Langmuir 2004, 20, 4677-4683
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Preparation, Characterization, and Solution Viscosity of Polystyrene-block-polyisoprene Nanofiber Fractions Xiaohu Yan and Guojun Liu*,† Department of Chemistry, University of Calgary, 2500 University Drive, NW, Calgary, Alberta, Canada T2N 1N4
Hexian Li State Key Laboratory of Functional Polymer Materials for Adsorption and Separation and Institute of Polymer Chemistry, Nankai University, Tianjin, China 300071 Received January 6, 2004. In Final Form: March 15, 2004 A polystyrene-block-polyisoprene (PS-b-PI) sample with 130 styrene and 370 isoprene units was synthesized and characterized. The diblock formed mostly cylindrical micelles in N,N-dimethylacetamide with a PI core and a PS corona. The PI core of the micelles was cross-linked by S2Cl2 to yield nanofibers. The nanofibers were shortened by ultrasonication to yield fractions with weight-average length (Lw) between ∼900 and ∼3400 nm. Transmission electron microscopy and light scattering were used to characterize the fractions. The zero-shear intrinsic viscosity data [η] of the fractions were obtained in tetrahydrofuran (THF), THF/N,N-dimethylformamide (DMF), and THF/cyclohexane (CHX), where THF is a good solvent for both the corona and the core, DMF solubilizes only the corona, and CHX is a theta solvent for the corona chains at 34.5 °C. The [η] data of the fractions were treated by the Bohdanecky method derived from the Yamakawa-Fujii-Yoshizaki (YFY) theory for wormlike polymer chains and yielded the persistence length lP and the hydrodynamic diameters dh for the nanofibers. The reasonable dh values and the reasonable trend of dh variation with solvent quality change establish unambiguously the validity of YFY theory.
I. Introduction Nanoscience and technology is an interdisciplinary area of research and development activity that has been growing explosively worldwide in the past decade.1 There have been many reports on the preparation and application of nanostructures of inorganic2 and organic compounds3,4 and of block copolymers.5 In most of the current publications, the characterization of nanostructures such as nanorods and nanowires is limited to showing some microscopic images. In this paper, we report on not only the preparation of polystyrene-block-polyisoprene nanofiber fractions of low polydispersity with length varying from submicrometers to several micrometers but also the characterization of the fractions by transmission electron microscopy (TEM), light scattering (LS), and viscometry. We also report the persistence length lP and the hydrodynamic diameter dh of the nanofibers by treating the intrinsic viscosity data of the nanofibers determined in different solvents using the Bohdanecky method6 derived from the Yamakawa-Fujii-Yoshizaki (YFY) theory7,8 for wormlike polymer chains. † Present address: Department of Chemistry, Queen’s University, Kingston, Ontario, Canada K7L 3N6.
(1) National Science and Technology Council (USA) Nanostructure Science and TechnologysA Worldwide Study, 1999. (2) For reviews on one-dimensional inorganic nanostructures see, for example: (a) Lieber, C. M. MRS Bull. 2003, 28, 486. (b) Kovtyukhova, N. I.; Mallouk, T. E. Chem. Eur. J. 2002, 8, 4355. (c) Xia, Y. N.; Yang, P. D.; Sun, Y. G.; Wu, Y. Y.; Mayers, B.; Gates, B.; Yin, Y. D.; Kim, F.; Yan, H. Q. Adv. Mater. 2003, 15, 353. (3) For a review on organic nanotubes see, for example: Bong, D. T.; Clark, T. D.; Granja, J. R.; Ghadiri, M. R. Angew. Chem., Int. Ed. 2001, 40, 988. (4) For a review on soft nanomaterials see, for example: Hamley, I. W. Angew. Chem. 2003, 42, 1692. (5) (a) Liu, G. J. Curr. Opin. Colloid Interface Sci. 1998, 3, 200. (b) Lazzarr, M.; Lopez-Quintela, M. A. Adv. Mater. 2003, 15, 1583. (6) Bohdanecky, M. Macromolecules 1983, 16, 1483. (7) Yamakawa, H.; Fujii, M. Macromolecules 1974, 7, 128. (8) Yamakawa, H.; Yoshizaki, T. Macromolecules 1980, 13, 633.
