Treating the polyelectrolytes as polymers with a draining effect. II. The behavior in the gel permeation chromatography

The behavior of the polyelectrolytes in the gel permeation chromatography (GPC) can be better understood if the modified universal calibration (log([η]M/Φ) vs. elution volume) is used instead of the “classical” universal calibration (log[η]M vs. elution volume). The value of Flory's parameter Φ is obtained from an equation established for nonionic polymers presenting a draining effect, considering that polyelectrolytes also behave as polymers with a draining effect. The modified universal calibration does not apply as successfully to polyelectrolytes as to nonionic polymers, because of their electrostatic exclusion in the pore surface of the GPC columns. Nevertheless, when polyelectrolytes are found in a high salt concentration solution, the modified universal calibration can be used to obtain their molecular mass, using nonionic hydrosoluble polymers as standard polymers. Moreover, considering polyelectrolytes as polymers presenting a draining effect and applying the modified universal calibration provides a better explanation for the electrostatic exclusion of these polymers from the pores of the GPC columns, using the Dubin–Tecklenburg model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1106–1113, 2006     

Gel permeation chromatography: On the shape of the calibration plot and molecular size separability

Data obtained from the calibration of GPC columns of different permeabilities with standard polystyrenes are reported. For single columns the logarithm molecular weight–elution volume plot is linear for approximately one and one-half decades in molecular weight. GPC separations are such that the separability of two samples of similar molecular weight improves as their mean molecular weight decreases. Because of this the analysis of high molecular weight polymers can best be accomplished on a series of columns in which each column has a high permeability limit. The elution volume for columns in series is shown to be the sum of the elution volumes of the individual columns. As higher molecular weights are eluted a pronounced tailing effect is observed.     

Applicability of the modified universal calibration of gel permeation chromatography on proteins

The modified universal calibration of gel permeation chromatography (GPC) has been applied in the case of native proteins. Plotting log([eta]M/Phi) versus elution volume, instead of log[eta]M versus elution volume used till now, we obtain unique curves with different proteins and non-proteonic polymers ([eta]: intrinsic viscosity, M: molecular mass, Phi: Flory's parameter). The values of Flory's parameter Phi are calculated for each protein using an indirect method based on GPC.     

Determination of polymer branching with gel-permeation chromatography. I. Theory

The effect of long-and short-chain branching in polymer molecules on gel-permeation chromatographic (GPC) separation is discussed. The calculation of calibration curves for branched polymers is developed from the universal calibration technique based on the hydrodynamic volume concept and previously established relationships for the effect of branching on molecular dimensions. Typical calibration curves are shown for different branching models and degrees of branching. As branching increases, the curves are shown to converge. Methods of characterizing branching and molecular weight distributions of franctions and whole polymers from GPC and intrinsic viscosity data are presented.     

Universal calibration in GPC: A study of polystyrene,poly-α-methylstyrene,and polypropylene

The theoretical justification for using M[_η], or a similar quantity, as a universal calibration parameter in GPC is reviewed. The equation based on this parameter is applied to transform the primary calibration curve, obtained by means of polystyrene samples, into calibration curves for poly-α-methylstyrene, polypropylene, and linear polyethylene. The Mark–Houwink equations for these polymers, as they are used in the transformation, are discussed. The resulting GPC calibration curves are compared with molecular weights and peak elution volumes of fractionated poly-α-methylstyrene and polypropylene. The same comparison is made with samples of polypropylene and polyethylene having very broad molecular weight distributions. The agreement lies within experimental error.     

Ein verfahren zur eichung der gelchromatographie (GPC) mit präparaten beliebiger,bekannter molekulargewichtsverteilung

If, in GPC calibration, the mean elution volume (or centre of gravity volume) of the elution curves obtained with monomolecular samples is used, the mean elution volume of a polymolecular mixture is a weight-average. According to the calibration curve, a molecular weight average can be attributed to the mean elution volume. For the special case of a logarithmic-linear calibration curve, this is the geometric (weight) mean of the molecular weight. Thus one can perform broad-standard calibration of GPC without interference by column dispersion. The potential application for non-linear calibration curves is discussed. It is considered how calibration functions for the higher moments of the monomolecular elution curves could be determined and how universal calibration should be performed if the standards are polydisperse relative to hydrodynamic volume. Absolute determination of polydispersity becomes possible with an additional z-detector.     

