Capacity peak ratio

As already mentioned, there are two so called "dead volumes" that are important in both theoretical studies and practical chromatographic measurements, namely, the kinetic dead volume and the thermodynamic dead volume. The kinetic dead volume is used to calculate linear mobUe phase velocities and capacity ratios in studies of peak variance. The thermodynamic dead volume is relevant in the collection of retention data and, in particular, data for constructing vant Hoff curves. 

Equation (16) was first developed by Purnell [3] in 1959 and is extremely important. It can be used to calculate the efficiency required to separate a given pair of solutes from the capacity factor of the first eluted peak and their separation ratio. It is particularly important in the theory and practice of column design. In the particular derivation given here, the resolution is referenced to (Ra) the capacity ratio of the first... 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

Figure 20. Graph of Peak Capacity against Capacity Ratio...

It has also been shown that the effect of sample volume on peak width will be most significant for the early peaks (the most narrow peaks). In addition, the degrading effect of sample volume will progressively decrease as the capacity ratio of the peak becomes larger. However, the resolution of both late and early peaks are equally important and, consequently, the limiting sample volume will be that which restrains the dispersion of the first peak to 5% or less. 

Equation (33) shows that the maximum capacity ratio of the last eluted solute is inversely proportional to the detector sensitivity or minimum detectable concentration. Consequently, it is the detector sensitivity that determines the maximum peak capacity attainable from the column. Using equation (33), the peak capacity was calculated for three different detector sensitivities for a column having an efficiency of 10,000 theoretical plates, a dead volume of 6.7 ml and a sample concentration of l%v/v. The results are shown in Table 1, and it is seen that the limiting peak capacity is fairly large. 

Table 1. Capacity Ratios and Peak Capacities for Detectors of...

Column design involves the application of a number of specific equations (most of which have been previously derived and/or discussed) to determine the column parameters and operating conditions that will provide the analytical specifications necessary to achieve a specific separation. The characteristics of the separation will be defined by the reduced chromatogram of the particular sample of interest. First, it is necessary to calculate the efficiency required to separate the critical pair of the reduced chromatogram of the sample. This requires a knowledge of the capacity ratio of the first eluted peak of the critical pair and their separation ratio. Employing the Purnell equation (chapter 6, equation (16)). 

Capacity Ratio (first eluted peak of the Critical Pair) (k ) Capacity Ratio (first eluted peak of the Critical Pair) (k") Viscosity of the Mobile Phase (r])... 

The function f(k ) is shown plotted against the thermodynamic capacity ratio in Figure 1. It is seen that for peaks having capacity ratios greater than about 2, the magnitude of (k ) has only a small effect on the optimum particle diameter because the efficiency required to effect the separation tends to a constant value for strongly retained peaks. From equation (1) it is seen that the optimum particle diameter varies as the square root of the solute diffusivity and the solvent viscosity. As, in... 

Capacity Ratio (first eluted peak of the Critical Pair) (k ) 2.5... 

Employing equation (1), curves relating maximum sample volume to the capacity ratio of the first eluted peak for different separation ratios were calculated and constructed and the results are shown in Figure 2. 

Figure 2. Curves Relating Maximum Sample Volume to the Capacity Ratio of the First Peak for Different Separation Ratios...

The dimensionless ratio P/ corresponds to the ratio between the number of visible peaks, under the proposed chromatographic conditions, with the chromatographic column having a peak capacity . Differentiation of equation 5.6 with respect to a gives the maximum possible value of the ratio P/ and shows this to occur at a = 1 then, the maximum ratio P/ can be estimated by the following equation ... 

The columns must be designed or chosen such that the critical pair are separated and, as a second priority, the last peak must be eluted in a reasonable time. The first peak in the chromatogram is not considered part of the reduced chromatogram and is included as the dead volume marker from which the capacity factors of each solute can be calculated, together with the separation ratio of the critical pair. 

The effect of temperature on column efficiency, however, is frequently exploited, particularly in size exclusion chromatography (SEC). As has already been discussed, high efficiencies are essential in SEC due to the limited peak capacity of the column and consequently, the very small separation ratios. However the effect of temperature on column efficiency is not well understood by many analysts and consequently, will be discussed in some detail. It was shown on page... 

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