In Situ Measurements of Nanotube Dimensions in Suspensions by

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In Situ Measurements of Nanotube Dimensions in Suspensions by Depolarized Dynamic Light Scattering Ste´phane Badaire, Philippe Poulin, Maryse Maugey, and Ce´cile Zakri* Centre de Recherche Paul Pascal - CNRS, Av. Schweitzer, 33600 Pessac, France Received April 9, 2004. In Final Form: July 22, 2004 We show that the dimensions of carbon nanotubes (CNTs) in suspension can be characterized by depolarized dynamic light scattering. Taking advantages of this in situ technique, we investigate in detail the influence of sonication procedures on the length and diameter of CNTs in surfactant solutions. Sonication power is shown to be particularly efficient at unbundling nanotubes, whereas a long sonication time at low power can be sufficient to cut the bundles with limited unbundling. We finally demonstrate the influence of CNT dimensions on the electrical properties of CNT fibers. Slightly varying the sonication conditions, and thereby the suspended nanotube dimensions, can affect the fibers conductivity by almost 2 orders of magnitude.

The properties of materials comprised of carbon nanotubes (CNTs) are expected to strongly depend on the nanotube dimensions or on that of their bundles. For example, the percolation threshold in a composite should decrease with increasing the anisotropy of the nanotubes.1 Mechanical reinforcement and strain transfer efficiency in composite materials should also be favored with long and thin tubes or bundles.2-4 By contrast shorter tubes can exhibit a rich chemistry and be more suitable for applications such as molecular electronic devices.5,6 From a general point of view, the fabrication of CNT materials such as composites, coatings, films, and fibers require their dispersion in a solvent or a polymeric matrix. These materials commonly exhibit a large variability of properties that are often not at the expected level. Difficulty in reproducing the results is still a major hindrance for the standardization and development of nanotube materials. We argue that a possible reason for this large variability is the lack of control of nanotube length and diameter in their dispersions. It is also of great interest to have information about the length and diameter of nanotubes to better understand the thermodynamical and rheological behavior of their dispersions. As recently shown,7,8 CNT solutions can exhibit liquid crystalline ordering and rich rheological behavior, which is expected to depend on the tube or bundle aspect ratio. In this letter, we show that the dimensions of CNTs in their dispersed state can be measured via depolarized dynamic light scattering (DDLS). This technique consists of analyzing the time fluctuations of the light scattered * Corresponding author. E-mail: [email protected]. Tel.: +33 5 56 84 56 60. Fax: + 33 5 56 84 56 00. (1) Balberg, I.; Binenbaum, N.; Wagner, N. Phys. Rev. Lett. 1984, 52, 1465. (2) Thostenson, E. T.; Chou, T.-W. J. Phys. D: Appl. Phys. 2003, 36, 573. (3) Cox, H. L. Br. J. Appl. Phys. 1952, 3, 72. (4) Cadek, M.; Coleman, J. N.; Ryan, K. P.; Nicolosi, V.; Bister, G.; Fonseca, A.; Nagy, J. B.; Szostak, K.; Be´guin, F.; Blau, W. J. Nano Lett. 2004, 4, 353. (5) Liu, J.; Rinzler, A. G.; Dai, H.; Hafner, J. H.; Bradley, R. K.; Boul, P. J.; Lu, A.; Iverson, T.; Shelimov, K.; Huffman, C. B.; RodriguezMacias, F.; Shon, Y.-S.; Lee, T. R.; Colbert, D. T.; Smalley, R. E. Science 1998, 280, 1253. (6) Yudasaka, M.; Zhang, M.; Jabs, C.; Iijima, S. Appl. Phys. A 2000, 71, 449. (7) Song, W.; Kinloch, I. A.; Windle, A. H. Science 2003, 302, 1363. (8) Davis, V. A.; Ericson, L. M.; Parra-Vasquez, A. N. G.; Fan, H.; Wang, Y.; Prieto, V.; Longoria, J. A.; Ramesh, S.; Saini, R. K.; Kittrell, C.; Billups, W. E.; Adams, W. W.; Hauge, R. H.; Smalley, R. E.; Pasquali, M. Macromolecules 2004, 37, 154.