Molecular weight determination of acrylonitrile polymers by gel permeation chromatography in N,N-dimethylformamide

Peculiar elution behavior of the GPC of acrylonitrile polymers was investigated. The peculiarity was considered to be due to some substances which form a supermolecular structure with acrylonitrile polymers to cause a large UV absorption, detectable at 280 nm. The Mark-Houwink-Sakurada parameters of acrylonitrile polymers in 0.01M LiBr-DMF at 60°C, needed for GPC universal calibration, were determined to be K=2.12 × 10⁻⁴ and a=0.75. The parameters obtained by us were different from the ones by other investigators, however, these values were reasonable for random coil polymers. The addition of inorganic salt, such as LiBr, in DMF removed the peculiar elution behavior of the GPC. The universal calibration using monodisperse poly(ethylene oxide) standards and the Mark-Houwink-Sakurada parameters could be applied for the determination of the molecular weights. The invalidity of the universal calibration for acrylonitrile polymers in DMF containing LiBr, seems to be caused by the difficulty in the determination of the molecular weight of polyacrylonitrile standards by absolute methods, such as light scattering and osmometry.     

Universal calibration in GPC

The M[η]-elution volume calibration curve for gel-permeation chromatography (GPC) is based on the implicit assumption that the hydrodynamic volume of a solvated polymer species in the GPC columns is that which pertains at infinite dilution. This is not true of highly solvated high molecular weight fractions and results in apparent failure of this calibration in some instances. A model is presented to estimate hydrodynamic volumes of polymers at finite concentrations. The parameters required are polymer concentration, molecular weight, amorphous density, and the Mark-Houwink constants for the particular polymer–solvent combination. The calculated log (hydrodynamic volume)–elution volume relation provides a universal GPC calibration. The model accounts for the occasional shortcomings of the infinite dilution calibration and is essentially equivalent to it in noncritical cases. The use of the proposed calibration method is illustrated.     

Evaluation of a Commercial Differential Viscometer as a GPC Detector and Its Application to Polymer Characterization

Abstract

When used as a GPC detector, Viscotek's differential viscometer (DV) measures specific viscosities at each elution volume across the chromatogram. With the addition of a concentration detector, intrinsic viscosities may be calculated. As a result, true molecular weights can be calculated via the universal calibration method.

It was found that true molecular weights and branching analysis obtained using DV for acrylate polymers initiated by VAZO and benzoyl peroxide show excellent agreement with those from low angle laser light scattering (LALLS) measurement. Moreover, comparison of intrinsic viscosities for different polymers at the same molecular weights can be made from the DV technique. In general, linear polymers will have a higher IV than branches ones and the concept has been verified for acrylate polymers in this work.

A comparison between DV and LALLS in terms of capabilities, ease of use, and maintenance is also included.     

On-line viscometry combined with gel permeation chromatography. I. Instrumental calibration and testing with linear polymers

Gel permeation chromatography (GPC) was combined with flow time measurements on the eluent to provide both the distribution of hydrodynamic volumes and the distribution of intrinsic viscosities in linear polymers. Standard polystyrene samples were used to establish a universal hydrodynamic volume calibration as well as the zone spreading and viscometer transfer line tailing parameters. Viscometry data are particularly helpful in establishing the zone spreading parameters and the calibration curve at very high molecular weights. The results were applied to measurements on samples of linear polybutadiene and polyvinyl acetate. Agreement between values of M _w from GPC with those obtained by light scattering confirmed the universal calibration principle.     

