Synthesis and Characterization of a Mesogen-Jacketed

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Synthesis and Characterization of a Mesogen-Jacketed Polyelectrolyte Wei Qu,† Xingqi Zhu,‡ Jiahui Chen,† Lin Niu,† Dehai Liang,† Xinghe Fan,† Zhihao Shen,*,† and Qifeng Zhou† †

Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China ‡ Anton Paar China, Shanghai 200233, China S Supporting Information *

ABSTRACT: In an attempt to construct a new kind of rodlike polyelectrolyte, poly[sodium 2,5-bis(4′-sulfophenyl)styrene] (PSBSS) was prepared from its precursor, poly[2,5-bis(4′-neopentylsulfophenyl)styrene] (PBNSS), which was polymerized by atom transfer radical polymerization. Small-angle X-ray scattering (SAXS) results demonstrate that PBNSS exhibits a hexagonal columnar phase and PSBSS exhibits a smectic A phase in bulk. The conformation of PSBSS in the aqueous solution is cylindrical, and the length and the diameter of the cylinder are ca. 25 nm and ca. 2.4 nm, respectively. The persistence length (lp) of the PSBSS chain in the aqueous solution is 11.50 ± 0.09 nm calculated by fitting the SAXS profile with the modified wormlike chain model. The conformation, the maximum length, and the lp of the chain are only weakly dependent on the concentration of the added salt. These results indicate that we have successfully obtained a new kind of polyelectrolyte with a highly rigid chain, a high charge density, and a narrow molecular weight distribution, which can serve as a new model macromolecule in studying rodlike polyelectrolytes.

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INTRODUCTION In the past few decades, extensive studies on polyelectrolytes have been carried out from theory, simulation, and experimental aspects.1,2 However, the understanding of polyelectrolytes remains controversial, with many issues lacking satisfactory explanations. Scattering experiments are probably the most important techniques to study the behaviors of polyelectrolyte solutions. Static and dynamic light scattering (SLS and DLS),3−5 small-angle X-ray scattering (SAXS),6−9 and small-angle neutron scattering (SANS)3,4,10−13 techniques are commonly used for studying the structures of polyelectrolytes like charged spheres, rodlike molecules, and flexible chains in solutions. Most scattering profiles of polyelectrolyte solutions without salt show a characteristic maximum q*, which depends on the polyelectrolyte concentration (cp). The q* of all types of polyelectrolyte solutions exhibits a very similar concentration dependence. In the dilute regime, q* ∝ cp1/3, while in the semidilute regime, q* ∝ cp1/2.3,6,14−16 The relationship in the dilute regime can be understood as the correlation among centers of polyions, while that in the semidilute regime is assigned to the nearest-neighbor intersegmental correlation.17 A decrease in the ionic strength may lead to an expansion of flexible polyelectrolytes due to stronger intramolecular forces and intermolecular electrostatic interactions. On the other hand, regardless of the ionic strength of the system, rodlike polyelectrolytes retain their extended-chain conformation.18 Given these points, a number of studies have been performed © 2014 American Chemical Society

using rodlike helical polyelectrolyte systems such as DNA or xanthane.19,20 However, the helical conformation (and thus the rodlike shape) is lost at very low ionic strengths and at elevated temperatures.18,21 One major limitation of natural polyelectrolytes is that we can not change the chemical structures, such as the number of ionic groups per unit length. Therefore, it is necessary to develop well-defined synthetic rodlike polyelectrolytes to study the nature of polyelectrolytes, such as Manning condensation and some conformational problems.22 The first kind of synthetic rodlike polyelectrolyte based on poly(1,4-phenylenebenzobisoxazoles) and poly(1,4-phenylenebenzobisthiazoles) was reported in the early 1980s.23,24 During the following decade, two kinds of rodlike polyelectrolytes with the main chain of poly(p-phenylene) (PPP) were synthesized via various efficient precursor routes.25−28 Long alkyl chains were introduced to the side chains to solubilize the main chain in both kinds of polyelectrolytes. Hydrophilic groups were linked to the main chain directly by Wegner and co-workers, who found that the polyelectrolytes could form lyotropic liquid crystalline phases when the concentration was above a certain value,27 and a similar phenomenon was also found in DNA systems.29 Rehahn and co-workers also synthesized polyelectrolytes with alkyl-chain spacers.25,26 Aggregated polyelectrolyte chains were in the form of cylindrical micelles in bulk. Ballauff Received: November 14, 2013 Revised: March 31, 2014 Published: April 11, 2014 2727