by optically anisotropic particles subjected to Brownian motion in a solvent of a given viscosity. Considering this motion in terms of translational and rotational diffusion, the dimensions of the particles can be determined. The used model to interpret the data considers the anisotropic character of the translational diffusion coefficients and the fact that the nanotube length is on the order or larger than that of the light wavelength. We give in this letter the details of the used model and the analysis conditions which can in our opinion be generalized to all types of CNT dispersions. As previously observed by direct imaging techniques such as atomic force microscopy (AFM) or scanning electron microscopy (SEM), we confirm that the dispersion conditions, via sonication and high shear mixing, can strongly affect the tube dimensions by unbundling and cutting the nanotubes.9-11 Nevertheless, by contrast with imaging techniques, DDLS does not need the drying of the dispersion. This is a significant advantage for dispersions that contain a high-molecular-weight solvent or dispersants that cannot be easily removed upon drying. More importantly, by contrast with imaging techniques, the statistics is larger and the measurements are performed faster. We believe that these advantages can make DDLS a highly valuable technique for the development and standardization of materials made from CNTs. To illustrate the efficiency of the technique and the importance of nanotube dimensions, we show in this letter that slight variations of the sonication conditions can significantly affect the conductivity of fibers made from the same batch of CNTs. Fibers prepared with exactly the same tubes and chemicals can exhibit conductivity differences by almost 2 orders of magnitude. We also show that DDLS can simply provide important information about the distributions of diameters and lengths of CNT bundles. It allows comparisons of sonication time and power effects. Sonication power is shown to be particularly important to unbundle CNTs. However, a long sonication time at low power can be sufficient to cut the bundles with limited unbundling. We hope that these examples and more generally the (9) Ausman, K. D.; O’Connell, M. J.; Boul, P.; Ericson, L. M.; Casavant, M. J.; Walters, D. A.; Huffman, C.; Saini, R.; Wang, Y.; Haroz, E.; Billups, E. W.; Smalley, R. E. AIP Conf. Proc. 2001, 591 (1), 226. (10) Islam, M. F.; Rojas, E.; Bergey, D. M.; Johnson, A. T.; Yodh, A. G. Nano Lett. 2003, 3, 269. (11) O’Connell, M. J.; Bachilo, S. M.; Huffman, C.; Moore, V. C.; Strano, M. S.; Haroz, E.; Rialon, K. L.; Boul, P. J.; Noon, W. H.; Kitrall, C.; Ma, J.; Hauge, R. H.; Weisman, R. B.; Smalley, R. E. Science 2002, 297, 593.

10.1021/la049096r CCC: $27.50 © 2004 American Chemical Society Published on Web 10/26/2004

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analysis procedures described in this letter can be helpful to the future development of CNT applications. For the experiments reported here, single wall carbon nanotubes (SWNTs) made by the HiPCO process (Carbon Nanotechnologies, Inc., batch #R0217) are purified12 to remove free iron catalytic particles. All the sonication experiments are performed in a dispersion of 4 cm3 that contains 0.3 wt % nanotubes and 1 wt % sodium dodecyl sulfate (SDS, Fluka ref. 71727, assay g99%) in milli-Q water, filtrated two times on a 0.22-µm membrane. The dispersions are obtained using a Branson homogenizer, Sonifier model S-250A associated to a 13-mm step disruptor horn and a 3-mm tapered microtip, operating at a 20-kHz frequency. This allows the power and the sonication time to be precisely adjusted. Cooling the samples in a water-ice bath prevents the suspension from overheating. Homogeneity of the dispersions is then checked by optical microscopy. For each sonication power applied, only one sample is used, so that the effect of the sonication time is always applied to the same starting dispersion. The light scattering experiments are performed at 20 °C with 1.7 × 10-3 wt % nanotube suspensions, by diluting the 0.3 wt % dispersions with milli-Q water filtrated two times on 0.22-µm membranes. We checked that diluting the dispersions again down to a concentration of 8.5 × 10-4 wt % does not have any influence on the light scattering experiments. These experiments are carried out using a Coherent Innova 90 krypton ion laser operating at λ ) 647.1 nm and Plaser ) 70 mW and a Brookhaven BI-9000AT digital autocorrelator to compute the scattered photons time autocorrelation function (ACF). Finally, the samples are equilibrated 2 weeks before any measurement, to allow big dust particles possibly present to sediment. We have checked by performing experiments at different laser powers that reproducible results could only be obtained when Plaser is weaker than 150 mW. At higher power, we believe that the diffusion of the nanotubes is affected by uncontrolled thermal convection because of their strong light absorption. Under typically 150 mW, such effects are not observed and the results do not depend on the laser power. To illustrate the importance of the nanotube dimensions on the properties of nanotube materials, we have spun fibers using a particle coagulation process already described in the literature.13 The same batch of SWNTs, purified HiPCO #R0217, and the same chemicals have been used in the following spinning conditions: temperature, 22 °C; concentrations of the tube dispersion, 0.3 wt % SWNTs and 1 wt % SDS; concentration of the coagulating solution, 5 wt % poly(vinyl alcohol) 72 000 g‚mol-1. However, different homogenization procedures have been used to prepare the nanotube dispersions. We have used again sonication but also high shear mixing, with a Silverson mixer L4RT at 9000 rpm, before sonicating the samples. High shear mixing allows the nanotube powder to be finely split in the solution so that lower sonication times are needed to obtain homogeneous and spinnable dispersions. We have then measured the electrical resistivity of the fibers at room temperature using a four gold wires setup associated to a Keithley 2000 multimeter. Many studies on rodlike and optically anisotropic rigid molecules, most of the time in the limit of short size and low aspect ratio,14 have been reported in the literature. In the case of CNTs, their length L is much larger than

