Chromatographic theory retention time

Analytical chromatographic options, based on linear and nonlinear elution optimization approaches, have a number of features in common with the preparative methods of biopolymer purification. In particular, both analytical and preparative HPLC methods involve an interplay of secondary equilibrium and within the time scale of the separation nonequilibrium processes. The consequences of this plural behavior are that retention and band-broadening phenomena rarely (if ever) exhibit ideal linear elution behavior over a wide range of experimental conditions. First-order dependencies, as predicted from chromatographic theory based on near-equilibrium assumptions with low molecular weight compounds, are observed only within a relatively narrow range of conditions for polypeptides and proteins. 

The majority of chromatographic separations as well as the theory assume that each component elutes out of the column as a narrow band or a Gaussian peak. Using the position of the maximum of the peak as a measure of retention time, the peak shape conforms closely to the equation C = Cjjjg, exp[-(t -1] ) The modelling of this process, by traditional descriptive models, has been extensively reported in the literature. 

The chromatographic separations of isotopic hydrogens have indeed verified all of the above mentioned predictions of the theory. The measured retention times, tu or net retention volumes Vm give directly the separation factors... 

A general account of chromatographic theory was presented in volume 2 of Encyclopedia of Pharmaceutical Technology.Therefore, the following discussion will focus specifically on GC theory. The separation of the component of a mixture depends upon the column performance (efficacy) and the relative retention capability of the stationary phase (selectivity). The former determines the width of the peaks relative to the length of time a component spends in the column, while the latter determines the relative position of each emerging component (resolution). 

The use of a typical equilibrium constant K in chromatographic theory indicates that the system can be assumed to operate at equilibrium. As the analyte (X) proceeds through the system, it partitions between the two phases and is retained in proportion to its affinity for the stationary phase. At any given time, a particular analyte molecule is either in the mobile phase, moving at its velocity, or in the stationary phase and not moving at all. The individual properties of each analyte control its thermodynamic distribution and retention, and result in differential migration of the components in the mixture—the basis of the chromatographic separation. The effectiveness of the separation, however, is a function of both thermodynamics and kinetics. 

These basic parameters, retention time and peak width, can be used to derive a number of other parameters that express the quality of the achieved chromatographic separation. In the following paragraphs, a brief summary of the most important parameters of chromatographic theory are discussed. 

Many workers have discussed the first time moment or centre of gravity of a chromatographic peak undergoing elution. In the absence of longitudinal or eddy diffusion this property has been shown to be equal to the ideal thermodynamic retention time for zero-pressure-drop columns. More recently, theories regarding the first time moment have been extended by Hicks and by Buffham to include pressure-drop columns and the first time moment has been related to thermodynamic properties. Buflfham used the mean residence time t which is equivalent to the first time moment ... 

Theoretical plate a concept borrowed from distillation theory and countercurrent extraction a chromatographic column is modeled as a series of discrete plates in each of which local equilibrium of analyte partitioning between stationary and mobile phases is established. The Plate Theory accounts for retention of analytes, i.e., retention times, but not the peak shapes (widths), for isocratic elution. 

It is possible to correct this ultra-simple approach with a Plate Theory model for the variation of peak width with retention time (volume), conveniently expressed via the capacity factor k. The derivation and final result are complex (Scott, http //www.chromatography-online.org/) and are not reproduced here. Instead, Figure 3.5 shows representative plots of Cp vs k for several values of N, calculated from this more realistic model. The values of N and k are of course those for the last-eluting peak, but this last peak will be different for different chromatographic detectors with different sensitivities. It is clear from Figure 3.5 that any chromatographic conditions that limit the k value for the last-detected peak will thus limit the peak capacity, particularly at lower values of k. ... 

In a somewhat different theoretical approach based on information theory, and using an example directly pertinent to the concerns of this book (Fetterolf 1984), the logic gates concept is replaced by that of informing elements such as clean-up procedure, chromatographic retention time, ionization efficiency with a particular technique, selection of mJz values of a precursor ion and of one or more product ions (possibly via more than one stage of... 

The separation ability of a chromatographic column is often measured by the number of theoretical plates, N. This concept comes originally from distillation theory in which the ability to separate volatile compounds by fractional distillation was related to the number of actual plates in the packed distillation column. In chromatography the number of theoretical plates in a column is calculated from the retention time, t, and the average peak width, lu... 

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