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Scheme 1. Synthetic Route of Monomer and Polymers

SAXS. The results show that the lp is 11.50 ± 0.09 nm in the dilute solution. The effects of polymer concentration and added salt concentration on the structures of PSBSS were also investigated.

et al. discussed the distribution of counterions around the cylindrical macroion using SAXS and anomalous small-angle Xray scattering (ASAXS).30 However, the persistence length (lp) of the polyelectrolytes with a PPP main chain characterized by Wegner et al. was 12.6 nm.31 Because of the long alkyl chains, the solubility of this kind of polyelectrolyte in the aqueous solution is poor. The complexity and polydispersity of the precursors are another problem for polyelectrolytes with a PPP main chain. Gong and co-workers synthesized and characterized poly(2,2′-disulfonylbenzidine terephthalamide) (PBDT),32 which had a rigid polyamide structure in the main chain. There was hydrogen-bonding interaction between the PBDT chains in addition to the electrostatic interaction. In our previous study, we have systematically investigated a special type of liquid crystalline polymers, mesogen-jacketed liquid crystalline polymers (MJLCPs),33,34 which use a very short spacer or a single bond between the side-on attached side chains and the main chain. MJLCPs take an extended-chain conformation because of the “jacketing” effect introduced by the steric effect of the bulky side groups. They can be easily synthesized by radical polymerizations, including living radical polymerizations such as atom transfer radical polymerization (ATRP), and the diameters of the rodlike MJLCPs can be tuned by controlling the chemical structures of side chains.34 It is a new way to obtain rigid polyelectrolytes by taking advantage of the “jacketing” effect, leading to mesogen-jacketed polyelectrolytes (MJPEs) as one new kind of rodlike model chain molecule. Previously, we synthesized two MJPEs by conventional radical polymerization,35 in which the side-chain mesogens had a rigid core containing an amide or ester linkage, with sulfonated groups appended on the two ends of the core. The two MJPEs exhibit smectic A (SmA) phases in bulk, and lamellar phases are observed when the two MJPEs complex with surfactants in the solid state. In this work, we report the design and synthesis of a new kind of MJPE, poly[sodium 2,5-bis(4′-sulfophenyl)styrene] (PSBSS), the precursor of which is polymerized by ATRP. The side-chain core of PSBSS is terphenyl, which is rigid and introduces the “jacketing” effect and π−π interaction. The structures of PSBSS in bulk and in solution were studied by

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EXPERIMENTAL SECTION

Materials. 2,5-Dibromotoluene (99%, Acros), N-bromosuccinimide (NBS, 99%, Aldrich), triphenylphosphine (PPh3, 99%, Acros), bis(pinacolato)diboron (99%, Acros), tetrakis(triphenylphosphine)palladium(0) (Pd(PPh3)4, 99%, Acros), tetrachloromethane (CCl4, AR, Beijing Chemical Co.), and aqueous formaldehyde (40%, AR, Beijing Chemical Co.) were used as received. Tetrahydrofuran (THF, AR, Beijing Chemical Co.) was refluxed with sodium and distilled out just before use. Dimethyl sulfoxide (DMSO, AR, Beijing Chemical Co.) and N,N-dimethylformamide (DMF, AR, Beijing Chemical Co.) were distilled out from calcium hydride. Methanol was purified by distillation. All other reagents were used as received from commercial sources. Measurements. Elemental analysis, thermogravimetric analysis (TGA), and Fourier-transform infrared spectroscopy (FT-IR) experiments were performed according to the procedures previously described.36 GPC experiments were conducted on a Waters 2410 instrument equipped with a Waters 2410 RI detector, with the Styragel HR (High-Resolution) columns (4.6 × 300 mm) and with DMF as the eluent (1.0 mL/min). The calibration curve was obtained with linear polystyrenes as standards. The elution profiles of the polystyrene standards and the fitting equation of the calibration curve are shown in the Supporting Information. 1H NMR spectra were obtained using a Bruker ARX400 MHz with tetramethylsilane (TMS) as the internal standard at ambient temperature in CDCl3 and dimethyl-d6 sulfoxide. Mass spectra were recorded on a Bruker Apex IV FTMS spectrometer. SAXS experiments were performed using a SAXSess instrument (Anton Paar) equipped with a Kratky block collimation system. The X-ray was generated using a Philips PW3080 sealed-tube X-ray generator with the Cu target. The wavelength was 0.1542 nm. A highly sensitive SAXS imaging plate which was 264.5 mm away from the sample was used to collect the signal in vacuum. Samples in bulk were placed in between aluminum foils which were folded and sandwiched in a steel sample holder. Scattering data were acquired for a 30 min exposure. The background scattering from aluminum foils was acquired and then subtracted from the sample profiles. Solution samples for SAXS measurements were carefully loaded into a quartz capillary with a diameter of 1 mm. After background subtraction, desmearing was performed according to Lake’s method.37 The pair2728

