Calibration of size-exclusion chromatography columns with polydisperse polymer standards. I. Theory

Relationships have been derived between the spreading factor and the respective slopes of actual and effective linear calibrations in size-exclusion chromatography. On this basis a new calibration procedure has been developed for determining simultaneously the dependences of sample molecular weight and of the spreading factor on elution volume from chromatograms of polydisperse polymer samples with known values of number-and weight-average molecular weight. No assumptions about the shape of sample molecular weight distribution are required. If necessary, the calibration dependences may be further improved by an iteration procedure described.     

Calibration of gel permeation chromatography columns using polydisperse polymer standards

Two methods of calibrating gel permeation chromatography columns are given. The first method uses polymer standards that may have broad molecular weight distributions. Either the weight-, number-, or viscosity-average molecular weight of each standard must be known. This method neglects column peak spreading. The second method requires polymer standards of moderately narrow molecular weight distributions for which both the weight- and number-average molecular weights are known. However, the second method determines both the column peak spreading and calibration of the column. The second method is applied to calibration of a column using polystyrene standards. The column peak spreading is found to be small and independent of molecular weight for this column.     

Calibration of GPC with polydisperse standards

An iteration method has been developed to prepare a calibration curve for gel permeation chromatography (GPC). It requires a number of samples of the same polymer which may have broad molecular weight distributions (MWD) of which two molecular weight averages must be known previously. The method has been applied to dextran standards with known M _w and M _n. Modifications involving the use of branched polymers are discussed.     

Simple methods of gel permeation chromatography calibration developed from one or two polydisperse polymer standards

Applying the formalism of averaged elution volumes corresponding to average molecular weights or intrinsic viscosities of polydisperse polymer standards simple, single-valued equations were developed for iterative evaluation of calibration parameters of both direct and universal GPC calibration relationships. The developed evaluation procedures are simpler and converge faster than corresponding methods described in the literature.     

Polyelectrolytes as secondary calibration standards for aqueous size-exclusion chromatography

The effect of the ionic strength of the solvent on the size-exclusion chromatography of narrow molecular weight dextrans and monodisperse sodium polystyrene sulfonates has been investigated. In both NaOH and NaCl solutions the elution volume of the sodium polystyrene sulfonates increased as the ionic strength was increased, while the elution volume of the dextrans decreased slightly as the ionic strength was increased. The elution data for various ionic strength solvents could not be described by the traditional universal calibration procedure of plotting the product of the intrinsic viscosity and the molecular weight vs. the elution volume. By using a modified calibration procedure which includes excluded volume effects, the elution data can be described for NaOH solution of moderate and high ionic strength. This modified calibration technique was unable to describe the elution data for very low ionic strength NaOH solutions and for the NaCl solutions. Possible explanations of the inability of straightforward size exclusion chromatographic calibration techniques to quantitatively described all the observed elution behavior are discussed.     

The differential viscometer. II. On-line viscosity detector for size-exclusion chromatography

The new technique of differential viscometry measures directly the specific viscosity of a solution by subtracting the contribution of solvent in a balanced capillary bridge. The present work adapts the differential viscometry principle to the design of a viscosity detector for use in size-exclusion chromatography. It is shown that the resulting viscosity detector possesses excellent sensitivity and baseline stability with a minimum detectable specific viscosity of 2.7 × 10^?5. The viscosity detector can be operated together with a refractive index detector to determine the intrinsic viscosity of polymer solute fractions as they elute from the SEC column. The bandspreading of the viscosity detector is compared to the refractive index detector by measuring the peak width of a compound having a single discrete molecular weight. The peak width at half-height was 0.29 mL for the viscosity detector and 0.25 mL for the refractive index detector.     

Calibration of GPC columns

Abstract

Calibration in gel permeation chromatography is reviewed with special reference to M[η] as the parameter for universal calibration in the case of polymers     

N-methylation of wholly aromatic polyamides for size-exclusion chromatography

Wholly aromatic polyamides, including poly(1,4-phenyleneisophthalamide) and poly(1,4-phenyleneterephthalamide) are N-methylated to render them soluble in N,N-dimethylformamide, a common size-exclusion chromatography eluent. The procedure N-methylates 50–55% of the total amide linkages in these two examples, permitting reproducible measurement of their absolute molecular weight distributions using differential viscometry detection. There is no observable degradation in molecular weight resulting from the N-methylation, provided the excess methylating reagent is destroyed shortly after completion of the derivatization by quenching with potassium acetate. The validity of the molecular weight data obtained by the method is confirmed by light-scattering measurements on derivatized polymer and by comparison to the molecular weight of underivatized polymer that can be approximated from the intrinsic viscosity in concentrated sulfuric acid. The method is applicable to a variety of wholly aromatic polyamide structures. Examples are given.     

