Countercurrent chromatographic separation: a hydrodynamic approach developed for extraction columns

In countercurrent chromatography (CCC) both stationary and mobile liquids undergo intense mixing in the variable force field of a coil planet centrifuge and the separation process, like the separation in conventional solvent extraction column, is influenced by longitudinal mixing in the phases and mass transfer between them. This paper describes how the residence time distribution (or the elution profile) of a solute in CCC devices and the interpretation of experimental peaks, can be described by a recently developed cell model of longitudinal mixing. The model considers a CCC column as a cascade of perfectly mixed equal-size cells, the number of which is determined by the rates of longitudinal mixing in the stationary and mobile phases. Experiments were carried out to demonstrate the validation of the model and the possibility of predicting the partitioning behaviour of the solutes. The methods for estimating model parameters are discussed. Longitudinal mixing rates in stationary and mobile phases have been experimentally determined and experimental elution profiles are compared with simulated peaks. It is shown that using the cell model the peak shape for a solute with a given distribution constant can be predicted from experimental data on other solutes.     

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.     

Interpretation on Band‐Broadening in Chromatography with Spatial Peak Profiles Obtained Using Whole‐Column Detection

Fifteen liquid chromatographic experiments were investigated using a whole‐column detection (WCD) system and a conventional post‐column UV/Vis detector. The peak widths obtained from chromatograms were found dependent on the retention factor; the larger the retention factor was the greater the peak width. However, the on‐column spatial peak widths were dependent on the locations where they were measured in the column. The peak widths monitored at 17 cm from the column inlet were found essentially the same no matter what their retention factors were. In addition, a linear relationship was found between the chromatographic peak width and the reciprocal of the average linear rate of the solute migration. The peak widths on chromatograms did not reflect how they appeared in the column; instead, the widths were determined by the solute speed passing the detector.     

Advantages of a small-volume counter-current chromatography column

Counter-current chromatography (CCC) works with a support-free liquid stationary phase. This allows for preparative separations and purifications. However, there are serious technical constraints because of the need to keep a liquid stationary phase in a column. Centrifugal fields are used. A new commercial hydrodynamic 18 mL column made with a narrow-bore 0.8 mm Teflon tubing was evaluated by comparing it with older hydrodynamic CCC columns and a similar 19 mL column but made with 1.6 mm Teflon tubing. A small-volume CCC column allows for reliable and fast solute partition coefficient determination. When resolution is required, both high efficiency and liquid stationary phase retention are needed. Unfortunately, these two requirements bear technical contradictions. A column coiled with a narrow tubing bore will provide a high chromatographic efficiency while a column containing wider tubing bore will achieve higher stationary phase retention. In all cases, increasing the magnitude of the centrifugal field also increases the stationary phase retention. The solution is to build centrifuges able to produce high fields that will provide acceptable liquid phase retention with narrow-bore tubes. The new 18 mL 0.8 mm tubing bore column is able to rotate as fast as 2100 rpm generating a 240 × g field. The two older CCC columns cannot compete with the new one. However, the small 19 mL column with 1.6 mm bore tubing can be useful when fast results are desired without top resolution.     

A calculation method for the prediction of effective plate height in capillary gas chromatography

The effective plate height, h_eff, is considered to be a better measure of the efficiency of capillary column than the conventional plate height, h, in isothermal conditions. By using experimental data of 1-alcohols and n-alkanes, 2-ketones and 1-alkenes measured on capillary columns coated with non-polar stationary phases in isothermal and isobaric conditions, the peak width at half height is predicted with a function similar at that of adjusted retention time. The results obtained under different analytical conditions as the head pressure and the temperature of the column confirm the validity of the model, whose parameters are linear, and as a consequence a unique solution is obtained.     

