Dilute Solution Properties of a Polymacromonomer Consisting of a

Oct 14, 2013 - The experimental λ–1 for cyclohexane solutions was close to the value predicted by the first-order perturbation theory, but the valu...
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Dilute Solution Properties of a Polymacromonomer Consisting of a Polystyrene Main Chain with Polyisoprene Side Chains. Relation of Molecular Parameters to Polymer Segment Interactions Kouta Inoue, Seiji Yamamoto, and Yo Nakamura* Department of Polymer Chemistry, Kyoto University, Katsura, Kyoto 615-8510, Japan ABSTRACT: Light scattering and viscosity measurements were made on dilute solutions of a polymacromonomer consisting of a polystyrene main chain and polyisoprene (PI) side chains, which was synthesized by anionic polymerization. The second virial coefficient A2 in 1,4-dioxane was positive at the theta temperature for linear PI, 35.3 °C, and became zero at 31.0 °C. The positive A2 at 35.3 °C was ascribed to the effect of the intermolecular interaction between the PI unit and the main-chain unit. From analyses of the mean-square radius of gyration, intrinsic viscosity, and A2 obtained as functions of molecular weight, the stiffness parameter λ−1 and the excluded-volume parameter B in cyclohexane at 25.0 °C (good solvent) and in 1,4-dioxane at 35.3 °C were determined. The experimental λ−1 for cyclohexane solutions was close to the value predicted by the first-order perturbation theory, but the value for 1,4-dioxane solution was larger than the theoretical one, showing that the contribution of the interaction between the side-chain and the main-chain units is essential. The smoothed-density theory for B gave a close value to the experimental one for cyclohexane solutions, while it gave a much larger value than the experimental one for 1,4-dioxane solutions. This was attributed to the defect of the theory ignoring the chain connectivity.

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INTRODUCTION It is known that polymacromonomers behave as stiff chains in solution.1−6 Although some applications of polymacromonomers to real world are suggested,7,8 it is still in a stage to seek specialty of this polymer, where basic researches play an important role. We have studied polymacromonomers consisting of a polystyrene (PS) main chain and PS side chains with a benzyl group at each end (benzyl-PS PM)9−16 and showed that the stiffness parameter λ−1 is expressed by a sum of two terms: one is for the contribution of segmental interactions among side chains, and the other is for other contributions including the short-range interactions among side-chain moieties near the main chain.17 It was shown that the firstorder perturbation theory for the former term almost quantitatively predicts the experimental results. Our analyses also showed that the dimensional properties of these polymacromonomers were affected by the intramolecular excluded-volume effect, which was represented by the excluded-volume parameter B. Recently, we formulated B for brush-like polymers based on the smoothed-density theory.18 The theory gave a close value of B for good solvent systems.19 It is important to see whether dimensional properties of other polymacromonomer−solvent systems can be explained by these theories. Another purpose of this study is to compare the theta temperature of the polymacromonomer with that for linear polymer with the same chemical structure as the polymacromonomer side chain. Zhang et al. made neutron scattering measurements and determined A 2 for solutions of a © 2013 American Chemical Society

polymacromonomer with a poly(methacrylate) main chain and PS side chains with a butyl group at the end (PMA−PS PM).20 They showed that A2 values of d12-cyclohexane solutions were positive even at the temperature more than 20 °C lower than the known theta temperature for linear PS in this solvent. The order of magnitude of A2 was 10−5 cm3 mol g−2 and was the same as that for toluene solutions, a good solvent system. We obtained different results from studies on benzyl-PS PM. The theta temperature of cyclohexane solutions of this polymacromonomer was 34.5 °C, regardless of the number of the styrene residues in a side chain ranging from 15 to 110.9,10,13,16 This temperature agrees with the theta temperature for linear PS in this solvent. Therefore, the positive A2 of PMA−PS PM was considered to be the reflection of the effect of the chain ends or the effect of the main chain. To see which effect is dominant to A2, we studied a polymacromonomer consisting of a polystyrene main chain and polystyrene side chains with a butyl group (butyl-PS PM).21 The values of A2 for cyclohexane solutions of butyl-PS PM were found to be positive and almost independent of temperature. The order of magnitude of A2 was 10−5 cm3 mol g−2. A different result was obtained from studies on a polymacromonomer with polyisoprene (PI) main chain with PS side chains with a benzyl group at each end (PI−PS PM).22 It was found that A2 Received: August 19, 2013 Revised: September 27, 2013 Published: October 14, 2013 8664

