Comparison of retention models for polymers 1. Poly(ethylene glycol)s

The suitability of three different retention models to predict the retention times of poly(ethylene glycol)s (PEGs) in gradient and isocratic chromatography was investigated. The models investigated were the linear (LSSM) and the quadratic solvent strength model (QSSM). In addition, a model describing the retention behaviour of polymers was extended to account for gradient elution (PM). It was found that all models are suited to properly predict gradient retention volumes provided the extraction of the analyte specific parameters is performed from gradient experiments as well. The LSSM and QSSM on principle cannot describe retention behaviour under critical or SEC conditions. Since the PM is designed to cover all three modes of polymer chromatography, it is therefore superior to the other models. However, the determination of the analyte specific parameters, which are needed to calibrate the retention behaviour, strongly depend on the suitable selection of initial experiments. A useful strategy for a purposeful selection of these calibration experiments is proposed.     

Density functional theory of polymer-polymer phase separation behavior

Polyatomic density functional theory is applied to a binary polymer blend. The polymer reference interaction site model (PRISM) liquid state theory provides the homogeneous state correlation functions necessary for the application of density functional theory. An effective chi parameter can be recognized from the density functional expression; however, the phase separation criteria does not depend solely upon the chi parameter, rather it depends upon various combinations of the species-dependent direct correlation functions of the blend. The Flory-Huggins chi parameter along with the associated phase diagram is obtained when the monomer volumes of the blend species are equal and for a range of monomer-monomer attractive interactions. Calculations are performed both with and without the assumption of incompressibility. The density functional theory along with the PRISM determined “input” predict that an isotopic polymer blend shows an upper critical solution temperature (UCST) phenomena. © 1995 John Wiley & Sons, Inc.     

Nonlinear gas chromatography as a way of studying inhomogeneous sorbents

A way of organizing and processing the results from gas–chromatographic experiments to obtain chromatographic retention characteristics for a fixed concentration of sorbate in the gas phase or on the surface of the sorbent is proposed and substantiated. The suitability and expediency of such retention characteristics for describing the sorption properties of inhomogenous sorbents is demonstrated using a wide variety of adsorbents of different natures (activated carbons, swelling and nonswelling polymers, silicas and their silver derivatives) as examples.

     

Prediction of retention times and peak widths in temperature-programmed gas chromatography using the finite element method

Optimization of separations in gas chromatography is often a time-consuming task. However, computer simulations of chromatographic experiments may greatly reduce the time required. In this study, the finite element method was used to predict the retention times and peak widths of three analytes eluting from each of four columns during chromatographic separations with two temperature programs. The data acquired were displayed in predicted chromatograms that were then compared to experimentally acquired chromatograms. The differences between the predicted and measured retention times were typically less than 0.1%, although the experimental peak widths were typically 10% larger than expected from the idealized calculations. Input data for the retention and peak dispersion calculations were obtained from isothermal experiments, and converted to thermodynamic parameters.     

Application of the reversed-phase liquid chromatographic model to describe the retention behaviour of polydisperse macromolecules in gradient and isocratic liquid chromatography

This paper illustrates how conventional models of chromatographic behaviour can be used to predict the separation behaviour of polydisperse macromolecules. Using polystyrene and polymethylmethacrylate homo- and co-polymeric standards, the models were validated by comparing experimental retention behaviour with that predicted by the chromatographic model. The experimental retention time of each of the samples was entered into a spreadsheet application, which calculated the parameters that best described retention (for a given model). When a correlation between the relevant parameters and molecular mass was established, that correlation was used to predict the change in retention behaviour over the molecular-mass range. An expression introduced in a previous paper, to calculate the critical mobile-phase composition of a homopolymer was validated using polystyrene homopolymers. A second expression, which can predict the elution behaviour of copolymers, was also validated. This expression can predict the retention of a copolymer, based solely onthe retention of the homopolymeric units that make up the copolymer.     

