Injection profiles in liquid chromatography. I. A fundamental investigation

This is a fundamental experimental and theoretical investigation on how the injection profile depends on important experimental parameters. The experiments revealed that the injection profile becomes more eroded with increased (i) flow rate, (ii) viscosity of the eluent, (iii) size of the solute, (iv) injection volume and (v) inner diameter of the injection loop capillary. These observations cannot be explained by a 1D-convection-diffusion equation, since it does not account for the effect of the parabolic flow and the radial diffusion on the elution profile. Therefore, the 1D model was expanded into a 2D-convection-diffusion equation with cylindrical coordinates, a model that showed a good agreement with the experimental injection profiles dependence on the experimental parameters. For a deeper understanding of the appearance of the injection profile the 2D model is excellent, but to account for injection profiles of various injection volumes and flow rates in preparative and process-chromatography using computer-optimizations, a more pragmatic approach must be developed. The result will give guidelines about how to reduce the extra-column variance caused by the injection profile. This is important both for preparative and analytical chromatography; in particular for modern analytical systems using short and narrow columns.     

Poppe plots for size-exclusion chromatography

Poppe plots provide a clear and unambiguous way to discuss the performance limits of separation systems. The effects of particle size, pressure drop and column permeability can be illustrated using such plots. The performance limits of size-exclusion chromatography are of interest, due to developments in combinatorial chemistry and high-throughput experimentation. In these fields, fast separations of high-molecular-weight analytes are required. In this paper, Poppe plots will be presented for size-exclusion chromatography. Because of the very high-reduced velocities encountered, the Poppe plots are found to be significantly different from those commonly observed in HPLC. Fast separations in size-exclusion chromatography are not as unfavourable as suggested by conventional theory. The results are based on experimental data obtained for a wide range of polystyrenes (1.7-3.25 kDa) using THF as mobile phase, but may be equally valid in other cases.     

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。     

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.     

Fractionation and Size Distribution of Water Soluble Polymers by Flow Field-Flow Fractionation

Abstract

Flow field-flow fractionation (flow FFF) is introduced as a chromatographic-like method with a potential for separating and characterizing water soluble polymers. The theory of the method is summarized, showing that one gets a size distribution curve based on the Stokes diameter, d. Problems in interpreting the elution profile in both flow FFF and gel permeation chromatography are discussed in the light of complications arising from electrostatic chain expansion in polyelectrolytes.

The experimental approach is described using a channel of 2.00 ml volume. Sulfonated polystyrenes of three different molecular weights are separated from one another with and without added salts. The dependence of retention on sample size is shown to be least in the salt solution, indicating that this is most suitable for analytical work.

The sodium salts of polyacrylic acid are also investigated. Distinct elution profiles are noted for two of these polydisperse polymers. Size distribution curves for the 2,000,000 MW sample curves are obtained from, the elution profiles and are shown to be independent of experimental variations. Finally, fractions are collected after separation and rerun through the coloumn, showing a reasonable confirmation of the expected fractionation effect.     

Liquid adsorption chromatography of polyethers: experiments and simulation

The adsorption behavior of poly(ethylene glycol) (PEG) in reversed-phase chromatography is studied both experimentally and theoretically and a computer simulation of chromatograms is performed on the basis of these studies. The experimental conditions were: different reversed-phase adsorbents and a solvent methanol–water system as the mobile phase. At varying mobile phase compositions highly resolved chromatograms of PEG samples were obtained, in which all peaks could be identified, and the dependencies of the distribution coefficient on the degree of polymerization for PEG molecules were evaluated by processing these chromatograms. The data were interpreted by using a theory of homopolymers based on a continuum Gaussian chain model of flexible macromolecules and a slit-like model of pores of stationary phase. The theory proved to describe well the experimental data in the whole range of studied molecular masses, and the thermodynamic parameters characterizing interactions of ethylene oxide repeating units in PEG molecules with the adsorbent pore walls have been determined from the comparison of the theory with the experimental data. The dispersion of chromatographic peaks corresponding to individual oligomer molecules is also estimated. In the system studied the peak width occurred to be proportional to the distribution coefficient of corresponding macromolecule. The theory is used to develop a computer-assisted procedure for simulation of chromatograms for samples of linear homopolymers. Using the obtained data on the thermodynamic parameters and the estimates of peak dispersion, chromatograms are simulated for PEG samples at two different chromatographic conditions. These simulated chromatograms were in good quantitative agreement with the real chromatograms.     

