Determination of the Chain Stiffness Parameter of Molecular Rod

Dec 4, 2015 - The λM–1 values were compared to those of rod brushes consisting of a flexible polystyrene (PSt) main chain [ Macromolecules 2008 , 4...
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Determination of the Chain Stiffness Parameter of Molecular Rod Brushes Consisting of a Polymethacrylate Main Chain and Poly(n‑hexyl isocyanate) Side Chains Yuta Saito,† Moriya Kikuchi,‡ Yuji Jinbo,§ Atsushi Narumi,† and Seigou Kawaguchi*,† †

Department of Polymer Science and Engineering, Graduate School of Science and Engineering, ‡Faculty of Engineering, and Department of Biochemical Engineering, Graduate School of Science and Engineering, Yamagata University, 4-3-16, Jonan, Yonezawa 992-8510, Japan §

S Supporting Information *

ABSTRACT: The main chain stiffness parameter (λM−1) of cylindrical rod brushes consisting of a flexible polymethacrylate (PMA) main chain and poly(n-hexyl isocyanate) (PHIC) rod side chains has been determined in tetrahydrofuran (THF) at 25 °C by static light and small-angle X-ray scattering measurements. Furthermore, we have rationalized λM−1 as a function of the degree of polymerization of HIC, Ns. The λM−1 values were compared to those of rod brushes consisting of a flexible polystyrene (PSt) main chain [Macromolecules 2008, 41, 6564] to reveal how the molecular conformation of the rod brush is influenced by the difference in the primary structure or chemical nature of the main chain. A series of rod brushes, poly(MA-HIC-Ns-Ac) with different side chain lengths, where Ns ranged from 26 to 82, were prepared by radical homopolymerization of α-methacryloyloxyethoxy-ω-acetyl ended PHIC macromonomers (MA-HIC-Ns-Ac) in n-hexane at 60 °C. The mean-square cross-section radius of gyration (⟨Sc2⟩) of poly(MA-HIC-Ns-Ac) was essentially consistent with those of the rod brushes consisting of a PSt main chain, poly(VB-HIC-Ns-H), and could be quantitatively described by the wormlike comb model. The z-averaged mean-square radius of gyration (⟨S2⟩z) of the brush, determined as the function of molecular weight, was analyzed with the aid of the cylindrical wormlike chain model theory to determine the λM−1 value. The scattering form factor of poly(MA-HIC-Ns-Ac) was also quantitatively described by the wormlike chain model, and the corresponding λM−1 parameter was determined. The λM−1 value of poly(MA-HIC-Ns-Ac) was much greater than that of poly(VB-HIC-Ns-H) having the same Ns and increased in proportion with increasing side chain length (λM−1 ∝ Ns1.5). The chemical nature of the main chain, which is the minor component in the brush polymers, was found to play an essential role in the overall conformation of the rod brushes.

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these have found that both the intrinsically flexible main and side chains behave as stiff chains in both dilute solutions and the solid state.7−19 Such stiffening is understood to result from the interactions among the densely grafted side chains. The main chain stiffness parameter (λM−1) in brush polymers is given by eq 1:16

INTRODUCTION Cylindrical molecular brushes are regularly branched comb or graft polymers. Among several synthetic methods for the preparation of brush polymers, well-defined bush polymers are usually prepared by homopolymerization of styryl- or methacrylate-end-functionalized macromonomers.1−6 Therefore, the main chain in most brush polymers consists of either a flexible polystyrene (PSt) or polymethacrylate (PMA) chain. Although the main chain is a minor component (less than several wt %) in brush polymers, it can affect the conformational properties of the brush. However, how the chemical nature or primary structure of the main chain influences the properties of the brush is an important and fundamental question that remains unanswered. Polymer brushes are classified into two categories: the so-called “flexible brushes”, in which flexible side chains are grafted to a flexible main chain, and the “rod brushes”, in which semiflexible or rodlike side chains are grafted to the main chain, as investigated in this study. Many studies of flexible brushes have been made, and © XXXX American Chemical Society

λM −1 = λ 0−1 + λb−1

(1)

where λ0−1 is the intrinsic backbone stiffness parameter and λb−1 is related to the excess free energy against bending that results from interactions between side chains. The values of λ0−1 for linear PSt and PMMA chains are 1.84 nm20 and 1.42 nm,21 respectively, when they were considered as Kratky− Porod (KP) chains. On the other hand, typical λM−1 values of Received: October 6, 2015 Revised: November 25, 2015

A

DOI: 10.1021/acs.macromol.5b02195 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Scheme 1. Reaction Schemes for Cylindrical Rod Brushes Using PHIC Macromonomers

