Krzysztof Kaczmarski

Modeling of thermal processes in high pressure liquid chromatography: II. Thermal heterogeneity at very high pressures.

Advanced instruments for liquid chromatography enables the operation of columns packed with sub-2 microm particles at the very high inlet pressures, up to 1000 bar, that are necessary to achieve the high column efficiency and the short analysis times that can be provided by the use of these columns. However, operating rather short columns at high mobile phase velocities, under high pressure gradients causes the production of a large amount of heat due to the viscous friction of the eluent percolating through the column bed. The evacuation of this heat causes the formation of significant axial and radial temperature gradients. Due to these thermal gradients, the retention factors of analytes and the mobile phase velocity are no longer constant throughout the column. The consequence of this heat production is a loss of column efficiency. We previously developed a model combining the heat and mass balance of the column, the equations of flow through porous media, and a linear isotherm model of the analyte. This model was solved and validated for conventional columns operated under moderate pressures. We report here on the results obtained when this model is applied to columns packed with very fine particles, operated under very high pressures. These results prove that our model accounts well for all the experimental results. The same column that elutes symmetrical, nearly Gaussian peaks at low flow rates, under relatively low pressure drops, provides strongly deformed, unsymmetrical peaks when operated at high flow rates, under high pressures, and under different thermal environments. The loss in column efficiency is particularly important when the column wall is kept at constant temperature, by immersing the column in a water bath.

Concentration dependence of lumped mass transfer coefficients: Linear versus non-linear chromatography and isocratic versus gradient operation

The general rate model provides a reliable platform to predict elution bands in both linear and non-linear chromatography provided the required equilibrium functions and the coefficients quantifying the mass transfer in and around the particles are available. If further the variation of the equilibrium functions with changes in the mobile phase composition is known, this model is also able to predict gradient elution chromatography. Significant disadvantages of the model are the need to specify three kinetic coefficients and the amount of computing time required for the numerical solution of the underlying equations. Thus, several simplified models have been suggested lumping mass transfer resistances together. In this work the accuracy of predicting chromatographic bands based on the numerical solution of two lumped models has been analyzed. Elution profiles calculated by (a) the transport-dispersive and (b) the equilibrium-dispersive models were compared between each other and with the solution of the more detailed general rate model. In the analysis performed both linear and non-linear chromatography was considered under isocratic and gradient conditions.

Calculation of chromatographic band profiles with an implicit isotherm.

The numerical method for solving the mathematical model of chromatography process coupled with implicit isotherm has been proposed. The exemplary predictions of elution band profiles were performed for competitive adsorption data of 2-phenylethanol and 3-phenylpropanol on ODS-silica with methanol-water as the mobile phase. The simulations of chromatography process with various isotherm models taking into account lateral interactions in adsorbed phase and surface heterogeneity were discussed.

Use of the isopycnic plots in designing operations of supercritical fluid chromatography: IV. Pressure and density drops along columns.

The pressure- and the density-drops along a chromatographic column eluted with supercritical fluid carbon dioxide were mapped as a function of the outlet column pressure and the temperature on the P-T diagram of neat CO(2). At low densities, the viscosity of CO(2) is low, which is expected to result into a low pressure drop along the column. However, at these low densities, the volumetric flow rates of the mobile phase at constant mass flow rates are high, which might result into a high pressure drop along the column. These conflicting effects of an adjustment in the mobile phase density on the pressure drop of the mobile phase along the column makes it nearly impossible to develop a simple intuitive understanding of the relationships between the net pressure drops and the operating temperatures and pressures. The development of a similar understanding of their relationships with the density drop along the column is even more complex, because this density drop depends also on the compressibility of the mobile phase, itself a function of the operating pressures and temperatures. Numerical calculations of the pressure and density drops along columns packed with particles of different sizes, under different operating conditions (temperature, outlet pressure, and flow rate), provide important insights regarding the extent of the pressure and density drops under these operating conditions.

