The Instrument Spreading Correction in GPC. I. The General Shape Function Using a Linear Calibration Curve

Abstract

A general shape function is proposed for describing the instrumental spreading behavior in gel permeation chromatography (GPC) columns due to axial dispersion and skewing effects. The general shape function contains statistical coefficients which describe the axial dispersion, skewing, and flattening of ideal monodisperse standards. A method denoted as the “method of molecular weight averages” is used to derive equations to correct GPC number- and weight-average molecular weights and intrinsic viscosities calculated from linear molecular weight calibration curves. The validity of these equations is experimentally verified with data for polystyrene, polybutadiene, and polyvinyl chloride polymers in tetrahydrofuran. The physical significance of the correction equations and their statistical coefficients is discussed in relation to the observed GPC chromatograms. Application of this shape function to the numerical Fourier analysis method for correcting differential molecular weight distribution (DMWD) curves is outlined. Also, a method is presented for obtaining corrected DMWD curves from a fitted molecular weight calibration curve corrected for instrument spreading by use of the hydrodynamic volume concept.     

SEC–viscometer detector systems. II. Resolution correction and determination of interdetector volume

The closely related topics of resolution correction and the determination of interdetector volume were examined. In determining the interdetector volume (δ) by searching to superimpose two types of intrinsic viscosity calibration curve (one from narrow standards and one from a broad standard), the underlying equation based upon symmetrical axial dispersion theory was derived. This equation combined with experimental results showed that the local intrinsic viscosity value is very similarly affected by interdetector volume and by band spreading. The result supported the idea of using an effective δ to effect an axial dispersion correction to local intrinsic viscosity data. However, it also increased the difficulty of finding both δ and standard deviation (δ) simultaneously by numerical search. Furthermore, attempts to apply the method to the chromatograms of narrow standards showed inadequate superposition. Following calculation of skewing factors, the superposition problems were attributed to skewing of the chromatograms of the monodisperse polymer standards used. © 1993 John Wiley & Sons, Inc.     

The Instrument Spreading Correction in GPC. II. The General Shape Function Using the Fourier Transform Method with a Nonlinear Calibration Curve

Abstract

The instrument spreading function suggested in Part I of this series is investigated for use with the Fourier transform method for generating corrected elution volume chromatograms. The instrument spreading parameters are obtained using linear theory on narrow molecular weight distribution standards, as indicated in Part I. The corrected chromatogram is then combined with a nonlinear molecular weight calibration curve which was fit with a function suggested by Yau and Malone to generate true values of the number- and weight-average molecular weights.

The instrument spreading function is shown to qualitatively and quantitatively describe the dispersion, skewing, and flattening effects ordinarily found in GPC chromatograms due to imperfect resolution by the GPC columns. The Yau-Malone function is shown to be a very useful function for fitting nonlinear molecular weight vs elution volume calibration data. Although the Fourier transform method is shown to work well with analytically generated data, it is shown that a number of numerical problems must be overcome before it can quantitatively produce corrected elution volume chromatograms. Some of these numerical problems are discussed.     

Calibration of instrumental spreading for GPC

The proper use of the method for correcting instrumental spreading in GPC requires a precise calibration of the spreading characteristics of the instrument. Heretofore, such a calibration could be obtained only through the tedious reverse-flow experiments. A more rapid method of calibrating instrumental spreading is presented in this work. This method uses the leading halves of the chromatograms of several standard polystyrene samples. These chromatograms are normally used in the calibration of molecular weight; additional experimental steps are therefore not required. The calculation of the instrumental spreading characteristics from these chromatograms is also relatively simple. The instrumental spreading characteristics were found to depend on the elution volume but not on the nature of the polymer. Thus, calibration results from using polystyrene standards can be used to treat chromatograms for other polymers. For the present GPC instrument, the spreading was found to reach a maximum at an elution volume near 400,000 in polystyrene molecular weight. The existence of this maximum is in agreement with observations made by other investigators and is and indication that diffusion in the mobile phase is not an important contribution to instrumental spreading. The problem of skewing or tailing is discussed. Indication of skewing was observed for one of the higher molecular weight polystyrene samples but the extent of skewing was not severe at the present flow rate of 2 ml/min.     

