Molecular Weight Dependence of Viscoelastic Properties for

Aug 22, 2013 - By subtracting the responses from grains/defects from G*SP, the responses from component chains, ΔG*chain, are obtained. At M/Me < 1.5...
0 downloads 0 Views 3MB Size
Download PDF
Article pubs.acs.org/Macromolecules

Molecular Weight Dependence of Viscoelastic Properties for Symmetric Poly(styrene‑b‑2-vinylpyridine)s in the Nanophase Separated Molten States Long Fang† and Yoshiaki Takahashi* Department of Molecular & Material Sciences, and Institute for Materials Chemistry and Engineering, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan

Atsushi Takano and Yushu Matsushita Department of Applied Chemistry, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan ABSTRACT: Viscoelastic properties of symmetric poly(styrene-b-2vinylpyridine)s (SP), whose thermorheological properties of components are identical, are studied over a wide range of molecular weight M for nanophase separated melts. Plateau modulus G0N for SP was almost the same with those of components. At low angular frequency ω, power law behavior of dynamic moduli of SP, G*SP ∼ ω0.5, is observed. When a universal liquid-like behavior exists between plateau and power law regions for G*SP, the latter can be attributed to motions of grains/defects. By subtracting the responses from grains/defects from G*SP, the responses from component chains, ΔG*chain, are obtained. At M/Me < 1.5−2 per components, ⟨τ⟩w (= η0Je), obtained from ΔG*chain, showed the same M dependence with PS, but the magnitude was about 1 order higher than PS. At M/Me > 1.5−2, ⟨τ⟩w can be fitted to exp(νM/Me) with ν = 2, implying that the retraction mode becomes dominant for relaxation of entangled SP. At M/Me > 6−7, the power law behavior is smoothly connected with plateau region, without showing liquid-like behavior, denoting that the junction is practically frozen in the interface at M/Me > 6−7.

1. INTRODUCTION

In the experimental studies, scattering, birefringence, dielectric relaxation, and so on are utilized to elucidate structural characters related to the viscoelastic properties and/or relaxation mechanisms of component polymers.2−7 When the lamellae are aligned to different directions (e.g., parallel, perpendicular, and transverse), somewhat different dynamic viscoelastic behaviors, which can be related to different mechanisms such as compression, bending and sliding of lamellae, etc., are observed. Moreover, when the lamellae are well aligned, the power law behavior almost disappear and the terminal region behavior becomes apparent at low ω.12 Though large-amplitude oscillatory shear flow is more effective to control the alignment of lamellae than steady shear flow,13,14 typical viscoelastic liquid behaviors can be more clearly observed under steady shear flow than the oscillatory flow when lamellae are well aligned.15 In these cases, the power law behavior observed for nonaligned samples can be attributed to the responses from grains/defects.9 Even in those studies, detailed discussions of chain relaxation mechanisms are still difficult due to the viscoelastic heterogeneity of components.

It is well-known that block copolymers exhibit phase transition between ordered (nanophase separated) and disordered (homogeneous) states (ODT), which depend on the Flory− Huggins interaction parameter χ, degree of polymerization N, and composition of components ϕ.1 In the ordered state, block copolymer chains can achieve thermodynamically equilibrium conformation in the nanophase separated domain. The nanophase separated domains have coherence in a certain length scale, but they are randomly oriented in much larger length scale, possessing multigrain structure with probable defects.2−4 Because of such structural characters and the viscoelastic heterogeneity of components, viscoelastic properties of block copolymers become very complicated. A huge number of studies have been carried out to understand the viscoelastic properties of block copolymers.2−7 One of the most studied systems is lamellar forming diblocks. A unique power law behavior in angular frequency ω (or frequency f (= ω/2π)) dependencies of storage G′(ω) and loss G″(ω) moduli, G′ ∼ G″ ∼ ω0.5, are observed at the low ω end.8 Theoretically, both large scale motions of grains/defects9 and relaxation processes of component chains10,11 can explain the power law behavior. © XXXX American Chemical Society

