Peak volume

Peak volume is the volume of mobile phase or eluate containing the eluting peak. Peak volume is proportional to k and VM. This relationship between peak volume and these factors can be derived by rearranging Eq. 2.10  

Since for a given column and a set of operating conditions N is approximately constant and (1 + k) is roughly equal to k in most cases where k is much greater than 1, peak volume is proportional to k and VM. This relationship is important because of the increasing use of smaller-diameter columns (column i.d. 3 mm) with smaller VM, since the smaller peak volumes from these columns are highly affected by the deleterious effect of dispersion by the instrument (extra-column bandbroadening). This effect will be discussed section 4.10 of Chapter 4. 

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Figure 6 Steps in automated assignment. (1) Select the lowest energy structures from iteration / — 1 that are used to interpret the spectra. (2) For each peak, list all possible assignments compatible with the resonances within a frequency mnge. (3) Extract a distance for each assignment possibility from the ensemble of structures. (4) Use the distances to assign ambiguous NOEs. (5) Calibrate the peak volumes to obtain distance restraints. (6) Calculate structures based on the new restraints.

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

This extreme condition rarely happens but serious peak distortion and loss of resolution can still result. This is particularly so if the sensor volume is of the same order of magnitude as the peak volume. The problem can be particularly severe when open tubular columns and columns of small diameter are being used. Scott and Kucera measured the effective sensor cell volume on peak shape and their results are shown in Figure 13. 

The column is a small bore column and, thus, the eluted peaks have a relatively small peak volume, which is commensurate with that of the sensing cell. It is seen that even a sensor volume of 1 pi has a significant effect on the peak width and it is clear that if... 

For an LC column operating at a flow rate of 1 ml/min., a peak with a base width of 4 seconds would represent a peak volume of about 67 pi. Consequently, the peaks... 

To confirm the pertinence of a particular dispersion equation, it is necessary to use extremely precise and accurate data. Such data can only be obtained from carefully designed apparatus that provides minimum extra-column dispersion. In addition, it is necessary to employ columns that have intrinsically large peak volumes so that any residual extra-column dispersion that will contribute to the overall variance is not significant. Such conditions were employed by Katz et al. (E. D. Katz, K. L. Ogan and R. P. W. Scott, J. Chromatogr., 270(1983)51) to determine a large quantity of column dispersion data that overall had an accuracy of better than 3%. The data they obtained are as follows and can be used confidently to evaluate other dispersion equations should they appear in the literature. 

Small-diameter packed columns offer (17) the substantial advantages of small volumetric flow rates (1-20 (p.L min )), which have environmental advantages, as well as permitting the use of exotic or expensive mobile phases. Peak volumes are reduced (see Table 1.1), driven by the necessity of analysing the very small (pico-mole) amounts of substance available, for example, in small volumes of body fluids, or in the products of single-bead combinatorial chemistry. 

Now from figure 3 it is seen that the retention volume is about 22 ml and thus a mean value for the peak volume can be calculated. 

Using the usual equation, the peak volume is given by... 

The small peak volumes typical of samples eluted from small bore columns and short small diameter particle columns used in high-speed liquid chromatography place severe demands on the dispersion characteristics of all components of the liquid chromatograph. The standard deviation of a peak eluting from a column is given by... 

The peak volume is directly proportional to the square of the column diameter and the column length and decreases with Increasing column efficiency (decreases for smaller particle packings). The concentration at the peak maximum, C—, is given by... 

TYPICAL RANGES FOR VALUES OF COLUMN VARIANCE AND PEAK VOLUMES OF AN UNRETAINED PEAK... 

Detector selectivity is much more important in LC than in GC since, in general, separations must be performed with a much smaller number of theoretical plates, and for complex mixtures both column separation and detector discrimination may be equally significant in obtaining an acceptable result. Sensitivity is important for trace analysis and for compatibility with the small sizes and miniaturised detector volumes associated with microcolumns in LC. The introduction of small bore packed columns in HPLC with reduced peak volume places an even greater strain on LC detector design. It is generally desirable to have a nondestructive detector this allows coupling several detectors in series (dual... 

Reduced analysis volumes minimal peak volumes... 

Comparing the small and the large bore columns, if we injected the same mass of solute each time, then for the small bore column the same mass of solute would be present in a smaller peak volume, which means that we can get the same concentration of solute in a peak from a small bore column using a smaller mass of solute. The detector in our system will respond to the concentration of solute, so that with the small bore columns we will be able to detect smaller amounts of material. This is important in dealing with samples where only small quantities are available, for instance those of biological origin. 

As early GC peaks elute in a few seconds or less, rapid scanning of the mass range of interest is necessary. Fast scanning also allows partially resolved GC peaks to be sampled several times,peak slicing, to facilitate identification of the individual components (Figure 12.5) provided that the dead volume of the interface is small compared to peak volumes. For the speedy interpretation of spectral data from complex chromatograms a... 

Calculated Peak Volumes, Theoretical Column Efficiencies without Dispersion, and Column Efficiencies with Assumed Dispersion of 20 jiL for Different Dimensions and Particle Sizes... 

Column Dimension Peak Volume without Theoretical Efficiency with 20 jiL... 

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