Experimental data modeling chromatography

Ishihara T, Kadoya T, Yamamoto S. Application of a chromatography model with linear gradient elution experimental data to the rapid sacle-up in ion-exchange process chromatography of proteins. Journal of Chromatography A 2007 1162 34-40. 

Molecular properties depend on molecular structures and, with appropriate methods and software, it is possible to compute these on the basis of structural information, established by experiment or computation (see Sections 2 and 3.2).18,155,156 This allows for the design of new materials with given properties and often is used for structure determination (see Section 3.2 for more examples in this area). Complex stabilities will be discussed separately and in detail in Section 3.5 the application of molecular modeling in the area of isomer distributions (conformational equilibria), in combination with experimental data (usually spectroscopy and chromatography), is discussed in Section 3.2. 

The resolution of a multicomponent system involves the description of the variation of measurements as an additive model of the contributions of their pure constituents [1-10]. To do so, relevant and sufficiently informative experimental data are needed. These data can be obtained by analyzing a sample with a hyphenated technique (e.g., HPLC-DAD [diode array detection], high-performance liquid chromatography-DAD) or by monitoring a process in a multivariate fashion. In these and similar examples, all of the measurements performed can be organized in a table or data matrix where one direction (the elution or the process direction) is related to the compositional variation of the system, and the other direction refers to the variation in the response collected. The existence of these two directions of variation helps to differentiate among components (Figure 11.1). 

In the frontal analysis experiment described in Section 5.3.2, the transport model of chromatography was used to fit the experimental data [40]. Neglecting axial and eddy diffusion, band broadening was accounted for by one single mass transfer rate coefficient. The mass transfer rate coefficients estimated were small and strongly dependent on the temperature and solute concentration, particularly the rate coefficients corresponding to the imprinted L-enantiomer (Fig. 5.12). Above a concentration of ca. 0.1 g/L the mass transfer rate coefficients of the two enantiomers are similar. 

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. 

Figures 4.26A and 4.26B compare the results of the experimental determination of isotherms using the traditional mass balance method (MMB) and those obtained with MMC. The adsorption isotherm predicted by MMC deviates significantly from the isotherm data obtained by MMB. This may be due to the limited applicability of the Langmuir competitive model for the modeling of the adsorption behavior even of such simple systems as p-cresol and phenol in reversed-phase chromatography. Figures 4.26C and 4.26D compare the results obtained by MMB and HMMB for the same system. Over most of the concentration range, the agreement between the experimental data and the results of these two methods is...

Thus, it will be extremely difficult at best to separate the influences of the various phenomena that may be responsible for the effects of a slow kinetics of mass transfer and a slow kinetics of the retention mechanism. The fitting of experimental data obtained in overloaded elution chromatography to various models of chromatography will not permit the choice of a best model, nor the identification of the slowest step in the chromatographic process. Independent measurements of the kinetic parameters are necessary. 

The previous part showed that inverse gas chromatography is a very useful tool in the investigation of long-chain aliphatic alcohol monolayers adsorbed on the surface of porous silica gel. Now a simple theoretical model of the adsorbed layer that can be used to analyse the experimental data obtained by inverse gas chromatography is considered. The model is based on the theory of adsorption of simple gases on solid surfaces and, initially restricted to fully localized adsorption [36-38], was extended to treat also long chain molecules [39]. 

A theoretical model was developed to correlate molecular weight distribution of this system. This was compared to the experimental gel permeation chromatography trace with the theoretical model modified to Include the effect of the PEG central block, the spreading of the trace as it went through the columns and the slope of the log MW versus retention volume line. A good fit was found with kl/kp = 0.0070. When methyl tosylate was used to polymerize 2-lsobutyl oxazollne, a similar treatment of the data showed kl/kp = 0.22. The effect of the PEG Is explained as due to solvation of the Initial adduct by the neighboring ether group. 

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