Letters

the inverse of the scattering wavevector q-1, where q ) (4πnr/λ) sin(θ/2) with nr being the refractive index of the medium, λ the wavelength of light, and θ the scattering angle. Consequently, to describe these long, rigid, and optically anisotropic macromolecules in solution, we use the model developed by Maeda and Saitoˆ.15,16 The time ACF of the number of photons counted by the detector, C(t), is related to the time autocorrelation function of the scattered field gVH(t) by the following relation:14

[

|gVH(t)|2

]

C(t) ) 〈np〉 1 + f(A) |gVH(0)|2 2

where 〈np〉 is the average number of photocounts directly measured from the total count rate and f(A) is a spatial coherence factor depending on the optics of the detection system, which can be determined by a fit to the experimental data. The function G(t) ) |gVH(t)|2/|gVH(0)|2, which is used to fit our data, is given in Supporting Information. This function is a combination of exponential terms with only two free parameters for a monodisperse system: L the length and d the diameter of the tubes or bundles. The particle concentration and β, their optical anisotropy (difference between the indexes for propagation of light parallel or perpendicular to the tube axis), appear only in a prefactor. We do not need to know this factor quantitatively to fit the data. The diffusion coefficients D|t and D⊥t , associated to the translational motion parallel or perpendicular to the tube axis, and the rotational diffusion coefficient Dr which is introduced in gVH(t) are themselves only functions of L and d. The exponential terms of the form exp{-[(q2Dt + mDr)t]R} include m, an integer which is a function of n, the order of the spherical harmonics used to describe the diffusive motion of rodlike particles.15,16 The higher the order the more accurate the description. In our case no variation in the analysis could be observed above n ) 8. Because no new parameter is added to the model when n is increased, all the fits have been performed well above this limit with n ) 12. We stress that simpler models have been tested but could not correctly fit the experimental data. Because our systems are polydisperse, we artificially introduce a third parameter in our fit, a coefficient R, to stretch the exponential terms. This procedure is commonly used for classical dynamic light scattering when the ACF is broadened by the polydispersity of a given system.17 For long rigid rodlike particles in solution, the translational and rotational diffusion coefficients can be expressed in terms of the rod length L and the rod diameter d by using the Broersma’s equations18-20

D|t )

kBT (σ - γ|) 2πη0L Dt ) Dr )

D⊥t )

kBT (σ - γ⊥) 4πη0L

kBT (σ - γ) 3πη0L 3kBT

(σ - δ⊥) πη0L3

where η0 is the viscosity of the solvent, (12) Chiang, I. W.; Brinson, B. E.; Huang, A. Y.; Willis, P. A.; Bronikowski, M. J.; Margrave, J. L.; Smalley, R. E.; Hauge, R. H. J. Phys. Chem. B 2001, 105, 8297. (13) Vigolo, B.; Penicaud, A.; Coulon, C.; Sauder, C.; Pailler, R.; Journet, C.; Bernier, P.; Poulin, P. Science 2000, 290, 1331.

(14) Berne, B. J.; Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology and Physics; Dover: NewYork, 2000. (15) Maeda, H.; Saitoˆ, N. J. Phys. Soc. Jpn. 1969, 27 (4), 984. (16) Maeda, H.; Saitoˆ, N. Polym. J. 1973, 4 (3), 309.

