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Mathematical modelling of linear and nonlinear phenomena in capillary electrophoresis
Dvořák, Martin ; Dubský, Pavel (advisor) ; Kašička, Václav (referee) ; Gebauer, Petr (referee)
Capillary electrophoresis is one of the prominent analytical separation methods. Currently, many computer programs exist which are able to predict the result of an electrophoretic experiment. Firstly, there are programs based on numerical solving of corresponding continuity equations and equations of chemical equilibria. Secondly, there are programs based on approximative models of capillary electrophoresis. Programs belonging to the first group are applicable to a wide range of modes of capillary electrophoresis and provide a precise solution. Their disadvantage is though a considerable time demand. On the other hand, the approximative models give the results almost immediately and, in addition, provide some theoretical relationships which are useful for optimization of the separation process. This dissertation thesis is focused on improvement and extension of validity of existing approximative models of capillary electrophoresis. As a part of this thesis, a model capable of a full-blown description of capillary electrokinetic chromatography is introduced. This model is implemented into program PeakMaster 6. The attention is also paid to a nonlinear model of electromigration without diffusion. This model enables a very good description of electromigration dispersion including effects related to...
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Nonlinear phenomena in electrokinetic chromatography
Dovhunová, Magda ; Dubský, Pavel (advisor) ; Koval, Dušan (referee) ; Ševčík, Juraj (referee)
Capillary electrophoresis often uses complexing agents since the interaction between the analyte and the complexing agent can result in achieving or improving the separation. Examples of such methods can be electrokinetic chromatography or affinity capillary electrophoresis (ACE). ACE is used to determine the complexing parameters. In case of chiral separation, this issue gets complicated, since the parameters of the two analytes (enantiomers) are not completely independent to one another. Therefore, a procedure has been proposed in this thesis, that should always be used to evaluate the complexing parameters of two enantiomers. Statistical evaluation of these parameters was assessed as well. This work also proposes a method that allows to determine the relative migration order of two enantiomers in two different complexing separation systems. The mathematical description of electrophoresis is based on continuity equations, that are inherently nonlinear. However, these equations can be linearized to obtain an approximate analytical solution. There was recently presented a generalized model, that enables inclusion of complete complexing equilibria in the theoretical description of electromigration. Thus, various phenomena, including nonlinear ones, associated with complexation can be predicted. This...
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Peak shape distortions in capillary electrophoresis
Kalus, Michal ; Dovhunová, Magda (advisor) ; Šteflová, Jana (referee)
This Bachelor thesis dissertates about the influence of electromigration dispersion and Taylor dispersion to the total peak dispersion. Firstly, it deals with a solution to a new mathematical theory for peaks influenced by the EMD that was discovered in our research group and it experimentally proves the rightness of the solution. Specifically, it deals with comigration of two analytes with similar mobilities. Secondly, the goal was to find how the Taylor dispersion influences the separation process. This opens a way to further research on how these two effects collide and how they influence the system and separation process together.
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Automatic data analysis in capillary zone electrophoresis
Ördögová, Magda ; Dubský, Pavel (advisor) ; Heyda, Jan (referee)
Evaluating data in capillary zone electrophoresis usually involves many steps that require using several different programmes. Apart from evaluating the electrophoreogram itself, it is usual to process the obtained data in some other way. For example, a suitable model is fit to the data in order to obtain physical and chemical parameters of the separation (e.g. stability constant in case of complexation). It is also important to know the accuracy of the evaluation (the calculation error). In this work, new parts of the Eval programme, originally developed for electrophoreogram evaluation, were implemented. The programme now automatically estimates the Haarhoff-van der Linde function (solution of continuity equation in capillary) parameters for analyte peak. Complexing agents are often used to improve the separation in the capillary zone electrophoresis. Complexation in the capillary can be described by its physical and chemical parameters. A new part was added to the Eval programme that allows the user to fit a rectangular hyperbole function to the obtained data. Thus, the regression parameters of this dependence can be gained. The programme can also draw profile diagrams for these parameters, from which the confidence intervals can be read. An option that allows two dependencies to be fitted at...
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