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is positive at 34.5 °C, decreases with decreasing temperature, and vanishes at 29.0 °C. For this system, the positive A2 at 34.5 °C was considered to be the reflection of the interaction between the polystyrene side-chain and the main-chain residues. Since the behavior of A2 for the polymacromonomer of Zhang et al. was similar to that for the butyl-PS PM system, the positive A2 for PMA−PS PM was attributed to the effect of the chain-end group. Here, we study polymacromonomer with a PS main chain and polyisoprene (PI) side chains with a butyl group at each end (PS−PI PM) in good and theta solvents (see Figure 1 for

them easy. The polymacromonomer is expected to be used as filler to reinforce mechanical properties of rubber materials.

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EXPERIMENTAL SECTION

Polymacromonomer Samples. Macromonomer was synthesized by anionic polymerization of isoprene in hexanes with sec-BuLi as the initiator in a high vacuum reactor at the room temperature. After stirring overnight, excess amount of p-vinylbenzyl chloride (VBC) (supplied from AGC Seimi Chemical Co., Kanagawa, Japan) dissolved in tetrahydrofuran was added after cooling to −78 °C. Macromonomer thus obtained was reprecipited into methanol from a benzene solution several times to remove excess VBC. The 1H NMR spectrum in CDCl3 showed insertion of a vinyl group at the polymer end and 93% of the 1,4-addition with 71% of cis and 29% of trans contents. MALDITOF-MS measurement with all-trans-retionic acid as the matrix compound and silver trifluoroacetate as the catalyst was made to determine Mw and the ratio of Mw to the number-average molecular weight as 2600 and 1.03, respectively. Therefore, the number of polyisoprene units in a macromonomer was calculated to be 36. This macromonomer was separated into six and polymerized separately by anionic polymerization in benzene with n-butyllithium as the initiator under an argon atmosphere. After the reaction was finished the living end was killed by methanol. The reactant was reprecipitated into methanol. Since this polymer contained unreacted macromonomer and its molecular-weight distribution was rather broad, it was fractionally precipitated several times from benzene solution adding methanol as the precipitant. The polymacromonomer samples were preserved in a refrigerator as benzene solutions containing 0.05 wt % of butylated hydroxytoluene (BHT). The polymacromonomer sample was reprecipitated into methanol and dried in vacuum for a week before usage. Most of the samples were recovered after each measurement and reprecipitated before the next measurement. By this manipulation, molecular weight of the sample slightly differs in every measurement. Measurements. Each polymacromonomer sample was dissolved into 1,4-dioxane or cyclohexane containing 0.05 wt % BHT. These solvents were distilled fractionally after refluxing for 6 h on sodium metal. Solutions for light-scattering measurements were optically purified by passing through a polytetrafluoroethylene filter of 0.2 μm pore size. Scattering intensity from the solution at the scattering angle, θ ranging from 30° to 142.5° was measured by a Fica 50 light-scattering photometer (Fica, Saint Denis, France) to obtain the Rayleigh ratio Rθ. Wavelength of the incident light was chosen to be 436 nm. Measurements were taken on six solutions with different mass concentration, c, to obtain the extrapolated values of the reciprocal scattering intensities, Kc/Rθ, to c → 0, where K is the optical constant. The zero-concentration values of Kc/Rθ were plotted against the square of the magnitude of the scattering vector k2 with the Berry square-root plot to obtain Mw and ⟨S2⟩. Densities, ρ, of the polymacromonomer solutions were measured by a DMA5000 densitometer (Anton Paar, Graz, Austria). From the concentration dependence of ρ, the specific volume v ̅ for cyclohexane solution was obtained as 1.170 cm3 g−1. Values of υ̅ for 1,4-dioxane solution were determined at 30.0, 35.0, and 40.0 °C and found to be represented by the equation

Figure 1. Chemical structures of polymacromonomers.