the brushes have been reported to be on the order of 10−200 nm, depending on the side chain length. Therefore, the large difference in the λ0−1 and λM−1 values means that the differences in λ0−1 values, which reflect the individuality of the main chain, are insignificant. That is, the chain stiffness of the brush polymer is mainly determined by the λb−1value that results from the interactions of the major component, the long side chains, but not by the λ0−1 value of the flexible main chain. However, there are no reports on the relationship between the chemical nature or primary structure of the main chain and the conformation of the brushes. Previously, we reported the molecular characterization of rod brushes consisting of a flexible PSt main chain and rodlike, poly(n-hexyl isocyanate) (PHIC) side chains (poly(VB-HICNs-H) (Ns is the weight-averaged degree of polymerization of HIC).22−24 The rod brushes were much stiffer than flexible brushes comprising PSt main and side chains with the same contour length as the rod brushes, most likely due to the larger excluded-volume interactions among the rods. Recently, we have reported the dimensional characterization of a rod brush consisting of a PMA main chain: poly(MA-HIC-61-Ac).25 Contrary to the expectation mentioned above, the λM−1 value of poly(MA-HIC-61-Ac) was much larger than that of poly(VBHIC-62-H), in spite of its having side rods with the same Ns. This experimental observation suggested that the minor component, the main chain, plays a crucial role in the global conformation of the rod brushes. Here, we report in detail experimental works of the dimensional characterizations of rod brushes consisting of a PMA main chain in tetrahydrofuran (THF) at 25 °C. Characterization was carried out by small-angle X-ray scattering (SAXS) and light scattering (LS), as shown in Scheme 1. The value of λM−1 was rationalized as a function of Ns and compared to that of poly(VB-HIC-Ns-H) to experimentally clarify the influence of primary structure and chemical nature of the main chain on the conformational properties of rod brushes.

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Table 1. Characteristics of MA-HIC-Ns-Ac Macromonomers

a b

MA-HIC-Ns-Ac

Mw × 10−3 a (g mol−1)

Nsb

Mw/Mna

26 36 40 46 58 69 82

3.45 4.73 5.24 5.99 7.55 8.96 10.6

26 36 40 46 58 69 82

1.09 1.13 1.15 1.12 1.11 1.13 1.18

Determined by SEC calibrated with a series of PHICs as a standard. Weight-averaged degree of polymerization of HIC.

performed for the various macromonomer to initiator ratios with dimethyl-2,2′-azobis(2-methyl propionate) (V-601) as an initiator in n-hexane at 60 °C for 24 h (see Table S1).23 Measurements. The weight-averaged molecular weight (Mw) and z-averaged mean-square radius of gyration (⟨S2⟩z) of poly(MA-HICNs-Ac) were determined by size exclusion chromatography (SEC; eluent: THF; flow rate: 1.0 mL min−1; 40 °C; columns: Shodex KF802 + KF806L + KF806L + KF806L, degasser; Tosoh SD-8022, pump: Tosoh SD-8020, RI; Tosoh RI-8020, UV; Tosoh UV-8020) equipped with a multiangle laser light scattering detector (MALS; Wyatt Technology DAWN DSP, wavelength, λ = 632.8 nm) at room temperature of 25 °C. Details of the experimental procedures have been described in previous papers.22,25 The specific refractive index increment (dn/dc) of poly(MA-HICNs-Ac) was measured in THF at 25.0 ± 0.05 °C using a differential refractometer (Otsuka Electronics DRM-1021, wavelength, λ = 632.8 nm) and is listed in Table 2. All sample solutions were prepared by the gravimetric method. The weight fraction, Wp, can then be converted to the polymer concentration, Cp (g mL−1), by eq 2: C p (g/mL) =

Wp ρ0−1(1 − Wp) + νWp

(2) −1

where ρ0 is the density of pure solvent (0.8830 g mL for THF at 25 °C) and ν is the partial specific volume of the brush, which was determined by using a DMA 4500 M densimeter (Anton Paar) to be 0.971 mL g−1 at 25 °C. Small-angle X-ray scattering (SAXS) measurements were carried out at 25 ± 0.05 °C. A NANO-Viewer (Rigaku Co., Tokyo, Japan) was used as the X-ray source. The wavelength of the X-rays was 1.5418 Å, and the sample-to-detector distance ranged from 643 to 650 mm. The scattering vector, q, defined as 4π sin(θ)/λ, with 2θ being the scattering angle, was calibrated from the Bragg reflection of powdered lead stearate. The scattering intensity, I(q), was detected using a highspeed 2D X-ray detector (PILATUS 100 K; DECTRIS Ltd., Baden, Switzerland) with a detector size of 487 × 195 pixels, covering the range of the scattering vectors from 0.1 to 1.0 nm−1. The excess scattering intensities, ΔI(q), were obtained as the difference between

EXPERIMENTAL SECTION

Materials. Spectroscopic grade THF (Kanto Chemical Co., Tokyo, Japan) was used for the specific refractive index increment (dn/dc) and SAXS measurements. α-Methacrylate-ω-acetyl-terminated PHIC macromonomer (MA-HIC-Ns-Ac) was prepared by living coordination polymerization of HIC using 2-methacryloyloxyethoxydichloro(cyclopentadienyl)titanium(IV) as the initiator. The details of preparation of the macromonomers have been described in previous papers.22,25,26 Characteristics of the synthesized MA-HIC-Ns-Ac macromonomers used in this study are listed in Table 1. The radical homopolymerizations of MA-HIC-Ns-Ac macromonomers were B

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Macromolecules Table 2. Characteristics, Aspect Ratio, dn/dc, and ⟨Sc2⟩ of Poly(MA-HIC-Ns-Ac) sample

Mw × 10−6 a (g mol−1)

Mw/Mna

NMb

LM/2Lsc

dn/dcd (mL/g)

⟨Sc2⟩1/2 e (nm)

poly(MA-HIC-26-Ac) poly(MA-HIC-36-Ac) poly(MA-HIC-40-Ac) poly(MA-HIC-46-Ac) poly(MA-HIC-58-Ac) poly(MA-HIC-69-Ac) poly(MA-HIC-82-Ac)

