Analysis and classification of tea varieties using high-performance liquid chromatography and global retention models.

As a result of their metabolic processes, medicinal plants produce bioactive molecules with significant implications for human health, used directly for treatment or for pharmaceutical development. Chromatographic fingerprints with solvent gradients authenticate and categorise medicinal plants by capturing chemical diversity. This work focuses on optimising tea sample analysis in HPLC, using a model-based approach without requiring standards. Predicting the gradient profile effects on full signals was the basis to identify optimal separation conditions. Global models characterised retention and bandwidth for 14 peaks in the chromatograms across varied elution conditions, facilitating resolution optimisation of 63 peaks, covering 99.95 % of total peak area. The identified optimal gradient was applied to classify 40 samples representing six tea varieties. Matrices of baseline-corrected signals, elution bands, and band ratios, were evaluated to select the best dataset. Principal Component Analysis (PCA), k-means clustering, and Partial Least Squares-Discriminant Analysis (PLS-DA) assessed classification feasibility. Classification limitations were found reasonable due to tea processing complexities, involving drying and fermentation influenced by environmental conditions.

Performance and modelling of retention in microemulsion liquid chromatography.

The capability of liquid chromatography with microemulsions (MEs) as mobile phases was studied for the analysis of four parabens (butylparaben, ethylparaben, methylparaben, and propylparaben) and seven ß-adrenoceptor antagonists (acebutolol, atenolol, carteolol, metoprolol, oxprenolol, propranolol, and timolol). MEs were formed by mixing aqueous solutions of the anionic surfactant sodium dodecyl sulphate, the alcohol 1-butanol that played the role of co-surfactant, and octane as oil. In order to guarantee the formation of stable MEs, a preliminary study was carried out to determine the appropriate ranges of concentrations of the three components. For this purpose, mixtures of variable composition were prepared, and the possible separation of two phases (formation of an emulsion) was visually detected. The advantage offered by the addition of octane to micellar mobile phases, inside the concentration range that allows the formation of stable MEs, was evaluated by comparing the retention behaviour, peak profile and resolution of mixtures of the probe compounds, in the presence and absence of octane. The final aim of this work was the proposal of a mathematical equation to model the retention behaviour in microemulsion liquid chromatography. The derived global model that considered the three factors (surfactant, alcohol and oil) allowed the prediction of retention times at diverse mobile phase compositions with satisfactory accuracy (in the 1.1‒2.5% range). The behaviour was compared with that found with mobile phases without octane. The model also yielded information about the retention mechanism and revealed that octane, when inserted inside the micelle, modifies the interaction between solutes and micelles.

Modified Gaussian models applied to the description and deconvolution of peaks in chiral liquid chromatography.

The description of the profiles of chromatographic peaks has been studied extensively, with a large number of proposed mathematical functions. Among them, the accuracy achieved with modified Gaussian models that describe the deviation of an ideal Gaussian peak as a change in the peak variance or standard deviation over time, has been highlighted. These models are, in fact, a family of functions of different complexity with great flexibility to adjust chromatographic peaks over a wide range of asymmetries and shapes. However, an uncontrolled behaviour of the signal may occur outside the region being fitted, forcing the use of different strategies to overcome this problem. In this work, the performance of the LMG (Linear Modified Gaussian), PVMG (Parabolic Variance Modified Gaussian), and PLMG (Parabolic-Lorentzian Modified Gaussian) models is compared with variants obtained by combination of the modified Gaussian models with an equation that adds an exponential tail and with other functions that limit the growth of the independent variable. The behaviour of the approaches is checked through the simultaneous fitting of enantiomeric peaks showing a wide range of characteristics, obtained in the separation of drugs with chiral activity by liquid chromatography using enantioselective columns. The study is also carried out with the purpose of performing the deconvolution of the peaks of the enantiomers, when these are not completely resolved, in order to evaluate the enantiomeric fraction.

Extension of the linear solvent strength retention model including a parameter that describes the elution strength changes in liquid chromatography.

