Emerging approaches to estimate retention factors in high performance liquid chromatography

The retention factor is one of the most universally used parameters in chromatography. The errors associated with the conventional ways to determine the retention factor of compounds in liquid chromatography are studied and compared with those corresponding to new approaches. The later avoid the use of extra-column time and hold-up time values, which have proven to be tedious and ambiguous. Simulations and real data, used to examine the accuracy of four different approaches (two classic and two new), suggest that the new approaches could be considered more satisfactory than the classic ones.     

Hold-up volume and its application in estimating effective phase ratio and thermodynamic parameters on a polysaccharide-coated chiral stationary phase

As an "unretained" marker, 1,3,5-tri-tert-butylbenzene (TTBB) has been commonly used to measure the hold-up volume. Despite many racemates have been resolved on Chiralcel OJ column, the hold-up volume of the column is still not well characterized. The aim of this work was to evaluate the chromatographic behavior of TTBB on the OJ column, and its application in estimating the effective phase ratio and thermodynamic parameters. The hold-up volume was affected not only by the mobile phase composition but also the solvents used for dissolving TTBB. A higher concentration of TTBB (0.500 mg/mL) showed a better reproducibility than when used at a lower concentration. After correction for thermal expansion of the mobile phase, TTBB was found to have slight retention on the OJ phase. The effective phase ratio increased with an increase in the temperature and decrease in the strength of the mobile phase. The enthalpy and entropy of enantiomers of imidazolinone herbicides were independent of the temperature in a linear van't Hoff plot when the effective phase ratio was changed. This study shows that, based on the hold-up volume from TTBB, thermodynamic evaluation with parameters derived from the distribution constant is valuable for understanding chromatographic retention and enantioseparation mechanisms of chiral analytes.     

Effect of extra-column volume on practical chromatographic parameters of sub-2-μm particle-packed columns in ultra-high pressure liquid chromatography

Effects of extra-column volume on apparent separation parameters were studied in ultra-high pressure liquid chromatography with columns and inlet connection tubings of various internal diameters (id) using 50-mm long columns packed with 1.8-μm particles under isocratic conditions. The results showed that apparent retention factors were on average 5, 11, 18, and 41% lower than those corrected with extra-column volumes for 4.6-, 3.0-, 2.1-, and 1.0-mm id columns, respectively, when the extra-column volume (11.3 μL) was kept constant. Also, apparent pressures were 31, 16, 12, and 10% higher than those corrected with pressures from extra-column volumes for 4.6-, 3.0-, 2.1-, and 1.0-mm id columns at the respective optimum flow rate for a typical ultra-high pressure liquid chromatography system. The loss in apparent efficiency increased dramatically from 4.6- to 3.0- to 2.1- to 1.0-mm id columns, less significantly as retention factors increased. The column efficiency was significantly improved as the inlet tubing id was decreased for a given column. The results suggest that maximum ratio of extra-column volume to column void volume should be approximately 1:10 for column porosity more than 0.6 and a retention factor more than 5, where 80% or higher of theoretically predicted efficiency could be achieved.     

Approaches to characterise chromatographic column performance based on global parameters accounting for peak broadening and skewness

Peak broadening and skewness are fundamental parameters in chromatography, since they affect the resolution capability of a chromatographic column. A common practice to characterise chromatographic columns is to estimate the efficiency and asymmetry factor for the peaks of one or more solutes eluted at selected experimental conditions. This has the drawback that the extra-column contributions to the peak variance and skewness make the peak shape parameters depend on the retention time. We propose and discuss here the use of several approaches that allow the estimation of global parameters (non-dependent on the retention time) to describe the column performance. The global parameters arise from different linear relationships that can be established between the peak variance, standard deviation, or half-widths with the retention time. Some of them describe exclusively the column contribution to the peak broadening, whereas others consider the extra-column effects also. The estimation of peak skewness was also possible for the approaches based on the half-widths. The proposed approaches were applied to the characterisation of different columns (Spherisorb, Zorbax SB, Zorbax Eclipse, Kromasil, Chromolith, X-Terra and Inertsil), using the chromatographic data obtained for several diuretics and basic drugs (β-blockers).     