Received: May 8, 2013 Revised: August 2, 2013

A

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

It is expected that the situation can be simplified when block components have almost the same physical properties. Poly(styrene-block-2-vinylpyridine) (SP) is one of such model samples since polystyrene (PS) and poly(2-vinylpyridine) (P2VP) have the same Kuhn segment length,16 quite similar glass transition temperature Tg, and almost the same viscoelastic properties at melt states and in common good solvents.17 Phase diagrams of ordered SPs, PSP triblocks, and few others are well established and molecular weight M dependence of the long period of lamellar structure D of SP and PSP are reported as ∼M0.64 in wide ranges of M.18 By utilizing small-angle neutron scattering (SANS) and neutron reflectivity measurements, it is also elucidated that the radius of gyration of component PS chain perpendicular to lamellar plane is elongated in consistency with D, while those parallel to the interface are contracted preserving constant volume of the chain as that of unperturbed chain.19,20 The junction of PS and P2VP chains are located in a narrow interface region whose thickness is about 3 nm at χN ∼ 90, within which 1 nm can be attributed to interfacial fluctuation. A part of chains adjacent to the junction are elongated while free chain ends are almost unperturbed and broadly distributed in lamella with their maximum distribution at the center of each domain.21 We studied ODT, flow-induced structure, and viscoelastic properties of symmetric SP solutions in a common good solvent near the ODT.22 In the disordered states, fluctuation effects are only observed for G′, resulting in higher steady state compliance Je than those for PS and P2VP solutions while zero shear viscosity η0 are practically the same as those for components. Under the steady shear flow, it was observed by SANS that the fluctuation effects are suppressed and consequently η0 and Je of SP solutions became practically the same as those of PS and P2VP solutions. In the ordered states, it was observed under the steady shear flow that shear stress σ and first normal stress difference N1 become proportional to shear rate in a certain range of lower shear rate.15,22 This behavior can be understood as textured fluid behavior.23,24 The major origin of stresses are interfacial tension whose magnitudes contributing to σ and N1 are governed by orientation and deformation of lamellar interface, similar to the behaviors observed for binary immiscible fluid mixtures in which deformed domains exist under steady state.24 The degree of perpendicular alignment of lamellae under steady shear flow is mainly controlled by χN and reduced shear rate, reduced by a characteristic shear rate for non-Newtonian behavior.22 When lamellae are well aligned at high shear rates as observed by SANS under the flow, ordinary viscoelastic liquid behaviors for σ and N1 are observed and η0 and Je of SP solutions became practically the same as those of PS and P2VP solutions. In these studies, however, χN range examined was limited close to the ODT. We further studied viscoelastic properties of symmetric SPs with relatively low M in the disordered and ordered molten states based on the experimentally determined χ (= 0.0072 + 30/T (K)).25 In the disordered state, the fluctuation effects on dynamic moduli G* for SP, G*SP, appeared at around χN = 3, and the effects became stronger with increase of χN so that η0 and Je became about 3 times and nearly 1 order higher than those of corresponding PS homopolymers, respectively, near the ODT.25 In the ordered state, textured fluid behavior23 is observed for SP-21K, SP-29K, and SP-46.9K (see Table 1) under steady shear flow similarly as in solutions,15,22 implying

Table 1. Molecular Characteristics of Poly(styrene-b-2vinylpyridine)s samples SP-21K SP-29K SP-30.3K SP-38K SP-46.9K SP-68.3K SP-98.6K SP-109K SP-135K SP-209K SP-224K SP-386K a

Mwa (g mol−1)

Mw/Mnb

ϕSc

× × × × × × × × × × × ×

1.03 1.01 1.16 1.01 1.04 1.04 1.02 1.05 1.04 1.03 1.01 1.15

0.50 0.52 0.54 0.52 0.51 0.52 0.50 0.51 0.46 0.51 0.51 0.51

2.1 2.90 3.03 3.8 4.69 6.83 9.86 10.9 13.5 20.9 22.4 38.6

104 104 104 104 104 104 104 104 104 104 104 104

By MALLS. bBy GPC. cBy 1H NMR.

