Comparison of number–average molecular weights calculated by GPC and membrane osmometry

Data are presented which show that when a polymer contains an appreciable amount of low molecular weight species below the diffusion limit of the osmometer membrane, the osmotic molecular weight, M?_n, is generally higher than the M?_n calculated from gel-permeation chromatography (GPC). Experiments were performed on samples of poly(vinyl chloride) (PVC) and high-cis polybutadiene polymers. Osmotic data were obtained in the usual manner, while GPC data were obtained using the universal calibration approach. It was found that when all polymer species below approximately 10,000 molecular weight were excluded from the calculation of M?_n by GPC, agreement in M?_n was obtained between membrane osmometry and GPC. The data obtained suggest that the choice of M?_n as measured by membrane osmometry in the calibration of the GPC should not be done casually, as the measured M?_n may not reflect the “true” value of that sample, especially when the polymer sample contains an appreciable amount of low molecular weight material.     

Universal Calibration and Molecular Weight Averages in Gel Permeation Chromatography Illustrated by Cellulose Nitrate and Poly(oxypropylene)

Abstract

The nature of the averaging process in the analysis of gel permeation chromatograms was examined for cases where the molecules in the detector cell of the apparatus were of different molecular weight and of the same molecular weight. When the molecules have the same molecular weight, the hydrodynamic volume (1), [?]M, averaged across a chromatogram was found to become KM^a+1 for any molecular weight average at the elution volume corresponding to that average. [η] is intrinsic viscosity, M is molecular weight, and K and a are the appropriate Mark-Houwink constants. Thus when size separation is by molecular weight, the universal GPC calibration functions include KM_n ^a+1 where M_n is the number average molecular weight.

Cellulose nitrate and poly(oxypropylene) were analyzed using three sets of columns and two GPC instruments. KM_n ^a+1, KM_w ^a+1, and [η]M_w were found to represent the hydrodynamic volume since these functions fell on the universal calibration plot for nearly nono-disperse polystyrene standards. The function [η]M_n was displaced from the polystyrene universal calibration plot by factor which equaled M_w/M_n. The slopes and intercepts of the universal calibration plots were found to be completely consistent with the slopes and intercepts of the molecular weight calibration plots showing that the Mark-Houwink constants were correct. Intrinsic viscosity - molecular weight relations were presented for 12.0–12.6%N cellulose nitrate and for low molecular weight poly(oxypropylene), the latter relation being a correction of that of Sholtan and Lie (18).     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Characterization of poly(D,L-lactic acid) by gel permeation chromatography

A number of samples of poly(D ,L -lactic acid) (PLA) with weight-average molecular weights M?_w in the range 15,000–350,000 were prepared by a ring-opening polymerization. The molecular weight distributions (MWDs) of these samples were determined by gel permeation chromatography (GPC). The method involves a universal calibration of the columns on the basis of polystyrene standards and a rapid iteration algorithm leading to the establishment of the Mark–Houwink relationship. In addition, osmometry and viscometry data are presented. The effect of hydrolytic degradation on the MWD of two PLA samples was studied by GPC.     

Analysis of Low Molecular Weight Polymers with Gel Permeation Chromatography

Intrinsic viscosities and gel permeation chromatography (GPC) elution times were determined in toluene on commercially available standards of polystyrene (PSTY) and polymethyl methacrylate (PMMA) having M_n in the range of 10³ to 10⁵ and 10⁴ to 10⁶, respectively. In addition, elution times were determined on the discrete GPC peaks of dimer, trimer, tetramer, etc. as seen in lower molecular weight PSTY and PMMA. Intrinsic viscosities of oligomers were estimated by extrapolation of the Mark-Houwind-Sakurada equations determined from our data, and the results were used to establish a universal calibration curve over a wide range of molecular weights. A similar approach was taken by using literature data for the intrinsic viscosities of PSTY and PMMA in tetra-hydrofuran. It was verified by proton NMR that the universal calibration curve so constructed is useful at M_n, values as low as 300. No correction was necessary for chain length dependence of the detector response.     

