Dielectric percolative composites

Dielectric percolative composites have been synthesized [95]. The materials are based on sulfonated PEEK and multi-walled acidified carbon nanotubes coated with poly(aniline). The multi-walled acidified carbon nanotubes are modified by an situ polymerization technique. This method is useful to achieve eventually a good dispersion of the carbon nanotubes... 

Zhang Y, Huo P, Wang J, Liu X, Rong C, Wang G, et al. Dielectric percolative composites with high dielectric constant and low dielectric loss based on sulfonated poly(aryl ether ketone) and a-MWCNTs coated with polyaifiline. J Mater Chem C 2013 1(25) 4035-41. 

Huang C, Zhang QM, deBotton G, Bhattacharya K (2004) All-organic dielectric-percolative three-component composite materials with high electromechanical response. Appl. Phys Lett 84 4391... 

The possibility of realizing via percolated w/o microemulsion conductor/insulating composite materials with very large dielectric constant and exotic optical properties has been pointed out [284],... 

In addition to the amount of filler content, the shape, size and size distribution, surface wettability, interface bonding, and compatibility with the matrix resin of the filler can all influence electrical conductivity, mechanical properties, and other performance characteristics of the composite plates. As mentioned previously, to achieve higher electrical conductivity, the conductive graphite or carbon fillers must form an interconnected or percolated network in the dielectrical matrix like that in GrafTech plates. The interface bonding and compatibility between... 

The dielectric breakdown problem can be solved very easily from the solution of the fuse problem in two dimensions using the concept of duality. This concept is largely used in the case of composite materials and in percolation for problems in d = 2 or with cylindrical symmetry (Mendelson 1975, Bowman and Stroud 1989). Here we follow the derivation of Bowman and Stroud. 

Recently, Sen and Kar-Gupta (1994) and Kar-Gupta and Sen (1995) proposed a new percolation model to mimic the properties of nonlinear composites. However, it can also be interpreted as a special model for the dielectric breakdown problem. 

In the majority of numerical calculations of the anomalous frequency behavior of such composites (in particular, near the percolation threshold pc) under the action of an alternating current, lattice (discrete) models have been used, which were studied in terms of the transfer-matrix method [91,92] combined with the Frank-Lobb algorithm [93], Numerical calculations and the theoretical analysis of the properties of composites performed in Refs. 91-109 have allowed significant progress in the understanding of this phenomenon however, the dielectric properties of composites with fractal structures virtually have not been considered in the literature. 

In Ref. 67 the behavior of Hall coefficient near the percolation threshold pc in a composite containing a dielectric and metal phase was examined for... 

Over the last decade, there has been considerable interest in the development of off-lattice models and theories describing percolation phenomena. Interest in percolation concepts has been spurred by the rather wide variety of applications for which such ideas are thought to be useful. These applications include the electrical conductivity and dielectric properties or permeability of composite materials, gelation, analysis of hydrogen bond networks, and reactions in porous catalysts. Recent progress in the development of off-lattice or, as they are most often called, continuum models of percolation began with the work of Coniglio et and Haan... 

Nevertheless the use of dielectric materials obtained by conductive filler dispersion (carbon black, graphite fibres, metallic powders) is limited. As a matter of a fact material performances are dependent on the filler content as well as particle aggregation phenomena. These composites require a high level of reproducibility and their behaviour is linked to the control of electronic inter-particular transfer. The measured parameter (complex permittivity) depends on the texture of the percolation aggregates and consequently on the processing conditions. The percolation threshold (the particle concentration, after which particles are in contact and the electrical current exists) depends on the particle shape (sphere, plates or fibres). 

For the sample PPX -f Cu the calculated fractal dimension Df is equal to 2.609 [70]. It should be noted that the above-mentioned size distribution of metal nanoparticles leads to the mutual charging of such particles in the percolation cluster. This effect is discussed in the following section in coimection with catalysis by nanoparticles. As stated in reference 70, the specific low-temperature peak of dielectric losses in the synthesized composite samples PPX -t-Cu is probably due to the interaction of electromagnetic field with mutually charged Cu nanoparticles immobilized in the PPX matrix. The minor appearance of this peak in PPX -i- Zn can be explained by oxidation of Zn nanoparticles. 

Effective medium theories characterize the frequency-dependent transport in systems with large-scale inhomogeneities such as metal particles dispersed in an insulating matrix [118,119]. An IMT in the effective medium model represents a percolation problem where a finite a c as T 0 is not achieved until metallic grains in contact span the sample. To understand the frequency dependence of the macroscopic material, an effective medium is built up from a composite of volume fraction /of metallic grains and volume fraction 1 — / of insulator grains. The effective dielectric function semaCw) and conductivity function (Tema(w) are solved self-consistently. 

The characteristic composite behavior of (t maM for medium consisting of spherical particles with volume fractions / of Drude conductor and 1 - / of insulator is shown in Figure 15.5. For a volume fraction / less than the percolation value (/ = 1/3 for spheres), (Tema (impurity band of localized plasmon-like excitations. As the system approaches the percolation threshold, the localized peak o-ema(w) shifts to lower frequency. Above the percolation threshold, a Drude peak corresponding to the carriers that have percolated through the composite structure occurs at low frequency. Only a fraction ( (3/— l)/2 [119]) of the full conduction electron plasma frequency appears in the Drude peak, depending on the proximity to the percolation threshold. The same percolating free electron behavior is observable in the dielectric response ema(w) for the system. 

The other feature that emerges from the experimental data is the functional dependence of the observed o x) that is manifested in particular by the conductivity exponent t. Having the framework given in Sections 5.2-S.4, we can understand the various observed values of t as follows. In the cases where the onset of percolation is associated with the coalescence of particles (as in granular metals [42]) or coalescence-like (as in semiconductor-dielectric composites [41] shown in Figure 5.6), the values of t [35, 39, 40, 42, 59] are, within the experimental uncertainty, very close to the classical critical values of 1.7 < t < 2 that were derived from calculations or computations [1, 3, 15]. This observation is well understood by following two considerations. Either, as suggested above, we approach the S Z picture, or we can virtually divide the continuous phase network into small elements (say, spheres or... 

Composites can be divided into two subgroups statistical mixtures and matrix-inclusion type composites. The effective dielectric function of the first subgroup can be calculated by equations, which are symmetrical with respect to phase indices. Statistical mixtures exhibit the so called percolation Phenomenon which is extremely important in conductor-insulator composites. Percolation threshold is a critical... 

Han, C., Gu, A., Liang, G., Yuan, L. Carbon nanoUrbes/cyanate esUa- composites with low percolation threshold, high dielectric constant and outstanding thcamal property. Compos. A Appl. Sci. Manuf. 41, 1321-1328 (2010)... 

The conductivity of metallopolymeric nanocomposites is substantially affected by the dispersity of an inorganic component. Different nanocomposites are characterized by different relationships between the conductivity and the metal content. The percolation threshold of composites containing layered polypyromellitimide films filled by inserted silver particles is attained at a filler content >9 wt%. When nanosize silver particles (10-15 nm), were prepared by thermolysis of a solution of silver acetate in poly(pyromellitamide acid), they became uniformly distributed over a film. This composite does not exibit conducting properties at the same filler content. The dielectric characteristics of films (o = 10 - 10 Sm ) are retained at a high... 

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