Martin’s rule revisited

Separation of Molar Weight-Distributed Polyethylene Glycols by Reversed-Phase Chromatography—Analysis and Modeling Based on Isocratic Analytical-Scale Investigations

The separation of polyethylene glycols (PEGs) into single homologs by reversed-phase chromatography is investigated experimentally and theoretically. The used core–shell column is shown to achieve the baseline separation of PEG homologs up to molar weights of at least 5000 g/mol. A detailed study is performed elucidating the role of the operating conditions, including the temperature, eluent composition, and degree of polymerization of the polymer. Applying Martin’s rule yields a simple model for retention times that holds for a wide range of conditions. In combination with relations for column efficiency, the role of the operating conditions is discussed, and separations are predicted for analytical-scale chromatography. Finally, the approach is included in an efficient process model based on discrete convolution, which is demonstrated to predict with high accuracy also advanced operating modes with arbitrary injection profiles.

Influence of Microstructure on the Elution Behavior of Gradient Copolymers in Different Modes of Liquid Interaction Chromatography

We studied the influence of microstructure on the chromatographic behavior of gradient copolymers with different gradient strengths and block copolymer with completely segregated blocks by using gradient liquid adsorption chromatography (gLAC) and liquid chromatography at critical conditions (LCCC) for one of the copolymer constituents. The copolymers consist of repeating units of poly(propylene oxide) and poly(propylene phthalate) and have comparable average chemical composition and molar mass, and a narrow molar mass distribution to avoid as much as possible the influence of these parameters on the elution behavior of the copolymers. On both reversed stationary phases, the elution volume of gradient copolymers increases with the increasing strength of the gradient. The results indicate that for both modes of liquid interaction chromatography, it is important to consider the effect of microstructure on the elution behavior of the gradient copolymers in addition to the copolymer chemical composition and molar mass in the case of gLAC and the length of the chromatographically visible copolymer constituent in the case of LCCC.

Revisiting molecular adsorption: unconventional uptake of polymer chains from solution into sub-nanoporous media

Adsorption of polymers from the solution phase has been extensively studied to cope with many demands not only for separation technologies, but also for the development of coatings, adhesives, and biocompatible materials. Most studies hitherto focus on adsorption on flat surfaces and mesoporous adsorbents with open frameworks, plausibly because of the preconceived notion that it is unlikely for polymers to enter a pore with a diameter that is smaller than the gyration diameter of the polymer in solution; therefore, sub-nanoporous materials are rarely considered as a polymer adsorption medium. Here we report that polyethylene glycols (PEGs) are adsorbed into sub-nanometer one-dimensional (1D) pores of metal-organic frameworks (MOFs) from various solvents. Isothermal adsorption experiments reveal a unique solvent dependence, which is explained by the balance between polymer solvation propensity for each solvent and enthalpic contributions that compensate for potential entropic losses from uncoiling upon pore admission. In addition, adsorption kinetics identify a peculiar molecular weight (MW) dependence. While short PEGs are adsorbed faster than long ones in single-component adsorption experiments, the opposite trend was observed in double-component competitive experiments. A two-step insertion process consisting of (1) an enthalpy-driven recognition step followed by (2) diffusion regulated infiltration in the restricted 1D channels explains the intriguing selectivity of polymer uptake. Furthermore, liquid chromatography using the MOFs as the stationary phase resulted in significant PEG retention that depends on the MW and temperature. This study provides further insights into the mechanism and thermodynamics behind the present polymer adsorption system, rendering it as a promising method for polymer analysis and separation.

Temperature Gradient Interaction Chromatography: A Perspective

The application of temperature gradient interaction chromatography (TGIC) as an advanced technique for the characterisation of polymers is discussed, in comparison to other liquid chromatography techniques and in particular the ubiquitous size exclusion chromatography. Specifically, the use of reversed-phase TGIC for the interrogation of complex branched polymers and normal-phase TGIC for characterisation of high-molar mass end-functionalised polymers is highlighted.

