Peak Separation

Another error can arise when two partially resolved peaks are asymmetrical, e.g., the rear half of the peak is broader the front half. In such a situation, it is clear that there can be two sources of error, which are depicted in Figure 4. Firstly, the retention times, as measured from the peak envelope, will not be accurate. Secondly, because the peaks are asymmetrical (and most LC peaks tend to be asymmetrical to the extent shown in the Figure 4), the second peak appears higher. This can incorrectly imply that the second solute is present at a higher concentration in the mixture than the first. It follows that it is important to know the value of the specific separation ratio above which accurate measurements can still be made on the peak maxima of the individual peaks. The apparent peak separation ratio, relative to the actual peak separation ratio for columns of different efficiency, are shown in Figure 5. The data has been obtained from theoretical equations. 

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. 

In our early evaluations, three parameters were utilized for the resolving power of the columns (3,4,7). These were the valley-to-peak height ratio, v, the peak separation parameter, P, and the parameter mentioned earlier, Djcr. The valley-to-peak height ratio is defined as... 

TABLE 21.4 Peak Resolution Parameters Valley-to-Peak Ratios, v, and Peak Separation Parameters, P, for Batch 52 Gel... 

The final step in the process of standardizing our columns was to try and maintain the high quality of columns from batch to batch of gel from the manufacturer. This was done by following the basic procedures outlined earlier for the initial column evaluation with two exceptions. First, we did not continue to use the valley-to-peak ratios or the peak separation parameters. We decided that the D20 values told us enough information. The second modification that we made was to address the issue of discontinuities in the gel pore sizes (18,19). To do this, we selected six different polyethylenes made via five different production processes. These samples are run every time we do an evaluation to look for breaks or discontinuities that might indicate the presence of a gel mismatch. Because the resins were made by several different processes, the presence of a discontinuity in several of these samples would be a strong indication of a problem. Table 21.5 shows the results for several column evaluations that have been performed on different batches of gel over a 10-year period. Table 21.5 shows how the columns made by Polymer Laboratories have improved continuously over this time period. Figure 21.2 shows an example of a discontinuity that was identified in one particular evaluation. These were not accepted and the manufacturer quickly fixed the problem. 

A bimodal distribution is a frequency distribution of a certain phenotype with two peaks separated by an antimode. 

Thus, the peak separation can be used to determine the number of electrons transferred, and as a criterion for a Nemstian behavior. Accordingly, a fast one-electron process exhibits a AEp of about 59 mV Both the cathodic and anodic peak potentials are independent of die scan rate. It is possible to relate the half-peak potential (Ep/2. where the current is half of the peak current) to the polarographic half-wave potential, El/2 ... 

The peak-shaped response of differential-pulse measurements results in unproved resolution between two species with similar redox potentials, hi various situations, peaks separated by 50 mV may be measured. Such quantitation depends not only upon the corresponding peak potentials but also on the widths of the peak. The width of the peak (at half-height) is related to the electron stoichiometry ... 

The increased peak separation is not normally kinetic in origin, although it can have a kinetic component. Its origins have been discussed... 

To determine the band dispersion that results from a significant, but moderate, sample volume overload the summation of variances can be used. However, when the sample volume becomes excessive, the band dispersion that results becomes equivalent to the sample volume itself. In figure 10, two solutes are depicted that are eluted from a column under conditions of no overload. If the dispersion from the excessive sample volume just allows the peaks to touch at the base, the peak separation in milliliters of mobile phase passed through the column will be equivalent to the sample volume (Vi) plus half the base width of both peaks. It is assumed in figure 10 that the efficiency of each peak is the same and in most cases this will be true. If there is some significant difference, an average value of the efficiencies of the two peaks can be taken. 

Sodium has 1 valence electron, and 10 bound electrons. The first two excited states are the 3 Pi/2 and the 3 P3/2 states. Transitions to these levels give rise to the Di and D2 transitions respectively. There are two h)q)erfine levels in the 3 ground state, and four h)q)erfine levels in the 3 Pa/2 excited state (Fig. 3). There is no significant energy difference between the h)q)erfine levels in the 3 Pa/2 state. Thus, the six permitted fines appear in two groups, producing a double peaked spectral distribution, with the peaks separated by 1.772 GHz. 

Figure 4. Absorption cross-section I or the Na >2 line. The center wavelength is 589.158 and the peak separation is 1.772 GHz.

The cyclic voltammograms of ferrlcyanlde (1.0 mM In 1.0 M KCl) In Fig. 2 are Illustrative of the results obtained for scan rates below 100 mV/s. The peak separation is 60 mV and the peak potentials are Independent of scan rate. A plot of peak current versus the square-root of the scan rate yields a straight line with a slope consistent with a seml-lnflnlte linear diffusion controlled electrode reaction. The heterogeneous rate constant for the reduction of ferrlcyanlde was calculated from CV data (scan rate of 20 Vs using the method described by Nicholson (19) with the following parameter values D 7.63 X 10 cm s , D, = 6.32 X 10 cm s, a 0.5, and n =1. The rate constants were found to be... 

The slopes of the calibration curves for the HDC and Fractosil systems are 0.512 and 0.289, respectively. This indicates that the "resolution of the peak separation" for the Fractosil system is superior to that of HDC, since resolution is considered to be inversely proportional to the slope of the log particle diameter - AV calibration curve (26). However when peak spreading is taken into account, the actual relative resolution between particle populations is less for the Fractosil system 2k) a result which indicates that overall, for size distribution resolution, the HDC system is superior. 

A were packed. They were individually calibrated. All three 3000 A columns showed similar peak separation characteristics for particle sizes between 312 nm and 5TQnm. However, peak broadening was much larger for one of the 3000 A 0olumns. This column was discarded. Of the remaining two 3000 A columns, one was subjected to the following ... 

Calibration of each column one at a time results in the weeding out of those columns which have inadequate peak separation, excessive peak broadening and significant particle loss by entrapment in the packing. 

Attempts to do this indicated that differences on the order of 30% of the peak separation shown in Figure 16 were probably due to such effects. At other sampling points, better and worse results were observed likely because the tail heights of distributions were being sampled. 

Optimization of Peak Separation and Broadening in Aqueous Gel Permeation Chromatography... 

In the investigation reported herein, an attempt has been made to maximize peak separation and minimize peak broadening for aqueous GPC of polyacrylamides with CPG porous glass packings. 

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