 10−3M p

(SIS)p

1st S

2nd I

3rd S

4th I

5th S

6th I

7th S

8th I

9th S

10th I

11th S

0.5 1 2 3 5

SI diblock SI2S triblock SISI2S pentablock SISI2SIS heptablock SISISI2SISIS undecablock

10.4 10.4 10.4 10.4 10.4

20.3 40.6 37.1 37.1 37.1

10.4 21.6 21.6 21.6

38.7 36.8 38.0

10.4 21.6 21.8

37.1 40.6

10.4 21.8

38.0

21.6

37.1

10.4

dielectrically estimated ϕloop and to the SCF prediction,7,11,15,16 whereas the entangled loops behave similarly to bridges in mechanical test, in particular under large strains. For this reason, the mechanical estimation gives a very small ϕloop.17 In relation to the block connectivity addressed above, it should be also emphasized that some properties of multiblock copolymers such as mechanical toughness are influenced by the number of repeating blocks, p.18−26 Focusing on this point, we examined mechanical and dielectric behavior for a series of (SIS)p-type multiblock copolymers that were composed of almost identical SIS units (with MI ≅ 4.0 × 104 and MS ≅ 1 × 104) connected in sequence.27 The repeating number in the sequence, p = 1, 2, 3 and 5, corresponds to tri-, penta-, hepta-, and undecablock. The dipole inversion was introduced to a particular I block to estimate ϕloop of that block. For the (SIS)ptype copolymers being diluted with C14 (copolymer concentration = 40 wt %) and forming an almost identical bcc lattice structure of the S domains, ϕloop was found to vary with the I block location (ϕloop = 0.5−0.6 for the center I block and ϕloop = 0.6−0.8 for the off-center I block) and gradually increase with increasing p. These (SIS)p/C14 systems exhibited the gel-like elasticity under uniaxial elongation, and the maximum stretch ratio at rupture, λmax, increased with increasing p. In particular, the (SIS)5 undecablock system had λmax ≥ 36, which is much larger than λmax (≅10) of ordinary rubbers. This remarkably high extensibility was partly related to an osmotic effect on the bridge-type I blocks due to the looptype I blocks:27 The loop segments can stay nearby the S domain surface even under large elongation to osmotically repel the bridge segments from the surface, thereby stretching the bridge ends and enhancing the extensibility of the middle part of the bridge.27 However, no further detail of the high extensibility was elucidated. Thus, we have revisited the high extensibility of the (SIS)p/ C14 systems, placing our focus on the reversibility of the stress−strain behavior and the nanodomain alignment under elongation not examined previously. The reversibility is related to the memory of the physical network of the (SIS)p chains that can be reduced by pullout/transfer of the S blocks. On the basis of this molecular picture, we conducted linear viscoelastic tests, nonlinear elongational tests, and small-angle X-ray scattering (SAXS) measurements for 30 wt % (SIS)p/C14 systems at 20 °C, a temperature not significantly lower than Tg,PS (≅ 38 °C) of the S blocks swollen with C14. The maximum stretch ratio λmax was found to increase with increasing p, as noted previously.27 More importantly, the 30 wt % (SIS)5 system could be stretched up to the apparatus limit, λ ≅ 90, without macroscopic rupture, and the system fully recovered its size, shape, and SAXS profile during a load-free rest after such high elongation. This observation, being useful for a potential application of the multiblock system as a soft and tough material with shape memory, suggested that the system exhibited plasto-elastic deformation under large elongation

view.1−4 Needless to say, block copolymers usually form nanodomain structures according to the interblock interaction determined by the block molecular weight (M), architecture, composition, and the quality of solvent (if any). The nanodomain shape in diblock/triblock copolymers changes from sphere to cylinder, gyroid, and to lamella on a decrease of asymmetry in the composition and also on an increase of the segregation power in the case of asymmetric copolymers.1,2 Such nanodomain shape as well as the long-range order of the domain alignment strongly influences physical properties.4−6 In addition to the nanodomain structure, the block connectivity strongly affects the mechanical property. Focusing on this effect, extensive studies have been made for styrene (S)−isoprene (I) diblock and SIS triblock copolymers (with small S content) forming spherical S domains.7−10 At low temperatures (T), the SI and SIS copolymers commonly form glassy S domains and exhibit the equilibrium elasticity under small strains. The elasticity of the SI copolymers reflects the thermodynamic stability of the cubic lattice of the S domains that is determined by compromise of the osmotic requirement of uniformly filling the I phase with the I segments and the other thermodynamic requirement of randomizing the I block conformation in this phase.7−10 (Thus, the lattice is disordered and the elasticity vanishes on addition of homo-I chains that screen the osmotic requirement.7,8) In contrast, the equilibrium elasticity of the SIS copolymer is contributed not only from this lattice stability but also from the rubber elasticity of the I blocks connecting/bridging the adjacent S domains, and the latter contribution overwhelms the former for the copolymers having long, entangling I blocks. (The rubber elasticity due to the bridging I blocks remains even on addition of homo-I chains.9) At low T well below Tg,PS, the SIS copolymer does not flow plastically but exhibits macroscopic rupture under large strains because of those bridging chains. Thus, the bridge-type I blocks play an important role for determining the mechanical property of the SIS triblock copolymer. Since the bridge-type I blocks coexist with the loop-type I blocks having the two ends anchored on the same S domain, the loop fraction ϕloop is an important factor affecting the rheological property. The I blocks have the type A dipoles parallel along the block backbone so that their global (largescale) motion activates the dielectric relaxation. Utilizing this feature, we roughly estimated ϕloop dielectrically for a special class of SIS copolymer having the I blocks with symmetrically once-inverted type A dipoles (that allowed dielectric detection of the midpoint motion of the I block).11−14 The estimate, ϕloop ≅ 0.6 for bulk SIS as well as for concentrated SIS solutions in Iselective solvent, n-tetradecane (C14), was close to the prediction of the self-consistent-field (SCF) calculation.15,16 This ϕloop increases on dilution of SIS with C14 because the dilution increases the interdomain spacing to destabilize the bridge conformation.13 It should be also noted that both dangling and entangled (knotted) loops contribute to the 2682


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plates at room temperature, kept under a nitrogen atmosphere at 60 °C (where the samples became viscous fluids) for 30−40 min to erase a history of slight compression on sample loading, and then slowly cooled to the experimental temperature, 20 °C. The storage and loss moduli, G′ and G″, thus measured as a function of the angular frequency ω (10−2 < ω/s−1 < 102), were qualitatively similar to those of the 40 wt % (SIS)p/C14 systems and are presented in the Supporting Information (cf. Figure S4). All systems exhibited equilibrium elasticity associated with almost identical low-ω storage modulus. The elasticity of the SI/C14 diblock system is attributable to the thermodynamic stability of a bcc lattice of spherical S domains formed therein, whereas the elasticity of the (SIS)p multiblock is contributed from this lattice stability and also from the rubber-like elasticity of the I blocks connecting/bridging the S domains, as fully discussed in the previous work7−9,27 and also explained in the Supporting Information. The uniaxial elongational test, the main rheological test in this study, was made with the extensional viscosity fixture (EVF, TA Instruments) mounted on ARES. The EVF consists of two vertical cylindrical shafts to stretch/wind up the test specimen. A rectangular test specimen was attached horizontally to the two shafts with tiny clips (as seen later in Figure 4). One shaft rotates around the other shaft that is connected to the torque transducer and fixed in space. The rotating shaft spins around its own axis during the circular rotation around the fixed shaft, so that the specimen is wound equally on the two shafts and stretched equally from the both sides. The uniaxial elongation is achieved when the wound-up portion of the specimen can freely change its width. The Hencky strain of the specimen, ε = ln λ with λ being the stretch ratio of the specimen, is related to the radius r of the two shafts, the distance L0 between the shaft axes that corresponds to the length of the sample being stretched at every moment, and the angle φ of shaft rotation as

possibly through pullout/transfer of the S blocks, but some memory of the initial physical network remained to result in the recovery during the rest. This paper presents and discusses details of these results.

