Truths and myths about the determination of molar mass distribution of synthetic and natural polymers by size exclusion chromatography

This article discusses various aspects of the determination of molar mass distribution by means of size exclusion chromatography (SEC) in various application modes. The effects of erroneous specific refractive index increment (dn/dc), branching, column performance, and enthalpic interactions on the results obtained by different SEC techniques are discussed. Combination of SEC and a light scattering detector represents the most direct way to the molar mass distribution of all natural and synthetic polymers as it completely eliminates the need for column calibration and to a certain extent eliminates the dependence of the obtained results on some operational variables such as flow rate, temperature, or injected mass. A multiangle light scattering (MALS) photometer has become the most frequently used light scattering detector capable of determination of molecular size as another important polymer characteristic. This article contrasts SEC‐MALS method with other application modes of SEC from the viewpoint of some frequent confusions and misunderstandings. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40111.     

Characterization of poly (N‐vinyl formamide) by size exclusion chromatography–multiangle light scattering and asymmetric‐flow field‐flow fractionation–multiangle light scattering

The molar mass and the radius of gyration of three poly N‐vinyl formamide (polyNVF) synthesized in aqueous solution polymerization were characterized using two different fractionation techniques: size exclusion chromatography (SEC) and asymmetric‐flow field‐flow fractionation (AF4) coupled with a multiangle light scattering (MALS) and a refractive index (RI) detector. For the sake of comparison, the polymers were also characterized by MALS using the Zimm plot approach (no fractionation). The dn dc^?1 of the poly (N‐vinyl formamide) was measured (0.1564 mL g^?1) and it was found to be insensitive to the molar mass (in the range 150–450 kDa) and also to the eluents used (DDI water or mixed eluent DDI water/acetonitrile (80 : 20) at pH = 5.5). Interestingly, the concentrations of the samples injected in the SEC and AF4 should be different because concentrations in the range of 20–40 mg mL^?1 used for the AF4 caused overloading and anomalous elution in the SEC and hence misleading molar masses. At adequate concentrations in each fractionation equipment, the molar masses were in reasonable good agreement although AF4/MALS provided larger values than the other two techniques likely because samples were not filtered before injection. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42434.     

Molecular characterization of α,β-poly(N-2-hydroxyethyl)-dl-aspartamide derivatives as potential self-assembling copolymers forming polymeric micelles

A family of graft copolymers derivatives obtained from α,β-poly(N-2-hydroxyethyl)-dl-aspartamide (PHEA) have been studied as potential self-assembling macromolecules forming stable polymeric micelles at low critical micellar concentration. These polymers are obtained grafting on PHEA poly(ethylene glycol) (PEG) (M_w 5000 g/mol) (PHEA-PEG), hexadecylamine (PHEA-C₁₆) or both moieties (PHEA-PEG-C₁₆). The PHEA derivatives were characterised by a multi-angle light scattering (MALS) photometer on line to a size exclusion chromatography system in obtaining the molar mass distribution of the polymers. In addition, to investigate the capacity to form micellar aggregates in aqueous medium the MALS photometer was used in off-line batch mode in obtaining molar mass and dimension of the polymeric aggregates.     

Characterization of molecular structure of acrylic copolymers prepared via emulsion polymerization using A4F‐MALS technique

The study is primarily focused on the possibility to utilize organic asymmetric flow field‐flow fractionation (A4F) coupled to a multi‐angle light scattering (MALS) detector for the characterization of copolymers of methyl methacrylate with various acrylates prepared by emulsion polymerization. The effects of acrylate monomer type and content on the molar mass distribution and degree of branching of acrylic copolymers have been studied by A4F‐MALS using tetrahydrofuran as a carrier solvent. It has been found that the growing amount of acrylate results in the increase of molar mass, polydispersity, and branching degree as a result of chain transfer to polymer. Highly branched compact macromolecules with ultra‐high molar mass were identified in all copolymers containing a high level of acrylate. In contrast to size traditionally used exclusion chromatography, organic A4F‐MALS has been proved as a very efficient technique for the characterization of high molar mass acrylic emulsion copolymers. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40995.     

