Chromatographic theory peak width

Recalling that a separation is achieved by moving the solute bands apart in the column and, at the same time, constraining their dispersion so that they are eluted discretely, it follows that the resolution of a pair of solutes is not successfully accomplished by merely selective retention. In addition, the column must be carefully designed to minimize solute band dispersion. Selective retention will be determined by the interactive nature of the two phases, but band dispersion is determined by the physical properties of the column and the manner in which it is constructed. It is, therefore, necessary to identify those properties that influence peak width and how they are related to other properties of the chromatographic system. This aspect of chromatography theory will be discussed in detail in Part 2 of this book. At this time, the theoretical development will be limited to obtaining a measure of the peak width, so that eventually the width can then be related both theoretically and experimentally to the pertinent column parameters. 

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). 

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. 

N column efficiency defined as the number of theoretical plates in the column, i.e., in Plate Theory N describes the number of effective equilibrations of the analyte between mobile and stationary phases N = 4.(Vj/AVj) =4.(tj/Ati) = 5.545.(tf/Atp, where AV and At are the chromatographic peak widths in terms of elution volume and elution time, respectively, and subscripts i and j refer to widths measured at the peak inflection points and at half peak height, respectively. 

It is intuitively obvious that the greater the number of plates, i.e., the greater the number of equilibration steps, the better will be the separation, and this implies more narrow chromatographic peaks. Therefore, the strategy will be to examine the implications of the Plate Theory for peak widths. Note, however, that the Plate Theory does not pretend to explain or understand the peak widths, but only describes them. Examination of a typical peak shape (Figure 3.2) and the theoretical elution equation (Equation [3.11]) that describes its shape suggests that a... 

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. ... 

Thus, the plate theory supplies an approximate description of the spreading of a component band. If the chromatographic peak width is known, one can calculate the number of theoretical plates, which characterize the column efficiency and hence the equivalent height of a theoretical plate ... 

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... 

HPLC theory could be subdivided in two distinct aspects kinetic and thermodynamic. Kinetic aspect of chromatographic zone migration is responsible for the band broadening, and the thermodynamic aspect is responsible for the analyte retention in the column. From the analytical point of view, kinetic factors determine the width of chromatographic peak whereas the thermodynamic factors determine peak position on the chromatogram. Both aspects are equally important, and successful separation could be achieved either by optimization of band broadening (efficiency) or by variation of the peak positions on the chromatogram (selectivity). From the practical point of view, separation efficiency in HPLC is more related to instrument optimization, column... 

All physicochemical parameters derived from chromatographic measurements are related to the concentration profile of the eluted substance. To make measurements plausible, it is important to know the determinants of the substance s concentration profile. The elution peak always has a finite width, and, although often approximately Gaussian in shape, it is actually asymmetrical to a greater or lesser degree. In such cases, the theory of statistical moments has to be employed for characterizing the peaks of any shape, whether Gaussian or non-... 

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. 

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