2. EXPERIMENTAL SECTION 2.1. Materials. A series of symmetrical (SIS)p multiblock copolymers were synthesized previously via stepwise living anionic polymerization followed by anionic coupling and through fractionation.27 The materials were sealed under argon atmosphere and kept in a deep freezer until use. Prior to the sample preparation, lack of degradation of the copolymers during the storage was confirmed from gel permeation chromatograph measurements utilizing CO-8020 and DP-8020 (Tosoh) combined with ultraviolet adsorption and refractive index monitors (UV-8020 and RI-8020, Tosoh) and a low-angle light scattering detector (270 Dual-detector, Malvern). Table 1 summarizes the molecular characteristics of the (SIS)p copolymers and SI diblock copolymer (precursor of SIS) determined previously. Figure 1

ε = 2rφ /L0 Figure 1. Schematic illustration of block sequences of (SIS)p multiblock copolymer samples. I2 in the sample code specifies the I block having dipole inversion.

(1)

with r = 5.15 mm and L0 = 12.7 mm for the EVF utilized in this study. (The corresponding clearance gap between the surfaces of the two shafts is 2.4 mm.) From eq 1, one revolution of the shaft (φ = 2π) gives ε = 5.1. However, in actual experiments, the two clips attaching the specimen to the shafts face to each other in the gap between the two shafts after the shaft rotation by φ = 3π/2, and further rotation brings the clip on the rotating shaft in contact to the back-surface of the specimen, thereby cutting the specimen at the clip edge (as can be easily noted from the photos in Figure 4 shown later). This geometrical problem gave an experimental limitation for the maximum attainable φ (≅ 7π/4) and the corresponding maximum attainable Hencky strain, εmax ≅ 4.5 (maximum stretch ratio λmax ≅ 90). The elongational tests were conducted at 20 °C in two modes: oneway mode and reverse mode. In the one-way mode, the (SIS)p/C14 multiblock specimens were stretched up to the rupture point at a constant Hencky strain rate, ε̇/s−1 = 0.003 and/or 0.01 (these rates were close to the lowest rate limit attainable with the fixture utilized). The one-way mode tests were made for each sample at least 2−3 times to confirm the reproducibility. The specimens for the repeated tests were cut from sheets of the (SIS)p/C14 sample with the aid of sharp razor and had the length, width, and thickness of 18 mm, 8 mm, and 0.3 mm, respectively. (The sample sheets were prepared by compression at 60 °C followed by annealing at 20 °C for ∼1 day.) Because the (SIS)5/C14 undecablock specimen exhibited remarkably high extensibility (beyond the experimental limitation), this specimen was also subjected to the reverse mode test to characterize its high extensibility. In the test, the strain of the specimen was increased at a constant rate (ε̇/s−1 = 0.01) up to a given value (εrev = 1, 2, 3, and 4) and then decreased at the same rate. (No rest time was given at the reversal point.) The specimens for this test, having the length, width, and thickness of 20 mm, 10 mm, and 0.7 mm, were prepared by compression at 60 °C and annealing at 20 °C in a metal mold of this size. (These width and thickness of the specimens were the same as those for SAXS tests under elongation explained later.) The sample shape during the elongation was monitored with a compact digital camera attached directly to EVF.

illustrates the block sequence for visual understanding of the copolymer structure: The (SIS)p chain is composed of almost identical SIS units with MS−MI−MS ≅ 10K−40K−10K connected in sequence, with the repeating number of this units along the block sequence, p = 1, 2, 3 and 5, corresponding to tri-, penta-, hepta-, and undecablocks. (In Figure 1, the arrows attached to the I blocks indicate the type A dipoles which enabled the dielectric estimation of ϕloop in the previous study.27 However, no dielectric test was made in this study.) The samples subjected to rheological, small-angle X-ray scattering (SAXS), and thermal measurements were 30 wt % solutions of the (SIS)p multiblock copolymers and the SI diblock copolymer in an Iselective, high-boiling point solvent, n-tetradecane (C14; Wako). (Shortage of the material did not allow us to make all those measurements at the previously examined concentration, 40 wt %. Thus, we made this study at a little lower concentration, 30 wt %.) These sample solutions were prepared by dissolving prescribed masses of the (SIS)p copolymer and C14 in excess benzene (cosolvent) to make a homogeneous solution and then allowing benzene to thoroughly evaporate at 40 °C under reduced pressure. (The copolymer concentration, 30 wt %, was determined after this evaporation.) A small amount of an antioxidant, dibutylhydroxytoluene (BHT), was added to the benzene solution to prevent thermal degradation. The samples were colorless, transparent, and sticky. In particular, the (SIS)5 undecablock/C14 sample was very sticky, which was useful for achieving the rheological test. 2.2. Measurements. 2.2.1. Rheological Measurements. For the (SIS)p/C14 systems, the dynamic linear viscoelastic and uniaxial elongation measurements were conducted at 20 °C with a laboratory rheometer, ARES (TA Instruments). The dynamic tests were conducted with a parallel-plate fixture of 8 mm diameter. For comparison, the test was made also for the 30 wt % SI/C14 diblock sample. All samples were loaded between the fixture 2683


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Here, a comment needs to be made for a relationship between the specimen thickness and the type of elongation achieved with EVF. The uniaxial elongation, associated with the shrinkage of both width and thickness by a factor of λ−1/2 on the stretch by a factor of λ, was satisfactorily achieved in the one-way mode test utilizing the thin specimens having the initial thickness of Θ0 = 0.3 mm. In contrast, the reverse mode test utilizing the thick specimens (Θ0 = 0.7 mm) achieved almost planar elongation (keeping a constant width), rather than the ideal uniaxial elongation, when the specimens were stretched well above λ = 2.7 (ε = 1). This planar elongation resulted mostly from the disturbance of the width shrinkage due to the sticky adhesion of the (SIS)5/C14 specimen: Under large elongation, the thick specimen as a whole exhibited a large tensile force (compared to the thin specimen), and this force pushed the wound-up portion of the specimen strongly toward the EVF shafts. Then, the wound-up portion was stickily adhered on the shafts, which disturbed this portion as well as the portion being stretched to freely reduce their width. The reverse mode test could be made also for the thin specimens (to achieve the uniaxial elongation). However, the two-dimensional SAXS measurement explained below required the specimen width to remain sufficiently larger than the X-ray beam diameter throughout the elongation process and thus preferred the planar elongation achieved for the thick specimens. For this reason, we made the reverse-mode rheological test utilizing the thick specimens as a reference for this SAXS measurement. 2.2.2. Small-Angle X-ray Scattering (SAXS) Measurements. For the SI/C14 and (SIS)p/C14 samples having isotropic orientation at rest, SAXS measurements were conducted at 20 °C with a laboratory goniometer (RINT-2000, Rigaku) equipped in Professor Kanaya’s laboratory at Institute for Chemical Research, Kyoto University. The wavelength of X-ray was λ = 0.154 nm (Cu Kα line). The scattering intensity I(q), measured with one-dimensional goniometric system as a function of the magnitude of scattering vector q = {4π/λ}sin(θ/2) (θ = scattering angle), was similar to that of the 40 wt % (SIS)p/C14 systems examined previously and is presented in the Supporting Information (cf. Figure S1). The I(q) data confirmed that the bcc lattice of spherical S domains was formed and the cell-edge length a was nearly the same in all systems. For the (SIS)5/C14 undecablock sample exhibiting very high extensibility, SAXS measurements were made also under elongation. Since the anisotropy of the scattering is important for this case, the measurements were conducted with a laboratory SAXS system (Nanoviewer, Rigaku; a common facility at ICR, Kyoto University) having a built-in two-dimensional detector (PILATUS utilizing a semiconductor system). The wavelength of X-ray was λ = 0.154 nm (Cu Kα line). A homemade elongational device was attached to this system, as shown in Figure 2. Differing from the EVF utilized in the rheological tests, this device consisted of two geared shafts both rotating at the same speed but in the opposite directions. (The rotation of the drive shaft was conducted manually.) This counter rotation of the shafts allowed the sample to stay at the right alignment with respect to the X-ray beam even under elongation. In addition, the shaft radius r (= 8.0 mm) and the distance between the shaft axes (L0 = 20.0 mm) were designed to be larger than those for the EVF so as to make the clearance gap (4.0 mm) large enough for the X-ray beam to go through without any disturbance from the shafts. Except these points, the device was similar to the EVF. The (SIS)5/C14 specimens of the length, width, and thickness of Λ0 = 25 mm, H0 = 10 mm, and Θ0 = 0.7 mm were prepared by compression at 60 °C and annealing at 20 °C in a metal mold and attached to the shafts of the elongational device with clips. The width and thickness of these specimens were the same as those utilized for the reverse mode rheological test. At 20 °C, the specimen was manually stretched slowly to Hencky strains ε = 1, 2, and 3 (as evaluated from the rotational angle φ; cf. eq 1), and then the twodimensional I(q) data were measured with an exposure time of 60 min. Under large ε > 1, the specimens exhibited almost planar elongation, rather than the uniaxial elongation, because of their sticky adhesion on the shafts, as explained earlier for the protocol of the reverse mode rheological test. This planar elongation allowed the specimen width to