Probing the kinetic performance limits for ion chromatography. II. Gradient conditions for small ions

A gradient kinetic plot method is used for theoretical characterisation of the performance of polymeric particulate anion exchange columns for gradient separations of small inorganic anions. The method employed requires only information obtained from a series of isocratic column performance measurements and in silico predictions of retention time and peak width under gradient conditions. Results obtained under practically constrained conditions provide parameters for the generation of high peak capacities and rapid peak production for fast analysis to be determined. Using this prediction method, a maximum theoretical peak capacity of 84 could be used to achieve separation of 26 components using a 120 min gradient (R_s > 1). This approach provides a highly convenient tool for development of both mono- and multidimensional ion chromatography (IC) methodologies as it yields comprehensive understanding of the influence of gradient slope, analysis time, column length and temperature upon kinetically optimised gradient performance.     

Optimization and identification in any kind of multi-step temperature programmed gas chromatography

The theory which predicts the retention time, retention temperature, and peak width for any kind of multi-step TPGC and the principle of optimization has been described. Software for optimization and identification in TPGC has been developed on the basis of this theory. It has also been proven that the relationship between peak width in TPGC and the derived or “invented” retention time is similar to that between peak width and retention time in isothermal processes. The validity of the software has been proved by using it to predict retention temperature, retention time, and peak width for any kind of temperature programming and to predict the optimum temperature program for separation of a multihomolog mixture of industrial alcohols and 15 enantiomeric pairs of amino acids.     

Retention time and effective separation factor in series-coupled columns with different stationary phases

Basic expressions are derived for both the retention time and the effective separation factor in serially coupled GC columns. The retention time is determined by two main parameters. The first is the fractional time spent by an unretarded solute in each column which, in turn, is determined by the relative column lengths and flow velocities through each column. The second parameter is the relative mass distribution coefficient of a particular solute in each column; a variable that can be adjusted by changing the relative temperatures of the columns. The expression for the effective separation factor relates the measured separation factor for the series combination to the separation factors on the individual columns, the fractional time spent by an unretarded peak in each column, as well as the relative values of the mass distribution coefficients of a particular solute on the different columns.     

Retention and column efficiency in reversed phase liquid chromatography as a function of pH for optimization purposes

Summary The effects of pH on both the solute retention and the peak shape of ionogenic compounds are studied in order to propose accurate models for pH optimization purposes. Several mathematical models (theoretical and empirical) for describing the variation of the retention factor versus pH are compared within different pH ranges. Limits of such models used for optimizing the pH by requiring only 3 preliminary experimental runs, are discussed in terms of deviations (≤±5%) of predicted retention times from experimental retention times. An original procedure is developed for selecting the most convenient retention model, from a given set of three retention data. This set is also applied to modeling the variation of both peak width and peak asymmetry with mobile phase pH conditions. Such a procedure is demonstrated as helpful for the separation of ionogenic solutes by considering mobile phase pH as an additional variable that can be useful during optimization procedures.     

Evaluation of the van Deemter equation in terms of open‐ended flow to chromatography

Plate theory and adsorption theory are the main tools available for understanding chromatographic experiments. Both theories predict a Gaussian distribution of solute molecules within the tubular system. However, Gaussian concentration distributions are observed predominantly at slow linear flow rates, while asymmetric concentration distributions are observed at the linear flow rates most used in chromatography. Allegedly, this asymmetry originates from an inhomogeneous distribution of grain sizes in the column and column overload. However, it is an experimental fact that the distribution of chemicals within an injected volume of solute changes as a function of time, while the response is measured simultaneously. Accordingly, the obtained signal cannot be compared to the theory before some type of time‐based deconvolution of the data has been performed. Adjustments to high‐performance liquid chromatography data were thus proposed through empirical equations that describe the relevant time values, peak height, peak area, and parameters of the van Deemter equation. It was proposed that the transfer of solute from the front to the rear part of the pulse during laminar open‐ended flow occurs at rate that depends on the linear flow rate, and to a lesser extent, on properties of the response function.     

Prediction of retention times and efficiency in linear gradient programmed pressure analysis on capillary columns

A method for the prediction of the retention time and the resolution of chromatographic peaks in different experimental conditions by starting from few experimental data measured in isothermal and isobaric analyses was published previously. In this paper, the same mathematical model was implemented for calculating the retention times and the column efficiency in programmed pressure runs. Some models originated from the Golay equation and reported in the literature are compared, and a new modified equation for the calculation of the peak width at half height is proposed. The procedure for the prediction of the retention time and the peak width at half height at programmed pressure of the carrier gas and different column temperature and linear gradient by using retention data of different compounds obtained in few isobaric runs is described. The prediction of the retention time and the separation efficiency of compounds with different polarity gave good results for the programmed pressure runs with linear gradient. The effect of the variation of the initial parameters of the experimental analyses and of the mathematical model on the accuracy of the prediction has been evaluated.     