Poly(2,6-diphenyl-1,4-phenyl oxide): Characterization by gel-permeation chromatography,light scattering,and solution viscosity

Ten unfractionated poly(2,6-diphenyl-1,4-phenylene oxide) samples were examined by gel permeation chromatography (GPC) and intrinsic viscosity [η] at 50°C in benzene, by intrinsic viscosity at 25°C in chloroform, and by light scattering at 30°C in chloroform. The GPC column was calibrated with ten narrow-distribution polystyrenes and styrene monomer to yield a “universal” relation of log ([η]M) versus elution volume. GPC-average molecular weights, defined as M?gpc = \documentclass{article}\pagestyle{empty}\begin{document}$\Sigma w_i [\eta ]_i M_i /\Sigma w_i [\eta ]_i$\end{document}, w_i denoting the weight fraction of polymer of molecular weight M_i, were computed from the GPC and [η] data on the polyethers. The M?GPC were then compared with the weight-average M?_w from light scattering. The intrinsic viscosity (dl/g) versus molecular weight relations for the unfractionated poly(2,6-diphenyl-1,4-phenylene oxides) determined over the molecular weight range 14,000 ≤ M?_w ≤ 1,145,000 are log [η] = ?3.494 + 0.609 log M?_w (chloroform, 25°C) and log [η] = ?3.705 + 0.638 log M?_w (benzene, 50°C). The M?_w(GPC)/M?_n(GPC) ratios for the polymers in the molecular weight range 14,000 ≤ M?_w ≤ 123,000 approximate 1.5 according to computer integrations of the GPC curves with the use of the “universal” calibration and the measured log [η] versus log M?_w relation. The higher molecular weight polymers (326,000 ≤ M?_w ≤ 1,145,000) show slightly broadened distributions.     

Block copolymers of polystyrene and poly(dimethyl siloxane). I. Synthesis and characterization

The block copolymers of the ABA type, poly(dimethyl siloxane-b-styrene-b-dimethyl siloxane), were synthesized by the anionic polymerization of styrene and cyclic siloxane monomer, hexamethyl cyclotrisiloxane (D₃) or octamethylcyclotetrasiloxane (D₄), with lithium or sodium biphenyl as initiator. The effect of initiator concentration, gegenion, and the polymerization temperature for styrene on molecular weight distribution (MWD) was investigated. Gel permeation chromatography (GPC) data show broader MWD of polystyrene prepared by sodium biphenyl in comparison to that produced by lithium biphenyl. The block copolymers have been characterized by infrared (IR) and nuclear magnetic resonance (NMR) spectra. The influence of dimethylsiloxy units on thermal stability of the copolymers has also been discussed.     

On-line viscometry combined with gel permeation chromatography. I. Instrumental calibration and testing with linear polymers

Gel permeation chromatography (GPC) was combined with flow time measurements on the eluent to provide both the distribution of hydrodynamic volumes and the distribution of intrinsic viscosities in linear polymers. Standard polystyrene samples were used to establish a universal hydrodynamic volume calibration as well as the zone spreading and viscometer transfer line tailing parameters. Viscometry data are particularly helpful in establishing the zone spreading parameters and the calibration curve at very high molecular weights. The results were applied to measurements on samples of linear polybutadiene and polyvinyl acetate. Agreement between values of M _w from GPC with those obtained by light scattering confirmed the universal calibration principle.     

Polymer characterization by coupling gel-permeation chromatography and automatic viscometry

A method is proposed for use of the universal calibration curve, i.e., the product of molecular weight and intrinsic viscosity versus retention volume, in calculating the molecular weight distribution of a polymer from gel-permeation chromatography (GPC) when the Mark-Houwink relation of the polymer in the solvent used for the GPC is unknown. This is achieved by measuring the viscosity of each fraction with an automatic capillary tube viscometer. Application of this technique to poly(vinyl chloride) and poly(vinyl acetate) proved to be successful.     

Development of gel permeation chromatography for polymer characterization. II. Universal calibration

GPC appearance volumes have been determined for a series of linear polyethylene, polystyrene, and polybutadiene fractions (M_w/M_n < 1.1) in trichlorobenzene at 130°C. and for the latter two series in tetrahydrofuran at 23°C. A polymer-type independent relationship between appearance volumes and the equivalent hydrodynamic radii of the polymer molecules has been demonstrated. The equivalent hydrodynamic radius is calculated from intrinsic viscosity data. It is proposed that this relationship can be used to construct a universal GPC calibration curve for polymers that assume a spherical conformation in solution. Methods for applying the universal curve to the determination of molecular weight averages and molecular weight distribution are described. In addition, a method is outlined by which the universal calibration curve can be empolyed for determining number-average Mark-Houwink constants from polydisperse samples.     

