Correctness of the van 't Hoff analysis for homogeneous or heterogeneous retention.

It is already known that the physical meaning of the numerical values of the calculated enthalpy (ΔH) and entropy (ΔS) change in chromatography via the van 't Hoff plot analysis is rather questionable. In the former work of these authors, it has been demonstrated that by serially coupling two reversed-phase columns of the same inner diameter but of different retention mechanism, the obtained thermodynamic values are not related to the numerical results obtained on the individual columns respectively. Since surface heterogeneity of the stationary phase is intrinsically present in chiral chromatography (enantioselective and non-selective sites), the calculation of ΔH and ΔS should be revisited in that field. In this study, more details of the pressure dependence were investigated. Using special POPLC columns, the effect of the column length on the calculated thermodynamic values was investigated. The calculated values differ by 30-400% when the column length is increased from 4 cm to 12 cm. The dependence of the calculated results on the applied flow rate was already highlighted earlier, and here the emphasis was put on the instrument on which the separation was performed. It turns out that there is a difference when using a Shimadzu HPLC system compared to using a Waters Acquity UPLC system. Because the Eyring method serves as an alternative route to calculate the thermodynamic values from chromatographic data, the differences obtained by the two methods were also investigated.

The correctness of van 't Hoff plots in chiral and achiral chromatography.

van 't Hoff plots (logarithm of the retention factor, ln k, vs. the reciprocal of absolute temperature, 1/T) are commonly used in chromatographic studies to characterize the retention mechanisms based on the determined enthalpy (ΔH∘) and entropy (ΔS∘) change of analyte adsorption. In reversed phase liquid chromatography, the thermodynamic parameters could help to understand the retention mechanism. In chiral chromatography, however, the conclusions drawn based on van 't Hoff plots can be deceptive because several different types of adsorption sites are present on the surface of stationary phase. The influence of heterogeneity, however, cannot be studied experimentally. In this study, we employed two reversed phase columns with different retention mechanisms to show that by serially coupling the columns, the obtained thermodynamic parameters are not related to the results obtained on the respective individual columns. Furthermore, our results show that the experimental conditions - such as flow-rate or choice of instrument - will strongly influence the calculated enthalpy and entropy values.

Rate constant determination of interconverting enantiomers by chiral chromatography using a stochastic model.

It may happen under the conditions employed that enantiomers interconvert to each other. In this case, obviously, the kinetics of the process is to be examined. When enantiomers dynamically interconvert to each other during the separation process, a plateau is observed between the adjacent peaks (so-called Batman peak appears). The peak shape depends on the rate constant of this dynamic reaction. A novel stochastic model was derived which takes both the separation and the interconversion into account at the molecular level - thus the effects of the parameters affecting the separation can be investigated. The novel model was used for the study of quetiapine, a drug molecule that interconverts during the separation to evaluate the rate constant based on the enantiomerization. Various flow rates and temperatures were used, and good agreement was obtained with the rate constant obtained from optical rotation experiments and with the software written by Trapp [1]. The most important result we concluded is the need of mild conditions during the separation to ascertain the rate constant the most accurately (low flow rates and temperatures where the enantiomerization process is limited to a few interconversions). The comparison of the rate constants of the on-column and the off-column experiments should be done by considering the stationary phase effects that are absent in the off-column experiments.

Solvent minimization in two-dimensional liquid chromatography.

An algorithm was developed for the minimization of consumption of organic solvent in comprehensive two-dimensional liquid chromatography (2DLC). It was shown that one can reach higher peak capacities only by using more eluent. The equilibration volume of the second dimension, however, did not affect the solvent consumption significantly. Calculations confirmed that the same target peak capacity could be achieved by consuming significantly different volume of organic modifier depending on the number of fractions analyzed in the second dimension suggesting that 2D separations can be optimized for eluent consumption. It was shown that minimization of eluent usage requires the use of small and high efficient columns in the second dimension. A simple equation was derived for the calculation of the optimal number of collected fractions from the first dimension that allowed the minimization of eluent usage, cost and environmental impact of comprehensive 2DLC separations.

Polydispersity in size-exclusion chromatography: a stochastic approach.

We investigate the impact of polydispersity of the sample molecules on the separation process and on the efficiency of size-exclusion chromatography. Polydispersity was integrated into the molecular (stochastic) model of chromatography; the characteristic function, the band profile and the most important moments of the elution profiles were calculated for several kind of pore structures. We investigated the parameters affected by polydispersity on the separation for a number of pore shapes. Our results demonstrate that even a small distribution in the molecular size (i.e. polydispersity) can contribute substantially to the total width of the chromatographic peak. The pure effect of polydispersity can only be investigated via mathematical modeling, because its contribution to an experimental chromatogram cannot be separated from other band-broadening effects.

The pore size distribution of the first and the second generation of silica monolithic stationary phases.

The mesopore structure (pore size and its distribution) for the first and second generations of silica-based monolithic columns was determined by inverse size-exclusion chromatography. The effect of pore size distribution was considered via the molecular theory of size-exclusion chromatography. The molecular theory of chromatography allows taking into account the kinetics of the pore ingress and egress processes, the heterogeneity of the pore sizes and polymer polydispersity. Besides, the mesopore structure, the characteristic domain sizes of the macropores present in the first and second generations of silica-based monolithic columns were also characterized.

Effect of particle size distribution on the separation efficiency in liquid chromatography.

In this work, the influence of the width of particle size distribution (PSD) on chromatographic efficiency is studied. The PSD is described by lognormal distribution. A theoretical framework is developed in order to calculate heights equivalent to a theoretical plate in case of different PSDs. Our calculations demonstrate and verify that wide particle size distributions have significant effect on the separation efficiency of molecules. The differences of fully porous and core-shell phases regarding the influence of width of PSD are presented and discussed. The efficiencies of bimodal phases were also calculated. The results showed that these packings do not have any advantage over unimodal phases.

Determination of the pore size distribution of high-performance liquid chromatography stationary phases via inverse size exclusion chromatography.

Stationary phases in liquid chromatography exhibit quite different pore structures. Whereas most of the fully porous packing materials possess a narrow pore size distribution, core-shell particles are usually of rather wide pore size distribution. Recently a novel theory of size exclusion chromatography was introduced to model the effect of pore size distribution. The molecular theory of chromatography allows taking into account the kinetics of the pore ingress and egress processes, the heterogeneity of the pore sizes and polymer polydispersity as well. The novel model was applied to inverse size exclusion chromatography data. In this study, we have determined the actual pore size distribution of a number of HPLC stationary phases. Our results agree well with the results obtained with the model introduced by Knox and Scott.

Molecular theory of size exclusion chromatography for wide pore size distributions.

Chromatographic processes can conveniently be modeled at a microscopic level using the molecular theory of chromatography. This molecular or microscopic theory is completely general; therefore it can be used for any chromatographic process such as adsorption, partition, ion-exchange or size exclusion chromatography. The molecular theory of chromatography allows taking into account the kinetics of the pore ingress and egress processes, the heterogeneity of the pore sizes and polymer polydispersion. In this work, we assume that the pore size in the stationary phase of chromatographic columns is governed by a wide lognormal distribution. This property is integrated into the molecular model of size exclusion chromatography and the moments of the elution profiles were calculated for several kinds of pore structure. Our results demonstrate that wide pore size distributions have strong influence on the retention properties (retention time, peak width, and peak shape) of macromolecules. The novel model allows us to estimate the real pore size distribution of commonly used HPLC stationary phases, and the effect of this distribution on the size exclusion process.