Can the theory of gradient liquid chromatography be useful in solving practical problems?

Advances in the theory of gradient liquid chromatography and their practical impacts are reviewed. Theoretical models describing retention in reversed-phase, normal-phase and ion-exchange modes are compared. Main attention is focused on practically useful models described by two- or three-parameter equations fitting the experimental data in the range of mobile phase composition utilized for sample migration during gradient elution. The applications of theory for gradient method development, optimization and transfer are addressed. The origins and possibilities for overcoming possible pitfalls are discussed, including the effects of the instrumental dwell volume, uptake of mobile phase components on the column and size of the sample molecules. Special attention is focused on gradient separations of large molecules.     

Prediction of Retention Time of Solutes under Linear Gradient Elution Conditions in RP-HPLC

A model for prediding retention time of solutes undeir linear gradient elulioa conditions has been established. In this model,the theorelkal expressions under different eluflon modes were derived and tested with the retention behaviors of p-hydroxy-benzaldehyde, vanilUn, biphenyl, phenanthrene in gradient elution. With halting into account the dwell time of the instrumeatal system, the theoretically predicted retention times agreewell with those experimentally determined.     

Controlling the retention in capillary LC with solvents, temperature, and electric fields

Once a suitable stationary phase and column dimensions have been selected, the retention in liquid chromatography (LC) is traditionally adjusted by controlling the mobile phase composition. Solvent gradients enable achievement of good separation selectivity while decreasing the separation time as compared to isocratic elution. Capillary columns allow use of other programming parameters, i.e. temperature and applied electric fields, in addition to solvent gradient elution. This paper presents a review of programmed separation techniques in miniaturized LC, including retention modeling and method transfer from the conventional to micro- and capillary scales. The impact of miniaturized instrumentation on retention and the limitations of capillary LC are discussed. Special attention is focused on the gradient dwell volume effects, which are more important in micro-LC techniques than in conventional analytical LC and may cause significant increase in the time of analysis, unless special instrumentation and (or) pre-column flow-splitting is used. The influence of temperature upon retention is also discussed, and applications where the temperature has been actively used for retention control in capillary LC are included together with the instrumentation utilized. Finally the possibilities of additional selectivity control by applying an electric field over a packed capillary LC column are discussed.     

利用HCI程序确定儿茶酚化合物的反相高效液相色谱最佳分离条件

有效地确定了反相高效液相色谱分离儿茶酚化合物的最佳条件。在水和甲醇的二元流动相里分别加入乙酸缓冲液,利用基于ln k=ln kw +SF, k=A+B/F, ln k=L+MF+NF2 (F是流动相中有机物甲醇的体积分数)等保留因子的一次或二次方程式的塔板理论得到色谱分离结果;利用保留原理得到等度和梯度洗脱的最佳条件。得出最佳初始流动相是含0.1%乙酸的水和含0.1%乙酸的甲醇(体积比为75∶25)的混合溶液;梯度洗脱条件：初始流动相保持15 min,然后用10 min的时间将上述二元流动相的体积比线性变换成50∶50,直到完成全部分离。通过实验证实该计算结果与实验值相近。     

Characterization of unstable ion-exchange chromatographic separation of proteins.

Very fine separation of proteins by stepwise elution ion-exchange chromatography is very often a unstable process. To characterize the unstability of such processes the elution volume variations were examined by the model equation which contained the ion-exchange capacity and the number of adsorption sites. The data needed for the model calculation were obtained from gradient elution experiments. As a model separation system stepwise elution of a model protein (beta-lactoglobulin) near the isoelectric point on a weak cation-exchange chromatography column was chosen. The elution volume varied significantly with a small change in the ion-exchange capacity. It was found that the ionic strength of the elution buffer must be adjusted in order to compensate a change in the elution volume due to the ion-exchange capacity variations. The ionic strength and the pH of the elution buffer were also found to be important variables affecting the elution volume. In this model separation system, it was indicated that the pH should be within +/-0.1 unit and the ionic strength within +/-0.002 mol/l in order to meet the criteria (+/-5% elution volume variation). It is recommended that gradient elution data be obtained for predicting elution volume variations in stepwise elution. By using the gradient elution data the process diagnosis can be performed, and the important information on the process stability can be obtained.     