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Figure 1. 1H NMR spectra of the monomer (curve 1), PBNSS (curve 2), PBSS (curve 3), and PSBSS (curve 4). 5 °C. After the complete addition of chlorosulfonic acid, the reaction mixture was stirred for another 45 min at ambient temperature, and the mixture was poured on to crushed ice. Three portions of CHCl3, 50 mL each, were used to extract the mixture. The organic layers were combined and dried over anhydrous MgSO4. Chloroform was then distilled off. The product was sufficiently pure and was not further purified. To a mixture of 4-bromobenzene-1-sulfonyl chloride (5.10 g, 20.0 mmol) and neopentyl alcohol (1.80 g, 24.0 mmol) in CH2Cl2 (30 mL) at 0 °C, pyridine (3.24 mL, 40.0 mmol) was added dropwise over a period of 30 min. The reaction mixture was stirred at ambient temperature for 12 h and diluted with Et2O. The organic layer was washed with 0.1% aqueous HCl, water, and brine, dried over MgSO4, and concentrated in vacuo. The crude sulfonate was purified by recrystallization in ethanol. Yield: 61.0%. 1H NMR (300 MHz, CDC13, δ, ppm): 0.92 (s, 9H, −CH3), 3.69 (s, 2H, −OCHH2), 7.64− 7.81 (dd, 4H, Ar). Synthesis of Neopentyl 4-(4,4,5,5-Tetramethyl-1,3,2-dioxaborolan-2-yl)benzenesulfonate (NTDB). To a solution of neopentyl 4-bromobenzenesulfonate (1.00 g, 3.25 mmol) in dioxane (15 mL), bis(pinacolate)dibron (0.910 g, 3.54 mmol), PdCl2(PPh3)2 (0.0300 g, 0.0400 mmol), and KOAc (0.950 g, 9.69 mmol) were added, and the mixture was stirred at 100 °C for 6 h under nitrogen. The mixture was diluted with EtOAc and water. The organic layer was separated, washed with brine, and dried over anhydrous MgSO4. After evaporation of the solvent, the residue was purified by column chromatography on silica gel with EtOAc/petroleum ether (1/10, v/v) as the eluent to give 0.920 g of product as a white solid. Yield: 80.0%. 1 H NMR (300 MHz, CDC13, δ, ppm): 0.89 (s, 9H, −CH3), 1.37 (s, 12H, −CH3), 3.66 (s, 2H, −OCHH2), 7.87−7.96 (dd, 4H, Ar). Synthesis of 2,5-Bis(4′-neopentyl sulfophenyl)styrene (BNSS). To a degassed mixture of 2,5-dibromostyrene (1.10 g, 4.23 mmol), anhydrous K2CO3 (5.84 g, 42.3 mmol), hydroquinone (0.130 g, 1.18 mmol), NTDB (3.30 g, 9.30 mmol), and Pd(PPh3)4 (0.150 g, 0.130 mmol), toluene (30.0 mL) and water (10.0 mL) were added under a continuous stream of argon. The mixture was vigorously stirred at reflux for 36 h under argon. The organic layer was then separated and dried over anhydrous MgSO4. The solvent was removed

