Optimization of stepwise gradient elution in columns chromatography

Summary A general equation for the final retention of a solute chromatographed under conditions of stepwise gradient elution has been derived. The elution process and the distances travelled by solutes as a function of eluent volume were simulated by computer for the optimization of stepwise gradient prorams from isocratic HPLC data. The validity of the equations was experimentally veritied.     

Fundamental equation of the dual flow rate-solvent gradient elution in liquid chromatography

An alternative expression of the fundamental equation of multi-mode gradient elution involving simultaneous changes in mobile phase composition and flow rate is derived using simple kinetic arguments and graphic interpretation. The new expression consists of a system of two integral equations and provides an easy and direct way of predicting retention times under dual-mode gradient conditions.     

HPLC Analysis of complex mixtures of triglycerides using gradient elutions and an ultraviolet detector

Summary A method of reserved-phase HPLC analysis for mixtures of triglycerides (TG's) that provides good resolution at acceptable analysis times for high-ECN TG's has been developed. An elution gradient of methyltert-butyl-ether (MTBE) in acetonitrile (ACN) was used with an ultraviolet detector operated at 215nm. The effect of the proportion of MTBE in the mobile phase, gradient time, temperature and sample solvent on TG retention and resolution was studied. Linear relationships were derived between the logarithm of the capacity factor (log k'), and the logarithm of selectivity (log α) and the above-mentioned chromatographic factors. The conditions selected were: an elution gradient of from 23 to 30% MTBE, an elution gradient time of 25 minutes, and a temperature of 30°C, which provided good resolution of soybean oil TG's in less than 30 minutes.     

梯度液相色谱保留时间公式在梯形梯度洗脱研究中的应用

根据前期得到的梯度液相色谱保留时间计算公式,在不指定溶剂强度模型形式的前提下,探讨了梯形梯度洗脱的一些特点。对于溶质在梯形梯度坡度上流出时的情形,推导得到溶质流出色谱柱所对应的流动相组成(φ_R)随梯度斜率(B)变化的表达式。该公式表明,在该情形中φ_R将会随着B值的增加而增加。对于溶质在梯形梯度最后一个等度区间流出时的情形,如果初始和终止流动相组成保持不变而仅有梯度的斜率发生变化时,从理论上证明了溶质保留时间(t_R)与梯度斜率的倒数(1/B)之间呈线性关系。实验中以C18色谱柱为固定相,甲醇-水为流动相,联苯为样品,测定了不同流动相组成以及梯形梯度条件下的保留时间,所得到的实验值与理论值吻合,从而验证了理论方法的正确性。     

Continuous TLC as a pilot technique for optimization of gradient HPLC. 1. Theoretical considerations for stepwise gradient TLC with binary mobile phase

Equations describing gradient elution in TLC, with a mobile phase of a constant composition in each step, have been derived. These equations are useful for calculating retention volumes from isocratic TLC data. Equations originally derived for gradient HPLC were adapted for TLC. The validity of the equations has been experimentally verified. The satisfactory agreement between experiment and theory for binary mobile phase composed of methyl ethyl ketone and n-heptane suggests that TLC can be used as a pilot technique for gradient HPLC.     

Determination of retention factors of phospholipids in gradient HPLC

Summary The mechanism of separation of solutes under gradient elution conditions has been studied. Separation of a mixture of soybean phospholipids (phosphatidylethanolamine, phosphatidylinositol, and phosphatidylcholine) in the ternary mobile phase: methanol, hexane, isopropanol was considered as an example. An analytical expression in terms of the composition of the ternary mobile phase was obtained to calculate retention factors in two-step gradient modes. The following new polynomial equation was derived: logk=A+BF+CF ²+DG+EG ² where A, B, C, D, and E are empirical coefficients; F and G are volume fractions of isopropanol and methanol respectively in the mobile phase based on hexane. The coefficients for phospholipids were obtained under gradient conditions.     

Interconversion of gradient and isocratic retention data in reversed-phase liquid chromatography: Effect of the uptake of eluent modifier on the retention of analytes

The experimental technique of mass spectrometric tracer pulse chromatography was used to study the effect of the sorption of eluent components by a C₁₈-bonded silica RPLC packing on the retention of a series of test analytes during isocratic and gradient elution experiments. The analytes of interest were a substituted phenol, a substituted nitroaniline, an anti-malaria drug, tetrahydrofuran, and methanol. The eluent used was a mixture of acetonitrile and water. The solutes and isotopically labeled eluent components were injected at fixed time intervals during each gradient run. The mass specific detector allowed the assignment of individual analyte peaks even when there was overlap in the chromatograms from successive injections. Thus, the retention time of each analyte could be determined as a function of gradient slope and initial eluent composition at the time of each injection. Experimental gradient retention time data were then compared with the calculated results from two theoretical models. The first model assumed the velocity of the mobile phase and eluent were equal. The second and most realistic model assumed the velocity of the eluent was less than the velocity of the mobile phase due to the uptake of eluent by the stationary phase. Gradient retention times predicted by the two models were reasonably accurate with the sorption model giving slightly more accurate values. Inverse calculations, i.e., calculation of isocratic retention factors from gradient elution data were also carried out with very similar results. That is, the model allowing for the uptake of eluent was slightly more accurate than the model assuming no eluent-stationary phase interaction.     