Universal calibration in GPC

The M[η]-elution volume calibration curve for gel-permeation chromatography (GPC) is based on the implicit assumption that the hydrodynamic volume of a solvated polymer species in the GPC columns is that which pertains at infinite dilution. This is not true of highly solvated high molecular weight fractions and results in apparent failure of this calibration in some instances. A model is presented to estimate hydrodynamic volumes of polymers at finite concentrations. The parameters required are polymer concentration, molecular weight, amorphous density, and the Mark-Houwink constants for the particular polymer–solvent combination. The calculated log (hydrodynamic volume)–elution volume relation provides a universal GPC calibration. The model accounts for the occasional shortcomings of the infinite dilution calibration and is essentially equivalent to it in noncritical cases. The use of the proposed calibration method is illustrated.     

Size Exclusion Chromatography of Poly(vinylpyrrolidone)

Abstract

Poly(vinylpyrrolidone) and poly(ethylene oxide) separate by hydrodynamic volume on Toyo Soda TSK-PW columns in a mixed solvent mobile phase of 50:50 (v/v) MeOH/H₂O containing 0.1M LiNO₃. From this separation a single universal calibration curve based on hydrodynamic volume [η]M can be obtained. Accurate weight average molecular weights of PVP were obtained by both SEC/LALLS and universal calibration showing good agreement between the two methods. SEC/LALLS overestimates the number average molecular weight for broad distribution polymers due largely to the lack of sensitivity of the LALLS detector to the low molecular weight portion of the polymers, while the universal calibration method slightly underestimates the number average molecular weight as compared to osmometric values.     

Separation system for fractionation of polyacrylamide by gel permeation chromatography

Samples of polyacrylamide were prepared by radical polymerisation of monomer in aqueous solution. Fractions of polyacrylamide were produced by a fractional precipitation technique with methanol as non-solvent. Molecular weights of the polyacrylamides were determined by solution viscometry. Analytical gel permeation chromatography (GPC) of the polyacrylamide samples and fractions was performed with porous silicas having a chemically bonded aminopropyl phase and with an eluent consisting of formamide-water (1:5). The GPC retention results indicated the successful separation of polyacrylamides having molecular weights in the range 10⁴–10⁶. GPC of polyacrylamide with this separation system appeared to be dominated by a steric exclusion mechanism.     

A Comparison of Polymer Separation Efficiency and Resolution by Gradient LC,GPC and TLC

Abstract

The specific resolution of gradient LC and reversed phase TLC methods for the separation of different molecular weight standards of poly(isoprene), poly(ethylene glycol), poly(ethylene oxide), poly(styrene) and poly(α-methylstyrene) were determined. It was found that gradient LC has an order of magnitude greater resolving power (for high polymers) than gel permeation chromatography (GPC) while TLC had from two to five times the resolving power of GPC in the molecular weight range investigated. This is a direct result of the greater selectivity of gradient LC and TLC techniques. The specific resolution is also dependent on the type of gradient used to achieve fractionation for the LC technique.     

Determination of molecular weight distribution of cellulose by conversion into tricarbanilate and fractionation

Two samples of cellulose (molecular weight 2.97 × 10⁵ and 1.25 × 10⁵) were transformed into carbanilates (CTC) which were then fractionated by the elution method at a constant composition of the acetone-water elution mixture with the column temperature gradually increasing from ?30°C to 30°C, and by the GPC method in acetone and tetrahydrofuran. Tetrahydrofuran appeared to be a more suitable solvent. The molecular weights of fractions obtained by the elution fractionation were determined by the light-scattering method in tetrahydrofuran. The width of fractions was determined by the GPC method (average M _w/M _n = 1.37); the [η] values and the Mark-Houwink constants (K = 5.3 × 10^-3, a = 0.84) for tetrahydrofuran at 25°C were determined. The calibration curve for the GP method was constructed by means of the fractions thus obtained; it was demonstrated that the universal calibration curve according to Benoit can also be used. It was demonstrated that the molecular weight distribution of cellulose can be conveniently determined by conversion into CTC followed either by the elution fractionation (for preparative purposes) or by fractionation by the GPC method (for analytical purposes).     