distance distribution functions (PDDFs) of scattering curves were calculated using the generalized indirect Fourier transform (GIFT)38,39 program included in the SAXSess software package. Synthesis of Monomer and Polymers. The synthetic route of the monomer and polymers is represented in Scheme 1. The experimental details are described as follows. Synthesis of 2,5-Dibromostyrene. A solution of 2,5-dibromotoluene (10.0 g, 40.6 mmol), NBS (7.12 g, 40.6 mmol), and benzoyl peroxide (BPO, 0.200 g, 0.800 mmol) in CCl4 (250 mL) was refluxed for 8 h. After the solvent was evaporated under reduced pressure, the residue was suspended in CHCl3, and the insoluble solid was removed by filtration. The filtrate was washed with water twice, and the combined aqueous phase was extracted with CHCl3. The combined organic solution was dried over MgSO4 and concentrated in vacuo. The crude product obtained was mixed with PPh3 (10.5 g, 40.6 mmol) and acetone (250 mL). The mixture was heated to reflux, and a lot of precipitates appeared immediately. The reaction was allowed to continue for 4 h. The solids were collected by filtration and washed with cold acetone and then dissolved in aqueous formaldehyde (40%, 250 mL). With rapid stirring, 10 wt % NaOH aqueous solution was added dropwise at ambient temperature. The mixture was stirred for 24 h. When the reaction was completed, three portions of CH2Cl2, 150 mL each, were used to extract the mixture. The organic layers were combined and dried over anhydrous MgSO4. The solvent was evaporated under reduced pressure, and the residue was purified by column chromatography on silica gel with dichloromethane/ petroleum ether (1/3, v/v) as the eluent to give 6.40 g of product as a yellow liquid. Yield: 61.0%. 1H NMR (300 MHz, CDC13, δ, ppm): 5.40−5.43 (d, 1H, =CH2), 5.68−5.74 (d, 1H, =CH2), 6.92− 7.02 (q, 2H, =CH), 7.22−7.67 (m, 3H, Ar). Synthesis of Neopentyl 4-Bromobenzenesulfonate. To a mixture of bromobenzene (15.7 g, 100 mmol) in chloroform (50.0 mL) in a 500 mL flask equipped with a dropping funnel, a thermometer, and a reflux condenser, chlorosulfonic acid (250 mmol) was added dropwise over a period of about 60 min. The reaction mixture was mechanically stirred at 0 °C in a bath containing a freezing mixture of ice and salt. Chlorosulfonic acid was added in such a rate that the temperature of the reaction mixture did not exceed 2729

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under reduced pressure, and the residue was purified by column chromatography on silica gel with EtOAc/petroleum ether (1/10, v/v) as the eluent to give 0.950 g of product as a white solid. Yield: 82.0%. 1 H NMR (300 MHz, CDC13, δ, ppm): 0.95−0.98 (m, 18H, −CH3), 3.78−3.80 (s, 2H, −OCHH2), 3.76−3.78 (s, 2H, −OCHH2), 5.32− 5.35 (d, 1H, CH2=), 5.80−5.85 (d, 1H, CH2=), 6.62−6.70 (q, 1H, CH=), 7.40−7.44 (d, 1H, Ar), 7.56−7.60 (d, 2H, Ar), 7.60−7.64 (q, 1H, Ar), 7.82−7.84 (d, 2H, Ar), 7.86−7.88 (d, 1H, Ar), 7.96−8.00 (d, 2H, Ar), 8.04−8.00 (d, 2H, Ar). 13C NMR (100 MHz, CDC13, δ, ppm): 145.76, 145.70, 139.42, 138.90, 136.75, 135.17, 134.90, 130.67, 130.47, 128.52, 127.82, 127.77, 126.81, 125.34 (p-terphenyl), 116.99 (CHCH2), 79.78, 31.80, 26.05 (neopentyl). Anal. Calcd for C30H36O6S2 (%): C, 64.72; H, 6.52. Found: C, 64.96; H, 6.58. MS (EI, m/z): 556.2 (M•+). Polymerization of BNSS through ATRP. In a typical experiment for polymerization, the monomer BNSS (1.99 g, 3.57 mmol), N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA, 12.1 mg, 0.0710 mmol), (1-bromoethyl)benzene (BEB, 3.25 mg, 0.0170 mmol), CuBr (5.22 mg, 0.0360 mmol), and dry DMF (9.06 g) were charged into a polymerization tube. After being stirred and degassed by three freeze−pump−thaw cycles, the tube was sealed under vacuum and subsequently immerged into an oil bath thermostated at 90 °C for 48 h. It was then quenched in liquid nitrogen and taken out to ambient condition. The solution was passed through a neutral alumina column in order to remove copper salt. Finally, the polymer was precipitated out from a large volume of hexane and dried in vacuum overnight. Preparation of Poly[sodium 2,5-bis(4′-sulfophenyl)styrene] (PSBSS). PBNSS (100 mg) was converted to acid by thermolysis under nitrogen at 150 °C for 30 min. The resulting material was dissolved in 50.0 mL of H2O and dialyzed versus 10.0 L of Milli-Q water, which was exchanged every 24 h (membrane pore size 10 000 g/mol). After the conductivity of the water dropped to about 0.1 mS, dialysis continued for another 12 h. Freeze-drying yielded the desired product.