Modelling the retention behaviour of solutes in liquid chromatography, based on the composition of the mobile phase is a common task in the chromatographic practice. Along the development of liquid chromatography (LC), several models have been proposed to help in understanding the retention mechanisms, and especially, allow the prediction of retention times with optimisation purposes. Particular models are used for different LC modes, such as normal phase (NPLC), reversed phase (RPLC), hydrophilic interaction (HILIC), and micellar (MLC). In this work, a general equation is proposed that includes a parameter (the elution degree, g), which characterises the way the elution strength varies with the modifier concentration. The elution degree adopts the value g = 1 when the system follows the linear solvent strength (LSS) model, where the elution strength is constant. When g > 1, the elution strength decreases, and for g < 1, it increases with the modifier concentration. The proposed equation was applied to experimental retention data obtained for several chromatographic systems in RPLC, HILIC, MLC, and microemulsion LC. It was found that values in the 1 < g < 2 range are most usual. The general behaviour of the proposed equation was studied for isocratic and gradient elution. A general expression to calculate the compression factor of chromatographic peaks in gradient elution was also developed. It is shown that an increasing g value makes retention factors close to zero more difficult, since the elution strength decreases as the modifier concentration increases. For this reason, the larger the g value, the harder it is to reach significant peak compression. In contrast, an elution mode with g < 1 would yield increased elution strength with the modifier concentration, giving rise to significant peak compression.

Peak dispersion in gradient elution: An insight based on the plate model.

Gradient elution in liquid chromatography reduces the analysis time, improves the efficiency and increases the peak capacity. The study of this chromatographic mode has been based mainly on kinetic dispersion models. The plate model has been applied to a lesser extent, despite being the basis for the concepts of plate height and chromatographic efficiency. In this work, a general equation describing peak dispersion in HPLC gradient elution is derived from the plate model. This equation is studied and validated for three types of gradients: (i) a reference gradient without ramp in which the retention factor varies with time identically throughout the column, (ii) a gradient of stationary phase in which the nature of the stationary phase varies continuously inside the column, resulting in a ramp of constant retention factor over time, and finally, (iii) a mobile phase gradient, which produces a retention factor ramp that varies over time. In the latter case, the results are similar to those derived from the mass-transport equation in linear solvent gradients when the linear solvent strength model is applied. The final equations are expressed based on the initial and final instantaneous retention factors, thus they can be applied independently of the deviation of the elution model, being fully compatible with isocratic elution. Results predicted with the proposed equations are identical to those obtained by numerical resolution of the elution differential equation system. The additional compression due to the presence of a ramp of modifier is also verified. However, useful compressions will appear only when the retention factor changes with time. Finally, the study indicates that the extra-column variance undergoes a compression process when the retention factor varies over time, whether or not there is a ramp inside the column.

Study of the column efficiency using gradient elution based on Van Deemter plots.

Performance of chromatographic columns is of major importance in the development of more efficient separation methods. So far, a common practice is to study the column behavior in isocratic elution by modifying the flow rate and fitting the theoretical plate height values versus the mobile phase linear velocity, according to the Van Deemter equation. In this work, an approach is presented to extend the measurement of efficiency to linear gradient elution, where the mean retention factor is kept constant at each assayed flow. This avoids a possible source of uncertainty due to the change in the distribution equilibria profile, and makes the mean interactions with the stationary phase in gradient elution similar to those in isocratic elution. The approach was applied to Zorbax Eclipse XDB C18 and Chromolith SpeedROD C18 columns, using four sulphonamides as probe compounds. The results are compared with those obtained in isocratic elution, and gradient elution where the gradient program is kept constant while the flow is varied, giving rise to changes in the mean retention factor at each flow rate. The mean compression factor obtained experimentally was higher than expected, with mean values of 0.98 and 1.02 for the Zorbax and Chromolith columns, whereas the predicted values were 0.87 and 0.92, respectively. Better efficiencies were obtained at lower flow and higher gradient slope. The resolution shows similar values in isocratic and gradient elution when the mean retention factor is kept constant. When the gradient slope is constant, the resolution is usually smaller, although it improves at higher flows.

