Statistical moments of elution bands and their application in gel permeation chromatography of polydisperse macromolecules

Equations have been derived that relate the statistical moments of uncorrected and spreading-corrected chromatograms for a general form of the spreading function in gel permeation chromatography of polydisperse macromolecules. The first moment (centroid) of the chromatogram is shown to be directly given by the centroid, In M^*, of a suitably defined molecular weight distribution function of the polydisperse sample, regardless of the position of the calibration dependence, provided it is linear. Both the molecular weight M^* associated with the centroid of the chromatogram and its second central moment (variance) are but little sensitive to the shape of sample molecular weight distribution and can be easily calculated from the polydispersity index M_w/M_n, at least for polymers of a not excessively broad distribution. The derived relations are shown to find application in the calibration of GPC columns by means of characterized, polydisperse standards and in the separation of independent contributions to peak width which originate in sample polydispersity and in band broadening processes in the column. Improved column- and packing performance criteria are also proposed.     

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.     

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.     

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     

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.     

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.     

High performance gel permeation chromatography of polystyrene

Microparticulate crosslinked polystyrene packings in short columns have been investigated with high performance liquid chromatography instrumentation. Reliable molecular weight data for six polystyrene standards having narrow molecular weight distributions and for a polystyrene having a broad distribution have been obtained by optimizing the injection procedure, using a constant flow pump, and incorporating an internal standard into each injected solution. Experimental determinations of the dependence of the polydispersity for polystyrene standards on eluent flow rate and polymer diffusion coefficient were in agreement with a relation predicted from theoretical considerations of chromotogram broadening. Because of the dependence of chromatogram broadening on polystyrene molecular weight, high efficiency separations for high polymers were only obtained at low eluent flow rates. For low polymers, high efficiency separations may be performed at fast eluent flow rates. It was concluded that accurate molecular weight distributions can only be determined from chromatograms obtained at low eluent flow rates, which was supported by experimental measurements of polydispersity on polystyrene sample prepared by a radical polymerization at low monomer conversion. A differential weight distribution calculated from an experimental chromatogram for the polydisperse polystyrene determined at the lowest eluent flow rate (0.1 cm³min^?1) was compared with distributions predicted theoretically for polystyrenes prepared by radical polymerization. It was concluded that the experimental distribution contained a small contribution from chromatogram broadening and that most of the radicals in the polymerization of styrene terminated by combination.     

Calibration of thermal field-flow fractionation using broad molecular weight standards

Thermal field-flow fractionation (ThFFF) is a new elution-based separation method for determining molecular weight distributions of polymers. Calibration can be achieved using monodisperse standards of the specific polymer of interest. In order to expand the range of polymer types for which absolute molecular weight data can be obtained using ThFFF a calibration procedure has been developed and tested which uses only broad molecular weight polymer samples. The method requires two polydisperse molecular weight standards of the required polymer whose average molecular weight (normally M?_w) is measured by an independent method (e.g. light scattering). From the average molecular weight data and the ThFFF elution pattern (fractogram) the required calibration constants can be calculated. The method has been tested using the polystyrene-tetrahydrofuran system and gave satisfactory results when checked against a series of monodisperse polystyrene standards. This calibration approach should expand the applicability of ThFFF to include a wide range of polymer types.     

Mechanical degradation of high molecular weight polymers in dilute solution

The mechanical shear degradation of polydisperse polyisobutene and monodisperse polystrene in oils of different viscosities in the concentration range of 0.1% to 1% was studied using a high-shear concentric cylinder viscometer under laminar and uniform well-defined shear field conditions. Molecular weight distributions (MWDs) were measured by gel permeation chromatography (GPC). Degradation of polydisperse polyisobutene solutions narrows the distributions principally through the breaking down of large molecules. Degradation of monodisperse polystyrene broadens the distributions at lower shear stress. At higher shear stresses, the distributions do not broaden as much but are still broader than those of the original polymer. The final M_w/M_n ratios are considerably different from the value of 2 expected for random degradation. Hence, the degradation is likely a nonrandom process. It was found that the extent of degradation has a negative concentration dependence coefficient at relatively high molecular weight and a positive concentration dependence at lower molecular weight. Competing mechanisms of “stretching” and “entanglements” for degradation were postulated to explain the results. The degradation data indicate that the shear stress is the controlling parameter, not the shear rate. The shear degradation is independent of initial molecular weight and viscosity of the solvent.     