Figure 2. Homemade elongational device attached to a SAXS system equipped with a 2-dimensional detector.

stay larger than the X-ray beam diameter even under large elongation, which was very helpful for measuring I(q). After the SAXS measurements, the specimens were detached from the device and kept at rest without load. During this rest, the specimen shape was monitored with a digital camera, and its I(q) data were measured (by using a sample holder attached to Nanoviewer). After a sufficiently long rest time (∼3 weeks), the specimen recovered its shape and I(q) data before the elongation. 2.2.3. Transmission Electron Microscopy (TEM). The (SIS)5/C14 sample recovered after the reverse mode elongation test was subjected to TEM observation to confirm the spherical shape of the S domains therein. The experimental protocol and the TEM image are presented in the Supporting Information. 2.2.4. Differential Scanning Calorimetric (DSC) Measurements. For the (SIS)5/C14 sample, DSC measurement was conducted to determine the glass transition temperature Tg,PS (≅ 38 °C) of the S domains being swollen with C14. (This Tg,PS is important for discussion of the remarkably high extensibility of the sample.) For comparison, the measurements were conducted also for monodisperse homopolystyrene (PS-18 obtained from Tosoh; M = 1.81 × 104) swollen with C14 to several different extents, and the Tg,S data of those PS-18/C14 samples were utilized to estimate the swelling ratio (∼82 vol % S blocks and ∼18 vol % C14 in the S domain) in the 30 wt % (SIS)5/C14 sample. The corresponding volume fraction of the S domains in the system was υS ≅ 0.10. The protocol of the DSC measurements and the data are presented in the Supporting Information. 2684


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3. RESULTS AND DISCUSSION 3.1. Overview of Uniaxial Elongational Behavior of (SIS)p/C14 Multiblock Systems. Figure 3 shows the

DSC measurements suggested that the S domains in the (SIS)5/C14 undecablock system were swollen/plasticized with C14 to have the glass transition temperature Tg,PS ≅ 38 °C and the volume fraction in the system υS ≅ 0.10, as explained in the Supporting Information. This υS value is small enough to allow the S blocks to form the spherical domain. More importantly, Tg,PS of the S domains is just moderately higher than the experimental temperature, 20 °C, which becomes a key in our later discussion of the rheological behavior under large elongation. In Figure 3, we first note that the σE data obtained for the two rates, ε̇/s−1 = 0.003 and 0.01, coincide with each other. This coincidence suggests that the (SIS)p/C14 systems exhibit no significant relaxation process in a long time scale (≥100 s) corresponding to these rates. In fact, dynamic linear viscoelastic tests revealed that the storage shear moduli G′(ω) of the (SIS)p/C14 systems were insensitive to the angular frequency ω and much larger than the loss shear moduli G″(ω) at ω/s−1 = 10−2−102, and thus those systems behaved as elastic gels exhibiting no significant relaxation at those ω, as explained in the Supporting Information. The systems behave as the linearly elastic gels also under small elongation, as noted from the agreement of the σE data with the elastic stress 3Geε (dashed lines in Figure 3) expected from the equilibrium shear modulus, Ge (≅ 3.0 × 104 Pa for all (SIS)p/C14 systems, as explained in the Supporting Information). Under large elongation, the σE data deviate upward from the dashed lines to exhibit nonlinearity, as noted also in a previous study.27 For ordinary rubber/gel networks having chemical cross-links, such nonlinearity is well described by the Edwards− Vilgis (E−V) model28 considering the finite extensibility of the network strands between trapped entanglements, as demonstrated by Urayama et al.29−31 (For a network composed of infinitely extensible Gaussian strands with/without trapped entanglements, the EV model essentially reduces to the neoHookean model that merely expresses the tensorial nonlinearity.) Following the previous approach,27 we compared the σE data with the stress deduced from the E−V model to examine the characteristic features of the physical network sustained by the S domains in the (SIS)p/C14 systems. The results of this comparison are summarized below. 3.2. Comparison with Edwards−Vilgis (E−V) Model. For our (SIS)p/C14 systems, the expression of the elongational stress σE deduced from the E−V model28 can be summarized as ν σE = fc (λ ; α) + te {fs1 (λ ; α , η) + fs2 (λ ; α) FνIkBT νI

Figure 3. Elongational stress σE of the 30 wt % (SIS)p/C14 multiblock systems measured with the one-way mode (up to rupture) at 20 °C. The σE data are plotted against the Hencky strain ε in the doublelogarithmic scale (so that the linear and nonlinear behavior at small and large ε can be compared with a similar resolution). The dashed lines indicate the linear elastic behavior under small elongation, and the solid curves indicate the stress deduced from Edward−Vilgis (E− V) model with the values of the full-stretch ratio λfull as indicated.

elongational stress σE (true stress) of the 30 wt % (SIS)p/ C14 multiblock systems at 20 °C. In the experiments, thin specimens with the thickness of 0.3 mm were utilized to satisfactorily achieve the uniaxial elongation. The systems were stretched at a constant strain rate ε̇ up to the rupture point (one-way mode explained earlier), and the measured σE data are plotted against the strain ε (= ln λ). In the systems at rest, spherical S domains were formed and further organized into the bcc lattice (though not highly ordered), as confirmed from onedimensional SAXS data reported in the Supporting Information; cf. Figure S1 (the corresponding two-dimensional SAXS data are later shown in Figure 6). The cell-edge length estimated from those SAXS data was a ≅ 36 nm in all systems examined in Figure 3. The stress of the systems under small strains is contributed from the rubber elasticity of the I blocks connecting/bridging the S domains as well as the thermodynamic stability of the lattice of the S domains, as fully discussed previously7−9,27 and also explained in the Supporting Information.

