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.     

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.     

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).     

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.     

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.     

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.     

Studies on Simultaneous Molecular Weight and Spreading Calibration in Steric Exclusion Liquid Chromatography

Abstract

Two improved methods of molecular weight calibration are described where simultaneously parameters of a symmetrical spreading function are obtained through the use of polymolecular molecular weight standards and of average retention volumes. In the first method a linear molecular weight calibration is assumed and the second method is based on a universal molecular weight calibration curve obtained with narrow MWD polystyrene standards.

The proposed methods have been tested using two polymolecular polystyrene standards confirming good convergence of the applied iteration procedures and giving very promising results.     

Size Exclusion Chromatography of Poly(vinylpyrrolidone)

Abstract

Poly(vinylpyrrolidone) and poly(ethylene oxide) separate by hydrodynamic volume on Toyo Soda TSK-PW columns in a mixed solvent mobile phase of 50:50 (v/v) MeOH/H₂O containing 0.1M LiNO₃. From this separation a single universal calibration curve based on hydrodynamic volume [η]M can be obtained. Accurate weight average molecular weights of PVP were obtained by both SEC/LALLS and universal calibration showing good agreement between the two methods. SEC/LALLS overestimates the number average molecular weight for broad distribution polymers due largely to the lack of sensitivity of the LALLS detector to the low molecular weight portion of the polymers, while the universal calibration method slightly underestimates the number average molecular weight as compared to osmometric values.     

Synthesis and properties of a novel perfluorononenyloxy group containing polyarylates

A series of novel perfluorononenyloxy group containing polyarylates were synthesized by a high-temperature solution condensation of 5-(perfluorononenyloxy)-isophthaloyl chloride ( II ) with various aromatic diols in o-dichlorobenzene. All the polyarylates were amorphous and readily soluble in many organic solvents such as o-chlorophenol, o-dichlorobenzene, chloroform, and polar aprotic solvents at room temperature or on heating. Transparent, tough, and flexible films of these polymers could be cast from the o-chlorophenol solutions. The polymers having inherent viscosity of 0.61–1.63 dL/g were obtained in quantitative yields. These polymers were thermally quite stable. The glass transition temperatures of these polyarylates were in the range of 219–242°C by DSC and 224–251°C by DMA, and the 10% weight loss temperatures in nitrogen and air were above 415 and 397°C, respectively. Moreover, these polymers maintained good mechanical properties (G′ ∼ 10⁸ Pa) up to 220°C and had lower moisture absorption than common polyarylates. The dielectric constants of these polymers ranged from 3.23 to 3.75. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 645–653, 1998     

Modification of the universal calibration of gel permeation chromatography to include macromolecules presenting a draining effect

A new universal calibration for gel permeation chromatography is proposed in which the hydrodynamic volume of the macromolecular chains is expressed by the quantity [η]M/Φ instead of the commonly used quantity [η]M (where [η] is the intrinsic viscosity, M is the molecular mass, and Φ is Flory's parameter). Introducing Φ into the hydrodynamic volume is necessary because its value changes from one polymer to another when the polymers present a certain draining effect. The proposed procedure also allows the determination of Φ of any wormlike polymer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 707–710, 2003     

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).     

Effect of pressure in capillary flow of polystyrene

Several corrections possibly required for capillary flow are based on the existence of a linear relationship between the pressure drop along the capillary and the length-to-diameter ratio at a given temperature and shear rate. Recently, the appearance of nonlinearities in this relationship has created some concern as to the cause of this behavior. The occurrence and an explanation of the nonlinearities for polystyrene form the basis of this study. A narrow-distribution, low molecular weight (20,400) polystyrene was tested in eight capillaries at temperatures of 140 and 160°C to initiate the discussion of the nonlinearity in a ΔP (pressure) versus L/D (length/diameter of capillary) plot. The sample exhibits negligible extrudate swelling at all pressures which reinforces the idea that pressure is influencing the flow. The pressure dependence of viscosity is determined using the equivalent expression of the WLF equation derived from free volume theory. Justification for its use is presented. A pressure correction, representing the increased shear stress necessary for flow of the higher viscosity material, is found to linearize the ΔP versus L/D data. A narrow-distribution, high molecular weight polystyrene (670,000) is subjected to a similar analysis at 165°C by using nine capillaries. The situation is quite different, as the high molecular weight sample is not nearly as ideal as the low molecular weight polystyrene.     

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.     

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.     

Calibration in High Temperature Gel Permeation Chromatography of Linear Polyethylenes

Abstract

The mathematical relationship between the gel permeation chromatography calibration curves of polystyrene and linear polyethylene has been determined in 1,2,4-trichlorobenzene at 130, 135 and 140°C. The experimentally determined relationship is in good agreement with that predicted from application of the principles of the universal calibration technique and published Mark-Houwink coefficients. Definition of this relationship enables the use of polystyrene as a secondary standard for gel permeation chromatographic determination of linear polyethylene molecular weight determinations.     

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.     

Initiation and propagation steps in the equibinary polymerization of butadiene by bis(h3-allylnickel trifluoroacetate)

Polymerization of butadiene by bis(h³-allylnickel trifluoroacetate) in benzene and o-dichlorobenzene solvents yields an equibinary 1,4-polybutadiene, containing equal amounts of cis and trans isomers. Initiation proceeds by addition of the allylic moiety of the initiator to a butadiene molecule. The rate of initiation is high enough to ensure complete consumption of the catalyst for a monomer/catalyst molar ratio of about 10 at 5°C. The propagation exhibits the characteristics of a “living” polymerization: the molecular weight is proportional to the conversion, and at the end of the reaction, the average degree of polymerization is equal to the monomer/catalyst molar ratio. Living polybutadienyl-nickel trifluoroacetate is able to reinitiate not only butadiene polymerization but also allene polymerization. However, for high [monomer]/[catalyst] ratios, conversion-dependent transfer reactions limit the molecular weight to 7000 in benzene and to 70,000 in bulk polymerization in the presence of small amounts of o-dichlorobenzene.     

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.