The rheology and modeling of chemically treated carbon nanotubes suspensions

Abstract

This paper reports recent experimental findings and rheological modeling on chemically treated single-walled carbon nanotubes ͑CNTs͒ suspended within an epoxy resin. When a CNT suspension was subject to a steady shear flow, it exhibited a shear-thinning characteristic, which was subsequently modeled by a Fokker-Planck ͑FP͒ based orientation model. The model assumes that the shear flow aligns CNT in the flow direction, but there are events such as Brownian motion and tube-tube interaction trying to randomize the orientation. In the FP orientation model, randomizing events were modeled with an appropriate rotary diffusion coefficient ͑D r ͒ and the shear-thinning behavior was explained in terms of progressive alignment of CNTs toward the shear direction. In terms of linear viscoelasticity ͑LVE͒, small-amplitude oscillatory measurements revealed mild elasticity for semidilute treated CNT suspensions. The exact origin for this elasticity is not clear and both tube-tube interaction and bending/stretching of CNTs have been proposed by other authors as possible origins. It is, however, clear from the current modeling that the experimental evolution of storage modulus ͑GЈ͒ cannot be described using a single-mode Maxwell model or simple Brownian rod modeling. In this paper, experimental LVE data of the treated CNT suspensions were fitted using the FP orientation model with an "effective diffusion coefficient" term and an empirical relation was subsequently identified for the effective diffusion term. Intuitively, chemical treatment has created a weakly interconnected network of CNT and it is believed that the mild elasticity originated from this weak network as well as other randomizing events ͑Brownian motion and tube-tube hydrodynamic interaction͒. Finally, step strain experiments confirmed the presence of a weak network at small strains, which at large strains was found to be destroyed. Incorporation of a strain softening factor allowed for the formulation of a 1 self-consistent FP based orientation model describing both the steady shear and LVE responses of treated CNT suspensions.

On the role of standard and anomalous diffusion in suspensions of rigid rods

“…Thus, the loss modulus is found to scale linearly with the frequency ω of the applied oscillation in agreement with the experimental findings [21], however, the storage modulus G is expected scaling at small frequencies with ω 2 instead of ω 0.6 reported in [21], where authors propose the scaling D r ∝ ω p to control the slope of G (ω).…”

“…Thus an exponential decay for a and the shear stress τ is expected from the model, however a power-law behaviour is observed experimentally, as reported in [21].…”

“…Linear viscoelastic -LVE -analysis were carried out in [21] to suspensions consisting of functionalized CNTs. LVE involves small amplitude oscillations applied to an essentially isotropic suspension (a iso ≈…”

In-Situ Structural Characterization of Single-Walled Carbon Nanotubes in Dispersion

“…The observed oscillation frequency independent storage modulus G' and loss modulus G'' allow the author to infer the presence of SWCNT network structures in the dispersion. The network structure is formed by the physical association of the SWCNT rods, and the bonding energy responsible for the association is as high as ~ 40 k B T. The similar viscoelastic behavior studies were performed for the SWCNT dispersion in epoxy (Ma et al, 2009) and in unsaturated polyester (Kayatin & Davis, 2009). These polymeric resin based dispersion system presents a strong elastic response at relatively high volume fraction of SWCNTs, which also signifies the formation of SWCNT networks.…”

Thermal Conductivity of Suspension of Aggregating Nanometric Rods

“…The modeling of such aggregates requires the consideration of kinetic models at the meso-scale accounting for the flow induced aggregation/disaggregation mechanisms [20]. As soon as these particles are functionalized in order to avoid aggregation mechanisms, no aggregates are observed at the resolvable scales, and standard models developed for addressing dilute suspensions work well for describing their main rheological features [21].…”