Analysis of the influence of interdetector volume on local calibration in size exclusion chromatography with dual multiangle-light-scattering/concentration detection

A comparison of the s- and w-detections of molecular weight, a necessary condition for precise determination of interdetector volume in size exclusion chromatography of polymers with the dual light scattering--concentration detection, is examined. From the theoretical analysis for a polymer with the log-normal molecular weight distribution it follows that the error in determination of the local calibration, i.e., of a logarithmic dependence of molecular weight on elution volume obtained by the s-detection, from the known dependence of radius of gyration on elution volume and of molecular weight on the radius of gyration, remains linear and is slightly shifted with respect to that obtained by the w-detection (dual detection giving the weight-average molecular weight) towards higher molecular weights, the difference being below the experimental error. It also follows that the error in the slope of local calibration found by the w-detection is given by the ratio of the error in interdetector volume and the variance of the elution curve. This is demonstrated on several polymer samples with symmetric elution curves of polymer samples differing in polydispersity indices. The range of this rule depends on the broadness and symmetry of elution curves. The precision of the interdetector volume determination depends therefore strongly on the Mw/Mn ratio of the sample.     

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.     

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.     

Polymer analysis by fractionation with on-line light scattering detectors

Summary The classical method for the determination of the molecular weight distribution (MWD) curve of a polymer requires fractionation according to the molecular weight and prior calibration of the separator. It is shown that the use of a dual detection system which includes a molecular mass sensitive detector eliminates the need for prior calibration. The principles of operation of a low-angle light scattering photometer, working as such a detector, are presented, as well as the basic equations for determination of the MWD curve from the elution curve and of the average molecular weights. Then the performances of the light scattering photometer are discussed with special emphasis on the various sources of errors and unaccuracies in these determinations.     

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.     

Polymer-Gel Interactions in GPC with Organic Eluents

Abstract

The displacement of hydrodynamic volume universal calibration curves to high retention volumes for some polymer-solvent systems is explained in terms of a network-limited separation consisting of a steric exclusion mechanism and a second mechanism resulting from polymer-gel interactions. This treatment is consistent with a thermodynamic interpretation of GPC separations in which the distribution coefficient (≥ 1.0) for polymer-gel interactions is determined by an enthalpy change for polymer partition or polymer adsorption in the porous packing. Examples of the application of the network-limited treatment to experimental data obtained with crosslinked polystyrene gels and inorganic packings are presented. Network-limited separations in which the distribution coefficient for polymergel interactions is less than unity correspond to partial exclusion by polymer incompatibility with the gel. Experimental data for the early elution of poly(vinyl acetate) are consistent with an incompatibility mechanism, giving a dependence of the distribution coefficient for polymer-gel interactions on the molecular weight of poly(vinyl acetate).     

Quality control of clinical dextran by rapid gel-permeation chromatography

Summary Clinical dextran can be fractionated by rapid gel-permeation chromatography on Spheron^R with the aid of a high-performance liquid chromatograph. The linear calibration function is obtained by dextran fractions whose molecular weights Mw and Mn are determined by absolute methods (light scattering, membrane osmometry) and end group analysis. The transformation of elution diagrams into a molecular weight distribution is described. Characteristic data for dextran 40 and 70 were obtained from the integral distribution curves. The molecular weight distribution of dextran fractions was found to fit a Schulz-Zimm distribution which is typical for long chain polymers. For quality control purposes clinical dextran can be characterized by its molecular weight distribution with high accuracy within one hour.     

SIMULTANEOUS CALIBRATION OF MOLECULAR WEIGHT SEPARATION AND COLUMN DISPERSION OF SEC WITH CHARACTERIZED POLYMER STANDARDS

With the aid of the theoretical relationship between the calibration relation of a SEC column for the monodisperse polymer species under ideal working condition and the effective relations between the molecular weight and the elution volume for characterized polymer samples, a computational procedure for simultaneous calibration of molecular weight separation and column dispersion is proposed. From the experimental chromatograms of narrow MWD polystyrene standards and broad MWD 1,2-polybutadiene fractions the spreading factors of a SEC column was deduced by the proposed method. The variation of the spreading factor with the elution volume is independent upon the polymer sample used.     

Gel permeation properties of cellulose. I. Preliminary comparison of unmodified and crosslinked,decrystallized cotton cellulose

Decrystallized cotton cellulose was found to be have gel permeation properties comparable to those of the highly crosslinked dextran and polyacrylamide gels used in chromatography. Partial separations of pairs of sugars, ranging in molecular weight from 120 to 738, were studied by determining the optical rotations of fractions eluted from chromatographic columns, employing a sensitive automatic polarimeter. The elution volumes of individual sugars of known molecular weights provide a quantitative measure of changes produced in the cellulose polymer structure by crosslinking. A significant difference was found between unmodified cellulose and the same material crosslinked by formaldehyde treatment; although crosslinking reduced permeability to larger molecules, the crosslinked material was found to be more permeable than the untreated cellulose to compounds having molecular weights below approximately 1000.     

Gel permeation chromatography of branched polyethylene

The effect of long-chain branching must be considered in gel permeation chromatography to evaluate the molecular weight polydispersity of branched polyethylenes. Osmotic molecular weights of fractions of branched polyethylene were correlated with elution volumes; weight-average and number-average molecular weights of a branched polyethylene were determined. Molecular weight changes on crosslinking polyethylene by ionizing radiation are accompanied by branching and cannot be simply interpreted by gel permeation chromatography.     