Characterization of chromatographic peaks using the linearly modified Gaussian model. Comparison with the bi-Gaussian and the Foley and Dorsey approaches.

To characterize column performance in liquid chromatography, several parameters must be obtained from experimental data. These parameters can be computed through the numerical integration of the net signal to calculate the moments after subtraction of the baseline. This requires the establishment of the peak integration limits. The whole process introduces significant uncertainty. For this reason, several alternative procedures have been proposed to measure the area, mean time and variance, based on the assumption that the chromatographic peak can be described with a mathematical function. This allows the calculation of the peak position and variance making use of the values of the experimental half-widths. In this work, the linear modified Gaussian model is used to derive several equations for the evaluation of the associated moments. Affordable equations for the calculation of the area, mean time, variance and efficiency are provided, using the half-width values at 10% peak height. The behaviour of experimental peaks obtained under a large variety of experimental conditions is examined to verify the validity of the proposed equations. The values of the peak parameters are compared with those calculated based on the bi-Gaussian model, and the exponentially modified Gaussian model using the equations developed by Foley and Dorsey. The bi-Gaussian model offered the best quantifications for the mean time. The Foley and Dorsey approach gave rather satisfactory results for the area and the best results for the variance and efficiency for tailing peaks of small asymmetry. The LMG approach gave better evaluation of the area for peaks showing small asymmetry, and satisfactory values for the mean time, variance and efficiency in the whole range of asymmetries found in liquid chromatography.

Half-width plots, a simple tool to predict peak shape, reveal column kinetics and characterise chromatographic columns in liquid chromatography: state of the art and new results.

Peak profiles in chromatography are characterised by their height, position, width and asymmetry; the two latter depend on the values of the left and right peak half-widths. Simple correlations have been found between the peak half-widths and the retention times. The representation of such correlations has been called half-width plots. For isocratic elution, the plots are parabolic, although often, the parabolas can be approximated to straight-lines. The plots can be obtained with the half-widths/retention time data for a set of solutes experiencing the same kinetics, eluted with a mobile phase at fixed or varying composition. When the analysed solutes experience different resistance to mass transfer, the plots will be solute dependent, and should be obtained with the data for each solute eluted with mobile phases at varying composition. The half-width plots approach is a simple tool that facilitates the prediction of peak shape (width and asymmetry) with optimisation purposes, reveal the interaction kinetics of solutes in different columns, and characterise chromatographic columns. This work shows half-width plots for different situations in isocratic elution, including the use of different flows, the effect of temperature, the modification of the stationary phase surface by an additive, the existence of specific interactions within the column, and the comparison of columns. The adaptation to gradient elution is also described. Previous knowledge on half-width plots is structured and analysed, to which new results are added.

Approaches to model the retention and peak profile in linear gradient reversed-phase liquid chromatography.

The optimisation of the experimental conditions in gradient reversed-phase liquid chromatography requires reliable algorithms for the description of the retention and peak profile. As in isocratic elution, the linear relationship between the logarithm of the retention factor and the solvent contents is only acceptable in relatively small concentration ranges of modifier. However, more complex models may not allow an analytical integration of the general equation for gradient elution. Alternative approaches for modelling the retention in linear gradient elution are here proposed. Those based on the quadratic logarithmic model and a model proposed for normal liquid chromatography yielded accurate predictions of the retention time for a wide range of initial concentrations of organic modifier and gradient slopes, with errors usually below 1-2%. Based on the half-width changes of chromatographic peaks along one or more gradients, an approach is also reported to predict the peak profile with low errors (usually below 2-3%). The proposed approaches were applied to two sets of probe compounds (diuretics and flavonoids), eluted with acetonitrile-water gradients. The changes in retention and peak shape in isocratic and gradient elution are illustrated through diagrams that define triangular regions including all possible values of retention factors or peak half-widths (or widths) inside the selected working ranges.

