Percolation network formation

Non-linear viscoelastic properties were observed for fumed silica-poly(vinyl acetate) (PVAc) composites, with varying PVAc molar mass and including a PVAc copolymer with vinyl alcohol. Dynamic mechanical moduli were measured at low strains and found to decrease with strain depending on surface treatment of the silica. The loss modulus decreased significantly with filler surface treatment and more so with lower molar mass polymer. Copolymers with vinyl alcohol presumably increased interactions with silica and decreased non-linearity. Percolation network formation or agglomeration by silica were less important than silica-polymer interactions. Silica-polymer interactions were proposed to form trapped entanglements. The reinforcement and nonlinear viscoelastic characteristics of PVAc and its vinyl alcohol copolymer were similar to observations of the Payne effect in filled elastomers, characteristic of conformations and constraints of macromolecules. ... 

Barzic Razvan Florin, Barzic Andreea Irina, and Dumitrascu Gheorghe. Percolation network formation in poly(4-vinylpyridine)/aluminum nitride nanocomposites Rheological, dielectric, and thermal investigations. Polym. Compos. 35 no. 8 (2014) 1543-1552. 

The high viscosity of the two polymers blended could limit the equilibration of a co-continuous structure, as well as reduce the mobility of the CNTs. In other words, a co-continuous structure might never result, or, in the event that it does, the mobility of the CNTs in that structure is too low for the structure to direct the percolated network formation. To circumvent this, a system utilizing the same... 

This result of resistivity or electron conductivity, which is the inverse of resistivity, is well known and is called percolation [40]. Dramatic increase of conductivity is ascribable to network formation of the electron-conductive path. 

In random bond percolation, which is most widely used to describe gelation, monomers, occupy sites of a periodic lattice. The network formation is simulated by the formation of bonds (with a certain probability, p) between nearest neighbors of lattice sites, Fig. 7b. Since these bonds are randomly placed between the lattice nodes, intramolecular reactions are allowed. Other types of percolation are, for example, random site percolation (sites on a regular lattice are randomly occupied with a probability p) or random random percolation (also known as continuum percolation the sites do not form a periodic lattice but are distributed randomly throughout the percolation space). While the... 

Alternatively, Leung and Eichinger [51] proposed a computer simulation approach which does not assume any lattice as the classical and percolation theory. Their simulations are more realistic than lattice percolation, since spatially closer groups form bonds first and more distant groups at later stages of network formation. However, the implicitly introduced diffusion control is somewhat obscure. The effects of intramolecular reactions were more realistically quantified, and the results agree quite well with experimental observations [52,53],... 

It was shown, that the conception of reactive medium heterogeneity is connected with free volume representations, that it was to be expected for diffusion-controlled sohd phase reactions. If free volume microvoids were not connected with one another, then medium is heterogeneous, and in case of formation of percolation network of such microvoids - homogeneous. To obtain such definition is possible only within the framework of the fractal free volume conception. 

Martin CA, Sandler JKW, Shaffer MSP, Schwarz M-K, Bauhofer W, Schulte K, et al. Formation of percolating networks in multi-wall carbon-nanotube-epoxy composites. Composites Science and Technology. 2004 Nov 64(15) 2309-16. 

Zhang et al. studied the effect of conductive network formation in a polymer melt on the conductivity of MWNT/TPU composite systems (91). An extremely low percolation threshold of 0.13 wt% was achieved in hot-pressed composite film samples, whereas a much higher CNT concentration (3-4 wt%) is needed to form a conductive network in extruded composite strands. This was explained in terms of the dynamic percolation behavior of the CNT network in the polymer melt. The conductivity of extruded strand showed a hopping resistivity dominated behavior at low concentrations and a dynamic percolation induced network dominated behavior at higher concentrations. It was shown that a higher temperature can reduce the filler concentration required for the dynamic percolation to take effect. 

The effect of "residual water" on either protein stability or enzyme activity continues to be a topic of great interest. For example, several properties of lysozyme (e.g., heat capacity, diamagnetic susceptibility (Hageman, 1988), and dielectric behavior (Bone and Pethig, 1985 Bone, 1996)) show an inflection point at the hydration limit. Detailed studies on the direct current protonic conductivity of lysozyme powders at various levels of hydration have suggested that the onset of hydration-induced protonic conduction (and quite possibly for the onset of enzymatic activity) occurs at the hydration limit. It was hypothesized that this threshold corresponds to the formation of a percolation network of absorbed water molecules on the surface of the protein (Careri et al., 1988). More recently. Smith et al., (2002) have shown that, beyond the hydration limit, the heat of interaction of water with the amorphous solid approaches the heat of condensation of water, as we have shown to be the case for amorphous sugars. 

Statistical network models were first developed by Flory (Flory and Rehner, 1943, Flory, 1953) and Stockmayer (1943, 1944), who developed a gelation theory (sometimes referred to as mean-field theory of network formation) that is used to determine the gel-point conversions in systems with relatively low crosslink densities, by the use of probability to determine network parameters. They developed their classical theory of network development by considering the build-up of thermoset networks following this random, percolation theory. 

Percolation is the process of network formation by random filling of bonds between sites on a lattice. If one increases the fraction of bonds (p) formed, then larger clusters of bonds form until an infinite lattice-spanning cluster (at the percolation threshold, p=Pc) is formed. Figure 2.15 (Stanley, 1985) shows the growth of the network corresponding to values of the fraction p of (a) 0.2, (b) 0.4, (c) 0.6 (p=p ) and (d) 0.8. 

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