Percolation definition

Chromatography is a physical method of separation in which the components to be separated are distributed between two phases, one of which is stationary (the stationary phase), while the other (the mobile phase) moves in a definite direction. A mobile phase is described as a fluid which percolates through or along the stationary bed in a definite direction . It may be a liquid, a gas or a supercritical fluid, while the stationary phase may be a solid, a gel or a liquid. If a liquid, it may be distributed on a solid, which may or may not contribute to the separation process. ... 

The critical gel equation is expected to predict material functions in any small-strain viscoelastic experiment. The definition of small varies from material to material. Venkataraman and Winter [71] explored the strain limit for crosslinking polydimethylsiloxanes and found an upper shear strain of about 2, beyond which the gel started to rupture. For percolating suspensions and physical gels which form a stiff skeleton structure, this strain limit would be orders of magnitude smaller. 

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. 

Statistically defined structures may also arise from the formation of crosslinks in a melt the resulting gels are described within a percolation framework which predicts the existence of definite meshes [7, 8]. Contact-lenses, jellies or even jellyfish are common examples of gels. Latex beads with specific functionalities attached, such as antigens, are used in biodiagnostics. 

The percolation model suggests that it may not be necessary to have a rigid geometry and definite pathway for conduction, as implied by the proton-wire model of membrane transport (Nagle and Mille, 1981). For proton pumps the fluctuating random percolation networks would serve for diffusion of the ion across the water-poor protein surface, to where the active site would apply a vectorial kick. In this view the special nonrandom structure of the active site would be limited in size to a dimension commensurate with that found for active sites of proteins such as enzymes. Control is possible conduction could be switched on or off by the addition or subtraction of a few elements, shifting the fractional occupancy up or down across the percolation threshold. Statistical assemblies of conducting elements need only partially fill a surface or volume to obtain conduction. For a surface the percolation threshold is at half-saturation of the sites. For a three-dimensional pore only one-sixth of the sites need be filled. 

Although percolation theory deals with random systems, modeling and numerical calculations for percolation are usually carried out for a lattice of some definite geometry. To reach conclusions which do not depend on the details of lattice geometry but on dimensionality only, and thus are valid for the random system of interest, some invariant quantities must be constructed. 

Brovchenko I, Oleinikova A. Four phases of amorphous water simulations versus experiment. 1. Chem. Phys. 2006 124 164505. Kumar R, Schmidt IR, Skinner IL. Hydrogen bonding definitions and dynamics in liquid water. 1. Chem. Phys. 2007 126 204107. Geiger A, StiUinger FH, Rahman A. Aspects of the percolation process for hydrogen-bond networks in water. 1. Chem. Phys. 1979 70 4185-4193. 

By analogy with the mechanical fracture (discussed in the next chapter), the case (i) corresponds to a brittle failure and the case (ii) to a ductile failure. Although there is no definite answer, it is believed that in the case of percolation disorder, the electrical failures are mostly brittle-like failures the voltage (or the current) for the first failure is often the voltage (or the current) for the failure of the whole sample, especially for disorder concentrations near the percolation threshold. We shall see later a different type of disorder which can give ductile failure. 

Meteoric water. Water derived from rain, snow, streams, and other bodies of surface water that percolates in rocks and displaces interstitial water that may have been connate, meteoric, or of any other origin. Meteoric water in sedimentary basins is generally recharged at higher elevations along the margins of the basin. The time of last contact with the atmosphere is intentionally omitted from this definition, but may be specified to further define meteoric water. Thus, Recent meteoric water, Pleistocene meteoric water, or Tertiary meteoric water, would indicate the time of last contact with the atmosphere (Kharaka and Carothers, 1986). 

Fast extrusion furnace black with a particle size of 360 A, was used to verify different theoretical concepts of percolation which by definition predicts a rapid change in conductance when volume fraction of conductive particles attains a critical value. Figure 15.38 shows the effect of a carbon black addition to polychloroprene. Up to 30 phr carbon black, the conductivity of poly chloroprene is almost constant and then it increases linearly as concentration of carbon black increases. The following equation applies o = o (P - P Jwhere c is constant, P is concentration of conducting particles, Pc is percolation threshold, and P is exponent which accounts for cluster size."" When data from the Figure 15.38 are replotted as in Figure 15.39 it is evident that the percolation law is valid. 

An alternative to the site percolation problem described above assumes that all sites are occupied and that nearest neighbors are connected to each other by either open or closed bonds. In this case, p is the probability that a randomly selected bond is open (and thus, —p is the probability that it is closed). Sites connected to each other by open bonds belong to the same cluster (this definition makes sense if one recalls the coffee percolator water can only flow through open pores). Since the conclusions drawn from such bond percolation may be understood by using site percolation, we will here focus on the latter. 

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