1.22 1.75 1.58 2.60 3.69 6.69 3.20

1.92 3.38 1.52 2.69 3.17 3.86 1.22

385 418 346 486 543 844 356

11.1 8.94 6.92 8.23 7.40 9.37 3.97

0.0821 0.0830f 0.0834 0.0830f 0.0830f 0.0830f 0.0832

2.70 3.75 3.88 4.78 5.74 6.82 6.97

Determined by SEC-MALS in THF at 25 °C. bCalculated from Mw(brushes)/Mn(macromonomer). cAspect ratio of the rod brushes, calculated by eq 4. dIn THF at 25 °C. eDetermined by SAXS in THF at 25 °C. fCalculated value from the Ns dependence of the experimental value of dn/dc. a

the value of I(q) for the solvent and solution at the same q, taking into account the X-ray transmittance. To obtain the value of [Cp/ ΔI(q)]Cp=0 at infinite dilution, ΔI(q) at each q was extrapolated to Cp = 0.27 The AFM measurements were performed using a Nanoscope III and IV with a multimode AFM unit (Veeco Instruments Inc., Santa Barbara, CA) in air at room temperature with standard silicon cantilevers (NCH, NanoWorld, Neuchâtel, Switzerland) in tapping mode. Samples for AFM measurement was prepared by spin-casting a drop of THF solution (Wp = 3.0 × 10−6 w/w) on freshly cleaved mica at 2000 rpm. The measurement conditions were 1−1.3 V target amplitude, 500 nm scan size, 1.8−1.97 Hz scan rate, and 0.745−1.0 V amplitude set point. 1 H and 13C NMR spectra were recorded using a JEOL JNMECX400 instrument.

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RESULTS AND DISCUSSION Table 1 lists the characteristics of MA-HIC-Ns-Ac, including the sample name, the values of Mw and Mw/Mn determined by SEC calibrated with a series of PHIC’s as standards, and the Ns values, calculated from the corresponding Mw. Table 1 shows that MA-HIC-Ns-Ac macromonomers with Ns ranging from 26 to 82 with relatively narrow molecular weight distributions (e.g., Mw/Mn = 1.18 for Ns = 82) were prepared. The ω-end (acetyl group) functionality was identified from the intensity ratios of the 1H NMR peaks due to ω-acetyl group and ethoxy group of the α-HEMA terminal group and found to be quantitative for all samples. Typical examples of the radical homopolymerization results of MA-HIC-Ns-Ac are listed in Table S1. Root-Mean-Square Cross-Section Radius of Gyration, ⟨Sc2⟩1/2. Figure 1 shows the cross-section Guinier plots for poly(MA-HIC-Ns-Ac) (Ns = 26, 36, 40, 46, 58, 69, and 82) in THF at 25 °C. The mean-square cross-section radii of gyration (⟨Sc2⟩) of the poly(MA-HIC-Ns-Ac) at infinite dilution were determined from the initial slopes via eq 3:28 ⎡ ΔI(q) ⎤ k 2Nπ 1 ⎥ = ln − ⟨Sc 2⟩q2 + ... ln⎢q ⎢⎣ Cp ⎥⎦ L 2 C =0 p

Figure 1. Cross-section Guinier plots of ln[qΔI(q)/Cp]Cp=0 as a function q2 for poly(MA-HIC-Ns-Ac) in THF at 25 °C.

aspect ratio =

NMlMML,PHIC LM =1+ 2Ls 2NsM 0

(4)

where LM is the main chain contour length (= NMlM + δ); Ls is the side chain contour length, which is calculated from Ls = (NsM0)/ML,PHIC; lM is the contour length per backbone monomer (0.24 nm); M0 is the molecular weight of HIC (127.2 g mol−1); and ML,PHIC is the molecular weight per unit contour length of PHIC (725 g mol−1 nm−1) in THF at 25 °C.23 δ is due to the contribution of side chains near the ends to the main chain contour (δ = 2Ls), as schematically shown in Figure 2. lM = 0.24 nm and was experimentally determined, as described in the next section. The aspect ratios of the rod brushes ranged from 3.97 to 11.1, suggesting that the ⟨Sc2⟩ values can be determined accurately by using eq 3.28 Figure 3 shows the Ns dependence of ⟨Sc2⟩1/2 of poly(MAHIC-Ns-Ac) together with that of poly(VB-HIC-Ns-H)22,23 for comparison. The ⟨Sc2⟩1/2 values of poly(MA-HIC-Ns-Ac) increased almost linearly with increasing Ns and were essentially consistent, within experimental error, to those of poly(VB-HICNs-H) for the same Ns. This is due to the fact that ⟨Sc2⟩1/2 is mainly determined by the major componentthe side chain. The experimental data were compared to calculations from the wormlike comb model where the main and side chains were modeled with the stiffness parameters, λM−1 and λs−1, respectively. The ⟨Sc2⟩ for a wormlike comb is given by29,30

(3)