Prediction of Intact N-Glycopeptide Retention Time Windows in Hydrophilic Interaction Liquid Chromatography

Analysis of protein glycosylation is challenging due to micro- and macro-heterogeneity of the attached glycans. Hydrophilic interaction liquid chromatography (HILIC) is a mode of choice for separation of intact glycopeptides, which are inadequately resolved by reversed phase chromatography. In this work, we propose an easy-to-use model to predict retention time windows of glycopeptides in HILIC. We constructed this model based on the parameters derived from chromatographic separation of six differently glycosylated peptides obtained from tryptic digests of three plasma proteins: haptoglobin, hemopexin, and sex hormone-binding globulin. We calculated relative retention times of different glycoforms attached to the same peptide to the bi-antennary form and showed that the character of the peptide moiety did not significantly change the relative retention time differences between the glycoforms. To challenge the model, we assessed chromatographic behavior of fetuin glycopeptides experimentally, and their retention times all fell within the calculated retention time windows, which suggests that the retention time window prediction model in HILIC is sufficiently accurate. Relative retention time windows provide complementary information to mass spectrometric data, and we consider them useful for reliable determination of protein glycosylation in a site-specific manner.     

Optimisation of chromatographic separations by use of a chromatographic response function, empirical modelling and multivariate analysis

Summary The chiral separation of the drug substance R,S-oxybutynin chloride on a reversed phase HPLC system has been optimised by use of empirical modelling and multivariate analysis. The separation was characterised by a new chromatographic response function developed to modulate both quality of separation and retention time. The study includes a comparison between three different multivariate techniques (multi-layer feed-for-ward neural networks, multiple linear regression and partial least squares regression) of their capabilities to model the new chromatographic response function and predict its value for new experiments. It was indicated that the most accurate models were achieved with neural networks, although partial least squares regression could also be used to solve the problem since it gives the major directions for the optimal settings of the variables.     

Lattice-fluid model for gas-liquid chromatography

Lattice-fluid models describe molecular ensembles in terms of the number of lattice sites occupied by molecular species (r-mers) and the interactions between neighboring molecules. The lattice-fluid model proposed by Sanchez and Lacombe (Macromolecules, 1978;11:1145-1156) was used to model specific retention volume data for a series of n-alkane solutes with n-alkane, polystyrene, and poly(dimethylsiloxane) stationary liquid phases. Theoretical equations were derived for the specific retention volume and also for the temperature dependence and limiting (high temperature) values for the specific retention volume. The model was used to predict retention volumes within 10% for the n-alkanes phases; 22% for polystyrene; and from 20 to 70% for PDMS using no adjustable parameters. The temperature derivative (enthalpy) could be calculated within 5% for all of the solutes in nine stationary liquid phases. The limiting value for the specific retention volume at high temperature (entropy controlled state) could be calculated within 10% for all of the systems. The limiting data also provided a new chromatographic method to measure the size parameter, r, for any chromatographic solute using characteristic and size parameters for the stationary phase only. The calculated size parameters of the solutes were consistent, i.e. independent of the stationary phase and agreed within experimental error with the size parameters previously reported from saturated vapor pressure, latent heat of vaporization or density data.     

Optimization of gradient separation for chromatographic fingerprint of herbal medicine: a predictive model combined with grid search

A four-step strategy is described which is aimed at optimizing the separation parameters of the chromatographic fingerprint of herbal medicines. In the optimization procedure, a model is built to predict the retention time of components. The proposed model shows good retention prediction potency with an average relative deviation of 1.78%. The grid search method is used in optimizing gradient parameters. In addition, an iterative procedure is adopted to further improve the prediction accuracy of the gradient retention time and the quality of the chromatogram. The whole optimization process has been validated by real samples.     

Optimizing the relationship between chromatographic efficiency and retention times in temperature‐programmed gas chromatography

A methodology that can maximise the chromatographic efficiency that can be achieved within a defined time frame in temperature‐programmed gas chromatography is described. The efficiency can be defined as the inverse of peak widths measured in retention index units. This parameter can be described by a model similar to the van Deemter equation, which is expanded to account for the effect of the temperature rate in addition to the effect of carrier gas velocity. The model of efficiency is found by response surface methodology, where the temperature rates and the carrier gas velocities are systematically varied in the experiments. A second model that accurately explains the retention time of the last eluting compound can be found from the same experiments, and optimal conditions are found by combining the two models. The methodology has been evaluated with four capillary columns and three carrier gases, using fatty acid methyl esters as analytes. All experiments showed that there is a fairly linear decrease in efficiency with increasing temperature rates. At any temperature rate, optimal velocity is only marginally higher than the velocity that maximises chromatographic efficiency, since the carrier gas velocity has a limited effect on the retention times.     

