Overlap concentration apparent

Let us remark that relation (6) is given for polymer concentration c lower than the critical overlapping concentration c above which higher terms in c must be considered. In fact, the concentration practically used ( around 10 3 g/cm3) corresponds to the semi-dilute regim for which the behavior is not well known in the case of polyelectrolytes. We have however kept relation (6) by introducing for K a mean apparent value determined from our experiments ( K - 1 )... 

The concentration dependences of the apparent aggregation number (Figure 7.1), the cooperative diffusion coefficient (Figure 7.2), and the zero-shear viscosity (Figure 7.4) strongly suggest entanglement of worm-like micelles. The overlap concentrations are obtained to be about 0.7, 0.4, and 0.2 wt% at 35, 40, 45 °C, respectively, from the concentrations above which the zero-shear viscosity increases rapidly. 

In semidilute and concentrated solntions, polymer molecules are no longer isolated from one another. Chain-chain interactions at and above a critical concentration c, often termed the overlap concentration, lead to increased values of apparent viscosity rj. Apparent viscosity can be related to concentration and molecular weight by equation 4, in which b and d are scaling constants. 

Figure 4 displays the general behavior of the shear-thickening transition observed with imposed shear rate. The steady shear stress cj(7) and the steady apparent shear viscosity 17(7) are shown as a function of the applied shear rate for the hexadecyl-trimethylammonium/7-toluenesulfonate (CTAT) at c = 0.41 wt. %. For this system, the overlap concentration was estimated at c = 0.5 wt. % and the shear-thickening to be present over the range 0.05-0.8 wt. % [75,103]. 

In semidilute and concentrated solutions, polymer chains are no longer isolated. Above a critical concentration, c, often termed the overlap concentration, intermo-lecular interactions occur that lead to increased values of apparent viscosity [2]. The apparent viscosity is the viscosity of a non-Newtonian fluid at a single shear rate and is expressed in units of mPa-s (= cP, centipoise). The apparent viscosity -n is related to concentration c and molecxilar weight M through... 

Further, peak overlap results in nonlinear detector response vs concentration. Therefore, some other detection method must be used in conjunction with either of these types of detection. Nevertheless, as can be seen from Figure Ilf, chiroptical detection can be advantageous if there is considerable overlap of the two peaks. In this case, chiroptical detection may reveal that the lea ding and tailing edges of the peak are enantiomerically enriched which may not be apparent from the chromatogram obtained with nonchiroptical detection (Fig. He). 

Of the elements characteristically present as major components of nonsaline waters, only calcium produced a slight interference. A weak calcium line at approximately 190.73 nm partially overlaps the sulfur fine such that 1000 mg/1 Ca produces an apparent signal of 25 mg/1 sulfate. Correction for this interference is easily achieved by establishing the relationship between calcium concentration and apparent sulfate signal, and inserting this information in the controlling software. The effect of calcium was then automatically subtracted during the measurement of the sample. 

In hindsight, the primary factor in determining which approach is most applicable to a particular reacting flow is the characteristic time scales of the chemical reactions relative to the turbulence time scales. In the early applications of the CRE approach, the chemical time scales were larger than the turbulence time scales. In this case, one can safely ignore the details of the flow. Likewise, in early applications of the FM approach to combustion, all chemical time scales were assumed to be much smaller than the turbulence time scales. In this case, the details of the chemical kinetics are of no importance, and one is free to concentrate on how the heat released by the reactions interacts with the turbulent flow. More recently, the shortcomings of each of these approaches have become apparent when applied to systems wherein some of the chemical time scales overlap with the turbulence time scales. In this case, an accurate description of both the turbulent flow and the chemistry is required to predict product yields and selectivities accurately. 

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