Block copolymer nanofibers (BCNs) can be prepared from either cylindrical micelles9-11 formed in a blockselective solvent or block-segregated copolymer solids.12 Nanofibers are obtained in a block-selective solvent via the direct cross-linking of the core block of the cylindrical micelles.13,14 In bulk, block copolymers self-assemble forming various intricate nanometer-sized block segregation patterns. At the volume fraction of ∼30%, the minority block of a diblock normally forms hexagonally packed cylinders dispersed in the continuous matrix of the majority block.12 Nanofibers are obtained by cross-linking the minority block and separating the hairy cylinders via solvent dispersion.15-18 The polystyrene-block-polyiso(9) Price, C. Pure Appl. Chem. 1983, 55, 1563. (10) Zhang, L. F.; Eisenberg, A. Science 1995, 268, 1728. (11) Ding, J. F.; Liu, G. J.; Yang, M. L. Polymer 1997, 38, 5497. (12) For block segregation patterns see, for example: Bates, F. S. Fredrickson, G. H. Phys. Today 1999, February issue, 32. (13) (a) Tao, J.; Stewart, S.; Liu, G. J.; Yang, M. L. Macromolecules 1997, 30, 2738. (b) Stewart, S.; Liu, G. J. Angew. Chem., Int. Ed. 2000, 39, 340. (c) Liu, F. T.; Liu, G. J. Macromolecules 2001, 34, 1302. (14) Won, Y.-Y.; Davis, H. T.; Bates, F. S. Science 1999, 283, 960. (15) (a) Liu, G. J.; Qiao, L.; Guo, A. Macromolecules 1996, 29, 5508. (b) Liu, G. J. Adv. Mater. 1997, 9, 437. (c) Liu, G. J.; Ding, J.; Qiao, L.; Guo, A.; Gleeson, J. T.; Dymov, B.; Hashimoto, T.; Saijo, K. Chem. Eur. J. 1999, 5, 2740. (16) (a) Massey, J.; Power, K. N.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 1998, 120, 9533. (b) Massey, J. A.; Temple, K.; Cao, L.; Rharbi, Y.; Raez, J.; Winnik, M. A.; Manners, I. J. Am. Chem. Soc. 2000, 122, 11577. (17) (a) Yan, X. H.; Liu, G. J.; Liu, F. T.; Tang, B. Z.; Peng, H.; Pakhomov, A. B.; Wong, C. Y. Angew. Chem., Int. Ed. 2001, 40, 3593. (b) Yan, X. H.; Liu, G. J.; Liu, F. T. Macromolecules 2001, 34, 9112. (18) Templin, M.; Franck, A.; DuChesne, A.; Leist, H.; Zhang, Y. M.; Ulrich, R.; Schadler, V.; Wiesner, U. Science 1997, 278, 5344.
10.1021/la049955b CCC: $27.50 © 2004 American Chemical Society Published on Web 04/28/2004
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prene (PS-b-PI) nanofibers reported here were prepared from cross-linking PS-b-PI cylindrical micelles formed in N,N-dimethylacetamide (DMAC), which solubilizes PS and is a precipitant for PI. We have attempted a similar study with PS-b-PI nanofibers prepared from the chemical processing of a block-segregated PS-b-PI solid before.19 The nanofibers there had a relatively high polydispersity. The crosslinking reaction involving the cross-linker S2Cl2 and the PI double bonds in the solid state might not have been as uniform as it had been in a block-selective solvent. Because of these, the viscosity data there did not allow us to conclude unambiguously about the applicability of the YFY theory. We initiated this revisit because the applicability of the YFY theory may allow the presently challenging determination of the molar mass of long block copolymer nanofibers and even inorganic nanorods or nanowires to be achieved in the future by the simple viscosity experiments. In this work, we determined the intrinsic viscosity of the nanofiber fractions not only in tetrahydrofuran (THF) but also in THF/N,N-dimethylformamide (DMF) and THF/cyclohexane (CHX), where THF is a good solvent for both the corona and the core, DMF solubilizes only the corona, and CHX is a theta solvent for the corona chains at 34.5 °C.20 The hydrodynamic diameters, dh, for the nanofibers evaluated from the viscosity data decreased with DMF or CHX volume fraction φDMF or φCHX. The reasonable dh values and the reasonable trend of dh variation with solvent quality change establish unambiguously the validity of YFY theory. II. Experimental Section Materials. Unless stated otherwise all chemicals were purchased from Aldrich. Isoprene was distilled in the presence of n-butyllithium, and styrene was purified by double distillation first over CaH2 and then in the presence of benzylmagnesium chloride. Cyclohexane was refluxed over potassium and distilled before use. DMAC was dried by stirring overnight at 130 °C with BaO and then distilled under reduced pressure. Sulfur monochloride was used as received. Polymer Synthesis and Characterization. Polymer PSb-PI was prepared by living anionic polymerization in cyclohexane at 45 °C.21 Styrene and isoprene were polymerized for 4 and 17 h, individually. Polymerization was terminated by addition of degassed methanol. The diblock prepared was purified by precipitation into ethanol and dried at room temperature under vacuum. The diblock was characterized by 1H NMR, size exclusion chromatography (SEC), and light scattering (LS). SEC analysis was performed using a Styragel HT-4 broadband column (Waters) calibrated with poly(methyl methacrylate) (PMMA) or PMMA standards. The eluant used was tetrahydrofuran (THF). Light scattering was done using a Brookhaven model 9025 instrument equipped with a 632.8-nm He-Ne laser. The difference, ∆nr, between the refractive index of a diblock solution in THF and THF was determined using a differential refractometer (Precision Instruments Co.) with light that had passed a band-pass filter centered around 633 nm. The specific refractive index increments, dnr/dc, were determined from the intercept of a ∆nr/c vs c plot, where c denotes polymer concentration.22 Nanofiber Preparation and Purification. PS-b-PI, 6.12 g containing 58.5 mmol of isoprene units, was stirred in 400 mL of dry DMAC for 1 day to disperse the diblock as cylindrical (19) (a) Liu, G. J.; Yan, X. H.; Duncan, S. Macromolecules 2003, 36, 2049. (b) Liu, G. J.; Yan, X. H.; Ducan, S. Macromolecules 2002, 35, 9788. (20) Brandrup, J.; Immergut, E. H. Polymer Handbook, 3rd ed.; John Wiley & Sons: New York, 1989. (21) See, for example: Ren, Y.; Lodge, T. P.; Hillmyer, M. A. Macromolecules 2000, 33, 866. (22) Huglin, M. B. Light Scattering from Polymer Solutions; Academic Press: London, 1972.