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σ ) ln(2L/d) γ)

γ | + γ⊥ 2

γ| ) 0.807 + 0.15/σ + 13.5/σ2 - 37/σ3 + 22/σ4 γ⊥ ) -0.193 + 0.15/σ + 8.1/σ2 - 18/σ3 + 9/σ4 δ⊥ ) 1.14 + 0.2/σ + 16/σ2 - 63/σ3 + 62/σ4 By inserting these formulas in gVH(t), only three parameters (L, d, and R) are needed to analyze the data. As a consequence, each ACF can be fitted with a nonlinear least-squares fitting (NLSF) routine, which leads to the direct determination of the length L and the diameter d of the nanotubes. We study the effect of sonication time ts and power P on the dimensions of nanotubes dispersed in surfactant solutions. Each sample, for a given set {P, ts} of experimental parameters, is characterized at five different scattering angles (θ ) 30, 50, 90, 110, 120°), arbitrarily chosen within the limits of the experimental setup. The superposition of the ACFs obtained at constant sonication power, for different sonication times, is presented in Figure 1. This representation directly shows the influence of sonication on the size of the nanotubes and qualitatively agrees with previous studies.9-11 The relaxation time clearly decreases with the sonication time, which means that the size of the nanotubes is decreased. Exactly the same analysis can be used for the influence of the sonication power at constant sonication time. By increasing the sonication power, the relaxation time is decreased. As also shown in the example of Figure 2, the data can be well fitted by the used model. As a consequence, the length L and the diameter d of the SWNT bundles can be extracted from each function by using a NLSF routine. The variation of L and d as a function of the sonication time (at constant power) is represented in Figure 3a,b.We point out that the determination of L and d can vary with the wavevector. This is shown in Figure 4a,b with the values obtained at different q. For a monodisperse system, the size determination should not vary with q. The experimental variations observed in our case reflect the polydispersity of the nanotubes. We propose to use this effect to define limits of the nanotube size distribution, as shown in the bars of Figure 3a,b. In a polydisperse system, larger particles have generally a greater contribution to the total scattered intensity at small q, whereas the contribution of smaller particles is expected to become dominant at large q.14 Here, it is of great interest to note that the contribution of long and thin nanotube bundles (large anisotropy ratio) are observable at a small wavevector, whereas short and thick bundles (small anisotropy ratio) are dominating at large q. By doing experiments at several scattering angles, it is, thus, possible to measure an average size and also obtain qualitative information on the distribution. Ranging from L = 2.3 µm and d = 40 nm at ts ) 30 min to L = 1.1 µm and d = 12 nm after 2 h of sonication, the values, reported in Table 1, seem to be in reasonable agreement with the aspect ratio generally reported in the literature.4,5,9,10 When increasing the sonication power, the length and the diameter of the tubes decrease more quickly. Moreover, we note that the size distribution (17) Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80. (18) Broersma, S. J. J. Chem. Phys. 1960, 32, 1626. (19) Broersma, S. J. J. Chem. Phys. 1960, 32, 1632. (20) Broersma, S. J. J. Chem. Phys. 1981, 74, 6989.

Figure 1. ACFs measured at a scattering angle θ ) 30° for tubes dispersed with P ) 20 W and ts ) 30, 45, 60, 90, and 120 min. G(t) ) |gVH(t)|2/|gVH(0)|2. Inset: zoom of the ACFs.

Figure 2. ACF measured at a scattering angle θ ) 30° for tubes dispersed at P ) 20 W and ts ) 30 min. The solid line represents the fit of the data by the theoretical model described in the text.

becomes sharper with increasing the sonication time and power. Recently, we have characterized by DDLS isolated CNTs in suspension.21 The results agree with the electron microscopy and Raman spectroscopy investigations undertaken by Izard et al.21 on the same samples. We remark that a quantitative crosscheck with AFM or SEM could be interesting; unfortunately, it is difficult because the statistics with direct imaging techniques is more limited. This study thus shows that slight variations of the sonication conditions can significantly affect the nanotube dimensions and their polydispersity in suspension. To illustrate the importance of the nanotube dimensions on the properties of nanotubes materials, we have also undertaken the study of the resistivity of fibers spun from different suspensions. The homogenization procedures are slightly different from those presented in Table 1, but the results reported in Table 2 still clearly show their influence on the fiber resistivity. The optimization of the nanotube dimensions, by reducing the sonication time and power, (21) Izard, N.; Riehl, D.; Anglaret, E. Unpublished results. The authors provided us with a suspension of isolated CNTs (SWNTs MER Corp.). The tubes in this suspension, obtained after a high power sonication (500 W, 15 min) followed by a centrifugation at 120 000g for 4 h,11 have been investigated through electron microscopy (TEM, SEM) and Raman spectroscopy. The diameter measured by these techniques is 1.38 nm. We experimentally measure with DDLS L ) 402 ( 24 nm and d ) 2.3 ( 0.4 nm. Keeping in mind that DDLS provides the hydrodynamic diameter of the particles, we can conclude that a very good agreement is obtained between both techniques. Indeed, the difference of 0.9 nm in the diameter can be reasonably attributed to the SDS layer adsorbed on the surface of the nanotubes.22 We finally note that, in addition to the fact that dynamic light scattering confirms the presence of isolated CNTs in the suspension, it also provides, in contrast with the other techniques, their average length at the same time. (22) Richard, C.; Balavoine, F.; Schultz, P.; Ebbesen, T. W.; Mioskowski, C. Science 2003, 300, 775.

