Modeling interactions in carbon nanotube suspensions: Transient shear flow (original) (raw)
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Rheological modeling of carbon nanotube suspensions with rod–rod interactions
AIChE Journal, 2013
To explain the shear‐thinning behavior of untreated carbon nanotube (CNT) suspensions in a Newtonian matrix, a new set of rheological equations is developed. The CNTs are modeled as rigid rods dispersed in a Newtonian matrix and the evolution of the system is controlled by hydrodynamic and rod–rod interactions. The particle–particle interactions is modeled by a nonlinear lubrication force, function of the relative velocity at the contact point, and weighted by the contact probability. The stress tensor is calculated from the known fourth‐order orientation tensor and a new fourth‐order interaction tensor. The Fokker‐Planck equation is numerically solved for steady simple shear flows using a finite volume method. The model predictions show a good agreement with the steady shear data of CNTs dispersed in a Newtonian epoxy matrix as well as for suspensions of glass fibers in polybutene,1 demonstrating its ability to describe the behavior of micro‐ and nanoscale particle suspensions. © 2...
The rheological modelling of carbon nanotube (CNT) suspensions in steady shear flows
International Journal of Material Forming, 2008
This paper is concerned with the rheological modelling of both chemically treated and untreated carbon nanotube (CNT) suspended in a Newtonian epoxy resin. CNT suspensions generally exhibited shear-thinning characteristic-the apparent viscosity decreases as shear rate increases-when subject to steady shear flows. Chemically treated CNT suspensions with little optical microstructure were found to exhibit a less significant shear-thinning effect compared with untreated CNT suspensions where clear optical aggregates were observed. In the case of treated CNT suspensions, the shear-thinning characteristic could be described using a Fokker-Planck based orientation model. The model assumed that the treated CNTs behaved as high aspect ratio rods and that shear flow was able to align the CNTs in the flow direction, thereby resulting in a decrease in the shear viscosity. Despite the success in describing the rheological response of treated CNT in steady shear flows, the orientation model failed to explain the more pronounced shear-thinning effect observed in untreated CNT suspensions having a hierarchy of aggregate structures. A new model called the aggregation/orientation (AO) model was formulated by modifying the Fokker-Planck equation. The AO model considered elements of aggregation as well as CNT orientation and it was capable of capturing the steady shear response of untreated CNT suspensions.
Rheological modeling of carbon nanotube aggregate suspensions
Journal of Rheology, 2008
This paper reports the application of a recently developed filament stretching protocol for the study of the extensional rheology of both treated and untreated carbon nanotubes (CNT) suspended within an epoxy resin. It was experimentally observed that filaments formed by treated and untreated CNT suspensions behaved differently after initial stretching. The filament thinning process of the base epoxy was consistent with a simple Newtonian fluid, whilst the filament of treated CNT suspensions also thinned in a Newtonian way but with an enhanced extensional viscosity. Filaments formed with untreated CNT suspensions behaved in a non-uniform way with local fluctuation in filament diameter, and it was not possible to obtain reliable extensional viscosity data. Irregularity of the untreated CNT filaments was consistent with coupled optical images, where spatial variation in CNT aggregate concentration was observed. In the case of treated CNT suspensions, the enhanced extensional viscosity was modelled in terms of the alignment of CNTs in the stretching direction, and the degree of alignment was subsequently estimated using a simple orientation model.
The rheology and modeling of chemically treated carbon nanotubes suspensions
Journal of Rheology, 2009
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 a͒
Elongational and shear rheology of carbon nanotube suspensions
Rheologica Acta, 2009
Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids-castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel-Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel-Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel-Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.
A review of the microstructure and rheology of carbon nanotube suspensions
2008
The present review is concerned with the way that the incorporation of carbon nanotubes (CNTs) into a fluid matrix can modify the microstructure and rheology of the resulting suspensions. Some background to CNT manufacture and in particular methods of dispersing them into a suspension is presented for a range of different systems, where effective dispersion of CNTs remains a delicate and open issue. Steady shear, linear viscoelasticity, nonlinear viscoelasticity and extensional responses are classified for a range of different CNT/ matrix combinations together with their associated microstructure. The rheological modelling of certain CNT/matrix systems is reviewed, with particular attention given to the authors' work on modelling CNT suspension behaviour using Fokker-Planck advection-diffusion modelling.
Journal of Rheology, 2011
This paper analyzes the effect of flow history on the linear viscoelastic properties of suspensions of multiwalled carbon nanotubes in an epoxy as well as the evolution of the suspension microstructure under small deformations for different concentrations and temperatures. The effect of the flow history on the microstructure is interpreted in the light of the variation of the rheological percolation threshold, which is shown to increase with the pre-shear rate. After cessation of the shear flow, the storage modulus increased with time revealing the build-up of the structure. By decreasing the pre-shear rate, the resulting storage modulus increased and the relative increase of the storage modulus with respect to the pre-shear rate was more pronounced at lower concentrations. The rate of increase in the storage modulus drastically increased with the concentration and temperature, while its variation with respect to the pre-shear rate depended on the concentration. In dilute suspensions, it decreased dramatically by increasing the rate of pre-shear, revealing a slower structure build-up while it remained almost intact in more concentrated suspensions. The increase in kinetics of structure build-up with temperature suggests the importance of Brownian forces in the absence of flow regardless of concentration or applied pre-shear rate.
Shear Relaxation Behaviour in Linear Regime of Diluted Carbon Nanotube Suspensions
2011
Carbon nanotubes (CNT) are very long cylinders formed by rolled-up graphene sheets at the nano scale. In addition to their unique structure, interest for CNTs is based on their impressive physical properties [1]. CNTs have been envisaged as component-material in a large range of applications: electrical circuits, nano-probes for near-field microscopes, high-resolution gas-molecules detectors, drug and gene delivery systems, highstrength fibres and high-performance polymer-based composites. A large number of envisaged applications require dissolving CNTs and processing them in liquid phase. Control of those forming processes needs a deep understanding of the rheology of CNT suspensions [2]. In that context, this work tackles the modelling of the rheological behaviour of dilute and low semi-dilute suspensions of treated CNTs into a Newtonian solvent. CNTs have an important influence on the viscous behaviour of their suspensions. For example, dilute and low semi-dilute suspensions of t...
Dispersion rheology of carbon nanotubes in a polymer matrix
Physical Review B, 2006
We report on rheological properties of a dispersion of multiwalled carbon nanotubes in a viscous polymer matrix. Particular attention is paid to the process of nanotubes mixing and dispersion, which we monitor by the rheological signature of the composite. The response of the composite as a function of the dispersion mixing time and conditions indicates that a critical mixing time t * needs to be exceeded to achieve satisfactory dispersion of aggregates, this time being a function of nanotube concentration and the mixing shear stress. At shorter times of shear mixing t Ͻ t * , we find a number of nonequilibrium features characteristic of colloidal glass and jamming of clusters. A thoroughly dispersed nanocomposite, at t Ͼ t * , has several universal rheological features; at nanotube concentration above a characteristic value n c ϳ 2 -3 wt. % the effective elastic gel network is formed, while the low-concentration composite remains a viscous liquid. We use this rheological approach to determine the effects of aging and reaggregation.