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Decoding complex multicomponent chromatograms
No full textThis paper describes two mathematical approaches applied for decoding the complex signal of GC separations of multicomponent mixtures.
The methods are helpful in extracting analytical information since separation of all the components present in the sample is still far from being achieved.
One methos is based on the Statistical Degree of Peak Overlapping, the other studies the autocovariance function computed on the experimental digitized GC signal
Decoding complex multicomponent chromatograms by Fourier Analysis
No full textThe present work discusses the many attributes - classified as observable, intrinsic or hidden - which can be conceived for any complex multicomponent chromatogram. Discussion ensues on how to decode such chromatograms, i.e. determining the intrinsic and/or hidden attributes from those which can be observed. There are two main steps. The first is based on Fourier Analysis (FA) and determines the intrinsic attributes: i.e., the number of single components which can be detected; their distribution over the available Chromatographie space and peak capacity. The second evaluates the hidden attributes: i.e., the effects of incomplete separation, the number of peaks created by one or more single components as well as their degree of purity. The hidden attributes can be obtained by applying the theory of Statistical Degree of peak Overlapping (SDO) and the paper goes into the extent to which the SDO step depends on the FA results. In addition, the role Exponential distribution plays as a point of reference for the distribution of both single component peak position interdistances and peak heights is discussed. Finally, a simplified graphical FA procedure is presented and the main achievements in this field are reviewed. © 1997 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH
HRGC separation performance evaluation by a simplified Fourier analysis approach
No full textA simple procedure is presented for determining separation performance of HRGC analysis of multicomponent mixtures. The procedure is based on the computation of Autocovariance Function (EACVF) from the digitized experimental chromatogram. Graphic inspection of the EACVF plot permits easy computation of the width value of the single component peak, σ; from the EACVF value at t = 0 the number of component in the mixture, m, can be simply derived. From these two basic quantities all the other chromatographic performance attributes can be calculated. The consistency of the procedure is tested for different chromatograms and compared with the more complex EACVF fitting method. Several features of the multicomponent chromatogram, overloading effects included, are directly detected
Fourier Analysis of Multicomponent Chromatograms. Recognition of Retention Patterns
No full textA procedure based on fitting the experimentally computed autocovariance function (ACVF) of multicomponent chromatograms to theoretical models is introduced by which both the single component interdistance model (IM) of the retention times is tested and the statistical attributes of the multicomponent chromatogram (I.e. number m of single components, peak width, and parameters of the IM) are determined. Four different IM—exponential, uniform, normal, and gamma—are considered. In essence, when fitted to these theoretical models, the experimental ACVF—expressing the chromatographic response correlation on the time distance—provides the information necessary to establish both the type of retention pattern and gives the necessary parameter estimation. The procedure is tested by using computer-generated chromatograms with different IMs and uncorrelated peak heights, in which density and m are varied. It is shown that the chromatographic attributes m and peak width derived from the best fitting IM are unbiased. Moreover, even if the best fitting IMs do not always coincide with the true model, because of their flexibility and approximating properties they always give a correct description of the retention pattern provided that the results are correctly interpreted. © 1992, American Chemical Society. All rights reserved
Kinetic theories of liquid chromatography
No full textKinetic theories of liquid chromatography play a key role in evaluating the performance of stationary phases. The conventionally used plate height equations and the band broadening occurring in the different areas of liquid chromatography are accounted for by kinetic models. In this chapter, the most important macroscopic (lumped kinetic, lumped pore, and general rate) and microscopic (stochastic-dispersive) models are discussed. The plate height equations arising from those kinetic models are discussed and compare
Equivalence of the microscopic and macroscopic models of chromatography: Stochastic-Dispersive versus Lumped Kinetic Model
No full textThe microscopic model of chromatography is a stochastic model that consists of two fundamental processes: (i) the random migration of the molecules in the mobile phase, and (ii) the random adsorption-desorption of molecules on the stationary phase contained in a chromatographic column. The diffusion and drift of the molecules in the mobile phase is described with a simple one-dimensional random walk. The adsorption-desorption process is modeled by a Poisson process that assumes exponential sojourn times of the molecules in both the mobile and the stationary phases. The microscopic, or molecular model of chromatography studied here turns out to be identical to the macroscopic lumped kinetic model of chromatography, whose solution is well known in Chromatography. A complete equivalence of the two models is established via the identical expressions they provide for the band profiles
Statistical study of peak overlapping in multicomponent chromatograms: importance of the retention pattern
No full textA general method is reported for evaluating the statistical degree of overlapping (SDO) in a multicomponent chromatogram, whose retention pattern is known and described by the frequency function of interdistances between subsequent single component peaks (interdistance model, IM). The content of SDO is the expected numbers of singlet, doublet, triplet, etc., peaks, as a function of the number of components, the separation performance and the IM. The proposed method is exploited in practice for three cases of IMs: gamma, normal and uniform, which are known to represent a wide variety of cases. Two different approaches are presented and discussed: analytical expression and simulation computation, according to whether the IM can be analytically integrated or not. The advantages and differences of the two approaches are considered, even in the case of negative interdistances (normal case). A real case of chromatographic separation of a multicomponent mixture, composed of polychlorinated biphenyls, is also exploited. The separation requirements for obtaining a given separation goal are investigated and the relevance of the IM type in determining the overlapping pattern is proved. The basic underlying hypothesis of the present treatment is the stationarity of the component distribution along the chromatogram. Means to check this hypothesis are also reported. © 1995
Stochastic-dispersive theory of chromatography
No full textThe stochastic model of chromatography has been combined with mobile-phase dispersion. With the combined model, both the effect of slow mass transfer or adsorption-desorption kinetics and dispersion on the band profile can be characterized. The stochastic model of chromatography is addressed with the characteristic function method. The moments of the peaks are calculated analytically for homogeneous and heterogeneous surfaces. It is shown that even in cases when the characteristic function cannot be calculated in closed form, the moments of the peak, and therefore the retention time, the number of theoretical plates, the peak asymmetry, can be calculated with simple expressions. Therefore, a full description of the chromatographic peak is available for homogeneous and any heterogeneous surfaces provided that the distribution of the sorption energies is known
Fourier analysis of multicomponent chromatograms. Theory of nonconstant peak width models
No full textPower spectrum (PS) based analysis of multicomponent chromatograms is extended to chromatograms containing peak of different width. For Poissonian chromatograms the PS is derived both for cases where peak width and retention time are indipendent of one another and for cases of linear peak broadening. Computer generated chromatograms were used to test the derived model equations. The results obtained by simulation are explored on the basis of the theoretically derived equations, and the relevance of the results in handling practical cases is emphasized
Fourier analysis of multicomponent chromatograms. Numerical evaluation of statistical parameters
No full textA procedure based on the power spectrum (PS) model of a multicomponent chromatogram is introduced by which the number m of detectable components (or single-component peaks) and the parameters of the single-component peak such as standard deviation and asymmetry factor can be evaluated. In essence, when fitted to theoretical models, the experimental PS-expressing the chromatographic response variance dependence on the time distance-provides the Information necessary to accept or reject the model and to give the necessary parameter estimations. The procedure is tested by using computer-generated multicomponent chromatograms with Poissonian retention time distribution and random and uncorrelated peak heights, in which density, asymmetry and height distribution are widely varied. How to obtain unbiased PS numerical determination by windowing is also discussed. It Is shown that unbiased parameter estimations are obtained, the only procedure limitation being the approximation made In the evaluation of the single-component peak height dispersion. An example Is given of how a retention time distribution other than the Poissonian can be detected. © 1990, American Chemical Society. All rights reserved
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