Chromatography Gaussian

The absorption spectra are modelled by Gaussians (see 3.2 Chromatography / Gaussian Curves). 

Distribution Coefficients. Gel-permeation stationary-phase chromatography normally exhibits symmetrical (Gaussian) peaks because the partitioning of the solute between mobile and stationary phases is linear. Criteria more sophisticated than those represented in Figure 8 are seldom used (34). 

Gaussian curve and, thus, also has significance when dealing with chromatography theory. 

The profile of the concentration of a solute in both the mobile and stationary phases is Gaussian in form and this will be shown to be true when dealing later with basic chromatography column theory. Thus, the flow of mobile phase will slightly displace the concentration profile of the solute in the mobile phase relative to that in the stationary phase the displacement depicted in figure 1 is grossly exaggerated to demonstrate this effect. It is seen that, as a result of this displacement, the concentration of solute in the mobile phase at the front of the peak exceeds the equilibrium concentration with respect to that in the stationary phase. It follows that there is a net transfer of solute from the mobile phase in the front part of the peak to the... 

The area of a peak is the integration of the peak height (concentration) with respect to time (volume flow of mobile phase) and thus is proportional to the total mass of solute eluted. Measurement of peak area accommodates peak asymmetry and even peak tailing without compromising the simple relationship between peak area and mass. Consequently, peak area measurements give more accurate results under conditions where the chromatography is not perfect and the peak profiles not truly Gaussian or Poisson. 

Gel filtration chromatography has been extensively used to determine pore-size distributions of polymeric gels (in particle form). These models generally do not consider details of the shape of the pores, but rather they may consider a distribution of effective average pore sizes. Rodbard [326,327] reviews the various models for pore-size distributions. These include the uniform-pore models of Porath, Squire, and Ostrowski discussed earlier, the Gaussian pore distribution and its approximation developed by Ackers and Henn [3,155,156], the log-normal distribution, and the logistic distribution. 

The effects of various pore-size distributions, including Gaussian, rectangular distributions, and continuous power-law, coupled with an assumption of cylindrical pores and mass transfer resistance on chromatographic behavior, have been developed by Goto and McCoy [139]. This study utilized the method of moments to determine the effects of the various distributions on mean retention and band spreading in size exclusion chromatography. 

Resolution (R) is the measure of the chromatographic separation of two components. Ideally, mixtures should be completely separated, but in many instances spots or peaks will overlap (co-elute). For gas chromatography, where the components are isolated as Gaussian peaks, the resolution is given by ... 

The shape ofthe elution curve for a pulse injection can be approximated by the Gaussian error curve for AT > 100, which is almost the case for column chromatography [2]. The value of N can be calculated from the elution volume Vg (m ) and the peak width W (m ), which is obtained by extending tangents from the sides of the elution curve to the baseline and is equal to four times the standard deviation (Ty (m ) = as shown in Figure 11.7. 

A chromatography column of 10 mm i.d. and 100 mm height was packed with particles for gel chromatography. The interparticle void fraction e was 0.20. A small amount of a protein solution was applied to the column and elution performed in an isocratic manner with a mobile phase at a flow rate of 0.5 cm min. The distribution coefficient A of a protein was 0.7. An elution curve of the Gaussian type was obtained, and the peak width W was 1.30 cm . Calculate the Hs value of this column for this protein sample. 

This is an even function that has a maximum of 0.399 for x = 0. The function also has two inflection points x — 1 with a corresponding ordinate value of 0.242, which represents 60.6% of the maximum value of the function. The width of the function at the inflection points is approximately 2er (er = 1). In modern chromatography, Wj/2 represents the width of the peak at the half-height (wi/2 = 2.35er) and a2 the variance of the peak. The width of the peak at the base, w, is measured at 13.5% of the height. At this position, if the curve is Gaussian, w = 4a by definition. 

A band of solute broadens as it moves through a chromatography column. Ideally, an infinitely narrow band applied to the inlet of the column emerges with a Gaussian shape at the outlet (Figure 23-11). In less ideal circumstances, the band becomes asymmetric. 

In this system the bands (zones) broaden because of diffusion effects and nonequilibrium. This broadening mechanism is fairly symmetrical and the resulting elution bands approach the shape of a Gaussian curve. This system best explains liquid or gas partition chromatography. The system may be viewed in two ways ... 

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... 

In chemical engineering, there are many situations in which the response is montiform. Chromatography comes immediately to mind as a process in which sharp peaks are desirable for analysis or preparation. Such peaks can be very roughly characterized by their means and standard deviations, and if, as is quite often the case, we have reason to suppose that a distribution is asymptotically Gaussian, then these two statistics suffice for its description. If fa) is the distribution in question, its moments about the origin are... 

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