Rheo-Optical Study on Dynamics of Bottlebrush-Like

May 23, 2012 - Department of Macromolecular Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, ...
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Rheo-Optical Study on Dynamics of Bottlebrush-Like Polymacromonomer Consisting of Polystyrene. II. Side Chain Length Dependence on Dynamical Stiffness of Main Chain Hiroshi Iwawaki,† Osamu Urakawa,† Tadashi Inoue,*,† and Yo Nakamura‡ †

Department of Macromolecular Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan ‡ Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8510, Japan ABSTRACT: Dynamic birefringence and viscoelasticity measurements of bottlebrushlike polystyrene polymacromonomers having various branch (side chain) lengths were conducted over a wide frequency region covering from the glass-to-rubber transition zone to the flow zone in order to discuss effects of side chain length on dynamical stiffness of main polymer chain. Strain-induced birefringence at high frequencies was negative, similarly to linear polystyrenes, irrespective of side chain length, while birefringence in the flow zone strongly depended on side chain length. By using the modified stress-optical rule (MSOR), the complex modulus was decomposed into two components, main chain and branch components. With increasing the side chain length, the dynamical stiffness of main chain (number of repeating units per viscoelastic segment) first increased and then leveled off, suggesting that repulsive interaction between branches would be screened out over a certain branch length.

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INTRODUCTION Comb-branched polymers with dense side chains (branches) have attracted many researchers’ interest because of their unique properties.1−24 Polymerization of macromonomers is one of the methods to obtain such polymers, in addition to grafting the side chains onto a prepared linear chain.18 By controlling the molecular weight of macromonomer and the polymerization condition of macromonomer, the ratio of the polymerization index of the branch, nB, to the main chain, nM, R = n B /n M , can be varied. For the case of R ≪ 1, polymacromonomers, PMs, can be regarded as “molecular brushes” while R ≫ 1, PMs can be regarded as “star polymers”. In this study, we used “bPM” as an abbreviation of the molecular brush type polymacromonomer. bPMs behave as semi flexible chains in solutions2,4 and in melts19,24 due to repulsive interaction between neighboring branches. The complex shear modulus G* of bPM reflects two different chain dynamics corresponding to the branch and the main chain.10,14 In a previous study, we demonstrated that rheo-optical method using strain-induced birefringence was a useful and effective method to study dynamics of bPMs.24 The repulsive interaction with neighbors increases main chain stiffness. As a result, the stress-optical coefficient for the main chain is different from that for branches. This enables us to separately evaluate the dynamics of the main chain and the branches through the modified stress-optical rule. The separation revealed that branch motions were highly cooperative due to the interaction, contrast to the scarcely branched polymers. In this study, we apply the rheo-optical method to bPMs having various side chain lengths in order to clarify the effect of © 2012 American Chemical Society

side chain length on main chain stiffness and cooperativity of braches. In the case of dilute solutions, main chain stiffness increases monotonically with increasing branch length in the studied range, 15 < nB < 110.20 However, we will show that dynamical stiffness of bPMs in melts levels off over a certain branch length, nB ∼ 20. We tentatively attribute this difference to screening of the repulsive interaction due to the penetration of branches from other chains.

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EXPERIMENTAL SECTION

Sample. The polystyrene polymacromonomers having PS structure in both the main chain and the branches were synthesized in the manner reported by Tsukahara et al.1 Styrene was anionically polymerized in toluene using benzyllithium as an initiator, and the reaction was terminated by p-chloromethylstyrene (Seimi Chemical Co. Ltd.) to obtain the styrene macromonomer. The products were reprecipitated several times into methanol to remove unreacted pchrolomethylstyrene. Weight-average molecular weights MwB from 1.65 × 103 to 6.77 × 103 were determined by light scattering measurements. The number of sample code indicates the degree of polymerization of the macromonomer. The macromonomers were polymerized in benzene at 40−60 °C with azobisisobutylonitrile as an initiator to obtain polymacromonomer samples. The weight-average molecular weight MwTotal were determined by light scattering measurements and Mw/Mn were determined by gel permeation chromatography. Characteristics of the samples are summarized in Table 1. nB and nM indicate the degree of polymerization of the branch and the main chain, respectively. Received: February 8, 2012 Revised: April 21, 2012 Published: May 23, 2012 4801