New approaches based on modified Gaussian models for the prediction of chromatographic peaks.

The description of skewed chromatographic peaks has been discussed extensively and many functions have been proposed. Among these, the Polynomially Modified Gaussian (PMG) models interpret the deviations from ideality as a change in the standard deviation with time. This approach has shown a high accuracy in the fitting to tailing and fronting peaks. However, it has the drawback of the uncontrolled growth of the predicted signal outside the elution region, which departs from the experimental baseline. To solve this problem, the Parabolic-Lorentzian Modified Gaussian (PLMG) model was developed. This combines a parabola that describes the variance change in the peak region, and a Lorentzian function that decreases the variance growth out of the peak region. The PLMG model has, however, the drawback of its high flexibility that makes the optimisation process difficult when the initial values of the model parameters are far from the optimal ones. Based on the fitting of experimental peaks of diverse origin and asymmetry degree, several semiempirical approaches that make use of the halfwidths at 60.65% and 10% peak height are here reported, which allow the use of the PLMG model for prediction purposes with small errors (below 2-3%). The incorporation of several restrictions in the algorithm avoids the indeterminations that arise frequently with this model, when applied to highly skewed peaks.

Measurement of the elution strength and peak shape enhancement at increasing modifier concentration and temperature in RPLC.

Two approaches are proposed to measure the effect of different experimental factors (such as the modifier concentration and temperature) on the elution strength and peak shape in reversed-phase liquid chromatography, which quantify the percentage change in the retention factor and peak width (referred to the weakest conditions) per unit change in the experimental factor. The approaches were applied to the separation of a set of flavonoids with aqueous micellar mobile phases of the surfactant Brij-35 (polyoxyethylene(23)dodecanol), in comparison with acetonitrile-water mixtures, using an Eclipse XDB-C18 column. The particular interaction of each flavonoid with the oxyethylene chains of Brij-35 molecules (adsorbed on the stationary phase or forming micelles) changed the elution window, distribution of chromatographic peaks and partitioning kinetics, depending on the hydroxyl substitution in the aromatic rings of flavonoids. At 25 °C, peak shape with Brij-35 mobile phases was significantly poorer with regard to acetonitrile-water mixtures. At increasing temperature, the efficiency of Brij-35 increased, approaching at 80 °C the values obtained at equilibrium conditions, already reached with acetonitrile at 25 °C.

A theoretical plate model accounting for slow kinetics in chromatographic elution.

The chromatographic elution has been studied from different perspectives. However, in spite of the simplicity and evident deficiencies of the plate model proposed by Martin and Synge, it has served as a basis for the characterization of columns up-to-date. This approach envisions the chromatographic column as an arbitrary number of theoretical plates, each of them consisting of identical repeating portions of mobile phase and stationary phase. Solutes partition between both phases, reaching the equilibrium. Mobile phase transference between the theoretical plates is assumed to be infinitesimally stepwise (or continuous), giving rise to the mixing of the solutions in adjacent plates. This yields an additional peak broadening, which is added to the dispersion associated to the equilibrium conditions. It is commonly assumed that when the solute concentration is sufficiently small, chromatographic elution is carried out under linear conditions, which is the case in almost all analytical applications. When the solute concentration increases above a value where the stationary phase approximates saturation (i.e. becomes overloaded), non-linear elution is obtained. In addition to overloading, another source of non-linearity can be a slow mass transfer. An extended Martin and Synge model is here proposed to include slow mass-transfer kinetics (with respect to flow rate) between the mobile phase and stationary phase. We show that there is a linear relationship between the variance and the ratio of the kinetic constants for the mass transfer in the flow direction (τ) and the mass transfer between the mobile phase and stationary phase (ν), which has been called the kinetic ratio (κ=τ/ν). The proposed model was validated with data obtained according to an approach that simulates the solute migration through the theoretical plates. An experimental approach to measure the deviation from the equilibrium conditions using the experimental peak variances and retention times at several flow rates is also proposed.

Optimal experimental designs in RPLC at variable solvent content and pH based on prediction error surfaces.