+ fs3 (λ ; α , η) + fs4 (λ ; η)}

(2)

with fc (λ ; α) =

1 − 2α 2 + α 4(λ 2 + 2λ−1) ⎛ 2 1 ⎞⎟ ⎜λ − −1 2 ⎝ 2 2 λ⎠ {1 − α (λ + 2λ )}

(1 − α 2)α 2(1 + η) {1 − α 2(λ 2 + 2λ−1)}2 ⎛ λ2 2 ⎞ ⎜⎛ 2 1⎞ ×⎜ + ⎟× λ − ⎟ 2 η + λ⎠ ⎝ λ⎠ ⎝ 1 + ηλ

(3a)

fs1 (λ ; α , η) =

fs2 (λ ; α) = 2685

⎛ 2 −α 2 1 ⎞⎟ ⎜λ − 2 2 −1 ⎝ λ⎠ 1 − α (λ + 2λ )

(3b)

(3c)


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⎧ 1 λ2 ⎨ 2 − 2α 2(λ 2 + 2λ−1) ⎩ (1 + ηλ 2)2

⎫ λ ⎬ (η + λ)2 ⎭

fs4 (λ ; η) =

⎛ 2 ηλ 1 ⎞⎟ ⎜λ − 2 ⎝ λ⎠ (1 + ηλ )(η + λ)

Nevertheless, this osmotic stretching of the bridges is not the only mechanism that enhances the extensibility, as evidenced from the fact that the undecablock system is extensible to λ = 55 well above the full-stretch ratios of the trapped entanglement strand and the I block as a whole, λfull‑ent ≅ 14 and λfull‑I ≅ 18 (see Figure 3). Indeed, the elongational test utilizing thick specimens revealed that the undecablock system is extensible to λ ≥ 90 beyond the experimental limit,34 as explained later for Figure 4. This high extensibility beyond full stretch limit of the I block can be achieved only when the S blocks are pulled out from their domains. In relation to the above argument, it is informative to focus on the full stretch ratio λfull‑copolymer of the copolymer chain as a whole. (This λfull‑copolymer is achieved when the S blocks are pulled out and all I and S blocks are fully stretched.) The undecablock copolymer is composed of five inner I blocks with MI ≅ 4 × 104, four inner S blocks with MS1 ≅ 2 × 104, and two outer S blocks with MS2 ≅ 1 × 104 (cf. Figure 1), and the unperturbed end-to-end distance of respective blocks is evaluated from empirical equations in the literature33 (RI/nm = 0.082MI1/2, RS/nm = 0.066MS1/2) as RI = 16.4 nm, RS1 = 9.3 nm, and RS2 = 6.6 nm, respectively. Thus, the unperturbed endto-end distance of the copolymer chain is given by Rcopolymer = {5RI2 + 4RS12 + 2RS22}1/2 = 42.2 nm. The full stretch length of this chain can be evaluated as Lcopolymer = 5RI2/bK,I + (4RS12 + 2RS22)/bK,S = 1670 nm (where the Kuhn lengths have the values bK,I = 0.93 nm and bK,S = 1.9 nm).33 These Rcopolymer and Lcopolymer give the full stretch ratio:

(3d)

(3e)

Here, νI is the number density of the I blocks (network strands in our systems; νI = 2.8 × 1024 m−3), νte and η represent the number density and end-mobility of the strands between trapped entanglements, and α = 1/λfull‑ent with λfull‑ent being the full-stretch ratio of those trapped entanglement strands. In eq 2, we have introduced the factor F (= 1 + 2.5υS + 14.1υS2 = 1.39) representing the filler effect of the S domains having the volume fraction υS = 0.10. (This filler factor is not included in the original E−V model.) For the 30 wt % (SIS)p/C14 systems, the routine analysis of the SAXS data explained in the Supporting Information suggested that the I blocks at rest have the end-to-end distance close to the unperturbed distance. Thus, the trapped entanglement strands in the I/C14 matrix should also have the unperturbed dimension in the absence of the large elongation, which enables us to utilize the volume fraction ϕI (= 0.20) of the I block in the matrix to estimate the molecular weight Me of those strands:32 Me = Me,bulk/ϕI = 2.5 × 104 with Me,bulk = 5.0 × 103 being the Me value in bulk PI. From the unperturbed end-to-end distance corresponding to this Me, Re = 13.0 nm, and the Kuhn length of PI, bK,I (= 0.93 nm),33 the full-stretch ratio of the trapped entanglement strand can be estimated as λfull‐ent = R e/bK,I ≅ 14

λfull‐copolymer = Lcopolymer /R copolymer ≅ 40

(5)

In Figure 3, the elongational stress σE calculated from eqs 2 and 3 with α = 1/λfull‑copolymer is shown with the thick solid curve. The σE data of the undecablock system becomes smaller than the calculated σE for ε > 3 (λ > 20), but this system is extensible beyond the full stretch limit λfull‑copolymer. This fact unequivocally indicates that a large fraction of the S blocks was pulled out from their domains under large elongation and transferred to the other domains, thereby allowing the system to deform plastically or, more accurately, plasto-elastically, as explained later for Figures 5 and 8. It should be emphasized that the pullout/transfer of the S blocks occurs under slow but large elongation because Tg,PS (≅ 38 °C) of the S domains is not significantly higher than the experimental temperature, 20 °C. Such S domains behave as rigid domains against a small tensile force resulting from small elongation to sustain the equilibrium elasticity of the I blocks, whereas a large tensile force due to slow but large strain should deform the S domains plastically to allow the S blocks to be pulled out/transferred. In the remaining part of this paper, the plasto-elastic deformation of the (SIS)5/C14 system corresponding to the pullout/transfer of the S blocks is further characterized through the elongational test in the reverse mode and the SAXS measurements under/after elongation. The results are utilized to discuss the deformation mechanism as well as the difference of the rupture behavior of the (SIS)p/C14 multiblock systems having different numbers p of the repeating SIS units. 3.3. Rheological Behavior of Undecablock System in Reverse Mode Test. For the 30 wt % (SIS)5/C14 undecablock system at 20 °C, we utilized thick specimens (of 0.7 mm thickness) to conduct the reverse mode elongational test with EVF. The elongation was reversed at the strains εrev = 1, 2 3, and 4, and the strain rate was ε̇ = 0.01 s−1 for both

(4)

λfull‑ent specifies the value of the most important parameter in the E−V model, α = 1/λfull‑ent = 0.072. The νte/νI ratio appearing in eq 2 can be estimated also from Me as νte/νI = MI/ Me − 1 = 0.6. In Figure 3, σE calculated from eqs 2 and 3 with these α and νte/νI values is shown with the thin solid curves. In the calculation, the FνIkBT factor appearing on the left-hand side of eq 2 was replaced by the Ge data to match the calculation in the linear regime with the data. In addition, the previously utilized slippage parameter, η = 5, was utilized in the calculation. (In fact, the calculated σE was rather insensitive to the η value.) For ε < 2 (λ < 7.4 < λfull‑ent), the σE data of the (SIS)p/C14 systems agree well with the calculated σE (thin solid curves); see Figure 3. The triblock and pentablock systems exhibit the rupture at λmax well below λfull‑ent. However, the heptablock system can be stretched up to λmax = 7 ≅ λfull‑ent/2. Because most of physical gels cannot stand with the stretch by the factor of λ = 7, the heptablock system can be classified as a highly extensible and tough gel. This high extensibility of the heptablock system can be partly related to the loop-type I blocks. Those loops are not stretched in proportion to the macroscopic elongation but can stay nearby the S domains, thereby enlarging the I segment concentration around the S domains to osmotically push/stretch the bride-type I blocks in the elongational direction. This osmotic stretching possibly helps the heptablock system to exhibit the high extensibility and toughness, as discussed previously.27 2686


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Figure 5. Elongational stress σE of the 30 wt % (SIS)5/C14 undecablock systems measured with the reverse mode at 20 °C (large unfilled symbols). The strain rate is ε̇ = 0.01 s−1 for both forward and reverse processes. For comparison, σE measured with the one-way mode up to the rupture point is shown with small filled circles connected with a curve. The σE data are plotted against the stretch ratio λ (top panel) and the strain ε (bottom panel).