Separation of complex branched polymers by size-exclusion chromatography probed with multiple detection

Size-exclusion chromatography (SEC) separates polymers by hydrodynamic volume (the universal calibration principle). Molecular weights can be determined using viscometry (relying on universal calibration) and light scattering (independent of universal calibration). In the case of complex branched polyacrylates with tetrahydrofuran as eluent, universal calibration is valid, although the separation in term of molecular weight is incomplete: a given elution slice contains a range of molecular weights, described in terms of a 'local polydispersity'. The local polydispersity index decreases when the number of branches per chain increases and complete separation is reached for highly branched chains.     

The determination of the molecular weight distribution of amylose by gel permeation chromatography

The universal calibration for gel permeation chromatography (GPC) has been applied to amylose and dextrans. The molecular weight distribution of amylose has been measured starting from known data on dextrans. The agreement found between the molecular weight averages resulting from GPC and those obtained by other methods justifies the procedure followed. The GPC measurements were performed with dimethylsulfoxide as the elution solvent and deactivated silica gel (Porasil) as the column-filling material.     

Simulation of GPC‐Distribution Coefficients of Linear and Star‐Shaped Molecules in Spherical Pores

Simulations of the distribution coefficients of linear and star‐shaped polymers in spherical pores were performed in order to predict the GPC‐elution behavior of star‐shaped polymers relative to that of linear polymers. Self avoiding walks were generated on a tetrahedral lattice to simulate good solvent conditions. It was found that neither the molecular weight nor the mean squared radius of gyration of the polymer serves as a universal factor to determine the distribution coefficient. However, the calculated distribution coefficients correlate well with the calculated hydrodynamic radii even for different topologies. For molecules at same elution volume the ratios of molecular weights of star and linear polymer agree well with exact calculations for Gaussian chains. These ratios are nearly independent of pore geometry (spherical or cylindrical).     

Substrate–polymer interactions in liquid exclusion chromatography (GPC) in N,N-dimethylformamide

The importance of nonexclusion effects in the GPC behavior of several stationary phases was investigated with DMF, 0.01M LiBr, as the mobile phase. Various low MW solutes and narrow MWD polymers, encompassing a wide range of polarities, were studied. The elution of the polymers was examined in terms of “universal calibration” behavior. Styragel and silanized glass both exhibit affinity for apolar polymers in DMF; for the former substrate this effect shows a strong inverse dependence on MW. As a consequence, application of polystyrene calibration curves to GPC analysis of more polar polymers with these substrates leads to overestimations of MW parameters. These errors are not corrected when universal calibration procedures are used. Ideal exclusion chromatography is exhibited by a number of polymers on untreated porous glass substrates. However, polymers with strong hydrogen-bonding functionality appear to be susceptible to marked adsorption in this system.     

Development of gel permeation chromatography for polymer characterization. II. Universal calibration

GPC appearance volumes have been determined for a series of linear polyethylene, polystyrene, and polybutadiene fractions (M_w/M_n < 1.1) in trichlorobenzene at 130°C. and for the latter two series in tetrahydrofuran at 23°C. A polymer-type independent relationship between appearance volumes and the equivalent hydrodynamic radii of the polymer molecules has been demonstrated. The equivalent hydrodynamic radius is calculated from intrinsic viscosity data. It is proposed that this relationship can be used to construct a universal GPC calibration curve for polymers that assume a spherical conformation in solution. Methods for applying the universal curve to the determination of molecular weight averages and molecular weight distribution are described. In addition, a method is outlined by which the universal calibration curve can be empolyed for determining number-average Mark-Houwink constants from polydisperse samples.     