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distribution by ATRP. The contour length (L) of PBNSS was estimated to be about 35 nm. PSBSS has the same polymerization degree and contour length as PBNSS. TGA experiment was carried out to examine the thermal stability of PBNSS (Figure 3). To remove moisture in the sample, it was

Figure 3. TGA curve of PBNSS at a heating rate of 10 °C/min under a nitrogen atmosphere.

first heated at 80 °C for 30 min. At 150 °C, the weight percentage sharply drops down to 76.7%, close to the theoretical value of 74.8% when neopentyl groups are removed from the polymer. This gives the optimized condition for thermolysis as annealing at 150 °C for 30 min. FT-IR experiments were carried out to confirm the completion of the deprotection reaction. As shown in Figure 4, the vibration of the sulfonate ester groups in PBNSS at 1358

RESULTS AND DISCUSSION

Synthesis and Characterization of the Monomer and Polymers. The structures of the monomer, PBNSS, PBSS, and PSBSS were confirmed by 1H NMR. As shown in Figure 1, the signals of the vinyl group in the monomer at 5.35, 5.82, and 6.67 ppm in curve 1 completely disappear in curve 2, indicating the successful polymerization (in curve 2, the signals of benzene rings are partially shielded by the large neopentyl moieties). In curves 3 and 4 of Figure 1, the signals of the sulfonate ester groups in PBNSS disappear, indicating complete deprotection. As shown in Figure 2, the number-average molecular weight (Mn), polymerization degree, and polydispersity index (PDI) of PBNSS are 86 300 g/mol (relative to polystyrene), 150, and 1.10, respectively, indicating that we have synthesized the polyelectrolyte precursor with a narrow molecular weight Figure 4. FT-IR spectra of PBNSS, PBSS, and PSBSS.

cm−1 is not present after thermolysis. Instead, a broad peak is observed at 3500 cm−1 in PBSS and PSBSS, indicating the presence of hydroxyl groups either in the polymer structure or from absorbed water. Structures of the Polymers in Bulk. SAXS experiments were carried out to determine the bulk structures of PBNSS and PSBSS. About 10 mg of PBNSS was dissolved in THF and cast onto a glass substrate, and then THF was allowed to evaporate at ambient temperature. For PSBSS, water was used as the solvent. The samples were directly used for SAXS experiments without any further treatment.

Figure 2. GPC profile of PBNSS. 2730

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Figure 5 shows the SAXS profiles of PBNSS and PSBSS at ambient temperature. The SAXS profile of PBNSS shows three

Figure 6. SAXS profiles of PSBSS aqueous solutions without salt. The inset shows the log−log plot of q* versus concentration cp. Figure 5. SAXS profiles of PBNSS and PSBSS in bulk.

0.8 wt % is the critical overlapping concentration (cp*) of the PSBSS aqueous solution without salt. When the PSBSS concentration is less than c*p , the solution is dilute, and the polyelectrolyte molecules are well separated. The equivalent relationship, nPLc3 ≈ 10, where nP is the number concentration of polyions and Lc the polyion contour length, was observed by SAXS.15,16 The theoretical crossover concentration, c*t , can be estimated from the equivalent relationship. According to the GPC result of PBNSS, the degree of polymerization and Lc is estimated to be 150 and 35 nm, respectively. Therefore, the result of c*t ≈ 2 wt % is obtained, which is comparable with the experimental value of cp* ≈ 0.8 wt %. The difference may be caused by the deviations in the estimation and the experimental measurement. To further evaluate the polymer shape and dimensions, we calculated the PDDFs, which represent for homogeneous particles the value of distances within the particle, by fitting the scattering profiles with the model-free method of GIFT.38,39 Depending on the range and nature of ordering in the system, the p(r) function can have many peaks. Directly from p(r), a qualitative classification of the shape and the internal structure of the particle can be obtained. In addition, several structural parameters can be determined quantitatively, e.g., the maximum intraparticle distance rmax, because p(r) drops to zero at r = rmax.44 The disappearance of the q* when cp < 0.40 wt % indicates that the polyelectrolyte molecules are well separated, and the total scattering intensity is the sum of the scattering of individual molecules. The data for the 0.30 wt % PSBSS solution, shown in Figure 7, has a small overshoot and a nearly linear tail in the PDDF, which implies that the polyelectrolyte chains are cylindrical. Because PSBSS does not resemble a homogeneous particle with a smooth surface, we find that p(r) ≠ 0 at r = 0.45 The crossover of the decay of the PDDF curve with the abscissa, rmax, reflects the length of the cylinder. Therefore, the result in Figure 7 indicates that the conformation of PSBSS in water is cylindrical with a length of about 25 nm. The PDDF curve shows a pronounced central maximum and broad side maxima, depending on the size of the cross section. Oscillations about the linear descent and ripples in p(r) can occur for cylinders with homogeneous electron density along the long axis but varying cross section or vice versa.44 The steric hindrance and electrostatic repulsion between the side chains of PSBSS make the rotation difficult, which leads to inhomogeneous cylinders. This impedes the accurate determination of the diameter of the cylinder.