When pH is used as factor in reversed-phase liquid chromatographic (RPLC) separations, the need for providing quality and informative data with the minimal experimental effort becomes imperative. The most rational way to achieve this is by means of experimental designs. The interest in finding optimal designs involving solvent content and pH in RPLC is considerable, since these factors allow large variations in selectivity when ionisable compounds are involved. Unfortunately, the equations that describe the retention of these compounds with pH are nonlinear. As a consequence, factorial and other designs based on geometrical considerations are not well suited, whereas D-optimal and related designs can only be applied in an iterative fashion. In this work, an extension of G-optimal designs, aimed to enhance the quality of the predictions, is examined for problems involving solvent content and pH. The study was carried out with a set of probe ionisable compounds, for which information on retention behaviour was accurately known. A stepwise strategy was used to obtain a rapid estimation of the best design with a given number of experiments. The objective of the study was to investigate the distribution and number of points in the ideal design for compounds of different acid-base behaviour, and the possibility of finding common designs for groups of compounds. A further goal was to derive design construction rules containing the information requirements, without needing any further mathematical treatment.

Approaches to estimate the time and height at the peak maximum in liquid chromatography based on a modified Gaussian model.

The time and height at the peak maximum are key parameters to describe a chromatographic peak with prediction or optimization purposes, or in the qualitative/quantitative analysis of samples. Three different approaches to estimate these parameters, using the experimental points in the peak maximum region, are here described and compared. The approaches are based on the reliable description of the peak profile using a modified Gaussian model with a parabolic variance (PVMG). In the first approach, non-linear fitting of the chromatographic data to the PVMG model is carried out to obtain the time and height at the peak maximum (Approach I). In the other two approaches, the PVMG model is linearized to carry out a linear fitting. In each case, the optimal number of processed points was assessed. The three approaches yielded highly satisfactory results, being Approach I the best in terms of accuracy and robustness. The assessment of the accuracy in the estimations was carried out using simulated peaks. These peaks were built with the parameters obtained from real peaks for several probe compounds eluted under reversed-phase liquid chromatographic (RPLC) conditions, to which noise was added.

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 (beta-blockers).

Combined effect of solvent content, temperature and pH on the chromatographic behaviour of ionisable compounds. III: Considerations about robustness.

We previously reported a model able to predict the retention time of ionisable compounds as a function of the solvent content, temperature and pH [J. Chromatogr. A 1163 (2007) 49]. The model was applied further, developing an optimisation of the resolution based on the peak purity concept [J. Chromatogr. A 1193 (2008) 117]. However, we left aside an important issue: we did not consider incidental overlaps caused by shifts in the predicted peak positions, owing either to uncertainties in the source data, modelling errors, or the practical implementation in the chromatograph of the optimal mobile phase (or any other). These shifts can ruin the predicted separation, since they can easily amount several peak-width units at pH values close to the logarithm of the solutes' acid-base constants. A probabilistic optimisation is proposed here, which is able to evaluate the uncertainties associated with the model and the consequences when the optimal mobile phase is implemented in the chromatograph. This approach assumes peak fluctuations in replicated assays obtained through Monte Carlo simulations, which gives rise to a distribution of elementary peak purities. The results yielded by the conventional (i.e. non-robust), derivative-penalised, and probabilistic optimisations were compared, checking the predicted and experimental chromatograms at several critical experimental conditions. Among the three approaches, only the probabilistic one was able to appraise properly the practical difficulties of the separation problem.

Alternating iterative regression method for dead time estimation from experimental designs.

An indirect method for dead time (t (0)) estimation in reversed-phase liquid chromatography, based on a relationship between retention time and organic solvent content, is proposed. The method processes the retention data obtained in experimental designs. In order to get more general validity and enhance the accuracy, the information from several compounds is used altogether in an alternating regression fashion. The method was applied to nitrosamines, alkylbenzenes, phenols, benzene derivatives, polycyclic aromatic hydrocarbons and beta-blockers, among other compounds, chromatographed in a cyano and several C18 columns. A comprehensive validation was carried out by comparing the results with those provided by the injection of markers, the observation of the solvent front and the homologous series method. It was also found that different groups of compounds yielded the same t (0) value with the same column, which was verified in different solvent composition windows. The method allows improved models useful for optimisation or for other purposes, since t (0) can be estimated with the retention data of the target solutes.

