Percolation fibers

The composites with the conducting fibers may also be considered as the structurized systems in their way. The fiber with diameter d and length 1 may be imagined as a chain of contacting spheres with diameter d and chain length 1. Thus, comparing the composites with dispersed and fiber fillers, we may say that N = 1/d particles of the dispersed filler are as if combined in a chain. From this qualitative analysis it follows that the lower the percolation threshold for the fiber composites the larger must be the value of 1/d. This conclusion is confirmed both by the calculations for model systems [27] and by the experimental data [8, 15]. So, for 1/d 103 the value of the threshold concentration can be reduced to between 0.1 and 0.3 per cent of the volume. 

As already noted, the main merit of fibers used as a filler for conducting composite materials is that only low threshold concentrations are necessary to reach the desired level of composite conductivity. However, introduction of fiber fillers into a polymer with the help of ordinary plastic materials processing equipment presents certain difficulties which are bound up mainly with significant shearing deformations entailing fiber destruction and, thereby, a decrease of parameter 1/d which determines the value of the percolation threshold. 

For applications where only mechanical properties are relevant, it is often sufficient to use resins for the filling and we end up with carbon-reinforced polymer structures. Such materials [23] can be soft, like the family of poly-butadiene materials leading to rubber or tires. The transport properties of the carbon fibers lead to some limited improvement of the transport properties of the polymer. If carbon nanotubes with their extensive propensity of percolation are used [24], then a compromise between mechanical reinforcement and improvement of electrical and thermal stability is possible provided one solves the severe challenge of homogeneous mixing of binder and filler phases. For the macroscopic carbon fibers this is less of a problem, in particular when advanced techniques of vacuum infiltration of the fluid resin precursor and suitable chemical functionalization of the carbon fiber are applied. 

In cases where water is turbid, samples are generally filtered through glass fiber Alters (GEE) prior to percolation through sorbents. This step recovers waterborne particulates and microorganisms with average diameters >0.7 pm, which are analyzed separately. However, chemicals associated with colloid-sized particulates and DOC are not removed by GFFs. 

On the basis of this discussion, the mechanisms of mesophase carbon fiber formation are closely related to those of needle coke, the principal differences being the extent to which the deformation and relaxation mechanisms are able to act. Because delayed coking involves relatively gentle but random deformation processes by bubble percolation and the long dwell times in the coke drum afford opportunity for extensive disclination annihilation and micro-structural relaxation, the structure of needle coke can be well defined by polarized-light microscopy (2,36). 

For anisotropic particles, the percolation limit is a function of the aspect ratio. For ellipsoids of revolution, the percolation limit for a simple cubic lattice was studied by Boissonade et al. [85]. They found as the aspect ratio increases from 1 (a sphere) to 15 (a fiber), the percolation limit decreased from a volume fraction of 0.31 to 0.06 and the correlation length (i.e., aggregate size) did not change (i.e., it was the same as that of the sphere). 

A third important filler parameter is related to its shape. Figure 15.17 shows that the aspect ratio of carbon fiber affects conductivity. If the fiber is milled to almost spherical particles, its percolation threshold concentration is substantially increased. 

An important development, pioneered by Kuhn and coworkers,37 38 has been the deposition of conducting PAn s onto fibers and fabrics. Not only hydrophobic fibers such as polyesters and polypropylene but also hydrophilic textiles such as rayon and cotton can be coated with PAn with this in situ polymerization method. PAn/nylon-6 composite films have also been prepared by adsorbing aniline onto thin nylon-6 films and then treating with aqueous (Nn4)2S208.39 The composite films exhibited a low percolation threshold requiring just 4% PAn for electrical conductivity. 

The value of geometrical percolation threshold pc. The volume fraction at random close packing, d>m, is identified with . The pc of a dispersion of randomly placed monodisperse ellipsoidal filler particles as a function of Af is approximated by Equation 13.36. Equation 13.37 can then be used for fibers with Af>10, and Equation 13.38 for platelets of aspect ratio 1/Af, with the results summarized in Figure 13.14. 

Figure 13.14. Estimated maximum packing volume fraction m of randomly dispersed cylindrical particles, Om for spheres, and geometrical percolation threshold pc for ellipsoids of biaxial symmetry. A =height/diamctcr for cylindrical fibers and thickness/diameter for cylindrical platelets. Af=(c/a), where c is the length of the ellipsoid along its axis of symmetry and a=b is the the length of the ellipsoid in the normal direction, for ellipsoidal particles.

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...

In cellulosic ethanol production processes, a pretreatment procedure is needed to disrupt the recalcitrant structure of the lignocellulosic materials so that the cellulose can be more efficiently hydrolyzed by cellulase enzymes [2], These pretreatments include physical, biological, and chemical ways, such as uncatalyzed steam explosion, liquid hot water, dilute acid, flow-through acid pretreatment, lime, ammonium fiber/freeze explosion, and ammonium recycle percolation [3, 4], Most of these methods involve a high temperature requirement, which is usually achieved through convection- or conduction-based heating. 

The morphology depends on the blend concentration. At low concentration of either component the dispersed phase forms nearly spherical drops, then, at higher loading, cylinders, fibers, and sheets are formed. Thus, one may classify the morphology into dispersed at both ends of the concentration scale, and co-continuous in the middle range. The maximum co-continuity occurs at the phase inversion concentration, (()p where the distinction between the dispersed and matrix phase vanishes. The phase inversion concentration and stability of the co-continuous phase structure, depend on the strain and thermal history. For a three-dimensional, 3D, totally immiscible case the percolation theory predicts that = 0.156. In accord with the theory, the transition from dispersed to co-continuous stmcture occurs at an average volume fraction, = 0.19 0.09... 

By contrast, the ECP must have conjugated rigid-rod macromolecules. Several such polymers show high electrical conductivity (usually after doping), viz. polyacetylene (PAc), polyaniline (PANI), polypyrrole (PPy), polyparaphenylenes (PPP), or poly-3-octyl thiophene (POT). The resins are expensive, difficult to process, brittle and affected by ambient moisture, thus blending is desirable. For uniaxially stretched fibers the percolation threshold is 1.8 vol%, hence low concentration of ECP (usually 5-6 vol%) provides sufficient phase co-continuity to ascertain conductivity similar to that of copper wires (see Table 1.79). 

Pioneering research by Favier used crystallites derived from tunicates as cellulosic reinforcement in poly[styrene-co-butyl acrylate] films and concluded that hydrogen bonding between the tunicate crystallites caused their percolation through the polymer matrix, resulting in the enhanced mechanical properties observed, in the same way that the high strength of a paper sheet results from cellulose fiber percolation [13]. 

Adding ceramic whiskers in volume fractions above the percolation threshold has been found to improve creep resistance, often increasing the creep resistance by two orders of magnitude. One would expect a similar effect with fibers but, in some cases, the fibers have such a small grain size (for high strength) that they can show very poor creep resistance. Other important factors that can affect the creep rate of a material are composition, stoichiometry, defect density and environment, often through their dependence on diffusivity. 

D.P. Bentz Fibers, percolation, and Spalling of high-performance concrete, ACI Materials Journal, (2000), pp.351-359... 

Favier, V., Dendievel, R., Canova, G., Cavaille, J.-Y., Gilormini, P. Simulation and modeling of threedimensional percolating stractures case of a latex matrix reinforced by a network of cellulose fibers. Acta Mater. 45, 1557-1565 (1997)... 

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