Critical concentration, definition

At the same time, there are instances in which critical concentration determinations still do not offer the experimenter the opportunity to reach a definitive conclusion about important aspects of protomer-polymer interactions. The lack of agreement about the polymerization properties of the Tb GDP complex is an excellent example. Several investigators have claimed that the tubulin GDP complex can elongate microtubules (Carlier and Pantaloni, 1978 Karr et al, 1979b) others. 

At a temperature below the Curie point TC1 it is plain from Eq. (3.7) that for concentrations nearer than a certain critical concentration the alloys will bo below their Curie points and will be in partly ordered phases, while for x less than this critical concentration they will be above their Curie points and will be in the disordered state. This is indicated in Fig. XVIII-7, where wo show G as a function of w for different values of x, at a temperature of 0.8 Tc. The critical concentration for this temperature is 0.277, as can be found at once from Eq. (3.7) it is noted in Fig. XVIII-7 that the curves for x = 0.1 and 0.2 definitely have their minima at w = 0, indicating complete disorder, while that for x = 0.3 is very flat at the center, and those for 0.4 and 0.5 definitely have minima for w 0, indicating a partly ordered state. Finally, in Fig. XVIII-8 we show G as a function of x, for different values of w, at this same tern-... 

Rudin and Strathdee (1974) remarked that the equations presented for the viscosity of dilute polymer solutions were valid approximately up to the critical concentration. This leads to a more general definition of a concentrated polymer solution, viz. a solution for which c > ccr. 

Temperature dependence of the critical concentration Ce of a foam bilayer formation. The Cc concentration (see Eq. (3.129)) of formation of DMPC foam bilayer was determined on the basis of observations of the final state which the foam film reached during its drainage (see Section 3.2), i.e. either rupture at a definite critical thickness without formation of black spots occurs, or formation of foam bilayer via black spots is observed. Rupture at critical thickness occurred at lower DMPC concentrations in the solution (C < Cc) and black spots were formed at higher concentrations (C > Cc). These black spots encountered the film turning it into a foam bilayer of constant radius. At each temperature a series of observations were carried out at various DMPC concentrations for the determination of Cc (the minimum DMPC concentration at which a foam bilayer is formed). This concentration is... 

An Interesting formal treatment of risk estimation has recently been put forward by Nordberg and Strangert (4). Conceptually It deals with compartmental movement, metabolism and the definition of the critical organ, critical effects and critical concentration. It also defines a new concept, the "damage" function," relating to the critical Injury. 

Usually when one talks about the deficient, sufficient, and toxic concentrations of nutrients in crops, there is a range of values, rather than one definite number that can be considered as critical. Therefore, use of the term critical concentration in crops is somewhat misleading. A nutrient concentration considered critical by workers in some areas may not be critical under conditions in other areas. Likewise, use of the term optimum concentration of a nutrient, as used in the literature by some researchers to express a relationship to maximum crop yield, sometimes... 

Then there must be a minimum of energy, in other words, a limited Grosz-mizelle of a definite size is produced which is in equilibrium with the Hartley micelles. Stauff (1941) gives the following picture of this Groszmizelle (Fig. 20). These Groszmizellen accordit to Staxjff are produced from associated Hartley micelles. A definite critical concentration cannot be detected there is an equilibrium... 

Dependence of the adsorbed amount on the polymer concentration is given for a typical unhydrolyzed and a partially hydrolyzed polyacrylamide in Figures 5 and 6. Apart from the fact that the absolute values indicate considerable differences, it is characteristic that n increases with the pol3nner concentration. Within this general tendency, as it appears from these curves, the steep increase occurs after a definite pol3nner concentration in all cases. Before this critical concentration—similar to the equilibrium section of static adsorption isotherms—the adsorbed amount does not depend significantly on polymer concentration. Incidentally, the critical polymer concentration in 2 gdm" NaCl is increased twofold over values measured in distilled water for both polymers. 

Thickener Basin Area (Unit Area). The thickener basin area is determined from the solid flux rates at the critical concentration in the hindered settling regime. By definition, the critical point can be experimentally determined from the solids concentration just prior to the beginning of the compression zone. For a nonflocculated system, the basin area, expressed as the unit area (m /ton/d), Aq, can be calculated using the equation (Osborne, 1990)... 

While Bennhold s first studies were made on whole serum, he later proceeded to study serum fractions, and showed that the cbaracteristic dye binding in most cases was due almost entirely to the albumin fraction. These conclusions were further extended by a long series of studies on the cataphoresis of serum proteins and protein fractions, using the type of apparatus developed by Michaelis. The attachment of these various dyes to the proteins was clearly revealed, and the color of the dye-protein complex permitted the observation of a well-defined boundary. Definite limits to the binding capacity of serum albumin for dye were observed in these studies. Above a certain critical concentration free dye was recognizable in solution and moved in the electric field with a velocity different from that of the albumin-dye complex. Bennbold also showed that bilirubin, when added to serum, was quantitatively bound to the albumin, up to a certain limited binding power. 

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

Depth tends to be determined from the retention time and the surface overflow rate. As surface overflow rates were reduced, the depth of sedimentation tanks was reduced to keep retention time from being excessive. It was recognized that depth was a valid design parameter and was more critical in some systems than retention time. As mixed-liquor suspended-solids (MESS) concentrations increase, the depth should also be increased. Minimum sedimentation-tank depths for variable operations should be 3.0 m (10 ft) with depths to 4.5 m (15 ft) if 3000 mg/L MESS concentrations are to be maintained under variable hydraulic conditions. With MESS concentrations above 4000 mg/L, the depth of the sedimentation tank should be increased to 6.0 m (20 ft). The key is to keep a definite freeboard over the settled-sludge blanket so that variable hydraulic flows do not lift the solids over the effluent weir. 

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