diffraction peaks with q1 = 2.97 nm−1, q2 = 5.12 nm−1, and q3 = 5.83 nm−1. The scattering vector ratio of the three peaks, q1:q2:q3, is approximately 1:31/2:41/2, indicating a hexagonal columnar (ΦH) liquid crystalline phase with a periodicity of 2.11 nm (d100 = 2π/q1). The diameter of the cylinders can thus be calculated to be 2.43 nm, which is close to the calculated side-chain length (2.38 nm). Therefore, similar to other MJLCPs with a terphenyl rigid core,40,41 PBNSS behaves like a supramolecular cylinder and forms the columnar LC phase. The introduction of the sulfonate group at the ends of the terphenyl group does not change the conformation of the polymer chain. However, when the sulfonate groups are ionized, the polymer conformation changes from a cylinder to a tablet owing to the introduction of electrostatic interactions, consistent with our previous results.35 This is reflected in the SAXS profile of PSBSS, which has two diffraction peaks at q1 = 3.42 nm−1 and q2 = 6.69 nm−1 with a scattering vector ratio of 1:2, revealing a smectic phase with a periodicity of 1.84 nm. Because the layer spacing is close to the side-chain length (1.80 nm), PSBSS may have a SmA phase with the side chains perpendicular to the main chain, similar to the packing in SmA phases formed by other MJLCPs. To the best of our knowledge, this is the first report of the liquid crystalline phase transition upon the introduction of charges. Structures of PSBSS in Solution. SAXS experiments on PSBSS solutions with or without added salt were performed to investigate the structures of PSBSS in solution. Figure 6 shows the scattering profiles of PSBSS aqueous solutions of various concentrations, without added salt. The SAXS profiles show a maximum of q value (q*) when the concentration cp is higher than 0.40 wt %, common for polyelectrolyte solutions. With increasing cp, the peak shifts to higher q values, and its intensity is initially increased. This weak interference maximum of q may be attributed to inter- and intramolecular correlations at short length scales. In the dilute regime, the electrostatic repulsion between the polyions induces the formation of a threedimensional periodic lattice.42 The q* of the associated correlation peak is predicted to vary as cp1/3. In the semidilute regime, according to the isotropic model, the chains overlap without order in the solution, and they constitute a temporary network of mesh, with q* predicted to vary as cp1/2.15,16,43 The inset shows that q* ∝ cp1/2 for cp > 0.8 wt % while q* ∝ cp1/3 for cp in the range 0.4−0.8 wt %. Therefore, the concentration of 2731

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Figure 9. Comparison of measured and calculated scattering intensities. The open circles give the SAXS intensity of 0.30 wt % PSBSS aqueous solution without salt whereas the solid line displays the optimal fit by the modified WLC model, eq 1.

Figure 7. PDDF [p(r)] of 0.30 wt % PSBSS aqueous solution without salt. The inset shows that the GIFT simulated curve (solid line) fits the raw scattering data (gray dots) well.

The length of the cylinder is large compared to its cross section. The length contribution is taken into account by dividing the intensity by q, leading to Ic(q), which is then Fourier transformed. The resulting pc(r) is the cross-sectional PDDF. The crossover of the decay of PDDF of the crosssectional curve with abscissa reflects the true diameter of the cylinder, dc, shown in Figure 8. The value of dc is ca. 2.4 nm, which is close to the calculated length of the laterally attached side chain.

chain, the scattering function is modified by a cross-sectional scattering factor and is given by46,47 I(q) = I0IWLC(q) exp( −q2R cs 2/2)

(1)

