Extreme separation width

The extreme separation width shown with arrows in Fig. 8.2 gradually narrows and steeply drops with an increase in temperature. The temperature dependence of the extreme separation width for each specimen is shown in Fig. 8.3. The steep drop is caused by a micro-Brownian type molecular motion reflecting the glass-rubber transition. We can estimate a transition temperature of the molecular motion, Ts.omT where the extreme separation width is equal to 5.0 mT. The Ts.omT values of the spin-labeled PS at the chain end (Ts.omi.e) and the inside sites (Ts.omxi) are 423 and 435 K, respectively. The Ts.omx of the spin-labeled PS at the chain end is thus lower... 

Mn = 22 kDa). Separation between arrows shows extreme separation width. 

Fig. 8.3 Temperature dependence of extreme separation width for spin-labeled PS at chain end (solid) and at inside site (open). The figure is adapted from [7] with permission from the American Chemical Society...

Fig. 8.10 Temperature dependence of ESR extreme separation width for the spin-probed and spin-labeled PMMA films. The figure is adapted from [15] with permission from John WUey Sons...

Consider the separation depicted in Figure 1. It is assumed that the pair of solutes represent the elution of the solute of interest and its nearest neighbor. Now, when the sample volume becomes extreme, the dispersion that results from column overload, to the first approximation, becomes equivalent to the sample volume itself as the sample volume now contributes to the elution of the solutes. Thus, from Figure 1, the peak separation in milliliters of mobile phase will be equivalent to the volume of sample plus half the sum of the base widths of the respective peaks. 

When a particular component eluting at a certain retention volume is to be estimated, this approach can be outlined as follows. Since SEC is extremely reproducible, the peak shape, peak width and peak height are dependent on the amount of the species in the sample volume injected, sample volume and retention time. From these factors the SEC peaks can be simulated or elution pattern of any species within the separation range can be plotted as a function of mass vs. retention volume. The analysis data supplies the concentration of this particular species over two or more 0.5 ml intervals. A match-up computer program has to be developed so that it can pick up the peak shape and concentration based on 3 or 4 data points at known Intervals. 

Second, consider the quantity s(k ). This is an estimate of the standard error of k based on ( —2) degrees of freedom. We use the quantity standard error to describe the width of the distribution of k values which we would observe if we were able to make a vast number of separate determinations we use the term standard error rather than standard deviation to remind us that the distribution under consideration is a distribution of mean values, each of which is itself derived from a population. The term ( —2) degrees of freedom signifies that, out of our nt experimental pairs of observations, only ( —2) are available to give us an estimate of the precision of the measurement, the other two having been lost in fixing the two parameters, /j and k, of our fitted line. Now, clearly we can never obtain a vast number of determinations of a statistic such as k in order to obtain a value for its standard error necessarily, the number of observations which we can make is limited and so we cannot do any better than make an estimate of what the width of the distribution would b6 for a yast population. This estimate is extremely useful for it enables us to calculate from the sample mean, i.e. k[, the limits between which the population mean is likely to lie. Suppose we designate the population mean by the symbol. A). We now introduce the statistic, t,... 

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