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     

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.     

Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

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.     

凝胶渗透色谱在高聚物分子量测定中的应用

本文综述了近年来凝胶渗透色谱在油溶性和水溶性高聚物分子量测定中的应用,着重分析测试条件对水溶性样品分子量的影响并归纳了解决的办法。同时,介绍了配备紫外可见和示差折光检测器、示差和光散射检测器后凝胶色谱的应用。此外,还概述了几种常见高聚物分子量的标定和校准方法,以便多种方法相互验证,得到较准确的分子量值。     

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.     

Estimating the Polydispersity of GPC Slices Due to Coeluting Comb‐Polymers Synthesized by Grafting Monodisperse Side Chains Onto a Backbone Having Broad Molecular Weight Distribution

The molecular weight distribution, polydispersity and the distribution of side chains within a GPC‐slice have been calculated for coeluting comb‐shaped polymers. It is assumed that the polymers were synthesized by grafting monodisperse side chains onto a backbone having a broad molecular weight distribution. Despite the broad polydispersity of the backbone the polydispersity within a GPC‐slice is rather narrow, as is the distribution of side chains. Consequently the effect of polydispersity on properties, which can be obtained by GPC coupled with molar mass sensitive detectors is negligible. However, this result is true only for the specific branching mechanism investigated.     

Gel permeation chromatography and cellulose. II. Application of universal calibration

In previously reported work concerning the chain-length distributions obtained by gel permeation chromatography (GPC) in celluloses, degrees of polymerization (DP) of unusually high magnitude were reported. Later work in GPC has shown that the concept of relating extended nolecular chain length of different polymers to elution volume for obtaining molecular weight is not theoretically sound. Correlation of molecular hydrodynamic volume (indicated by the product of intrinsic viscosity and molecular weight) with elution volume has been found to place polymers of vastly different natures on a single curve, such is now designated universal calibration. Application of universal calibration to the determination of DP distributions in celluloses required a different method of converting counts to DP. This new procedure is described in detail. Weight-average DP's given by the procedure for samples of cellulose I, II, III, and IV were 5190, 4520, 4795, and 3390, respectively. These are decreases of 74–75% from the results obtained by the extended-chain procedure. The results compare favorably with the viscosity-DP's of the samples. Number-average DP's were 1580, 1040, 1140, and 490 for the four samples, respectively, these being decreases of 87–93% from the values formerly reported. The polymolecularity ratios for the samples are now unusually large, being 3.4, 4.7, 4.2, and 7.1, respectively.     

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.     

Data Treatment in Aqueous GPC with On-Line Viscometer and Light Scattering Detectors

Abstract

Gel Permeation Chromatography (GPC) is becoming a very powerful tool for polymer characterization with the coupling of mass detectors using viscometry and light scattering techniques. The triple coupling seems to be the best way since the light scattering detector gives absolute molecular weights and viscometric detection provides intrinsic viscosity, leading to absolute molecular weights through universal calibration and information on long-chain branching. However, instrumentation becomes more sophisticated, expensive and, simultaneously, very sensitive to several parameters which are not critical in classical GPC. Moreover, an on-line computer is required for data acquisition and appropriate software for reliable interpretation of chromatograms.

Our experiments were performed with a Waters Associates room temperature instrument in which a home-made continuous viscometer, using pressure transducers, and a light scattering detector (LALLS Chromatix-CMX 100) were inserted on-line between the column set and the refractometer. Data were interpreted through personal software written on HP9836 and PC-AT computers.

We describe, here, the behavior of some polymers in aqueous solutions, mainly those that are commonly used as calibration standards (polyethylene oxides, pullulans). Experiments were run using two different sets of columns (‘Ultrahydrogel’ from Waters Associates and ‘Shodex OH-Pak’ from Showa Denko K.K.) in several aqueous solvents, pure water or water with various salts (LiNO₃, NaNO₃, LiCl, NaCl, Na₂SO₄) at different concentrations. Intrinsic viscosities were determined through viscometric detection and weight average molecular weights through the LALLS detector, leading to a plot of universal calibration curves Log([ηl.M) versus elution volumes.     

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.     

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.     

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.     

