Conductivity percolation process

In the temperature interval of —70 to 0°C and in the low-frequency range, an unexpected dielectric relaxation process for polymers is detected. This process is observed clearly in the sample PPX with metal Cu nanoparticles. In sample PPX + Zn only traces of this process can be observed, and in the PPX + PbS as well as in pure PPX matrix the process completely vanishes. The amplitude of this process essentially decreases, when the frequency increases, and the maximum of dielectric losses have almost no temperature dependence [104]. This is a typical dielectric response for percolation behavior [105]. This process may relate to electron transfer between the metal nanoparticles through the polymer matrix. Data on electrical conductivity of metal containing PPX films (see above) show that at metal concentrations higher than 5 vol.% there is an essential probability for electron transfer from one particle to another and thus such particles become involved in the percolation process. The minor appearance of this peak in PPX + Zn can be explained by oxidation of Zn nanoparticles. 

Borkovec et al. [59] also reported on a two-stage percolation process for the ME AOT (Aerosol OT, bis(2-ethylhexyl)sodium sulfosuccinate) system AOT-decane-water. The structural inversions were investigated using viscosity, conductivity, and electro-optical effect measurements. The viscosity results showed a characteristic profile with two maxima, which was interpreted as evidence for two symmetrical percolation processes an oil percolation on the water-rich side of the phase diagram and a water percolation process on the oil-rich side. 

One can picture the percolation process detected in the dielectric response as proton transfer along a thread of hydrogen-bonded water molecules adsorbed on the protein surface (Careri et al., 1986). The water molecules are formally equivalent to the conducting elements of the familiar percolation model of a conducting network. Above the thresh-... 

One solution is based on the use of anisotropic graphite plates possessing a controlled intrinsic conductivity and processed by spray coating. In this case the percolation threshold is lower than 3.5%. 

Another approach to determining the viscoelastic properties of dense microemulsions at high frequencies is to conduct ultrasonic absorption experiments. In such experiments it has been found that the percolation process is correlated to a shift of the ultrasonic dynamics from a single relaxation time to a distribution of relaxation times [121]. Other experiments showed an increase in the hypersonic velocity for samples at and beyond the percolation threshold. The complex longitudinal modulus deduced from such experiments is also correlated with the occurrence of the percolation phenomenon, which suggests that the velocity dispersion is clearly correlated with structural transformations [122]. 

These structures are highly anisotropic with respect to their electrical conductivity. There is a difFerence of about 12 orders of magnitude in the conductivities of metallic Cu and CU2O. This difFerence is manifested in both the lateral (parallel to the layers) and perpendicular conductivities of the alternating layers. The lateral resistivity varied from 10 " f2-cm for very Cu rich samples to >10 f2-cm for Cu-poor ones. In particular, at a Cu concentration >9.8 vol%, the resistivity decreased suddenly, typical of a percolation process. The resistivity in the perpendicular direction was much larger than that in the lateral one for reasonably Cu-rich samples (ratios of >10 ). No less important is the fact that... 

It is tempting to mix metals and semiconductors to combine their respective positive and negative TCR to achieve a zero TCR. If a simple mixture is made, the conductivity and the TCR are determined by a percolation process. This imphes that in a very small composition region the TCR suddenly changes from positive to negative. Therefore, for such materials the reproducibility and the spread of both the resistivity and the TCR are unacceptable. 

The addition of a comonomer to a semicrystalline polymer typically causes a loss in crystallinity, unless the second monomer crystallizes with the first. The decrease in crystallinity is very significant as small quantities of the comonomer are added, and it is accompanied by reductions in stiffness, hardness and melting point. Because vinyl polymers are thermoplastic and completely miscible with most organic solvents, copolymerization with vinyl monomers is a logical route to conventional processability and environmental stability. This route was pursued by polymer chemists who desired these properties in an electrically conductive material. But with the low percolation threshold observed in simple blends of vinyl polymers and conducting polymers, work on copolymerization has been abandoned in favor of composites. The two principal drawbacks of composites are incompatibility of the components and lack of genuine solution processability. What follows is a brief review of efforts to obtain electrically conducting and processable random vinyl copolymers of 3-methylthiophene. 

Barzic Razvan Florin, and Barzic Andreea Irina. Thermal conduction in polystyrene/carbon nanotubes Effects of nanofiUer orientation and percolation process. Rev. Room. Chim. 6 no. 7-8 (2015) 803-807. 

The results of this study lead to the conclusion that poly(acetylene) oxidized by iodine essentially consists of three different components unreacted bulk polymer, iodine covered surfaces and/or amorphous regions containing iodine and a metallic conducting polymer-iodine complex salt structure with a new lattice composed of rearranged chains together with I -chains. The conductivity data indicated a percolation process involving the metallic conductive parts of the sample as component of a system with a complex texture. 

It may be mentioned here that two stage (or double) percolation has been reported by Ray and Moulik [92] and Maiti et al. [93] for (water/AOT/decanol) and water/DTAB (octadecyltrimethylammonium bromide)-butanol/heptane microemulsion systems, respectively. The double percolation process for AOT/ decane/NaCl (0.5%) was also reported by Eicke et al. by conductivity, viscosity, and electro-optical Kerr effect [94]. The two processes demarcated three structural regimes viz, o/w, w/o, and oil or water continuous. 

As a consequence of ion transfer, it yields a sigmoidal percolation process and is designated as the threshold temperature (9 ), threshold volume fraction )or the threshold water content (co ) characteristic feature of a percolating system [21-32]. Moulik et al. [28] have proposed the sigmoidal Boltzmann equation (SBE) to determine the threshold characteristics of microemulsion systems. In conductance percolation, the equivalent equation can be written as... 

The mechanism for conductance percolation consists of the formation of channels that allow the exchange of matter between the dispersed water droplets in the continuous phase. Therefore, it is necessary for there to be an effective collision between two water droplets of the microemulsion, causing the droplets to fuse together. Subsequently an exchange of matter between the water droplets takes place (allowing the charge conduction), which in turn brings about the separation of the droplets by means of a process of fission. 

At a critical volume fraction, the resistivity of the composite falls sharply to a level at which the composite can readily conduct electricity. Increases in filler concentration above the critical loading do not appreciably reduce the resistivity. The sharp change from insulator to conductor is due to the formation of a network among the filler particles. Network formation has most frequently been treated as a percolation process. The percolation model refers to a means of continuous network formation through a lattice, taking into account the relative amounts of the two materials comprising the network. It is a statistical representation and is most frequently analysed by Monte Carlo techniques. 

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