Influence of pressure on the chromatographic behavior of insulin variants under nonlinear conditions

The effect of pressure on the chromatographic behavior of two insulin variants in RPLC was investigated on a YMC-ODS C18 column, under nonlinear conditions. The adsorption isotherm data of porcine insulin and Lispro were measured at average column pressures ranging from 52 to 242 bar. These data fit well to the Toth and the bi-Langmuir isotherm models. The saturation capacity increases rapidly with increasing pressure while the affinity (or equilibrium) constant and the parameter characterizing the surface heterogeneity decrease. It is noteworthy that the distribution coefficient of the insulin variants increases with increasing pressure whereas their equilibrium constant b decreases for porcine insulin and increases for Lispro. The association constant b(ds), which characterizes the adsorption and desorption equilibrium of insulin in the system, increases with increasing pressure. The excellent agreement between the experimental overloaded profiles recorded under different pressures and those calculated using the POR model suggests that the chromatographic behavior of insulin is controlled more by equilibrium thermodynamics than by the mass transfer kinetics. The latter seems to be nearly independent of the average column pressure. Thus, increasing the average column pressure is an efficient, albeit costly, way to increase the loading capacity of the column, hence the production rate in preparative chromatography.

Modified Rouchon and Rouchon-like algorithms for solving different models of multicomponent preparative chromatography

Modified Rouchon and Rouchon-like algorithms were used to solve multicomponent equilibrium-dispersive chromatographic models as well as a more general lumped pore diffusion model. The modified algorithms enable remarkable reduction of computation time and avoid computation errors that result from the original Rouchon approach for some cases of multicomponent chromatography. A comparison is given between the general chromatographic model, the lumped pore diffusion model and the equilibrium-dispersive model.

Determination of mobile phase effect on single-component adsorption isotherm by use of numerical estimation.

Numerical estimation was used to determine adsorption isotherm parameters of a single-component in a normal-phase system. The distribution isotherm of methyl deoxycholate was described between the mobile phase containing hexane, ethyl acetate, methanol with varied concentration and a silica gel adsorbent. The effect of the mobile phase composition on the isotherm parameters and the band profiles was investigated. The results obtained were used to simulate the overload gradient elution. The validity of the method proposed was verified by comparison of the computer simulations with the experimental band profiles.

Adsorption/partition model of liquid chromatography for chemically bonded stationary phases of the aliphatic cyano, reversed-phase C8 and reversed-phase C18 types.

A novel approach was introduced to modeling solute retention in the liquid chromatography systems, employing silica-based aliphatic chemically bonded stationary phases of the cyano, reversed-phase C8 and reversed-phase C18 types, and the mixed binary eluents most frequently used in the reversed-phase and normal-phase chromatography modes (i.e. using the methanol-water and the 2-propanol-n-hexane liquid mixtures, respectively). This approach takes notice of the mixed (adsorption/partition) mechanism of solute retention, in which both, the adsorptive and the dispersive forces contribute to the overall energetics of this process. Performance of our new model was compared with that of the widely recognized and on a routine basis applied Schoenmakers approach, and it was found out that both models perform with a practically equal and outstanding accuracy.

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.

Use of the isopycnic plots in designing operations of supercritical fluid chromatography. V. Pressure and density drops using mixtures of carbon dioxide and methanol as the mobile phase.

The drops of pressure and density along chromatographic columns of different characteristics, eluted with different mixtures of carbon dioxide and methanol was mapped as functions of the column outlet pressure and the operating temperature. This paper extends an earlier report reporting the extent of the pressure and density drops along chromatographic columns eluted with neat CO(2)[1]. It illustrates the similarities and differences in the pressure and density profiles along columns operated with mixed mobile phases and with neat CO(2). Numerical calculations of the pressure and density drops along columns packed with particles of different sizes, under different operating conditions (temperature, outlet pressure, and flow rate), provide important insights regarding the extent of the pressure and density drops under these operating conditions.