Application of two-dimensional chromatography to the characterization of macromolecules and biomacromolecules

Modern polymeric materials are heterogeneous with respect to different structural features, for instance molar mass, composition, and architecture. One-dimensional separation methods such as size-exclusion chromatography (SEC) are insufficient to fully resolve the multidimensional distributions of such complex materials. Therefore, two-dimensional separation methods are increasingly employed to characterize macromolecules. The present article describes in detail the advantages and experimental aspects of two-dimensional macromolecular separations. Selected examples will be discussed to explain the strategies used to separate macromolecules with respect to specific structural features.

Separation of poly(styrene-block-t-butyl methacrylate) copolymers by various liquid chromatography techniques

The separation of a mixture of three poly(styrene-block-t-butyl methacrylate) copolymers (PS-b-PtBMA), consisting of polystyrene (PS) blocks of similar length and t-butyl methacrylate (PtBMA) blocks of different lengths, was performed using various chromatographic techniques, that is, a gradient liquid chromatography on reversed-phase (C18 and C8) and normal-phase columns, a liquid chromatography under critical conditions for polystyrene as well as a fully automated two-dimensional liquid chromatography that separates block copolymers by chemical composition in the first dimension and by molar mass in the second dimension. The results show that a partial separation of the mixture of PS-b-PtBMA copolymers can be achieved only by gradient liquid chromatography on reversed-phase columns. The coelution of the two block copolymers is ascribed to a much shorter PtBMA block length, compared to the PS block, as well as a small difference in the length of the PtBMA block in two of these copolymers, which was confirmed by SEC-MALS and NMR spectroscopy.

Separation of all oligomers in polyethylene glycols and their monomethyl ethers by one-dimensional liquid chromatography

Different polymer homologous series having the same repeat unit, but different end groups, can be separated by one-dimensional LAC according to the number of repeat units and functionality, if a favorable combination of the interaction parameters of the repeat unit and the end groups can be found. As an example, polyethylene glycol (PEG) can be determined in PEG monomethyl ethers. The molar mass distribution of the minor component in such samples can be determined even at concentrations of a few percent.

Signal processing of GC–MS data of complex environmental samples: Characterization of homologous series

Identification and characterization of homologous series by GC-MS analysis provide very relevant information on organic compounds in complex mixtures. A chemometric approach, based on the study of the autocovariance function, EACVF(tot), is described as a suitable tool for extracting molecular-structural information from the GC signal, in particular for identifying the presence of homologous series and quantifying the number of their terms. A data pre-processing procedure is introduced to transform the time axis in order to display a strictly homogenous retention pattern: n-alkanes are used as external standard to stretch or shrink the original chromatogram in order to build up a linear GC retention scale. This addition can be regarded as a further step in the direction of a signal processing procedure for achieving a systematic characterization of complex mixture from experimental chromatograms. The EACVF(tot) was computed on the linearized chromatogram: if the sample presents terms of homologous series, the EACVF(tot) plot shows well-defined deterministic peaks at repeated constant interdistances. By comparison with standard references, the presence of such peaks is diagnostic for the presence of the ordered series, their position can be related to the chemical structure of the compounds, their height is the basis for estimating the number of terms in the series. The power of the procedure can be magnified by studying SIM chromatograms acquired at specific m/z values characteristic of the compounds of interest: the EACVF(tot) on these selective signals makes it possible to confirm the results obtained from an unknown mixture and check their reliability. The procedure was validated on standard mixtures of known composition and applied to an unknown gas oil sample. In particular, the paper focuses on the study of two specific classes of compounds: n-alkanes and oxygen-containing compounds, since their identification provides information useful for characterizing the chemical composition of many samples of different origin. The robustness of the method was tested in experimental chromatograms obtained under unfavorable conditions: chromatograms acquired in non-optimal temperature program conditions and chromatographic data affected by signal noise.