that the multigrain structures of these samples are controlled by the shear rate when steady states are achieved. However, the well-aligned state was only achieved for SP-21K in those samples.26 We also examined a separation method of the responses from grains/defects, ΔG*grain, and the responses of polymer chains, ΔG*chain, in G*SP at low ω for SP-21K.26 A simple subtraction method (ΔG*chain = G*SP − ΔG*grain) was employed. Here, ΔG*grain was defined as asymptotic data (∼ω0.5) fitted to G*SP at low ω end and extended to higher ω (see Figure 5). By this method, ΔG*chain data having terminal region behavior are obtained irrespective of preshear flows. The consistency between η0 and Je obtained from ΔG*chain with those obtained from the data in well aligned state under steady shear flow for SP-21K supports validity of this separation method. The above separation method was also applied to a higher molecular weight sample SP-98.6K (Table 1), and ΔG*chain data having terminal region behavior are also obtained irrespective of the preshear flows.26 Since SP-98.6K is expected to be entangled, the above result implies that entanglement between chains from opposing lamellae are scarce and their disentanglement can occur, so that chain relaxation behavior still can be observed in the experimental window when the number of entanglement is not so high. It is expected that the relaxation mechanism will change with increase of number of the entanglements. In this paper, we examine dynamic viscoelastic properties of symmetric SP diblock copolymer melts over a wide range of molecular weight. Characteristic parameters such as plateau modulus are directly obtained from the data. Applicability of the above-mentioned separation method is further discussed to obtain η0 and Je for the most of the samples. The chain relaxation mechanisms of symmetric SPs are discussed based on comparison of the viscoelastic parameters for SP and homopolymers.

2. EXPERIMENTAL SECTION 2.1. Samples. The SP diblock copolymers and PS homopolymers are synthesized by anionic polymerization in vacuo as reported previously.16,25,26 Molecular weight heterogeneities, Mw/Mn, with Mw and Mn being weight-averaged and number-averaged molecular weights, respectively, are determined in THF by the Tosoh GPC system, equipped with an RI-8012 differential refractive index detector and three GMHHR columns. Standard PSs are used for the calibration. Absolute Mw of the samples are determined by multiangle laser light scattering (MALLS) measurement by Wyatt Technology DOWN EOS B

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

enhanced optical system at 35 °C in THF using reflective index increment, dn/dc = 0.185 mL/g for PS at 690 nm, since dn/dc for P2VP are very close to that for PS. Volume fractions of polystyrene ϕS in SPs are determined by NMR spectra obtained by Varian unity-500 1 H NMR spectrometer. Molecular characteristics of SPs and PSs are listed in Tables 1 and 2, respectively. Here, samples are named to show

are separately shown in three groups. Figures 2−4 show double-logarithmic plots of master curves of (a) G′SP, (b) G″SP,

Table 2. Molecular Characteristics of Polystyrenes

a

samples

Mwa (g mol−1)

Mw/Mnb

PS-19.6K PS-37.9K PS-113K

1.96 × 10 3.79 × 104 11.3 × 104

1.02 1.01 1.01

4

By MALLS. bBy GPC.

their total Mw in kg/mol; e.g., Mw of SP-21K is 21 kg/mol. We can safely assume that the highest measuring temperature employed for each sample is below the respective ODT.25 As already reported,17,22,25 Tg of PS, P2VP, and SP are practically the same (101−102 °C by DSC; heating rate 5 °C/min) at high M and decreases quite similarly with decrease of M ( 60 kg/mol are in between two lines, close to that for PS. The data for SP-38K, SP-46.9K, and hPS-37.9K are very close to each other and somewhat higher than others. This feature may be an artifact from narrow and nonflat plateau region due to lower Mw of these samples and the employed definition of G0N. As a whole, we conclude that there is no specific difference in the magnitude of G0N for SP and component PS and P2VP, implying that the same molecular weight for entanglement, Me, for SP and two components can be used for the data analysis. E

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

ω2. Since the difference between ΔG*grain and G*SP is large enough for these five samples so that ΔG*chain data can be successfully evaluated as shown later. Figure 10 shows double-logarithmic plots of G″SP and G′SP vs ωaT for SP-109K at lower ω region. In this figure, a solid line

Figure 8. Double-logarithmic plots of GX and ωX against Mw for SPs and PSs at Tr = 160 °C. Solid and dashed lines are guides for the eyes. Symbols are denoted in the figure.