Yan et al. micelles with PI core and PS shell. Sulfur monochloride, 1.85 mL or 23.1 mmol, was then added and stirred with the cylindrical micelles for 24 h to cross-link the PI cores. After this, the solution was diluted with THF to 700 mL and centrifuged at 2500 rpm (1100g) for 10 min to remove the insoluble gels. The supernatant was divided into six equal fractions, and the fractions were sonicated for 0, 0.75, 4.0, 14.5, 20, and 30 h, respectively, to yield fractions F1, F2, F3, F4, F5, and F6. After sonication, ∼35 vol % methanol was added into each fraction and the resultant mixture was left to stand for 1 to 2 days before centrifugation to separate the nanofibers from a trace amount of the crosslinked spherical micelles in the supernatant. The nanofibers were redispersed in THF and stirred constantly with a magnetic bar during storage. Transmission Electron Microscopy Study. To obtain the TEM images of the nanofibers, the fiber dispersions in THF were aspirated on to carbon-coated copper grids using a home-built device.23 The fibers were then stained with OsO4 vapor for 4 h before viewing by a Hitachi-7000 electron microscope operated at 75 kV. Light Scattering Studies. The dnr/dc value of the nanofibers in THF was determined following procedures used for diblock dnr/dc determination and was 0.150 mL/g. For light scattering characterization, the nanofibers at the concentration of ∼5 × 10-6 g/mL were dispensed in a vial with a special lid. The lid contained a gas inlet that was fitted with a 0.1-µm filter and an outlet that was fitted with a polyethylene tube. After the vial was centrifuged at 1550g for 30 min, it was carefully taken out of the centrifuge and secured in a clamp. Pressure was applied through a syringe connected to the filter to push out the nanofiber solution via the polyethylene tube that was suspended halfway into the nanofiber solution. After the initial portion was discarded, the middle fraction was collected in a clean cylindrical quartz cell with a diameter of 2.5 cm for light scattering measurements. A total of 19 scattering angles with an increment of 1° were used in each measurement with the lowest angle set at 12°. To ensure data precision, light intensity at each concentration was measured once in a low- to high-angle scan and another time in a high- to low-angle scan and the intensities in the two scans at each angle were then averaged. The light scattering instrument used was a Brookhaven model BI-200SM. Each sample was analyzed by light scattering at least twice, and the deviation between results from the two runs were typically less than (3%. Nanofiber Sedimentation Test. Two methods were used to check the extent of nanofiber settlement when the fiber solutions in THF were not stirred. In method 1, the scattering intensity of an unstirred F3 solution at 7.38 × 10-3 mg/mL in THF was monitored at 30° as a function of time. It was hoped that the aggregated nanofibers would settle to the bottom of the cell and stop contributing to light scattering. In method 2, two F3 samples each at 5.0 mL and at 1.03 mg/mL in THF were dispensed into two separate vials. The vials were then capped and securely wrapped with electrical tape to minimize THF evaporation. The sample in vial 1 was constantly stirred magnetically and vial 2 was allowed to remain still. After 1 week, the PS absorbance of the sample at 258 nm in vial 1 was measured before and after centrifugation at 1550g for 5 min, and the absorbances were found to be the same within experimental error. After centrifugation, the absorbance of the sample that was not stirred decreased by 6.7%. Rotational Cylinder Viscometer. A low-shear-rate rotational cylinder viscometer was built based on a design by Zimm and Crothers.24 The stationary part or the stator of the viscometer consists of a jacketed one-end-sealed glass cylinder with an inner diameter, din, of 1.24 cm. Water was allowed to circulate in the jacketed layer for temperature control. The moving part or the rotor of the viscometer is an 8.4-cm-long, one-end-sealed cylinder with an outer diameter, do, of 1.00 cm. Glued to bottom of the rotor is a steel pellet. The inner cylinder floats in the stator by its buoyancy, and its height is adjusted by the amount of Pb3O4 fixed in it by epoxy resin. The rotor is held in the center of the stator by the surface forces exerted by the testing liquid. The inner cylinder rotates relative to the stator because of a rotating (23) Ding, J. F.; Liu, G. J. Macromolecules 1999, 32, 8413. (24) Zimm, B. H.; Crothers, D. M. Proc. Natl. Acad. Sci. 1962, 48, 905.