2

where Rcs is the mean-square radius of gyration of the cross section. For L/b > 2, it is suggested to use the following interpolation expression:46,47 IWLC(q , L , b) = SSB(q , L , b) exp[−((qb)/q1) p1 ] + S loc(q , L)(1 − exp[− ((qb)/q1) p1 ])

(2)

where q1 and p1 are empirical constants. For L/b ≤ 2, the following expression is introduced:46,47 IWLC(q , L , b) = SDebye(q , L , b) exp[−((qb)/q2) p2 ] ⎛ a π ⎞ ⎟(1 − exp[− ((qb)/q2) p2 ]) + ⎜ 12 + Lq ⎠ ⎝ Lbq

(3)

where SDebye(q , L , b) = 2[exp( −u) + u − 1]/u 2 ,

u = q 2R g 2 (4)

Figure 8. PDDF of the cross section [pc(r)] of 0.30 wt % PSBSS aqueous solution without salt. The inset shows that the GIFT simulated curve (solid line) fits the raw scattering data (gray dots) well.

⟨R g 2⟩ =

⎛ Lb ⎞⎡ 3 3 3 ⎜ ⎟⎢1 − + − 2 ⎝ 6 ⎠⎣ 2nb 2nb 4nb 3 ⎤ × (1 − exp(− 2nb))⎥ ⎦

To further characterize the bending properties of PSBSS, we apply the wormlike chain (WLC) model to fit the scattering curves, which has been extensively used to characterize bending properties of polymers, e.g., dsDNA fragment. Intermolecular interactions are coarse-grained in terms of the constraints that connected segments impose on the orientation of connecting bonds. The fit in Figure 9 follows the modified WLC model.46,47 It deals with the local stiffness of chain segments at higher q values and also the Gaussian coiled structure at lower q values. Hence, the model can be used to fit the data in the entire q-range, and it also takes into account the excluded volume effect, IWLC(q,L,b), where L is the chain contour length and b is the chain Kuhn length. The Kuhn length b is related to lp by 2lp = b. To account for the finite thickness of the side

(5)

where nb (= L/b) is the number of Kuhn segments. Pedersen and co-workers46 have optimized the values of the parameters q1, p1, p2, a1, and a2 by a least-squares fit of eqs 2 and 3. In this work, we use the following optimized results from the literature:46,47 q1 = 5.53, p1 = 5.33, a1 = 0.065, p2 = 3.95, and a2 = 11.7. The radius R of the polyelectrolyte chain can be calculated from the cross-sectional PDDF, R = (1/2)dc. When cylindrical scatters are considered, R = √2Rcs, which leads to Rcs = 0.85 nm. The value of the contour length estimated from the GPC result was used as the initial fitting value (L = 35 nm). Uncertain of the degree of rigidity of the polyelectrolyte chain, we first fitted the scattering curves by eq 3. However, we 2732

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could not obtain a good fitting. The solid line in Figure 9 is a fit by eq 2 for this modified model, and the fitting parameters are shown in the figure. The optimized value of the contour length is 38 nm. Rg values obtained from the fitting results are compared with those obtained from the scattering data in Table 1. It is apparent from the table that the fitting result is

were 0.1, 0.3, 0.6, 0.8, 1.0, 1.5, and 2.0 times cp were performed, when cp = 0.6 wt %, which is 13.0 mM (mmol repeat units in 1 L of water). In Figure 11a, the q* shifts toward lower q values

Table 1. Comparison of Rg Data from SAXS with the Fitting Result Based on the Modified WLC Model sample 0.3 wt % PSBSS

Rg (nm) (measured, Guinier analysis)

Rg (nm) (measured, inverse transform)

Rg (nm) (by fitting, lp = 11.50 ± 0.09 nm)

6.44 ± 0.03

6.66 ± 0.02

6.74 ± 0.06

consistent with the measured Rg, which proves the good reliability of the fitting results. According to the fitting results, the polyelectrolyte chain is highly rigid, which is determined by the “jacketed” structure of PSBSS. In addition to the steric hindrance, there is also electrostatic repulsion interaction between the neighboring side chains in MJPEs such as PSBSS. Because the charges are on both ends of the side chains, the hydrophobic part of the side chains and the main chain form the hydrophobic core of the cylinder. In a dilute polyelectrolyte solution, salt added can screen the electrostatic interaction. Figure 10 shows the SAXS profiles of

Figure 11. SAXS profiles and PDDFs of PSBSS aqueous solutions with varying ionic strengths at a fixed PSBSS concentration of 0.60 wt %.

