Blends percolation

Figure 20.3. Comparison of the predicted Young s moduli of binary multiphase materials with morphologies best described by the aligned lamellar fiber-reinforced matrix model (Equation 20.1), the blend percolation model (Equation 20.2), and Davies model for materials with fully interpenetrating co-continuous phases (Equation 20.3). The filler Young s modulus in Equation 20.1 was assumed to be 100 times that of the matrix, and calculations were performed at Af=10, At-=100 and Af=l()00 to compare the effects of discrete filler particles with differing levels of anisotropy. It was assumed that E(hard phase)=100, pc=0.156 and (3=1.8 in Equation 20.2. For...

Figure 41. The percolation threshold determination for polymer blends undergoing the phase separation. Minority phase volume fraction, fm, is plotted versus the Euler characteristic density for several simulation runs at different quench conditions, /meq- = 0.225,..., 0.5. The bicontinuous morphology (%Euier < 0) has not been observed for fm < 0.29, nor has the droplet morphology (/(Euler > 0) been observed for/m > 0.31. This observation suggests that the percolation occurs at fm = 0.3 0.01.

Porosity characteristics also influence the degradation rate of blends containing intact starch grains. Amylase removal of starch from these films was not highly correlated with starch content, since films whose starch content was above possible "percolation thresholds" (6) were degraded at very different rates when starch content was not very different (Table I). 

The electrical conductivity of two-phase, incompatible polymer blends containing carbon black has been shown to depend on the relative affinity of the conductive particles to each of the polymer components in the blend, the concentration of carbon black in the filler-rich phase, and the structural continuity of this phase [82]. Hence, by judicious manipulation of the phase microstructure, these three-phase filled composites can exhibit double percolation behaviour. 

Typical pharmaceutical blends separate from each other by three common mechanisms sifting/percolation, air entrapment (fluidization), and particle entrapment (dusting). 

Because the conductive filler is located into a single component of the blend, these materials show an onset in the electrical conductivity at very low filler loadings of 2-3%. These findings have been explained by a double percolation effect. The CNT filled blends show superior mechanical properties in the tensile tests and in impact tests (25). 

The fusion temperature of these polymers is low enough to allow the spinning of fibres and melt pressing of films 263). They can also be blended with normal thermoplastics such as polystyrene or polyethylene oxide)2711. The conductivity shows a percolation threshold of about 16% which is expected for a random distribution of conducting spheres. 

According to the theoretical considerations, the following phase morphologies are expected for PPE/SAN blends (1) PPE contents below the percolation limit of around 19wt% (according to Utracki [46] SAN matrix, PPE fully dispersed,... 

The number of PPE particles dispersed in the SAN matrix, i.e., the potential nucleation density for foam cells, is a result of the competing mechanisms of dispersion and coalescence. Dispersion dominates only at rather small contents of the dispersed blend phase, up to the so-called percolation limit which again depends on the particular blend system. The size of the dispersed phase is controlled by the processing history and physical characteristics of the two blend phases, such as the viscosity ratio, the interfacial tension and the viscoelastic behavior. While a continuous increase in nucleation density with PPE content is found below the percolation limit, the phase size and in turn the nucleation density reduces again at elevated contents. Experimentally, it was found that the particle size of immiscible blends, d, follows the relation d --6 I Cdispersed phase and C is a material constant depending on the blend system. Subsequently, the theoretical nucleation density, N , is given by... 

In the present case, the foam density relates perfectly with the previously observed rheological properties, as a transition in the flow behavior was detected at approximately 20 wt% of PPE (Fig. 13). In the viscoelastic case (below the percolation limit), the PPE content neither significantly influences the foamability nor the blend rheology. At elevated contents (beyond percolation), however, the PPE content strongly affects the rheological response of the blend and, subsequently, degrades the foaming behavior, which is verified by a reduced expandability. 

Guo, Z., Fang, Z., and Tong, L. 2007. Application of percolation model on the brittle to ductile transition for polystyrene and polyolefin elastomer blends. eXPRESS Polymer Letters 1 37-43. http //www. expresspolymlett.com/... 

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