The prediction of the peak width at half height in HPLC

The prediction of the peak width at half height is an important aspect in the optimization of the chromatographic operating conditions. In this paper, a linear relationship, between the peak widths at half height and the retention values with various isocratic elution is observed. In gradient elution, however, the relationship between the peak widths at half height and the so-called invented retention values that correspond to the mobile phase composition by eluting the solute from the column end is developed. We believe that there is almost the same band width at half height inside the column (in unit of length) for different solutes. The peak width at half height in the chromatogram (in unit of time) is mainly determined by the capacity factor of the solute when it is eluted from the column end. The larger the capacity factor of a solute eluted from the column end, the more slowly will be the solute eluted from the column end and the wider will be the peak width at half height. It is possible to predict the peak width at half height in various isocratic and gradient elutions by using this linear relationship.     

The bandwidth in gradient elution chromatography with a retained organic modifier

The variance of a chromatographic band is derived in the case of RPLC gradient elution when the organic modifier is significantly retained onto the stationary phase. This derivation is based on the extension of a model due to Poppe et al. [H. Poppe, J. Paanakker, M. Bronckhorst, J. Chromatogr., 204 (1981) 77] which assumes that the gradient front remains unchanged and propagates along the column at the same speed as the mobile phase, following piston flow. Theoretical and experimental results are compared in the case of caffeine on a C(1)-silica stationary phase eluted with an acetonitrile gradient. The actual retention behaviors of caffeine and acetonitrile were implemented in the theoretical calculations. The model predicts compression factors between 0.71 and 0.34 for relatively smooth gradient steepness, betat(0), between 0.009 and 0.054 while the corresponding experimental band compression factors vary between 1.01 and 0.43 for the very same gradient steepness. The model underestimation of these factors arises likely from the strong deviation of the actual retention behavior from the prediction of the Linear Solvent Strength Model (LSSM).     

Method to predict the bandwidth of elution profile under the linear gradient elution in reversed‐phase HPLC

Solute migration in a chromatographic column is an important consideration when designing batch or continuous chromatographic separation processes. Most design methods for the chromatographic processes are based on the equilibrium theory which concerns only the migration velocity of the solute. However, in real cases, it is important to predict the zone spreading which occurs by axial dispersion and mass transfer resistance. To predict the actual solute profiles in the column or effluent stream, numerical methods to solve nonlinear partial differential equations have been used. However, these methods involve much time and expense. In this work, two different rate factors are considered to predict the characteristics of the solute profiles. The first is solute migration velocity and the second is the zone spreading rate. The zone spreading rate can be estimated by the apparent axial dispersion coefficient which is obtained from the height of the equivalent theoretical plate in particular. Four benzene derivatives (benzene, toluene, p‐xylene, and acetophenone) were used as model solutes, and two mobile phase systems, water/methanol and water/ACN, were used in RP‐HPLC. The bandwidths and retention times of the solutes were predicted under several linear gradient conditions. The predicted and experimental bandwidths and retention times showed good agreement.     

Modeling of salt and pH gradient elution in ion‐exchange chromatography

The separation of proteins by internally and externally generated pH gradients in chromatofocusing on ion‐exchange columns is a well‐established analytical method with a large number of applications. In this work, a stoichiometric displacement model was used to describe the retention behavior of lysozyme on SP Sepharose FF and a monoclonal antibody on Fractogel SO₃ (S) in linear salt and pH gradient elution. The pH dependence of the binding charge B in the linear gradient elution model is introduced using a protein net charge model, while the pH dependence of the equilibrium constant is based on a thermodynamic approach. The model parameter and pH dependences are calculated from linear salt gradient elutions at different pH values as well as from linear pH gradient elutions at different fixed salt concentrations. The application of the model for the well‐characterized protein lysozyme resulted in almost identical model parameters based on either linear salt or pH gradient elution data. For the antibody, only the approach based on linear pH gradients is feasible because of the limited pH range useful for salt gradient elution. The application of the model for the separation of an acid variant of the antibody from the major monomeric form is discussed.     