Modeling the structure of a polydisperse polymer brush

Numerical self-consistent field theory is used to study the structural characteristics of a polydisperse polymer brush. We consider the relevant case of a Schulz-Zimm distribution and find that even a small degree of polydispersity completely destroys the parabolic density profile. The first moment (average height) of the brush increases with polydispersity, while the average stretching in the brush decreases. The density profiles of separate chain length fractions in a single polydisperse brush are also strongly influenced by polydispersity. Short chains are found to be compressed close to the grafting interface, whereas longer chains have a characteristic flower-like distribution. These longer chains stretch strongly (stem) when surrounded by smaller chains and decrease their stretching (crown) when only surrounded by longer chains. In line with approximate analytical models, our numerical exact results show that the polymer chains in the brush have localized end-point positions (no fluctuations) in strong contrast to the anomalously large fluctuations in the end-point positions of the homodisperse brush. Despite these effects, the scaling of average height with grafting density and number average chain length is unaffected by polydispersity. Many results that we have presented can be understood qualitatively from the bidisperse brush.     

Investigation of block copolymer micellization by high-performance size-exclusion chromatography

The formation and decomposition of micelles of the three-block copolymer polystyrene-block-poly(ethene-stat-butene)-block-polystyrene (Kraton G 1652, Shell) were investigated by high-performance size-exclusion chromatography in a mixed solvent dioxan–heptane. The association equilibrium may be shifted from the pure unimer to pure micelles by changing the composition of the mobile phase, and also (at constant composition) by a change in temperature. The shape of the chromatograms observed under conditions of comparable equilibrium concentrations of both species may be explained by the disturbance and reestablishment of the association equilibrium during separation in the chromatographic column. Experiments with changing flow rate show the dominating effect of degrading separation efficiency with increasing linear velocity of the mobile phase.     

Fractionation of a polydisperse polymer using an antisolvent. Application of continuous thermodynamics

Continuous thermodynamics is used to calculate liquid-liquid equilibria in a ternary system containing polydisperse polymer, one good solvent and one poor solvent (antisolvent). The polymer has a semiinfinite molecular-weight distribution which can be described by a gamma distribution. From Flory-Huggins theory, the logarithm of the distribution ratio of the polymer is a linear function of the molecular weight. Because the distribution of polymer between the two liquid phases is very sensitive to the choice of binary Flory parameters. The Flory parameters must be fitted to the ternary data. Results are given for the system benzene, ethanol, and polydisperse polystyrene.     

Molecular mass calibration in size-exclusion chromatography of coal derivatives

A number of procedures have been investigated for the calibration of a size-exclusion chromatography (s.e.c.) column in the determination of molecular mass (MM) distributions of coal derivatives. The behaviour of narrow fractions of coal extracts in the MM range 200–3000 was compared with a variety of the more generally available calibration standards. Calibration with preparative s.e.c. subfractions of materials similar to those under study has been recommended. Polystyrene standards are satisfactory, however, for MM < 1000, but above this range other polymer standards should be sought. Universal and molar volume calibration do not apply to coal-derived materials.     

Influence of non-wetted fluored polymer packings in distillation columns—II Mass transfer

This study has been carried out on an industrial extractive distillation unit at atmospheric pressure with the ternary H₂O-HC1-H₂SO₄. The column is packed with non-wetted fluored polymer “Rashig” rings. The mass transfer is noticeably improved when the flooding percentage is high enough compared with classical wetted packings. A correction factor is introduced in Ramm's correlation for the calculation of the height of transfer unit in the liquid phase.     

Gel permeation chromatography of polyethylene. I. Calibration

An accurate GPC calibration is essential if computer techniques are to be utilized in obtaining the molecular weight distribution and degree of long-chain branching from an intrinsic viscosity and GPC trace of a polymer. The use of the National Bureau of Standards Linear Polyethylene Standard Reference Material, SRM 1475, to calibrate GPC is described. Employing this calibration, the Mark–Houwink relationship for linear polyethylene in 1,2,4-trichlorobenzene was established utilizing narrow molecular weight fractions derived through fractionation of SRM 1475 and other polymers. This Mark–Houwink equation was subsequently employed for the evaluation of high molecular weight fractions which were then used to extend the GPC calibration to the high molecular weight region not covered by SRM 1475. An iterative technique was used to obtain coincidence of the measured intrinsic viscosity and the viscosity calculated from the GPC data. The accuracy of the GPC calibration was demonstrated by obtaining coincidence of the measured and calculated viscosity of high and low molecular weight polymers of both narrow and broad polydispersity.     