υ ̅ = 2.95 × 10−4T (°C) + 1.109 (cm 3 g −1) The polymer mass concentration was calculated from the weight fraction w of polymer multiplied by the solution density, ρ, which was obtained from ρ = ρ0 + (1 − υ̅ρ0)ρ0w, where ρ0 denotes the density of the solvent. The refractive index increment, ∂n/∂c, at 436 nm was measured by a modified Shultz−Cantow type differential refractometer, DR-1 (Shimadzu, Kyoto, Japan). The value for cyclohexane solution (25 °C) was 0.117 cm3 g−1, and the values for 1,4-dioxane solution (30−40 °C) were expressed by the empirical equation

the chemical structure). Light scattering and viscosity measurements are made on the polymacromonomer in good and theta solvents to determine the mean-square radii of gyration ⟨S2⟩, A2, and the intrinsic viscosities [η] as functions of the weightaverage molecular weight Mw. The reason for choosing this polymer is as follows. The macromonomer can be synthesized by an anionic polymerization technique, which enables us to control precisely the length and the end group of the side chain. The solution properties of linear PI are well-known making comparison with the data for the polymacromonomer with

∂n/∂c = 3.35 × 10−4T (°C) + 0.109 (cm 3 g −1) 8665

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Small-angle X-ray scattering measurements were made at the beamline BL40B2 in the synchrotron facility SPring8 (Harima, Hyogo, Japan). The wavelength and the camera length were set to 0.1 nm and 1.5 m, respectively. The exposure time was 3 min for each solution. The two-dimensional intensity data detected by an imaging plate were integrated circularly by changing the distance from the center of the beam to obtain the scattering intensity I(θ). Measurements were taken on four solutions with different c for each sample to obtain the extrapolated values of c/ΔI(θ) to c → 0, where ΔI(θ) means the excess scattering intensity. Square-foot plots were employed to obtain ⟨S2⟩. Viscosities of cyclohexane and 1,4-dioxane solutions were measured by a Ubbelohde type viscometer at five concentrations for each sample to determine [η]. The results of these measurements for cyclohexane and 1,4-dioxane solutions are summarized in Tables 1 and 2, respectively, along with Mw/Mn values obtained from GPC measurements using a calibration curve for this polymacromonomer.

Figure 2. Temperature dependence of A2 for PS−PI PM (F4) in 1,4dioxane. The solid line is a guide to the eye.

Table 1. Properties of Polyisoprene Polymacromonomer in Cyclohexane at 25.0 °C sample 10−5Mw Mw/Mna F1 F2 F3 F4 F5 F6 a

30.1 17.5 12.9 9.92 6.48 2.21

1.17 1.15 1.12 1.17 1.08 1.07

⟨S2⟩1/2 (nm)

105A2 (cm3 mol g−2)

[η] (cm3 g−1)

37.5 29.1 24.1 21.3 14.3 7.5b

3.1 3.6 6.1 4.7 5.0 11.5

62.7 44.3 35.0 28.3 24.2 14.0

between the side-chain and main-chain segments. This is supported by recent our study on relatively short linear PI with a butyl group at one of the chain ends that A2 in 1,4-dioxane becomes negative at 35.3 °C,23 when molecular weight is reduced to less than 104. This shows that the interaction between the butyl end and the PI unit is negligibly small; the negative A2 is attributed to the three-segment interaction among PI segments.23 Thus, the positive A2 of PS−PI PM at 35.3 °C is concluded to come from the interaction between the PIunit and the main-chain unit. As mentioned in the Introduction, in the case that the interaction between the side-chain end and the middle of side chain is effective, e.g., PMA−PS PM or butyl-PS PM in cyclohexane, A2 does not vanish in a wide temperature range.20,21 Possibly, side-chain end groups covering the surface of the PM molecule avoid two molecules interpenetrating each other. Radius of Gyration. Figure 3 represents molecular weight dependence of ⟨S2⟩ for PS−PI PM in cyclohexane and 1,4-

From GPC. bFrom SAXS measurement.

