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.     

Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

Characterization of poly[di(carboxylatophenoxy)-phosphazene] by an aqueous gel permeation chromatography

A water-soluble phosphazene polyelectrolyte, poly[di(carboxylatophenoxy)phosphazene] (PCPP), was characterized using aqueous gel-permeation chromatography (GPC) with concentration (UV and RI) and molecular weight sensitive (multiangle laser light-scattering) detectors. Agreement was observed between the weight-average molecular weights determined by GPC with a light-scattering detector, conventional GPC using fractionated narrow PCPP standards, and also by static light-scattering measurements. The effect of chromatography conditions, such as ionic strength of the mobile phase, column resolution, and injection volume was investigated. Mark–Houwink constants of PCPP in aqueous solution (phosphate buffer, pH 7.4, 0.42MNaCl) were determined. The validity of the universal calibration curve and the occurrence of a secondary nonexclusion mechanism of separation in aqueous GPC of phosphazene polyelectrolytes are discussed. © 1996 John Wiley & Sons, Inc.     

Universal calibration assessment in aqueous gel permeation chromatography

It was the objective of this paper to assess the applicability of the universal calibration method to aqueous GPC/SEC with nonionic and anionic polymers using the Viscotek differential viscosity detector. Three water-soluble polymers—polyacrylic acid, dextran, and polyethylene oxide—were chromatographed using four Ultrahydrogel^TM columns with 0.3 M NaCl and 0.1M KH₂PO₄ as the mobile phase adjusted to pH 7. Three distinct calibration curves were obtained. Upon addition of 10% methanol, a reasonably good universal calibration curve was obtained. However, quantitative analysis of the data exhibited about 5% deviation in average M_w and M_n for sodium polyacrylate as calculated from the single curve as opposed to about 40% when calculated from the composite curve. The applicability of three theoretical models for the universal calibration method was assessed, and a recommendation was made for future work. © 1993 John Wiley & Sons, Inc.     

Use of continuous viscometer and light scattering detectors in characterization of polyolefins: Comparisons of data from individual and combined detectors

Molecular weights of polyethylenes have been characterized using differential refractometer (DRI), continuous viscometer (CV), and low-angle laser light (LALLS) detection. In normal operation with the latter two detectors, the DRI is also employed as a concentration detector. The intrinsic viscosity of the whole polymer can be derived from the CV without use of a DRI concentration detector. If one calibrates the size exclusion chromatography (SEC) columns using the CV detector, it is possible to use this universal calibration relation and the CV detector to calculate number average molecular weight (M_n) of the polymer. Weight average molecular weight (M_w) of the sample can be calculated using data from the LALLS alone, without reference to the DRI. These variations of the analysis were tested and the advantages and limitations of the different detectors were compared using standard reference polyethylene samples in solution in 1,2,4-trichlorobenzene at 145°C. © 1992 John Wiley & Sons, Inc.     

Calibration procedures in gel permeation chromatography

Procedures for the determination of the log molecular weight vs. elution volume calibration relation are reviewed for linear homopolymers. The calibration curve is readily established with narrow molecular weight distribution fractions. For broad molecular weight distribution fractions the peak molecular weight at the peak elution volume of a fraction's gel permeation chromatogram has to be calculated from average molecular weights. When well-characterised fractions of the polymer requiring analysis are unavailable, a calibration curve can be established by procedures which assume that the hydrodynamic volume of a polymer molecule in solution controls fractionation in gel permeation chromatography. These universal calibration procedures require information on Mark-Houwink viscosity constants or polymer unperturbed dimensions. The validity of hydrodynamic volume as the universal calibration parameter is discussed with special reference to the goodness of the solvent for a polymer and polymer polarity. Examples are given of the various calibration procedures which are employed in the determination of molecular weight distribution and average molecular weights for poly(methylmethacrylate), polyethylene and polyisoprene.     