with increasing ionic strength, which was also observed in some literatures.8,9 The peak disappears when cs/2cp ≥ 0.6. Because cp ≤ c*p , the polyelectrolyte chain is extended as shown in Figure 11b. The diameters of the cylinders are still 4 nm, the same with that of the chain in the solution without salt. However, the lengths of the cylinders (rmax values) decrease slightly, and the tails of the PDDF curves are close to a linear decay, which may be due to the screening of electrostatic repulsion between the side chains that reduces chain swelling. Figure 12 shows the Rg values obtained from Guinier analysis and the fitting results of lp by eq 1. According to the results from the Guinier plots (Figure S4 in Supporting Information), the Rg value is almost constant when cs/2cp ≤ 1. However, Rg abruptly increases when cs/2cp > 1, which indicates that the aggregation of the polyelectrolyte chains occurs because the hydrophobicity of the chains increases with increasing amount of added salt. The polyion charge is neutralized by condensed or territorially bound counterions, according to Manning.48 Theory proposed by Kuhn, Kunzle, and Katchalsky49 suggests that persistence length scales with the inverse of the square root of the salt concentration. However, OSF theory shows that the persistence length scales with the inverse of the salt concentration.50 OSF theory assumes a locally stiff chain for which electrostatic interactions can modify the bending properties. The ionic effects on the elasticity of single DNA

Figure 10. SAXS log−log profiles of PSBSS aqueous solutions with 50.0 mM NaCl. Inset shows the corresponding Kratky plots (I(q)q2 vs q).

PSBSS aqueous solutions with 50.0 mM NaCl. The polyelectrolyte peak disappears when cp < 2.00 wt % instead of cp < 0.40 wt % without salt, which is related to the restoration of the osmotic compressibility of polyelectrolyte with salt added. The conformational variation of chains in solution can be analyzed from the Kratky plot (I(q)q2 vs q), as shown in the inset of Figure 10. The data for both the 0.20 and 0.40 wt % solutions increase monotonically, indicating that the chain is dispersed in solution. However, for both the 1.00 and 2.00 wt % solutions, the curves have a hump with a peak around 1.5 nm−1. The distinct difference in the shape of the curves indicates the transition from dilute to semidilute regime. Polyelectrolyte in salt solution starts to behave as a neutral polymer. In order to explore the added salt effect on the polyelectrolyte conformation in solution, SAXS experiments on solutions with varied added salt concentrations (cs’s) which 2733

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ACKNOWLEDGMENTS

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REFERENCES

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This research was supported by the National Natural Science Foundation of China (Grants 21174006 and 20990232).

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Figure 12. Rg values from Guinier analysis and the fitting results of lp by the modified WLC model, eq 1, of PSBSS aqueous solutions with varying ionic strengths at a fixed PSBSS concentration of 0.60 wt %. Rg abruptly increases when cs/2cp > 1 due to aggregation.

molecules had been studied by Baumann and co-workers.51 Both theories cannot account for the observations in Figure 12, in which lp decreases slightly with salt added when cs/2cp ≤ 1. This discrepancy may lie in the fact that PSBSS has a well extended chain due to the “jacketing” effect, leading to a much larger contribution of the neutral chain to the persistence length than that of the electrostatic persistence length.

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CONCLUSIONS In summary, we synthesized a new kind of rodlike polyelectrolyte, PSBSS, containing a terphenyl core in the side chains via the themolysis of PBNSS. PBNSS forms a ΦH phase while PSBSS forms a SmA phase in bulk. We have performed SAXS measurements on PSBSS solutions with or without added salt. The critical overlap concentration cp* is about 0.8 wt %, which is the transition point of q* ∝ cp1/2 and q* ∝ cp1/3. In the semidilute regime, a single broad peak is observed, and q* ∝ cp1/2. q* shifts toward higher values with increasing cp and toward lower values with increasing salt concentration. In the dilute regime, the conformation of the chain is cylindrical, with the diameter and the length of 2.4 and 25 nm, respectively. The persistence length lp is 11.50 ± 0.09 nm by fitting the curves with the modified WLC model. With increasing amount of added salt, the increasing hydrophobicity of the chain leads to the aggregation while lp only decreases slightly because of the “jacketing” effect. This work paves a way to synthesizing model rodlike polyelectrolytes. Our results will be useful in understanding the behaviors of rodlike polyelectrolytes in bulk and in solution.

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S4. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Z.S.). Notes

The authors declare no competing financial interest. 2734

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