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The sign of K* is negative at high frequencies and positive at low frequencies although all repeating units for both of the main chain and the branch are styrene. As mentioned in the previous paper,24 it would be a reasonable assignment that the branch shows negative birefringence and the main chain shows positive birefringence because the main chain would have longer relaxation times. Very preliminary calculation of G* for a bottle-brush type bead−spring chain indicates that the model calculation well captures some features of bPMs: The clear separation of relaxation modes for side chains and main chains. The relaxation modes of side chains were found to be independent of main chain length. However the model gave only one stressoptical coefficient. This is because the bead−spring model is based on the assumption of phantom chain and the exclude volume effect is not considered. Thus, the complex relaxation behavior of strain-induced birefringence strongly suggests the orientational coupling of side chain and main chain due to exclude volume effects. Detailed results will be published in the near future. Effect of Relaxed Branches on the Birefringence of the Main Chain. As described in the previous section, the birefringence in the flow region (intrinsic birefringence of bPM) for bPMs having longer branches (nB ≥ 30) is positive. The origin of this positive intrinsic birefringence can be explained as follows. The conformation of each branch is not be spherical but ellipsoidal because the branches would be extended or stretched in perpendicular direction to the main chain axis due to condensed branched structure and therefore the branches show the optically opposite contribution of the main chain, which result in the positive birefringence (see Figure 3a).24 For the case of long branches, this positive contribution would overcome the negative main chain contribution. For short branches, negative contribution from the main chain would be dominant. Actually, for the case of PM15 having the shortest branches, positive birefringence was not observed at low frequencies.19 Figure 2 displays G* and K* for PM15 in the flow region. K* for PM15 is always negative over all frequency region although the two-step relaxation of G′, indicated by two arrows, is observed as well as other bPMs having longer branches. We note that the ratio of the birefringence to the modulus is different between at high and

Table 1. Characterization of Samples sample code

MwB/103

Mwtotal/106

nB

nM

Mw /Mn

PM15 PM20 PM30 PM40 PM65

1.65 1.93 2.96 4.18 6.77

1.58 2.07 1.97 1.23 1.32

15.9 18.6 28.5 40.2 65.1

745 817 698 472 195

1.06 1.10 1.29 1.25 1.14

For rheo-optical measurements, pellets were prepared by melting bPM samples in a vacuum oven at 180 °C and then cooling them down to the room temperature. Rheo-Optical Measurements. Since the experimental apparatus for rheo-optical measurements on oscillatory shear deformation is reported elsewhere,25 only a brief description is given here. As for the viscoelastic measurements, a small amplitude oscillatory deformation, γ(t) = γ0 sinωt (with γ0 = 0.06) is applied on the sample in order to measure the complex shear modulus G* and the complex shear strainoptical coefficient K*. G* and K* were determined in the temperature range from 120 to 190 °C. To check the consistency of the data, G* was measured with a Rheometric ARES system with a homemade parallel plate fixture having 4 mm diameter. Instrument compliance was carefully corrected with the method reported by McKenna et al.26,27

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RESULTS AND DISCUSSION Overview of Composite Curves for G*(ω) and K*(ω). For a representative example, the composite curves for G* and K* from the transition region to the flow region for PM40 are shown in Figure 1. Here, we used the method of reduced variables to construct the composite curves.28

Figure 1. Composite curves of the complex shear modulus G* and the complex shear strain-optical coefficient K* for PM40 measured with shear flow birefringence apparatus. The solid lines are G* data measured with ARES. The reference temperature is 140 °C.

As shown in Figure 1, G′ and G″ show a power law relationship, G′ ∼ G″ ∝ ω1/2, at high frequencies (ωaT > 1 × 101 s−1). Similar frequency dependence was observed for other polymacromonomers having different chemical structures in main and side chains12 and also for cross-linked molecular brushes.29 At lower frequencies than down-arrow (ωaT = 3 × 10−2 s−1), G′ and G″ show the terminal relaxation behavior, G′ ∝ ω2 and G″ ∝ ω1, corresponding to the slow motion of the main chain. At middle frequencies, a weak shoulder corresponding to the motion of the branch appears in G′ as indicated by the up-arrow (ωaT = 6 s−1). These two stepwise relaxations of G* were also observed for comb-like polymers.30

Figure 2. Composite curves of G* and K* for PM15. The reference temperature is 140 °C. The up-arrow and down-arrow indicate the relaxations of the branch and the main chain, respectively. 4802

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low frequencies, indicating the molecular origins of the two relaxations are different. (The faster relaxation is originated by the branches and the slower one is by the main chain) Negative birefringence in the flow region for PM15 indicates that the shape of branches is nearly a sphere having no optically contribution to the main chain component (see Figure 3b). As shown in Figure 3c, phenyl rings directly attached to the main chain originate the negative birefringence of the main chain component as the case of ordinary linear PS.

Figure 4. Composite curves of G* and K* for PM20 measured with shear flow birefringence apparatus. The reference temperature is 140 °C.