On the Determination of the Hold-Up Time in Reversed Phase Liquid Chromatography

Abstract

The determination of the hold-up time in reversed phase liquid chromatography has been studied extensively for the mobile phase system methanol-water. Hold-up times obtained by static methods, linearization of homologous series and so-called “unretained compounds” are discussed and mutually compared. Several n-alkyldimethylsilyl bonded phases have been used for this investigation.

A rough estimate of the hold-up time can be obtained by using components of the mobile phase or highly concentrated salt solutions, but only for mobile phase compositions around 60% (v/v) methanol. Hold-up times accurate to 1% can be obtained over the complete range of mobile phase compositions from the linearization of net retention times of homologous series.     

Dependence of the retention volumes of additional streaming current responses and of the column void volume on mobile phase composition

Summary The influence of the alcohol content of the mobile phase and water, acetic acid and aniline as mobile phase additives on the generation and shape of two additional changes of the streaming current, generated inside the liquid chromatography column by injection of any sample and recorded before the responses of retained solutes, was studied in a normal-phase system using silica gel as the stationary phase. The mobile phases were based on a n-heptane-1-propanol mixtures. Under the same conditions the relationships between the column interparticle volume, the column void volume and the total liquid volume in the column and the retention volumes of these two streaming current responses, having the form of chromatographic peaks, were studied. The column void volume was identified with the retention volume of n-octane. The total liquid volume in the column (column hold-up) was calculated from the weight loss of the column wetted with water at first and then dried in nitrogen stream. The retention volume of the first streaming current response equals the column interparticle volume disregarding the mobile phase composition. If the 95∶5 n-heptane-1-propanol mobile phase contains water up to 80% of its saturated concentration (up to 0.114% by vol.), the retention volume of the second response agrees with the total volume of the liquid in the silica gel column, with a precision better than 2%. At a higher relative water saturation the retention volume of the second response increases, while the column void volume decreases. Both changes are explained by the spontaneous formation of a highly polar stagnant liquid in the pores of the silica gel.     

Correction of the deviations in the retention times with Chromolith columns associated to the flow rate: implications in the modelling of the retention behaviour

In a previous work (J. Sep. Sci. 2009, 32, 2793-2803), we reported an interpretive optimisation approach to achieve maximal resolution in minimal analysis time, based on models describing the retention and peak shape as a function of mobile phase composition and flow rate. The method was applied to the separation of a group of basic drugs in a Chromolith column. In that work, we found that the retention factors were sensitive to the flow rate. The reason of the observed deviations in retention times is the increase in the column volume at the applied pressure, which decreases the linear velocity inside the column. This behaviour forced to include a correction term in the model that described the retention. We show here how the deviations in retention times can be evaluated, allowing retention models that do not include the flow rate as a variable, similar to isocratic chromatography at fixed flow rate. The logarithm of the deviations in the retention times with flow rate is shown to correlate with the solute polarity. This correlation is compared with similar correlations for the retention factor at fixed mobile phase composition and the extrapolated retention factor in water at fixed flow rate.     

Foundations of retention in partition chromatography

The connection between the observable output in column chromatography (retention time, retention volume, retention factor, separation factor, etc.) and system properties (hold-up volume, pressure, temperature, isotherm behavior, etc.) is discussed from a practical and mechanistic perspective for gas–liquid chromatography, reversed-phase liquid chromatography, supercritical fluid chromatography, micellar electrokinetic chromatography, and capillary electrochromatography. The unifying feature of these techniques is that retention can be described by a partition model, although not always exclusively. When over simplistic system models are used to explain variation in retention parameters they frequently mask the true reasons for poor repeatability and difficulties in transfer between system. Methods employing relative retention afford higher precision but may contain residual uncorrected errors. For those systems with several separate mechanisms contributing to retention the effective retention parameters can no longer be interpreted by simple partition models. The broadly based and practically focused material in this article affords an illustration of the often complicated relationship between system properties and retention, and the dangers that lurk in simplified retention models if the validity of their underlining approximations is not appropriate for the system under study.     