液相色谱中的半峰宽规律

本文介绍通过相同组分、不同配比冲洗剂等度和梯度冲洗样品的实验,首次发现在液相色谱中,溶质的色谱峰半宽度与保留值间存在同一线性关系;在梯度冲洗时流出组分的色谱峰半宽度与虚拟保留值间同样存在线性关系。该结果证明,我们提出的组分在柱末端有相近的以长度为量纲的谱带半宽度的正确性,同时该结果对梯度最佳分离条件的预测亦很有益。     

Characteristic of theophylline imprinted monolithic column and its application for determination of xanthine derivatives caffeine and theophylline in green tea

Theophylline imprinted monolithic columns were designed and prepared for rapid separation of a homologous series of xanthine derivatives, caffeine, and theophylline by an in situ thermal-initiated copolymerization technique. Caffeine and theophylline were fully separated both under isocratic and gradient elutions on this kind of monolithic molecularly imprinted polymers (MIP) column. The broad peak showed in isocratic elution could be improved in gradient elution. Some chromatographic conditions such as mobile phase composition, flow rate, and the temperature on the retention times were investigated. Hydrogen bonding interaction and hydrophobic interaction played an important role in the retention and separation. The binding capacity was evaluated by static adsorption and Scatchard analysis, which showed that the dissociation constant (KD) and the maximum binding capacity (Qmax) were 1.50 mol/L, and 236 micromol/g for high affinity binding site, and 7.97 mol/L and 785 micromol/g for lower affinity binding site, respectively. Thermodynamic data (DeltaDeltaH and DeltaDeltaS) obtained by Van't Hoff plots revealed an enthalpy-controlled separation. The morphological characteristics of monolithic MIP were investigated by scanning electron microscope, which showed that both mesopores and macropores were formed in the monolith. The present monolithic MIP column was successfully applied for the quantitative determination of caffeine and theophylline in different kinds of green tea.     

Multilinear gradient elution optimisation in reversed-phase liquid chromatography using genetic algorithms

The treatment presented in a recent paper [P. Nikitas, A. Pappa-Louisi, J. Chromatogr. A, 1068 (2005) 279] is extended to multilinear gradients, i.e. continuous gradients consisting of a certain number of linear portions. Thus, the experimental lnk versus phi curve, where k is the retention factor of a sample solute under isocratic conditions and phi is the volume fraction of the organic modifier in the water-organic mobile phase, is subdivided into a finite number of linear portions resulting in simple analytical expressions for the solute gradient retention time. These expressions of the retention time are directly used in an optimisation technique based on genetic algorithms. This technique involves first the determination of the theoretical dependence of k upon phi by means of gradient measurements, which in turn is used by the genetic algorithm for the prediction of the best gradient profile. The validity of the analytical expressions and the effectiveness of the optimisation technique were tested using fifteen underivatized amino acids and related compounds with mobile phases modified by acetonitrile. It was found that the adopted methodology exhibits significant advantages and it can lead to high quality predictions of the gradient retention times and optimisation results.     

Influence of temperature in reverse-phase high-performance liquid chromatography with gradient elution

The influence of temperature on the retention of several species separated by reverse-phase liquid chromatography by gradient elution is shown to be of enough importance to warrant careful control of temperature if reproducible results are to be obtained. The smaller the particle size in the column, the greater the effect of temperature, and therefore the control should be greater. Likewise, it has been verified that for a given solvent gradient, independent of its complexity, there is a linear relation between ln k′ and 1/T, which also occurs in separations by isocratic elution. Dufek's equation can be adjusted perfectly to the experimental data obtained from gradient elutions, and may be used in the simulation and optimization of gradient chromatographic processes.     