Gel permeation chromatography of polyoxymethylene

Gel permeation chromatography of polyoxymethylene has been studied using N,N-dimethylformamide as the solvent. Polyoxymethylene samples used here are a copolymer of tetraoxane with 1,3-dioxolane and a commercial polyoxymethylene whose molecular weight distributions are moderately broad. Their intrinsic viscosities [η] range from 1.4 to 2.8 dl/g. Factors affecting chromatograms are discussed, and the operating conditions were determined by using the analytical scale GPC. On the basis of these operating conditions, the molecular weight fractionation of polyoxymethylene was carried out by using the preparative scale GPC. It was found that polyoxymethylene can be effectively fractionated to give seven to ten fractions each of them containing the fractionated polymer ranging in weight from 0.2 to 8 mg when 40 mg polymer sample was used for a run of the measurement. The fractionated polymers were also found to have a narrow molecular weight distribution within a single peak, and their M_w/M_n values decrease with increasing molecular weight.     

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.     

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.     

Polyether polyols as GPC calibration standards for determination of molecular weight distribution of polyether polyols

Average molecular weights (M_n, M_w and M_p) are important characteristics of oligomers and polymers, and therefore there is a need to have a precise and reliable determination method. A gel permeation chromatography (GPC) coupled with a single refractive index detector was used to determine the molecular weight distributions of commercial polyether polyols calibrated against a series of polyether polyols with known molecular weights and low polydispersity. Results of these GPC analyses were compared to the ones calibrated against the commercially available polystyrene (PS) standards. The number‐average molecular weights (M_n) obtained with GPC using polyether polyols calibration were closer to the theoretical values than the M_n obtained using PS as calibration standards. Hence, these GPC analyses using polyether polyols as calibration standards can provide reliable determination of molecular weight distribution of polyether polyols and can be potentially applied to natural oil‐based polyols, including palm oil‐based polyols. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42698.     

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.     

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.     

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.     

On the accuracy of SEC analyses of molecular weight distributions of polyethylenes

Molecular weights of National Bureau of Standards SRM 1476 polyethylene have been reported by six laboratories. The measured values are in remarkably good agreements and all show that M _w from SEC/LALLS analyses is significantly lower than the same average determined by LALLS on the whole polymer itself. This is shown to be due to the presence of high molecular weight species which become too diluted on passage through the SEC columns to be observed in the LALLS detector. The resulting error in M _w and higher averages may vary from slight to very serioius, depending on the molecular weight distribution of the particular polyethylene. A procedure is described to detect the presence of such high molecular weight species.     

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.     

Concentration dependence of the diffusion coefficient in polymer solution and molecular weight distribution determined by the diffusion method

The effects of the concentration dependence of the diffusion coefficient of a polymer solution (polystyrene in benzene and cyclohexane) in determining molecular weight distribution by the diffusion method are briefly discussed. The value of the ratio D_m0/D_A0 in a good solvent was found to be close to 1.0 for a polydisperse polymer and less than 1.0 for monodisperse polymers. Molecular weight distribution curves of the polydisperse sample were obtained by the diffusion method in cyclohexane and benzene, respectively. The molecular weight distribution curve obtained for the polymer used in benzene solution looked as if the polymer had a narrow molecular weight distribution. The phenomena cited above were interpreted in the light of the concentration dependence of the diffusion coefficient of polymer solutions.