New approach to linear gradient elution used for optimisation in reversed-phase liquid chromatography

A new mathematical treatment concerning the gradient elution in reversed-phase liquid chromatography when the volume fraction psi of an organic modifier in the water-organic mobile phase varies linearly with time is presented. The experimental ln k versus psi curve, where k is the retention factor under isocratic conditions in a binary mobile phase, is subdivided into a finite number of linear portions and the solute gradient retention time tR is calculated by means of an analytical expression arising from the fundamental equation of gradient elution. The validity of the proposed analytical expression and the methodology followed for the calculation of tR was tested using eight catechol-related solutes with mobile phases modified by methanol or acetonitrile. It was found that in all cases the accuracy of the predicted gradient retention times is very satisfactory because it is the same with the accuracy of the retention times predicted under isocratic conditions. Finally, the above method for estimating gradient retention times was used in an optimisation algorithm, which determines the best variation pattern of psi that leads to the optimum separation of a mixture of solutes at different values of the total elution time.     

Measurement of retention in comprehensive two-dimensional gas chromatography using flow modulation with methane dopant

Flow modulation of methane-doped carrier gas is used to visualize the second dimension hold-up time in GC × GC continuously throughout the run. This provides an internal reference of hold-up time and presents a straightforward means of examining retention in each dimension of GC × GC. Retention factors on similar and dissimilar column pairs are examined. Stationary phase bleed is shown to be retained by the second dimension column.     

A simple,fast, and accurate thermodynamic‐based approach for transfer and prediction of gas chromatography retention times between columns and instruments Part III: Retention time prediction on target column

This is the third part of a three‐part series of papers. In Part I, we presented a method for determining the actual effective geometry of a reference column as well as the thermodynamic‐based parameters of a set of probe compounds in an in‐house mixture. Part II introduced an approach for estimating the actual effective geometry of a target column by collecting retention data of the same mixture of probe compounds on the target column and using their thermodynamic parameters, acquired on the reference column, as a bridge between both systems. Part III, presented here, demonstrates the retention time transfer and prediction from the reference column to the target column using experimental data for a separate mixture of compounds. To predict the retention time of a new compound, we first estimate its thermodynamic‐based parameters on the reference column (using geometric parameters determined previously). The compound's retention time on a second column (of previously determined geometry) is then predicted. The models and the associated optimization algorithms were tested using simulated and experimental data. The accuracy of predicted retention times shows that the proposed approach is simple, fast, and accurate for retention time transfer and prediction between gas chromatography columns.     

Evaluation of a reversed-phase column (supelcosil LC-ABZ) under isocratic and gradient elution conditions for estimating octanol-water partition coefficients

The solvation parameter model is used to identify suitable chromatographic models for estimating the octanol-water partition coefficient for neutral compounds of varied structure by reversed-phase liquid chromatography. The stationary phase Supelcosil LC-ABZ with methanol-water mobile phases affords a series of suitable correlation models for estimating the octanol-water partition coefficient (log KOW) under isocratic and gradient elution conditions. Isocratic separations with mobile phase compositions containing from about 25 to 40% (v/v) methanol provide the most accurate results for log KOW values in the range -0.1 to 4.0. Gradient separations programmed from 5 to 100% (v/v) methanol are suitable for faster separations of compounds with large log KOW values. The standard error in the estimate for the regression models of the predicted log KOW values against literature values are 0.135 log units for the 30% (v/v) methanol-water isocratic system and 0.263 log units for the methanol-water gradient system. Isocratic retention factors predicted from two gradient separations with gradient times of 15 and 45 min afford a poorer fit for the correlation models between log KOW and the estimated retention factors than that of either the above isocratic and gradient models. Plots of the retention factor (log k) as a function of mobile phase composition are generally non-linear. Values of log kw obtained by non-linear extrapolation to a volume fraction of 0% (v/v) methanol do not afford a useful model for estimating log KOW.     