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Table 1. Characteristics of PS-b-PI SEC Mw/Mn
dnr/dc in THF mL/g
LS Mw (kg/mol)
NMR n/m
NMR 1,4-content
n
m
1.05
0.143
39
1.00/2.8
90%
130
370
magnetic field applied at the bottom of the viscometer. Since there are no mechanical devices attached to the rotor, frictional dissipation of energy occurs in the liquid itself and the viscosity of the liquid is proportional to the time it takes for the rotor to make one circle relative to the stator. The rotor speed was adjusted by changing the size of the steel pellet in the rotor. The shear rate of the viscometer at the inner wall of the stator was estimated using25
τ)
4π/tc (do/din)2 - 1
(1)
where tc denotes the time taken for the rotor to rotate one cycle. Two rotors with the tc values of 283.41 and 490.93 s and thus the shear rates of 0.082 and 0.047 s-1 were used. Viscosity Measurements. All viscosity measurements were performed at 25.0 ( 0.1 °C. The solvents used included THF, THF/DMF at φDMF ) 50% and φDMF ) 70%, and THF/CHX at φCHX ) 40%. The nanofiber concentrations were so adjusted that the relative viscosity ηr of the most concentrated solution was around ∼1.4.
III. Results and Discussion PS-b-PI Characterization. The characteristics of the PS-b-PI sample are shown in Table 1. The diblock has a low dispersity of 1.05 based on PMMA standards. The PI block has 90% 1,4-content. The weight-average styrene and isoprene units n and m are 130 and 370, respectively. Cylindrical Micelle Cross-Linking. According to Price,9 PS-b-PI at ∼15 mg/mL with the composition shown in Table 1 should form mainly cylindrical micelles with PI core and PS shell in DMAC. This has been confirmed by our TEM results to be shown later. The PI cylindrical core was cross-linked via the following reaction:26
Because of the reaction, our elemental analysis results showed that the carbon content in the nanofibers decreased from 89.61% to 65.89% and hydrogen content decreased from 10.39% to 7.67%. In the absence of side reactions, the new C and H contents correspond to the incorporation of 0.281 and 0.277 mol of S2Cl2 per mol of isoprene unit. Since each S2Cl2 molecule reacts with two isoprene units, these values correspond to an average PI double bond conversion of 55.8%. This is in excellent agreement with the double bond disappearance rate of 59% that we determined from FTIR analysis following prcedures described prviously.27 TEM Results of the Nanofiber Fractions. Shown in panels a and b of Figure 1 are TEM images of fractions 1 and 5, respectively. The lengths of more than 500 nanofibers were measured manually for each fraction directly from such images at higher magnifications. Figure (25) See, for example, a) Elias, H. G. An Introduction to Polymer Science; VCH: Weinheim, 1997. (b) Sperling, L. H. Introduction to Physical Polymer Science; John Wiley & Sons: New York, 1992. (26) Ishizu K.; Onen, A. J. Polym. Sci., Part A: Polym. Chem. 1989, 27, 3721. (27) Liu, G. J.; Li, Z.; Yan; X. H. Polymer 2003, 44, 7721.