Table 2. Properties of Polyisoprene Polymacromonomer in 1,4-Dioxane at 31.0 and 35.3 °C sample

10−5Mw

⟨S2⟩1/2 (nm)

F1 F2 F3 F4 F5 F6

29.3 17.3 12.5 8.39 6.44 2.13

28.7 22.7 19.5 15.7 12.8

F1 F2 F3 F4 F5 F6

33.2 19.5 13.2 10.9 6.17 2.06

30.2 23.6 18.8 17.2 12.4 6.9a

105A2 (cm3 mol g−2)

[η] (cm3 g−1)

at 31.0 °C 0 0.15 0 0.09 −0.01 −0.22

27.6 22.1 19.4 16.5 14.7 9.70

at 35.3 °C

a

0.93 0.48 0.44 1.01 1.40 2.06

31.3 25.0 21.2 17.1 14.0

From SAXS measurement.

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RESULTS AND DISCUSSION Theta Temperature. In Figure 2, A2 for sample F4 in 1,4dioxane is plotted against temperature T. It is seen that A2 is positive at the theta temperature Θ for linear PI, 35.3 °C,23 and vanishes at 31.0 °C. The change of Θ from that for linear PI is different from the case for benzyl-PS PM in cyclohexane, whose Θ agreed with that for linear PS in the same solvent, but close to the case for PI−PS PM, whose Θ was 5.5 °C lower than that for linear PS. In the latter case, it was concluded that the interaction between PS and main-chain segments is effective. Therefore, the positive A2 of PS−PI PM at the theta temperature for linear PI could be attributed to the interaction

Figure 3. Molecular weight dependence of ⟨S2⟩ for PS−PI PM in cyclohexane at 25.0 °C (filled circles) and in 1,4-dioxane at 31.0 °C (unfilled circles with pip down) and at 35.3 °C (unfilled circles with pip up). The solid and dashed lines are calculated lines (see text).

dioxane. The figure shows that values for cyclohexane solutions are systematically larger than those for 1,4-dioxane solutions. There is essentially no difference between the data sets for 1,4dioxane solutions at 31.0 and 35.3 °C. The former and the 8666

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latter temperatures correspond to the theta temperatures for this polymacromonomer and linear PI, respectively. According to the theory for the wormlike chain, the unperturbed ⟨S2⟩ is given by the Benoit−Doty equation:24 ⟨S2⟩0 =

L 1 1 1 − 2 + 3 − 4 2 [1 − exp( −2λL)] 6λ 4λ 4λ L 8λ L (1)

In eq 1, L denotes the contour length of the polymacromonomer and may be calculated from the following equation11 with the molecular weight per unit contour length, ML. L = M w /ML + δ

(2)

Here, δ represents the contribution of side chains near the main-chain ends to L (see Figure 3 in ref 11). We also consider the effect of the thickness of the chain by adding d2/8 to eq 1.25 Since ⟨S2⟩ is not sensitive to d and δ in the molecular weight range studied, these parameters were determined from [η] (see the next subsection). From the data fittings shown by the lower solid lines in Figure 3, we determined ML and λ−1 in 1,4-dioxane as 9000 nm−1 and 16 nm, respectively. From the dashed line, ML and λ−1 in cyclohexane are also determined as 9000 nm−1 and 30 nm, respectively. However, in the good solvent, we may not ignore the expansion of the polymer by the excluded-volume effect. Therefore, we consider the radius expansion factor αS by the modified Domb−Barrett equation:26,27

