Critical concentration ratio

Laboratory studies of steel in mortar showed that by applying several intense flushings before the ingress of chlorides [6], the onset of corrosion during the test duration of 90 days could be prevented even at chloride concentrations as high as 2 % by mass of cement. A critical concentration ratio MFP/chloride greater than 1 had to be achieved, otherwise the reduction in corrosion rate was not significant [6]. MFP acts as a corrosion inhibitor in carbonated concrete as well. 

This interference arises as a result of overlapping of the spectral lines. Line coincidences become apparent only when a critical concentration ratio between the interfering and analyzed elements is reached. They are dependent on the spectral resolution of the spectrometer. The line coincidences which may occur in the analysis of wastewater have been established in a test. The results of this test are summarized in Table b. 

Elements such as tungsten, zirconium, uranium, and the rare earth elements have multiple spectral lines, which make line selection a difficult task. The degree of interference and sample composition is related to what is called the critical concentration ratio (CCR), which is defined as the ratio of the concentration of interferent i to that of the analyte a at which the ratio of the line intensities IJla is equal to unity. If the measured concentration ratio exceeds the CCR, the intensity of the interferent line will be higher than that of the analyte line and will be detrimental to accuracy. In some spectrometers, optical cross-talk in the region of the exit slit and detector will present itself as a direct overlap. 

Fig. 2-9. Effect of core thorium concentration on critical concentration, ratio of to Th required for criticality, and fraction of total power generated in blanket for some tw O-region slurry reactors, = 2.25, pressure vessel = 10 ft ID, poison fraction = 0, IP in blanket = 3 g/liter, temperature = 280° C.

Let us first introduce some important definitions with the help of some simple mathematical concepts. Critical aspects of the evolution of a geological system, e.g., the mantle, the ocean, the Phanerozoic clastic sediments,..., can often be adequately described with a limited set of geochemical variables. These variables, which are typically concentrations, concentration ratios and isotope compositions, evolve in response to change in some parameters, such as the volume of continental crust or the release of carbon dioxide in the atmosphere. We assume that one such variable, which we label/ is a function of time and other geochemical parameters. The rate of change in / per unit time can be written... 

Celzard A, McRae E, Deleuze C, Dufort M, Furdin G, Mareche JF. Critical concentration in percolating systems containing a high-aspect-ratio filler. Physical Review B. 1996 Mar 1 53(10) 6209-14. 

Fig. 5.12 Two different 3-D representations of the phase diagram of 3-methylpyridine plus wa-ter(H/D). (a) T-P-x(3-MP) for three different H2O/D2O concentration ratios. The inner ellipse (light gray) and corresponding critical curves hold for (0 < W(D20)/wt% < 17). Intermediate ellipses stand for (17(D20)/wt% < 21), and the outer ellipses hold for (21(D20)/wt% < 100. There are four types of critical lines, and all extrema on these lines correspond to double critical points, (b) Phase diagram at approximately constant critical concentration 3-MP (x 0.08) showing the evolution of the diagram as the deuterium content of the solvent varies. The white line is the locus of temperature double critical points whose extrema (+) corresponds to the quadruple critical point. Note both diagrams include portions at negative pressure (Visak, Z. P., Rebelo, L. P. N. and Szydlowski, J. J. Phys. Chem. B. 107, 9837 (2003))...

Fig. 6. Determination of the critical protein concentration. (A) Plot of protein in the supernatant fluid after quantitatively sedimenting polymer from a polymerized solution of tubules and tubulin at steady state. The critical concentration, Ko, is determined from the value of the y axis intercept, and the fraction of active protein, y, from the slope. (B) The conventionally used experimental method for estimating the critical concentration. Note that the x axis intercept is actually Ko/y, instead of Kj,. Interpretation of the slope from such plots requires knowledge of the ratio of polymer weight concentradon to turbidity (given here as a). Data from experiments such as those in A may be used in conjunction with this plot to obtain the cridcal concentration, and this can serve as an internal test for self-consistency of the data.