Computer-assisted method development and optimization in high-performance liquid chromatography

This paper reports the use of DryLab, a computer simulation software package, to assist in the development and optimization of a reversed-phase high-performance liquid chromatographic (HPLC) method for the separation of a model drug candidate and its degradation products. Prior to the optimization process, columns with various bonded phases are evaluated for their chromatographic performance using the sample of interest. Simultaneous optimization of two separation variables and the use of resolution maps to predict the optimal conditions are illustrated. Options to optimize column conditions (column length and flow-rate) to further reduce run time are briefly discussed. The accuracy of DryLab-predicted retention times and resolution is compared with experimental values. The DryLab software used in this study provided satisfactory predictions for the selected model, with average errors of less than 3.5 and 11.8% for retention time and resolution, respectively.     

Phase behaviour of SMA/PMMA blends: the influence of processing at low and high deformation rates

The influence of processing parameters (deformations) on SMA/PMMA blend phase behaviour is studied. It is found that injection moulding does change polymer blend phase behaviour. Phase separation kinetics are important to understand the injection moulding experiments and the kinetics are probably influenced by the deformations caused by the injection moulding proces. Capillary flow causes a complex change of polymer blend phase behaviour showing both deformation induced mixing and redemixing. Short capillaries, causing almost only uniaxial elongation in combination with pressure, cause no change to polymer blend phase behaviour. This is probably due to the short time the deformation is imposed to the material: it is expected that elongation is a main parameter causing changes in polymer blend phase behaviour. Parallel plate rheometer experiments show that applying only shear causes a complex change of phase behaviour showing both shear induced mixing and redemixing.     

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.     

Study on the concentration effects in size exclusion chromatography VII. A quantitative verification for the model theory of concentration and molecular mass dependences of hydrodynamic volumes for polydisperse polymers

A model theory of concentration effects for polydisperse polymers was proposed in 1988. It is successful in relating the concentration of the injected solution to the effective hydrodynamic volumes of peak, the retention volumes of peak and the polydispersity index (Dc = (Vhcw)/(Vhcn) of hydro-dynamic volume distribution for polydisperse polymers at a given concentration. The dependence of the concentration of injected polymer solution on the effective hydrodynamic volumes, the retention volumes of peak and the polydispersity index of hydrodynamic volume distribution for narrow disperse and polydisperse polystyrene, poly(dodecyl methacrylate), poly(tridecyl methacrylate) and poly(methyl methacrylate) in tetrahydrofuran solvent were studied. The proposed theory was verified by these experimental data. Results show that the proposed theory can predict the concentration effects in GPC for polydisperse polymers quantitatively and can provide a theoretical foundation for the two methods of calibrating the universal calibration curves with polydisperse polymers and of determining the second virial coefficients (A2) of polymers. It is found that the determined values of A2 for narrow disperse and polydisperse polymers by the proposed method are in agreement with those obtained by the LALLS method, and the two universal calibration curves with narrow disperse and polydisperse polymers are in excellent agreement.     

Quantitative aspects of gradient HPLC of copolymers from styrene and ethyl methacrylate

Summary Prerequisite of quantitative evaluation in chromatography is equivalence of sample composition and detector signal. This includes complete retention and proper elution of all sample constituents. In polymer HPLC, complete retention requires a poor starting eluent, a sufficiently active column, and a low ratio of injection volume to column volume. On small pore columns, insufficient retention caused the polymer to elute either in the interstitial volume (sample exclusion), together with the sample solvent, or immediately after the solvent plug.Stat-copoly(styrene/ethyl methacrylate) samples are more difficultly retained thanstat-copoly(styrene/acrylonitrile) specimes. With the former copolymer it could be shown that incomplete retention did not cause sample demixing. In order to gain complete retention, non-exclusion HPLC of polymers should be performed with columns whose solvent volume is at least 50 times as large as the injection volume. This consequence is of practical importance in chromatographic cross-fractionation where rather large volumes of SEC eluate are injected into the apparatus for gradient HPLC.     

