Typical percolation curve

Figure 2 shows a typical percolation curve for polyaniline in a film forming matrix. The resistivity of the system remains unchanged until a critical volume fi action of the polyaniline is reached, at which point there is a sudden very large decrease in the resistivity of the system. With forther addition of the polyaniline. 

Figure 2.17. Typical DMA curves of polyurethane elastomers tensile storage modulus, E, (left) and loss tangent, tan 6 = E"/E, (right). Measurements were performed at a frequency of 1 s The PEUU curves are typical for weakly phase-segregated elastomer, while PEU curves are typical for strongly phase-separated elastomer with percolated hard phase [27]...

The percolation threshold, cpc, is the fiUer loading level at which the polymer first becomes conductive, which is generally considered to be a value of about 10 S/cm. Comprehensive experimental and theoretical treatments describe and predict the shape of the percolation curve and the basic behaviors of composites as a function of both conductive filler and the host polymer characteristics (36-38). A very important concept is that the porous nature of the conductive carbon powders significantly affect its volume filling behavior. The typical inclusive stractural measurement for conductive carbon powder porosity is dibutyl phthalate absorption (DBF) according to ASTM 2314. The higher the DBF, the greater the volume of internal pores, which vary in size and shape. The crystalhnity of the polymer also reduces the percolation threshold, because conductive carbons do not reside in the crystalhtes but instead concentrate in the amorphous phase. Eq. (2) describes the percolation curve (39). 

Figure 18 shows the temperature dependence of the proton conductivity of Nafion and one variety of a sulfonated poly(arylene ether ketone) (unpublished data from the laboratory of one of the authors). The transport properties of the two materials are typical for these classes of membrane materials, based on perfluorinated and hydrocarbon polymers. This is clear from a compilation of Do, Ch 20, and q data for a variety of membrane materials, including Dow membranes of different equivalent weights, Nafion/Si02 composites ° ° (including unpublished data from the laboratory of one of the authors), cross-linked poly ary lenes, and sulfonated poly-(phenoxyphosphazenes) (Figure 19). The data points all center around the curves for Nafion and S—PEK, indicating essentially universal transport behavior for the two classes of membrane materials (only for S—POP are the transport coefficients somewhat lower, suggesting a more reduced percolation in this particular material). This correlation is also true for the electro-osmotic drag coefficients 7 20 and Amcoh...

Nitrogen adsorption/condensation is used for the determination of specific surface areas (relative pressure < 0.3) and pore size distributions in the pore size range of 1 to 100 nm (relative pressure > 0.3). As with mercury porosimetry, surface area and PSD information are obtained from the same instrument. Typically, the desorption branch of the isotherm is used (which corresponds to the porosimetry intrusion curve). However, if the isotherm does not plateau at high relative pressure, the calculated PSD will be in error. For PSD s, nitrogen condensation suffers from many of the same disadvantages as porosimetry such as network/percolation effects and pore shape effects. In addition, adsorption/condensation analysis can be quite time consuming with analysis times greater than 1 day for PSD s with reasonable resolution. 

The author together with V. Sukharev has shown [21] that the percolation behavior of nanocomposites conductivity is different from the one typical for composites containing larger particles (Fig. 4). It has been demonstrated that the threshold filler concentration values are lower for nanocomposites than for composites with micron-size particles, and the slope of the curve in the... 

While the existing approaches (such as the model of Qi and Boyce) often provide a good description of polyurethane tensile curves, th typically treat hard and soft phase volume fractions as adjustable (fitting) parameters. In a fully predictive theory, one needs to combine the Qi-Boyce or similar framework with a thermodynamic model to predict hard and soft phase volume fractions, as we discussed in the previous section. Below, we illustrate how one can build such a theory and obtain a qualitative, if not quantitative, agreement with experiment. We start from a micromechanical model of Figure 2.7. The initial value of Vfj (volume fi action of the elastically active regions of the percolated hard phase) is determined on the basis of thermodynamic considerations and the percolation model, as described in the previous section. We assume that each elastically active region of the har d phase can be described as an elasto-plastic material ... 

The electrical conductivity of Ni-YSZ cermet is between 500 and 1000 S/cm at 1000°C (Badwal et al. 1997). Dees et al. (1987) has demonstrated through their S-shaped curve (conductivity vs. amount of nickel) that these cermets develop higher values of electronic conduction at or above about 30vol% Ni and below this nickel content, the conductivity is dominated by that of YSZ with little connectivity for nickel particles. Fig. 17 is a typical S-shaped curve obtained by Pratihar et al. (1999). This percolation behavior is explained in terms of the... 

Figure 9.3 Example of typical MIP cumulative and derivative curves obtained when measuring Portland cement pastes with a maximum MIP pressure of 400 MPa. The hydration was stopped by isopropanol exchange for 7 days followed by 7 days in a desiccator. The three principal characteristic values of MIP results are identified as the total percolated pore volume, the critical pore entry radius and the threshold pore entry radius.

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