photos to evaluate the H/H0 ratio for each value of ε. The specimen thickness Θ was not directly measurable, but the Θ/ Θ0 ratio for incompressible materials was unambiguously calculated from the H/H0 ratio and the known value of λ (= exp(ε)) as Θ/Θ0 = H0/Hλ. These ratios in the forward process increasing ε from 0 to 4 are shown in the top panel of Figure 4. The dashed line in the top panel indicates the relationship for the uniaxial elongation of an isotropic, incompressible material, ln H/H0 = ln Θ/Θ0 = ln λ−1/2 = −ε/2. The H/H0 and Θ/Θ0 data are close to this line in the range of ε ≤ 1. However, for ε > 1, the H/H0 ratio remains constant, and a significant deviation from the uniaxial elongation is noted. The deformation at ε > 1 can be well approximated as the planar elongation with fixed width and decreasing thickness

Figure 4. Normalized width H/H0 and normalized thickness Θ/Θ0 of the 30 wt % undecablock specimen (top panel) and the photos of the specimen (bottom part) during the reverse mode elongational test (εrev = 4) conducted with EVF at 20 °C. The width H and its initial value H0 were directly determined from the photos to evaluate the H/ H0 ratio for each value of ε. The normalized thickness Θ/Θ0 was calculated from this H/H0 ratio and the known ε. The plots in the top panel show these ratios evaluated for the forward process (elongating process).

forward and reverse processes. During this test, we took photos of the specimen with a compact digital camera attached to EVF. Figure 4 shows those photos during the test with εrev = 4, and Figure 5 summarizes the σE data for all εrev values examined. In Figure 4, the photos clearly demonstrate that the specimen width H decreases from its initial value H0 on an increase of strain from ε = 0 to ε = 1 but a further increase of ε (>1) hardly changes H. For quantitative characterization of this deformation, we measured H and its initial value H0 on the

H(ε) = Hε = 1 ,

Θ(ε) = exp(1 − ε)Θε = 1

(for ε > 1) (6)

The crossover from the uniaxial elongation (ε < 1) to the planar elongation (ε > 1) seen for the thick undecablock specimen is mainly attributed to the sticky adhesion of the specimen onto the EVF shafts that occurred under a large tensile force of the specimen, as briefly explained in the Experimental Section. Namely, under small elongation, the 2687


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deformation/flow associated with unrecoverable strains. In contrast, our undecablock system exhibits just moderate hysteresis at small ε even after the reversal from large strains, εrev = 3 and 4, as clearly noted in Figure 5. Specifically, the residual strain just after the reversal from εrev = 4 (λrev = 55) was as small as εresidual = 0.5 (λresidual = 1.6). Because the hysteresis of the undecablock system seen at large ε > 2 after this reversal is undoubtedly associated with the pullout of the S blocks from their domains, such a small residual strain (weak hysteresis seen at small ε after the reversal) strongly suggests that the pullout/transfer of the S block during the forward process is largely mended in the reversal process within a rather short time scale (within 400 s for ε̇ = 0.01 s−1 and εrev ≤ 4). Further details of this structural change/mend are examined below with the aid of two-dimensional SAXS data during/after elongation to discuss the mechanism of structural mend. 3.4. Structure of (SIS)5/C14 Undecablock System during Elongation. The top part of Figure 6 shows the two-dimensional SAXS intensities I(qx,qy) of the 30 wt % (SIS)5/C14 undecablock system under elongation, with the x and y directions being the directions of the stretch and the specimen width, respectively. The bottom panel shows the I(qx,0) data along the stretch direction extracted from the I(qx,qy) profile. The decrease of the specimen thickness reduces the total scattering intensity, but no correction for this reduction was made for the data presented here. In the experiments, we utilized the homemade device (Figure 2) to manually stretch the thick specimen (of thickness = 0.7 mm) to ε = 1, 2, and 3 at 20 °C and measured the I(qx,qy) data under elongation for 60 min. The stretching device was similar to the EVF utilized in the rheological tests, and the thick specimen exhibited uniaxial elongation for ε ≤ 1 and (almost) planar elongation on a further increase of ε > 1. (The planar elongation keeping the constant width at large ε was helpful for measuring the I(qx,qy) data, as explained earlier.) For the undecablock system before the elongation (ε = 0), the I(qx,qy) profile indicates that the scattering is isotropic, and thus the bcc lattice of the S domains in the system is isotropically oriented. The I(qx,0) plot for ε = 0 shown in the bottom panel, corresponding to the one-dimensional SAXS data presented in the Supporting Information, clearly exhibits the first, second, and third scattering peaks due to this lattice structure. (The I(qx,0) plots are a little scattered because no circular/sector averaging was made. Thus, we have attached curves going through the plotted data just as a guide for eye.) On the elongation to ε = 1 (λ = 2.7), the I(qx,qy) profile becomes anisotropic in particular at small qx and qy, indicating that the lattice of the S domains are deformed and oriented. Comparing of the profiles for ε = 0 and 1, we note that the lattice is stretched in the x direction and compressed in the y direction. The lattice stretching can be confirmed also from the I(qx,0) plots showing shifts of the lattice peaks to lower qx on the increase of ε from 0 to 1. (The I(qx,0) plots for ε = 0 and 1 have different intensity distributions (peak height ratios) partly because of the lattice orientation for ε = 1. Full analysis of the two-dimensional I(qx,qy) profile, specifying both deformation and orientation of the lattice, is beyond the scope of this paper and will be discussed in our future work.) On further elongation to ε = 2 (λ = 7.4), the I(qx,qy) profile becomes a little less anisotropic compared to that for ε = 1, suggesting weaker orientation of the lattice at ε = 2. However, the strongest scattering peak along the x-axis should have shifted to small angles masked by the beam stopper, as

tensile force is small, and its component in the radial direction of the EVF shaft (pushing the wound-up portion of the specimen toward the shaft) is also small. For this case, the adhesion is weak so that the specimen can adjust/decrease its width rather freely to be stretched uniaxially. However, under large elongation, the tensile force increases to enhance this pushing force, which results in strong adhesion that disturbs the width shrinkage, thereby leading to the planar-like elongation the specimen. In fact, as the strain is decreased to ε = 1 or less on the reversal of elongation from εrev = 4, the portion adhered during the forward process was not quickly released from the shafts to give slack of the specimen (specimen was not tensioned in the common tangential direction of the shafts but exhibited spool-up to form slack), as can be noticed from careful inspection of the photos for ε = 1 and 0 in the reverse process shown in Figure 4. It should be also noted that the tensile force/pushing force was smaller for the thin specimens utilized in the one-way mode test (Figure 3) than for the thick specimen utilized in the reverse mode test. For this reason, the uniaxial elongation was achieved much more satisfactorily for the thin specimens. An additional comment is to be made for the type of elongation. The planar-like elongation has been observed also for highly entangled homopolyisoprene, when thin specimens (with Θ0/H0 < 0.1) were highly stretched with EVF.35 This phenomenon, being interpreted to reflect differences of the efficiency of transmitting the macroscopic deformation into strain-hardening specimens of different Θ0/H0 ratios and corresponding difference of the polymer motion,35 is opposite to the phenomenon observed for our undecablock system (uniaxial elongation for thin specimens). Thus, the crossover from uniaxial to planar elongation seen for our system is not related to the deformation transmission efficiency but is mainly due to the sticky adhesion explained above. For our undecablock system, the reverse mode elongational test could be made also for thin specimens. However, for the two-dimensional SAXS test explained later for Figures 6−8, the specimen width needed to remain sufficiently larger than the Xray beam diameter so that we had to utilize the thick specimens with its width not too much decreasing on large elongation. Thus, as a reference for that SAXS test, it was useful to measure σE for the thick specimens in the reverse mode test. Nevertheless, the σE data obtained for the thin and thick specimens (Figures 3 and 5) were almost identical to each other. Keeping this point in our mind, we now focus on the σE data obtained for the thick specimens in the reverse mode test (Figure 5). Figure 5 demonstrates that the undecablock system exhibits negligible hysteresis in its stress−strain relationship when the elongation is reversed at small εrev = ln λrev ≤ 1 (λrev ≤ 2.7). However, the hysteresis becomes detectable on the reversal at larger εrev. The small hysteresis seen at small ε ( λfull‑I ≅ 18) to give significantly nonaffine lattice stretching. The above argument, the pullout of the S blocks becoming significant for ε ≥ 2, is in harmony with the hysteresis of the

