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.     

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 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.     

Cellulose acetate butyrate in solution. I. Hydrodynamic behavior

Cellulose acetate butyrate has been studied in regard to its hydrodynamic properties in several solvents. The polymer was fractionated by precipitation, and the molecular weight distribution of the polymer fractions was determined by gel permeation chromatography. The number-average molecular weight was estimated by osmometry. The Mark–Houwink–Kuhn–Sakurada relations between viscosity and molecular weights were established, and the unperturbed dimensions of the polymer chains were evaluated. In light of these data, current theories of polymer solutions are discussed. A new method of estimating unperturbed dimensions is proposed for semiflexible linear polymers.     

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: 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.     

高分子无扰尺寸的测定

本文用GPC-[η]联用仪测定高聚物分子的无扰尺寸,GPC将高聚物分成不同的级分,连用自动粘度计测其相应级分的粘度,并由GPC的标定线或普适标定线,得到各级分的分子量,再用使Mark-Houwink公式线性化的理论方程,图解外推到无扰状态,获得高聚物分子的无扰尺寸,对于聚苯乙烯和聚甲基丙烯酸甲酯,所得结果与直接法、习惯法一致。     

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.     

Effects of lithium bromide on the gel-permeation chromatography of polyester-based polyurethanes in dimethylformamide

The hydrodynamic volume changes of the polyester-based polyurethanes, as dimethylformamide solutions with and without lithium bromide, were studied. Gel-permeation chromatographic (GPC) and intrinsic viscosity techniques were employed as methods for characterization. Decreases in intrinsic viscosity as well as dramatic changes in the GPC chromatograms were observed. These observations are explained by the polarity of these polyester-based polyurethane molecules and the resulting characteristics of molecular expansion, association, and polymer–column interaction normally associated with polyelectrolytes.     

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.     

Dependence of chain conformation and solution thermodynamics on composition for poly(ortho ester)s prepared from ketene acetals and mixtures of diols

The solution properties of a series of random copolymers prepared from ketene acetals with mixtures of diols have been characterized by dilute solution light scattering, chromatographic, and viscometric techniques. Five solvents with refractive indices ranging from 1.4 to 1.5 were used to obtain the correct weight average molecular weight. Changes in the unperturbed radius of gyration, obtained by combined size exclusion chromatography and low-angle light scattering techniques, parallelled that predicted by simple considerations of changes in repeat unit size. Thus the relative contributions of differing copolymer–solvent interactions and changing unperturbed radii of gyration to the hydrodynamic volume of random copolymers of different compositions were evaluated.     

Solution properties of NR/PU block copolymers by size‐exclusion chromatography and viscometry

Soluble block copolymers based on natural rubber and polyurethane oligomers derived from 1,3 butane diol and toluene diisocyanate were synthesized for the first time. The dilute solution properties of these block copolymers dissolved in tetrahydrofuran (THF) were studied by viscometry and gel permeation chromatography (GPC). The Mark–Houwink constants K and a of the block copolymer system were determined by the molecular weight data from GPC combined with the viscosity data. Both the values were found to be in the range usually given by flexible elastomers. The intrinsic viscosity values were found to decrease successively with a decrease in the NCO/OH ratio from 1.12 to 1.05. The unperturbed chain parameters, K_θ and B were determined from the viscosity data. The K_θ calculated was used to get the unperturbed end‐to‐end distance and radius of gyration of the block copolymer systems in THF. The viscosity data were also used to study the chain conformation in dilute solutions. It was found that the molecules adopt a compressed core and shell conformation in which the higher molecular weight component, NR, forms the shell, which compresses the PU core. All the block copolymers assume a compressed segregated core and shell model which changes to a partially segregated core and shell conformation, or partially Gaussian conformation, at the transition temperature located at 70 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2104–2111, 2006     

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).     

A new method for estimation of viscosity-average molecular weight of polymers from GPC

A novel approach for the determination of the viscosity-average molecular weight of polymers for which Mark–Houwink constants are not known is presented. This method can be applied to narrow as well as broad-molecular-weight-distribution polymer samples and requires only the GPC chromatogram and viscosity data. The proposed method was tested using polystyrene and poly(methyl methacrylate) in toluene and THF. Molecular weights computed by the proposed approach are in good agreement with those obtained using conventional techniques.     

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.     

A few characterization studies on some poly(methyl aryloxymethacrylates)

High polydispersity values obtained for the molecular weights, as determined by light scattering, osmometry, and GPC, of polymers prepared by different methods from the monomers recently synthesised indicate the presence of large quantities of low molecular weight species besides the high molecular weight species besides the high molecular weight species. Intrinsic viscosity data were used to evaluate Mark–Houwink constants K and “a” for this new series of monomers. DSC analyses show that the polymers have low T_g. X-ray diffraction studies made on the fibers show a high percentage of crystallinity in poly(methyl α-phenoxymethacrylate).     

Solution properties of ion-containing polymers in polar solvents

The placement of ionic groups within the molecular structure of a polymer produces marked modification in physical properties. A large number of studies have been performed on these ion-containing polymers, but few have focused on the effects of anion–cation interactions (i.e., counterion binding or ionization) on hydrodynamic volume, especially as the molecular structure of the solvent and nature of counterion are varied. In this study changes in hydrodynamic volume are followed through reduced viscosity measurements as a function of the abovementioned molecular parameters. The dilute solution properties of various polyelectrolytes that contain sulfonate and carboxylate groups were investigated as a function of the counterion structure, charge density, molecular weight, and solvent structure. The polymeric materials were selected because of their specific chemical structure and physical properties. In the first instance a (2-acrylamide-2 methylpropanesulfonic acid)-acrylamide-sodium vinyl sulfonate terpolymer was synthesized and subsequently neutralized with a series of bases. Viscometric measurements on these materials indicate that the nature of the cation affects the ability of the polyelectrolyte to expand its hydrodynamic volume at low polymer levels. The magnitude of the molecular expansion is shown to be due in part to the ability of the counterion to dissociate from the backbone chain, which, in turn, is directly related to the solvent structure. The changes in solution behaviour of these inomers lend support for the existence of ion pairs (i.e., site binding) and ionized moieties on the polymer chains. Measurements performed in a variety of solvent systems further confirm this interpretation. In addition, and acrylamide-sodium vinyl sulfonate copolymer was partially hydrolyzed with sodium hydroxide to study the effect of varying the charge density at a constant degree of polymerization and counterion structure. The results show that the charge density has a significant effect on the magnitude of the reduced viscosity and dilute solution behaviour. These observations, made in aqueous and nonaqueous solvents, are related to the interrelation of hydrodynamic volume, counterion concentration, and site binding. Again the controlling factor is the degree of site binding of the counterion onto the polymer backbone. Finally, we observe that the increased hydrodynamic volume affects viscosity behavior beyond the polyelectrolyte effect regime. If the average charge density on the macromolecule is relative high and/or the molecular weight is large (≥ 10⁶) sufficient intermolecular interactions will occur to produce rapid changes in reduced viscosity.     

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.     

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.