Figure 4. Molecular weight dependence of [η] for PS−PI PM in cyclohexane. The symbols have the same meaning as those in Figure 3.

consideration by multiplying the unperturbed [η] values by the viscosity expansion factor αη3, which was calculated by the modified Barrett equation:27,29 αη3 = (1 + 3.8z ̃ + 1.9z 2̃ )0.3

Here, B was taken to be 10 nm as in the analysis of ⟨S ⟩. The solid line calculated with the above expansion factor well describes the experimental values. Second Virial Coefficient. The filled and unfilled circles in Figure 5 represent A2 values for cyclohexane solutions at 25.0

αs2 = [1 + 10z ̃ + (70π /9 + 10/3)z 2̃ + 8π 3/2z 3̃ ]2/15 × [0.933 + 0.067 exp(− 0.85z ̃ − 1.39z 2̃ )]

(3)

Here, z̃ denotes the modified excluded-volume parameter (see ref 27 for details) as a function of the excluded-volume strength B. The upper solid line indicates the line for the perturbed wormlike chain, calculated from ⟨S2⟩0 multiplied by the above αs2. Here, we choose the excluded-volume strength as B = 10 nm, which was determined to explain both ⟨S2⟩ and [η] data consistently. It can be seen that the solid and dashed lines equally fit the experimental data, showing that the excludedvolume effect is not so important for ⟨S2⟩ for the current polymacromonomer samples in cyclohexane. Intrinsic Viscosity. Molecular weight dependence of [η] is illustrated in Figure 4. Being similar to Figure 3, the values for cyclohexane solutions are systematically larger than those for 1,4-dioxane solution. These data are analyzed by the theory for the touched-bead wormlike chain model, which describes [η] as a function of λL and the bead diameter db reduced by λ−1 as follows:28 [η] = f (λL , λdb)/(λ 3M )

(5) 2

Figure 5. Molecular weight dependence of A2 for PS−PI PM in cyclohexane at 25 °C (filled circles) and in 1,4-dioxane at 35.3 °C (unfilled circles). Lines show calculated values (see text).

(4)

°C and 1,4-dioxane solutions at 35.3 °C, respectively, plotted double-logarithmically against Mw. By the theory for the wormlike chain model, A2 may be expressed by30

The parameters to be assigned are λ−1, ML, db, and δ, where db may be regarded to be equal to d for the cylinder model.11 However, it was impossible to determine these four parameters uniquely. Thus, we used λ−1 obtained from ⟨S2⟩ and determine the other parameters. The lower solid line in Figure 4 represents the theoretical values with λ−1 = 16 nm ML = 10 500 nm−1, db = 7.5 nm, and δ = 4.0 nm for 1,4-dioxane solution. The difference between ML values for ⟨S2⟩ and [η] may be attributed to the rather broad molecular weight distribution. The dashed line represents the theoretical values with λ−1 = 30 nm ML = 10 500 nm−1, d = 9.5 nm, and δ = 3.5 nm. The difference between the data points and the dashed line can be attributed to the excluded-volume effect, which is taken into

A 2 = A 2 (λB) + a1,2 /M w

(6)

Here, the first and the second terms on the right-hand side of eq 6 represent A2 for the wormlike chains27 and the contribution of the chain end effect,27,30 respectively. The upper solid line in the figure represents the calculated values with ML = 9000 nm−1, λ−1 = 30 nm, B = 10 nm, and a1,2 = 14 cm3 g−1. The agreement between theoretical and experimental values is satisfactory. Therefore, the A2 data are explained consistently with ⟨S2⟩ and [η]. 8667

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Excluded-Volume Parameter. According to the zerothorder theory, B for brushlike segments, a small part of the main chain, is expressed as18

The lower solid line shows the calculated values for 1,4dioxane solutions at 35.3 °C with the parameter set, ML = 9000 nm−1, λ−1 = 16 nm, B = 2 nm, and a1,2 = 2 cm3 g−1. The theoretical values closely fit the data points. The molecular parameters obtained are summarized in Table 3.