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

The so‐called “fundamental equation for gradient elution” has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(t_s)), t_s being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t?l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the here called “general equation for gradient elution”, where k is expressed as a function of φ(t,l). However, this approach is more complex. In this work, a method that facilitates the integration of the “general equation” is described, which allows an approximate analytical solution with the quadratic retention model, improving the predictions offered by the “linear solvent strength model.” It also offers direct information about the changes in the instantaneous modifier content and retention factor, and gives a meaning to the gradient retention factor.     

Automated off-line optimisation of programmed elutions in reversed-phase high-performance liquid chromatography using ternary solvent mixtures

A new system for the unattended optimisation of gradient elutions in reversed-phase high-performance liquid chromatography has been developed. The system is based on the simulation of retention times under conditions of ternary solvent mixtures and ternary gradient programmes. This model is constructed departing from a few experimental data obtained in isocratic elutions and validated against experimental gradient elutions. Once validated, this retention model can be used for the unattended search of an optimum separation. The optimisation process is driven by an evolutionary algorithm (EA), specially developed to map the ternary gradient elutions problem. The development and characteristics of the retention modelling as well as those of the EA and its particularities are discussed and some real world examples of separation presented.     

液相色谱梯度洗脱中的谱带压缩效应

谱带压缩效应是梯度洗脱区别于等度洗脱的重要特征。经典的范德姆特(van Deemter)理论塔板高度方程基于等度洗脱推导得到,因此不能对谱带压缩效应进行描述。在梯度洗脱中,保留因子(k)会随流动相组成(φ)的改变而发生变化,这就使得对梯度洗脱机理的研究要比等度洗脱复杂许多。该文对近10年来谱带压缩效应的研究进展,特别是溶剂强度模型(即描述ln k与φ关系的数学表达式)的非线性特征对谱带压缩因子(G)的影响进行了述评,指出为了更好地认识谱带压缩效应需要将这种非线性因素考虑在内。     

Deformation of gradient shape as a result of preferential adsorption of solvents in mixed mobile phases

Gradient elution has been studied in typical normal and reversed-phase systems. Deformations of gradient profiles have been evidenced as a result of preferential adsorption of modifiers of the mobile phase. This phenomenon was pronounced in the normal-phase system, for which gradient profiles deviated significantly from those programmed. This influenced the retention and shapes of band profiles of the eluting solute. Hence, in order to predict gradient propagation correctly the adsorption equilibrium of modifiers has been quantified. Moreover, at low modifier content, deformations of band profiles of the solute has been registered as a result of the competitive adsorption in the system solute-modifier. This effect has been predicted by a competitive adsorption model. For the reversed-phase systems the influence of the modifier adsorption on gradient propagation was insignificant for typical mobile phases investigated. Therefore, the work has been focused on gradient predictions in the normal-phase system.     

Computerized optimization of gradient elution conditions with ternary solvent mobile phases in RPLC

Summary In this work, an optimization procedure for gradient RPLC separation, using ternary mobile phases, is described. This procedure requires eight preliminary experiments in gradient elution mode to predict the retention surface for each solute over the whole triangular space. This is followed by computerized calculations to determine the best ternary gradient elution profile with respect to both selectivity and analysis time. The efficiency of this procedure from the point of view of rapidity and of accuracy, is illustrated for the specific separation of twelve phenyl urea herbicides.     

黄芪中黄酮类组分的高效液相色谱分离条件的快速优化

以黄芪为研究对象,对黄芪中乙酸乙酯部位的化学成分进行了高效液相色谱分析并对其色谱操作条件进行了快速优化。根据几个线性梯度下的保留时间来计算各组分的保留参数,然后利用重叠分辨图法确定其最佳分析条件。在选定的最佳条件下各组分分离情况良好。利用梯度保留时间计算保留参数比较方便快速,并可以有效地避免以往等度线性回归法遇到的峰识别问题。该方法更适用于实际复杂样品色谱分析条件的优化。     

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.     

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.     

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。     

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.     

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.