Figure 7. Comparison of the SAXS data of the 30 wt % (SIS)5/C14 undecablock system under elongation (ε = 1, 2, and 3) with the isointensity contour curves calculated for the cases of affine stretching of the bcc lattice of the S domains formed in the system at rest.

stress−strain relationship observed on the reversal of elongation from εrev ≥ 2 (Figure 5). Nevertheless, this hysteresis is associated with just small residual strains, as explained for Figure 5. Thus, the undecablock system should preserve some memory of the initial connectivity of the physical network to recover the strain during the reverse process. This point is further examined below for the shape and SAXS profile of the specimens having experienced the elongation and then being kept in a load-free state. 3.5. Structure Recovery of (SIS)5/C14 Undecablock System after Elongation. The undecablock specimens 2690


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having been elongated to ε = 1, 2, and 3 (in the tests in Figure 6) were detached from the stretching device and kept at rest at 20 °C in a load-free state. SAXS data were measured for those specimens at several different times during this rest. For the specimen having been elongated to ε = 1, the I(qx,qy) data just after the elongation (measured with an exposure time of 60 min) were almost indistinguishable from the data for ε = 0 shown in Figure 6. In addition, the specimen recovered its original shape/size within a few seconds. Thus, the initial network connectivity was negligibly disrupted (i.e., S blocks are negligibly pulled out) under the elongation of ε = 1, which is in accord with the lack of hysteresis (Figure 5) and the agreement of the affine contour curve with the I(qx,qy) data (Figure 7), both being observed for ε = 1. In contrast, for the specimens having been elongated to ε = 2 and 3, rapid and slow recovery processes were observed during the rest. In Figure 8, the SAXS data of those specimens obtained at 3 h, 2 days, 1 week, and 3 weeks after the elongation are shown together with their photos. The photos were taken for the specimens placed on the metal mold (utilized for preparing the specimens) having a Teflon sheet at its back. In the photos, the white squares are the Teflon sheet seen through the holes of the mold and correspond to the original specimen shape. For easy comparison, the original length of the specimens is reproduced with the red bars, and the transparent specimens are enveloped with yellow dashed lines. From the photos in Figure 8, we first note that the original width has been almost recovered but the original length has not within 3 h rest: The length after 3h rest remains ∼30% (λ ≅ 1.3) and ∼50% (λ ≅ 1.5) longer than the original length for the cases of ε = 2 and 3, respectively, which roughly corresponds to the residual strain explained for Figure 5. However, this difference in the apparent recovery rates of the width and length needs to be carefully interpreted. For the thick specimens utilized in the SAXS test in Figure 6, the elongation to ε = 2 and 3 was equivalent to the uniaxial elongation (up to ε = 1) followed by the planar elongation (for ε > 1), as explained earlier. For this case, the width decreased just moderately on the elongation (cf. Figure 4), so that its recovery looked superficially fast. The specimen length under elongation was much larger than the original length (λ = 7.4 and 20 for ε = 2 and 3). Such enormously elongated specimens shrink to the length corresponding to λ ≅ 1.3 and 1.5 within 3 h rest (actually within ∼30 min as noted from visual observation). Thus, the length recovery was also fast. Corresponding to this rapid shape recovery, the SAXS profiles after 3 h rest (Figure 8) are much closer to the profile of the undeformed system compared to the profiles under the elongation (Figure 6). It should be also noted that the SAXS profiles after 3 h rest is considerably anisotropic (even compared to the profiles under deformation) and thus the lattice of the S domains was oriented during the rapid recovery of the specimen shape. This rapid recovery of the shape and SAXS profile indicates that some S blocks remain intact to preserve the initial network connectivity partially even for ε = 3, i.e., for λ = 20 being larger than the full stretch limit of the I blocks, λfull‑I ≅ 18. Surprisingly, such specimens having just a partial memory of the initial connectivity exhibit full recovery of their original shape and the SAXS profile after a sufficiently long rest (∼3 weeks or a little more); see Figure 8. Thus, there should exist a driving force for this full recovery even for the partially

Figure 8. Changes of shape and SAXS profile of the 30 wt % (SIS)5/ C14 undecablock specimens during the rest at 20 °C after elongation (ε = 2 and 3).

disrupted network. This driving force is discussed below in relation to the domain structure under elongation. 3.6. Connectivity of physical network and driving force for structural recovery. Summarizing all experimental results shown in Figures 3−8, Figure 9 illustrates possible structural changes in the undecablock system under elongation. The x-, y-, and z-directions correspond to those defined/ utilized in Figure 6. As shown in the left part of Figure 9, the bcc lattice of the S domains (pale red circles) being connected by the I blocks (blue curves) and having the cell-edge length a ≅ 36 nm is formed in the system at rest. (For simplicity, no 2691


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Figure 9. Possible structural changes in the 30 wt % (SIS)5/C14 undecablock system under large elongation. The macroscopic elongation is applied in x-direction, and the width and thickness directions of specimen are chosen to be the y- and z-directions. (Under uniaxial elongation, the y- and zdirections are equivalent to each other.) The initial network connectivity preferentially surviving in the y- and z-directions provides the material with the driving force for full structural recovery after elongation.

similar to stress-induced yielding of glassy polymers near Tg.) Then, the sequence of the blocks containing the pulled-out S block(s), for example, the −I−S−I− sequence at around the middle of the copolymer chain and the −I−S sequence at the end, would exhibit thermal Brownian motion. The S block pulled out in the solvent (C14)-rich I phase would exhibit enhanced Brownian motion compared to those in the lightly swollen S domains. This motion should allow the pulled out S blocks to be transferred to/mixed in a S domain that is spatially close to (or identical to) the S domain on which the I block(s) in that moving sequence is anchored. Furthermore, the elongational deformation of the specimen should displace the pulled out S block, thereby largely helping this transfer. The deformation may also squeeze this block against the S domain to help mixing of the block into the domain (at experimental temperature not significantly lower than Tg,PS of the swollen S domain). This deformation-assisted transfer/mixing process, occurring preferentially in a direction not increasing the I block tension, results in reorganization of the physical network to allow the plasto-elastic deformation of the material as a whole . This reorganization allows the lattice of the S domains to have the constant size, a∥ > a (in x-direction parallel to the elongation)

loop-type I blocks are illustrated.) This structure is equivalent to the network of the I blocks (physically cross-linked by the S domains) that contains trapped entanglements. For small ε (not shown in Figure 9), the tensile force of the I blocks remains small so that the S blocks (red curves) are not pulled out from their domains to preserve the connectivity of the initial network. For this case, the bcc lattice of the S domains is stretched affinely, on average, with respect to the macroscopic elongation thereby exhibiting the elastic behavior with negligible hysteresis. The rheological and SAXS data for ε = 1 should correspond to this affinely stretched lattice/network. For larger ε, the I block strands between the trapped entanglements begin to be highly stretched to exert a large tensile force on the S blocks connected to those strands. Although the osmotic stretching explained earlier tends to reduce this tensile force, the domain of those S blocks cannot stay intact when those I blocks approach their full-stretch limit (λfull‑I ≅ 18). As illustrated in the middle part of Figure 9, the S blocks connected to such highly stretched I blocks should be pulled out from the domains, but this pullout is not associated with macroscopic rupture of the specimen because the domains have Tg,PS ≅ 38 °C not significantly higher than the experimental temperature, 20 °C. (This pulling-out process is 2692