Gradient elution in normal-phase high-performance liquid chromatographic systems

Gradient elution is widely used for separation of complex samples in reversed-phase HPLC systems, but is less frequently applied in normal-phase HPLC, where it has a notoriously bad reputation for poor reproducibility and unpredictable retention. This behaviour is caused by preferential adsorption of polar solvents used in mixed mobile phases, which may cause significant deviations of the actual gradient profile from the pre-set program. Another important source of irreproducible retention behaviour is gradual deactivation of the adsorbent by adsorption of even traces of water during normal-phase gradient elution. To avoid this phenomenon, carefully dried solvents should be used. Finally, column temperature should be carefully controlled during normal-phase gradient elution if reproducible results are to be obtained. Working with dry solvents at a controlled constant temperature and using a sophisticated gradient-elution chromatograph, reproducibility of the retention data in normal-phase gradient elution better than 2% may be achieved even over several months of column use. The retention data in gradient elution can be calculated accurately if appropriate corrections are adopted for the gradient dwell volume and for the preferential adsorption of the polar solvents using experimental adsorption isotherms. The average error of prediction for the corrected calculated gradient retention data was lower than 2% for a silica gel column and lower than 3% for a bonded nitrile column, which may be suitable for the optimization of separation. Further, a simple approach is suggested for rapid estimation of changes in the retention induced by a change in the gradient profile in normal-phase HPLC. For such a rough estimation, it is not necessary to know the parameters of the dependence of the solute retention factors on the composition of the mobile phase.     

Column equilibration effects in gradient elution in reversed-phase liquid chromatography

The fundamental equations and conditions for linear and stepwise gradient elution in reversed-phase liquid chromatography are applied to a mixture of amino acids in their underivatized form in aqueous mobile phases modified by 2-propanol, acetonitrile or methanol for examining column equilibration effects. It was found in all cases systematic deviations between experimental and calculated retention times, which are prominent in 2-propanol, reduced in acetonitrile and practically negligible in methanol. These deviations appear within a chromatogram just after the first change in the composition of the mobile phase reaches the detector and last ca. 5 min, where the magnitude of errors reduces exponentially with time. Based on these observations we propose a simple way to correct the calculated from the gradient elution theory retention times of sample solutes. The origin of the discrepancies between theory and experiment as well as their impact on the resolution is also discussed.     

Exact peak compression factor in linear gradient elution. I. Theory

The only existing expression for the peak compression factor in linear gradient elution chromatography assumes that the linear-solvent-strength model (LSSM) applies to the retention of the compound studied, that the column efficiency is independent of the mobile phase composition, and that, during gradient elution, the relative retention factor of a compound inside its band varies linearly with the distance from the band center. Because the retention factors of many analytes in reversed-phase liquid chromatography do not rigorously follow the LSSM, we extend the theoretical approach of Poppe et al. to the prediction of peak compression factors in linear gradient elution chromatography for any retention model, when column efficiency varies with the mobile phase composition. Only the contribution of the chromatographic column to the peak compression was taken into account, the contribution of the dwell volume being neglected. A second restriction is the linearity of the relative retention factor as a function of the position along the band width inside the column. These constraints could be the sources for the difference observed between experimental and theoretical values of peak compression factors. When the retention factor varies steeply with the mobile phase composition, such as with proteins or large peptides in RP-HPLC, it is found that the thermodynamic compression term, which tends to sharpen the peak, is coupled with the column dispersion term, which tends to broaden the peak. This coupling term acts as an apparent dispersion term, contributing to broaden the peak. This result is consistent with the measurements of peak compression factors found in the literature.     

Theoretical background of short chromatographic layers. Optimization of gradient elution in short columns

Although linear salt gradient elution ion-exchange chromatography (IEC) of proteins is commonly carried out with relatively short columns, it is still not clear how the column length affects the separation performance and the economics of the process. The separation performance can be adjusted by changing a combination of the column length, the gradient slope and the flow velocity. The same resolution can be obtained with a given column length with different combinations of the gradient slope and the flow velocity. This results in different separation time and elution volume at the same resolution. Based on our previous model, a method for determining the separation time and the elution volume relationship for the same resolution (iso-resolution curve) was developed. The effect of the column length and the mass transfer rate on the iso-resolution curve was examined. A long column and/or high mass transfer rate results in lesser elution volume. The resolution data with porous bead packed columns and monolithic columns were in good agreement with the calculated iso-resolution curves. Although the elution volume can be reduced with increasing column length, the pressure drop limits govern the optimum conditions.     