Characterization of different reversed phase systems in liquid adsorption chromatography of polymer homologous series

The interaction parameter of a given repeat unit in liquid adsorption chromatography (LAC) can be determined from the slope in a plot of the elution volumes versus the difference in elution volumes of subsequent monomers. In such a plot, the intercept represents the void volume, and from the slope the adsorption interaction parameter can be calculated. This parameter is independent of column dimensions and pore diameter and can thus be used as a measure of the interaction of a given repeat unit with the surface of a stationary phase in a given mobile phase composition. The interaction parameter can also be obtained from the slope in a plot of the logarithmic retention factors k versus the number of repeat units n or from the slope in a plot of the logarithmic difference in elution volumes of subsequent monomers versus n. The values obtained by the three different approaches are in good agreement. In a given mobile phase, the interaction parameter of a given repeat unit was found to be almost the same for various alkyl bonded columns from different producers. The retention of a given oligomer depends as well on the interaction parameter as on the pore dimensions (and thus the internal pore surface) of the stationary phase. The pore surface can be determined from the intercept in a plot of the logarithmic difference in elution volumes of (subsequent) nonfunctional monomers as a function of n. As the interaction parameter of a given repeat unit in a given mobile phase is the same for stationary phases with the same chemical nature, retention can be adjusted by selection of the pore surface. On a given stationary phase, there is a linear dependence between interaction parameter and mobile phase composition.

Determination of the accessible volume and the interaction parameter in the adsorption mode of liquid chromatography

The main physical parameters in liquid chromatography of oligomers-the accessible volume and the adsorption interaction parameter-are discussed. It is shown, that in liquid adsorption chromatography (LAC) there is a linear relation between elution volume and the distance of two subsequent peaks of a homologous series. From the intercept of the regression lines in such a plot the accessible volume can be easily determined at any mobile phase in LAC (corresponding to conditions of weak or strong adsorption) without any information about the molar mass of the peaks. From the slope of this dependence the adsorption interaction parameter of a given repeat unit can be obtained. The accurate determination of the accessible volume and the adsorption interaction parameter in the LAC regime is presented for PEG, PPG and fatty alcohols on various reversed phase columns with different pore size in methanol-water or acetone-water mobile phases. The difference between the void volume, the dead volume or hold-up volume (from the solvent peak position) and the accessible volume (obtained by this procedure) is discussed.

Looking inside the pores of a chromatographic column

The dependence of void volume and pore volume on mobile phase composition was studied on a reversed phase column based on poly(divinyl benzene) in mobile phases consisting of 100% tetrahydrofuran (THF) and 40-90% THF-water. Void volumes V0 are obtained from a series of polymers with different molar mass by extrapolation of elution volume to M = 0, the interstitial volume Vi from the elution volume of polymers with a sufficiently high molar mass. The pore volume Vp is obtained as the difference (V0 - Vi). While Vi does not depend on mobile phase composition, a dramatic decrease of the pore volume is observed, when the mobile phase is changed from THF to THF-water. This effect of the mobile phase composition on the pore volume is observed using PEG and PPG as test macromolecules, regardless the retention mechanism: at 40-50% THF both PEG (in exclusion mode) and PPG (in adsorption mode) experience the same reduced pore volume, which is considerably lower than that in 100% THF.

Selectivity of electrospray response in small polymer analysis by mass spectrometry

The selectivity of electrospray was explored for a small poly(ethylene)glycol by comparing the oligomer response obtained from direct polymer introduction in flow injection analysis with the signal recorded in high-performance liquid chromatography/mass spectrometry (HPLC/MS). When the oligomer mixture was ionized, a suppression effect was measured for all but the more hydrophobic congeners for which the response was enhanced. This result would reflect the influence of electrospray droplet chemical composition on the equilibrium partitioning coefficient in Enke's model. On average, the electrospray selectivity observed for the studied poly(ethylene)glycol did not affect the molecular weight distribution parameters as response for the most concentrated oligomers was suppressed to the same extent while over-expressed largest congeners had a low contribution to the total polymer sample.

