Gaussian-shaped elution peaks

A constituent is characterized by its retention time which represents the time elapsed from the sample introduction to the detection of the peak maximum on the chromatogram. In an ideal case, t is independent of the quantity injected. 

A constituent which is not retained will elute out of the column at time t, called the hold-up time or dead time (formerly designated to) - It i the time required for the mobile phase to pass through the column. 

The difference between the retention time and the hold-up time is designated by the adjusted retention time of the compound, 

If the signal sent by the sensor varies linearly with the concentration of a compound, then the same variation will occur for the area under the corresponding peak on the chromatogram. This is a basic condition to perform quantitative analysis from a chromatogram. 

This is why ideal elution peaks are usually described by the probability density function (1.2). 

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The Heat of Adsorption Detector, devised by Claxton (16) in 1958 has been Investigated by a number of workers (17,18,19) but although once commercially available, has not been extensively employed as an LC detector. One reason for this is the curious and apparently unpredictable shape of the temperature-time curve that results from the detection of the usual Gaussian or Poisson concentration peak profile. The shape of the curve changes with detector geometry, the operating conditions of the chromatograph, the retention volume of the solute and for closely eluted peaks, it produces a complex curve that is extremely difficult to interpret. 

One may study zone broadening in gas chromatography by observing the shape of the elution peak which is Gaussian in ideal systems. The base width of the Gaussian curve is measured in standard deviation units, therefore... 

Molecules of solute travel as a zone in the chromatographic system. Recording of molecules eluting from the column yields a chromatogram (Fig. 1), whose characteristics are peaks. When peaks are symmetrical (Gaussian shape), retention times are taken at peak height. Since k is dimensionless, one can record retention distances or retention volumes on the chromatogram and... 

SEC by itself is not an absolute MW determination method but the analysis of the elution peak has been used extensively for estimating the molecular purity of dendrimers. If the shape of the elution peak of a size exclusion chromatography experiment is Gaussian, the total dispersion, oT of the curve is given by the sum of squares [47] ... 

The area under the component elution peak is proportional to the concentration of that particular component. Various methods can be used to measure this area and are based on the assumption that the shape of the peak is Gaussian. Electronic integration is the preferred method since very accurate and precise measurements are obtained this way (RSD < 0.5%). 

For the low concentrations used in liquid chromatography, the elution peak is Gaussian in shape and its retention factor is independent of the sample size. When isotherms are nonlinear (convex or concave, as illustrated in Fig. 1), an asymmetric elution peak is obtained and the retention factor measured at the peak apex is dependant on the sample size. 

Band dispersion at the elution in GC is shown in the chromatographic peak as its standard deviation cr. Supposing a gaussian distribution for peak shape, we can experimentally estimate cr from peak width measures, as peak width at the baseline Wb) or at half peak height (wh), the latter being the parameter most commonly used in order to decrease the influence of baseline noise. In GCxGC, peak shapes are approximately elliptical, and the values of their and axis correspond to peak width in the and columns Cwh and which can be measured from recorded data. 

The resolution factor is usually estimated from the peak retention times and widths observed in a chromatogram of a mixture of solutes. However, in a rigorous way, a more accurate estimation requires the separate injection of the individual compounds. This is particularly true for closely eluting peaks. It has been established that the retention times measured at the peak apex, and mote so the peak widths, are different if the measurement is made on individually injected solutes or on the peaks in a mixture. This difference is more pronounced when the peak shape cannot be described simply by a Gaussian profile, and where the center of gravity of the peak does not correspond to the peak apex (8). Nevertheless, the chief drawback of the resolution factor Rs is the fact that it does not take into account the relative peak height (9) of the... 

A double Gaussian was fit to the unresolved peaks at 28 min which are defined by 7 fractions using the average peak width, ct, of 0.7 min (fraction resolution of 2.8 fractions), shown as a thin dashed line in Figure 16.5. The fit shows a 2.6-min separation between the component peaks for a resolution of 0.93 (At/i ), which means that the two peaks are almost resolved, although there are no low fractions between the centroids. Despite apparently coarse fraction collections, precise quantitation of the area of fractions produces width and location estimates based on the expected Gaussian shape of elution peaks. Such finer estimates are not needed in comparative metabolism studies but may assist in linking quantification by LC-AMS with identification by LC-MS/MS. 

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-... 

Figure 3.2 The elution curve of a single component, plotted as the analyte concentration at the column exit (proportional to the detector response Rj,) as a function of V, the total volume flow of mobile phase that has passed through the column since injection of the analytical sample onto the column. (V is readily converted to time via the volume flow rate U of the mobile phase.) The objective of theories of chromatography is to predict some or all of the features of this elution curve in terms of fundamental physico-chemical properties of the analyte and of the stationary and mobile phases. Note that the Plate Theory addresses the position of the elution peak but does not attempt to account for the peak shape (width etc.). The inflection points occur at 0.6069 of the peak height, where the slope of the curve stops increasing and starts decreasing (to zero at the peak maximum) on the rising portion of the peak, and vice versa for the falling side the distance between these points is double the Gaussian parameter O. Modified from Scott, www.chromatography-online.org, with permission.

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