Figure 5. Composite curves of K* for PM20. The measurement temperatures used for constructing the composite cures are 120, 150, and 180 °C. The reference temperature is 140 °C. Figure 3. Schematic illustration of the shape of the branches for bPM composed of longer branches (a), shorter branches (b) and the contribution of phenyl rings directly attached to the trunk to the negative birefringence of the main chain component (c).

Thus, K* reflects the birefringence of the main chain at low frequencies (ωaT < 10 s−1). Here, we note that the maximum of K′, K′max, increases with increasing temperature. These features strongly suggest that the positive birefringence originated by the main chain decreases with decreasing temperature. K′/G′ at low frequencies (ωaT < 10 s−1) is very close to the stress-optical coefficient for the main chain.24 Figure 6 shows temperature dependence of K′/G′, which corresponds to the after-

Thus, we expect the intrinsic birefringence of bPMs will change the sign at a certain branch length. At this branch length the positive birefringence will be balanced with the negative birefringence. Actually, this happens for nB ∼ 20. The intrinsic birefringence of PM20 is very small. However, for the case of PM20, more complicated phenomena were observed. Figure 4 shows the composite curves of G* and K* for PM20. Here, the same shift factor was used for both G* and K*. The rheooptical measurements were conducted in the temperature range from 120 to 180 °C. In contrast with G*, the superposition of K* is not good. To see details of temperature dependence of K*, K* at representative temperatures is shown in Figure 5. Judging from G* data, the frequency region of ωaT < 10 s−1 corresponds to the region where the relaxation of the main chain is mainly observed. At lower temperatures (T ≤ 130 °C), only negative K′ and K″ were observed even at low frequencies. At higher temperatures (T > 130 °C), a weak positive birefringence was observed; positive K′ was observed at lower frequencies. The sign inversion of K′ or K″ is detected around the middle frequencies (ωaT ∼ 10 s−1) at 140 °C. This frequency region agrees with the frequency region where the branch mode is terminated, indicated by up-arrow in Figure 4.

Figure 6. Temperature dependence of K′/G′ at low frequencies of PM20. 4803

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even applied to other data as described in a letter.34 A further comment should be made for separability of modulus. One (or more) of these processes in eqs 1 and 2 may be a combined process that corresponds to two different relaxation mechanisms working in a series fashion as the MR version. This point can be understood if we consider a model case, two Maxwellian elements, e1 and e2, having stress-optical coefficients Ce1 and Ce2 (≠Ce1), respectively, and being connected in series (correspond to stain additivity). These elements reflect different relaxation mechanisms but the connected elements as a whole still satisfy the stress-optical relationship, i.e., the proportionality between the birefringence Δn and stress σ, Δn = (Ce1 + Ce2)σ. This is simply because the stress is common for each component in series connections. Namely, two different relaxation mechanisms can be observed rheo-optically as one relaxation process if they are combined in the “series fashion”, and the rheo-optical data cannot resolve the stress-optical coefficients for individual mechanisms. In addition, the above discussion shows the value of stress-optical coefficient is sensitive to molecular origin of stress. In what follows, we keep this point in our mind and discuss the relaxation processes (eqs 1 and 2) with the aid of their C values. Since eqs 1 and 2 include three unknown components, all the components could not be determined simultaneously. Assuming that the glassy component would be common for all the samples, eqs 3 and 4 can be regarded as simultaneous equations for GB* and GM*.

mentioned optical parameter for the main chain component, CM. The K′/G′ value was found to be constant at low frequencies irrespective of temperature. However, as we expected, the K′/G′ value decreased with decreasing temperature. Moreover, CM was negative at low temperatures. Similar inversion of sign of the intrinsic birefringence was reported for poly(merthyl methacrylate), PMMA.31,32 For the case of PMMA, the stress-optical coefficient is positive above 140 °C while negative T < 140 °C. This peculiar behavior is attributed to the conformation change of side groups. In molecular theories of strain-induced birefringence for polymers, anisotropy of polarizability of the repeating units, Δβ, is assumed to be independent of temperature for simplicity. In real polymers, Δβ can be a complex function of temperatures, especially for the case of Δβ ∼ 0 if the repeating units have the internal freedom. For the case of bPMs, molecular origin of the intrinsic birefringence (birefringence originated by main chain orientation), we have to consider the contribution of the conformation change of the branches with temperature in addition to the two contributions of positive birefringence originated by the branches having ellipsoidal conformation and negative birefringence originating in phenyl rings directly attached to the trunk, as explained in Figure 3. For the case of PM20, at lower temperatures (T ≤ 130 °C), the negative birefringence is dominant. This means that the shape of branch would be close to spherical. On the other hand, at higher temperatures (T > 130 °C) the positive birefringence would become dominant. This means that the shape of the branches for PM20 would be more extended in the direction of the long axis of the ellipsoid with increasing temperature. Thus, the anomalous temperature dependence of K* can be explained by the change of the conformation of branches, which is affected by the strength of repulsive interaction. Here, we note the reliability of data at higher frequencies. Data of G* and K* shown in Figure 4 are limited up to G* ∼ 106 Pa. This is because we used a large fixture in order to measure precisely G* and K* in the terminal region where modulus is lower than 103 Pa. For such a larger fixture, accessible upper limit of modulus is lowered because large compliance corrections of rheometer are necessary. In order to obtained data at higher frequencies we performed the mechanical and optical measurements with a tensile rheometer equipped with an optical train. The data covering the glassy region for PM15 were presented in a previous study.19 The data in the glass-to-rubber transition and glassy regions for PM20 and PM40 were consistent with data show in Figure 4. Thus, we did not observe significant molecular weight dependence of G* and K* in the glassy region and therefore the data are not shown here. nB Dependence of Optical Parameters. For the case of bPMs, the stress-birefringence relationship (modified stressoptical rule, MSOR) may be written as follows using stressoptical coefficient, C. G* = G B* + GM* + GG*