Mathematical model of computer-programmed intermittent dual countercurrent chromatography applied to hydrostatic and hydrodynamic equilibrium systems

Dual high-speed countercurrent chromatography (dual CCC) literally permits countercurrent flow of two immiscible solvent phases continuously through the coiled column for separation of solutes according to their partition coefficients. Application of this technique has been successfully demonstrated by separation of analytes by gas–liquid and liquid–liquid two-phase systems. However, the method cannot be directly applied to the system with a set of coiled columns connected in series, since the countercurrent process is interrupted at the junction between the columns. However, this problem can be solved by intermittent dual CCC by eluting each phase alternately through the opposite ends of the separation column. This mode of application has an advantage over the conventional dual CCC in that the method can be applied to all types of CCC systems including hydrostatic equilibrium systems such as toroidal coil CCC and centrifugal partition chromatography. Recently, the application of this method to high-speed CCC (hydrodynamic system) has been demonstrated for separation of natural products by Hewitson et al. using a set of conventional multilayer coil separation columns connected in series. Here, we have developed a mathematical model for this intermittent dual CCC system to predict retention time of the analytes, and using a simplified model system the validity of the model is justified by a series of basic studies on both hydrodynamic and hydrostatic CCC systems with a computer-programmed single sliding valve. The present method has been successfully applied to spiral tube assembly high-speed CCC (hydrodynamic system) and toroidal coil CCC (hydrostatic system) for separation of DNP-amino acid samples with two biphasic solvent systems composed of hexane–ethyl acetate–methanol–0.1 M hydrochloric acid (1:1:1:1 and 4:5:4:5, v/v).     

Evaluation of the Linear-Elution-Strength Model for the Prediction of Retention and Selectivity in Isothermal Gas Chromatography

Linear-elution strength theory and temperature-programmed gas chromatography is evaluated as a rapid method for predicting isothermal retention factors and column selectivity. Retention times for a wide range of compounds are determined at the program rates of 3 and 12 °C/min for the temperature range 60 to 160 °C on three open-tubular columns (DB-1701, DB-210 and EC-Wax) and used to predict isothermal retention factors for each column over the temperature range 60 to 140 °C. The temperature-program predicted isothermal retention factors are compared with experimental values using linear regression and the solvation parameter model. It is shown that isothermal retention factors predicted by the linear-elution-strength model only approximately represents the experimental data. The model fails to predict the slight curvature that exists in most plots of the experimental retention factor (log k) as a function of temperature. In addition, regression of the temperature-program predicted isothermal retention factors against the experimental values indicates that the slopes and intercepts deviate significantly from their target values of one and zero, respectively, in a manner which is temperature dependent. The temperature-program predicted isothermal retention factors result in system constants for the solvation parameter model that are different to those obtained from the experimental retention factors. These results are interpreted as indicating that linear-elution-strength theory predicts retention factors that fail to accurately model stationary phase interactions over a wide temperature range. It is concluded that temperature-program methods using linear-elution-strength theory are unsuitable for constructing system maps for isothermal separations.     

色谱灰色数模的建立及其应用研究(Ⅰ)──连续GM(1,N)模型的建立及色谱保留行为的预测

应用灰色系统理论和最小二乘原理，推导出连续GM（1，N）模型，并将该模型用于高效液相色谱中溶质保留行为的预测．研究了烷烃、烷基苯及对羟基苯甲酸酯等化合物的容量因子与流动相组成、容量因子与碳数、保留时间与温度、保留时间与碳数的关系，并建立了相应的数学模型，经验证，预测结果良好．     

Tubing modifications for countercurrent chromatography (CCC): Stationary phase retention and separation efficiency

Countercurrent chromatography (CCC) is a separation technique in which two immiscible liquid phases are used for the preparative purification of synthetic and natural products. In CCC the number of repetitive mixing and de-mixing processes, the retention of the stationary phase and the mass transfer between the liquid phases are significant parameters that influence the resolution and separation efficiency. Limited mass transfer is the main reason for peak broadening and a low number of theoretical plates along with impaired peak resolution in CCC. Hence, technical improvements with regard to column design and tubing modifications is an important aspect to enhance mixing and mass transfer.     