Here, ΔI(q) is the experimental excess scattering intensity, L is the contour length of the cylinder, k is the electron density contrast factor, and N is the number of cylinders. The values of ⟨Sc2⟩1/2 of poly(MA-HIC-Ns-Ac) samples are listed in Table 2, together with the characteristics of poly(MA-HIC-Ns-Ac) used in the SAXS measurements, the weight-averaged degrees of polymerization of the main chain, NM, the aspect ratios, and the dn/dc values. The aspect ratio of the main chain to the side chain contour was calculated using eq 4: C

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poly(MA-HIC-82-Ac), most likely due to the low aspect ratio and limitations in the camera length of the SAXS equipment.31 Root-Mean-Square Radius of Gyration, ⟨S2⟩1/2. A typical example of the RI signal, log Mw and log ⟨S2⟩z1/2, in the SEC chromatogram of the poly(MA-HIC-40-Ac) in THF is presented in Figure S1. The values of log Mw and log ⟨S2⟩z1/2 linearly decrease with increasing the retention volume, showing that the rod brushes are appropriately separated in order of their hydrodynamic volume.32 The z-averaged mean-square radius of gyration, ⟨S2⟩z, of the rod brush was determined from light scattering experiments by applying Berry’s equation (eq 8):33 ⎡ KCp ⎤1/2 1 = ⎢ ⎥ ⎣ R(q) ⎦C = 0 M w1/2P(q)1/2

Figure 2. Schematic cartoon of the end chain effect due to the side chains (δ) near the ends of the main chain contour length of the rod brushes.

p

P(q)−1/2 = 1 +

1 2 2 ⟨S ⟩z q + ... 6

(8) (9)

Here, K is the optical constant (K = 4π2n2(dn/dc)2/(λ4NA)) with the refractive index of the solvent, n; Avogadro’s number, NA; the Rayleigh ratio, R(q); the particle scattering form factor, P(q); and the scattering vector, q, which is defined by q = (4πn/ λ) sin(θ/2) where θ is the scattering angle. Figure 4 shows a

Figure 3. Ns dependence of ⟨Sc2⟩1/2 values for poly(MA-HIC-Ns-Ac) (○), poly(MA-HIC-61-Ac) (●),25 and poly(VB-HIC-Ns-H) (□)22,23 in THF at 25 °C. The solid line is the theoretical line calculated from eq 7. Figure 4. Angular dependence of P(q)−1/2 for the indicated fractions of poly(MA-HIC-26-Ac) in THF at 25 °C determined by SEC-MALS. The broken lines indicate an initial slope.

N ⎧ ⎡L 1 1 1 ⟨Sc ⟩ = M2 ⎨Ls 2⎢ s − + − 4λs 2 4λs 3Ls 8λs 4Ls 2 L T ⎩ ⎣ 6λs ⎡L ⎤ 1 × (1 − exp(− 2λsLs))⎥ + Ls(L T − Ls)⎢ s − 2λs 2 ⎣ 2λs ⎦ ⎪

2

⎪

+

⎤⎫ ⎪ 1 ⎥⎬ (1 exp( 2 )) L λ − − s s 3 ⎪ 4λs Ls ⎦⎭

L T = NMLs + (NM − 1)lM

typical example in which P(q)−1/2 is plotted against q2 for specimens of poly(MA-HIC-26-Ac) with different Mw’s. As seen in Figure 4, the ⟨S2⟩z value was determined from the initial slope (indicated by dotted lines) and listed in Tables S2−S8. Figure 5 shows the double-logarithmic plot of ⟨S2⟩z1/2 versus NM for poly(MA-HIC-26-Ac) and poly(VB-HIC-21-H)22 in THF at 25 °C, together with the data for linear PSt30 (black broken lines) and PMMA 25 (black solid line) under corresponding condition. There are two interesting observations to be noted. First, the value of ⟨S2⟩z1/2 of poly(MA-HIC26-Ac) is much larger than that of linear PMMA with a corresponding value of NM. This clearly indicates that the stiffness of the PMA main chain in poly(MA-HIC-26-Ac) is much larger than that of the linear PMMA. That is the PMA main chain stiffens due to the densely grafted stiff rods, as observed for many flexible and rod brushes. Second, the ⟨S2⟩z1/2 value for poly(MA-HIC-26-Ac) is much higher than that of poly(VB-HIC-21-H) with the same value of NM. This is one of the most important experimental findings in this paper because it indicates that the primary structure of the main chain

(5) (6)

When LT ≫ Ls and λsLs → 0 for the rod brushes, eq 5 is approximated by eq 7: 3

⟨Sc 2⟩ ≈

1 Ls 3 Ls + lM

(7)

Equation 7 shows that the ⟨Sc2⟩ of the rod brush is equal to the radius of gyration of the rod with contour length, 2Ls. In Figure 3, the solid line is the calculated radius of gyration, obtained using eq 7 and using lM = 0.24 nm, which quantitatively describes the experimental Ns dependence of ⟨Sc2⟩1/2 for the rod brushes. A downward deviation is noticeable for the data of D

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limited region (8 > nK > 4), a straight line can be approximated whose intercept and slope allow the evaluation of λM−1 and ML.22 Figure 6 shows examples of the plots of (Mw/⟨SM2⟩)1/2