Evaluation of GPC methods for estimation of Mark–Houwink–Sakurada constants

Constants for the Mark–Houwink–Sakurada relation can be established in principle from GPC measurements on broad distribution polymers. The method requires use of two samples with different intrinsic viscosities or a single polymer for which [η] and M ⁿ M ^w are known. The [η]–M ^w combination is not reliable because M ^v and M ^w are often very similar in magnitude. The [η]M _n method is likewise not recommended because of the influence of skewing and axial dispersion effects on the GPC measurement of M _n. The simplest and safest way to use GPC data to estimate the MHS constants involves the measurement of GPC chromatograms of two polymer samples with different intrinsic viscosities. The method is not confined to the solvent used as the GPC eluant. The MHS constants derived from GPC appear to reflect the molecular weight range of the calibration samples and may not be as widely applicable as those from the more tedious classical methods which employ a series of fractionated samples.     

Characterization of polyvinyl chloride part I. Molecular weight determinations by gel permeation chromatography

The universal calibration and universal correction curves for the correction of resolution dispersion and skewing are established for polyvinylchloride (PVC). The effect of solution concentration on skewing is also demonstrated. The application of these curves to the determination of number and weight average molecular weights of PVC samples is illustrated. The results obtained are consistent with those determined by membrane osmometry and light scattering.     

Polymer reactors and molecular weight distribution. VII. Further development of gel permeation chromatography

The results of an investigation into molecular weight and resolution calibration of a gel permeation chromatograph are reported. Effects of sample amounts and solvent flow rate were observed. Severe skewing and tailing of the standard chromatograms were observed at 2.0 ml/min flow rate, relative to 1.0 and 3.0 ml/min. Resolution calibration by flow reversal was inadequate when skewing and tailing or sample impurity effects were significant. Differential molecular weight distributions (MWD) of broad-distribution polystyrenes were compared for four methods of resolution correction. Inconsistent oscillations were observed in the MWD's at low resolutions and higher molecular weights. None of the methods was completely adequate in accounting for skewing and tailing.     

A valid method of calibration which includes correction for dispersion in gel permeation chromatography

Two independently derived distribution function methods validate both the calibration curve and the dispersion correction of the “effective linear calibration” method used in gel permeation chromatography (GPC). Experimental conditions are specified for making the method more useful by permitting linear extrapolation of the calibration line, and for using a minimum number of standards. The independent methods quantitatively relate known differential of integral distribution functions for standard samples to their respective chromatograms. As such, they are useful calibration methods also, but are limited in scope and range.     

The Gel Permeation Chromatography of Asphalt and the Characterization of Its Fractions in Terms of Molecular and Unit Sheet Weights

Abstract

Asphalt obtained from a refinery in Montreal was dissolved in toluene then fractionated in a preparative gel permeation chromatograph (prep.-GPC). Twenty-three fractions differing widely in molecular weights were collected and characterized by analytical GPC, viscometry, vapor pressure osmometry (VPO), element analyses, infrared spectroscopy (IR), and nuclear magnetic resonance spectroscopy (NMR). Similar studies were also carried out, for comparison purposes, on aliphatic and aromatic hydrocarbons to elucidate structure information on the different asphalt fractions.

The GPC chromatograms of the fractions generally revealed narrow distributions indicating that their separation into different component groups has been reasonably well achieved. The number-average molecular weights [mbar]n of the fractions, as computed from their GPC chromatograms making use of the calibration curve prepared with polystyrene, polyoxypropylene glycol, and polyoxyethylene glycol, did not correspond to those obtained by the VPO technique. To overcome the problem, an alternate approach was developed whereby a number of calibration curves were tested for the asphalt fractions, and the one which yielded the [mbar]n values closest to those found by VPO method was     

Method of calculating molecular weight distribution function from gel permeation chromatograms. III. Application of the method

Six examples were used to illustrate the application of a previously reported method of calculating molecular weight distribution from gel permeation chromatograms. These examples show that the correction for the imperfect resolution of the GPC column is important when the distribution is narrow but minor when the distribution is broad. They show also that the variation of the resolution factor h, defined previously, with eluent volume can be neglected in the calculation. When the chromatograms are very narrow in distribution or when they are complex some difficulties are encountered. The two computer programs written to implement the previously described numerical calculations are shown to be adequate for these difficult cases but there are also limitations.     