A thermodynamic study of retention of poly(ethylene glycol)s in liquid adsorption chromatography on reversed phases

The retention behaviour of poly(ethylene glycol)s (PEGs) on various reversed phase columns has been studied in liquid interaction chromatography at different temperatures. Similar separations could be achieved in different mobile phases. In methanol-water practically no temperature dependence was observed, while in acetone-water retention decreased with increasing temperature. From the van't Hoff plots the thermodynamic parameters were calculated, which showed, that retention is driven by enthalpy in methanol-water, while in acetone-water the driving force is entropy.

Molar mass distributions by gradient liquid chromatography: predicting and tailoring selectivity

Interactive liquid chromatography (iLC) for polymer analysis is usually applied to the characterisation of distributions other than molar mass. In particular, its use for the determination of chemical-composition, functionality-type and tacticity distributions has been demonstrated. The application of iLC for the determination of molar mass distributions (MMDs), however, has not yet been fully explored. An expanded version of the reversed-phase liquid chromatography model has been developed to describe and predict how the retention behaviour of polydisperse polystyrene samples changes with molar mass. The relationship between molar mass and the parameters of the model has been investigated in some detail and non-linear correlations were found. From the model and the relationships between the model parameters and molar mass, calibration curves (retention time versus molar mass) were constructed to predict changes in chromatographic selectivity across a given molar mass range. These calibration curves were compared to experimentally obtained curves and, in most cases, excellent agreement was found. The dramatic enhancement in selectivity that can be obtained with iLC in comparison to size-exclusion chromatography (SEC) was illustrated by measuring matrix-assisted laser desorption ionisation (MALDI) MS spectra of fractions collected during a gradient-LC separation. In the low-molar mass range, essentially monodisperse fractions were obtained. Calibration curves, predicted by the model and validated experimentally using narrow-dispersity standards and MALDI-MS spectra of fractions, were used to determine the molar mass distribution of some narrowly distributed polystyrene samples. Molar mass distributions for such standards were found to be somewhat lower than the values reported by the manufacturers. The results also deviated from those obtained by MALDI-MS.

Accurate prediction of the retention behaviour of polydisperse macromolecules based on a minimum number of experiments

This study illustrates how retention models can be used to accurately predict the retention behaviour of polydisperse macromolecules in LC separations. It highlights that the number of experiments required can be drastically reduced when the relationship between the model parameters and molecular structure parameters (e.g. molar mass) can be incorporated into one global model. A practical implication of this work is that an appropriate model can then be used for the determination of molar-mass distributions for polydisperse samples. The globalised model can predict retention time as a function of molar mass and gradient slope. Both the original and globalised versions of the model were rigorously validated in terms of the difference between the predicted and experimental retention times. The original model had very low residuals and there was no apparent dependence of the errors on the applied gradient, the molar mass or the retention times. Confidence intervals for the model parameters (S and ln k0) were determined using a bootstrapping analysis of the residual errors in the predicted retention times. Confidence intervals were seen to broaden significantly as the mass of the polymer increased. The parameters were also seen to be highly correlated. For the global model, retention-time residuals remained quite low, even when the number of experiments used to determine the model parameters was reduced from approximately 100 to 10.

Thermodynamic study of retention in liquid exclusion–adsorption chromatography

The retention behaviour of fatty alcohol ethoxylates and fatty acid methyl ester ethoxylates on various reversed-phase columns in acetone-water has been studied in the regime of liquid exclusion-adsorption chromatography at different temperatures. Straight lines were obtained in the van't Hoff plots. The entropy and enthalpy changes were found to be negative (at least in the range of lower oligomers) and showed a dependence of the number of oxyethylene units. For higher oligomers, both entropy and enthalpy changes approach a constant value. This can be explained by the existence of a rather thick layer of organic solvent close to the surface of the stationary phase.