Concentration effects in gel-permeation chromatography

Peak elution volume in gel-permeation analysis of polymers depends on sample concentration as well as molecular weight. Elution volume is related to the logarithm of the hydrodynamic volume of the solvated polymer species. The hydrodynamic volume of a given species is, in turn, inversely related to the concentration. Since molecular weight and concentration are interacting variables, the elution volume–molecular weight relation is not uniquely determined. A model is presented which accounts quantitatively for concentration effects, using parameters which are available a priori. The data required are polymer molecular weight, concentration, and density and the Mark-Houwink relation for the particular polymer-solvent combination.     

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.     

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.     

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.     

Gel-permeation chromatography: Examination of universal calibration procedures for polydimethylsiloxane in a poor solvent

Various procedures for universal calibration in gel-permeation chromatography with polystyrene gels are examined for polystyrene and polydimethylsiloxane fractions. For o-dichlorobenzene at 138°C, experimental intrinsic viscosity–molecular weight data show that the Mark-Houwink exponents are 0.70 and 0.57 for polystyrene and polydimethylsiloxane, respectively. In principle, this difference permits a distinction between the various polymer size parameters proposed for universal calibration. An interpretation of the experimental polydimethylsiloxane calibration for o-dichlorobenzene at 138°C requires a consideration of errors in average molecular weights and errors arising from the use of average molecular weight instead of peak molecular weight. When calibration procedures utilizing hydrodynamic volume and unperturbed dimensions are examined, the difference between them is comparable with experimental error. If the Flory-Fox viscosity expression is employed, the perturbed end-to-end distance (or radius of gyration) and the hydrodynamic volume give equivalent universal calibrations. The experimental data are sufficiently accurate to show that the perturbed dimension determined with the Ptitsyn-Eizner relation does not give an adequate universal calibration.     

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.     

一组线型聚苯乙烯和星形支化聚苯乙烯的凝胶色谱与热场流分级方法的比较

本文应用热场流分级方法,在两种不同的场强下(△T=30℃、△T=50℃),测试了一系列窄分布聚苯乙烯标样和星形支化聚苯乙烯的淋出体积V_r和分子量M的依赖关系。星形支化物的臂数不同,但臂的分子量相同,上述样品进行了GPC测试,实验表明,由TFFF得到的支化的与线型聚苯乙烯在V_r～M关系上的差别大于GPC的结果,表明链结构对扩散系数的影响大于对分子体积的影响。     

COMPARISON OF GPC AND THERMAL FIELDFLOW FRACTIONATION METHODS FOR LINEAR AND STAR BRANCHED POLYSTYRENE SAMPLES

The Thermal Field-Flow Fractionation (TFFF) method was used to determine the elution volumeof a series of star branched polystyrene having different number of arms but the same arm molecularweigh and polystyrene standards with narrow distribution whose molecular weight ranged from5.0×10~4 to 8.6×10~5. Results were obtained by measuring at two temperature difference (△T=30℃and △T=50℃in THF. The same star branched samples were measured by means of GPC method.Comparison of Vr-Mrelationships obtained from TFFF and GPC showed that the displacement of V_r-M curves for star and linear polystyrene is larger than that in GPC. This difference is caused by theentirely different mechanism of separation for these two methods. As the controlling factor is hy-drodynamic volume of the polymer chain in solution for GPC, it is the diffusion coefficient of polymermolecules for TFFF. The experimental results indicate that the influence of variance of chain struc-ture on diffusion coefficient is stronger than that on the hydrodynamic volume and that TFFF tech-nique may be used as a method for characterizing branching of polymer molecules. For this pur-pose a proper theoretical model and more accurate experiments are needed.     

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.     

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).     

Determination of the width of a narrow molecular weight distribution by gel-permeation chromatography

A recycle gel-permeation chromatography (GPC) method for extrapolating to infinite resolution is proposed. From the GPC calibration curve, the extrapolated elution peak width volume can be converted into peak width in decades of molecular weight. For an essentially Gaussian distribution, the weight-average/number-average molecular weight ratio can be determined from a calculated conversion table.     