Characterization of nylon 66 by gel permeation chromatography

The quantitative characterization of nylon 66 of various polydispersities has been carried out by gel permeation chromatography (GPC), using m-cresol solvent at 130°C. A Q-factor value of 13.9 for nylon 66 has been validated, by limiting viscosity-number determinations for the particular solvent/temperature combination described above. Using this value together with a simple correction technique for viscous fingering and unsymmetrical dispersion, the practical quantitative characterization of linear nylon 66 has been achieved. Construction of a universal calibration curve, based on hydrodynamic volume, gave a straight-line relationship for polystyrene fractions and nylon 66 samples covering a broad range of polydispersity values.     

Calibration of size-exclusion chromatography columns with polydisperse polymer standards. II. Applications

New methods for calibrating SEC columns by means of polydisperse polymer samples with known M_n and M_w have been tested with computer-generated chromatograms and with experimental data of high-performance SEC. Calculations with the artificial chromatograms show that accurate calibration dependences can be recovered even when polymers with broad and/or bimodal molecular weight distributions are used as standards. Polystyrene calibration calculated by the proposed method from chromatograms of five polydisperse polystyrenes follows closely the curve obtained in a conventional manner from nine narrow polystyrene standards. The dependence log M vs. ν for PMMA determined from chromatograms of six PMMA samples with moderately broad molecular weight distributions agrees well with the curve obtained by shifting the dependence for polystyrene using the universal calibration concept. The new method is particularly useful when SEC columns are to be calibrated for dextrans in water, where only a few standards having a rather broad molecular weight distribution are available, and can considerably improve the accuracy of molecular weight determination by SEC.     

Gel Permeation Chromatography Calibration. I. Use of Calibration Curves Based on Polystyrene in THF and Integral Distribution Curves of Elution Volume to Generate Calibration Curves for Polymers in 2,2,2-Trifluoroethanol

Abstract

A general method is proposed for obtaining gel permeation chromato-graphic (GPC) molecular weight (MW) and hydrodynamic volume (HDV) calibration curves for polymer-solvent systems where primary polymer standards are unavailable. The method is demonstrated by using a HDV calibration curve based on polystyrene in tetrahydrofuran (THF), in conjunction with integral distribution curves of elution volume for poly(methyl methacrylate) (PMMA) in THF and in 2,2,2-tri-fluoroethanol (TFE) for the generation of a HDV calibration curve in TFE. Transformation methods for generating secondary MW calibration curves from HDV calibration curves are discussed and applied to PMMA in THF and TFE, and to poly(trimethylene oxide), poly(vinyl acetate), and certain polyamides in TFE. The utility and reliability of the secondary calibration curves are demonstrated by comparing MW average and intrinsic viscosites obtained by GPC and by the classical methods. Molecular structural differences among th polyamide samples associated with the distribution of short- and long-chain branches are discussed in relation to their secondary calibration curves.     

Dispersion in gel permeation chromatography. A rapid numerical solution to Tung's integral equation

A rapid iteration method has been developed to correct the molecular weight averages calculated from raw GPC data for dispersion. Though simple in its performance, it covers the general case that the instrumental spreading characteristics (Tung's resolution factor h) depend on the elution volume. Moreover, it is irrelevant whether the calibration curve, being the logarithmic plot of the molecular weight versus the elution volume, is linear or not. The method has been applied to a number of well-characterized polystyrene mixtures and yields molecular weight averages which agree with those predicted theoretically. The effect of asymmetry exerted by the dispersion on both molecular weight averages M?_n and M?_w is also discussed.     

A cooperative molecular weight distribution test

The development of gel permeation chromatography (GPC) has provided a convenient tool for the rapid determination of molecular weight distribution. The question has arisen as to the suitability of the method for specification purposes. The present work, suggested by the Naval Air Systems Command, represents an attempt to assess the precision of the method through a series of tests carried out by a number of laboratories using identical procedures on the same samples. Ten laboratories agreed to take part. Naval Ordnance Station, Indian Head, worked out standard conditions for operation of the chromatograph, for calibration of the columns, and for analysis of the GPC curves. Two samples of polystyrene were used by the various organizations for calibration of their instruments. Number-average molecular weight, heterogeneity index, and cumulative molecular weight distribution curves were determined on four samples of carboxyl-terminated polybutadiene (CTPB) and two samples of hydroxyl-terminated polybutadiene (HTPB), all unidentified except by letter code. All laboratories used identical directions for setting up CTPB and HTPB calibration curves which were based on curves determined from vapor-pressure osmometer molecular weights and GPC count numbers of fractionated material. Variation among the different laboratories was 0.15 in heterogeneity index, and a maximum of 1200 in molecular weight provided one aberrant set of values was eliminated. The six samples had heterogeneity indices from 1.15 to 1.54, while molecular weight varied from approximately 3000 to 6000. The average coefficient of variation of the molecular weight values was 6.2 ± 0.7%, which is quite acceptable. Variation in heterogeneity index was too great for specification purposes when considered among the different laboratories, but may be sufficiently good when measured by any one laboratory.     