(1)

K * = C BG B* + CMGM* + CGGG*

(2)

G* − GG* = G B* + GM*

(3)

K * − CGGG* = C BG B* + CMGM*

(4)

By solving the above simultaneous equations after deducting the glassy component, GB* and GM* at each temperature can be determined. The detailed methods are reported in the previous papers.19,24 The decompositions of G* were conducted for various bPM samples having different nB from 15 to 65. With respect to the decision of CM for PM20, since K′/G′ value is temperaturedependent at low frequencies, we determined the CM values at each temperature in view of the temperature-dependent as shown in Figure 6. Equations 3 and 4 were solved for GB* and GM* at each temperature with the thus determined temperature-dependent CM values, and then composite curves for GB* and GM* were constructed. Optical parameters used for the decompositions are summarized in Table 2. The values of CB for bPMs are slightly smaller than that for linear PS (−4.8 × 10−9 Pa−1)35 and almost constant irrespective of nB. These constant CB values suggest that the branch length, nB, does not have significant effects on the segmental dynamics of branches. Table 2. Optical Parameters, Viscoelastic Segment Size and Je(B)

Here, the subscripts G, B, and M represent glass, branch and main chain components, respectively. Mott and Roland proposed a difference version of MSOR, (MR version).33 Unfortunately, within the range of detail provided in the paper, the MR version cannot be followed or

sample code

CB/10−9 Pa−1

CM/10−8 Pa−1

MsMain/MB

Je(B)/106 Pa−1

L-PS PM15 PM20 PM30 PM40 PM65

−4.80 −2.50 −2.30 −4.00 −3.00 −2.79

− −0.88 0.05a 1.40 2.40 4.80

8.6 49.6 103.6 90.1 118.8 101.6

− 3.04 6.67 7.25 15.3 22.5

CM/Pa−1 = −1.26 × 10−7 + 2.30 × 10−9T − 1.42 × 10−11T2 + 2.99 × 10−14T3.

a

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The slightly smaller CB could be explained if we consider highly branched structure of bPM. As explained before, each branch is in an extended state due to the repulsive interaction between branches. This means that there is an elastic coupling between the branches. Such an elastic coupling may result in larger stress than the entropic stress for the ordinary linear polymers. As a result, CB for bPMs could be smaller than that for linear PS. On the other hand, the values and the signs of CM vary with nB. As will be described later, we assume an orientation of a large coarse-grained main chain segment containing many relaxed branches when discussing the main chain component. Thus, the change of the branch shapes with nB mentioned in the previous section (see Figure 3) would be the most important factor affecting the nB dependence of CM. In order to elucidate the effect of nB on CM, nB dependence of CM for bPMs at the reference temperature (TRf = 140 °C) is shown in Figure 7. CM changes from negative to positive with increasing nB. The

and the segment polarizability, which determines birefringence, is normally thought to be independent of temperature if the chain conformation is insensitive to temperature. If we follow this prediction, temperature dependence of the trunk contribution decreases with increasing temperature. On the other hand, for the case of branch contribution, the repulsive interaction would increase with increasing temperature because the interaction would be originated by molecular motion of branches. The increase of the repulsive interaction would stretch the branch in the direction perpendicular to the main chain axis. As explained before, stretched chains have positive contribution and thus the positive birefringence increases with temperature. This positive contribution would increase with increasing nB because the branches having larger nB are stretched in the direction perpendicular to the main chain axis. Thus, as shown in Figure 8a, much larger “branch component” than “trunk component” for bPMs having longer branches makes the CM be positive over the whole temperature range while as shown in Figure 8b, negative CM is observed at low temperatures for bPMs having shorter branches. Frequency Dependence of GM*. The obtained composite curves of GG*, GB*, and GM* for PM40 are shown in Figure 9.

