Abstract
This paper reports recent experimental findings and rheological modeling on chemically treated single-walled carbon nanotubes (CNTs) 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 (FP) 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 (Dr) and the shear-thinning behavior was explained in terms of progressive alignment of CNTs toward the shear direction. In terms of linear viscoelasticity (LVE), 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...
Highlights
Carbon nanotubesCNTsare cylinders of rolled graphite sheets possessing high mechanical strength, low density, and special electronic propertiesIijima1991͒; Dresselhaus and Dai2004͔͒
This study aims to derive a simple constitutive model for chemically treated CNT suspensions and for this reason, tube–tube interaction is represented using an effective diffusion coefficient and CNT-polymer interaction is neglected in our current system where the suspending matrix is made up of small prepolymer molecules
Dr1 is the base diffusion coefficient accounting for randomizing effects, such as Brownian motion and tube–tube interaction, and was determined to be 0.005 s−1 in fitting the orientation model to steady shear experimental data; Dr2 is the diffusion coefficient corresponding to a weak network of CNT that is only present at small strain. ͑␥͒ is a function which approaches 1 at a very small strain and equals to 0 for an applied strain␥͒ larger than a critical strain␥cthat destroys the network
Summary
Laboratoire de Mécanique des Systèmes et des Procédés, 151 Boulevard de l’Hôpital, 75013, Paris, France. 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. 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, clear from the current modeling that the experimental evolution of storage modulusGЈcannot be described using a single-mode Maxwell model or simple Brownian rod modeling. 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 eventsBrownian motion and tube–tube hydrodynamic interaction. Incorporation of a strain softening factor allowed for the formulation of a self-consistent FP based orientation model describing both the steady shear and LVE responses of treated CNT suspensions
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