Chromatographic peaks simulations

Figure 1.8—Resolution factor. Simulation of chromatographic peaks using two identical Gaussian curves side by side, and the visual aspect of a separation corresponding to the R values indicated on the diagrams. At R = 1.5, it is said that the peaks are baseline resolved the valley between the peaks does not exceed 2%.

It may seem from the above discussion that it is impossible to use even batch isotherm measurements to design HPLC (or SPE) separations. This is not so, however, at least when the HPLC separation occurs under near-equilibrium conditions. Nonlinear chromatographic peaks can be simulated [38] once the corresponding isotherms have been measured. In this case one does not need a physical interpretation of the isotherm equation s constants they can be regarded merely as interpolation factors. Separately measured isotherms of the two compounds are satisfactory in many cases because - as mentioned above - competition often has only minor influence on the separated peaks position and shape. 

Figure 9. Kalman filter resolution of a chromatographic peak of an extract of an Altemaria culture on rice spiked with ATS standard (1 ng in the injected volume), after optimal alignment of the component ( l=AOH 2=ATS) by simulated annealing.

Chapter 4 starts with some basic equations, which relate the molecular-kinetic picture of gas-solid chromatography and the experimental data. Next come some common mathematical properties of the chromatographic peak profiles. The existing attempts to find analytical formulae for the shapes of TC peaks are subject to analysis. A mathematical model of migration of molecules down the column and its Monte Carlo realization are discussed. The zone position and profile in vacuum thermochromatography are treated as chromatographic, diffusional and simulation problems. 

Figure 1.9 Resolution factor. A simulation of chromatographic peaks using two identical Gaussian curves, slowly separating. The visual aspects corresponding to the values of R are indicated on the diagrams. From a value of R = 1.5 the peaks can he considered to be baseline resolved, the valley between them being around 2 per cent.

The same logic that leads to the simulation of the previous section can of course be used to obtain a closed-form expression for the chromatographic peak. As derived by, e.g., Fritz Scott in J. Chromat. 271 (1983) 193, and again assuming (as in section 6.5) unit sample size and detector sensitivity, we have... 

We now return to the simulated curves, in order to show how to extract the area, position, and width from a chromatographic peak. Several simple methods are available for symmetrical peaks (and even more for a special subset of these, Gaussian peaks), but since chromatographic peaks are often visibly asymmetric (and in that case obviously non-Gaussian), we will here use a method that is independent of the particular shape of the peak. It is a standard method that, in a chromatographic context, is described, e.g., by Kevra etal. in J. Chem. Educ. 71 (1994) 1023. 

S. Le Veng, Simulation of Chromatographic Peaks by Simple Functions. Anal. Chim. Acta. 312 (1995). 263-270. 

FIGURE 21.11 Simulated sample-to-sample chromatographic peak shifts and elution order for a typical reverse-phase gradient. Peak retention shifts are random inside the indicated area and therefore not predictable. 

Coque A Model for the Description, Simulation and Deconvolution of Skewed Chromatographic Peaks, Anal Chem., 69 3822 (1997). 

Figure 1.5—Theoretical plate model. Computer simulation of the elution of two compounds, A and B, chromatographed on a column with 30 theoretical plates (KA = 0.5 KB = 1.6 MA — 300 pg Mb = 300 pg) showing the composition of the mixture at the outlet of the column after the first 100 equilibria. As is evident from the graph, this model leads to a non-symmetrical peak. However, when the number of equilibria is very large, and because of diffusion, the peak looks more and more like a Gaussian distribution.

Because analytical chromatography is used inherently in quantitative analysis, it becomes crucial to precisely measure the areas of the peak. Therefore, the substances to be determined must be well separated. In order to achieve this, the analysis has to be optimised using all the resources of the instrumentation and, when possible, software that can simulate the results of temperature modifications, phases and other physical parameters. This optimisation process requires that the chromatographic process is well understood. 

FIGURE 4.1 Simulated HPLC-UV/visible chromatographic data set showing two overlapped peaks with different UV/visible spectra. 

---