Gradient elution calculation

Equation (13) is simpler than Eq. (12) and therefore more convenient for many gradient elution calculations. 

This equation, although originating from the plate theory, must again be considered as largely empirical when employed for TLC. This is because, in its derivation, the distribution coefficient of the solute between the two phases is considered constant throughout the development process. In practice, due to the nature of the development as already discussed for TLC, the distribution coefficient does not remain constant and, thus, the expression for column efficiency must be considered, at best, only approximate. The same errors would be involved if the equation was used to calculate the efficiency of a GC column when the solute was eluted by temperature programming or in LC where the solute was eluted by gradient elution. If the solute could be eluted by a pure solvent such as n-heptane on a plate that had been presaturated with the solvent vapor, then the distribution coefficient would remain sensibly constant over the development process. Under such circumstances the efficiency value would be more accurate and more likely to represent a true plate efficiency. 

Also in this case the calculated (predicted) retention values showed good agreement with the experimental results. It has been concluded that pH gradient elution may enhance the separation efficacy of RP-HPLC systems when one or more analyses contain dissociable molecular parts [81]. As numerous natural pigments and synthetic dyes contain ioniz-able groups, the calculations and theories presented in [80] and [81] and discussed above may facilitate the prediction of the effect of mobile phase pH on their retention, and consequently may promote the rapid selection of optimal chromatographic conditions for their separation. 

The method has been proposed for the prediction of retention data in isocratic systems from data measured in gradient elution and vice versa [84], Similar calculation methods may be very important in the analysis of natural extracts containing pigments with highly different chemical structure and retention characteristics. The calculations make possible the rational design of optimal separation conditions with a minimal number of experimental runs. 

By appropriate choice of the type (or combination) of the organic solvent(s), selective polar dipole-dipole, proton-donor, or proton-acceptor interactions can be either enhanced or suppressed and the selectivity of separation adjusted [42]. Over a limited concentration range of methanol-water and acetonitrile-water mobile phases useful for gradient elution, semiempirical retention equation (Equation 5.7), originally introduced in thin-layer chromatography by Soczewinski and Wachtmeister [43], is used most frequently as the basis for calculations of gradient-elution data [4-11,29,30] ... 

In gradient-elution NPC, the solvent strength of the mobile phase gradually increases with increasing concentration of the polar solvent. In NP systems where Equation 5.10 applies nnder iso-cratic conditions, the elution volnme of a sample solnte in NP LC with linear gradients described by Equation 5.4 can be calculated using [28] ... 

In NP systems where the retention is controlled by the three-parameter retention equation (Equation 5.11), the elution volumes in normal-phase gradient-elution chromatography can be calculated using [55-57]... 

In gradient elution of weak acids or bases, gradients of organic solvent (acetonitrile, methanol, or tetrahydrofuran) in buffered aqueous-organic mobile phases are most frequently used. The solvent affects the retention in similar way as in RPC of nonionic compounds, except for some influence on the dissociation constants, but Equations 5.8 and 5.9 usually are accurate enough for calculations of gradient retention volumes and bandwidths, respectively. 

In gradient-elution NPC where Equation 5.10 applies, the elution volumes affected by the gradient dwell volume can be calculated using Equation 5.22 [57] ... 

Figure 5.4A and B compares the uncorrected elution volumes, the elution volumes corrected by simple addition of and the elution volumes calculated using Equation 5.21 in RP gradient elution on a conventional and on a micro-bore C18 column. The effect of the gradient dwell volume is more important for separations on short columns and especially on narrow-bore columns with i.d. 2 mm. 

Under isocratic development, if the early peaks of the mixture are adequately separated, then the late peaks are often broad, and consequently, at concentrations so low that they are hardly detectable. Conversely, if the late peaks are eluted at a sufficiently low k values to improve detection limits, the early peaks become bunched together and are not resolved. This problem is obviated considerably by employing gradient elution, but if there are a large number of individual solutes present in the sample,then the same problems will arise. These difficulties are caused by the column having a limited peak capacity and it is, therefore, important to determine how to calculate peak capacity and how to control it. From the Plate Theory, the peak width at the base is given by -... 

In isocratic elution, a capacity factor k 5 provides separation from the solvent front and does not require excessive time. For gradient elution, k = 5 is a reasonable starting condition. Let s calculate a sensible gradient time for the experiment in Figure 25-31a, in which we chose a gradient from 10% to 90% B (A = 0.8) in a 0.46 X 25 cm column eluted at 1.0 mL/min. From Equation 25-4, Vm Ld2/2 = (25 cm) (0.46 cm)2/2 = 2.65 mL. We calculate the required gradient time by rearranging Equation 25-6 ... 

The retention factors of the polymers in 60 % THF were calculated from gradient elution and discussed together with those directly measured for oligomers with 2-12 repeat units or 2000, 4000, and 9000 g/mol molar mass. On a lOOnm-pore packing, the Martin equation was fulfilled for n = 19 repeat units. At higher values, the curve... 

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