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and a⊥ < a (in y- and z-directions), irrespective of the macroscopic stretch ratio λ even if it is comparable to/larger than λfull‑ent, as illustrated in the middle and right parts of Figure 9. This should be the structure reflected in the SAXS data shown in Figure 6 for ε = 2 and 3 (λ = 7.4 and 20). We also note that the lattice reorganization results in a largescale rearrangement of the S domains because the crosssectional area of the specimen decreases in proportion to λ−1 but the nearest-neighbor distance between the S domains, corresponding to a⊥ shown in Figure 9, remains independent of λ, and thus the areal number density of the S domains remains constant. (If the total number of the S domains on the whole cross section remains constant, the domains collide each other to collapse at large λ, which is physically impossible: For example, a⊥ = a/λ1/2 ≅ 13 nm if the lattice is affinely stretched uniaxially up to λ = 7.4. This a⊥ is unreasonably smaller than the S domain diameter ≅ 16 nm.) The large-scale rearrangement should have occurred in both y- and z-directions if the material exhibits uniaxial elongation and mainly in z-direction if the elongation is planar. The undecablock copolymer chain has six S blocks in its backbone, and a probability of pulling out all these S blocks simultaneously should be considerably small. Then, a given undecablock chain having two (or more) S blocks in the intact S domains is physically connected to the other chains that also have two (or more) S blocks in the same intact S domains. This type of connected chains should percolate throughout the system, so that the initial network connectivity of the I blocks can be partially preserved through those chains. (In other words, those connected chains behave together as a long effective strand preserving the initial network topology in a large length scale.) This preserved connectivity possibly allows the rapid recovery of the SAXS profile/material shape observed on removal of external elongation (Figure 8) and also reduces the residual strain after the reversal of elongation (Figure 5). However, the partially preserved initial connectivity is not enough for the undecablock system to exhibit the very slow but full recovery of the SAXS profile/material shape seen in Figure 8. A key for this full recovery could be a difference of the pullout probabilities for the I blocks connecting the S domains in the stretching and shrinking directions (x- and y/z-directions depicted in Figure 9). Obviously, the former type of I blocks should pull out the S blocks with a higher probability, so that the initial connectivity of the network survives more significantly in the y−z plane. In addition, the pulled out S blocks would be transferred preferentially in the x−y plane (shrinking plane) in which the transfer reduces the I block tension, as illustrated in Figure 9. As a result, the density of the I blocks connecting the S domains in the y−z plane (some of which preserve the initial connectivity) appears to be larger than the density of the I blocks connecting the domains in the x-direction. Then, after the rapid recovery process that largely releases the stretching of the I blocks in the x-direction, the net tension of the whole ensemble of the I blocks would be larger in the y- and z-directions. This difference in the I block tension in the x- and y/z-directions, being equivalent to anisotropy of the internal pressure, possibly drives the material back to the initial state because the initial connectivity should survive considerably in the y/z-direction. This driving force for the full recovery certainly exists but would be rather weak because the specimen and the I blocks therein are not significantly stretched after the rapid recovery process, as noted in Figure 8. This weak force can induce, just slowly, the anisotropic pull out/transfer of

the S blocks and the resulting rearrangement of the S domains into the undeformed lattice. The full recovery appears to occur very slowly for this reason. (This full recovery can be regarded as slow, internal self-healing.) It should be emphasized again that the above argument is intimately related to the softness of the swollen S domain having Tg,PS ≅ 38 °C not significantly higher than the experimental temperature, T = 20 °C. We naturally expect that the physical network of the I blocks becomes less extensible and the recovery of the strain in the load-free state becomes more difficult at lower T. In fact, a preliminary test at 7 °C (made in response to comments from reviewers for this paper) suggested that the system was less extensible (the strain at rupture was smaller) at 7 °C than at 20 °C, being in harmony with the expectation and lending support to the above argument.37 A comprehensive test in wide ranges of T and strain rate is now being planned, and the results (including that preliminary result) will be presented in our future paper. 3.7. Changes of Rupture Behavior with Repeating Number of SIS Units in Copolymer Backbone. As noted in Figure 3, the strain at rupture of the (SIS)p/C14 system increases significantly with repeating number p (= 1−5) of SIS units in copolymer backbone, despite the fact that molecular weights of the constituent blocks are almost identical for the series of the (SIS)p multiblock copolymers (and the SAXS profile is also nearly the same; cf. Supporting Information). This difference of the rupture behavior can be naturally related to the number (p + 1) of the S blocks contained in the copolymer chain backbone. Namely, the network of the I blocks can preserve the connectivity if two (or more) S blocks are not pulled out from the S domains for respective copolymer chains. Obviously, the probability of having two (or more) intact S block under a given elongational stress increases with increasing p. For this reason, the rupture strain quite possibly increases with increasing p. This argument is examined a little more quantitatively below. Because the series of copolymers having different p have almost identical molecular weights of the constituent blocks, the probability of pulling out a given S block, either at the end or inner part of the copolymer chain, should be insensitive to p. Then, the probabilities P0 and P1 that the copolymer chain has no intact S block or just one intact S block can be written as P0 = ψ n − 2ψ ′2 ,

P1 = (n − 2)(1 − ψ )ψ n − 3ψ ′2

+ 2ψ n − 2(1 − ψ ′)ψ ′

(11)

where ψ and ψ′ represent the probabilities of pulling out the inner and end S blocks, respectively, and n = p + 1 (number of S blocks per copolymer chain). The probability that the copolymer chain has two or more intact S blocks to (partially) preserve the initial connectivity of the physical network is given by P≥2 = 1 − P0 − P1. The probabilities ψ and ψ′ should be determined by a free energy increment on mixing one S block into the I/C14 matrix phase, ΔG, and the tensile force acting on the S block, f. In the simplest case, we may assume ⎧ ΔGinner − fξ ⎫ ⎬, ψ = exp⎨− kBT ⎩ ⎭

⎧ ΔGend − fξ′ ⎫ ⎬ ψ ′ = exp⎨− kBT ⎭ ⎩ (12)

for the inner and end S blocks, respectively. Here, kB and T are the Boltzmann constant and absolute temperature, respectively, 2693


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and ξ and ξ′ denote the displacement of the inner and end S blocks driven by the tensile force f. Note that the factors fξ and fξ′ are equivalent to the mechanical work externally given to the inner and end S blocks through the elongation of the material. Because ΔG should be essentially proportional to the molecular weight of the S block,26 we have ΔGinner = 2ΔGend (MS ≅ 2 × 104 and 1 × 104 for the inner and end S blocks, respectively). The (SIS)p/C14 systems with p = 1−5 had essentially the same number density of the S blocks and exhibited almost identical stress−strain relationship up to respective rupture points (cf. Figure 3). Thus, at a given level of the stress, we may safely assume that each S block in these systems has received the same amount of mechanical work, w = fξ = fξ′. For this case, we may utilize the above relationship ΔGinner = 2ΔGend to relate ψ and ψ′ as w ψ = ψ ′(2 − α)/(1 − α) with α = ΔGend (13)