2 gives results of such measurements for fractions 1, 3, and 5. Similar plots were obtained for fractions 2, 4, and 6. The term P(Li) in Figure 2 is proportional to the probability of finding fibers with length between (1/2)(Li + Li-1) and (1/2)(Li + Li+1). Using the distribution data P(Li), we computed the number-average length, Ln, and weight-average length, Lw, of the fiber fractions with results shown in Table 2. Both Lw and Ln decreased with ultrasonication time as expected. The polydispersity indices Lw/Ln of the fiber fractions are between 1.19 and 1.39, which are substantially lower than those in the range of 1.36 and 1.58 found for the PS-b-PI nanofiber fractions that we prepared previously from the solid-state synthesis approach.19 We have also taken TEM images of the nanofibers at higher magnifications to estimate the PI core diameter. Analysis of 50 nanofibers yielded a TEM core diameter of 35.7 (2.8 nm. Weight-Average Mw of the Nanofiber Fractions. The light scattering data of the nanofiber solutions in THF were treated with
Kc 1 ) [1 + (1/3)q2RG2 - kq4RG4] + 2A2c ∆Rθ Mw
(2)
where c denotes nanofiber concentration, ∆Rθ is the Rayleigh ratio, A2 is the second virial coefficient, K is the optical constant of the system including terms such as the refractive index n0 of the solvent, the laser wavelength λ, and the specific refractive index increment of the nanofiber, etc., and k is a fitting constant. The term q is the scattering wave vector with magnitude given by
q)
4πn0 sin(θ/2) λ
(3)
where θ is the scattering angle. Equation 2 is valid only at low scattering angles for which
qRG/31/2 , 1
(4)
where RG denotes the z-average radius of gyration of the nanofibers. The two parts in Figure 3 show an incomplete Zimm plot for the light scattering data of F3 in the scattering angle range of 12-30°. The plot is incomplete for the limitation of the plotting program. In part a, the method for data extrapolation to zero concentration is illustrated at the scattering angles of 19, 21, and 30°. Part b shows how the extrapolated data of part a are further extrapolated to zero angle following eq 2 to yield the molar mass Mw and the radius of gyration RG. For this sample, Mw ) 4.3 × 108 g/mol and RG ) 384 nm. The data of other fractions were treated similarly with results shown in Table 2. Figure 4 plots the Mw values against Lw determined from TEM. The data follow
Mw ) 1.7 × 107 + MuLw
(5)
with the molar mass Mu of the unit-length nanofibers equal to 2.35 × 1012 g/(mol‚cm). The fact that Mw increased linearly with Lw confirms the accuracy of the LS Mw values. As mentioned above, the TEM PI core diameter is 35.7 ( 2.8 nm. Assuming that the cross-linked PI core had the same density of 0.91 g/cm3 as the un-cross-linked PI20 and making use of the weight fraction of 65% for PI, we estimated a Mu value of 8.5 × 1012 g/(mol‚cm). This is much larger than 2.35 × 1012 g/(mol‚cm) and suggests
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Figure 1. TEM images of nanofiber fractions 1 (left) and 5 (right).
Figure 2. Length distribution functions of nanofiber fractions 1 (0), 3 (b), and 5 (O) generated from TEM image analysis. Table 2. Characteristics of the PS-b-PI Nanofiber Fractions LS 10-8Mw LS LS Lw 105A2 sample (nm) Lw/Ln (g/mol) (mol‚mL/g3) RG (nm) lP (nm) F1 F2 F3 F4 F5 F6
3490 2210 1650 1300 1200 930
1.35 1.35 1.21 1.19 1.39 1.31
8.3 5.4 4.3 3.2 3.1 2.4
-2.82 -1.36 -1.55 -1.82 -1.89 -1.68
572 490 384 314 288 237
282 402 390 277 260 260
that the PI core of the nanofibers was trapped in a swollen state after their aspiration from THF. Radius of Gyration RG Data. The RG values obtained from treating the light scattering data with eq 2 are shown in Table 2 and range from 237 nm for F6 to 572 nm for F1. Since the Kc/∆Rθ vs sin2(θ/2) data were curved and treated by eq 2 containing a -kq4RG4 term, we are uncertain of the accuracy of RG values determined particularly for the longer fractions such as F1 and F2. The precision for the data was, however, good at (3%. Using the RG values thus determined, we have plotted log(RG/nm) vs log(Mw/(g/mol)) for the fractions in Figure 5. The exponent v to the scaling relation
RG ∝ Mwv
(6)
is 0.67, which is close to 0.69 found for the PS-b-PI nanofibers prepared from the solid-state synthesis approach.19a The exponent is higher than 0.60 expected
Figure 3. Zimm plot for the light scattering data of F3 in the scattering angle range of 12-30°. The solid circles represent the experimental data. The hollow circles represent the extrapolated Kc/∆Rθ|cf0 data. In part a, linear extrapolation of data to zero concentration at the scattering angles of 12, 21, and 30° is illustrated. Part b shows the result of curve fitting of the Kc/∆Rθ|cf0 data by (1/Mw)[1 + (1/3)q2RG2 - kq4RG4].
for polymer chains in a good solvent but smaller than 1.00 expected for rigid rod chains, which suggests that the nanofibers are semirigid on this length scale. The PS-b-PI nanofibers have a finite cross section. If the diameter of this cross section is small relative to their length, the fibers can be approximated as wormlike chains. For wormlike chains, the LS radius of gyration is
RG(lP) )
(
)
∑i P(Li)Li2RG2(Li,lP) ∑i P(Li)Li
2
1/2
(7)
where RG(Li,lP) denotes the radius of gyration of chains
Polystyrene-block-polystyrene Nanofiber Fractions
Figure 4. Plot of LS Mw as a function of TEM Lw for the different fractions.
