Volume fraction threshold

Figure 7. Silicon oxide cluster aggregate distribution below and above percolation volume fraction threshold...

Relaxation in Nanocomposites. At concentrations above the percolation threshold polymer/nanoparticle interactions dominate the viscoelastic terminal behaviour of polymer nanocomposites. As has been reported for phenoxy based nanocomposites [8], the analysis of tan 5 relaxation at low frequencies constitutes a reliable rheological method to investigate the strength of phenoxy/nanoclay interactions. Moreover, since coordinates ((o)Max (tan 5)Max)) reflect the blocking effect of nanoparticles on polymer chains, the dependence of (o)Max with nanoparticles volume fraction can be used in the percolation equation X=Xq (volume fraction threshold [Pg.69]

In these expressions Xc is the critical (subscript c) value of x which marks the threshold at which immiscibility sets in, and 1 - 0j or 0j is the volume fraction of the solvent in the solution at this point. Rearranging Eq. (8.56), we obtain... 

Effects of additives (electrolytes, surfactants, nonelectrolytes) on the volume fraction and temperature percolation thresholds of a water/AOT/n-heptane system have been investigated [280,281]. 

However, in some special cases, the lost of information due to the thresholding procedure may cause a noticeable systematic error, because each lattice point such that < )(r) > < )0 contributes the same volume fraction 1/L3 regardless of the field magnitude. Consider an asymmetric binary mixture undergoing the phase separation. The local volume fraction distribution P(< >) has maxima at the equilibrium volume fractions, 1, and is asymmetric relatively to... 

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.

Thus, one could expect to find a droplet morphology at those quench conditions at which the equilibrium minority phase volume fraction (determined by the lever rule from the phase diagram) is lower than the percolation threshold. However, the time interval after which a disperse coarsening occurs would depend strongly on the quench conditions (Fig. 40), because the volume fraction of the minority phase approaches the equilibrium value very slowly at the late times. 

Similar to the percolation threshold, the effective electrical conductivity of a porous Ni-YSZ cermet anode depends on the morphology, particle size, and distribution of the starting materials as well. In general, the effective conductivity increases as the NiO particle size is reduced when other parameters are kept constant. As shown in Figure 2.4 (samples 1 and 2), the cermet conductivity increased from -10 S/cm to 103 S/cm as the NiO particle size was decreased from 16 to 1.8 pm while using the same YSZ powder (primary particle size of -0.3 pm) and the same Ni to YSZ volume fraction [30],... 

One of the characteristics of weak flocculation is that the system is reversible. At low volume fractions the system will form some clusters and some single particles. The clusters can be easily disrupted by gentle shaking. As the concentration is increased the system will reach a percolation threshold . The number of nearest neighbours around any test particle reaches 3 at about (p — 0.25 and the attractive forces between... 

At the high volume fraction end (Vf > 10 %), well above the percolation threshold, equation (8.3) can be approximated as... 

The side chain separation varies in a range of 1 nm or slightly above. The network of aqueous domains exhibits a percolation threshold at a volume fraction of 10%, which is in line with the value determined from conductivity studies. This value is similar to the theoretical percolation threshold for bond percolation on a face-centered cubic lattice. It indicates a highly interconnected network of water nanochannels. Notably, this percolation threshold is markedly smaller, and thus more realistic, than those found in atomistic simulations, which were not able to reproduce experimental values. 

With the U-Type systems (i.e. with the low chain alcohols) the trends in the conductivity - curve are consistent with percolative conduction originally proposed to explain the behaviour of conductance of conductor-insulator composite materials (27). In the latter model, the effective conductivity is practically zero as long as the conductive volume fraction is smaller than a critical value called the percolation threshold, beyond which k suddenly takes a non-zero value and rapidly increases with increase of Under these conditions. 

This model, when applied to Nation as a function of water content, indicated a so-called quasi-percolation effect, which was verified by electrical impedance measurements. Quasi-percolation refers to the fact that the percolation threshold calculated using the single bond effective medium approximation (namely, x = 0.58, or 58% blue pore content) is quite larger than that issuing from a more accurate computer simulation. This number does not compare well with the threshold volume fraction calculated by Barkely and Meakin using their percolation approach, namely 0.10, which is less than the value for... 

Knowing that 1 mg/cm2 of product water is a threshold, how much water can be stored at maximum within each component of the fuel cell, and how much can be removed to the outside For the cathode catalyst layer (CCL) with typical thickness of 10 p,m and 50% pore volume fraction, the CCL water storage capacity is approximately 0.5 mg/cm2. A 30- un-thick membrane can store 1.5 mg/cm2 of water, but its actual water storage capacity depends on the initial water content, A., and therefore is proportional to (ks.where A.sa, denotes the water content of a fully hydrated membrane. The escape of water into the GDL is unlikely due to the very low vapor pressure at cold-start temperatures (Pv>sa, = 40 Pa at —30°C). For reference, the GDL with 300 pm thickness and 50% porosity would store about 15 mg/cm2 of water, if it could be fully utilized. This capacity is too large to be used for cold start. From this simple estimation we can conclude that the CCL water storage capacity alone is not sufficient for successful cold start and that a successful strategy is to store water in the membrane. 

Fig. 11.4. Schematic sketch of granular metal structure depending on metal volume fraction a. Volume fraction corresponding to the percolation threshold is denoted as xc.

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