Figure 5. NM dependence of the ⟨S2⟩z1/2 value of poly(MA-HIC-26Ac), together with those of poly(VB-HIC-21-H)22 and PSt30 and PMMA25 in THF at 25 °C. The blue solid and broken lines are the theoretical curves calculated for the perturbed and unperturbed wormlike cylinder using the parameters listed in Table 3. Figure 6. Plots of (Mw/(⟨S2⟩z − ⟨Sc2⟩))1/2 versus Mw−1, constructed form the experimental ⟨S2⟩z and ⟨Sc2⟩ data for poly(MA-HIC-26-Ac) (○) and poly(MA-HIC-40-Ac) (□). The broken lines show a linear region, and the solid lines are theoretical values calculated from eq 13 using the parameters listed in Table 3.

influences the overall conformation of the rod brushes. The weight fraction of the main chain of poly(MA-HIC-26-Ac) and poly(VB-HIC-21-H) was calculated to be 0.033 and 0.048, respectively, showing that the main chain is very minor component in the brush polymers. However, this minor component plays a crucial role in determining the conformational properties of the rod brushes. In order to determine the λM−1 value of poly(MA-HIC-26Ac), the NM dependence of ⟨S2⟩z1/2 was analyzed using the cylindrical wormlike chain model with the chain-end effect.22,34 The physical meaning of the chain-end effect is shown schematically in Figure 2. In Figure 2, δ/2 is the contribution of the side chains near the chain ends to the main chain contour. Thus, the main chain contour length, LM, is given by eq 10: LM =

Mw +δ ML

against Mw−1 and is constructed from the experimental data (⟨SM2⟩ = ⟨S2⟩z − ⟨Sc2⟩) for poly(MA-HIC-26-Ac) and poly(MA-HIC-40-Ac). The plots show upward curves but are straight lines (denoted by dotted lines) in the region of 8 > nK > 4, affording λM−1 = 48 nm and ML = 1.26 × 104 g mol−1 nm−1 for poly(MA-HIC-26-Ac) and λM−1 = 59 nm and ML = 1.85 × 104 g mol−1 nm−1 for poly(MA-HIC-40-Ac). The value of λM−1 = 48 nm for poly(MA-HIC-26-Ac) is twice that of poly(VBHIC-21-H), λM−1 = 25 nm. In this figure, theoretical data are given by solid curves and are constructed from eq 13 using the determined values of λM−1 and ML. The contour length per backbone monomer (lM), calculated from lM = Mn(macromonomer)/ ML, for the brushes is 0.24 ± 0.01 nm, where Mn(macromonomer) is the number-averaged molecular weight of MA-HIC-Ns-Ac (Ns = 26 and 40). This value of lM seems reasonable and is similar to that of the all-trans conformation of the main chain (0.25 nm). Similar plots for MA-HIC-36-Ac, MA-HIC-46-Ac, and MA-HIC-58-Ac are shown in Figure S2 and yield λM−1 values of 55, 80, and 99 ± 5 nm, respectively. For poly(MA-HIC-69-Ac) and poly(MA-HIC-82-Ac), the λM−1 values were determined by assuming lM to be 0.24 nm. The λM−1 and ML values determined are summarized in Table 3. Figure 5 shows the comparison of experimental N M dependence of ⟨S2⟩z1/2 data for poly(MA-HIC-26-Ac) against the theoretical curve (blue broken line), calculated using eqs 10−12 with the model parameters λM−1 = 48 nm, ML = 1.26 × 104 g mol−1 nm−1, ⟨Sc2⟩1/2 = 2.70 nm, and δ = 9.5 nm. It is clear that the experimental N M dependence of ⟨S 2 ⟩ z 1/2 is quantitatively described by the wormlike cylinder model.22,34 Because THF is a good solvent for both PMMA and PHIC chains, one may consider the intramolecular excluded-volume effects on ⟨S2⟩z1/2 in the region of nK > 5 (NM > 103; see Table S2). The influence of the intramolecular excluded volume was considered by using the quasi-two-parameter theory,37−39 given by eqs S1−S4. The blue solid line in Figure 5 is the theoretical curve for the wormlike cylinder model perturbed by an excluded volume with strength, B, being 1.0 nm. The

(10)

where ML is the molecular weight per unit contour length of the brushes. The mean-square radius of gyration (⟨S2⟩) of a cylindrical wormlike chain is expressed by20 ⟨S2⟩ = ⟨SM 2⟩ + ⟨Sc 2⟩

(11)

where ⟨SM ⟩ is the main-chain mean-square radius of gyration of the brush. The unperturbed mean-square radius of gyration ⟨SM2⟩0 of the wormlike chain having λM−1 and LM is expressed as35 L 1 1 1 ⟨SM 2⟩0 = M − + − 6λM 4λM 2 4λM 3L M 4λM 4L M 2 2

× [1 − exp( −2λML M)]

Equation 12 is approximated by eq 13:

(12) 22,36

⎛ ⎛ M ⎞1/2 3ML ⎛ 1 δ⎞ 1 ⎞ ⎟ = (6λMML)1/2 ⎜⎜1 + ⎜ − ⎟ ⎟⎟ ⎜ 2 2 ⎝ 2λM 3⎠M⎠ ⎝ ⟨SM ⟩0 ⎠ ⎝ (13)

with the maximum error from the exact value being less than 2% for the Kuhn segment number, nK = λMLM > 4. Equation 13 indicates that the plot of (M/⟨SM2⟩0)1/2 against the inverse of M with δ = 2Ls should give an upward curve; however, within a E

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Macromolecules Table 3. Cylindrical Wormlike Chain Model Parameters for Poly(MA-HIC-Ns-Ac) in THF at 25 °C

a

P(MA-HIC-Ns-Ac)

