Retention modeling under organic modifier gradient conditions in ion-pair reversed-phase chromatography. Application to the separation of a set of underivatized amino acids

The combined effect of the ion-pairing reagent concentration, C _ipr, and organic modifier content, φ, on the retention under φ-gradient conditions at different constant C _ipr was treated in this study by using two approaches. In the first approach, the prediction of the retention time of a sample solute is based on a direct fitting procedure of a proper retention model to 3-D φ-gradient retention data obtained under the same φ-linear variation but with different slope and time duration of the initial isocratic part and in the presence of various constant C _ipr values in the eluent. The second approach is based on a retention model describing the combined effect of C _ipr and φ on the retention of solutes in isocratic mode and consequently analyzes isocratic data obtained in mobile phases containing different C _ipr values. The effectiveness of the above approaches was tested in the retention prediction of a mixture of 16 underivatized amino acids using mobile phases containing acetonitrile as organic modifier and sodium dodecyl sulfate as ion-pairing reagent. From these approaches, only the first one gives satisfactory predictions and can be successfully used in optimization of ion-pair chromatographic separations under gradient conditions. The failure of the second approach to predict the retention of solutes in the gradient elution mode in the presence of different C _ipr values was attributed to slow changes in the distribution equilibrium of ion-pairing reagents caused by φ-variation.     

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.     

A general strategy for performing temperature-programming in high performance liquid chromatography--prediction of segmented temperature gradients

In the present work it is shown that the linear elution strength (LES) model which was adapted from temperature-programming gas chromatography (GC) can also be employed to predict retention times for segmented-temperature gradients based on temperature-gradient input data in liquid chromatography (LC) with high accuracy. The LES model assumes that retention times for isothermal separations can be predicted based on two temperature gradients and is employed to calculate the retention factor of an analyte when changing the start temperature of the temperature gradient. In this study it was investigated whether this approach can also be employed in LC. It was shown that this approximation cannot be transferred to temperature-programmed LC where a temperature range from 60°C up to 180°C is investigated. Major relative errors up to 169.6% were observed for isothermal retention factor predictions. In order to predict retention times for temperature gradients with different start temperatures in LC, another relationship is required to describe the influence of temperature on retention. Therefore, retention times for isothermal separations based on isothermal input runs were predicted using a plot of the natural logarithm of the retention factor vs. the inverse temperature and a plot of the natural logarithm of the retention factor vs. temperature. It could be shown that a plot of lnk vs. T yields more reliable isothermal/isocratic retention time predictions than a plot of lnk vs. 1/T which is usually employed. Hence, in order to predict retention times for temperature-gradients with different start temperatures in LC, two temperature gradient and two isothermal measurements have been employed. In this case, retention times can be predicted with a maximal relative error of 5.5% (average relative error: 2.9%). In comparison, if the start temperature of the simulated temperature gradient is equal to the start temperature of the input data, only two temperature-gradient measurements are required. Under these conditions, retention times can be predicted with a maximal relative error of 4.3% (average relative error: 2.2%). As an example, the systematic method development for an isothermal as well as a temperature gradient separation of selected sulfonamides by means of the adapted LES model is demonstrated using a pure water mobile phase. Both methods are compared and it is shown that the temperature-gradient separation provides some advantages over the isothermal separation in terms of limits of detection and analysis time.     

Modeling the combined effect of temperature and organic modifier content on reversed-phase chromatographic retention. Effectiveness of derived models in isocratic and isothermal mode retention prediction

Models considering simultaneously mobile phase organic content and column temperature were developed in this study by an extension of different equations describing the influence of temperature on solute retention. This extension was achieved by two methods: a semi-thermodynamic and a direct combination of equations expressed separately the dependence of the retention upon each of these factors. The above approaches gave a great number of expressions for the logarithm of the solute retention factor in terms of both temperature and organic content in the mobile phase, ln k(T,phi), determined from the dependence of the standard enthalpy of the retention process on T. From the final expressions of ln k(T,phi) we tested only those with the minimum number of adjustable parameters, i.e. those that correspond to a constant standard enthalpy of the retention process. For this test we examined the retention behaviour of a sample of alkylbenzenes in aqueous acetonitrile eluents. These compounds exhibit ln k versus 1/T plots with a very small curvature. We found that a new equation for ln k(T,phi) based on the adsorption model for retention performs better than all the others. The average percentage prediction error ranges from 0.7 to 1.4%.     