those I blocks. In the linear viscoelastic regime under small elongation, the systems exhibited gel-like elasticity sustained by those I blocks. This linear elastic behavior corresponded to affine stretching of the bcc lattice (as revealed from SAXS data) and was very similar for all (SIS)p/C14 systems. In contrast, a remarkable difference was found under large but slow elongation: The maximum stretch ratio at rupture, λmax, significantly increased with the repeating number p of the SIS units, λmax ≅ 1.7, 2.2, 6.6, and ≥90 for p = 1, 2, 3, and 5, respectively. In particular, λmax ≥ 90 found for the undecablock system (p = 5) was much larger compared to the full-stretch ratio of the trapped entanglement strand (λfull‑ent ≅ 14) and even to the full-stretch ratio of the (SIS)5 copolymer chain as a whole (λfull‑copolymer ≅ 40). This remarkably high extensibility of the undecablock system was attributed to reorganization of the physical network of the I blocks occurring through pullout of the S block from its domain followed by transfer of this S block to the other domain. (This pullout/transfer occurred because the experimental temperature, 20 °C, was not significantly lower than Tg,PS ≅ 38 °C.) Large hysteresis in the stress−strain relationship and the nonaffine stretching of the lattice of the S domains (having an ε-insensitive magnitude of stretching), revealed from rheological and SAXS measurements under large elongation, naturally resulted from the network reorganization. Thus, under large elongation, the undecablock system deformed plasto-elastically through this network reorganization. This deformation differed from unrecoverable plastic flow, as evidenced from spontaneous, full recovery of the size, shape, and SAXS profile of the undecablock specimen having experienced large elongation and then being kept in a loadfree state at 20 °C. This recovery strongly suggests that the memory of initial connectivity of the physical network was partially preserved anisotropically in the direction perpendicular to the elongation, thereby giving the driving force for the full recovery. This argument in turn provides us with a clue for understanding the difference of λmax for the series of (SIS)p/ C14 systems. The network connectivity can (partially) survive and the material can stand with the elongation if at least two S blocks, on average, remain intact (not pulled out) in each (SIS)p copolymer backbone. The probability of having such intact S blocks increases with the repeating number p of the SIS units, which is in harmony with the observed difference of λmax. Finally, a comment needs to be added for a potential similarity between our multiblock copolymer and the other type of associating polymers that include the ionomers. The key concept for the high extensibility and strain recovery of the multiblock copolymer, the deformation-induced disruption of the physical bonds (pull-out of the S blocks for the copolymers) and the deformation-assisted transfer/re-formation of the bonds (transfer of the pulled out S blocks and reorganization of the network) occurring within the experimental time scale, would apply in general, for example, to the ionomers. For the copolymers, the bonding sites (S blocks) are regularly arranged along the chain backbone, which may help these disruption/transfer/re-formation processes to occur rapidly. Thus, appropriate molecular design of the ionomers (for the association intensity of the ionic groups and their periodicity along the chain backbone) could provide them with high extensibility and strain recoverability. This issue deserves further attention.

Figure 10 shows P≥2 (= 1 − P0 − P1) calculated from eqs 11 and 13 with α = 0.9 (elongation of the material supplies 90% of

Figure 10. Probability P≥2 of (partially) preserving the initial network connectivity plotted against the probability ψ of pulling out the inner S block. The mechanical work given to respective S blocks were set to be 90% of the energy required for mixing the end S block into the I/C14 matrix.

the energy required for mixing the end S block into the I/C14 matrix): P≥2 is plotted against the pullout probability of the inner S block, ψ. For a given ψ value, the probability P≥2 of (partially) preserving the initial network connectivity is considerably larger for the copolymer having more SIS units in its backbone, which is in harmony with the qualitative argument presented above. We should note that eq 11 does not consider the reorganization of the network (through transfer of the pulledout S blocks) and cannot quantitatively describe the difference of the rupture behavior of the (SIS)p/C14 systems having different p. Nevertheless, the basic physics giving this difference, the increased choice of two or more intact S blocks per copolymer backbone for larger p, appears to be well captured by eq 11.

4. CONCLUDING REMARKS We have examined rheological and structural behavior for the series of (SIS)p multiblock copolymers in C14. At 20 °C, the 30 wt % (SIS)p/C14 systems formed the bcc lattice of spherical S domains swollen with C14 to have Tg,PS ≅ 38 °C. These S domains physically cross-link the I blocks to form a network of 2694


Macromolecules

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(25) Nagata, Y.; Masuda, J.; Noda, A.; Cho, D.; Takano, A.; Matsushita, Y. Macromolecules 2005, 38, 10220. (26) Matsumiya, Y.; Matsumoto, M.; Watanabe, H.; Kanaya, T.; Takahashi, Y. Macromolecules 2007, 40, 3724. (27) Watanabe, H.; Matsumiya, Y.; Sawada, T.; Iwamoto, T. Macromolecules 2007, 40, 6885. (28) Edwards, S. F.; Vilgis, T. Polymer 1986, 27, 483. (29) Urayama, K.; Kawamura, T.; Kohjiya, S. Macromolecules 2003, 34, 8621. (30) Urayama, K.; Kawamura, T.; Kohjiya, S. J. Chem. Phys. 2003, 118, 5658. (31) Urayama, K. Nihon Reoroji Gakkaishi 2005, 33, 257. (32) (a) In usual solutions of homo-polyisoprene (hI) having free ends, the entanglement molecular weight Me scales with the hI volume fraction ϕ I as M e = M e,bulk /ϕ I 1.3 , as noted from extensive experiments.32b,c However, the I blocks in the (SIS)p/C14 multiblock solutions have the ends fixed on the S domains and are more easily entangled compared to the free hI chains. For this reason, the classical relationship giving a moderately smaller Me value,32d Me = Me,bulk/ϕI (>Me,bulk/ϕI1.3), has been utilized in this (and previous27) work. (b) Matsumiya, Y. Nihon Reoroji Gakkaishi 2011, 39, 197. (c) Watanabe, H. Nihon Reoroji Gakkaishi 2012, 40, 209. (d) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley: New York, 1980. (33) Fetters, L. J.; Lohse, D. J.; Colby, R. H. Chain Dimension and Entanglement Spacing. In Physical Properties of Polymers Handbook, 2nd ed.; Mark, J. E., Ed.; Springer: New York, 2007. (34) The rupture point of λmax = 36 reported previously for the 40 wt % (SIS)5/C14 system27 was obtained for thin specimens (with a little rough edge). In this study, we conformed that thick specimens of this system were extensible up to the experimental limitation (λ ≅ 90). (35) Nielsen, J. K.; Hassager, O.; Rasmussen, H. K.; McKinley, G. H. J. Rheol. 2009, 53, 1327. (36) Guinier, A.; Fournet, G. Small Angle X-ray Scattering; Wiley: New York, 1995. (37) (a) Reviewers for this paper asked an interesting question for an effect(s) of the strain rate on the elongational behavior of the multiblock copolymer systems, partly in relation to the behavior of entangled homopolymers. The elongational behavior of homopolymers is strongly affected by the Rouse time τR of the chain, and the strain-hardening is observed for branched polymer melts37b as well as solutions of linear polymers37c at the strain rate larger than 1/τR. In contrast, for the multiblock copolymer systems, the time τ* required for deformation-induced pullout of the S blocks and the deformationassisted transfer of the S blocks, not the Rouse time of the copolymer chain as a whole, appears to be the essential factor governing the elongational behavior. In fact, a preliminary experiment suggested that the undecablock system became less extensible at lower T (= 7 °C), which is in harmony with this argument for τ*. (b) Rolon-Garrido, V. H.; Pivokonsky, R.; Filip, P.; Zatloukal, M.; Wagner, M. H. Rheol. Acta 2009, 48, 691. (c) Bhattacharjee, P. K.; Oberhauser, J. P.; McKinley, G. H.; Leal, L. G.; Sridhar, T. Macromolecules 2002, 35, 10131.

ASSOCIATED CONTENT

S Supporting Information *

Dynamic linear viscoelastic data of the 30 wt % (SIS)p/C14 systems, one-dimensional SAXS profiles of those systems in a quiescent state, and TEM image and DSC data of the (SIS)5/ C14 system. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors appreciate kind help for SAXS measurements by Professor K. Nishida and Professor T. Kanaya at ICR, Kyoto University. This work was supported by the Grant-in-Aid for Scientific Research (A) (Grant No. 24245045) from MEXT, Japan, Grant-in-Aid for Scientific Research (C) (Grant No. 24550135) from JSPS, Japan, and partly by Collaborative Research Program of ICR, Kyoto University (Grant No. 201235).

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REFERENCES

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Uniaxial Extensional Behavior of (SIS)p-Type Multiblock Copolymer

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