Low-angle laser light scattering–aqueous size exclusion chromatography of polysaccharides: Molecular weight distribution and polymer branching determination

A low-angle laser light scattering detector (LALLS) used with size exclusion chromatography (SEC/LALLS) has been applied for the determination of molecular weight, molecular weight distribution (MWD), and degree of branching of polysaccharides in 0.5N NaOH aqueous solution. Data from both detectors [differential refractive index (DRI) and LALLS] are used to calculate the absolute molecular weight at each point in a sample chromatogram. The correct average molecular weight and MWD can be obtained without calibration methods used in conventional SEC. As a consequence of this technique, Mark—Houwink coefficients can be predicted from a single broad-distribution, homopolymer without recourse to time-consuming fractionation methods. Moreover, the hydrodynamic volume separation mechanism of SEC can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper, SEC/LALLS has been employed to obtain data about the branching parameters g_v and g_M for samples of amylose, amylopectin, starch, and glycogen. For three homopolymers (amylose, amylopectin, and glycogen), branching frequency (as measured by chemical means), and the branching parameters (g_v and g_M) are inversely related. This trend is consistent with theoretical predictions. For starch, a nonhomogeneous branching distribution is observed as a function of molecular weight.     

Change in GPC elution volume of polymers by adsorption onto porous glass as column packing

The elution volume of polystyrene or of poly(ethylene glycol) of various molecular weights was measured in both tetrahydrofuran and benzene at 40 or 60°C by means of gel permeation chromatography utilizing columns packed with crosslinked polystyrene gel or porous glass. When the polystyrene gel was used as the column packing, a relationship between log [η]M and the peak elution volume for polystyrene agreed with that for poly(ethylene glycol). Using columns packed with glass, however, the elution volume of polystyrene was smaller than that of poly(ethylene glycol) at the same log [η]M. The results are considered to be attributable to the adsorption of poly(ethylene glycol) onto the glass. The effect of the adsorption on the elution volume was evaluated by assuming a universal calibration for columns containing porous glass; the deviation of the elution volume from the universal calibration curve increased with increase in molecular weight. At lower temperatures, even polystyrene was adsorbed onto the glass. Therefore, to reduce the adsorption of polymers on glass, it is necessary to increase the temperature or use surface treatment when porous glass is used as a GPC column packing.     

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.     

Determination of molecular weight averages and molecular weight distribution by g.p.c. of N-trifluoroacetylated polyamides

To determine their molecular weight averages and molecular weight distribution, N-trifluoroacetylated (TFA) polyamides are studied using gel permeation chromatography in tetrahydrofuran at 25°C. Several calibration methods (calibration with polydisperse standards, universal calibration) are tested; among these, direct calibration of M_w of polydisperse samples vs. peak maximum of the corresponding g.p.c. chromatogram leads to the best results. Calculated molecular weight averages of nylon 6-TFA and Trogamid^R-TFA are compared with data from light scattering, viscometry and osmometry.     

Molar mass determination of poly(octadecene-alt-maleic anhydride) copolymers by size exclusion chromatography and dilute solution viscometry

The number average molar mass M_n of poly(octadecene-alt-maleic anhydride) (PODMA) copolymers calculated from data obtained by size exclusion chromatography (SEC) using a polystyrene (PS) calibration was found to be inaccurate. The use of SEC combined with dilute solution viscometry enabled a method to be developed using an iterative approach, which does not require knowledge of the Mark-Houwink constants for PODMA samples. A new calibration curve was constructed as a plot of molar mass M_u for PODMA. True number-average molar masses M_n (true) calculated using the new calibration are approximately twice the apparent molar mass M_n (app) based on a PS calibration for higher molar mass samples (>10?000 g mol⁻¹).     

Size exclusion chromatography with multiple detectors: Solution properties of linear chains of varying flexibility in tetrahydrofuran

Narrow molecular weight distribution polyisoprenes (PI), polybutadienes (PBD), poly(isobuty1enes) (PIB), poly(methylmethacry1ates) (PMMA), polystyrenes (PS), and poly(octadecy1 methacrylates) (PODMA) have been studied by size exclusion chromatography (SEC) in tetrahydrofuran (THF) with light scattering and viscometric detectors. The molecular weight (M) dependence of the intrinsic viscosity, [η], and radius of gyration, R_g, is reported for THF solutions of these polymers, in many instances for the first time. The availability of these data for a series of chains of varying flexibility allows a test of the universal calibration principle in SEC. Furthermore, an apparent dependence of the hydrodynamic parameter in good solvents, Φ, on chain stiffness is observed. All chains appear to exhibit hydrodynamic draining in THF. © 1996 John Wiley & Sons, Inc.     

