Rheological percolation threshold

Composites with filler concentrations close to the percolation threshold exhibit conductivity which is sensitive to compressive deformation, since this brings the metal particles into contact, thereby forming percolation pathways. This sensitivity has been exploited especially in anisotropic composites. These are made by prealigning the metal particles with either electric or magnetic fields. This alignment is identical with that produced by external fields in electro- and magneto-rheological fluids where at a critical field continuous threads of... 

At low concentration of the second polymer, blends have dispersed-phase morphology of a matrix and dispersed second phase. As the concentration increases, at the percolation threshold volume fraction of the dispersed pase, ([) = 0.16, the blends structure changes into co-continuous. Full co-continuity is achieved at the phase inversion concentration, ( ). The morphology as well as the level of stress leads to different viscosity-composition dependencies (for more details see Chapter 7. The Rheology of Polymer Alloys and Blends ). 

The blend produced by in situ growth presents a low percolation threshold and therefore the same rheologic properties as the matrix. In addition, this technique Creates blends with a very high reproducibility of radioelectric properties due to the growing process by itself... 

The latter contribution is the most sensitive to concentration, sharply increasing above the percolation threshold, (pxpp. Experimentally, was determined by plotting low-frequency G values versus clay content. At

rheological behavior was observed, whereas above it, (p xpp, the behavior was solidlike. The stress overshoot at startup increased with clay loading and deformation rate, and it was scaled by strain. Similarly, the stress overshoot after a rest period in the intercalated CPNC also scaled with strain hence, the randomizing Brownian motion has a small effect on the behavior of these systems. 

Khalkhal and Carreau (2011) examined the linear viscoelastic properties as well as the evolution of the stmcture in multiwall carbon nanotube-epoxy suspensions at different concentration under the influence of flow history and temperature. Initially, based on the frequency sweep measurements, the critical concentration in which the storage and loss moduli shows a transition from liquid-like to solid-like behavior at low angular frequencies was found to be about 2 wt%. This transition indicates the formation of a percolated carbon nanotube network. Consequently, 2 wt% was considered as the rheological percolation threshold. The appearance of an apparent yield stress, at about 2 wt% and higher concentration in the steady shear measurements performed from the low shear of 0.01 s to high shear of 100 s confirmed the formation of a percolated network (Fig. 7.9). The authors used the Herschel-Bulkley model to estimate the apparent yield stress. As a result they showed that the apparent yield stress scales with concentration as Xy (Khalkhal and Carreau 2011). 

PCL/PLA 70/30 MWCNT and carboxylic MWCNT PCL phase and interface Unfunctionalized MWCNT is located exclusively in the PCL phase, while carboxylic MWCNT is located in the PCL phase and at the interface. The reinforcing and compatibilization effect of nanotubes results in a higher improvement in electrical conductivity and mechanical properties compared to pure blend. Improved phase stability and lower rheological and electrical conductivity percolation threshold were observed Wu et al. 2009... 

Penu C, Hu G-H, Fernandez A, Marchal P, Choplin L (2012) Rheological and electrical percolation thresholds of carbon nanotube/polymer nanocomposites. Polym Eng Sci 52 2173 Pike GE, Seager CH (1974) Percolation and conductivity a computer study. I. Phys Rev B 10 1421... 

Relaxation in Nanocomposites. At concentrations above the percolation threshold polymer/nanoparticle interactions dominate the viscoelastic terminal behaviour of polymer nanocomposites. As has been reported for phenoxy based nanocomposites [8], the analysis of tan 5 relaxation at low frequencies constitutes a reliable rheological method to investigate the strength of phenoxy/nanoclay interactions. Moreover, since coordinates ((o)Max (tan 5)Max)) reflect the blocking effect of nanoparticles on polymer chains, the dependence of (o)Max with nanoparticles volume fraction can be used in the percolation equation X=Xq (volume fraction threshold [Pg.69]

The comparatively high rheological percolation threshold (between 10 and 15 wt%) observed for this particular PEEK/CNF system (Fig. 7.5) is in agreement with studies on similar systems but is much higher than that... 

The Winter and Chambon criterion was adopted to define the critical rheological gel point (i.e. the percolation threshold at the formation of an incipient continuous network of infinite molecular weight). This condition is marked where a power-law variation of G and G viscoelastic moduli with a is obeyed, hence G (co) G (co) cd, and irrespectively of o, tan 5 (=G"/G )... 

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