Elution Behaviors and Rationalized Calibration for Low-Molecular-Weight Polymers in Size Exclusion Chromatography

Abstract

Molecular weight relationships among oligostyrene, n-hydrocarbon, epoxy resin, p-cresol novolak resin, and oligoethylene glycol having the same retention volume were discussed using SEC gels of different pore sizes in chloroform and tetrahydrofuran. Gel capacity and the maximum number of components resolvable increased with the use of chloroform except the case of epoxy resin. Different elution behaviors of oligomers in different eluents make it difficult to use molar volumes or effective chain lengths as calibration parameters. The influence of the pore size and shape of the gel on the elution order among oligomers was negligible except some cases. Molecular weight conversion equations for several oligomers based on molecular weight of oligostyrene or n-hydrocarbon were derived. These equations make it possible to use oligostyrene or n-hydrocarbon as a reference standard when molecular weights of oligomers are measured.     

Gel permeation chromatography: calibration procedures for chains containing p-phenylene units

Experimental gel permeation chromatography calibrations have been obtained for polystyrene standards, polysulphone fractions, and polycarbonate fractions in chloroform at 30°. Chloroform is a good solvent for all three polymers which have similar polymer solvent interactions. The fractions have narrow molecular weight distributions, so that viscosity average molecular weight can be taken as the peak molecular weight of a chromatogram. The experimental polysulphone and polycarbonate calibrations are compared with curves calculated from the polystyrene calibration using equations which assume that the unperturbed mean-square end-to-end distance and hydrodynamic volume are universal calibration parameters. For molecular weights between 20,000 and 100,000 both universal calibration procedures were found to be acceptable. For polycarbonate extended chain length was also found to be satisfactory for universal calibration. For polycarbonate molecular weights below 20,000, the predicted molecular weight calibration deviated from the experimental data. Possible reasons for this difference are discussed.     

Characterization of Nylons by Gel Permeation Chromatography and Low Angle Laser Light Scattering in 2,2,2-Trifluoroethanol

Abstract

A GPC method was developed for the analysis of several commercial nylons in trifluoroethanol + 0.05M LiBr using a styrene-divinylbenzene column custom-packed by Jordi Associates.

A broad molecular weight standard method was developed by interfacing GPC with LALLS to give the absolute molecular weight for each data point or elution volume along the chromatographic peak from a nylon sample of known molecular weight. The integrity of the interface was verified by static LALLS measurements; no loss or adsorption of solute was found in the chromatographic system.

A strong ionic effect was observed for nylon samples and the method to alleviate it was described. The molecular weights and distribution of the following nylons were determined by this method: nylon 6, nylon 4,6, and nylon 6,6. Much higher than quoted molecular weights were obtained for nylons when polymethyl methacrylates and ethylene glycols were used as standards; this necessitated the use of this broad molecular weight method for column calibration. The ambient operating conditions offered several advantages over the conventional m-cresol solvent which required operation at higher than 100 C in order to reduce the viscosity, possessed a strong odor, and occasionally resulted in degradation of polyamides.     

一种新的标定体积排除色谱（SEC）的方法

基于体积排除色谱中测得的淋出体积和动态激光光散射中测得的平动扩散系数都直接依赖于高分子的流体力学体积这一事实，本文在理论上提出了一种把淋出体积分布和平动扩散系数分布二者结合起来标定体积排除色谱的新方法，并且在实验上通过对宽分布的聚苯乙烯标准样品的测试证实了该方法的可行性．     

用多分散高聚物标样作凝胶色谱的分子量分离和扩展效应同时校准

根据凝胶色谱柱在理想工作条件下单分散高分子组分的校准关系与多分散试样的实效关系之间的理论联系,建议了一种简单的觅数方法,同时作凝胶色谱柱的分子量分离和扩展因子的校准。用本法从窄分布的聚苯乙烯和宽分布的1,2-聚丁二烯级分的实验谱图得到的所用凝胶色谱柱的扩展因子与淋出体积间的关系相互重合,与试样种类无关。     

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).     

Universal calibration in GPC: A new approach for the calculation of molecular weights

A method has been developed for determining simultaneously the molecular weight of a broad-distribution polymer and the Mark-Houwink coefficients for that polymer type by using only GPC and intrinsic viscosity data. Standardized samples of poly(vinyl chloride), polystyrene, polybutadiene, and an experimental cycloolefin polymer were analyzed by this method. Shear-corrected intrinsic viscosities were used in all cases because of the high molecular weights involved. Molecular weight data for all samples were found to be in good agreement with molecular weight data obtained by membrane osmometry and from other GPC techniques. The proposed technique provides a means for calculating the molecular weight of a single polymer sample through universal calibration of GPC without knowledge of the Mark-Houwink coefficients for that polymer type.     

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.     

An indirect GPC calibration method for the low-molecular-weight region

A new gel permeation chromatography indirect calibration method is proposed for a polymer for which samples of known molecular weight and narrow molecular weight distribution are not available. This method is based on conversion of an experimentally obtained calibration curve for another polymer (polymer standard) through the universal calibration concept but using a new intrinsic viscosity-molecular weight relation. This indirect calibration curve is proposed especially for the low-molecular-weight region, where the method based on the Mark-Houwink-Sakurada equation gives erroneous results.