B=

n2 β h2 2

(9)

However,eq 9 with β2 = 0.036 nm for PI in cyclohexane gives B = 690 nm, a much larger value than the experimentally obtained one. This suggests the poor convergence of the perturbation series. As a closed equation, we may use the smoothed-density theory for B of a brushlike segments with a straight main chain with the length a:18 3

Table 3. Molecular Parameters for Polyisoprene Polymacromonomer in 1,4-Dioxane (Diox) at 35.3 °C and Cyclohexane (CH) at 25.0 °C solvent Diox CH a

ML (nm−1) a

10500 (9000) 10500 (9000)a

λ−1 (nm)

d (nm)

δ (nm)

B (nm)

16 30

7.5 9.5

4.0 3.5

2 10

Values from ⟨S2⟩.

B=

3/2 ⎫ 2 ⎛ n ⎞2 β3 1 ⎛⎜ n ⎞⎟ ⎧ 4 ⎛ 3 ⎞ ⎜ ⎟ ⎜ ⎟ ⎨β2 + ⎬ β + 0.02334 3 ⎝ b ⎠ h3 σ ⎝ 2πb2 ⎠ 8π ⎝ h ⎠ ⎩ ⎭ ⎪

⎪

⎪

⎪

∫ ⟨1 − exp[−W12(r)/kBT ]⟩ dr

(10)

In eq 10, kB is the Boltzmann constant and W12(r) is the intersegment potential as a function of the distance of the centers of the two segments, r, and may be given by

Stiffness Parameter. If the side chains are assumed to obey the Gaussian statistics, the first-order perturbation theory represents the contribution of the binary and ternary interactions of side-chain segments on λ−1 as17 λ −1 =

1 a2

W12(r) = β2 ∑ ∑ P(0 pq ; rij, pi , qj) i j kBT i,j p,q i

(11)

j

Here, P(0piqj;rij,pi,qj) is the probability density that the pith and the qjth segments of the ith and jth side chains, respectively, are in contact and rij the distance between junction points of ith and jth side chains, each belonging to the different brushlike segment, with the main chain; rij is a function of r and the azimuthal and rotational angles of the main chain of the second segment around the direction of the z axis, on which the main chain of the first segment lays (see Figure 1 of ref 18). The functional form of P(0piqj;rij,pi,qj) is given by18

(7)

Here, n, h, b, σ, β2, and β3 denote the number of segments in a side chain, the length between junction points of neighboring side chains along the main chain, the segment length in a side chain, the minimum number of segments for a side chain to make a loop, the binary-cluster integral, and the ternary-cluster integral among (middle) side-chain segments, respectively. In a good solvent, the β2 term of the right-hand side of eq 7 may be dominant. We may use β2 = 0.036 nm3 for PI in cyclohexane31 and h = 0.25 nm calculated from ML = 10 500 nm−1 and the molecular weight of the macromonomer. If we take n as the number of repeating units, 36, we obtain λ−1 = 30 nm from eq 7. This value agrees with the experimental value in cyclohexane. This shows that the contribution of the shortrange interaction among side-chain moieties near the main chain (λ0−1 in ref 17) is negligible for this polymer. In a theta solvent for the side chain, the terms in the braces of eq 7 is considered to cancel out and λ−1 may be calculated from the last term.17 The Gaussian segment length b for PI chain may be equated to 0.67 nm, which was calculated from the ⟨S2⟩ data for linear PI in 1,4-dioxane.31,32 With the β3 = 0.0021 nm6 estimated from the third virial coefficient for linear PI,23 we obtain λ−1 = 9 nm. This value of λ−1 is about a half of the experimentally observed value, 16 nm. The difference (7 nm) between the calculated value and the experimental one is attributable to the contribution of the interaction between PS main chain and PI segments, since the contribution of the interaction between PI and chain-end segments is negligible in this solvent.23 This contribution may be considered by adding the following term to λ−1: n (λ−1)T = β (8) 4πh2 01