Figure 5. Plot of log RG vs log Mw for the nanofiber fractions.
Figure 6. From top to bottom, plot of RG calculated from eq 7 as a function of persistence length lP for fractions 1-6, respectively.
with persistence length lP and contour length Li and is given by28
RG(L,lP) ) lp(L/3lP - 1 + (2lP/L)[1 - (lP/L)(1 - e-(L/lP))])1/2 (8) Figure 6 plots the RG(lP) values given by eq 7 as a function of lP. Checking the experimental RG values denoted by the square symbols in Figure 6 against lP yielded for the fractions lP values between 260 and 402 nm (Table 2). The large lP values suggest the fibers were indeed semirigid. The LS lP values, however, should not be overinterpreted, as they were obtained based on the unrealistic thin-fiber cross-section assumption. Furthermore, the accuracy of the RG values determined from the use of eq 2 is questionable. Second Virial Coefficient A2. Also shown in Table 2 are the second virial coefficients A2 for the nanofiber fractions, and the values are negative. Negative A2 values suggest attraction between and aggregation of the nanofibers. To confirm this, we performed two experiments. In experiment 1, the variation in the scattering intensity of an unstirred nanofiber solution at 7.38 × 10 - 3 mg/mL was monitored as a function time with results shown in Figure 7. The scattering intensity normalized relative to (28) Benoit, H.; Doty, P. J. Phys. Chem. 1953, 57, 958.
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Figure 7. Variation in the relative scattering intensity, It/I0, of F3 solutions in THF as a function of time t under stirring (9 and c ) 8.40 × 10-3 mg/mL) and no stirring (b and c ) 7.38 × 10-3 mg/mL).
that at time zero decreased initially with time and then leveled off at ∼90% after some 10 days. In experiment 2, we prepared two F3 samples at an equal concentration of 1.03 mg/mL. While one of the samples was allowed to remain still for 1 week, the other was stirred constantly. After centrifugation at 1550g for 5 min, the PS absorbance at 258 nm was compared. The absorbance of the sample that was not stirred decreased by 6.7% relative to that of the stirred sample. The fact that the nanofiber concentration decreased with time in both cases for the unstirred samples suggests the partial settlement of the fibers. While the fibers could have settled individually under the gravitational force or as bundles after aggregation, the fact that A2 is negative suggests that the fibers settled probably after aggregation. Other evidence suggesting nanofiber aggregation in an unstirred sample included the observation that the absorbance of the stirred sample in experiment 2 mentioned above did not change after centrifugation. The nanofibers, particularly the longer ones, may aggregate because the van der Waals force between the fibers increases with their length.29 The aggregated fibers may settle for their reduced buoyancy. The partial settlement of the unstirred samples prompted the question if the nanofibers were fully dispersed even under stirring. The answer to this question is partially provided by examining the TEM images of Figure 1 closely. Most of the fibers in the images are seen separate from one another. The observation of a small fraction of aggregated fibers can be accounted for by noting the possibility of nanofiber aggregation during TEM specimen preparation, which involved aspiration of nanofiber dispersion in THF onto carbon-coated copper grids. Other evidence suggesting the absence of aggregation in a stirred sample included the observation that the scattering intensity of a stirred nanofiber sample at 8.40 × 10 - 3 mg/mL did not change with time as shown in Figure 7. Furthermore, we determined that the scattering intensity of nanofibers at 90° increased linearly with nanofiber concentration in THF over the concentration range from 0.056× to 1.07 × 10-1 mg/mL. The linear dependence of the scattering intensity on concentration over such a wide range suggests that the stirred sample contained only individual fibers. If there had been an equilibrium between the fiber bundles and the individual fibers, an increase in nanofiber concentration would have led to an increased degree of fiber aggregation and a linear increase in the scattering intensity with nanofiber concentration would have been impossible. Viscosity Data. Most of the relative viscosity, ηr, data of the nanofiber solutions were measured using a rota(29) For size-dependence of van der Waals forces between different objects see, for example: Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1991; Vol. 1.
