Viscosity percolation

Figure 13.12. Schematic illustration of the shear viscosity r and the equilibrium shear modulus G as functions of the particle volume fraction <1>. Note that r —as <1> approaches the viscosity percolation threshold from below, while the onset of a nonzero G (indicative of the onset of true solid-like rigidity) occurs immediately above d>. ...

Saidi, Z., Boned, C., and Peyrelasse, J., Viscosity-percolation behavior of waterless Microemulsions a curious temperature effect, In Trends in Colloid and Interface Science VI (C. Hehn, M. Losche, H. Mohwaldt, Eds.) Springer, The Netherlands, 1992, pp. 301-316. 

Since pc 1/2, we observe that Me 2Mg, as commonly observed. Mg is determined from the onset of the rubbery plateau by dynamic mechanical spectroscopy and Me is determined at the onset of the highly entangled zero-shear viscosity law, T) M. This provides a new interpretation of the critical entanglement molecular weight Mg, as the molecular weight at which entanglement percolation occurs while the dynamics changes from Rouse to reptation. It also represents the... 

The classical theory predicts values for the dynamic exponents of s = 0 and z = 3. Since s = 0, the viscosity diverges at most logarithmically at the gel point. Using Eq. 1-14, a relaxation exponent of n = 1 can be attributed to classical theory [34], Dynamic scaling based on percolation theory [34,40] does not yield unique results for the dynamic exponents as it does for the static exponents. Several models can be found that result in different values for n, s and z. These models use either Rouse and Zimm limits of hydrodynamic interactions or Electrical Network analogies. The following values were reported [34,39] (Rouse, no hydrodynamic interactions) n = 0.66, s = 1.35, and z = 2.7, (Zimm, hydrodynamic interactions accounted for) n = 1, s = 0, and z = 2.7, and (Electrical Network) n = 0.71, s = 0.75 and z = 1.94. 

Galgali and his colleagues [46] have also shown that the typical rheological response in nanocomposites arises from frictional interactions between the silicate layers and not from the immobilization of confined polymer chains between the silicate layers. They have also shown a dramatic decrease in the creep compliance for the PP-based nanocomposite with 9 wt% MMT. They showed a dramatic three orders of magnitude drop in the zero shear viscosity beyond the apparent yield stress, suggesting that the solid-like behavior in the quiescent state is a result of the percolated structure of the layered silicate. 

Loveless DM, Jeon SL, Craig SL. Chemoresponsive viscosity switching of a metaUo-supra-molecular polymer network near the percolation threshold. J Mater Chem 2007 17 56-61. 

A correlation exists between conductivity and viscosity but it is limited to the range x 0 0.4. The percolation approach leads to similar conclusions. 

The number of PPE particles dispersed in the SAN matrix, i.e., the potential nucleation density for foam cells, is a result of the competing mechanisms of dispersion and coalescence. Dispersion dominates only at rather small contents of the dispersed blend phase, up to the so-called percolation limit which again depends on the particular blend system. The size of the dispersed phase is controlled by the processing history and physical characteristics of the two blend phases, such as the viscosity ratio, the interfacial tension and the viscoelastic behavior. While a continuous increase in nucleation density with PPE content is found below the percolation limit, the phase size and in turn the nucleation density reduces again at elevated contents. Experimentally, it was found that the particle size of immiscible blends, d, follows the relation d --6 I Cdispersed phase and C is a material constant depending on the blend system. Subsequently, the theoretical nucleation density, N , is given by... 

In Eq. 5, [rj] is the intrinsic viscosity of the dispersed phase and Pm is the maximum packing volume fraction (in most cases, Pm = 1 - Per, Per is the critical volume fraction or percolation threshold). 

Many nonaqueous solutions have a low viscosity. Therefore, in the preparation of metal embedded in a plastic material, the machining has to be sufficiently good to prevent there being a space between the metal and the insulator into which the nonviscous solution can percolate. 

Second, the spatially periodic model suggests further interpretations and experiments. That no kink exists in the viscosity vs. concentration curve may be related to the fact that the average dissipation rate remains finite at the maximum kinematic concentration limit, ma>. Infinite strings of particles are formed at this limit. It may thus be said that although the geometry percolates, the resulting fields themselves do not, at least not within the context of the spatially periodic suspension model. 

Kaler et al. [50] reported on the viscosity changes in association with a percolative phenomenon for systems containing the commercial surfactant TRS 10-80, octane, tertiary amyl alcohol, and various brines. Their viscosity results were interpreted as evidence for a smooth transition from an oil-continuous to a bicontinuous one in which both oil and water span the sample. A second transition was observed and was attributed to a transition from a bicontinuous to a water-continuous system. 

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. 

Pressurized solvent extraction (PSE), also called pressurized fluid extraction (PEE), accelerated solvent extraction (ASE ), pressurized liquid extraction (PEE), or enhanced solvent extraction (ESE), is a solid-liquid extraction that has been developed as an alternative to conventional extractions such as Soxhlet, maceration, percolation, or reflux. It uses organic solvents at high pressure and temperature to increase the efficiency of the extraction process. Increased temperature decreases the viscosity of the liquid solvent, enhances its diffusivity, and accelerates the extraction kinetics. High pressure keeps the solvent in its liquid state and thus facilitates its penetration into the matrix, resulting in increase extraction speed [30]. 

At the percolation limit, the rheological behavior of the suspension changes from Newtonian to either the Cross equation with a low shear limit viscosity or the Bingham plastic equation with an apparent yield... 

Beyond the percolation limit, the bridging network is more concentrated. Below the critical volume fraction, no continuously bridging networks are formed and the viscosity is low. As shown in Figure 12.7, this bridging network breaks up as the shear rate increases, giving different viscosities at different shear rates. As a result, this gives low and high shear limit viscosities observed at steady state for concentrated poljmier solutions and concentrated particulate suspensions (discussed later). 

FIGURE 12 As aggregation proceeds, the low shear viscosity increases drastically as the percolation limit is reached at the gel time, tg. 

This space-filling network of percolating and interacting fumed silica particles may result in an enormous high viscosity or even a yield point. The thickened liquid gets a gel-like consistence and will resists shear stress until the shear stress overcomes the strength of the particle-particle interactions and... 

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