that “frozen lamellar structure” retards disentanglement procedure and partly sustain the plateau modulus at the lower ω end of the plateau region; however, we cannot proceed with further discussions for these data. Figure 9 shows double-logarithmic plots of G′/GX and G″/ GX vs ωaT/ωX. It is clear that the data at ωaT/ωX < 1 show

Figure 10. Double-logarithmic plots of master curves of G*SP and ΔG*chain against ωaT for SP-109K at Tr = 160 °C. Symbols are denoted in the figure. The solid line with slope of 0.5 is drawn to fit G′SP at low ω end. This line is extended to higher ω and used as ΔG*grain data to obtain ΔG*chain (= G*SP − ΔG*chain), assuming that G″SP asymptotes to the power law behavior at still lower ω. The lines with slope of 1 and 2 represent terminal region behavior for ΔG*chain.

with slope of 0.5 is fitted to G′SP data at low ω end and extended to the lower ω end of plateau region. G″SP data do not coincide with the solid line in the experimental range of ω. The situation is the same for SP-68.3K and SP-98.6K. However, the above-mentioned feature of asymptotic behavior observed for lower Mw samples strongly suggests that even if the asymptotic behavior is only observed for G′SP, it is expected that G″SP merge with G′SP at still lower ω. Thus, we can further assume that whenever the asymptotic behavior of G′SP to the power law behavior is observed, the fitted line extended to higher ω can be used as ΔG*grain data to separate the responses from grains/defects and chain relaxations, as long as ΔG*grain are appropriately lower than G″SP and G′SP at ω where liquidlike behavior exists. The ΔG′chain and ΔG″chain data for SP-109K thus obtained are also shown in Figure 10 by fewer points than the original data as in Figure 5. The same procedure was used to evaluate ΔG′chain and ΔG″chain for SP-68.3K and SP-98.6K. Figure 11 summarizes the ΔG*grain data used to obtain ΔG*chain (Figure 12). Note that the absolute values of these data are subject to change maintaining ω0.5 dependence, reflecting the difference in multigrain structure. Their exists ambiguity for the upper limit of ΔG*grain, but the important point is the fact that terminal region behavior observed for ΔG*chain are independent of the choice of the upper limit of ΔG*grain.26 Figure 12 shows double-logarithmic plots of ΔG′chain and ΔG″chain against ωaT obtained by the subtraction method. From these data, η0 and Je for SPs are evaluated by ordinary methods. Figures 13 and 14 respectively show Mw dependences of η0 and Je, together with the data obtained for disordered SPs.25 Data for linear PS are shown by black solid lines in consistency with literature data27 for comparison. η0 and Je for SP in the disordered state have steeper Mw dependence than those for PS, but they become proportional to Mw in the ordered state as shown by red solid lines (slope: 1) in the respective figures. η0

Figure 9. Double-logarithmic plots of G′/GX and G″/GX against ωaT/ ωX for entangled SPs at Tr = 160 °C. Symbols are denoted in the figure.

universality before asymptoting the respective power law behavior. The observed universality is qualitatively the same as those for the terminal relaxation behaviors of entangled linear and star homopolymers,28 implying that there exist terminal relaxation behaviors of block chains for these SP samples. At the lower ω, the power law behavior due to grains/ defects motions are overlapped on the terminal relaxation behaviors.

4. DISCUSSION Apparent liquid-like behavior was not observed in G*SP for the three highest Mw samples (Figure 7), while universal liquid-like behaviors are observed for other samples (Figure 9). The asymptotic behaviors to the power law in low ω regime are observed at higher ω for G′SP than G″SP for 5 lower Mw SPs in Table 1. This feature is understandable since the contribution of ΔG′chain for G′SP disappear at higher ω than that of ΔG″chain for G″SP with decrease of ω because ΔG″chain ∼ ω > ΔG′chain ∼ F

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

Figure 11. Double-logarithmic plots of ΔG*grain vs ωaT for SPs at Tr = 160 °C, used to obtain ΔG′chain and ΔG″chain data in Figure 12. Symbols are denoted in the figure.