The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

Simple models for the effect of aliphatic alcohol additives on the retention in reversed-phase liquid chromatography

Four retention models for the effect of aliphatic alcohol additives on the retention of analytes in reversed-phase liquid chromatography have been developed following either a semi-thermodynamic treatment or an empirical approach. Their performance was tested using the experimental retention times of six non-polar analytes (alkylbenzenes) and ten o-phthalaldehyde derivatives of amino acids under different isocratic chromatographic runs when a small amount of ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol or 1-heptanol was added to methanol/water mixtures containing a constant amount of methanol. It was shown that for the structurally simple alkylbenzenes all the models can be adopted for retention prediction with good results. In contrast, just one out of four models, that with the fewest approximations, predicts satisfactorily the retention properties of amino acids derivatives. However, the most interesting feature is that this model can predict the effect of an alcohol-additive on the retention properties of solutes, even if this additive was not used in chromatographic runs done for the fitting procedure, provided that it belongs to the same homologous series of alkanols. This feature is also observed in all models described the retention of alkylbenzenes.     

Retention models for isocratic and gradient elution in reversed-phase liquid chromatography

One- and multi-variable retention models proposed for isocratic and/or gradient elution in reversed-phase liquid chromatography are critically reviewed. The thermodynamic, exo-thermodynamic or empirical arguments adopted for their derivation are presented and discussed. Their connection to the retention mechanism is also indicated and the assumptions and approximations involved in their derivation are stressed. Special attention is devoted to the fitting performance of the various models and its impact on the final predicted error between experimental and calculated retention times. The possibility of using exo-thermodynamic retention models for prediction under gradient elution is considered from a practical point of view. Finally, the use of statistical weights in the fitting procedure of a retention model and its effect on the calculated elution times as well as the transferability of retention data among isocratic and gradient elution modes are also examined and discussed.     

Optimisation of multilinear gradient elutions in reversed-phase liquid chromatography using ternary solvent mixtures

The multilinear gradient elution theory for binary mobile phases in reversed-phase liquid chromatography presented in [P. Nikitas, A. Pappa-Louisi, A. Papageorgiou, J. Chromatogr. A 1157 (2007) 178] is extended to ternary gradients. For the evaluation of this theory and the performance of the various fitting and optimisation algorithms we used 13 o-phthalaldehyde (OPA) derivatives of amino acids with mobile phases modified by acetonitrile and methanol. It is shown that the theory can lead to high quality predictions of the retention times under gradients elutions and optimisation of ternary gradients provided that we use a six-parameter expression for the logarithm of the retention factor, lnk, and the adjustable parameters of this expression are determined from ternary isocratic data.     

Application of diode array detectors for solute identification in toxicological analysis

Summary The possibilities and limitation of automated solute identification via UV/VIS spectroscopy in HPLC are demonstrated and applications in toxicologic analysis are described. A standard isocratic system is used. The influence of various chromatographic parameters on retention time is shown. A retention time window of ±15% is required. In addition to retention time, derived spectral data are calculated (minima and maxima of derivatives, area counts under standardized spectral ranges, absorption at various wavelength) and used for positive solute identification. It is possible to identify solutes with a high degree of certainty in urine and plasma if their concentration is at least 10 ppm.     

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。     

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.     

Retention behaviour of carboxylic acid methyl esters in supercritical fluid chromatography

The study on retention behavior in supercritical fluid chromatography (SFC) is necessary to understand the mechanism of the various interactions in SFC. The retention of SFC in carboxylic acid methyl ester/polymethylsiloxane/CO2 system was studied systematically and the retention behavior of this kind of compounds under various typical operation conditions was described using the method of an alternative unified theory of chromatographic retention. The results illustrated that expression: Ink.= a + b/T + cp + dp/T + ep2/T can be used to describe quantitatively the retention behavior of carboxylic acid methyl ester/polymethylsiloxane/CO2 system in the ranges of reduced density from 0.549 to 1.411. It was also found that the entropy of solute in stationary phase is dependent on the density of supercritical fluid (SF) under typical operating conditions of SFC.     

