Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography.

A general method for the calculation of the flow and pressure of a gas in a network of cylindrical capillaries is presented. This method is used specifically for gas chromatographic systems in this work. With this approach, it is possible to easily calculate flow and pressures in complex gas chromatographic systems, like flow-modulated or thermal-modulated multidimensional gas chromatographic systems, or systems with multiple outlets at different pressures. A mathematic abstraction using graph theory is used to represent the system of capillaries. With this graph, the flow balance equations at the connections of the capillaries can easily be set up. Using a computer algebra system, the system of flow balance equations can be solved for the pressures at the connection points. For simple systems, this approach is presented, and calculated flows, pressures, and hold-up times are compared with measured values. In addition, two complex systems (4-Way-Splitter, Deans Switch system) of capillaries are presented with calculations only. For these systems, certain conditions were formulated, that is, a certain difference in hold-up times and a defined split ratio between different paths of these systems. Using a numeric non-linear solver, configurations of these systems were found, that fulfill these conditions.

Relation between characteristic temperature and elution temperature in temperature programmed gas chromatography - Part II: Influence of column properties.

The method development process in gas chromatography can be accelerated by suitable computer simulation tools using knowledge about the solute-column interactions described by thermodynamic retention parameters. Since retention parameters usually are determined under isothermal conditions, the presented work offers a step to estimate one of the most important retention parameters, the characteristic temperature Tchar by less laborious temperature programmed measurements. In the first part an empirical multivariate model was introduced describing the correlation between the elution temperature Telu of a solute and its characteristic temperature Tchar. Now in the second part a simulation model of GC and available retention data from a retention database was used to investigate the correlation between Telu and Tchar for an expanded range of heating rates and initial temperatures. In addition to part I, the simulation is used to investigate the influences of different properties of the separation column such as different phase ratios and column geometries like length and diameter or various stationary phases including SLB-5 ms, SPB-50, Stabilwax, Rtx-Dioxin2, Rxi-17Sil MS, Rxi-5Sil MS, ZB-PAH-CT, DB-5 ms, Rxi-5 ms, Rtx5 and FS5ms. The fit model is valid for all investigated stationary phases. The influence of the phase ratio to the correlation could be determined. Therefore, the model was expanded to this parameter. The expanded range of heating rates and the normalization for the system independent dimensionless heating rate required a further modification of the previously presented correlation model. The model now fits also under isothermal conditions. The results were used for estimation of the Tchar of an analyte from the elution temperature in the temperature program. The prediction performance was investigated and evaluated for 20 different temperature program conditions and at two phase ratios (ß=125 and ß=250). Under best conditions the estimated and the measured Tchar values show relative differences <0.5 %. With this novel model estimations for Tchar are possible at 20 °C above the initial temperature, which expands the prediction range even for low and medium retained analytes compared to earlier approaches.

Simulation of gas chromatographic separations and estimation of distribution-centric retention parameters using linear solvation energy relationships.

For method development in gas chromatography, suitable computer simulations can be very helpful during the optimization process. For such computer simulations retention parameters are needed, that describe the interaction of the analytes with the stationary phase during the separation process. There are different approaches to describe such an interaction, e.g. thermodynamic models like Blumberg's distribution-centric 3-parameter model (K-centric model) or models using chemical properties like the Linear Solvation Energy Relationships (LSER). In this work LSER models for a Rxi-17Sil MS and a Rxi-5Sil MS GC column are developed for different temperatures. The influences of the temperature to the LSER system coefficients are shown in a range between 40 and 200 °C and can be described with Clark and Glew's ABC model as fit function. A thermodynamic interpretation of the system constants is given and its contribution to enthalpy and entropy is calculated. An estimation method for the retention parameters of the K-centric model via LSER models were presented. The predicted retention parameters for a selection of 172 various compounds, such as FAMEs, PCBs and PAHs are compared to isothermal determined values. 40 measurements of temperature programmed GC separations are compared to computer simulations using the differently determined or estimated K-centric retention parameters. The mean difference (RSME) between the measured and predicted retention time is less than 8 s for both stationary phases using the isothermal retention parameters. With the LSER predicted parameters the difference is 20 s for the Rxi-5Sil MS and 38 s for the Rxi-17Sil MS. Therefore, the presented estimation method can be recommended for first method development in gas chromatography.