Figure 14. Double-logarithmic plots of Je vs Mw for SPs and PSs27 at Tr = 160 °C. The filled symbols are the data for SPs in the disordered state. 25 M′ C‑hPS denotes characteristic M for appearance of entanglement effect for Je of linear PS. Red line with slope of 1 is a guide for the eyes.

and Je for SPs in the nonentangled region are about 3 times and nearly 1 order higher than those for PS, respectively. The above results are remarkably different from the results for SP solutions.22 That is, η0 and Je for well-aligned SP solutions are the same as those for PS and P2VP solutions even in the entangled region. It can be considered that the diffusion of junctions confined in the interface of lamellae significantly retard and affect the relaxation processes of SP melts even for the nonentangled chains. With further increase of Mw, the Mw dependence of η0 of SP becomes steeper, denoting the entanglement effect at around characteristic M for appearance of entanglement effect for η0 of linear PS,27 MC‑hPS. Mw dependence of η0 for SP becomes close to that for polystyrene again at around 1.5MC‑hPS. The most of Je data are obtained at Mw below characteristic M for appearance of entanglement effect for Je of linear PS,28 M′C‑hPS, so that entanglement effect is not observed for Je. To further discuss the entanglement effects, we examine products of Je and G0N, which denotes broadness of relaxation time distributions.27−29 Figure 15 shows JeG0N vs MS/MSe and

Figure 12. Double-logarithmic plots of ΔG′chain and ΔG″chain against ωaT for SPs at Tr = 160 °C. Symbols are denoted in the figure. The data for SP-21K obtained in the previous study26 are shown by solid lines.

Figure 13. Double-logarithmic plots of η0 vs Mw for SPs and PSs27 at Tr = 160 °C. The filled symbols are the data for SPs in the disordered state.25 MC‑hPS denotes characteristic M for appearance of entanglement effect for η0 of linear PS. Red line with slope of 1 is a guide for the eyes.

Figure 15. Plots of JeG0N against MS/MSe for entangled SPs at Tr = 160 °C. The data for star polymers are also shown by the dotted line against Ma/Me.29 Red line is a guide for the eyes. G

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

Ma/Me for SP and star29 polymers, respectively. Here MS/MSe and Ma/Me denote M/Me for PS component in SP and that for span (2 arms) of stars. It is clear that JeG0N for SP are much higher and have steeper MS/MSe dependence than the stars. Note that JeG0N for linear polymers asymptote to a limiting value (2−3.5) with increase of M/Me.27,28 The data for stars are well explained by retraction mode of arm, having exponential dependence of η0 on Ma/Me and broad distribution of relaxation time up to Ma/Me = 25.29 These results strongly suggest that relaxation mechanisms of entangled diblock chains are retraction mode of component chains similar to those of star chains but relaxation times of SP are much more retarded and their distribution is broadened. To further discuss the overall feature of viscoelastic properties of symmetric SP blocks, we use an averaged relaxation time ⟨τ⟩w (= η0Je),27−29 which is close to the longest relaxation time, obtained from the data in Figures 13 and 14. Figure 16 shows double-logarithmic plots of ⟨τ⟩w against Mw,

This is consistent with the retraction mode of component chain whose junction point is almost frozen in the interface.10,11 Thus, we conclude that the retraction mode of component chain is the main relaxation process of entangled SP diblock copolymers. Figure 17 shows schematic illustration of relaxation processes for block copolymers in the ordered state. For nonentangled

Figure 17. Schematic illustration of relaxation processes for (a) nonentangled, (b) slightly entangled, and (c) entangled block copolymers in the ordered state. Chains in the right domain represent original state while those in the left domain represent chains under relaxation process. Existing and disappeared entanglements are denoted by ○and × , respectively. Figure 16. Double-logarithmic plots of ⟨τ⟩w against Mw for SPs at Tr = 160 °C. The filled symbols show the data in the disordered state.25 The data for PSs27 are shown by solid lines with slopes of 2 (M < MC‑hPS), 4.4 (MC‑hPS < M < M′C‑hPS), and 3.4 (M′C‑hPS < M), from left to right, respectively. Red lines are guide for the eyes. Blue line denotes exponential type equation for relaxation time.10,11