Retention prediction of a set of amino acids under gradient elution conditions in hydrophilic interaction liquid chromatography

The analysis of amino acids presents significant challenges to contemporary analytical separations. The present paper investigates the possibility of retention prediction in hydrophilic interaction chromatography (HILIC) gradient elution based on the analytical solution of the fundamental equation of the multilinear gradient elution derived for reversed‐phase systems. A simple linear dependence of the logarithm of the solute retention (ln k) upon the volume fraction of organic modifier (φ) in a binary aqueous‐organic mobile is adopted. Utility of the developed methodology was tested on the separation of a mixture of 21 amino acids carried out with 14 different gradient elution programs (from simple linear to multilinear and curved shaped) using ternary eluents in which a mixture of methanol and water (1:1, v/v) was the strong eluting member and acetonitrile was the weak solvent. Starting from at least two gradient runs, the prediction of solute retention obtained under all the rest gradients was excellent, even when curved gradient profiles were used. Development of such methodologies can be of great interest for a wide range of applications.     

Prediction of experimental parameters in combined isocratic and gradient elution reversed phase high performance liquid chromatography (RP-HPLC) using acetonitrile as organic modifier

The use of gradient elution in RP-HPLC is increasing. Aqueous buffers, such as phosphate at pH 1.7, with acetonitrile as the organic modifier are particularly advantageous as eluents with linear elution strength (LES). In the isocratic mode, under the experimental conditions used, fairly good linearity exists between logk' and x_B (x${}_{\text{B}}^{\text{º}}$ is the volume ratio of the organic modifier, i.e. acetonitrile) with a correlation coefficient of 0.9995. The relationship between isocratic and gradient elution parameters, such as x_B, x${}_{\text{B}}^{\text{º}}$ (starting composition in gradient elution), m (slope of the linear gradient), is transparent and the parameters of interest can be predicted fairly accurately using simple equations. The proposed system could be used in elaboration of a general retention index system for organic molecules in RP-HPLC.     

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.     

A new approach to the prediction of RP-HPLC retention times in gradient elution from isocratic data

Summary A general chromatographic model has been set up starting from a set of equations based on the concept of the velocity of a solute along the column. The composition of the mobile phase is taken into account solely as a numerical factor entering into suitable equations and totally independent of the chemical-properties of the constituents. A few isocratic experimental runs are necessary as input data, and subsequently a small amount of computational effort is sufficient to make predictions of retention times under gradient elution conditions for solutes of whatever chemical structure. The prediction errors are dependent on the steepness of the linear gradient chosen but are, in any case, acceptably low.     

A practical approach to transferring linear gradient elution methods

Attempts to theoretically address the problems involved in transferring linear gradient elution methods have been somewhat ad hoc due to the simplifying assumptions usually made in conventional gradient elution theory. Until now, all equations based on the k* parameter of linear gradient elution theory used as the basis for predicting the separation selectivity have not explicitly included the effect of the dwell volume (VD). Using an exact equation for predicting k*, that is, one which fully accounts in an a priori fashion for VD, we find a set of simple yet exact equations which unequivocally must be satisfied to transfer an optimized linear gradient elution method from one system (column or instrument or both) to another. These relationships absolutely mandate that a change in the instrument dwell volume requires a proportional change in the column volume; in turn, a change in the column volume requires a proportional change in the flow rate and/or gradient time to maintain a constant gradient steepness. Although we are not the first to suggest these guidelines, this work provides a complete theoretical foundation for these exact guidelines for the maintenance of gradient selectivity for the case of transferring a linear gradient elution method between different columns packed with the same particles and/or between different instruments.     

Methodological developments in overpressured-layer chromatography

Summary Since its introduction around 1977, OPLC has found widespread application and its methodology has been further developed. A possible development is gradient elution. Different continuous development methods (e.g. with eluent changeover, multistep gradient) and the possible system configurations for their execution are discussed. The advantages of the newly developed continuous development techniques are compared to earlier data. The most versatile method is demonstrated on lipid samples derived from human plasma, giving separation of six lipid classes and intra-class separation of the most polar classes in the same run.     

Preparative separation of bioactive constitutes from Zanthoxylum planispinum using linear gradient counter‐current chromatography

Counter‐current chromatography is a chromatographic technique with a support‐free liquid stationary phase. In the present study, a successful application of linear gradient counter‐current chromatographic method for preparative isolation of bioactive components from the crude ethanol extract of Zanthoxylum planispinum was presented. The application of n‐hexane/ethyl acetate/methanol/water quaternary solvents, in terms of “HEMWat” or “Arizona” solvent families, in gradient elution mode was evaluated. Results indicated that slightly proportional changes of biphasic liquid systems provided the possibility of gradient elution in counter‐current chromatography, maintaining stationary phase retention in the column. With the selected quaternary solvent systems composed of n‐hexane/ethyl acetate/methanol/water (2:1:2:1 and 3:2:3:2, v/v), and optimized gradient programs, in total seven fractions were separated in 4.5 h. Most of the purified compounds could be obtained at the milligram level with over 80% purity. The present study indicated that the linear gradient counter‐current chromatographic approach possessed unique advantages in terms of separation efficiency, exhibiting great potential for the comprehensive separation of complex natural extracts.     