Figure 7. Degree of branch length, nB, dependence of CM for bPMs. Broken line indicates the value of C for linear PS (−4.8 × 10−9 Pa−1). The reference temperature is 140 °C.

increase of CM continues with nB while as we will see later the segment size of the main chain levels off at a certain nB value. Characteristic features of temperature dependence and nB dependence of CM may be summarized in Figure 8. CM is

Figure 9. Decomposition of G* into three components (GG*, GB*, and GM*) for PM40. The reference temperature is 140 °C.

Here, the method of reduced variable was used separately to construct the composite curves for each component. The frequency dependence of GM* is similar to that of the Rouse model consisting of a few Maxwellian models, as indicated by red solid lines. This means that by considering larger coarsegrained main chain segments containing many branches, GM* spectra for bPMs with highly branched structure can be described by the Rouse model, which represents the dynamics for linear polymers without entanglements. However, as seen in the frequency region (ωaT > 3 s−1) in Figure 9, the shape of GM″ curve is broader than that of monodisperse linear polymers indicated by the red broken line. The limiting modulus of GM′ at high frequencies, GM′(∞), may be related to the molecular weight of the viscoelastic segment (Rouse segment) of the main chain, Msmain.

Figure 8. Schematic illustration of the temperature dependence of CM for bPMs having longer branch (a) and bPMs having shorter branch (b). The blue line is CM which is summation of the trunk component and the branch component.

determined by two contributions, negative birefringence originated mainly by the phenyl rings directly attached to the trunk, “trunk component”, and the positive birefringence originated by the oval sphere-shaped branches, “branch component”. For the case of linear polymers, the molecular theory predicts that the stress-optical coefficient decreases with increasing temperature, C ∼ T−1 in the first approximation. This is because the entropic stress increases with temperature

Ms main =

ρRT GM′(∞)

(5)

Here, ρ is the density and R is the gas constant. The number of repeating unit per main chain segment, Msmain/MB, corresponds to the dynamic stiffness of the main chain. The estimated values of Msmain/MB for all the bPM samples are summarized in Table 2. The stiffness, Msmain/MB, first increases with increasing nB 4805

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and then levels off at about Msmain/MB = 100. This means that the highly branched structure of bPMs makes the dynamic stiffness of the main chain about 10 times larger than that for linear PS (8.6).35 For PM40, since the polymerization degree of the main chain, nM, is 472, the number of the main chain segment is only 4. It can be considered that if the main chain segment regarded as one bead in the Rouse model has a large distribution in its size, the number of the segment has a distribution. That is why the disagreement between GM″ and the Rouse model described above could be caused. Comparison of the Dynamic Stiffness to the Static Stiffness. The Kuhn segment size corresponds to the static stiffness of the main chain while the Rouse segment size, Msmain/MB, calculated from the limiting modulus of GM* corresponds to the dynamic stiffness. For the case of linear polymers, the Rouse segment size agrees with the Kuhn segment size regardless of chemical structures.36,37 In order to examine the correlation between the Rouse segment size and the Kuhn segment size for bPMs, we will compare them. Nakamura et al. determined the Kuhn segment length, λPM−1, for bPMs having various nB by light scattering experiments in dilute solution.8,13,20 The molecular weight of the Rouse segment for linear PS, Ms(L‑PS) determined by Inoue et al. with rheo-optical study is 850 g/mol.35 Apapov and Sokolov estimated the Rouse segment size as 5000 g/mol38 with neutron scattering but this estimation seems too much large considering the G* data for PS melts having Mw = 5000 g/mol, which shows still a few Rouse modes clearly.34 The λL‑PS−1 value determined by Apapov and Sokolov with neutron scattering is 1.8 nm.38 By converting λPM−1 into nK which is the number of repeating unit per the Kuhn segment, the dynamic stiffness could be compared with the static stiffness quantitatively. nK =