Influence of the errors made in the measurement of the extra-column volume on the accuracies of estimates of the column efficiency and the mass transfer kinetics parameters

The influences of the errors made in the measurement of the extra-column volume of an instrument on the accuracies of the estimates made of the column efficiency and of the parameters of the mass transfer kinetics were investigated from an experimental point of view. A standard HP1090 apparatus (extra-column volume, approximately 50 micro L) was used to measure the efficiency of a Sunfire-C(18) RPLC column (column hold-up volume, approximately 1.50 mL). The first and second moments of the peaks of phenol (a retained compound) and of thiourea (a practically non-retained compound) were measured at six different temperatures between 22 and 78 degrees C, for flow rates between 0.10 and 4.70 mL/min (i.e., for linear velocities between 0.025 and 1.179 cm/s). Each series of measurements was successively made with the instrument being fitted with and without the column. The experimental HETP data must be corrected for the solute dispersion in the connected tubes in order properly to assess the true column efficiency. Even with a modern, high performance instrument, the dispersion of a non-retained compound is essentially due to the band broadening phenomena that take place in the extra-column volumes, the sum of all these extra-column band broadening contributions accounting for more than 80% of the total band broadening measured. The contribution of the sampling device is particularly deleterious since, for a 2 mu L injection, the maximum solute concentration in the peak that enters into the column is nearly ten-fold lower than that of the sample. Nevertheless, the impact of the extra-column volumes on the estimates of the kinetic parameters (e.g., molecular diffusion coefficient D(m) and effective particle diffusivity D(e)) remains negligible. Obviously, the relative error made on the column efficiency of a retained compound depends much on its retention factor. It decreases from 8 to 1% when the retention factor increases from 5 to 17.     

A simple procedure for the rapid optimization of reversed-phase separations with ternary mobile phase mixtures

Summary A simple rapid procedure is described for estimating optimum compositions of ternary mobile phase mixtures for the separation of samples by reversed-phase liquid chromatography (RPLC). Retention data in two iso-eluotropic binary mobile phase mixtures (mixtures with equal retention times) are required to initiate the procedure. The logarithm of the capacity factor is assumed to vary linearly with the composition of isoeluotropic ternary mixtures formed by mixing the two limiting binaries. Using the product of resolution factors of adjacent peaks as the criterion, an optimum ternary composition is then calculated. After a chromatogram has been obtained with the predicted optimum ternary mobile phase, the procedure is repeated until no further improvement can be achieved. Examples of the application of the present procedure are described to illustrate its effectiveness.     

非等时空距灰色模型在液相色谱保留值研究中的应用

本文运用灰色理论中的非等时空距ＧＭ（１，１）模型，对液相色谱中的流动相组成及容量因子的关系进行了研究。所建灰色模型经过检验其精度为Ｉ级。实验结果表明，不仅等时空距灰色模型，而且非等时空距灰色模型，同样适用于色谱保留值的研究。     

Retention mechanisms in super/subcritical fluid chromatography on packed columns

Whereas the retention rules of achiral compounds are well defined in high-performance liquid chromatography, on the basis of the nature of the stationary phase, some difficulties appear in super/subcritical fluid chromatography on packed columns. This is mainly due to the supposed effect of volatility on retention behaviours in supercritical fluid chromatography (SFC) and to the nature of carbon dioxide, which is not polar, thus SFC is classified as a normal-phase separation technique. Moreover, additional effects are not well known and described. They are mainly related to density changes of the mobile phase or to adsorption of fluid on the stationary phase causing a modification of its surface. It is admitted that pressure or temperature modifications induce variation in the eluotropic strength of the mobile phase, but effects of flow rate or column length on retention factor changes are more surprising. Nevertheless, the retention behaviour in SFC first depends on the stationary phase nature. Working with polar stationary phases induces normal-phase retention behaviour, whereas using non-polar bonded phases induces reversed-phase retention behaviour. These rules are verified for most carbon dioxide-based mobile phases in common use (CO(2)/MeOH, CO(2)/acetonitrile or CO(2)/EtOH). Moreover, the absence of water in the mobile phase favours the interactions between the compounds and the stationary phase, compared to what occurs in hydro-organic liquids. Other stationary phases such as aromatic phases and polymers display intermediate behaviours. In this paper, all these behaviours are discussed, mainly by using log k-log k plots, which allow a simple comparison of stationary phase properties. Some examples are presented to illustrate these retention properties.     