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.     

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).     

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 DETERMINATION OF ADSORPTION ISOTHERMS AND SOLID DIFFUSION COEFFICIENTS OF MANNITOL AND SORBITOL BY LIQUID CHROMATOGRAPHY TECHNIQUE

The parameter identification model is proposed for determining the linear adsorption isotherms and the solid diffusion coefficients by using adsorption chromatorgaphy.Axial dispersion coefficients is firstly determined by pulse-respond experiment technique with an inert substance as tracer,then the elution curves of chromatography separating the isomer mannitol and sorbitol are determined by the chromatographic measuring technique,and pinally the adsorption isotherms and the solid diffusion coefficients of mannitol and sorbitol on Ca^2+ resins are estimated by using this model.The results show that the axial dispersion coefficients increase with fluid velocity increasing,The adsorption equilibrium constants decrease with temperature rising;and the solid diffusion coefficients increase with temperature rising.The theoretical elution curves are good agreement with the experimental elution curves of the liquid adsorption chromatography separating the mannitol and the sorbitol.The model provides a simple and reliable procedure to estimate the kinetic and thermodynamic parmeters of the adsorption.     

Non-equilibrium model of liquid column chromatography : II. Explicit solutions and non-ideal conditions

the analysis begun in the previous paper of a general model for liquid chromatography in a column is continued here. Explicit solutions are obtained for small-zone and large-zone non-equilibrium chromatography models both without and with diffusion. The effects on the moments of the elution profile of a distribution function which characterizes molecular heterogeneity (such as molecular size) or bead non-uniformities are analyzed. A first-order correction to the mean value of the elution profile when sorption—desorption kinetics are concentration dependent is derived.Numerical simulations of the elution profile indicate the following. (1) The peak and mean may differ by as much as a factor of two for slow mass transfer (k₁ 0.01). Since the mean is uniquely detemined by the equilibrium constant but the peak is not, the use of the peak to characterize the equilibrium constant for broad asymmetric profiles may lead to serious errors. (2) When the rate of mass transfer from the void to penetrable volumes becomes comparable to u/h, a second peak will develop in the elution profile. This happens even for a completely homogeneous population under conditions, and is caused by molecules that traverse the column without penetrating beads. The dispersion of this peak is therefore determined entirely by effects other than mass transfer. (3) In the non-linear regime (i.e., when mass transfer rates are concentration dependent), the equilibrium constant is, in general, no longer uniquely determined by the mean. Uniqueness is, however, obtained in the limit as both mass transfer coefficients become very small, with their ratio remaining moderate.     

Surface heterogeneity and surface area from linear inverse gas chromatography. Application to glass fibers

A new method of measuring surface heterogeneity of non-porous adsorbents by inverse gas chromatography (IGC) is developed. In contrast with the methods described in the literature which are based on nonlinear chromatography (thermodynamics of adsorption) this method is based on linear chromatography (kinetics of adsorption). The mass balance equation of linear chromatography with axial diffusion term and the Langmuir kinetic equation on an open (non-porous) heterogeneous surface are solved by the method of Laplace transforms. The expressions for four semi-invariants of an elution profile are obtained. These are linear combinations of the moments of the distribution of sites in residence time of adsorbed molecule with coefficients determined from elution profile of non-adsorbing gas. Four semi-invariants of elution profiles of benzene and methane on a column packed with E-glass fiber were determined experimentally at temperatures around 100 degrees C. The mean, the standard deviation of the normal distribution in adsorption energy as well as the sticking coefficient and pre-exponential factor of the Frenkel equation are determined for benzene on E-glass. A method of the specific surface determination from linear IGC is proposed.     