Gel permeation chromatography of poly(dimethyl siloxane). I. The universal calibration

The Benoit universal calibration method has been tested for evaluation of GPC data of polydimethylsiloxane (PDMS) in toluene at 60°C. For the conversion of the calibration curve for polystyrene to the PDMS calibration curve, the Mark–Houwink equation for PDMS in toluene at 60°C was derived: [η] = 9.77 × 10^?5 M^0.725. The applicability of this universal calibration was proved by the experimental results on five PDMS model samples. For the correct evaluation of the PDMS elution curve, the use of the true calibration is inevitable, because the hydrodynamic volume of PDMS molecular weight unit is somewhat different from the polystyrene one.     

A new method for determining molecular weight distributions of copolymers

Measurement of the molecular weight distributions of copolymers by size exclusion chromatography (SEC) presents problems because the elution volume of any species may depend on its composition as well as its molecular weight. Also, the response of the usual concentration detectors may also be influenced by the copolymer composition as well as its concentration. These problems arise when the copolymer composition may vary with molecular size. Conventional SEC techniques are suitable for copolymers with invariant compositions. This article describes and illustrates a method for measuring molecular weight distributions of copolymers. In many cases, the variation of copolymer composition with molecular weight can also be determined. The technique uses three detectors: (a) an evaporative detector (ED) to measure the concentration, Δc, of the eluting species; (b) a differential refractive index detector (DRI) to measure the refractive index difference, Δn, between the solution and solvent at any given elution volume; and (c) a low-angle laser light scattering (LALLS) detector that measures the corresponding molecular weight of the eluting solutes. This latter measurement is possible because the appropriate values of Δn/Δc are available from the outputs of the other two detectors. For LALLS measurements of molecular weight all the species in the detector cell at any instant must have the same composition or, at least not have Δn/Δc that varies with composition. The method is illustrated with data from ethylene-propylene and ethylene-propylene-diene copolymers.     

Randomly branched styrene/divinylbenzene copolymers. I. Preparation,molecular weight characterization,and GPC analysis

A series of randomly branched copolymers of styrene and divinylbenzene were prepared using a benzoyl peroxide-initiated free-radical bulk polymerization at 78°C. DVB contents were varied from 0.01% to 2%. Two samples were polymerized with 0.4% DVB to different conversions: series 9A at 6% conversion and series 9B at 15% conversion (just short of the gelation point). Both samples were fractionated and the fractions characterized by ultracentrifugation, light scattering, osmometry, viscometry, and gel permeation chromatography. The data indicated that the fractions were not of narrow MWD and that the breadth of the MWD of the fractions from series 9B were greater than those of 9A. GPC calibration curves of M, [η], and M [η] were generated for both 9A and 9B fractions by employing curve-fitting techniques to the GPC data. For all of the fractions 9B, the molecular weight calibration provided accurate values of M?_z, M?_w, and M?_n, suggesting that no serious peak spreading had occurred in the GPC experiments. The universal calibration parameter M[η] for the 9A fractions agreed with that of linear polystyrene, while that of the high-conversion series 9B did not. It will be shown in a later paper that series 9B is highly branched, while 9A is lightly branched. Consequently, it is recommended that any GPC analysis of branching units make an allowance for the deviation of highly branched polymers from the linear M[η] calibration curve.     