An analytical solution to Tung's axial dispersion equation. Applications in gel permeation chromatography

Equations developed for correcting M_n, M_w, and [μ] for imperfect resolution are generally satisfactory. Choosing the appropriate instrumental spreading function is however a very difcult task. There is need for further research on this problem, in particular with polymer standards for which the DMWD or even M_z is known (in addition to M_n and M_w). A criterion for resolution in GPC which is based on a solution of Tung's axial dispersion equation has been proposed. The operation of GPC in recycle mode appears very promising. Equations have been developed to interpret data obtained in this operational mode. It is probable that a great deal of work will be done in this area in the very near future.     

Comparaison des méthodes de fractionnement par chromatographie de perméation et par gradient d'elution pour la détermination des répartitions moléculaires des polypropylénes

Molecular weight distributions for polypropylene samples have been determined by a permeation fractionation method (GPC). Porous silica beads were used as a packing material for the columns. The set of columns allows a good separation of the polypropylene macromolecular chains in a range of molecular weights from 5000 to 1.5 × 10⁶, and the thermal and mechanical stabilities of these beads are very good. The calibration has been carried out with fractions of polypropylene of narrow molecular weight distribution prepared by a large-scale column fractionation. The molecular weights M?_w and M?_n and the ratios M?_w/M?_n calculated from the GPC curves show, in general, good agreement with the ones calculated from the column fractionation curves. However, the M?_w/M?_n ratios are always highter in the case of GPC fractionation. This could be due to diffusion phenomena.     

Determination of Polymer Branching with Gel Permeation Chromatography. Abstract of a Review

Abstract

The effect of long- and short-chain branching in polymer molecules on GPC separation is reviewed (1–4). The calculation of branched GPC curves is developed from the uiiiversal calibration techniques, which is based on the concept of hydrodynamic volume (M [η]) 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 the branching level increases, the curves arc shown to approach a limiting value. Methods of characterizing branching level3 and molecular-weight distributions of fractions and whole polymers from GPC and intrinsic viscosity data arc prcsentecl. An iterative computer program is described which was written to calculate the degree of branching in whole polymers. Long-chain branching in beveral low-density polyethylene samples was determined, using both the fraction and the whole polymer methods. Effects of various experimental errors and branching models were investigated. For polyethylene, the data show that the effect of branching in intrinsic viscosity is best described by the relationship (g ₃) _w = [η]_br/[η] whre (g _s is the Zimin-Stockmeyer expression for trifunctional branch points in a polydisperse sample.     

Differential gel permeation chromatography for quality control

For the direct comparison of similar polymers, as, for example, for quality control, differential gel permeation chromatography provides a simple, sensitive technique that is relatively insensitive to operational variables. One polymer is chosen as a standard and a solution of that polymer is used as the eluent in an otherwise conventional GPC. Differential chromatograms of slightly different polymers are both positive and negative with respect to the baseline. Positive portions represent an excess and negative portions a deficiency as compared to the standard. As in conventional GPC, the elution volumes of the differences indicate the molecular size ranges of the differences. The algebraic sum of the differences is zero. Examination of the raw curves with only general information about calibration and operating conditions tells nearly as much about the differences as carefully executed conventional GPC with complex data reduction.     

A new method for correcting axial dispersion in GPC

In this paper, a new method for correcting GPC results in order to take into account the axial dispersion of a given set of columns is proposed. The idea is to evaluate the different average molecular weights and the polydispersity for a given elution volume. In order to do so, one needs only to know the efficiency of the set of columns and the different derivatives at a given point of the chromatogram. Some possible applications of this method are reviewed mainly for the characterization of polydispersity and for the determination of the viscosity law if one uses the universal calibration.