Peculiarities of polyacrylamide analysis by aqueous GPC

Various commercially available stationary phases of gel permeation chromatography (GPC) were tested to determine their effectiveness in aqueous exclusion chromatography. It was found that controlled pore glass (GPG) is the most suitable material for the separation of polyacrylamides and poly(acry1amide-co-sodium acrylate), dextrans, and poly(sodium styrene–sulfonates) in 0.1M aqueous Na₂S0₄ solutions of ionic strength 0.3. A calibration curve was established by using broad molecular weight distribution polyacrylamide standards in a trial and error procedure. To avoid artificial oscillations on the evaluated distribution curves a cubic B-spline representation of the calibration curve was used instead of the conventional polynomials. By applying this system the solution instability of polyacrylamides was observed by GPC and is discussed because of its general importance to the applicability of indirect molecular weight determination methods for polyacrylamides. The effectiveness of aqueous GPC was demonstrated in an evaluation of thermal degradation measurements of polyacrylamides. Finally, the feasibility of universal calibration of aqueous GPC by means of poly(sodium styrene–sulfonates) was investigated. It is apparent that in spite of some problems concerning adsorption of the polymer universal calibration is a successful tool for calibrating aqueous GPC.     

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.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.     

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.     

Viscoelasticity of dilute chain-molecule solutions: Evaluation of hydrodynamic interaction

The viscoelastic properties of chain molecules varying in flexibility and length have been calculated by use of the bead-spring model theory of Zimm. In the evaluation of the hydrodynamic interaction parameter, the number of springs in the bead-spring model, N, has been selected from the range in which the properties predicted by the theory are insensitive to the value of N. The results for limiting viscosity number agree with those predicted by the Yamakawa–Fujii theory of the limiting viscosity number of wormlike chains. The theory also fits the experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in theta solvents at infinite dilution. The viscoelastic properties of some moderate molecular weight deoxyribonucleic acid solutions are predicted to deviate from the non-free-draining behavior toward the free-draining behavior.     

Study On The Concentration Effect In Gel Permeation Chromatography. I. A New Model Theory For Concentration Dependence Of Hydrodynamic Volumes And Gpc Elution Volumes

Abstract

A new model theory for concentration dependence of hydrodynamic volumes and GPC elution volumes was proposed. In this theoretical model both the reduction of hydrodynamic volumes and the viscosity phenomena in the interstitial volume are taken into account at the same time. The effective hydrodynamic volumes, Vhs, of a solvated macromolecule decrease with increasing reduced viscosity, (7_sp/c), and the GPC elution volumes,Ves, increase with increasing concentration, c, and intrinsic viscosity,(7), respectively according to the following relations.     

Comparison of number–average molecular weights calculated by GPC and membrane osmometry

Data are presented which show that when a polymer contains an appreciable amount of low molecular weight species below the diffusion limit of the osmometer membrane, the osmotic molecular weight, M?_n, is generally higher than the M?_n calculated from gel-permeation chromatography (GPC). Experiments were performed on samples of poly(vinyl chloride) (PVC) and high-cis polybutadiene polymers. Osmotic data were obtained in the usual manner, while GPC data were obtained using the universal calibration approach. It was found that when all polymer species below approximately 10,000 molecular weight were excluded from the calculation of M?_n by GPC, agreement in M?_n was obtained between membrane osmometry and GPC. The data obtained suggest that the choice of M?_n as measured by membrane osmometry in the calibration of the GPC should not be done casually, as the measured M?_n may not reflect the “true” value of that sample, especially when the polymer sample contains an appreciable amount of low molecular weight material.     

Polymer characterization by coupling gel-permeation chromatography and automatic viscometry

A method is proposed for use of the universal calibration curve, i.e., the product of molecular weight and intrinsic viscosity versus retention volume, in calculating the molecular weight distribution of a polymer from gel-permeation chromatography (GPC) when the Mark-Houwink relation of the polymer in the solvent used for the GPC is unknown. This is achieved by measuring the viscosity of each fraction with an automatic capillary tube viscometer. Application of this technique to poly(vinyl chloride) and poly(vinyl acetate) proved to be successful.     

Study on the determination of the molecular weight of polyethylene with ultrahigh temperature GPC

Ultrahigh or high molecular weights of polyethylenes (PE) and their distributions are for the first time determined at 160° or 170°C by gel permeation chromatography (GPC). The thermostability of PE at high temperatures is discussed. In order to calculate the real molecular weight of PE, a new calibration curve is established. For PE with high molecular weight more reliable and accurate results can be obtained by GPC measurements at these temperatures. The application of ultrahigh temperature GPC for polymer characterization is demonstrated in this paper.