Anisotropy of Sheared Carbon-Nanotube Suspensions D. Fry, 1 B. Langhorst, 1 H. Kim, 2 E. Grulke, 3 H. Wang, 4 and Erik K. Hobbie 1, * 1 National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 2 Department of Chemistry, Kyunghee University, Yongin, Kyungkido, 449-701, Korea 3 Department of Chemical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA 4 Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931, USA (Received 21 July 2004; published 15 July 2005) We measure the anisotropy of sheared carbon-nanotube suspensions for a broad range of concentration, aspect ratio, and strain rate using a variety of methods. Our measurements highlight the importance of excluded-volume interactions in the semidilute regime, with scaling in terms of a dimensionless shear rate. Our results also suggest that such interactions might be exploited to fractionate carbon nanotubes by length in simple shear flow. DOI: 10.1103/PhysRevLett.95.038304 PACS numbers: 82.70.2y, 47.55.Kf, 61.46.+w Carbon nanotubes exhibit remarkable physical proper- ties and there is considerable interest in using them as nanoscale building blocks for a new generation of materi- als and applications [1–6]. Despite this promise, funda- mental issues related to the dispersion, fractionation, orientation, and manipulation of individual nanotubes re- main unresolved and efficient bulk processing schemes do not exist. Single-walled carbon nanotubes (SWNTs), for example, have strong van der Waals attractions that inhibit nematic ordering in surfactant-stabilized suspensions [7], and routes to liquid crystallinity have thus far required volume compression [7] or dispersion in superacid solvents [8]. Multiwalled carbon nanotubes (MWNTs) are easier to disperse, but flow instabilities related to mechanical entan- glement hinder processibility [9] and the tubes must be shortened considerably to achieve a nematic phase [10]. In light of these issues, establishing routes to proficient processing will depend in part on a detailed understanding of the response of carbon-nanotube dispersions to changes in such parameters as composition, temperature, aspect ratio, and shear stress. In this Letter, we use a variety of methods to measure the anisotropy of sheared carbon- nanotube suspensions over the entire semidilute regime. Our measurements highlight the importance of excluded- volume interactions, with scaling over a broad range of reduced strain rate, or Peclet number. Our results also suggest how these interactions might be exploited to frac- tionate carbon nanotubes by length in simple shear flows. SWNTs synthesized via the high-pressure catalytic de- composition of carbon monoxide (HiPCO) were obtained commercially. They were purified through thermal oxida- tion at 260  C, refluxing in HCl solution, and ultrasonica- tion in nitric acid. Suspensions were made by sonicating purified SWNTs in 0.6% by mass sodium dodecylbenze- nesulfonate (SDBS) D 2 O solution, which has been shown to be an effective means of preparing stable aqueous SWNT dispersions [11]. After cold ultrasonication for 10 h, the tubes exist in suspension as SWNT ropes. Atomic-force microscopy (AFM) of dried films gave a mean diameter d of 13.5 nm and a mean length L of 0:75 m (L=d  60). Further processing led to less de- tectable anisotropy in shear flow. We focus on 0.08% and 0.16% SWNT by mass, with cL 3  1:7 and 3.5, respec- tively, where c is the number of tubes per unit volume. The shear viscosity is   1 mPa s, and we denote these sus- pensions S1. The MWNTs were grown via chemical vapor deposition (CVD). Electron microscopy gave d  50 nm and the mean length was determined optically to be L  10 m (L=d  200). The length distribution is nearly log-normal with a polydispersity of 2. They were suspended in low- molecular-mass polyisobutylene (PIB) fluids as described elsewhere [9,12]. We use two PIB fluids; an elastic Boger fluid (M w  800 with 0.1% M w  4:7  10 6 ,  0  10 Pa s) and a Newtonian fluid (M w  500,  0  0:5 Pa s). Suspensions in the former, which we denote M1, were prepared at 0.1% to 0.8% MWNT by mass, with cL 3  24 to 200. Suspensions in the latter, which we denote M2, were prepared at 0.025% to 0.85% MWNT by mass, with cL 3  6 to 210. For both M1 and M2,  is comparable to the solvent viscosity,  0 . For all suspensions, 0:01 <cL 2 d< 1, with our measurements spanning the semidilute regime [13]. We consider linear shear flow along ^ x, with a constant velocity gradient along ^ y and vorticity along ^ z. The shear rate is _   @v x =@y and we probe structure in the x-z plane at 25  C, with pure surfactant suspensions showing negli- gible anisotropy. Birefringence, dichroism, and  were measured simultaneously as a function of _  in a 200 m gap parallel-plate optical shear cell with a 670 nm diode laser. A modulated linear polarization with a lock-in tech- nique was used to extract n 0 and n 00 , the real and imaginary parts of the difference between the largest and smallest eigenvalue of the complex refractive-index tensor in the x-z plane [14]. For S1, small-angle neutron scatter- ing (SANS) measurements were performed on the 8 m SANS instrument at the NIST Center for Neutron Research using a 0.5 mm gap Couette shear cell, with a PRL 95, 038304 (2005) PHYSICAL REVIEW LETTERS week ending 15 JULY 2005 0031-9007= 05=95(3)=038304(4)$23.00 038304-1  2005 The American Physical Society