Evaluation of high-performance liquid chromatography column retentivity using macromolecular probes. II. Silanophilic interactivity traced by highly polar polymers

A new method of HPLC column retentivity testing utilizes polymeric probes instead of conventional sets of low molar mass substances. The procedure allows at least semiquantitative, separate and independent evaluation of adsorption and partition properties of column packings. In this present work, the method is applied for comparison of the polar interactivities of selected silica gel C18 HPLC columns. It is shown that free silanols which remained on the surface of the end-capped silica C18 column packings are accessible for interaction with highly polar macromolecules. High molar mass polymeric test probes are adsorbed on the surface silanols and their retention volumes increase. As result, deviations from regular size-exclusion chromatographic (SEC) behavior are observed. The extent of retention volume changes depends on both the nature of polymer probes and on column packing type. Adsorption of macromolecules can be suppressed by addition of a highly polar substance to the mobile phase. The amount of polar additive which is needed to attain regular SEC elution of the polymer probe depends on the column packing type and can be used as a characteristic of silanophilic column interactivity. Courses of dependences of retention volumes on sizes of macromolecules indicate the presence of "U-turn" adsorption which allows two and more silanols situated among C18 groups to be occupied simultaneously with the same macromolecule.     

基于遗传算法的色谱指纹峰配对识别方法

指纹峰配对识别是色谱指纹图谱分析中的关键环节之一，本文提出一种基于遗传算法的色谱指纹峰配对识别方法。该法根据对照色谱指纹图谱的峰分布特性初选出若干标定蜂，将其存入一个候选标定蜂库；同时根据这些候选标定峰从待测指纹图谱中选出相应的候选标定峰，也存入候选标定峰库；再用遗传算法从库中选取一组标定峰用于校正待测指纹图谱中各峰的峰位，并自动识别出与对照色谱指纹图谱相对应的各指纹峰。仿真实验及实际分析实验结果均表明，该法识别指纹峰准确可靠，可用于色谱指纹图谱相似度的快速自动计算。     

Enthalpy assisted size exclusion chromatography. Part 2. Adsorption retention mechanism

A novel high performance liquid chromatographic method for separation of synthetic polymers has been tested. It involves combination of the enthalpic and entropic retention mechanisms, resulting in increased selectivity of separation within a specific molar mass range. In this present case, the enthalpic retention mechanism is adsorption of macromolecules on a bare silica gel column packing. Under critical conditions of enthalpic interactions, homopolymers are known to elute irrespective of their molar mass. However, in the vicinity of critical conditions, a situation can be identified when retention volumes (V(R)) rapidly decrease with increasing molar mass. Typically, this happens for polymer species close to or above their exclusion limit observed with the same column in the absence of enthalpic interactions between macromolecules and packing, that is near "ideal SEC" conditions. The dependence of polymer retention volume on molar mass closely resembles size exclusion conditions. However, the witnessed rate of change in V(R )with polymer molar mass is more pronounced, thus indicating increased selectivity of separation. This situation not only offers the benefit of more selective separation according to molar mass but efficient discrimination of macromolecules possessing different nature and interactivity with the column packing can be accomplished as well.     

Experimental designs for modeling retention patterns and separation efficiency in analysis of fatty acid methyl esters by gas chromatography-mass spectrometry

The retention behavior of components analyzed by chromatography varies with instrumental settings. Being able to predict how changes in these settings alter the elution pattern is useful, both with regards to component identification, as well as with regards to optimization of the chromatographic system. In this work, it is shown how experimental designs can be used for this purpose. Different experimental designs for response surface modeling of the separation of fatty acid methyl esters (FAME) as function of chromatographic conditions in GC have been evaluated. Full factorial, central composite, Doehlert and Box-Behnken designs were applied. A mixture of 38 FAMEs was separated on a polar cyanopropyl substituted polysilphenylene-siloxane phase capillary column. The temperature gradient, the start temperature of the gradient, and the carrier gas velocity were varied in the experiments. The modeled responses, as functions of chromatographic conditions, were retention time, retention indices, peak widths, separation efficiency and resolution between selected peak pairs. The designs that allowed inclusion of quadratic terms among the predictors performed significantly better than factorial design. Box-Behnken design provided the best results for prediction of retention, but the differences between the central composite, Doehlert and Box-Behnken designs were small. Retention indices could be modeled with much better accuracy than retention times. However, because the errors of predicted tR of closely eluting peaks were highly correlated, models of resolution (Rs) that were based on retention time had errors in the same range as corresponding models based on ECL.