Quantitative assessment of polymer molecular shape based on changes in the slope of the Mark-Houwink plot derived from size-exclusion chromatography with triple detection

A new approach is presented for gaining additional insights from the molecular weight distribution and intrinsic viscosity of polymers as obtained using size-exclusion chromatography in combination with refractive index, viscometry, and multiangle light scattering detectors. The approach allows for a more quantitative interpretation of the Mark-Houwink plot by assessing the variation of the slope as a function of molecular weight. No prior information on the inter- and intramolecular interactions of the polymer is needed. The proposed curvature parameter can be correlated to the structural and chemical properties (e.g., branching, composition, randomness) of the polymer. The influence of the covered molecular weight interval and the sample concentration on the precision of the method was studied. This new workflow can be utilized to assess the effect of the solvent system and conditions on the solvation behavior of polymers. To evaluate the applicability of the workflow, three case studies have been performed, including an analysis of ethylene-propylene-diene monomer, cellulose ether, and polyamide-4,10 samples. In addition, an open-access tool is provided, to aid polymer researchers in incorporating this approach in their work. The developed method can be used to quickly investigate whether an industrial polymer batch contains unwanted branched species or exhibits particular solvation behavior.     

Hydrodynamics of semibatch slurry bubble columns with polymer solutions

In this work we perform an experimental study of the hydrodynamics of semibatch slurry bubble columns in which the liquid phase is a solution of a high molecular weight hydrolyzed polyacrylamide. Experiments were conducted in bubble columns with two different diameters (10 and 29 cm.) In gas-liquid operation, the gas holdup decreases as the polymer concentration increases due to the formation of large stable bubbles. In the presence of high solids concentration, this trend is reversed in the larger column due to an increase in the number of small bubbles and an appreciable increase in the residence times of the large bubbles brought about by an increase in slurry circulation. The distribution of solid phase becomes more uniform as the polymer concentration increases. This trend is quantified by means of the application of a modified form of the sedimentation-dispersion model. The macromolecular conformation of the polymer in solution is altered by adding NaCl, whose positive ions screen negative charges in the polymer molecule producing a contraction of the coil. At the concentration levels used in this work, the addition of salt decreases the ability of the polymer to produce a more uniform solids distribution.     

High performance size-exclusion chromatography of anionic polymers in aqueous solutions

The applicability of high performance size-exclusion chromatography was tested for anionic polymers with a new type of column. It was found that a solvent salt concentration of 0.1M and an elevated temperature (60°C) prevented adsorption of the polystyrene sulfonate standards on the column packing. The calibration curve and the effect of the concentration on the retention volume remained, however, colum-dependent. We concluded also that the use of the column was restricted to the linear range of the calibration curve and to concentrations below 1 mg mL^?1 for the highest molecular weight standards. The influence of the flow rate (below 1 mL min^?1) on the retention volume was negligible. The main cause of errors when the universal calibration technique is used originated in the experimental determination of the intrinsic viscosities of the standards. The combination of the errors on the viscosity and on the experimentally determined retention volume easily introduced an error of 15% on the determined molecular weight of the sulfated polysaccharide k-carrageenan. The use of the universal calibration method for an exact molecular weight determination of anionic natural polymers is therefore still questionable.     

The onset of tube-like constraining effects in polydisperse polymer melts

Summary This paper describes the onset of the influence of entanglement effects on the mobility of polymer chains in a polydisperse melt. Extending a scaling relation between the critical molecular mass of homodisperse melts and segment number density yields in the case of polydisperse melts a functional equation for the critical chain length. The case of the normal distribution will be solved and discussed.     

体积排阻色谱法测定介孔材料的孔结构

分别合成了球形的苯基桥键和乙烷桥键两种新型杂化介孔材料.选用已知平均相对分子质量且具有窄相对分子质量分布的葡聚糖为探针溶质,采用动态光散射法测定了粒径,与经验公式计算结果接近.通过体积排阻法对两种材料的孔隙率和孔径分布进行测定并与氮气吸附法结果进行比较,实现介孔材料孔结构快速测定.结果表明,体积排阻色谱法测定苯基桥键和...