λM−1 a (nm)

λM−1 b (nm)

ML × 10−4 (g mol−1 nm−1)

δ (nm)

B (nm)

poly(MA-HIC-26-Ac) poly(MA-HIC-36-Ac) poly(MA-HIC-40-Ac) poly(MA-HIC-46-Ac) poly(MA-HIC-58-Ac) poly(MA-HIC-69-Ac) poly(MA-HIC-82-Ac)

48 55 59 80 99 ± 5 135 ± 10 268 ± 40

48 55 59 80 97 130 270

1.26 1.69 1.85 2.29 2.90 3.30c 3.73c

9.5 13.1 14.5 16.5 20.8 24.7 29.1

1 1

Determined from NM dependence of ⟨S2⟩z1/2. bDetermined from the scattering form factor. cCalculated from ML = Mn(macromonomer)/0.24 nm.

experimental data over 2 orders of magnitude of NM are described perfectly by the theory. Because the high λM−1 and small B values result in a small λMB value, the poly(MA-HIC26-Ac) chain in the NM region studied behaves like an unperturbed KP chain. Figure 7 shows the NM dependence of

and P0(q) = {[1 − χ (q; λML M)]PC(q) + χ (q; λML M)PR (q)}Γ(q; λML M)

(16)

where PC(q) and PR(q) are the Debye scattering function and the scattering function for the rod, respectively. The Debye scattering function for the Gaussian coil with the same ⟨SM2⟩0 as that of the wormlike chain is given by PC(q) = PD(q) =

2 [exp(−⟨SM 2⟩0 q2) + ⟨SM 2⟩0 q2 − 1] (⟨SM 2⟩0 q2)2

(17)

The scattering function for the rod with a contour length, LM, is given by 2 [qL MSi(qL M) + cos(qL M) − 1] (qL M)2

PR (q) =

(18)

where Si(x) is the sine integral defined by eq 19: Si(x) =

∫0

x

t −1 sin t dt

(19)

The function χ(q; λMLM) is given by χ (q; λML M) = exp(ξ −5)

(20)

where Figure 7. NM dependence of the ⟨S2⟩z1/2 value for poly(MA-HIC-NsAc) in THF at 25 °C. The solid lines are the theoretical values calculated for the perturbed wormlike cylinder model using the parameters listed in Table 3.

ξ=

(21)

and Γ(q; λMLM) is given by 5

⟨S2⟩z1/2 for poly(MA-HIC-Ns-Ac)s with Ns = 40, 58, 69, and 82, and Figure S3 shows that for poly(MA-HIC-Ns-Ac)s with Ns = 36 and 46. The solid lines are theoretical curves using the parameters listed in Table 3, which quantitatively describe the experimental data. Scattering Form Factor. To demonstrate the validity of the chain stiffness parameters determined from the NM dependence of the ⟨S2⟩z data, the scattering form factor was compared to the theory. According to Yoshizaki and Yamakawa,40,41 the scattering function for the unperturbed wormlike chain with a circular cross section is expressed by eq 14:

Γ(q; λML M) = 1 + [1 − χ (q; λML M)] ∑ Ai ξ i i=2 2

+ χ (q; λML M) ∑ Bi ξ −i

(22)

i=0

where 2

Ai =

2

∑ a1,ij(λMLM)−j e−10/λ

ML M

j=0

+

∑ a2,ij(λMLM) j e−2λ

ML M

j=1

(23)

and

⎧ 24 ⎡ ⎛ qd ⎞ ⎛ qd ⎞ ⎛ qd ⎞⎤⎫2 P(q) = P0(q)⎨ sin⎜ B ⎟ − ⎜ B ⎟ cos⎜ B ⎟⎥⎬ 3⎢ ⎩ (qdB) ⎣ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠⎦⎭

2

Bi =

2

∑ b1,ij(λMLM)−j + ∑ b2,ij(λMLM) j e−2λ

ML M

j=0

(14)

j=1

(24)

The coefficients a1,ij, a2,ij, b1,ij, and b2,ij in eqs 23 and 24 are listed in Table 1 of ref 41. Pedersen et al.43 afforded P′C(q) and ξ′ for infinitely thin wormlike chains having the intramolecular excluded-volume

with the bead diameter, dB, for the cylindrical brushes taken to be42 dB = [0.913 + 0.205 exp( −5.0λMLs)]2Ls

π ⟨SM 2⟩0 q 2L M

(15) F

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Figure 8. (a) Reduced Kratky plots and (b) Holtzer plots for poly(MA-HIC-26-Ac) in THF at 25 °C. The solid and broken lines are the theoretical values for unperturbed wormlike chain calculated from eqs 10, 12, and 14−24 and perturbed wormlike chain calculated from eqs 10, 12, 16, 18−20, and 22−27 and eqs S1−S4 using the model parameters listed in Table 3.

interactions (perturbed wormlike chain). These function are given by P′C (q) = [1 − w(q⟨SM 2⟩1/2 )]PD(q) + w(q⟨SM 2⟩1/2 ) × [1.220(q⟨SM 2⟩1/2 )−1.701 + 0.4288(q⟨SM 2⟩1/2 )−3.401 − 1.651(q⟨SM 2⟩1/2 )−5.102 ]

(25)

and ⎞3/2 ⎛ π ξ′ = qλM −1⎜ ⎟ (⟨SM 2⟩λM 2)1.282 ⎝ 1.103λML M ⎠

(26)

with w(x) =

⎛ x − 1.523 ⎞⎤ 1⎡ ⎟⎥ ⎢1 + tanh⎜⎝ 2⎣ 0.1477 ⎠⎦

Figure 9. Image from phase AFM measurements of poly(MA-HIC-40Ac) (Mw = 1.58 × 106, Mw/Mn = 1.52) on mica at room temperature.