Generic approach to the method development of intact protein separations using hydrophobic interaction chromatography

We describe a liquid chromatography method development approach for the separation of intact proteins using hydrophobic interaction chromatography. First, protein retention was determined as function of the salt concentration by isocratic measurements and modeled using linear regression. The error between measured and predicted retention factors was studied while varying gradient time (between 15 and 120 min) and gradient starting conditions, and ranged between 2 and 15%. To reduce the time needed to develop optimized gradient methods for hydrophobic interaction chromatography separations, retention‐time estimations were also assessed based on two gradient scouting runs, resulting in significantly improved retention‐time predictions (average error < 2.5%) when varying gradient time. When starting the scouting gradient at lower salt concentrations (stronger eluent), retention time prediction became inaccurate in contrast to predictions based on isocratic runs. Application of three scouting runs and a nonlinear model, incorporating the effects of gradient duration and mobile‐phase composition at the start of the gradient, provides accurate results (improved fitting compared to the linear solvent‐strength model) with an average error of 1.0% and maximum deviation of –8.3%. Finally, gradient scouting runs and retention‐time modeling have been applied for the optimization of a critical‐pair protein isoform separation encountered in a biotechnological sample.     

A comparison of isoconversional and model-fitting approaches to kinetic parameter estimation and application predictions

A variety of isoconversional and model fitting approaches, all of which use multiple heating schedules, are used to analyze selected data from the ICTAC kinetics and lifetime projects as well as additional simulated data sets created for this work. The objective is to compare the accuracy and suitability of various approaches for various types of chemical reactions. The various simulated data sets show that model fitting and isoconversional methods have comparable reliability for extrapolation outside the range of calibration. First, there is as much variability in prediction for various isoconversional methods as there is between isoconversional methods as a group and different plausible explicit models. Of the three isoconversional models investigated, the Friedman method is usually the most accurate. This is particularly true for energetic materials that have a drop in apparent activation energy in the latter stages of reaction, which leads to a delayed onset of rapid autocatalysis at lower temperatures. It is difficult to determine a priori whether isoconversional or model fitting approaches will give more accurate predictions. The greatest reliability is attained by using both the isoconversional and model fitting approaches on a combination of isothermal and constant heating rate data.     

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。     

Prediction of elution bandwidth for purine compounds by a retention model in reversed-phase HPLC with linear-gradient elution

In reversed-phase liquid chromatography, the retention mechanism of solute has been studied under linearly programmed gradient mobile-phase conditions. The separation of a mixture of four purine compounds (purine, theobromine, theophylline, and caffeine) was considered as a practical case in two binary mobile phase systems, water/methanol and water/acetonitrile. The retention model which describes how the retention factor is related to the mobile-phase composition has been developed in various mathematical forms to predict the retention time in both linear and gradient elutions. For a pulse injection of sample, two important factors, the retention time and the bandwidth of solute, might be computable to predict the elution profiles estimated by the distribution function, such as the Gaussian distribution function. In this work, a prediction method based on the analogue of the retention model was proposed to calculate the bandwidth in linear gradient elutions. Band broadening was caused by the different migration velocities of the front and rear ends of the solute band in a chromatographic column. Therefore, the migration behaviors of the front and rear ends of the solute band were explained with the same retention model which had been used to predict the retention time of solute. For the well retained solutes, theophylline and caffeine, the predicted bandwidth and experimentally obtained bandwidth showed good agreement in both isocratic and gradient elutions.     

Chromatographic terminal band lengths

A terminal band length is defined here as the length of a dispersed solute band as it emerges from the chromatographic column. The number of terminal band lengths per column can be used in the same way that the number of theoretical plates per column is used to measure and compare chromatographic efficiencies, but with greater insight since the proposed unit of measure is an easily visualized, real entity. In addition, the height equivalent to a theoretical plate (HETP) can be regarded as a ratio of the terminal band lenght to sixteen times the number of equivalent terminal band lengths that could be contained in tandem in the column. This concept offers another approach to understanding the meaning of the term, HETP. The terminal band length of a series of homologues is constant and independent of retention time above a certain solute molecular size and column capacity ratio. Within those conditions the correlation between the recorded peak width and retention time during isothermal analysis occurs primarily as a result of change in solute velocity.     

Computational method for modeling of gradient separation in ion-exchange chromatography

A model for the simulation of the gradient separation in ion-exchange chromatography is presented. It is based on discontinuous plate model and simulates the distribution of analytes in the ion-exchange column during the separation process. It enables calculations of chromatograms for the analytes with integer and non-integer effective charges under complex gradient profiles. Equilibrium concentrations of all analytes are calculated using the same mathematical equations and expressions regardless of the effective charge on the analyte. The main parameters required for the simulations have to be determined under isocratic elution. The suitability of the model was tested with different types of gradients. A comparison of retention times and chromatograms shows that reliable predictions for all tested gradients are achieved. The observed average of the absolute values of the relative errors of the retention times obtained for any analyte in the present study from the calculated chromatograms is below 4%, while the average error considering all analytes in the study is below 2%.