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Technical Highlights in Nanotechnology
 

Elastic Flow Instability in Polymer-Dispersed Carbon Nano-tubes
 
Novel composites engineered from polymers and carbon nanotubes offer the promise of plastics with enhanced thermal, electronic, and mechanical properties, but the ability to control and quantify particle dispersion in such materials is an unresolved issue of fundamental importance. Of particular interest is how processing flows influence tube dispersion and orientation. We are developing metrologies and methods that directly address the fundamental nature of elastic flow instabilities in polymer-dispersed carbon nanotubes, enabling better control of dispersion during flow processing of melts and suspensions.
 
Erik K. Hobbie
 
The clustering of small spherical particles has been studied extensively in a broad range of systems. In contrast, relatively little is known about the flocculation of asymmetrical particles, such as platelets, rods, or fibers. Given the current interest in dispersing anisotropic nanoparticles in organic materials to enhance physical properties, a deeper understanding seems warranted. An almost universal aspect of aggregation is inter-particle attraction, but external hydrodynamic forces, often used to disperse such particles, can alone induce clustering in highly anisotropic suspensions, creating unique challenges and issues relating to the flow processing of such materials.
 
We recently observed an elastic instability associated with flow-induced clustering in polymer dispersed carbon nanotubes. Kinetic measurements under varied confinements and shear stresses were compared with simulations of flocculation in flowing fiber suspensions, and we found an intriguing rheological signature consistent with highly elastic domains. Small-amplitude oscillatory shear measurements reveal this extraordinary elasticity, with homogenized semi-dilute suspensions showing gel-like behavior at long time scales. The data suggest that the underlying instability may in fact be universal to a number of flowing complex fluids, with important implications for the flow processing of polymer-carbon nano-tube composites.
 
Multi-walled carbon nanotubes (MWNTs) were grown via chemical vapor deposition. A typical electron micrograph is shown in the inset to Fig. 1(a). Based on such measurements, the mean diameter is d =50 nm. Due to their length and optical contrast, individual MWNTs are discernable in optical micrographs of 25x or higher, and from 200x images of thin-film dispersions, the mean length is L = 12 µm. The suspending polyisobutylene fluid (PIB) is Newtonian over a broad range of shear rates, with a shear viscosity of 10 Pas at 25 °C. Dispersions are prepared by dissolving the PIB in sonicated MWNT-toluene suspensions, which are stirred continuously as the solvent is removed. Suspensions of primary interest contain 1.7 x 10-3 mass-fraction MWNT in PIB and are semi-dilute, with " 45 and " 0.19, where n is the number of tubes per unit volume. The tubes in PIB are non-sedimenting over the time scales in question.
 
Figure 1: (a) Optical micrograph of MWNTs in a quiescent PIB dispersion. The inset (width = 1.3 mm) is an SEM image of the MWNTs before dispersion in PIB. (b) Optical micrograph 30 min after quenching the mixture to a shear rate of = 0.03 s<sup>-1</sup>. The flow (x) direction is horizontal. (c) Optical micrograph 2 h after the quench. (d) Optical micrograph 15 min after quenching the sample in (c) to = 10 s<sup>-1</sup>.
Figure 1: (a) Optical micrograph of MWNTs in a quiescent PIB dispersion. The inset (width = 1.3 µm) is an SEM image of the MWNTs before dispersion in PIB. (b) Optical micrograph 30 min after quenching the mixture to a shear rate of ro= 0.03 s -1. The flow (x) direction is horizontal. (c) Optical micrograph 2 h after the quench. (d) Optical micrograph 15 min after quenching the sample in (c) to = 10 s-1.
 
Optical microscopy (5x to 25x) is used to observe the motion of MWNTs and the formation of aggregates under shear, with flow along the x-axis, a constant velocity gradient along the y-axis, and vorticity along the z-axis. Measurements are taken in the x-z plane. The sample is confined between two parallel quartz plates separated by a variable gap, . The upper plate rotates at an angular speed that sets the shear rate, r = ðvx/ðy, at a fixed point of observation in the middle of the plates. A controlled-strain rheometer in cone-and-plate and parallel-plate configurations provides steady and oscillatory shear measurements of the rheology. All measurements were performed at 25 °C.
 
The aggregates have 'melted' and the redispersed tubes broadly orient with the direction of flow, as evident in the light-scattering pattern (inset Fig. 1(d), scale bar = 1 µm-1). The scale bar is 10 mm and the gap (h) is 70 µm.
 