λPM −1 MK(L − PS) λPM −1 Ms(L − PS) ∼ λL − PS−1 M 0 λL − PS−1 M 0

In dilute solution, bPM molecules are isolated and therefore the branches could be extended toward the outside of the bPM. As a result, with increasing nB the main chain is statically stiffened by the enhancement of repulsive interactions between the main chain and branch and between neighboring branches.8,13,20,39 On the other hand, in melt state end part of the branches of neighboring bPMs could interpenetrate instead of absorbing the solvents. This interpenetration of the branches could not cause the increase of the repulsive interaction unlike in dilute solution. This will screen the repulsive interaction between the branches. However, due to the high density of the branched structure, near the branching point of the main chain, the space which the branches can interpenetrate would be limited. Thus, in melt state the dynamic stiffness levels off for bPMs having larger nB value because the repulsive interaction could be maintained at the some level. The rheo-optical study on the dynamic stiffness in bPM solution is under progress. A preliminarily result shows that the dynamic stiffness in solution is higher than in melt and supports the above discussion. Dynamics of Branches. As seen in Figure 9, the frequency dependence of GB′ and GB″ are very similar to the Rouse model representing the dynamics for the linear polymers without entanglements, indicated by blue solid lines. This suggests that the interaction of entanglement between branches can be ignored. From the previous studies on the scarcely branched polymers like comb-like polymer or star-like polymer, it is known that dynamics for their branches can be described by the Rouse-Ham theory considering the molecular weight of their branch. The theory assumes no specific interaction between branches and therefore the branch motions do not become cooperative. Figure 11 shows the comparison of GB* for PM40

(6)

Here, M0 is the molecular weight of repeating units. Figure 10 compares nB dependences of Msmain/MB in melt with nK in

Figure 11. Comparison of GB* for PM40 and GRouse‑Ham*.

and GRouse‑Ham* calculated by the theory for star chains having the molecular weight of the branch of PM40. GB* does not agree with GRouse‑Ham* and the longest relaxation mode of GB* is observed at much lower frequencies than GRouse‑Ham*. In other word, the branch of PM40 has apparently larger molecular weight than the actual value. It is reported that an elastic coupling originated by the repulsive interaction between the neighboring branches could cause the cooperative motion of the branches in our previous paper.24 In order to elucidate this cooperative motion of the branches, the steady state compliance, Je, was estimated from the terminal relaxation behavior, G′ ∝ ω2 and G″ ∝ ω1, as shown in Figure 11 and summarized in Table 2. The nB dependence of the obtained Je for various bPMs is shown in Figure 12. It is seen that Je is proportional to nB. This nB dependence coincides with that for linear polymers indicated by the broken line in Figure 12. However, the values of Je for

Figure 10. Comparison of nB dependence of Msmain/MB in melt and nK in dilute solution for bPMs. Solid line indicates the values of Msmain/ MB and nK for linear PS (8.6).

dilute solution for bPMs. There is a good correlation between the dynamic stiffness and the static stiffness for bPMs with smaller nB as with the case of linear polymers. However the static stiffness continues to increase with increasing nB while the dynamic stiffness levels off over nB = 20. 4806

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much longer branches are desired to elucidate the effect of the radial gradient of the excluded volume on branch motions.

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CONCLUSION Dynamic birefringence and viscoelastic measurements of bottlebrush-like polystyrene polymacromonomers having various branch lengths were conducted over a wide frequency region covering from the glass-to-rubber transition zone to the flow zone in order to discuss effects of branch length on dynamical stiffness of main polymer chain and dynamics of the branches. Strain-induced birefringence at high frequencies was negative irrespective of branch length, similarly to linear polystyrenes (PS), while birefringence in the flow zone was strongly depended on the branch length. For the case of short branches, the conformation of branches is nearly a sphere having no optical contribution to the birefringence. For such polymers, the phenyl rings directly attached to the trunk originate the negative birefringence like linear PS. With increasing branch length, the conformation of branches is extended and turns the main chain birefringence positive. By using the modified stress-optical rule (MSOR),the complex modulus was decomposed into two components, main chain and branch components. The values of the stressoptical coefficient of the branch component, CB, which is optical parameter used for the decompositions, are slightly smaller than that for linear PS and almost constant with nB. Smaller CB value suggests that the segmental dynamics of branches is insensitive to branch length, but indicates the existence elastic coupling between the branches. On the other hand, the values and the signs of the stress-optical coefficient of the main chain component, CM, vary with nB. CM changes from negative to positive with increasing nB due to the conformation change of branches. With increasing nB, the dynamical stiffness of the main chain (number of repeating units per viscoelastic segment) first increased and leveled off, suggesting the repulsive interaction between the branches would be screened out over a certain branch length. Since the obtained composite curves of GB* was very similar to the Rouse model prediction, it suggested that the branches do not have an entanglement interaction. However the termination of GB* mode was observed at much lower frequencies than the prediction of the Rouse−Ham theory. This difference suggests the cooperative motion of branches. In order to evaluate the degree of the cooperativity, steady state compliance, Je, was determined from the terminal relaxation behavior. While the nB dependence of Je for bPMs agreed with those for the linear polymers and star polymers, the values of Je for bPMs were 30 times larger than those for the linear polymers. Considering the elastic coupling originated by the repulsive interaction between the neighboring branches, the large Je for bPMs suggested that about 30 branches would move cooperatively in bPMs.

