Percolation concentration

The electric properties of soft ferromagnetic nanoparticles in an insulating matrix strongly depend on the concentration of a metallic filler x and are varied between properties of the matrix and those of the filler. In binary nanocomposites a critical concentration (percolation threshold Xq) is reached when a continuous current-conducting cluster of the filler particles is formed through out the sample. 

Dialyze the concentrated percolate fraction from Step 5 against 1000 ml of 25 mM PB, pH 8.0, for 2 days, changing the buffer twice, and apply to a column of DEAE-Sephadex (1.5x20 cm, Pharmacia Biotech) equilibrated with 25 mM PB, pH 8.0. After washing the column with 50 ml of the buffer, elute component I with a gradient from 0 to 0.4 M NaCI in 600 ml of 10 mM PB, pH 8.0. Collect the fractions containing component I. 

The sohd can be contacted with the solvent in a number of different ways but traditionally that part of the solvent retained by the sohd is referred to as the underflow or holdup, whereas the sohd-free solute-laden solvent separated from the sohd after extraction is called the overflow. The holdup of bound hquor plays a vital role in the estimation of separation performance. In practice both static and dynamic holdup are measured in a process study, other parameters of importance being the relationship of holdup to drainage time and percolation rate. The results of such studies permit conclusions to be drawn about the feasibihty of extraction by percolation, the holdup of different bed heights of material prepared for extraction, and the relationship between solute content of the hquor and holdup. If the percolation rate is very low (in the case of oilseeds a minimum percolation rate of 3 x 10 m/s is normally required), extraction by immersion may be more effective. Percolation rate measurements and the methods of utilizing the data have been reported (8,9) these indicate that the effect of solute concentration on holdup plays an important part in determining the solute concentration in the hquor leaving the extractor. 

When concentrated acids are used, the carbohydrates are recovered in high yields, but the problem of economically recovering the large quantities of acid used has not been solved. At the present state of development, the dilute acid processes, especially percolating and two-stage, appear more promising. 

Calcium chloride is found in the marine environment. The elemental composition of seawater is 400 ppm calcium, 18,900 ppm chlorine, and many organisms and aquatic species are tolerant of these concentrations. Toxicity arises either from the invasion of freshwater in otherwise saltwater environments or possible toxic doses of calcium chloride from spills, surface mnoff, or underground percolation into typically freshwater streams or aquifers. Various agencies have guidelines for calcium and chloride in potable water (41). The European Economic Community (EEC) is the only agency to have a minimum specification for calcium in softened water. 

The flavor of instant coffee can be enhanced by recovering and returning to the extract or finished dry product some of the natural aroma lost in processing. The aroma constituents from the grinders, percolation vents, and evaporators may be added dkectly or in concentrated or fractionated form to achieve the deskable product attributes. 

Areas affected by significant atmospheric concentrations of contaminants exhibiting the foregoing physical and chemical properties should also be considered as potentially affected by contaminant rainout and settling to surface media. Contaminants dissolved in rainwater may percolate to ground water, run off or fall directly into surface waters, and adsorb to... 

The aqueous percolate is concentrated to dryness by lyophilization, and the solid product obtained is purified by taking up In boiling absolute ethanol, cooling and recovering the solid product paromomycin = -t64° (1% in water). 8y analysis it contains 45.17%... 

The main notion of the percolation theory is the so-called percolation threshold Cp — minimal concentration of conducting particles C at which a continuous conducting chain of macroscopic length appears in the system. To determine this magnitude the Monte-Carlo method or the calculation of expansion coefficients of Cp by powers of C is used for different lattices in the knots of which the conducting par-... 

Experimental dependences of conductivity cr of the CPCM on conducting filler concentration have, as a rule, the form predicted by the percolation theory (Fig. 2, [24]). With small values of C, a of the composite is close to the conductivity of a pure polymer. In the threshold concentration region when a macroscopic conducting chain appears for the first time, the conductivity of a composite material (CM) drastically rises (resistivity Qv drops sharply) and then slowly increases practically according to the linear law due to an increase in the number of conducting chains. 

The maximum values of the percolation threshold are characteristic of matrix systems in which the filler does not form the chain-like structures till large concentrations are obtained. In practice, statistical or structurized systems are apparently preferable because they become conductive at considerably smaller concentrations of the filler. The deviation of the percolation threshold from the values of Cp to either side for a statistical system ( 0.15) can be used to judge the nature of filler distribution. 

The composites with the conducting fibers may also be considered as the structurized systems in their way. The fiber with diameter d and length 1 may be imagined as a chain of contacting spheres with diameter d and chain length 1. Thus, comparing the composites with dispersed and fiber fillers, we may say that N = 1/d particles of the dispersed filler are as if combined in a chain. From this qualitative analysis it follows that the lower the percolation threshold for the fiber composites the larger must be the value of 1/d. This conclusion is confirmed both by the calculations for model systems [27] and by the experimental data [8, 15]. So, for 1/d 103 the value of the threshold concentration can be reduced to between 0.1 and 0.3 per cent of the volume. 

In pressing, the threshold concentration of the filler amounts to about 0.5% of volume. The resulting distribution of the filler corresponds, apparently, to the model of mixing of spherical particles of the polymer (with radius Rp) and filler (with radius Rm) for Rp > Rm as the size of carbon black particles is usually about 1000 A [19]. During this mixing, the filler, because of electrostatical interaction, is distributed mainly on the surface of polymer particles which facilitates the forming of conducting chains and entails low values of the percolation threshold. 

For the second method the threshold concentration of the filler in a composite material amounts to about 5 volume %, i.e. below the percolation threshold for statistical mixtures. It is bound up with the fact that carbon black particles are capable (in terms of energy) of being used to form conducting chain structures, because of the availability of functional groups on their surfaces. This relatively sparing method of composite material manufacture like film moulding by solvent evaporation facilitates the forming of chain structures. 

In the case of the filler localization in one of the polymer components of the mixture, an increase of the portion of the second unfilled polymer component in it entails sharp (by a factor of lO10) rise of a in the conducting polymer composite. In this case the filled phase should be continuous, i.e. its concentration should be higher than the percolation threshold. 

As already noted, the main merit of fibers used as a filler for conducting composite materials is that only low threshold concentrations are necessary to reach the desired level of composite conductivity. However, introduction of fiber fillers into a polymer with the help of ordinary plastic materials processing equipment presents certain difficulties which are bound up mainly with significant shearing deformations entailing fiber destruction and, thereby, a decrease of parameter 1/d which determines the value of the percolation threshold. 

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. 

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