(27)

The comparison of the experimental form factor for poly(MAHIC-26-Ac) with different Mw’s against theory is shown in Figure 8. The reduced Kratky plots (a) and Holtzer plots (b) are indicated. The same plots for the rod brushes other than poly(MA-HIC-26-Ac) are shown in Figures S4−S9. The solid and broken lines are the theoretical values for the unperturbed wormlike chains, calculated using eqs 10, 12, and 14−24 and the perturbed wormlike chain calculated using eqs 10, 12, 16, 18−20, and 22−27 and eqs S1−S4, respectively. The best fit parameters of the λM−1 values describing the experimental scattering form factors are listed in Table 3. The experimental form factors of poly(MA-HIC-Ns-Ac) with different Mw’s are almost perfectly described by the scattering function for the wormlike chain having the same λM−1 value as those determined from the NM dependence of ⟨S2⟩z data. This result strongly supports the reliability of the λM−1 values determined in this study. Figure 9 shows the AFM phase image for poly(MA-HIC-40Ac) (Mw = 1.58 × 106 g mol−1, Mw/Mn = 1.52) on mica at room temperature. A single, cylindrical, brushlike macromolecule is clearly seen. Trajectory analysis on the image was carried out by using the “2D Single Molecules” software developed by Minko et al.,44 and λM−1 was determined to be 66 nm in a two-dimensional state; moreover, this value compares well with the value calculated in THF at 25 °C, 59 nm. Comparison of λM−1 between PMA and PSt Main Chains. Figure 10 shows the comparison of the Ns dependence of λM−1 between poly(MA-HIC-Ns-Ac) and poly(VB-HIC-Ns-

Figure 10. Ns dependence of main chain stiffness parameter (λM−1) for poly(MA-HIC-Ns-Ac) and poly(VB-HIC-Ns-H)22,23 in THF at 25 °C.

H). It is clear that the PMA main chain stiffens significantly more than a PSt main chain with the same value of Ns. The difference in λM−1 between these two chains increases with increasing Ns. The power law exponent for λM−1 vs Ns is 1.5 and 1.0 for poly(MA-HIC-Ns-Ac) and poly(VB-HIC-Ns-H), respectively. The experimental exponent for poly(MA-HICNs-Ac) is is similar to the theoretical result, calculated using the mean-field approximation.45 G

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demonstrate that although PSt and PMMA are typical flexible polymers, their local or instantaneous conformations are remarkably different.20,21 The atactic PMMA chain had the strongest helical nature of typical flexible polymers, while atactic PSt was of the weakest. Thus, the PMA main chain is subject to greater steric hindrance due to the long side chain rod. This effect may increase the λM−1 value. Systematic studies to clarify the influence of the flexible oxyethylene spacer, αmethyl group, ω-acetyl group, and steric hindrance effects on the main chain stiffness of the rod brushes are now in progress and will be published soon.

As mentioned in the Introduction, if eq 1 is valid, brushes with chemically identical side chains should have similar λM−1 values in the same solvents and at the same temperatures, irrespective of the nature of the flexible main chain. However, the current results indicate that both the absolute value of λM−1 and the power law exponent change drastically depending on the primary structure of the main chain. Although we cannot definitively explain these experimental findings at this stage, some feasible explanations are given. First, we discuss the microstructure of the PMA main chain. The radical polymerization of the methacrylate monomer with a bulky substituent, such as (1-phenyldibenzosuberyl)methacrylate, is reported to produce an almost perfect isotactic helical polymer.46 Because the present macromonomer is considered to be methacrylate monomer with a bulky substituent (PHIC chain), the microstructure of the brushes may be affected. To determine the tacticities of the main chain, the rod brush was hydrolyzed and converted to PMMA. The experimental procedures47 are presented in the Supporting Information. Figures S10 and S11 show 1H and 13C NMR spectra. The triad tacticities were determined to be mm = 0.036, mr = 0.346, and rr = 0.618 for PMMA derived from poly(MA-HIC-29-H). These values are consistent with those of PMMA prepared by conventional radical polymerization of MMA. Therefore, the PMA main chain of the brush has an atactic but syndiotactic-enriched configuration, as does conventional atactic PMMA. Second, we discuss the difference in the extent of excludedvolume effects produced among the side rods. The excludedvolume interactions may be a function of the strength of the interaction and the collision probability. In the present study, the side chains of the brushes have the same chemical nature; i.e., they have the same strength of interaction at the same solvent and temperature. Therefore, a higher value of λM−1 for the PMA main chains than that of PSt likely results from the increase in collision probability. This situation is schematically shown in Figure 11. For poly(MA-HIC-Ns-Ac) chain, a freely