Distribution ratio, distribution constant and partition coefficient. Countercurrent chromatography retention of benzoic acid

There is some confusion in chromatography between terms such as solute distribution ratio, distribution constant and partition coefficient. These terms are very precisely defined in the field of liquid-liquid systems and liquid-liquid extraction as well as in the field of chromatography with sometimes conflicting definitions. Countercurrent chromatography (CCC) is a chromatographic technique in which the stationary phase is a support-free liquid. Since the mobile phase is also liquid, biphasic liquid systems are used. This work focuses on the exact meaning of the terms since there are consequences on experimental results. The retention volumes of solutes in CCC are linearly related to their distribution ratios. The partition coefficient that should be termed (IUPAC recommendation) distribution constant is linked to a single definite species. Using benzoic acid that can dimerize in heptane and ionize in aqueous phase and an 18 mL hydrodynamic CCC column, the role and relationships between parameters and the consequences on experimental peak position and shape are discussed. If the heptane/water distribution constant (marginally accepted to be called partition coefficient) of benzoic acid is 0.2 at 20 °C and can be tabulated in books, its CCC measured distribution ratio or distribution coefficient can change between zero (basic aqueous mobile phase) and more than 25 (acidic aqueous mobile phase and elevated concentration). Benzoic acid distribution ratio and partition coefficient coincide only when both dimerization and ionization are quenched, i.e. at very low concentration and pH 2. It is possible to quench dimerization adding butanol in the heptane/water system. However, butanol additions also affect the partition coefficient of benzoic acid greatly by increasing it.     

Parameters affecting the separation of intact proteins in gradient-elution reversed-phase chromatography using poly(styrene-co-divinylbenzene) monolithic capillary columns

An experimental study was performed to investigate the effects of column parameters and gradient conditions on the separation of intact proteins using styrene-based monolithic columns. The effect of flow rate on peak width was investigated at constant gradient steepness by normalizing the gradient time for the column hold-up time. When operating the column at a temperature of 60 °C a small C-term effect was observed in a flow rate range of 1–4 μL/min. However, the C-term effect on peak width is not as strong as the decrease in peak width due to increasing flow rate. The peak capacity increased according to the square root of the column length. Decreasing the macropore size of the polymer monolith while maintaining the column length constant, resulted in an increase in peak capacity. A trade-off between peak capacity and total analysis time was made for 50, 100, and 250 mm long monolithic columns and a microparticulate column packed with 5 μm porous silica particles while operating at a flow rate of 2 μL/min. The peak capacity per unit time of the 50 mm long monolithic column with small pore size was superior when the total analysis time is below 120 min, yielding a maximum peak capacity of 380. For more demanding separations the 250 mm long monolith provided the highest peak capacity in the shortest possible time frame.     

Using the liquid nature of the stationary phase. VI. Theoretical study of multi-dual mode countercurrent chromatography

Countercurrent chromatography (CCC) is a separation technique using a biphasic liquid system and centrifugal forces to maintain a support-free liquid stationary phase. Either one of the two phases can be the liquid stationary phase. It is even possible to switch the phase role during the separation. The dual-mode method is revisited recalling its theoretical background. The multi-dual mode (MDM) CCC method was introduced to enhance the resolution power of a CCC column. The theoretical study of the MDM method is validated by modeling the separation of two solutes. The basic hypothesis is that the forward step (partial classical elution) is followed by a backward step that returns the less retained solute to the column head. The equations show that the most important parameter to maximize resolution is not the number of MDM steps but the total volume of liquid phases used to elute the solutes. The model is validated calculating correctly the peak position of previously published MDM experiments.