A theoretical approach to the interpretation of the transient data in scanning laser ablation inductively coupled plasma mass spectrometry: Consideration of the geometry of the scanning area

This paper represents a further development of the theoretical basis for the interpretation of transient data obtained by scanning laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) to overcome the non-linear distortion of the transient signal as well as to improve spatial resolution. The reconstruction of the relative concentration profile from transient data is suggested in terms of simple models of analytical information gathering for extreme cases of depth distribution of the analyte. The main attention is focused on the geometry of the overlap between the laser spot and the concentration profile, the consideration of which allows defining explicitly the response function necessary for the deconvolution procedure. The profile of the transient signal simulated according the proposed model for a real system (copper conductor lines in polymer matrix) is in good agreement with the measured data. The feasibility of the deconvolution procedure to reconstruct the relative concentration profile for a model system is demonstrated. The suggested analytical framework is intended to overcome certain limitations of scanning LA-ICP-MS which are caused by the measuring process independently from the optimization of hardware and experimental conditions.     

Simultaneous correlation of hydrophobic interactions in HIC and protein solubility in aqueous salt solutions and mixed solvents

The chromatographic retention in hydrophobic and reversed phase chromatography and the solubility of proteins display some common features. The chromatographic retention, as well as the solubility, is modulated by the thermodynamic properties of the solute in the fluid phase. The retention measurements at linear conditions provide information of the solution properties of the protein at infinite dilution, and the solubility measurements produce the supplementary information about the solution properties at the saturation limit. This provides a useful approach to simultaneous correlation of the chromatographic retention and the solubility.The experimental data, used for the correlation, comprise retention measurements of lysozyme on different HIC adsorbents using an aqueous ammonium sulphate eluant, an aqueous ammonium sulphate eluant with an admixture of ethanol, as well as published solubility data.The chromatographic retention data and the corresponding solubility data have been correlated using a chemical potential model derived from Kirkwood's theory of solutions of charged macro-ions and zwitterions in electrolyte solutions. The model correlated the chromatographic retention factor and the solubility data within the precision of the measurements. The model was applied in a pH range from 4 to 11. It was demonstrated experimentally, as well as theoretically, that an admixture of ethanol to the aqueous eluant changes the thermodynamic retention factor on various adsorbents identically when compared to the thermodynamic retention factor in an ethanol free eluant.     

The effect of input pulse duration on the elution curve profile

Numerical simulation and new analytical solutions have been used to study the effect of the duration of the input pulse of an adsorbate on the development of the elution curve profile in the adsorption dynamics. Elution curves calculated with regard to finite input pulse duration have been compared with those determined for the instantaneous injection of an adsorbate in the absence of extracolumn broadening. Quantitative regularities of variations in curve parameters measured as the time corresponding to the maximum of the curve and its width at a fixed height as depending on the length of an adsorbent layer have been estimated. The influence of the input pulse duration on the statistical moments of the elution curve has been determined, with the obtained moments being in agreement with the published solution that was previously found using the Laplace transformations. Correspondence between the theoretical and experimental data has been revealed for argon elution from a helium flowing through an activated carbon layer.     

Multistep elution chromatography model of a multicomponent mixture

An interpretation of the conditions under which there is a likeness between chromatography and the Craig method during the processing of a multicomponent mixture is given. Equations for calculating the height equivalent to a theoretical separation step are discussed. Using the results from theoretical studies, the chromatographic system is described as a multistep cascade, and the generalized thermodynamic separation theory for binary and multicomponent mixtures is extended to elution chromatography.     

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.     

DETERMINATION OF THERMODYNAMIC AND KINETIC PARAMETERS OF LARGE SCALE CHROMATOGRAPHIC SEPARATION OF SUGAR AND REDUCING SUGAR

The parameter identification model of large scale chromatography separation process is proposed.The phase equilibrium constants and lumped mass transfer coefficients of sugar and reducing sugar adsorption on D1,D2 and D3 resins as well as the axial dispersion coefficients of the fluid through packed columns are determined by means of the pulse-response experiment technique with an inert substance as a tracer and the chromatography measuring technique.The elution curve calculated from these parameters is good agreement with the experimental elution curve.The sensitivity analysis of these parameters is carried out ,and the result shows that the elution curves of chromatography separation are more sensitive to the variations of the phase equilibrium relationship than to the variation of the axial dispersion as well as the lumped mass transfer coefficients.