Characterization of Methocel™: Correlation of static light-scattering data to GPC molar mass data based on pullulan standards

Using low-angle laser light-scattering (LALLS) and multiangle laser light-scattering (MALLS) techniques, absolute molar mass averages were determined for a wide variety of polymers in the Methocel™ product line produced by The Dow Chemical Company. These data were correlated to GPC molar mass averages obtained from column calibration using pullulan standards. It was determined that the pullulan equivalent molar mass averages overestimated the values determined by light scattering by a factor as high as 3.2. Mark-Houwink parameters were calculated based upon values for the pullulan standards and application of the universal calibration concept. Sample preparation issues and chromatographic conditions that impact data quality are also presented. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 70: 2197–2210, 1998     

Mark–Houwink equation and GPC calibration for linear short-chain branched polyolefines,including polypropylene and ethylene–propylene copolymers

The reduction in molecular dimensions due to the presence of short side chains in otherwise linear polyolefins can very simply by calculated by assuming that the configuration of the main chain is not influenced by the side chains. This enables us to express the intrinsic viscosity–molar mass relationship as a function of the mass fraction of side chains (S): [η] = (1 ? S)^α+1K_PEM_ν^α and, with use of the universal calibration principle, to convert the GPC calibration for purely linear polymers samples into the calibration for short-chain branched polymers: M^* = (1 ? S)M. Experimental data from literature on short-chain branched poly-ethylenes, and our own data on ethylene–propylene copolymers are used to verify the above assumption. It appears that the experimentally found relations between [η], M_w and M^*_w (GPC) within the usual accuracy justify this approach.     

Molar Mass Characterization and Solution Behaviour of Poly(ether amide) Dendrimers

Summary Poly(ether amide) dendrimers with different molar masses were investigated using Size Exclusion Chromatography (SEC) with linear standard calibration and Matrix Assisted Laser Desorption/Ionization – Time-of-Flight – Mass Spectroscopy (MALDI-TOF-MS). The SEC behaviour of the dendrimers was investigated in different column systems, in pure and in mixed N,N-dimethylacetamide with water and LiCl. This behaviour was compared to linear poly(styrene) and poly(2-vinyl pyridine) standards. Kuhn-Mark-Houwink-Sakurada relationship yielded evidence about the molecular shapes of the polymers in solution and explained the different solution behaviour of the polymers. The universal calibration method was tested for its application to molar mass determination of poly(ether amide) dendrimers.     

Characterization of polyamideamine‐epichlorohydrin (PAE) resin: Roles of azetidinium groups and molecular mass of PAE in wet strength development of paper prepared with PAE

Polyamideamine‐epichlorohydrin (PAE) resin is a crosslinked heteropolymer having cationic charges, and has been widely used as a wet strength agent of paper in the papermaking process. In this study, more accurate molecular mass values of PAE were determined by size exclusion chromatography attached with a multi angle laser light scattering detector (SEC‐MALS). The obtained weight average molecular mass (M_w) values of commercial and laboratory‐made PAE samples were 1,140,000 and 494,000, respectively, and these values were much higher than those reported so far. SEC‐MALS analysis also revealed that PAE molecules had highly crosslinked structures and extremely wide molecular mass distributions. Molecular mass values and content of 3‐hydroxy‐azetidinium (AZR) groups in PAE and PAE intermediates during the course of PAE synthesis were also determined by the SEC‐MALS and ¹H NMR methods, and the relationships between these values and the wet strength development of handsheets prepared with these PAE samples were studied. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 2249–2255, 2005     

Depolarization behaviour of dilute polymer solutions: II. Angular dependence and analyzer absorption

Study of the depolarization behaviour of dilute polymer solutions leads to determination of the Cabannes factor, necessary for correcting the Rayleigh ratio used in light‐scattering calculations for deviations due to anisotropy. We present here a method to determine the Cabannes factor for polymers as a simultaneous function of both scattering angle and molar mass, accomplished by coupling size‐exclusion chromatography with depolarization multi‐angle light scattering (SEC/D‐MALS). The depolarization behaviour of brominated polystyrene (PSBr), previously studied at a right‐angle geometry, is seen to possess a non‐trivial angular dependence in addition to being a function of molar mass. We also demonstrate initial attempts at correcting SEC/D‐MALS results for absorption of light by the Polaroid filters that act as analyzers in the optical train of the system. Copyright © 2003 Society of Chemical Industry     

