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Notes Colloidal Nature of Single-Walled Carbon Nanotubes in Electrolyte Solution: The Schulze-Hardy Rule Masahito Sano,* Junko Okamura, and Seiji Shinkai Chemotransfiguration Project, JST, 2432 Aikawa, Kurume, Fukuoka 839-0861, Japan Received May 9, 2001. In Final Form: August 2, 2001
Dispersing single-walled carbon nanotubes (SWNTs) in solution are highly desirable for performing efficient chemical modifications and forming composite materials.1-4 It is also useful for spreading SWNTs on solid surfaces and isolating a single SWNT from bundles. Commercially available pristine SWNTs, however, are too long to be dispersed in most solvents and have no well-defined functional groups to modify.5,6 A standard procedure calls for cutting of pristine SWNTs by ultrasonication in strong acids.1 Shortened SWNTs are further etched in H2SO4/ H2O2 to introduce oxygen-containing groups at both ends. The resulting SWNTs can be dispersed relatively well in water or N,N-dimethylformamide. Despite great improvement of dispersing ability by these acid treatments, it is easily seen that SWNTs in these solvents form a kinetically stable dispersion. This colloidal behavior poses various complications for further treatments. In general, numerous forces, such as van der Waals, electrostatic, hydration, steric, hydrophobic, and other chemically specific interactions, are known to act between colloidal particles in solution.7 Geometrical shapes of particles also couple strongly with these interactions. So far, practically nothing is known about structures and interactions of SWNTs in solution. It thus becomes important to understand the colloidal nature of SWNTs in these dispersions. In aqueous systems, electrolyte ions are known to coagulate certain colloidal sols. It is well-known that the critical coagulation concentration (ccc), the minimum concentration of ions necessary to cause rapid coagulation of colloids, follows the Schulze-Hardy rule8,9
ccc ∼ (1/z)n where z is the valency of the electrolyte counterions. * Corresponding author. E-mail:
[email protected]. Fax:+81942-39-9012. (1) 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. (2) Chen, J.; Hamon, M. A.; Hu, H.; Chen, Y.; Rao, A. M.; Eklund, P. C.; Haddon, R. C. Science 1998, 282, 95. (3) Sano, M.; Kamino, A.; Okamura, J.; Shinkai, S. Science 2001, 293, 1299. (4) Liu, Z.; Shen, Z.; Zhu, T.; Hou, S.; Ying, L.; Shi, Z.; Gu, Z. Langmuir 2000, 16, 3569. (5) Ausman, K. D.; Piner, R.; Lourie, O.; Ruoff, R. S.; Korobov, M. J. Phys. Chem. B 2000, 104, 8911. (6) Bahr, J. L.; Mickelson, E. T.; Bronikowski, M. J.; Smalley, R. E.; Tour, J. M. Chem. Commun. 2001, 193. (7) Israelachvili, J. N. Intermolceular and Surface Forces; Academic: London, 1992. (8) Schulze, H. J. Prakt. Chem. 1882, 25, 431. (9) Hardy, W. B. Proc. R. Soc. London 1900, 66, 110.
Figure 1. Normalized concentrations of SWNTs against NaCl concentrations.
Typically, n is 6 in three dimensions (3D)10 and 9 in two dimensions.11 According to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory,12 the Schulze-Hardy rule results from interplay between van der Waals attraction and electric double-layer repulsion. Thus, confirming that a system follows the Schulze-Hardy rule gives us deep insight into the interactions between colloidal particles.7 SWNTs were purchased from Tubes@Rice and had an average diameter of 1.2 nm. After the standard acid treatments,1 SWNTs were washed on a Teflon filter with pure water until the filtrate was neutral. Large aggregates of SWNTs were removed by centrifuging at 1500g in water, to minimize errors in the initial concentration. Electrophoresis light scattering (ELS-800, Otsuka Electronics), analyzed assuming spherical geometry, yielded a ζ-potential of -12 mV. Although the stringlike shape of SWNTs may require correction to its magnitude, it can be still inferred that SWNTs are anionically charged in water and the colloidal stability is low. All electrolytes are supplied as chloride salts in the form of XClz, where X ) Na+, K+, Mg2+, Ca2+, La3+, and Ce3+. After rinsing with water, shortened SWNTs were divided into several portions of equal amounts. Each portion of SWNT was ultrasonicated (60 s in a laboratory ultrasonic cleaner, 42 kHz, 90 W) in electrolyte solutions. The concentration of SWNTs initially added to the solution was 0.6 mg/mL. The dispersion was left undisturbed for 12 h at room temperature. It was centrifuged at 3500g, and the concentration of SWNTs in the supernatant solution was determined by measuring the absorbance.13 The absolute amount of SWNTs in the solution depended on the strength of centrifugation and the initial concentration of SWNTs. It also depended on a batch of SWNTs that had been treated with the acids. As long as the same conditions were applied to obtain the supernatant solutions and the SWNTs from the same batch of acid (10) Overbeek, J. Th. G. Pure Appl. Chem. 1980, 52, 1151. (11) Sano, M.; Kamino, A.; Shinkai, S. J. Phys. Chem. B. 2000, 104, 10339. (12) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the stability of lyophobic colloids; Elsevier: Amsterdam, 1948. (13) We have constructed a calibration curve for the absorbance at 350 nm and the dispersed amount (mg/mL). For the low concentrations of SWNTs that have been treated here, they were linearly related.
10.1021/la010698+ CCC: $20.00 © 2001 American Chemical Society Published on Web 10/02/2001
Notes
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Table 1. Critical Coagulation Concentrations (ccc) for Various Ions ions ccc (mM)
Na+ 37
K+ 26
Mg2+ 0.31
Ca2+ 0.20
La3+ 0.050
Ce3+ 0.052
treatments were used for the entire range of concentrations, plots of the dispersed amounts against the ion concentration could be reduced to a single curve by normalizing the dispersed amounts with a value at a very low ionic concentration. Figure 1 displays such a curve for Na+. It is clear that the coagulation takes place rapidly once the ion concentration exceeds a threshold value. All other ions produced a similar curve shape. We take the concentration at which the normalized dispersed amount becomes 0.5 as ccc. Table 1 summarizes the ccc for all ions. These values are typical of inorganic particles. They are double-logarithmically plotted against the ionic valency in Figure 2. Clearly, ccc is inversely related to z. Furthermore, they lie very close to the straight line with a slope of -6. Thus, SWNT dispersions follow the 3D Schulze-Hardy rule. While the present study offers a clear experimental demonstration of the Schulze-Hardy rule, the exponent of 6 gives rise to the next question. It is well-known that both van der Waals and electric double-layer interactions depend on the exact geometry of colloidal particles. An analytical solution in DLVO theory has been obtained only in the case of spherical particles and gives n ) 6. We know that SWNTs in a vacuum or air take a stringlike shape when they are observed by various microscopic techniques. The present samples also have broad size distributions (in both lengths and diameters by bundle
Figure 2. Double logarithmic plot of the critical coagulation concentrations against the ionic valency. The solid line has a slope of -6.
formations as well) of SWNTs. Thus, either these geometrical conditions happen to produce the same exponent as the solid sphere case, or an individual SWNT has been collapsed to a spherelike aggregate before ccc is reached. Further works are necessary to clarify these points. In any case, the present result indicates that the interactions between SWNTs in electrolyte solution, when the ionic concentration is close to ccc, can be reduced to a simple model of solid spheres with van der Waals and electric double-layer interactions. On practical sides, it is important to keep the salt concentrations far below ccc if chemical reactions with higher efficiency or mixing with other reagents are desirable. LA010698+