Comparison between the isocratic and gradient retention behaviour of polypeptides in reversed-phase liquid chromatographic environments.

The isocratic and gradient elution behaviour of beta-endorphin and glucagon, two polypeptides known to exist in amphipathic alpha-helical conformations in lipophilic environments, have been examined under reversed-phase high-performance liquid chromatographic (RP-HPLC) conditions with low pH, aquo-acetonitrile mobile phases. The effects of changes in the volume fraction, psi, of the organic solvent modifier and temperature, T, on the magnitudes of the S and log k(o) values of these two polypeptides, obtained from the plots of logarithmic capacity factor (log k') vs. psi using isocratic elution conditions have been determined. These data have then been compared to the corresponding S and log k(o) values, obtained from the plots of logarithmic median capacity factor (log k) versus the median volume fraction of the organic solvent modifier (psi) derived from the linear gradient elution data, using the same n-butyl silica sorbent and related aquo-acetonitrile mobile phase conditions. As apparent from these studies, substantial differences occur in the temperature-dependent trends and magnitudes of the corresponding S and S values, or the log k(o) and log k(o) values, when these parameters are derived from experimental data acquired by these two different elution methods. Moreover, when gradient elution data for beta-endorphin and glucagon are utilised, the extrapolated values of the intercept and slope of the plots of log k vs. 1/T (corresponding to an apparent change in the median enthalpy of association, deltaH(o)assoc, or an apparent change in the median entropy of association, deltaS(o)assoc) substantially deviated from the values obtained for the thermodynamic parameters, deltaH(o)assoc and deltaS(o)assoc, derived from the log k' vs. 1/T plots using the corresponding isocratic data. These findings thus have important implications for biophysical and thermodynamic investigations when gradient elution data are employed to assess the molecular basis of the interaction of polypeptides with non-polar ligates.     

Unusual signal enhancement in reversed-phase chromatography of polystyrene monitored by UV detector

Summary Gradient elution of polystyrene standards on reversed phase C18 columns by methanol/tetrahydrofuran or methanol/dichloromethane mixtures yielded a strange effect of the molecular weight of the sample on the specific peak are (mAUs per g sample injected). The effect did not occur when pure dichloromethane was used as an eluent. Further to this, dependence of specific peak area on flow rate was observed in gradient elution with methanol/tetrahydrofuran mixtures. It was found that these effects were due to polymer elution at the verge of precipitation. Depending on the dwell time of the sample in the column, opalescence occurred that added to the UV signal used for monitoring the elution.     

Separation of Peptides by Pressurized Capillary Electrochromatography

A novel gradient pressurized capillary electrochromatography (pCEC) instrument was developed to separate peptides.Two gradient elution modes,hydrophobic and hydrophilic interaction mode in pCEC,were performed on this instrument.Baseline separation of six peptides was obtained on two gradient modes with C18 column and strong cationic exchange column respectively.The effects of mixer volume and total frow rate of pumps on resolution were also discussed.     

Application of a chromatography model with linear gradient elution experimental data to the rapid scale-up in ion-exchange process chromatography of proteins

We applied the model described in our previous paper to the rapid scale-up in the ion exchange chromatography of proteins, in which linear flow velocity, column length and gradient slope were changed. We carried out linear gradient elution experiments, and obtained data for the peak salt concentration and peak width. From these data, the plate height (HETP) was calculated as a function of the mobile phase velocity and iso-resolution curve (the separation time and elution volume relationship for the same resolution) was calculated. The scale-up chromatography conditions were determined by the iso-resolution curve. The scale-up of the linear gradient elution from 5 to 100mL and 2.5L column sizes was performed both by the separation of beta-lactoglobulin A and beta-lactoglobulin B with anion-exchange chromatography and by the purification of a recombinant protein with cation-exchange chromatography. Resolution, recovery and purity were examined in order to verify the proposed method.     