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Letters

Figure 3. (a, b) Variation of the length L and the diameter d of the SWNT bundles as a function of the sonication time (at constant power, P ) 20 W). (See text for the explanations concerning the distribution size bars.)

Figure 4. (a, b) Variation of the average measured length L and diameter d of the SWNT bundles as a function of q. Table 1. Influence of Sonication Time and Power on the Dimensions of CNT Bundles sonication power 20 W

40 W

sonication time (min)

length (nm)

diameter (nm)

15 30 45 60 90 120

2286 ( 948 1494 ( 163 1368 ( 30 1208 ( 121 1146 ( 187

40.6 ( 28.6 29.6 ( 17.6 21.4 ( 10.7 13.9 ( 3.0 12.1 ( 2.5

length (nm)

diameter (nm)

1156 ( 192 926 ( 155

37.9 ( 5.4 30.7 ( 6.5

863 ( 38 895 ( 34 822 ( 83

9.7 ( 3.0 3.8 ( 1.1 2.9 ( 0.7

Table 2. Influence of the Homogenization Conditions on the Electrical Resistivity of SWNTs Fibers at Room Temperature high shear mixer (min)

sonication power (W)

sonication time (min)

resistivity (Ω‚cm)

20 20 20 Ø

20 20 20 40

5 10 15 120

0.4 4.5 14 32.1

lead to an improvement of the fiber conductivity by almost 2 orders of magnitude. For severe sonication conditions, and thereby short tubes, the fiber resistivity is about 32.1 Ω‚cm. In contrast, more gentle conditions lead to longer tubes and a fiber resistivity of only 0.4 Ω‚cm. Fibers spun from long and thick bundles, thus, exhibit a much lower resistivity. We believe that the electrical conductivity of CNT materials is mainly limited by defects and contacts between nanotube bundles. Indeed, we think that large and facetted bundles induce less resistive and fewer contacts in the fiber compared to short and thin bundles. This could explain why fibers made of long and thick nanotube bundles exhibit a lower resistivity.

One of the main reasons in the interest toward CNTs is their potential for the production of high-performance materials. The present results illustrate the critical importance of controlling the length and the diameter of CNTs for electrical properties in fibers. Nevertheless, other properties such as mechanical, actuation, or sensing properties of fibers, films, and composites are also expected to be strongly influenced by these factors. DDLS, using an appropriate model in the conditions presented in the manuscript, allow in situ measurements of the dimensions of suspended nanotubes. It can, thus, become a highly valuable technique for the standardization of the suspensions and the development of future nanotubes applications. We think that this technique could also be extended to other anisotropic particles such as non-CNTs or nanowires. Acknowledgment. We are grateful to E. Freyssingeas for helpful discussions and complementary light scattering experiments realized at a different wavelengths. We also thank F. Nallet for enlightening comments and N. Izard and E. Anglaret for providing us with isolated CNT suspensions and helpful discussions about Raman spectroscopy. Supporting Information Available: Listings of parameters used. In this file, all parameters follow the international system of units (SI). We point out that q is the wavevector and has to be changed with each scattering angle, a1 corresponds to qL where L is the length of the nanotubes, a2 corresponds to d, the diameter of the nanotubes or bundles, a3 corresponds to R, R0 is the rotational diffusion coefficient, Dt is the translational diffusion coefficient, and y is G(t) ) |gVH(t)|2/|gVH(0)|2, the function used to fit our data. This material is available free of charge via the Internet at http://pubs.acs.org. LA049096R