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CONCLUSIONS Dimensional properties of cylindrical rod brushes consisting of a polymethacrylate main chain were studied by static light and small-angle X-ray scattering (SAXS) in THF at 25 °C. The mean-square cross-section radius of gyration (⟨Sc2⟩) of poly(MA-HIC-Ns-Ac) was essentially consistent with that of the rod brushes consisting of a PSt main chain, poly(VB-HICNs-H), and was quantitatively described by the wormlike comb model theory. The z-averaged mean-square radius of gyrations (⟨S2⟩z) of the brush determined as the function of molecular weight were analyzed with the aid of the theories for the cylindrical wormlike chain model to determine the λM−1 value. The scattering form factors of poly(MA-HIC-Ns-Ac) were quantitatively described by the wormlike chain model having the corresponding λM−1 parameter determined. The λM−1 values of poly(MA-HIC-Ns-Ac) were much larger than those of poly(VB-HIC-Ns-H) having the same Ns and also increased with increasing Ns according to the following scaling law: λM−1 ∝ Ns1.5. In summary, the chemical nature of the main chain, which is the minor component in the brush polymers, was found to play an essential role in the overall conformation of the rod brushes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b02195. Homopolymerization results, tables of ⟨S2⟩z vs Mw for poly(MA-HIC-Ns-Ac), SEC-MALS curve for poly(MAHIC-26-Ac), plots of (Mw/(⟨S2⟩z − ⟨Sc2⟩))1/2 versus Mw−1 for poly(MA-HIC-36-Ac), poly(MA-HIC-46-Ac), and poly(MA-HIC-58-Ac), quasi-two-parameter theory, NM dependence of ⟨S2⟩z1/2 for poly(MA-HIC-36-Ac) and poly(MA-HIC-46-Ac), reduced Kratky and Holtzer plots for poly(MA-HIC-36-Ac), poly(MA-HIC-40-Ac), poly(MA-HIC-46-Ac), poly(MA-HIC-58-Ac), poly(MAHIC-69-Ac), and poly(MA-HIC-82-Ac), the experimental procedure for the determination of main-chain microstructure of the rod brushes, and 1H and 13C NMR spectra of PMMA prepared from radical polymerization, and PMMA converted from poly(MA-HIC-29H) (PDF)

Figure 11. Schematic representation showing the effects of different effective excluded-volumes in the side rods of PMA and PSt main chains.

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rotating oxyethylene chain is located as a spacer between the methacryloyloxy main chain and PHIC side chain. This flexible segment may produce an apparently larger effective excludedvolume among the rods, when compared to poly(VB-HIC-NsH). Third, we discuss the individuality of the PMA and PSt chain. Yamakawa, Yoshizaki, and their co-workers have studied the conformations of these chains in dilute solutions to

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel 81-238-26-3182 (S.K.). Notes

The authors declare no competing financial interest. H

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(31) Nakamura, Y.; Norisuye, T. Brush-Like Polymers. In Soft Matter Characterization; Borsali, R., Pecora, R., Eds.; Springer: Netherlands, 2008; pp 235−286. (32) Kikuchi, M.; Nakano, R.; Jinbo, Y.; Saito, Y.; Ohno, S.; Togashi, D.; Enomoto, K.; Narumi, A.; Haba, O.; Kawaguchi, S. Macromolecules 2015, 48, 5878−5886. (33) Berry, G. C. J. Chem. Phys. 1966, 44, 4550−4564. (34) Amitani, K.; Terao, K.; Nakamura, Y.; Norisuye, T. Polym. J. 2005, 37, 324−331. (35) Benoit, H.; Doty, P. J. Phys. Chem. 1953, 57, 958−963. (36) Murakami, H.; Norisuye, T.; Fujita, H. Macromolecules 1980, 13, 345−352. (37) Shimada, J.; Yamakawa, H. J. Chem. Phys. 1986, 85, 591−600. (38) Yamakawa, H.; Shimada, J. J. Chem. Phys. 1985, 83, 2607−2611. (39) Domb, C.; Barrett, A. J. Polymer 1976, 17, 179−184. (40) Nagasaka, K.; Yoshizaki, T.; Shimada, J.; Yamakawa, H. Macromolecules 1991, 24, 924−931. (41) Yoshizaki, T.; Yamakawa, H. Macromolecules 1980, 13, 1518− 1525. (42) Nakamura, Y.; Norisuye, T. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 1398−1407. (43) Pedersen, J. S.; Schurtenberger, P. Macromolecules 1996, 29, 7602−7612. (44) Roiter, Y.; Minko, S. http://people.clarkson.edu/~sminko/. (45) Subbotin, A.; Saariaho, M.; Stepanyan, R.; Ikkala, O.; ten Brinke, G. Macromolecules 2000, 33, 6168−6173. (46) Nakano, T.; Matsuda, A.; Okamoto, Y. Polym. J. 1996, 28, 556− 558. (47) Narumi, A.; Baba, H.; Akabane, T.; Saito, Y.; Ohno, S.; Togashi, D.; Enomoto, K.; Kikuchi, M.; Haba, O.; Kawaguchi, S. Macromolecules 2015, 48, 3395−3405.

ACKNOWLEDGMENTS The authors thank Prof. J. Kumaki at Yamagata University for the SPM measurements. Support in part by Grants-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan (16550105 and 19550117), by The Foundation for Japanese Chemical Research, and by the Saneyoshi Scholarship Foundation is gratefully acknowledged.

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