Reinforcement percolation model

Let us consider the physical foundations of reduction at IL growth. The main equation of the reinforcement percolation model is the following one [9] ... 

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...

These qualitative effects can be described quantitatively within the framework of percolation model of reinforcement and multifractal model of gas transport processes for nanocomposites polymer/organoclay [3, 4]. It has been supposed that two structural components are created for a barrier effect to fire spreading actually organoclay and densely packed regions on its surface with relative volume fractions (p and (p respectively. In other words, it has been supposed, that the value should be a diminishing function of the sum ((p -l-(pp. For this supposition verification let us estimate the values (p and (p The value (p is determined according to the well-known equation [5] ... 

On the nano-scale, the discrete moleculai structure of the polymer has to be considered. Segmental immobilization seems to be the primary reinforcing mechanism in true polymer nanocomposites at temperatures near and above the Tg. Reptation model and simple percolation model were used to describe immobilization of chains near solid nanopaiticles and to explain the peculiarities in the viscoelastic response of polymers near solid surfaces of lar ge polymer-inclusion contact areas. The inteiphase in the continuum sense does not exist at the nano-scale when relaxation processes in individual discrete chains are taken into account and the chains with retarded reptation catr be considered forming the iirterphase analogue irr the discrete matter. For a common polymer, all the chains in the composite are immobilized when the internal filler-matrix interface area reached about 42 m per 1 g of the nanocomposite. 

Of course, this equation and its theoretical underpinnings does not constitute a model as such and certainly does not address the structural specifics of Nafion, so that it is of no predictive value, as experimental data must be collected beforehand. On the other hand, the results of this study clearly elucidate the percolative nature of the ensemble of contiguous ion-conductive clusters. Since the time of this study, the notion of extended water structures or aggregated clusters has been reinforced to a degree by the morphological studies mentioned above. 

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)... 

Starch nanocrystals were used to reinforce a non-vulcanised NR matrix. The NR was not vulcanised to enhance biodegradability of the total biocomposite. Non-linear dynamic mechanical experiments demonstrated a strong reinforcement by starch nanocrystals, with the presence of Mullins and Payne effects. The Payne effect was able to be predicted using a filler-filler model (Kraus model) and a matrix-filler model (Maier and Goritz model). The Maier and Goritz model showed that adsorption-desorption of NR onto the starch surface contributed the non-linear viscoelasticity. The Kraus model confirmed presence of a percolation network. ... 

For the polymers containing filler that touch each other, the percolation theory has been developed. This assumes a sharp increase in the effective conductivity of the disordered media, polymer matrix composite, at a critical volume fraction of the reinforcement known as the percolation threshold (( )percoi) which long-range connectivity of the system appears. The model that best expresses these aspects is the one created by Vysotsky (Vysotsky and Roldughin 1999), which presumes a percolation network of nanofiller particles inside the polymer matrix as shown in equation (11.10) ... 

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