chain, slow diffusion of junction along interface control the longest relaxation process as shown in Figure 17a. At 1.5−2 < M/Me < 6−7 per components, ⟨τ⟩w can be fitted to exp(νM/ Me) with ν = 2. The distribution of relaxation times (JeG0N) is much broader than linear and star homopolymers. Disentanglement of chains by retraction motion of the chain still allows slow diffusion of junction along the interface as shown in Figure 17b. At M/Me > 6−7 per component (Mw > 200K), the liquid-like behavior is not observed and the power law behavior is smoothly connected with plateau region. The retraction modes for chains whose junctions are frozen in the interface as shown in Figure 17c become dominant at M/Me > 6−7 per component chain. To understand higher values of viscoelastic parameters in nonentangled region, a similar idea with the ideas for cooperative motions of branches of bottle-brush-type polymacromonomers30 and for block chains in spherical domain31 might be reasonable. The same idea may be used to explain the relaxation process of slightly entangled chains. However, it cannot be discussed further in this paper.

including the values in the disordered state (filled symbols). The data for linear PS27 are shown by three dotted lines having slopes of 2 (M < MC‑hPS), 4.4 (MC‑hPS < M < M′C‑hPS), and 3.4 (M′C‑hPS < M), from left to right, respectively. In the disordered state, ⟨τ⟩w (= η0Je) for SP and PS coincide with each other at the lowest MW (χN ∼ 2−3). With increase of MW, ⟨τ⟩w for SP increases much steeper than those for PS and connected to the data in the ordered state without any gap. In the ordered state, ⟨τ⟩w of SP become proportional to Mw2, say up to Mw = 40 kg/ mol. Note that plateau region was not observed for the three lowest Mw samples in the ordered state. With further increase of Mw, ⟨τ⟩w data deviate from the red solid line (slope = 2) due to the entanglement effects. In Figure 16, red broken line is drawn parallel to the line for PS with slope of 4.4, while blue line denotes theoretically predicted exponential type equation;10,11 ⟨τ⟩w ∼ exp(νMS/MSe) with ν = 2 as a fitting parameter. It is impossible to judge from this figure that which is the better representation of M dependence of ⟨τ⟩w. For samples with higher Mw (>200 kg/mol), the liquidlike behavior was not observed in G*SP and the power law behavior is smoothly connected with plateau region behavior.

5. CONCLUDING REMARKS In this paper and in two preceding papers,25,26 viscoelastic properties of symmetric SP diblock copolymers are examined in the disordered and ordered states in comparison with those of component PS and P2VP, which are almost identical in viscoelastic properties. In the disordered state, ⟨τ⟩w (= η0Je) for SP and PS coincided with each other at the lowest Mw (χN ∼ H

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

Article

2−3). With increase of M, ⟨τ⟩w for SP increased much steeper than those for PS and became about 1 order higher than linear PS near the ODT. In the ordered state, G0N values for SP and component PS and P2VP are practically the same so that the entanglement effect can be discussed by using M/Me of components. Terminal relaxation behaviors of SP chains are apparently observed in slightly higher ω region than that for power law behavior due to motions of grains/defects, up to M/ Me ∼ 4−5, per a component chain. The viscoelastic parameters obtained in ordered state is smoothly connected with those in disordered state at ODT. For the entangled system, the retraction mode becomes dominant and the junction is practically frozen in the interface at M/Me > 6−7. Finally, we point out a few consistencies for viscoelastic properties of block copolymers with those of diffusion properties summarized in a review.32 Though it is reported for spherical domains, the slowing down of mean diffusion coefficient starts at around χN ∼ 4 for SP diblock copolymer, consistent with our observation about the fluctuation effects. Self-diffusion coefficients of block copolymers are insensitive to ODT in consistent with the fact that viscoelastic parameters are rather smoothly connected at ODT. The self-diffusion coefficients parallel to the lamellar interface become about 1 order smaller than that for hypothetical disordered sample at around χN ∼ 15−20, implying that the longest relaxation time will be about 1 order higher than corresponding uniform sample, if the longest relaxation process is controlled by the self-diffusion. Since ⟨τ⟩w of SP-21K, SP-29K, and SP-30.3K (χN ∼ 14−20 at 160 °C) is about 1 order higher than those of PS, the change in the order of relaxation time also seems to be consistent.