There are several potential sources of error in these methods. The filters routinely used have a relatively high and somewhat variable sulfate content, so that, at concentrations lower than 10 Mg/m and sampling periods less than 24 h, the reliability of tlie sulfate measurement is reduc. Several different types of filtering media adsorb sulfur dioxide during the ftrst few hours of sampling this alters the amount of sulfate observed. This interference can become critical when sampling periods are less than 24 h and the concentration ratio of sulfur dioxide to sulfate is greater than 5 1. Interference can also be introduced by hot-water extraction when reduced sulfur compounds like sulfite are present, because they are oxidized to sulfates in this process. Another possible error source is that some of the various analytic procedures us for sulfate determination may be influenced by other substances also present in the particulate matter. 

There is a critical need to understand the interaction of multiple pollutants on individual plant species and ecosystems. Multiple-pollutant effects are generally important, but little is known of their effects on most plants. Variable concentrations, ratios of pollutants, and age of plants all affect response. 

The surface of the membrane is also critical in determining membrane efficacy, with more hydrophilic surfaces enabling water to permeate easily. As the surface becomes more and more hydrophobic, it also becomes less permeable to water molecules. With pathogens, studies have shown that a consideration of the volumes of water to be treated (e.g., liters per hour), concentration ratio, or volume of the permeate, which is typically 75-95% of the feed volume and the expected permeate flux (e.g., liters per hour), a reliable prediction about the efficacy of membranes can be made. Similar parameterization needs to be done to determine what works best when it comes to rejecting PPCPs since parameters that are effective for rejecting pathogens may not necessarily apply wholesale to PPCPs. 

When Co grows, the network volume slightly decreases and the concentration of surfactant q within the network increases. When cjj, exceeds a critical concentration of micelle formation (at this point cq = c, see Figs.14,15), the network collapses because the surfactant molecules aggregated in micelles cease to impose osmotic pressure which causes additional expansion of the network. At relatively small values of the ratio Vf/V, the collapse is continuous (Figs. 14, 15), so that the number of surfactant molecules in micelles increases from zero starting at the concentration c. However, when the ratio Vf/V is sufficiently large, a discrete first-order phase transition takes place. 

Figure 5 shows the dependence of the swelling ratio, X, on the acetone content, a, in a water-acetone mixtures of ionized poly(acrylamide) networks the charges onto PAAm chains were introduced by the copolymerization of acrylamide with a low amount of sodium methacrylate [11] (the molar fraction xMNa = 0, 0.004, 0.008, 0.012, 0.016 and 0.024 for series A, B, C, D, E and F, respectively). While in series A and B the dependence of X on composition of the mixtures is continuous, in the other series (C-F) with xMNa > 0.008 a collapse takes place. The extent of the transition and the critical concentration of the acetone at which the collapse appears, ac, increase with increasing xMNa. 

Tn the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. At the critical concentration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, II, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity (15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Omstein and Zemike (25), Debye (3) made the assumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local... 

The critical concentration was obtained from measurements of the phase-volume ratio of coexisting phases near the critical temperature. At an over-all concentration of 8.5 wt % this ratio was unity. According to the lever rule this concentration is the critical one. 

The value of this critical concentration, (/i)c, lies within the permissible range 0 < fi < 1 only if both rx and r2 are greater than unity or if both are less than unity. The case of f > 1 and r2 > 1 is unknown. If one of the reactivity ratios exceeds unity while the other is less than unity, no critical composition exists. 

FIGURE 20.5 Cumulative particle size distribution pt= 0.62 for different ratios of the binary mixture lactose (L)/corn starch (MS). The granule diameter is critically linked to the concentration ratio (percolation effect ). (From Leuenberger, H., Usteri, M., Imanidis, G, and Winzap38ll,. Chem. Farrn 128, 54-61... 

Making some assumptions on the chemical filiation between some organo-sulfur compounds, it was possible to establish the mathematical variation law for the concentration ratio of the various detected species and consequently to deduce the depletion rate constant of these compounds. From the measurements at the "Pointe de Penmarc h" in September 1983, the DMS lifetime estimations obtained are reported in Table I. This method for determining chemical lifetimes can only be applied for local and intensive sources. The most critical point concerns the chemical relation between the various sulfur compounds which should be verified in order to validate these estimations. However, the other assumptions do not seem to have a significant influence on the lifetime estimation within an order of magnitude. 

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