SEC–viscometer detector systems. I. Calibration and determination of mark–houwink constants

Five different types of calibration curve currently used in size exclusion chromatography-differential viscometer (SEC–DV) systems were identified and their use summarized. A simple method of deriving weighting factors for fitting local intrinsic viscosity calibration curves was shown to greatly improve the precision of calculated molecular weight distributions. The problem of reliably extrapolating the fitted curves to allow for differences in sensitivity among detectors has yet to be examined. With regard to Mark—Houwink constants, a method of fitting data from the SEC–DV system to obtain more statistically sound values was derived. For the data used here, the new method involves fitting a plot of logarithm of the local intrinsic viscosity of the sample vs. logarithm of the universal calibration curve parameter, J_i. Results for the data obtained appeared only slightly more precise than those for the traditional method. However, the new method promises improved reliability. © 1993 John Wiley & Sons, Inc.     

Molecular weight distribution of polyphenylene sulfide by high temperature gel permeation chromatography

Poly(phenylene sulfide) (PPS) has been characterized using a novel high temperature gel permeation chromatograph (GPC). Samples were injected in slurry form at ambient temperature, and redissolved by an in-line precolumn heater at 250°C. A viscometer consisting of a capillary tube with inlet and outlet taps connected to a sensitive differential pressure transducer was used as sole detector, with deflections converted to concentration using the column calibration. Columns and viscometer were operated at 210°C. Universal calibration was carried out using intrinsic viscosity/molecular weight relations for polystyrene and PPS, determined by light scattering. Satisfactory operation was confirmed by agreement between intrinsic viscosity calculated from GPC with independently measured values, and comparisons with melt flow data. Samples of PPS tested were found to be of relatively narrow distribution, with M_w/M_n typically less than two.     

Polystyrene-equivalent molecular weight versus true molecular weight in size-exclusion chromatography

The evaluation of the size-exclusion chromatography (SEC) concentration elution curves by means of a calibration dependence obtained in a given SEC set for a polymer different from the polymer to be analyzed results in an error in the determination of both molecular weight and molecular-weight distribution (MWD). The problem is analyzed assuming the validity of the universal-calibration concept. The differences between the true and apparent values of molecular weight, MWD and M_w/M_n depend on and are expressed in terms of the parameters of the Mark-Houwink-Kuhn-Sakurada equation, describing the molecular-weight dependence of intrinsic viscosity, for the polymer to be analyzed and the polymer used for calibration. The differences in molecular weight and the M_w/M_n ratio are typically tens of percent and, in extreme cases, can amount up to a factor of three for molecular weight and a factor of two for the M_w/M_n ratio.     

Light-scattering and size-exclusion chromatographic characterization of hydroxyethyl cellulose acetate

A recently developed analytical method of combining off-line laser light scattering (LLS) and size exclusion chromatography (SEC) was used to investigate a set of moderately distributed hydroxyethyl cellulose acetate (HECA) samples in tetrahydrofuran (THF) at room temperature. Our results have shown that this new LLS + SEC method is suitable for the characterization of molecular weight distribution of HECA. By using this method, we have simultaneously determined two calibrations of V (cm³) = 45.3 ? 1.89 log (M) and D (cm²/s) = 2.45 × 10^?4 M^?0.60, where M is the molecular weight of HECA; V, the elution volume in SEC; and D, the translational diffusion coefficient in dynamic LLS. In addition, our results have also indicated that the chain conformation of HECA in THF at room temperature is a slightly extended linear coil. © 1995 John Wiley & Sons, Inc.     

Exclusion chromatography using porous glass. II. Application to hydrophilic polymers

A chromatograph employing five columns packed with porous glass of pore size 1250 Å to 75 Å provided peak retention volumes (V_R) that were reproducible and essentially independent of sample size and flow rate when aqueous eluents were used. Calibration was carried out with a series of dextran fractions and polystyrene sulfonate samples, both of moderately narrow molecular weight distribution. The universal calibration method, based on hydrodynamic volume, was tested for four different polymer types. All four types produced a common curve within experimental error, which indicates that absolute molecular weight distributions may be derived from aqueous exclusion chromatography data for at least these polymer types. Additional study using a higher salt concentration produced hydrodynamic-volume plots that superposed with those above. The use of the same set of porous glass columns with polystyrene standards in three different organic solvents produced calibration curves that agreed well with the aqueous curves after corrections were made for differences in available pore volumes.