Correlation between molecular structure and copolymer composition and the Mark-Houwink constants of methyl methacrylate/N-phenylmaleimide copolymers

The determination of Mark-Houwink constants using gel permeation chromatography data, based on a universal calibration and Ubbelohde capillary viscosimetry, for methyl methacrylate (MMA)/N-phenylmaleimide (NPI) copolymers of different molar mass or molar mass distribution has been examined. Mark-Houwink constants of bimodal molar mass distributions could not be obtained. They give, under the prerequisite of similar chemical composition, considerable deviations from the usual relation between intrinsic viscosity and molar mass. The Mark-Houwink constants determined for MMA/NPI copolymers with monomodal molar mass distributions containing 20–30 mol-% NPI at 35°C in tetrahydrofuran were K = 1.34 · 10^–4 and α = 0.73. Comparison with poly(methyl methacrylate) (PMMA) under the same measurement conditions shows constants of the Mark-Houwink relation with K = 1.43 · 10^–4 and α = 0.71, similar to those for monomodal MMA/NPI copolymers with 20–30 mol-% NPI. Higher contents of NPI in monomodal MMA/NPI copolymers or poly(N-phenylmaleimide) (PNPI) give no clear linear proportionality of the intrinsic viscosity to molar mass.     

Number-average molecular weight and functionality of poly(tetramethylene glycol) by multidetector SEC

Multidetector size exclusion chromatography (SEC) is used to simultaneously determine molecular weight and number of reactive end groups per chain (functionality) of poly(tetramethylene glycol)s. Hydroxyl groups are first quantitatively derivatized with phenyl isocyanate, providing an end-group-selective UV-absorbing tag. The number of end groups per chain is then determined from the SEC chromatogram using a UV detector. Molecular weight at each retention volume and the number-average molecular weight of the whole polymer are calculated by four methods involving (1) a concentration detector and a narrow standard log M calibration curve, (2) the UV detector and a narrow standard log M calibration, (3) a viscometry detector and a universal calibration curve, and (4) combined differential viscometry and concentration detectors using a universal calibration curve. The multidetector experiment provides a unique opportunity to assess the accuracy and limitations of each approach on low-molecular-weight polymers. In particular, the effect of end groups on the concentration detector response and the application of universal calibration principles at small molecular sizes are important factors. It is shown that the concentration response can be corrected by a simple relationship between detector response and reciprocal molecular weight. Also, the quality of calibration curves is critical to the calculation of accurate molecular weight. In general, log M calibration curves provide superior results to universal calibration methods. © 1995 John Wiley & Sons, Inc.     

Characterization of Anacardium occidentale exudate polysaccharide

The composition, structure and molar mass distribution of Anacardium occidentale exudate polysaccharide of Brazilian origin was investigated. The composition from gas–liquid chromatography (GLC) and ¹³C NMR was 72% β-D -galactopyranose, 14% α-D -glucopyranose, 4·6% α-L -arabinofuranose, 3·2% α-L -rhamnopyranose and 4·5% β-D -glucuronic acid. A thorough analysis of high resolution ¹³C NMR spectra from intact, partially hydrolysed and Smith-degraded polysaccharide enabled reliable chemical shift assignments to be made, and indicated the presence of three types of unit within the branched galactan core: linked at C-1 and C-3, at C-1 and C-6, and at C-1, C-3 and C-6. The polysaccharide was fractionated with respect to molar mass using water/ethanol as a solvent/non-solvent system. The polysaccharide and fractions were characterized by gel permeation chromatography (GPC), intensity light scattering, dilute solution viscometry and sedimentation velocity. The intrinsic viscosity in 0·1M aqueous NaCl at 25°C was found to depend on molar mass according to: [η]/(cm³g^-1)=0·052M^0·42. The molar mass distribution for the whole polysaccharide, determined by GPC using a universal calibration, exhibited two main peaks at 28000 and 67000gmol^-1, together with traces of much higher molar mass material. © 1998 SCI.     

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.     