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Figure 8. From top to bottom, plot of (ηr - 1)/c vs c for nanofiber fractions 2, 3, 4, and 6 in THF. All the ηr data were obtained using the viscometer at the shear rate of 0.082 s-1 with exception to those denoted by (∆) that were obtained at a shear rate of 0.047 s-1. Table 3. Intrinsic Viscosity and Huggins Parameters of PS-b-PI Nanofiber Fractions in Different Solvents THF sample
kh
[η] (mL/g)
F1 F2 F3 F4 F5 F6
0.33 0.42 0.28 0.36 0.33 0.32
828 507 342 242 234 178
φDMF ) 0.50
φDMF ) 0.70
[η] (mL/g)
kh
[η] (mL/g)
kh
[η] (mL/g)
0.38 0.24 0.22 0.26 0.27
720 445 309 224 204
0.26 0.42 0.27 0.25 0.42
682 413 290 205 196
0.22 0.25 0.21 0.32 0.30
670 398 264 186 179
Table 4. The Ll and Lu Values at Some Relevant dr Values dr
Ll
Lu
1 × 10-2 2 × 10-2 5 × 10-2
0.4 1.0 1.0
300 400 500
A ) A0Mu/φ01/3
(11)
B ) B0Mu1/2/(φ01/3(2lP)1/2)
(12)
and
with φ0 ) 2.87 × 1023 mol-1. The A0 and B0 values in eqs 11 and 12 are functions of dr with
A0 ) 0.46 - 0.53 log dr
(13)
B0 ) 1.00 - 0.0367 log dr
(14)
and
tional viscometer at a shear rate of 0.082 s-1. Figure 8 plots (ηr - 1)/c vs nanofiber concentration c in THF. We have also obtained the (ηr - 1)/c data for F4 using a shear rate of 0.047 s-1. The fact that the (ηr - 1)/c data from the two different shear rates coincided in Figure 8 suggests that the data obtained at 0.082 s-1 approached the zeroshear viscosity [η]. The solid lines represent the best fit to the experimental data by the empirical relation25
(9)
where kh is the Huggins coefficient. Table 3 summarizes the [η] and kh results for samples thus obtained in THF, in THF/DMF at φDMF ) 50% and φDMF ) 70%, and in THF/ CHX at φCHX ) 40%. The kh values are between 0.21 and 0.42, the same as those expected for polymer chains. In a given solvent, [η] increased with nanofiber length. Treatment of Intrinsic Viscosity Data in THF. The theoretical expressions for [η] were first derived by Yamakawa and Fujii7 for wormlike polymer chains of contour length L and hydrodynamic diameter dh. The expressions were later refined by Yamakawa and Yoshizaki8 to accommodate spheroid cylinders, which are cylinders with spheroidal end caps and were complex. Bohdanecky6 determined that the YFY expressions could be cast in a much simpler form
(Mw2/[η])1/3 ) A + BMw1/2
relevant reduced hydrodynamic diameter dr values with dr ) dh/(2lP) are given in Table 4. The intercept A and slope B in eq 10 are given by
φCHX ) 0.50
kh
(ηr - 1)/c ) [η] + kh[η]2c
Figure 9. Plot of (Mw2/[η])1/2/(g/(mol2/3‚cm)) vs Mw1/2/(g/mol)1/2 for the nanofiber fractions in THF (O), in THF/DMF at φDMF ) 50% (b), and in THF/CHX at φCHX ) 40%. The solid lines represent the best fit to the experimental data by eq 10.
(10)
if Ll e Lr e Lu, where Lr, equal to L/(2lP), is the reduced contour length and Ll and Lu denote the lower and upper Lr bounds, respectively. The Ll and Lu values at some
Figure 9 plots the intrinsic viscosity data of the nanofiber fractions in THF following eq 10. Treating the data of fractions F1-F5 yielded A ) (4.44 ( 0.25) × 104 g/(mol2/3‚ cm) and B ) 1.71 ( 0.12 g1/2/(mol1/6‚cm), where the uncertainties for A and B were calculated using standard equations presented in textbooks on error analysis.30 The data of F6 were not included in the plot as the Lr value is smaller than Ll for this fraction. The A and B values together with eqs 11-14 gave lP ) 1040 ( 150 nm and dh ) 69 (18 nm (Table 5). The lP value of 1040 ( 150 nm is larger than ∼620 nm that we estimated before for PS-b-PI nanofibers prepared from the solid-state synthesis approach19 probably for the different polydispersities of the samples used. The polydispersity in samples can change the A and B values determined using eq 10 and thus introduce errors to the lP and dh values. Alternatively, the difference may be real and the nanofibers from the solid-state synthesis approach bent more because of the slightly different cross-linking densities on the two hemicylinders. As mentioned before, the cross-linking in the solid state may not be as uniform as it could have been in a block-selective solvent despite our effort in ensuring uniform cross-linking. Last, the lP can be different for the different PS-b-PI diblocks used. The dh value of 69 ( 18 nm is reasonable. As mentioned before, the PI core of the nanofibers used for TEM examination was ∼36 nm. The diameter might be larger in THF at, for example, ∼40 nm. The dh value of 69 nm thus gave a PS corona thickness of ∼14.5 nm. This is smaller than the contour length of ∼23 nm for PS chains with 130 units but larger than the root-mean-square radius of ∼8 nm of the chain in an unperturbed state by assuming Gaussian chain statistics. (30) See, for example: Christian, G. D. Analytical Chemistry, 5th ed.; John Wiley & Sons: New York, 1994.