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 determinations by gel-permeation chromatography and viscometry

The hydrodynamic volume concept can be used effectively with gel-permeation chromatographic (GPC) and viscosity data to estimate the molecular weight of a variety of polymers. Agreement is within ±5–10% of the absolute values and thus is satisfactory for many purposes. An iterative computer technique and a method developed by Funt and Hornof for analyzing GPC–viscosity data were found to be equivalent with respect to estimating the molecular weights for the five cases studied. The latter is easily employed but restricted to the case where the sample of interest and the GPC calibration standards have approximately equal Mark-Houwink parameters. Since GPC measurements are commonly performed in thermodynamically good solvents, the general applicability of the method is not impaired. Using the unperturbed dimensions of the polymer chain to estimate the molecular weight of a variety of polymers was not as satisfactory as the above techniques. This approach generally gave biased molecular weight values (consistently low or consistently high). Agreement with the absolute values ranged from 10 to 30%. We therefore believe that either of the techniques based on the hydrodynamic volume concept can be used more effectively to estimate the molecular weight of a series of polymers than the treatment based on the unperturbed dimension.     

Laser light scattering as GPC detector

The use of low angle laser light scattering (LALLS) as a detector in gel permeation chromatography (GPC) is discussed. The advantage of this technique is primarily based on the ability of LALLS to continously measure the absolute molecular weight and also to detect minute concentrations of high molecular weight species such as microgel. The weakness of the system is in the low sensitivity for low molecular weight material. In this paper, our experience of the KMX-6 from Chromatix illustrates the possibilities for the characterization of polymers by the combination of LALLS and GPC. The applications discussed are mainly from our work with polyethylene and poly(vinyl chloride). Special emphasis is given to the determination of long chain branching and microgel.     

On-line viscometry combined with gel permeation chromatography. II. Application to branched polymers

Gel permeation chromatography (GPC) combined with on-line flow time measurements have been applied to the analysis of branching in polymers. Three sets of branched polymers were examined: polybutadienes lightly crosslinked by high energy radiation, a styrene-divinyl benzene copolymer and several of its fractions, and polyvinyl acetates branched by polymer transfer reactions during polymerization. The reduction in intrinsic viscosity due to branching was determined for each GPC fraction of the polybutadiene samples. The branching frequency in these fractions was known from other information, so the results were used to establish a relationship between viscosity ratio G and the theoretical size ratio g. This relationship was then used to calculate the distribution of branching and M _w in the styrene copolymers and the polyvinyl acetates. The results were compared with independent information on these polymers. The agreement was generally good.     

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.     

Characterization of Branched Poly (vinyl Acetate) by GPC and Low Angle Laser Light Scattering Photometry

Abstract

Poly (vinyl acetate), PVAC, synthesized by bulk polymerization over a range of initiator concentrations ([AIBN] = 10^?5 to 4 × 10^?3 g-mole/1), temperatures (50°C, 60°C, 70°C, and 80°C) and conversion levels (3 to > 90%) were characterized using low angle laser light scattering (LALLS) photometry to measure M_w of the whole polymers. A number of these samples were characterized using GPC with a differential refractive index (DRI) and LALLS detector to measure the molecular weight distribution (weight fraction versus M_w). M_w for PVAC samples synthesized at suitably low initiator levels at various conversions were found to agree with classical light scattering measurements after Graessley.

An electronic device and a technique which optimizes the sensitivity and the signal-to-noise ratio of the LALLS photometer throughout the molecular weight distribution (MWD) of the GPC chromatogram were devised. These considerably simplify the operation of the LALLS for both offline and online operation with GPC.

Most importantly it was unambiguously shown that the commonly used universal calibration parameter (UCP) with GPC, [n]M_w, is incorrect for polymers with molecules having the same hydrodynamic volume but different molecular weights, i. e., those with only chain branching (LCB), copolymers with compositional drift, and polymer blends. The correct UCP was found to     

陶瓷先驱体——含钛聚碳硅烷凝胶渗透色谱校准方程研究

采用以气相渗透法测定了数均分子量的宽分布含钛聚碳硅烷作标样,通过计算机辅助建立了具有较低分子量和较高支化度的陶瓷先驱体聚合物——含钛聚碳硅烷的凝胶渗透色谱校准方程ｌｎＭ＝２０．９－０．８４３Ｔ。将这一方程应用于实际样品分析时,测定的数均分子量值与气相渗透法测定结果基本一致,偏差绝对值小于８．０％。钛的引入使其与聚碳硅烷本体的校准方程相差很大。