Resolution capacity factor

The modern analytical laboratory employing instrumental chromatography uses a computer data collection system and associated software to acquire the data and display the chromatogram on the monitor. Parameters important for qualitative and quantitative analysis, including retention times and peak areas, are also measured and displayed. The software can also analyze the data to determine resolution, capacity factor, theoretical plates, and selectivity. 

Efficiency or plate count (N)—an assessment of column performance. N should be fairly constant for a particular column and can be calculated from the retention time and the peak widths. Selectivity (a)—the ratio of retention k ) of two adjacent peaks. Sample capacity— the maximum mass of sample that can be loaded on the column without destroying peak resolution. Capacity factor k )—a measure of solute retention obtained by dividing the net retention time by the void time. 

Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

Now that we have defined capacity factor, selectivity, and column efficiency we consider their relationship to chromatographic resolution. Since we are only interested in the resolution between solutes eluting with similar retention times, it is safe to assume that the peak widths for the two solutes are approximately the same. Equation 12.1, therefore, is written as... 

Finally, solute A s capacity factor is eliminated using equation 12.11. After rearranging, the equation for the resolution between the chromatographic peaks for solutes A and B is... 

Equations 12.21 and 12.22 contain terms corresponding to column efficiency, column selectivity, and capacity factor. These terms can be varied, more or less independently, to obtain the desired resolution and analysis time for a pair of solutes. The first term, which is a function of the number of theoretical plates or the height of a theoretical plate, accounts for the effect of column efficiency. The second term is a function of a and accounts for the influence of column selectivity. Finally, the third term in both equations is a function of b, and accounts for the effect of solute B s capacity factor. Manipulating these parameters to improve resolution is the subject of the remainder of this section. 

One of the simplest ways to improve resolution is to adjust the capacity factor for solute B. If all other terms in equation 12.21 remain constant, increasing k improves resolution. As shown in Figure 12.11, however, the effect is greatest when the... 

Any improvement in resolution obtained by increasing ki generally comes at the expense of a longer analysis time. This is also indicated in Figure 12.11, which shows the relative change in retention time as a function of the new capacity factor. Note that a minimum in the retention time curve occurs when b is equal to 2, and that retention time increases in either direction. Increasing b from 2 to 10, for example, approximately doubles solute B s retention time. 

The relationship between capacity factor and analysis time can be advantageous when a separation produces an acceptable resolution with a large b. In this case it may be possible to decrease b with little loss in resolution while significantly shortening the analysis time. 

Adjusting the capacity factor to improve resolution between one pair of solutes may lead to an unacceptably long retention time for other solutes. For example, improving resolution for solutes with short retention times by increasing... 

If the capacity factor and a are known, then equation 12.21 can be used to calculate the number of theoretical plates needed to achieve a desired resolution (Table 12.1). For example, given a = 1.05 and kg = 2.0, a resolution of 1.25 requires approximately 24,800 theoretical plates. If the column only provides 12,400 plates, half of what is needed, then the separation is not possible. How can the number of theoretical plates be doubled The easiest way is to double the length of the column however, this also requires a doubling of the analysis time. A more desirable approach is to cut the height of a theoretical plate in half, providing the desired resolution without changing the analysis time. Even better, if H can be decreased by more than... 

Generally it was found that resolution R is practically the same for isoeluotropic mixtures methanol and acetonitrile with water. The dependencies were obtained between capacity factors for derivatives of 3-chloro-l,4-naphtoquinone at their retention with methanol and acetonitrile. Previous prediction of RP-HPLC behaviour of the compounds was made by ChromDream softwai e. Some complications ai e observed at weak acetonitrile eluent with 40 % w content when for some substances the existence of peak bifurcation. 

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... 

As described above, resolution can be improved by variations in plate number, selectivity or capacity factor. However, when considering the separation of a mixture which contains several components of different retention rates, the adjustment of the capacity factors has a limited influence on resolution. The retention times for the last eluted peaks can be excessive, and in some cases strongly retained sample components would not be eluted at all. 

To a first approximation the three terms in equation (1.46) and (1.47) can be treated as independent variables. For a fixed value of n Figure 1.8 Indicates the influence of the separation factor and capacity factor on the observed resolution, when the separation factor equals 1.0 there is no possibility of any separation. The separation factor is a function of the distribution coefficients of the solutes, that is the thermodynamic properties of the system, and without some... 

Figure 1.9 Observed change in resolution In a two peak chroaatogreuB for different values of the sepeuratlon factor or nunber of theoretical plates. The average capacity factor Is Indicated by k with a bar on top. (Reproduced with pemisslon fron ref. 108. Copyright Elsevier Scientific Publishing Co.)...

The plate number in equation (4.56) corresponds to the value when the effective value of the capacity factor (equal to k when the band is at the column midpoint) is equal to the capacity factor in isocratic elution for the same column. The effective value of the capacity factor, k, is simply 1/1.15b. In most cases k, will be large and equation (4.57) is simplified by equating l/k, to zero. The resolution between two adjacent bands in a gradient program, again analogous to isocratic elution, is e q>ressed by equation (4.58)... 

Figure 1.8 Influence of varying the separation factor and capacity factor on the observed resolution for two closely spaced peaXs.

Figure 1.9 illustrates the relationship between resolution, the separation factor, the average capacity factor and the column efficiency for some real chromatographic peaks [lOS]. The central portion of the figure illustrates how resolution increases with the capacity factor for a fixed separation factor and column efficiency. At first the resolution increases quickly as the... 

Any optimization strategy that considered only efficiency is inadequate to describe accurately resolution, which is a strong function of the capacity factor at low capacity factor values. The... 

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