Volume fraction, excess, conductivity

Figure 4.37. Comparison between the present theory (dashed), the Fixman theory (solid curves) and the exact numerical results by DeLacey and White (diamonds) Ka = 20, a = 200 nm, Ff /RT = 4. Left excess conductivity per unit volume fractions of the colloid right, excess dielectric loss.

Figure 9. Log-log plot of conductivity vs. excess volume fraction (c-Co) of the aqueous phase. Typical error bars for the determination of volume fraction are shown. The corresponding errors for conductivity are much smaller and omitted for clarity. The straight line is a fit of the percolation prediction Equation 1 to the data with n = 1.5, Co = 0.10, and

FIGURE 4.8.9. Log-log plot of conductivity vs excess volume fraction (C-Cq) of the aqueous diase with the clustra -network model [23]. (Reprinted with permission from the American Chemical Society.)... 

In order to conduct these analyses, the detection limit of the instrument must be known. The detection limit is defined (in ppm or ppb) as the concentration of analyte that allows a detectable signal to be measured with certainty - for example, three times the standard deviation of the background signal or the blank. If the volume of solution needed to obtain these results is known, the preceding values can be transformed to the absolute quantities or mole fractions (pico-mole, femtomole, etc.) that are needed to obtain the signal. In general, these values are excessively small because current instruments use excessively small volumes. 

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