Under weak shear, the tubes form macroscopic domains consisting of diffuse MWNT networks. Figure 1 shows optical micrographs of (a) a quiescent dispersion, (b & c) aggregation at ro= 0.03 s-1, and (d) redispersed MWNTs after dissolution at rm = 10 s-1, where light scattering reveals a steady-state distribution of orientations broadly peaked around X. In simple shear, the long axis of an isolated rod rotates around Z with a period, T, that scales as r-1. In semi-dilute suspensions, hydrodynamic interactions determine the distribution of such orbits. The Peclet number is less than 10-4, implying that hydrodynamic forces overwhelm Brownian forces.
 
Figure 2: Evolution of a confined dispersion (upper), where the micrographs have been converted to binary images. The lower images are the corresponding c(r). The flow direction is horizon-tal, the vorticity axis is vertical, and the red scale bar (125 µm) applies to all six images. As in Fig. 2, h = 70 µm. The inset to the lower left image is its FFT (width = 1.2 µm<sup>-1</sup>), which gives the ubiquitous 'butterfly' pattern.
Figure 2: Evolution of a confined dispersion (upper), where the micrographs have been converted to binary images. The lower images are the corresponding c(r). The flow direction is horizontal, the vorticity axis is vertical, and the red scale bar (125 µm) applies to all six images. As in Fig. 2, h = 70 µm. The inset to the lower left image is its FFT (width = 1.2 µm-1), which gives the ubiquitous 'butterfly' pattern.
 
By varying h, we observe the transition from bulk to confined growth. To quantify the latter, we convert micrographs into binary images in which the clusters are black and the surrounding fluid white (upper images, Fig. 2), defining a coarse composition field a function. Ensembles at each annealing time, t, are used to compute the two-point correlation function,an equation (lower images, Fig. 2), and the steady-state morphology diagram in the h - r plane is shown in Fig. 3. In region A, moderate aspect ratio domains exhibit broad vorticity alignment. In region S, these domains coarsen along Z into macroscopic striped patterns. The dashed curve marks a region of 'metastability' in which the striped pattern is transient.
 
Recent simulations of flow-induced flocculation in non-Brownian fiber suspensions suggest that inter-particle friction leads to aggregation in the absence of attractive interactions, particularly at low shear stress and high fiber stiffness. The MWNT bending modulus can be compared with values for typical organic fibers, as can the shape of the inter-particle potential and coefficient of friction. Our measurements are in agreement with simulation. With an elastic bending modulus 103 times larger than that of a typical fiber, the MWNTs are flexible enough to exhibit shape deformation, yet they readily entangle and inter-lock to form large coherent structures under weak shear. Held together by elastic forces, the diffuse clusters store sizeable energy, which we infer from linear viscoelastic measurements of the storage modulus, G'(w), as a function of n. Other unusual features, such as a negative first normal stress difference, are currently under in-depth investigation.
 
Figure 3: The measured late-t 'pattern diagram' in the plane for the semi-dilute, non-Brownian MWNT-PIB suspensions of interest, with homogeneous (H), aggregated (A), and 'striped' (S) regions as indicated.
Figure 3: The measured late-t 'pattern diagram' in the h-r plane for the semi-dilute, non-Brownian MWNT-PIB suspensions of interest, with homogeneous (H), aggregated (A), and 'striped' (S) regions as indicated.
 
We have observed the early-time domain pattern [Fig. 2 (left), weak minima in ] in a host of flowing complex fluids, including polymer blends, semi-dilute polymer solutions, physical polymer-clay gels, and thixotropic clay gels, all of which fall within the simple paradigm of weakly interacting elastic domains suspended in a less viscous fluid. The homogenized semi-dilute dispersions also exhibit solid-like behavior at long timescales, suggesting the presence of a weak 'network' or gel, further reminiscent of other systems that exhibit this type of flow-induced macrostructure. The role of confinement in the growth of periodic structures in these systems is intriguing and merits detailed computational consideration. We expect that these issues will have direct consequences for the processing of nanocomposite melts, and we are currently extending these measurements to single-walled carbon nanotubes.
 

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E. K. Hobbie, S. Lin-Gibson, J. Pathak (Polymers Division, NIST); H. Wang (Michigan Tech); E. Grulke (University of Kentucky)
 
 
 
 
 
 
 
 
 
 
NIST Material Science & Engineering Laboratory - Polymers Division