Peak capacity estimation in isocratic elution.

Peak capacity (i.e. maximal number of resolved peaks that fit in a chromatographic window) is a theoretical concept with growing interest, but based on a situation rarely met in practice. Real chromatograms tend to have uneven distributions, with overlapped peaks and large gaps. The number of resolved compounds should, therefore, be known from estimations. Several equations have been reported for this purpose based on three perspectives, namely, the intuitive approach (peak capacity as the size of the retention time window measured in peak width units), which assumes peaks with the same width, and the outlines of Giddings and Grushka, which consider changes in peak width with retention time. In this work, the peak capacity concept is discussed and three new approaches are derived based on realistic descriptions of peak shape. The first one is based on the Grushka's approach and considers the contributions of column and extra-column peak variances. The second one relies on Giddings' and assumes asymmetrical peaks where left and right peak half-widths depend linearly on retention time. The third equation, based on the intuitive approach, uses a mean peak width obtained by integration, instead of a mean value from several representative peaks. The accuracy of the classical Giddings' approach for ideal peaks, a modification of the Grushka's approach that considers variation of peak width at half-height, and the three new approaches were checked on combined chromatograms built by adding real peaks. The results demonstrate that the change in efficiency (and not in skewness) is the relevant factor, at least in the studied examples. Also, peak width should be measured at low peak height ratios (i.e. 10%) to better account peak deformation.

Combined effect of solvent content, temperature and pH on the chromatographic behaviour of ionisable compounds II: benefits of the simultaneous optimisation.

A previously reported eight-parameter mechanistic model [Part I of this work, J. Chromatogr. A 1163 (2007) 49] was applied to optimise the separation of 11 ionisable compounds (nine diuretics and two beta-blockers), considering solvent content, temperature and pH as experimental factors. The data from 21 experiments, arranged in a central composite design, were used to model the retention. Local models were used to predict efficiency and peak asymmetry. The optimisation strategy, based on the use of peak purity as chromatographic objective function and derived concepts, was able to find the most suitable experimental conditions yielding full resolution in reasonable analysis times. It also allowed a detailed inspection of the separation capability of the studied factors, and of the consequences of the shifts in the protonation constants originated by changes in solvent content and temperature. The size of the resolution structures suggested that the ranked importance of the factors was pH, organic solvent and temperature, giving rise to relatively narrow domains of full resolution. The three factors were found, however, worthwhile in the optimisation of selectivity. Predicted optimal conditions corresponding to two different optimal resolution regions were verified experimentally. In spite of the difficulties associated to the use of pH as optimisation factor, satisfactory agreement was found in both cases.

Prediction of peak shape in hydro-organic and micellar-organic liquid chromatography as a function of mobile phase composition.

A simple model is proposed that relates the parameters describing the peak width with the retention time, which can be easily predicted as a function of mobile phase composition. This allows the further prediction of peak shape with global errors below 5%, using a modified Gaussian model with a parabolic variance. The model is useful in the optimisation of chromatographic resolution to assess an eventual overlapping of close peaks. The dependence of peak shape with mobile phase composition was studied for mobile phases containing acetonitrile in the presence and absence of micellised surfactant (micellar-organic and hydro-organic reversed-phase liquid chromatography, RPLC). In micellar RPLC, both modifiers (surfactant and acetonitrile) were observed to decrease or improve the efficiencies in the same percentage, at least in the studied concentration ranges. The study also revealed that the problem of achieving smaller efficiencies in this chromatographic mode, compared to hydro-organic RPLC, is not only related to the presence of surfactant covering the stationary phase, but also to the smaller concentration of organic solvent in the mobile phase.