Universal calibration in GPC: A study of polystyrene,poly-α-methylstyrene,and polypropylene

The theoretical justification for using M[_η], or a similar quantity, as a universal calibration parameter in GPC is reviewed. The equation based on this parameter is applied to transform the primary calibration curve, obtained by means of polystyrene samples, into calibration curves for poly-α-methylstyrene, polypropylene, and linear polyethylene. The Mark–Houwink equations for these polymers, as they are used in the transformation, are discussed. The resulting GPC calibration curves are compared with molecular weights and peak elution volumes of fractionated poly-α-methylstyrene and polypropylene. The same comparison is made with samples of polypropylene and polyethylene having very broad molecular weight distributions. The agreement lies within experimental error.     

Molecular weight analysis of pitches and polymeric pitches by gel-permeation chromatography

The technique of gel-permeation chromatography (GPC) has been developed as a method for measuring molecular weight distribution in pitch materials. Molecular weight calibration data were obtained from measurements made on GPC fractions collected from a standard pitch. By solubilization of the polymeric portion of pitch through a reduction with lithium in ethylenediamine, the molecular weight range for analysis was extended to in excess of 3000. Mass spectroscopy has been used to further analyze some of the GPC fractions. The GPC calibration data can be employed, with the aid of computer analysis, to determine quantitatively number-average molecular weights M?_n weight-average molecular weights M?_w, and molecular weight distribution D (= M?_w/M?_n) in pitch materials.     

Further Studies on the Anionic Copolymerization of Styrene and Glycidyl Methacrylate in Toluene

Sequential anionic copolymerization of styrene and glycidyl methacrylate (GMA) was performed with the protection of argon under normal pressure, where styrene, GMA, toluene, THF, n-butyllithium and a small amount of lithium chloride (LiCl) were used as first monomer, second monomer, solvent, polar reagent, initiator and additive, respectively. Polystyrene-b-poly(glycidyl methacrylate) diblock copolymers (PS-b-PGMA) with well-defined structure and narrow molecular weight distribution were prepared by the copolymerization reaction of poly(styryl)lithium with GMA under certain temperatures. The copolymers were characterized using gel permeation chromatography (GPC), ¹H-NMR, ¹³C-NMR, thin layer chromatography (TLC) and hydrochloric acid-dioxane argentimetric methods. The effects of additives, copolymerization temperature and THF dosage on the copolymerization were studied. No chain transfer reaction of anionic polymerization of styrene in toluene was observed. Slightly broader molecular weight distribution of PS-b-PGMA was observed with the increase the GMA repeat units. Using THF/toluene blend solvent could reduce the polydispersity index (M _w /M _n ) and dissolve the copolymer better than toluene alone. Lower temperature (< -40°C) and LiCl are required to prepare PS-b-PGMA with narrower molecular weight distribution.     

Application of gel permeation chromatography to polyelectrolytes: Salt rejection mechanism and molecular-weight distribution

Gel permeation chromatography (GPC) of polyelectrolytes in dimethylformamide (DMF) is studied. Three methods of monitoring elution (conductimetry, viscosimetry, refractometry) are used to investigate the molecular-weight distribution and, independently, the chemical composition expressed in terms of the ionic charge density as a function of the chain length in two copolymers of acrylonitrile and sodium methallylsulfonate. The distribution on the gel of the neutral salt NaNO₃ added to the DMF and used for elution is discussed in terms of Donnan exclusion; in addition, it is concluded that to obtain the correct molecular-weight distribution, GPC measurements must be performed with an eluent containing a neutral salt at a concentration at least 5 × 10^?2M to prevent electrostatic exclusion. The main difficulty in reaching rigorous conclusions comes from the dependence of the calibration curve on the salt composition of the eluent owing to interactions—dependent on the quality of the solvent—between the polystyrenes used as standards and the porous silica gel. Nevertheless, this perturbation is small and the agreement between the average molecular weights obtained by GPC and by direct determination is good and indicates that the universal calibration proposed for neutral polymers is also valid for polyelectrolytes.     

Determination of the viscometric constants for chitosan and the application of universal calibration procedure in its gel permeation chromatography

The viscometric constantsa andK in the Mark-Houwink equation were determined in 0.5 M acetic acid-0.5 M.sodium acetate solution for chitosan fractionated by gel filtration. The weight-average molecular weight of each fraction was measured by the light-scattering method. The values obtained area=0.59 andK=0.119 cm³ g^–1.The molecular weightsMw andMn for fractionated chitosan were measured by GPC. The value ofMw by GPC was much different from that by light scattering and, therefore, a universal calibration procedure was applied to the data by GPC. It was concluded that, also in the case of a cationic polysaccharide such as chitosan, the universal calibration procedure is effective for obtaining the reliable molecular weight by GPC.