The Varigrad and similar apparatus in gradient liquid chromatography: A systematic computational approach. Part 1: Theoretical development

Different methods for producing a pre-assigned gradient in liquid chromatography are presented. A systematic approach to the calculations involved is given. The derived equations are mostly Poisson and Poisson summation distributions which are tabulated in the literature. The incremental method of gradient elution developed by Scott has been modified. In the modified apparatus two mixing chambers are used instead of one. This leads to an appreciable decrease in the number of reservoirs needed for the same precision in fitting a desired gradient. The application of the derived equations, together with other Varigrad modifications, will be given in Part 2 of this paper (to be published shortly in this Journal).     

The theory of gradient elution under hydrostatic equilibrium in liquid chromatography. Part 3: Using solvents of different densities

Gradient elution under hydrostatic equilibrium is extended to the treatment of the case where the two liquids have different densities. Analytic expressions are derived only for the cases where both mixing chamber and reservoir have constant cross-sectional areas. As in the case where the densities of the liquids are equal, pressigned concentration gradients can be duplicated quite satisfactorily by combining a mixing chamber having a constant cross-sectional area and a reservoir having an area which changes linearly with reservoir height. A numerical example is given to illustrate the use of the derived equations.     

Chromatographic behaviour of low molar-mass polyesters in normal-phase high-performance liquid chromatography

Summary The normal-phase chromatographic retention behaviour of polyesters on bare silica and on a polymer-based polyamine (PA) column has been studied with a variely of binary mobile phases under isocratic conditions. The dependence of experimental retention data on the degree of polymerization (p) and on mobile phase composition (φ) was characterized by to an approach developed by Jandera et al. The bulky repeating unit and the relatively highly polar end groups of the polyesters both had a large influence on retention behaviour. The two effects in combination explain the molar-mass-independent retention observed experimentally at a particular mobile phase composition for all the mobile phase—stationary phase combinations investigated. These conditions were found to be independent of the type of end group. End group separation on a silica column improves when the polarity of the less polar solvent is increased. End group separation is better on the PA column because of a greater difference between the adsorption energy of the alcohol and acid end groups. Better prediction of retention data on the PA column was achieved by use of an approach which assumes two different types of adsorption site. Results enabled further understanding of retention behaviour in normalphase gradient polymer-elution chromatography (NPGPEC) and explained both the dependence of the order of elution onp and differences between the end-group selectivity of different systems.     

The gradient volume principle for fast evaluation of optimum conditions for isocratic analysis

Summary The paper describes by simple experiments in a pragmatical way by easy rules of thumbs gradient optimization. Besides selection of the stationary phase and initial and final conditions the two other important variables are program time and eluent flow rate. It is demonstrated, that when the product of both, the gradient volume, is kept constant, the solutes are always eluted with the same eluent composition at column outlet. At constant gradient volume, peak broadening depends on flow rate and on the eluent properties (viscosity) at which the solutes elute, and on the time the solutes spend in the column. Because peak broadening increases with increasing gradient volume, the peak capacity in gradient elution shows an optimum at gradient volumes around 15 empty column volumes (program times 45 to 60 min at flow rates of 1 ml/min with standard columns).Gradient elution can also be used for fast evaluation of optimum eluent composition for isocratic analysis. This procedure requires a calibration of the equipment for determination of eluent composition at column outlet. The sample is chromatographed in a standard gradient run of 10 to 15 empty column volumes. The eluent composition at which the solute of interest elutes during the gradient is used for isocratic analysis, where the k' value of this solute will then be around 2.Part of Ph. D. Thesis H. Elgass, Saarbrücken, 1978, present address Hewlett-Packard, Waldbronn, FRG. In part presented at Eastern Analytical Symposium, New York, 1982.     

Theoretical background of monolithic short layer ion-exchange chromatography for separation of charged large biomolecules or bioparticles

The retention and peak spreading in linear gradient elution of charged large biomolecules were investigated by using numerical simulations. Oligo-DNA separation by monolithic anion-exchange chromatography was chosen as a model system. The peak width and the retention were well predicted by using the parameters obtained by gradient elution experiments at different gradient slopes. As the distribution coefficient at the peak retention volume K_R decreases with increasing molecular size, the peak became sharper for larger DNAs. This is due to very large effective charge (binding site) values of large DNAs (20–60). The peak width was well correlated with K_R based on the model equation developed for linear gradient elution of proteins. It was shown that the monolithic disk is best suited for very large charged biomolecule separations at high flow velocities with shallow gradients slopes.     

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.