从特性粘数和GPC图谱获得重均分子量的新方法

本文提出了从未知样品的特性粘数和GPC图谱计算重均分子量的新方法,该方法可用于计算窄分布和宽分布的未知Mark-Houwink 常数的样品的重均分子量。用七个不同分子量和不同分布的实例验证了所提出的方法。结果与已知Mark-Houwink常数用普适校准法得到的结果一致。     

Viscosimetric detection in size-exclusion chromatography (SEC/GPC): The Goldwasser method and beyond

Size-exclusion chromatography (SEC or GPC) is the most widely used separation method to characterize polymers. The high level of complexity of most polymeric materials necessitates the use of not only concentration-sensitive detection but also structure-sensitive detection. Viscometry is usually used in conjunction with a concentration-sensitive detector and universal calibration to determine molecular weights of polymers. Goldwasser proposed to use a viscometer as a single detector to determine number-average molecular weights, M(n) (ACS Symposium Series, 521, 143). The method is particularly of interest when concentration-sensitive detection is not available, because the sample is isorefractive or not UV-absorbing, or because composition is not constant (copolymers). It has known very little applications so far. It actually does not only allow determining M(n), but also the number hydrodynamic volume distribution. This opens a wider range of applications for the Goldwasser method. Size-exclusion chromatography only yields inaccurate molecular weight distributions for some complex branched polymers. Hydrodynamic volume distributions have then a strong potential for comparative studies owing to their far higher accuracy. Our experimental tests highlight the fact that the method is highly sensitive to noise and careful optimization of the injection concentration is needed, but number distribution can be obtained as well as M(n).     

Universal Calibration and Molecular Weight Averages in Gel Permeation Chromatography Illustrated by Cellulose Nitrate and Poly(oxypropylene)

Abstract

The nature of the averaging process in the analysis of gel permeation chromatograms was examined for cases where the molecules in the detector cell of the apparatus were of different molecular weight and of the same molecular weight. When the molecules have the same molecular weight, the hydrodynamic volume (1), [?]M, averaged across a chromatogram was found to become KM^a+1 for any molecular weight average at the elution volume corresponding to that average. [η] is intrinsic viscosity, M is molecular weight, and K and a are the appropriate Mark-Houwink constants. Thus when size separation is by molecular weight, the universal GPC calibration functions include KM_n ^a+1 where M_n is the number average molecular weight.

Cellulose nitrate and poly(oxypropylene) were analyzed using three sets of columns and two GPC instruments. KM_n ^a+1, KM_w ^a+1, and [η]M_w were found to represent the hydrodynamic volume since these functions fell on the universal calibration plot for nearly nono-disperse polystyrene standards. The function [η]M_n was displaced from the polystyrene universal calibration plot by factor which equaled M_w/M_n. The slopes and intercepts of the universal calibration plots were found to be completely consistent with the slopes and intercepts of the molecular weight calibration plots showing that the Mark-Houwink constants were correct. Intrinsic viscosity - molecular weight relations were presented for 12.0–12.6%N cellulose nitrate and for low molecular weight poly(oxypropylene), the latter relation being a correction of that of Sholtan and Lie (18).     

GPC analysis of model compounds. I. Phenyl- and benzo-substituted aromatic compounds

A series of 36 compounds of known structure was used in a study to elucidate the mechanism of separation of gel-permeation chromatography (GPC). The various molecular dimensions were defined and measured for these compounds. The elution volume for these compounds was determined by GPC under specified and controlled conditions. The relationships between elution volume and molecular dimension were investigated using computer-based statistical analysis for the entire set of compounds and manual simultaneous equations for smaller sets of compounds. It was found that, as increasingly more molecular dimensions are considered, (1) the importance of the maximum molecular dimension A_p′ (the only dimension considered by many investigators) significantly decreases and (2) a significantly better prediction of the elution volume of these compounds could be made.     

A NEW METHOD FOR ESTIMATION OF WEIGHT-AVERAGE MOLECULAR WEIGHT OF POLYMER FROM THE INTRINSIC VISCOSITY AND CHROMATOGRAM

A new method is proposed for estimation of weight-average molecular weight from the intrinsicviscosity and GPC chromatogram of a polymer sample for which Mark-Houwink coefficients are notknown. The method bases on an approximate relationship between GPC data and the intrinsicviscosity of the sample. Reliability of this method was tested by comparing with the universalcalibration method which requires known Mark-Houwink coefficients for seven samples havingdifferent molecular weight distributions. Results obtained by the new method are in excellent agree-ment with those by the universal calibration method.