P(0 pq ; rij, pi , qj) = i j

⎛ 3 ⎞3/2 1 ⎜ ⎟ ⎝ 2πb2 ⎠ (p + q )3/2 i j

⎡ ⎤ 3rij 2 ⎢ ⎥ × exp − 2 ⎢ 2b (p + q ) ⎥ ⎣ i j ⎦

(12)

Substituting eq 11 with eq 12 and β2 = 0.036 nm into eq 10, we obtain B = 11.2 nm3, which is close to the experimental value in cyclohexane. However, we do not believe that this coincidence indicates the Gaussian conformation of the side chain because the length of it is rather small. The agreement may show that the distribution of the side-chain segments around the main chain is approximately expressed by the Gaussian function. For the 1,4-dioxane solution at 35.3 °C, the contribution of β01 to B may also be calculated by the smoothed-density theory. The smoothed-density potential can be represented by the equation 3

W12(r) = 2β01 ∑ ∑ P(0 p 0j ; rij, pi , 0j) i kBT i,j p i

(13)

Here, 0j means the segment at the junction point of the jth side chain with the main chain. If we substitute β01 = 0.15 nm obtained from the analysis of λ−1 into eq 13, B can be estimated as 7.2 nm, which is much larger than the experimental value, 2 nm. Moreover, we do not count the contribution of the threesegment interactions on B. The intersegment potential may be calculated by the equation

Here, β01 is the binary integral for the PI and the main-chain segments (the subscript T means “trunk”). The above expression is the same as that for the contribution of the interaction between the middle side-chain and the side-chain end segments.21 From the above equation with (λ−1)T = 7 nm, we can estimate β01 = 0.15 nm3. 8668

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Macromolecules W12(r) = β3 kBT

where

∑ ∑

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P(0 pq , 0 psk ; rik , rij, pi , qj , sk) i j

i

i , j , k pi , qj , sk

(14)

18

⎛ 3 ⎞3 ⎜ ⎟ ⎝ 2πb2 ⎠ ⎤ ⎡ 3rij 2 1 ⎥ ⎢− exp × × ⎢⎣ 2b2(pi + qi) ⎥⎦ (qi − pi )3/2 (pi + sj)3/2

P(0piqi ; 0pisj ; rij, pi , qi , sj) =

(15)

We obtained B = 9.0 nm if we use β3 = 0.0021 nm and eq 10 with eqs 14 and 15. If we add this value to the B from the interaction between middle side-chain and main-chain segments, we obtain 16.2 nm, again a much larger value than the experimental one. This discrepancy shows the defect of the smoothed-density model, possibly originated in its ignorance of the chain connectivity.33 3

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CONCLUSION In this study, we synthesized PS−PI polymacromonomer and made light scattering and viscosity measurements on its dilute solutions. The theta temperature of the macromonomer in 1,4dioxane became 31.0 °C, which was 4.3° lower than that for linear PI. This was attributed to the interaction between the middle side-chain and the main-chain units. The radius of gyration, intrinsic viscosity, and second virial coefficient determined as functions of molecular weight were analyzed with the theories of the wormlike chain model to determine the stiffness parameter of the main chain λ−1 and the excludedvolume parameter B. The calculated value with the first-order perturbation theory for λ−1 agreed with the experimental value of the cyclohexane solution showing that the contribution of the short-range interaction among side-chain moieties near the main chain is negligible. By the similar calculation for the 1,4dioxane solution, it was shown that the contribution of the interaction between the middle side-chain and the main-chain segments is effective in this solution. The smoothed-density theory for B gave a close value to the experimental value for the cyclohexane solution, but it gave much larger B for 1,4-dioxane solution than the experimental value. This was ascribed to the ignorance of the chain connectivity in the theory.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.N.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was financially supported by a Grant-in-Aid (22550111) from the Ministry of Education, Culture, Sports and Technology, Japan. The SAXS measurements were made at the synchrotron facility SPring-8 (Proposal No. 2012B1452).

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REFERENCES

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