Polystyrene-block-polystyrene Nanofiber Fractions
Langmuir, Vol. 20, No. 11, 2004 4683
Table 5. Persistence Length, lP, and Hydrodynamic Diameter, dh, of the Nanofibers Calculated from the Viscosity Data of F1-F5 in Different Solvent Mixtures solvent THF φDMF ) 50% φDMF ) 70% φCHX ) 40%
10-4A B [g/(mol2/3‚cm)] [g1/2/(mol1/6‚cm)] 4.44 ( 0.25 4.37 ( 0.21 4.51 ( 0.15 5.10 ( 0.31
1.71 ( 0.12 1.89 ( 0.10 1.91 ( 0.07 1.72 ( 0.14
dh/nm
lP/nm
69 ( 18 1040 ( 150 61 ( 18 850 ( 90 51 ( 12 830 ( 60 31 ( 15 1040 ( 170
Effect Varying Solvent Quality. The [η] data of the fractions in other solvents were treated similarly as those obtained in THF. Figure 9 shows the (Mw2/[η])1/3 data for the samples measured in THF/DMF with φDMF ) 50% and in THF/CHX with φCHX ) 40%. From such plots we obtained the slope B and intercept A and subsequently lP and dh in Table 5. Table 5 reveals that dh decreases with increasing φDMF. As mentioned before, DMF is a selective solvent for PS. Intuitively we expect that the PI core to shrink with increasing φDMF in agreement with the observed dh variation trend. Table 5 also suggests that lP decreases somewhat with increasing φDMF. This can be reasonable as well. As the core shrank, the interfacial tension between the solvent and the core increased. This higher interfacial tension would help fold the fibers to minimize the interfacial area. The full impact of this interfacial tension increase was not felt as the fibers were stabilized by PS corona chains. Furthermore, the interfacial tension acted against the elastic restoring force of the cross-linked PI cores. Table 5 further shows that dh decreased also in THF/ CHX. CHX is a theta solvent for PS at 34.5 °C.27 At 25 °C, PS of high molar masses is insoluble in CHX. A decrease in dh with increasing CHX content is thus expected. What surprises us is the magnitude of dh decrease in this case. While a more thorough and detailed examination is required for this abnormality, we suspect that some aggregation, either static or dynamic in nature, of the nanofibers might have taken place in THF/CHX. Although the aggregation did not exhibit any visual consequence such as nanofiber precipitation within days, the aggregation or partial aggregation might have been sufficient to change the viscosity behavior and thus the resultant dh value.
Comparison between lP from the LS and Viscosity Data. The lP value from the viscosity data in THF is substantially higher than those estimated from the LS data. This is in agreement with the trend that we observed before for the lP results of the nanofibers prepared from the solid-state synthesis approach.19 While we do not know the exact reason for the discrepancy, we tend to trust the lP values derived from the viscosity data. This is so because we made an unrealistic assumption that the fibers had a negligible cross-section diameter when estimating the lP values from the LS RG. Then, the RG values could be in error because the Kc/∆Rθ vs sin2(θ/2) data were curved and eq 2 containing the kq4RG4 term was used to fit the data. IV. Conclusions PS-b-PI nanofibers with relatively low polydispersity were obtained from cross-linking cylindrical micelles of the diblock formed in the block-selective solvent DMAC. The fibers were ultrasonicated to yield shorter fractions. The fractions were characterized by TEM and light scattering. The linear dependence of LS Mw on TEM Lw suggests the validity of the LS Mw data. The LS RG data scaled with Mw with exponents typical for wormlike chains, suggesting the semiflexibility of the nanofibers. The fact that the [η] data in different THF/DMF mixtures could be treated by the Bohdanecky method quantitatively to yield reasonable dh values proves the validity of the YFY theory unambiguously. The validity of the YFY theory should allow its use in the future for the determination of molar masses of longer nanofibers for which the LS technique fails. The viscosity characterization technique may be generalized also to inorganic nanowires and nanorods in solvents. Acknowledgment. NSERC of Canada is gratefully acknowledged for sponsoring this research and NSF (29928003) of China is acknowledged for covering H. X. Li’s travel to Calgary. Dr. Zhao Li prepared the polymer used in this study and his contribution is also gratefully acknowledged. LA049955B
