Elution curve equation derivation

Once the elution-curve equation is derived, and the nature of f(v) identified, then by differentiating f(v) and equating to zero, the position of the peak maximum can be determined and an expression for the retention volume (Vr) obtained. The expression for (Vr) will disclose those factors that control solute retention. 

Said [1] developed the Martin concept [2] to derive the elution curve equation in the following way. 

The equation for the retention volume of a solute, that was derived by differentiating the elution curve equation, can be used to obtain an equation for the retention time of a solute (tr) by dividing by the flowrate (Q), thus,... 

The form of equation (27) is very similar to that obtained by Reilly et ai. [11] but the derivation is simpler, as those authors utilized the approximate binomial form of the elution curve in their procedure. 

In the development of the plate theory and the derivation of the equation for the elution curve of a solute, it was assumed that the initial charge was located In the first plate of the column. In practice, this is difficult to achieve, and any charge will, in fact, occupy a finite column volume and consequently a specific number of the first theoretical plates of the column. Consider the situation depicted in figure 1 where the initial charge is distributed over (r) theoretical plates. 

Density gradient ultracentrifugation is used to measure hpoprotein subclasses it is performed in a vertical rotor with measurement of cholesterol continuously in the fractions eluted from the gradient. Mathematical curve resolution derives the component lipoprotein profiles and allows calculation of their cholesterol concentrations. The method can determine concentrations of VLDL, IDL, LDL, Lp(a), and HDL cholesterol. LDL cholesterol subclasses can be expressed separately or combined to give a measurement similar to that provided by the Friedewald equation or beta-quantification. A disadvantage is that the procedure is technically demanding and requires instrumentation not usually available in clinical laboratories. 

This equation was derived by comparison of the elution curve approximated by the normal distribution and the equation derived from the plate theory The similarity of Eqs (10-11) and (10-12) is not surprising Eq (10-11) can be considered to be a more generalized form Eq (10-11) is further simplified in the cases of liquid phase chromatography since the contribution of the first term of R H S becomes negligible since molecular diffusion in liquid phase is small... 

The feasibility of Kj determinations in the context of one-atom-at-a-time chemistry is very promising and the collection of Kj values will allow establishment of reliable variations of the chemical properties (complexation, hydrolysis) of elements within a group, for comparison with theoretical predictions, and, perhaps, for determination of thermodynamic constants. Moreover, other information can be derived from chromatography experiments. The mathematical treatment of elution curves can be carried out with various models, especially Glueckauf s, which offers the advantages of using simple equations and takes into account the possible dissymmetry of elution bands [31, 32]. The parameters included in Glueckauf s equations allow the determination of the distribution... 

Considering the derivations of equation (1), it can be predicted that all molecules having the same value of [rj M would have the same value of Vh, the hydrodynamic volume. Also, if v/, is the parameter that uniquely determines the elution volume, Ve, these molecules should have the same elution volume. The arguments presented by these authors do not predict that the relationship between these parameters should necessarily be linear. Most universal calibration curves shown in the literature that cover 4 to 6 decades of M show a definite upward curvature at high values of M (28). 

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