Figure 12. nB dependence of Je for bPMs, linear polymers, and star-like polymers. The broken line and dotted line are nB dependence of Je for linear polymers and star-like polymers.

bPMs are 30 times larger than those for the linear polymers having the same chain length as the branch of bPM. According to the Rouse-Ham theory, Je for star-like polymers without the interaction can be calculated (see Figure 12).30,40−42 Je =

g2 =

2 g2M 5 ρRT

(7)

f (15f − 14) (3f − 2)2

(8)

Here, g2 and f are factors reflecting the effect of the branching point and a number of the branch, respectively. The value of g2 can be approximated to be 5/3 for large f. Thus, with the effect of the branching point, Je for star-like polymers is 5/3 as large as that for the linear polymers. Equations 7 and 8 imply that Je is related with number density of entropic stress-sustaining unit. In this context, Je can be regarded as a measure of the size of stress-sustaining unit. The estimated compliance for the side chain component is larger by a factor of ≅ 30 than the compliance expected for entropic elasticity of individual side chains calculated with eq 7 and suggested that ≅ 30 branches cooperatively behave as one entropic stress-sustaining unit (under an implicit assumption that the applied strain is affinely transmitted to individual branches). This number is close to the limiting value of Msmain/MB ∼ 100. We believe that there should be a simple relationship between the number of the branches moving cooperatively and the viscoelastic segment size of the main chain (dynamic stiffness). As described above, the excluded volume effect originating the repulsive interaction would cause the cooperative motion of branches and increases the main chain stiffness. The present study revealed that the repulsive interaction is screened out nB > 20 in melt. This conclusion suggests that the repulsive interaction would be gradually weakened along the branches from the main chain side to the free end side (i.e., in the radial direction of the bottle-brush type bPMs). For bPMs having much longer branches, we expect the dynamics of the portion of branches in the free end side would be close to that of the ordinary linear polystyrenes. In such a case, the stress-optical coefficient of the branches may depend on the position in radial direction. Unfortunately, such an effect was not clearly observed in the present range of branch lengths, probably due to short branch length. Measurements on bPMs having

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 4807

dx.doi.org/10.1021/ma300269b | Macromolecules 2012, 45, 4801−4808

Macromolecules

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Article

(29) Pakula, T.; Zhang, Y.; Matyjaszewski, K.; Lee, H. I.; Boerner, H.; Qin, S. H.; Berry, G. C. Polymer 2006, 47 (20), 7198−7206. (30) Roovers, J.; Graessley, W. W. Macromolecules 1981, 14 (3), 766−773. (31) Wimberger-Friedl, R. Rheol. Acta 1991, 30 (4), 329−340. (32) Ryu, T.; Inoue, T.; Osaki, K. Nihon Reoroji Gakk 1996, 24 (3), 129−132. (33) Mott, P. H.; Roland, C. M. Macromolecules 1998, 31 (20), 7095−7098. (34) Inoue, T.; Onogi, T.; Yao, M. L.; Osaki, K. J. Polym. Sci., Polym. Phys. 1999, 37 (4), 389−397. (35) Inoue, T.; Okamoto, H.; Osaki, K. Macromolecules 1991, 24 (20), 5670−5675. (36) Inoue, T.; Osaki, K. Macromolecules 1996, 29 (5), 1595−1599. (37) Inoue, T. Macromolecules 2006, 39 (13), 4615−4618. (38) Agapov, A.; Sokolov, A. P. Macromolecules 2010, 43 (21), 9126− 9130. (39) Nakamura, Y.; Norisuye, T. Polym. J. 2001, 33 (11), 874−878. (40) Ham, J. S. J. Chem. Phys. 1957, 26 (3), 625−633. (41) Graessley, W. W.; Roovers, J. Macromolecules 1979, 12 (5), 959−965. (42) Raju, V. R.; Menezes, E. V.; Marin, G.; Graessley, W. W.; Fetters, L. J. Macromolecules 1981, 14 (6), 1668−1676.

ACKNOWLEDGMENTS This work was partly supported by Grant-in-Aid for Scientific Research on Priority Area “Soft Matter Physics” from the Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 18068009 and 20340112). H.I. expresses his special thanks for the Global COE (center of excellence) Program “Global Education and Research Center for BioEnvironmental Chemistry” of Osaka University.

