Characterization of Metallo Bis(terpyridine) Diblock Polymers by Nonaqueous Capillary Zone Electrophoresis

A method of nonaqueous capillary zone electrophoresis (CZE) has been developed to characterize block (co)polymers of poly(ethylene oxide) and poly(styrene) containing metallo bis(terpyridine) complexes as bridging units. Specific CZE separation conditions had to be applied, with barium perchlorate dissolved in N-methylformamide (NMF) as background electrolyte and OV-1701-OH deactivated capillaries. For detection UV absorption was measured at a wavelength of 316 nm. Metallo diblock polymers with molecular weights up to 30,000 Da could be analyzed by the proposed nonaqueous CZE method. Experiments performed with polymeric compounds containing Fe, Ni or Ru as central metal ions showed that their electrophoretic mobilities were independent of the type of metal ion. Therefore, the data on the size of the polymeric compounds could be obtained using just one set of calibration standards. Polydispersities of the samples calculated from the experimental results were in correlation with the polydispersities of the polymers used in the synthesis of the metallo diblock polymers. Several polymeric samples contained metallo mono(terpyridine) complexes as impurities. These by-products could be separated from the main product. With symmetrical diblock polymers only one by-product was detected, while with an asymmetric diblock polymer two types of mono-complexes were found. The amount of the mono-complexes present as impurities was dependent on the type of central metal ion (Ni > Fe >> Ru).     

On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002     

The effects of the column pressure drop on retention and efficiency in packed and open tubular supercritical fluid chromatography

The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available.     

Breakthrough of polymers in interactive liquid chromatography

Two separate peaks are observed for narrow polymer standards in both isocratic and gradient HPLC. One peak appears around the solvent front (the "solvent-plug peak" or "breakthrough peak"), whereas the second peak is retained significantly--or even highly. Although the effect has been observed many times before, it has never been rigorously explained. In this paper we provide a detailed explanation for the breakthrough peak. The two completely separate peaks are demonstrated not to represent to different fractions of the sample (e.g., the low- and high-molecular-mass parts of the distribution). Both peaks are representative of the entire polymeric sample for narrow polymer standard. Because the amount of the polymer in the breakthrough peak may vary, the quantitative analysis of the polymers by LC is jeopardized. The effects of the sample solvent, the (initial) mobile phase composition, the injection volume, the injected sample concentration, the column temperature, and the analyte structure and molecular mass on the breakthrough peak were investigated in LC experiments involving standards of polystyrene and poly(methyl methacrylate). Three necessary and sufficient conditionsare suggested for the breakthrough phenomenon to be observed. Recommendations to avoid the breakthrough phenomenon are given, culminating in a structured method for selecting the best possible sample solvents.     

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.     

Optimisation of the chlorthalidone chiral separation by capillary electrochromatography using an achiral stationary phase and cyclodextrin in the mobile phase

The separation of chlorthalidone enantiomers in capillary electrochromatography on an achiral stationary phase when adding a chiral selector, hydroxypropyl-β-cyclodextrin, to the mobile phase, was optimised. The goal was to investigate the feasibility of modelling retention times and resolution when during the optimisation procedure regular replacement of columns is required due to their fragility. Therefore, it is essential that the packing procedure delivers reproducible columns. The optimisation of an existing chlorthalidone separation was chosen as case study. The influence of two factors, chiral selector concentration and organic modifier content, on the responses was modelled. The experiments performed prior to modelling were defined by a central composite design. Results on different columns, obtained under identical experimental conditions, were found comparable and thus modelling was possible in situations where several columns were required to complete a design. A second-order polynomial model was built for both responses. Optimal separations were also predicted using Derringer’s desirability functions. The optimum was found at 33 mM cyclodextrin and 16% (v/v) acetonitrile on two types of columns (with different packing times) leading to a strong reduction in analysis time for an equally good separation compared to the initial conditions. Measured and predicted responses were found comparable, indicating that acceptable models were obtained.     

Contactless conductivity detection of synthetic polymers in non-aqueous size-exclusion electrokinetic chromatography

A capacitively coupled contactless conductivity detection (CCD) system has been applied for the detection of neutral synthetic polymers in capillary size-exclusion electrokinetic chromatography (SEEC). Polystyrene standards, that were used as a model compounds, were separated on a capillary column packed with porous 10 microm silica particles with an electrokinetically driven mobile phase, and detected by CCD and UV detection simultaneously. Mass-calibration curves for polystyrene were constructed. Satisfactory results were obtained for the linearity, the run-to-run repeatability (<0.2% for the relative retention and <4% for the peak area) and the robustness of the detector. One of the major issues in this preliminary study was to investigate the origin of the peaks observed for the polystyrene standards. The effect of the molar mass of the polystyrenes on the sensitivity was small. Therefore, the signals obtained could not be explained as the result of an increased viscosity and a decreased solution conductivity of the solute zone. An alternative hypothesis is suggested, and recommendations for further research are given.