Mobile phase viscosity and velocity dependence on protein retention using nonequilibrium chromatographic techniques

Nonequilibrium chromatography (NEC) is an alternative chromatographic procedure for the separation of macromolecules. The retardation of a protein series is studied using a phosphate buffer as a mobile phase with various concentrations of glycerol fraction (used as a viscosity modifier) at different mobile phase velocities and a C1 column with a very low packing particle diameter as a stationary phase. It is shown that the two factors (viscosity and velocity) of the mobile phase constituted important parameters in the retention mechanism of the proteins in NEC. The retardation velocity domain is divided into two regions. For low velocity regions, the protein retention decreased with a mobile phase velocity increase. This retention is enhanced above a critical value of the mobile phase velocity. The transition between the two well-known NEC methods, slalom chromatography and hydrodynamic chromatography, is clearly visualized for the first time for the protein retention of particular values of the mobile phase velocity.     

A simple,fast, and accurate thermodynamic‐based approach for transfer and prediction of gas chromatography retention times between columns and instruments Part I: Estimation of reference column geometry and thermodynamic parameters

The transfer of retention times based on thermodynamic models between columns can aid in separation optimization and compound identification in gas chromatography. Although earlier investigations have been reported, this problem remains unsuccessfully addressed. One barrier is poor predictive accuracy when moving from a reference column or system to a new target column or system. This is attributed to challenges associated with the accurate determination of the effective geometric parameters of the columns. To overcome this, we designed least squares‐based models that account for geometric parameters of the columns and thermodynamic parameters of compounds as they partition between mobile and stationary phases. Quasi‐Newton‐based algorithms were then used to perform the numerical optimization. In this first of three parts, the model used to determine the geometric parameters of the reference column and the thermodynamic parameters of compounds subjected to separation is introduced. As will be shown, the overall approach significantly improves the predictive accuracy and transferability of thermodynamic data (and retention times) between columns of the same stationary phase chemistry. The data required for the determination of the thermodynamic parameters and retention time prediction are obtained from fast and simple experiments. The proposed model and optimization algorithms were tested and validated using simulated and experimental data.     

Zwitterionic ion chromatography using a dynamically coated column and mobile phase recycling

An investigation into the use of zwitterionic ion chromatography for the determination of inorganic anions in water samples was carried out. When using an ODS stationary phase precoated with Zwittergent 3-14 and a pure water mobile phase, the stability of the adsorbed coating was insufficient for quantitative work. Recycling of the water mobile phase was used to stabilise the zwitterionic coating, and resulted in improved retention time precision (15.2% RSD down to 2.4% RSD for nitrate). Post-detection cation- and anion-exchange columns in acid and hydroxide form removed sample ions from the recycling mobile phase, with the desorbed Zwittergent 3-14 passing through unretained and passing back through the pump to the analytical column. A 200-ml volume of mobile phase was recycled over a 3-week period with retention times for sulphate, chloride and nitrate standards injected at the start and end of the period varying less than 2.5%. The same system was then used with a mobile phase containing 2 mM Zwittergent 3-14. This resulted in further improvements in retention time (0.2-0.5% RSD, n = 10) and peak area precision (2.6-6.0% RSD, 1 mM standards) and improved peak efficiencies (2421-4047 N). The developed method was applied to water samples, and results compared to those obtained using anion-exchange chromatography. All sample cations were exchanged to sodium using an off-line cation-exchange procedure prior to injection.