Physicochemical characterization of carrageenans—A critical reinvestigation

Kappa‐, iota‐, and lambda‐carrageenan (food grade) were analyzed by static light scattering (MALS in batch mode) in 0.1M NaNO₃ at 25 and 60°C, earlier heated up to 90°C or not. At 25°C, there was a strong tendency for a concentration‐dependent aggregation in the order lambda < kappa < iota. At 60°C, all samples were molecularly dispersed. The strongly temperature‐dependent refractive index increments (equilibrium dialysis) differ. Data interpretation in terms of the wormlike chain model using the Skolnik‐Odijk‐Fixman approach led to an intrinsic persistence length around 3 to 4 nm and expansion factors as high as 1.5 and above in a thermodynamically good solvent for all three types. Triple‐detector HPSEC (DRI, MALS, viscometry) on the three commercial samples plus a degraded (by acidic hydrolysis) kappa‐carrageenan in the same solvent/eluant at 60°C yielded a uniform and slightly curved [η]‐M relationship for 5 × 10³ ≤ M/(g mol) ≤ 3 × 10⁶ and a nearly identical molar mass dependence of the radius of gyration. HPSEC at 25°C on kappa‐carrageenan confirmed formation of soluble aggregates. Special emphasis was put on analytical and methodological aspects. The reliability of the experimental data was demonstrated by analogous measurements on dextran calibration standards. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

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     

Molecular weight and the Mark‐Houwink relation for ultra‐high molecular weight charged polyacrylamide determined using automatic batch mode multi‐angle light scattering

This study presents an automatic batch mode (i.e., off‐line) multi‐angle light scattering (MALS) method for the molecular weight (MW) determination of ultra‐high MW (UHMW) polyacrylamide (PAM) homopolymer and acrylamide copolymers. This method combines a MALS detector with a sample dilution and injection device that automatically delivers a concentration gradient from a stock solution. The automation makes it practical to use the batch MALS method for routine MW analysis of UHMW polymers. The automatic batch MALS analyses of a series of poly(sodium acrylate‐co‐acrylamide) (30:70 mol %) in 1.0M NaCl show a non‐linear Mark‐Houwink relation in the MW range of 1.2 × 10⁶ to 12.6 × 10⁶ g mol^?1. The entire molecular weight range can be fit with a quadratic relation or two linear equations, one for molecular weight up to 5.3 × 10⁶ g mol^?1 and the other from 5.3 × 10⁶ to 12.6 × 10⁶ g mol^?1. The non‐linear Mark‐Houwink relation suggests that the extrapolation of the Mark‐Houwink equation beyond the measured MW range into the UHMW regions can significantly overestimate the MW of the UHMW polymers. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43748.     

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.     

Simplified preparation of low polydispersity,low molecular weight poly(D,L‐lactic acid) by liquid/liquid phase separation for drug delivery systems with discussion of molecular weight characterization

Poly(D ,L ‐lactic acid) (PLA) has been widely used in pharmaceutics and medicine. Low molecular weight (LMW) PLA is especially useful for rapidly degrading biomaterials such as those used for short‐duration drug delivery systems. There is scant information available in the literature regarding the purification and analysis of LMW PLA. In this paper we report (1) a convenient and effective polymer purification/fractionation technique to produce LMW PLA with narrow molecular weight distribution (MWD) and (2) analyses that were used to characterize the molecular weight and MWD of these polymers. A novel, convenient and effective temperature‐induced solution‐phase separation method was developed to produce narrow MWD, LMW (600–2000 g mol^?1) PLA. Molecular weights determined using gel permeation chromatography (GPC) with universal calibration, unlike those determined with the commonly used conventional calibration, showed good agreement with those obtained using several independent direct techniques. The phase separation induced by temperature reduction of a polymer in a single solvent system provided a simple and effective technique to produce narrow MWD, LMW PLA polymers. Additional advantages of this technique are: (1) only one solvent is required; (2) the risk of local complete solid polymer precipitation is eliminated; (3) it is reversible and not dependent on the rate of cooling; and (4) use of chlorinated solvents is avoided. This technology may open up a new opportunity for manufacturing LMW polymers with narrow MWD. We also found that GPC with universal calibration is a more accurate method than GPC with the commonly used conventional calibration for characterizing these polymers, and is straightforward to use especially now that on‐line viscosity detectors are widely available. Copyright © 2010 Society of Chemical Industry     

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).