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REFERENCES

(1) Tsukahara, Y.; Inoue, J.; Ohta, Y.; Kohjiya, S.; Okamoto, Y. Polym J 1994, 26 (9), 1013−1018. (2) Wintermantel, M.; Schmidt, M.; Tsukahara, Y.; Kajiwara, K.; Kohjiya, S. Macromol. Rapid Commun. 1994, 15 (3), 279−284. (3) Nemoto, N.; Nagai, M.; Koike, A.; Okada, S. Macromolecules 1995, 28, 3854−3859. (4) Wintermantel, M.; Gerle, M.; Fischer, K.; Schmidt, M.; Wataoka, I.; Urakawa, H.; Kajiwara, K.; Tsukahara, Y. Macromolecules 1996, 29 (3), 978−983. (5) Maeno, K.; Nakamura, Y.; Terao, K.; Sato, T.; Norisuye, T. Kobunshi Ronbunshu 1999, 56 (4), 254−259. (6) Shiokawa, K.; Itoh, K.; Nemoto, N. J. Chem. Phys. 1999, 111 (17), 8165−8173. (7) Terao, K.; Takeo, Y.; Tazaki, M.; Nakamura, Y.; Norisuye, T. Polym J 1999, 31 (2), 193−198. (8) Terao, K.; Nakamura, Y.; Norisuye, T. Macromolecules 1999, 32 (3), 711−716. (9) Terao, K.; Hokajo, T.; Nakamura, Y.; Norisuye, T. Macromolecules 1999, 32 (11), 3690−3694. (10) Namba, S.; Tsukahara, Y.; Kaeriyama, K.; Okamoto, K.; Takahashi, M. Polymer 2000, 41 (14), 5165−5171. (11) Terao, K.; Hayashi, S.; Nakamura, Y.; Norisuye, T. Polym. Bull. 2000, 44 (3), 309−316. (12) Vlassopoulos, D.; Fytas, G.; Loppinet, B.; Isel, F.; Lutz, P.; Benoit, H. Macromolecules 2000, 33 (16), 5960−5969. (13) Hokajo, T.; Terao, K.; Nakamura, Y.; Norisuye, T. Polym. J. 2001, 33 (6), 481−485. (14) Tsukahara, Y.; Namba, S.; Iwasa, J.; Nakano, Y.; Kaeriyama, K.; Takahashi, M. Macromolecules 2001, 34 (8), 2624−2629. (15) Kolodka, E.; Wang, W. J.; Zhu, S. P.; Hamielec, A. E. Macromolecules 2002, 35 (27), 10062−10070. (16) Nakamura, Y.; Amitani, K.; Terao, K.; Norisuye, T. Kobunshi Ronbunshu 2003, 60 (4), 176−180. (17) Amitani, K.; Terao, K.; Nakamura, Y.; Norisuye, T. Polym. J. 2005, 37 (4), 324−331. (18) Rathgeber, S.; Pakula, T.; Wilk, A.; Matyjaszewski, K.; Beers, K. L. J. Chem. Phys. 2005, 122 (12), 124904. (19) Inoue, T.; Matsuno, K.; Watanabe, H.; Nakamura, Y. Macromolecules 2006, 39 (22), 7601−7606. (20) Sugiyama, M.; Nakamura, Y.; Norisuye, T. Polym. J. 2008, 40 (2), 109−115. (21) Kanemaru, E.; Terao, K.; Nakamura, Y.; Norisuye, T. Polymer 2008, 49 (19), 4174−4179. (22) Kikuchi, M.; Lien, L. T. N.; Narumi, A.; Jinbo, Y.; Izumi, Y.; Nagai, K.; Kawaguchi, S. Macromolecules 2008, 41 (17), 6564−6572. (23) Hu, M.; Xia, Y.; McKenna, G. B.; Kornfield, J. A.; Grubbs, R. H. Macromolecules 2011, 44 (17), 6935−6943. (24) Iwawaki, H.; Inoue, T.; Nakamura, Y. Macromolecules 2011, 44 (13), 5414−5419. (25) Hayashi, C.; Inoue, T. Nihon Reoroji Gakk 2009, 37 (4), 205− 210. (26) Schroter, K.; Hutcheson, S. A.; Shi, X.; Mandanici, A.; McKenna, G. B. J. Chem. Phys. 2006, 125 (21), 214507. (27) Hutcheson, S. A.; McKenna, G. B. J. Chem. Phys. 2008, 129 (7), 074502. (28) Ferry, J. D. Dependence of Viscoelastic Behavior on Temperature and Pressure. In Viscoelastic Properties of Polymers, 4th ed.; Wiley: New York, 1980; pp 264−320. 4808

dx.doi.org/10.1021/ma300269b | Macromolecules 2012, 45, 4801−4808