Computer-assisted transfer of programmed elutions in reversed-phase high-performance liquid chromatography

Computer-assisted procedures were used to simulate modifications in chromatograms caused by the transfer of elution programmes between instruments with significantly different dwell volumes. Moreover, for the first time the same approach was used to modify the elution programmes to match the chromatograms produced in the different instruments. The process may consist of making minor modifications to gradient programmes or transforming the original gradient programme into a stepwise gradient profile and/or the simultaneous programming of flow and solvent composition. The combination of these approaches has been shown to have an enormous potential for producing matched chromatograms in instrumental systems with dwell volumes that differ by several millilitres. The efficiency and robustness of the proposed procedure is demonstrated with a variety of compounds (two different mixtures of 10 and 11 analytes), mobile phases (methanol and acetonitrile gradients), flow rates (0.5-1.5 mL/min range), temperatures (35-45 degrees C interval) and gradient profiles (linear, multilinear, curved and stepwise).     

Development of an ion chromatographic gradient retention model from isocratic elution experiments

When facing separation problems in ion chromatography, chromatographers often lack guidelines to decide a priori if isocratic elution will give enough separation in a reasonable analysis time or a gradient elution will be required. This situation may be solved by the prediction of retention in gradient elution mode by using isocratic experimental data. This work describes the development of an ion chromatographic gradient elution retention model for fluoride, chloride, nitrite, bromide, nitrate, sulfate and phosphate by using isocratic experimental data. The isocratic elution retention model was developed by applying a polynomial relation between the logarithm of the retention factor and logarithm of the concentration of competing ions; the gradient elution retention model was based on the stepwise numerical integration of the corresponding differential equation. It was shown that the developed gradient elution retention model was not significantly affected by transferring data form isocratic experiment. The root mean squared prediction error for gradient elution retention model was between 0.0863 for fluoride and 0.7027 for bromide proving a very good predictive ability of developed gradient elution retention model.     

Large injection volumes in capillary liquid chromatography: Study of the effect of focusing on chromatographic performance

This paper describes a multivariate approach to study the effect on chromatographic conditions and to optimize such conditions in capillary liquid chromatography when high injection volumes are required. Several separations have been evaluated by using isocratic and gradient solvent elution, as well as isocratic elution combined with temperature programming. In this study, easily ionisable organic compounds with low logP have been used as representative analytes. Injection volume and nature of the injection solution have been evaluated in order to increase the sensitivity (peak area) and column performance (N values). The equations obtained by multiple linear regressions and response surfaces allow achieving the optimum on-column focusing conditions for chlorophenoxy acids, carbamates and heterocyclic amines.     

The ultimate band compression factor in gradient elution chromatography

The equations predicting the ultimate time band compression factor, G=(t(R)-t(F))/t(p) in linear gradient elution chromatography, for an infinitely narrow injection (injection time t(p)-->0) were derived for an ideal-model column (dispersionless chromatography, H=0) assuming the Linear Solvent Strength Model for the retention behavior of the analyte. Numerical solutions can readily be obtained when the LSSM model does not apply. The results can be generalized to any retained organic modifier (k'(A)) in the mobile phase. The stronger the retention of the organic modifier, the more effective the band compression. Dispersion in real chromatographic column (H not equal 0) affects the limits that can be reached in linear gradients but poorly in step gradients. Examples based on a conventional HETP of about 12 microm using a 5 microm particle packed column reveal that the best time compression factor that could be expected is twice the one predicted with an ideal column.     

反相高效液相三元流动相台阶梯度分离条件的快速优化方法

 根据溶质在柱内的迁移规律 ,建立了一种利用线性梯度实验快速获得溶质保留值方程系数 ,然后以串行响应函数为优化指标进行多台阶梯度分离条件优化的方法。与利用等度实验获得保留值方程的方法相比 ,该法可以大大缩短优化时间。通过该方法对芳香胺和衍生化氨基酸样品进行了分离 ,获得了满意的分离度 ,表明该方法的预测精度很好。     

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.