■

(15) Takahashi, Y.; Noda, M.; Ochiai, N.; Noda, I. Polymer 1996, 37, 5943. (16) Matsushita, Y.; Shimizu, K.; Nakao, Y.; Choshi, H.; Noda, I.; Nagasawa, M. Polym J. 1986, 18, 361. (17) Takahashi, Y.; Ochiai, N.; Matsushita, Y.; Noda, I. Polym J. 1996, 28, 1065. (18) Matsushita, Y. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 1645. (19) Matsushita, Y.; Mori, K.; Mogi, Y.; Saguchi, R.; Noda, I.; Nagasawa, M.; Chang, T.; Glinka, C. J.; Han, C. C. Macromolecules 1990, 23, 4317. (20) Matsushita, Y.; Mori, K.; Saguchi, R.; Noda, I.; Nagasawa, M.; Chang, T.; Glinka, C. J.; Han, C. C. Macromolecules 1990, 23, 4387. (21) Torikai, N.; Matsushita, Y.; Langridge, S.; Buckmall, D.; Penfold, J.; Takeda, M. Physica B 2000, 12−16, 283 and references therein. (22) Takahashi, Y.; Imaichi, K.; Noda, M.; Takano, A.; Matsushita, Y. Polym J. 2007, 39, 632 and references therein. (23) Doi, M.; Ohta, T. J. Chem. Phys. 1991, 95, 1242. (24) Takahashi, Y.; Kurashima, N.; Noda, I.; Doi, M. J. Rheol. 1994, 38, 699. (25) Takahashi, Y.; Fang, L.; Takano, A.; Torikai, N.; Matsushita, Y. Nihon Reoroji Gakkaishi 2013, 41, 83. (26) Fang, L.; Takahashi, Y.; Takano, A.; Matsushita, Y. Nihon Reoroji Gakkaishi 2013, 41, 93. (27) Graessley, W. W. Polymer Liquids & Networks: Dynamics and Rheology; Garland Science Talyor & Francis Group: London, 2008; Chapter 2. (28) Raju, V. R.; Menezes, E. V.; Marin, G.; Graessley, W. W. Macromolecules 1991, 14, 1668. (29) Watanabe, H. Prog. Polym. Sci. 1999, 24, 1253. (30) Iwawaki, H.; Inoue, T.; Nakamura, Y. Macromolecules 2012, 45, 4801. (31) Tamura, E.; Kawai, Y.; Inoue, T.; Watanabe, H. Macromolecules 2012, 45, 6580. (32) Yokoyama, H. Mater. Sci. Eng. 2006, R53, 199.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.T.). Present Address †

L.F.: Ablestik (Shanghai) Co Ltd., No. 332 MeiGui South Rd., WaiGaoQiao Free Trade Zone, Shanghai, 200131, China. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Leibler, L. Macromolecules 1980, 13, 1602. (2) Bates, F. F.; Fredrickson, G. H. Annu. Rev. Chem. Phys. 1990, 41, 525. (3) Fredrickson, G. H.; Bates, F. S. Annu. Rev. Mater. Sci. 1996, 26, 501. (4) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, UK, 1998. (5) Watanabe, H. Structure and Properties of Multiphase Polymeric Materials; Araki, T., Qui, T. C., Shibayama, M., Eds.; Marcel Dekker: New York, 1998; Chapter 9. (6) Zeng, Y.; Wiesner, U. Macromol. Chem. Phys. 1998, 199, 1771. (7) Lodge, T. P. Macromol. Chem. Phys. 2003, 204, 265. (8) Bates, F. S. Macromolecules 1984, 17, 2607. (9) Kawasaki, K.; Onuki, A. Phys. Rev. A 1990, 42, 3664. (10) Witten, T. A.; Leibler, L.; Pincus, P. A. Macromolecules 1990, 23, 824. (11) Rubinstein, M.; Obukov, S. P. Macromolecules 1993, 26, 1740. (12) Bates, F. S.; Rosedale, J. H.; Fredrickson, G. H. J. Chem. Phys. 1990, 92, 6255. (13) Wiesner, U. Macromol. Chem. Phys. 1997, 198, 1997. (14) Meins, T.; Hyun, K.; Dingenouts, N.; Fotouhi Ardakani, M.; Struth, B.; Wilhelm, M. Macromolecules 2012, 45, 455. I

dx.doi.org/10.1021/ma400957p | Macromolecules XXXX, XXX, XXX−XXX