Steady Shear Response of Carbon Nanotube Networks Dispersed in Poly(ethylene oxide) Tirtha Chatterjee † and Ramanan Krishnamoorti* Department of Chemical and Biomolecular Engineering, UniVersity of Houston, Houston, Texas 77204-4004 ReceiVed March 23, 2008; ReVised Manuscript ReceiVed May 20, 2008 ABSTRACT: The response of fractal networks of dispersed single walled carbon nanotubes in poly(ethylene oxide) to continuous constant-rate shear flow is examined as functions of shear rate and nanotube concentration. The steady shear viscosity values are strong functions of shear rate and follow a power-law shear-thinning character, while the nanotube concentration dependence of the viscosity (at a fixed shear rate) is somewhat weaker than the scaling of the equilibrium modulus values. For dispersions with nanotube concentrations corresponding to the semidilute regime, the stress response to constant-rate continuous shear from rest demonstrates a stress maximum that decays to a steady value at long times. The stress maximum and steady shear behavior can be reconciled in terms of the changing structure at the mesoscale for the fractal networks. On the other hand, the transient development of the stress during the start-up experiments can be qualitatively reconciled in the context of a cluster dynamics model. I. Introduction Efficient dispersion of nanoparticles in polymer matrices can potentially lead to the development of advanced materials with unique properties and competitive manufacturing cost that are similar to the processing of the original polymers. 1–4 Single walled carbon nanotubes (SWNTs) with their remarkable set of intrinsic properties 1 are outstanding nanoparticles to incor- porate in polymer nanocomposites. 3,5 Despite this promise, the successful dispersion of nanotubes has remained a significant challenge in the production of SWNT-based polymer nanocom- posites. 4 To overcome this problem, nanotubes are dispersed either as chemically functionalized moieties 6 or with the aid of surfactants acting as compatibilizers. 7 In a well-dispersed nanocomposite, the large aspect ratio of the nanotubes and their short-range attraction lead to the formation of a solidlike material with a network structure at relatively low nanotube loading (the onset of which is referred to as the percolation threshold, p c , in vol %, without necessarily satisfying all the criteria of percola- tion). 3 This network superstructure, along with the ability to transfer stress from the continuous polymer matrix to the nanotube network, is responsible for the significant improvement of the nanocomposite mechanical properties. 2 In fact, as has been demonstrated previously, for nanocomposites with nano- particle loadings well in excess of the percolation threshold the fractal nanotube network dominates the linear viscoelastic response. 2,8 More interestingly, under constant rate steady shear these nanocomposites demonstrate non-Newtonian behavior similar to a range of complex fluids such as emulsions, pastes, and slurries. 9 In particular, the shear stress (σ) response to a constant shear rate (γ ˙ ) demonstrates the presence of an yield stress (σ y ), and the system flows like a power law fluids beyond that stress. Nevertheless, the underlying length and time scales that determine the flow properties, beyond the yield stress, are yet to be fully understood. Further, an understanding of the network deformation as a function of the particle concentration and the shear rate will lead to a significant improvement in the processing of such nanocomposites. Previous studies related to the rheology of nanotube suspen- sions have examined SWNT suspensions in aqueous 10 or superacid 11 media. In those studies the shear viscosities of the nanocomposites were measured as functions of shear rate and of nanotube loading and associated with either the intrinsic properties of the nanotubes at low concentrations or their collections as liquid crystalline domains at high concentrations. Recently, Hobbie and co-workers 8 explored the yield and flow behavior following yield for suspensions of multiwalled nano- tubes (MWNTs) dispersed in a low-molecular-mass fluid (polyisobutylene (PIB)) at intermediate concentrations, where they form a fractal superstructure, under controlled strain and controlled stress conditions. Kharchenko and co-workers have reported the flow-induced properties of MWNTs network in polypropylene matrix where significant shear thinning and more importantly large and negative normal stress difference were observed. 12 The negative normal stress differences result in die-contraction properties and presumably arise from the large- scale deformation of the network and the local deformation of nanotubes under shear. In the present study we report the nonlinear viscoelastic properties of networks of SWNTs 2,3 dispersed in poly(ethylene oxide) (PEO) under shear. For this system the geometrical percolation threshold (p c ) is found to be ∼0.09 vol % with an effective anisotropy (R) of the percolating members being ∼650. 13 Semidilute concentrations of the nanotubes, 3.0 e p/p c e 8.0, are selected for this work. The merit of this selection is to ensure a fully developed network (which does not occur for p/p c < 3) while not exceeding the critical loading required for inherently nematic structure formation. 2,9 A representative optical microscopy image of the dispersion in the melt state of the polymer (T ) 80 °C) is shown in Figure 1a and demonstrates a homogeneous dispersion primarily consisting of small ag- gregated clusters or flocs. The overall mass fractal dimension of the network is found to be 2.3 ( 0.2. 2 A small- and ultrasmall-angle neutron scattering study revealed at least a two- level structural hierarchy where inside the flocs individual or small nanotube bundles overlap each other to form a relatively dense mesh. 3 A schematic of the hierarchical network structure showing different length scales is presented in Figure 1b. With increasing nanotube loading, the network becomes denser and the mesh size () decreases following a scaling relation ( ∼ (p - p c ) -0.35(0.04 ), but the average floc size (R) is found to be largely independent of the particle concentration and ∼4 µm. On the other hand, the total number of flocs (N) increases with * To whom correspondence should be addressed. † Current address: Materials Research Laboratory, University of Cali- fornia, Santa Barbara, CA 93106. 5333 Macromolecules 2008, 41, 5333-5338 10.1021/ma800640w CCC: $40.75  2008 American Chemical Society Published on Web 06/18/2008