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).     

Characterization of Branched Poly (vinyl Acetate) by GPC and Low Angle Laser Light Scattering Photometry

Abstract

Poly (vinyl acetate), PVAC, synthesized by bulk polymerization over a range of initiator concentrations ([AIBN] = 10^?5 to 4 × 10^?3 g-mole/1), temperatures (50°C, 60°C, 70°C, and 80°C) and conversion levels (3 to > 90%) were characterized using low angle laser light scattering (LALLS) photometry to measure M_w of the whole polymers. A number of these samples were characterized using GPC with a differential refractive index (DRI) and LALLS detector to measure the molecular weight distribution (weight fraction versus M_w). M_w for PVAC samples synthesized at suitably low initiator levels at various conversions were found to agree with classical light scattering measurements after Graessley.

An electronic device and a technique which optimizes the sensitivity and the signal-to-noise ratio of the LALLS photometer throughout the molecular weight distribution (MWD) of the GPC chromatogram were devised. These considerably simplify the operation of the LALLS for both offline and online operation with GPC.

Most importantly it was unambiguously shown that the commonly used universal calibration parameter (UCP) with GPC, [n]M_w, is incorrect for polymers with molecules having the same hydrodynamic volume but different molecular weights, i. e., those with only chain branching (LCB), copolymers with compositional drift, and polymer blends. The correct UCP was found to     

Characterization of Copolymers and Polymer Mixtures by Gel Permeation Chromatography

Abstract

Estimation of molecular weights from GPC data is complicated when the polymer sample consists of a mixture of homopolymers or of statistical copolymers with nonuniform compositions. This is because sizes of solvated polymer coils depend on solvent interaction with both the homo-and hetero-units of the copolymers and because the extent of solvation of different homopolymers can differ. The overall degree of solvation may change effectively with composition and use of a single “average” set of Mark-Houwink constants in calibration procedures will then produce false molecular weight data from the GPC data. A new molecular weight average, M _x, is defined to overcome this problem. This average can be determined from the GPC chromatogram and intrinsic viscosity of the sample in the GPC solvent. Mark-Houwink coefficients are not needed. M _x lies between M _w and M _z.     

Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

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.     

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.     

Molecular characterization of poly(diisopropyl fumarate) by the absolute calibration method in molecular exclusion chromatography (GPC)

The present work demonstrates that it is possible to obtain the parameters K and a of the Staudinger-Mark-Houwink relationship between the intrinsic viscosity [η] and the molecular weight M of a polymer by applying the absolute method of exclusion chromatography to samples of poly (diisopropyl fumarate). The procedure is based on deducing the relationship between molecular weight and elution volume V from chromatographic runs of a stoichiometrically labeled polymer sample with a broad molecular weight distribution. By using double detection it is possible to obtain the relationship f(V)/h(V) = M(V)/M_n = exp (A-BV)/M_n where M_n is the osmotically determined number average of the molecular weight of the eluted polymer while f(V) and h(V) are the normalized elution curves obtained by the use of the polymer mass detector and the label detector respectively. A and B are the parameters of the calibration curve, i.e., the relationship between M and V which together with the intrinsic viscosity and the elution curves of several samples of the polymer allows us to obtain the relationship between [η] and M. The results have been verified with chromatographic data through the use of the universal calibration concept.     

Synthesis of Amphiphilic Azobenzene Functionalized Branched-Type Copolymer Based on Branched Poly(2-(Dimethylamino) ethyl methacrylate) and Investigation of Its Drug Release Properties

Here, we reported the synthesis of branched poly(2-(dimethylamino) ethyl methacrylate) (PDMAEMA) via a combination of activator generated by electron transfer atom transfer radical polymerization (AGET ATRP) and self-condensing vinyl polymerization (SCVP) techniques. The typical linear kinetics of the AGET ATRP of DMAEMA with the initiation of 2-(2-bromoisobutyryloxy) ethyl methacrylate (BIEM) was observed. The molecular weight (M_n ) of the branched PDMAEMA increased with the monomer conversion. The GPC traces of these polymers were unimodal and the molecular weight distributions (M_w/M_n ) were in the range of 1.30–2.10. The degree of branching (DB) determined by NMR spectra agreed with theoretical value. The branched amphiphilic copolymer functionalized with azobenzene was then prepared via AGET ATRP chain-extension of branched PDMAEMA with azobenzene monomer, 6-[4-(4-methoxyphenylazo)phenoxy]hexyl(meth)acrylate as the second monomer. The GPC traces of these branched copolymers showed the mono-peaks, which proved the successful preparation of copolymers. The properties of this branched copolymer in controlling drug release were also investigated. It was found that the drug release rate of chlorambucil can be controlled by various factors, such as polymer structure, light, temperature and pH values.     

Chromatographic mass of a polymer and its use for determining the molecular mass characteristics

The method has been proposed for determining the molecular characteristics of flexible-chain polymers that obey the universal calibration principle and for which there are available experimental data on the intrinsic viscosity. This method is based on studying the dependence of the hydrodynamic volume M _n[η], M _w[η], M _z[η], and M _η[η] on parameter a in the Mark-Kuhn-Houwink equation. It has been found that, for parameter a varying in the range from 0.5 to 0.8, the weight-average hydrodynamic volume M _w[η] remains almost unchanged. This allows estimation of M _w based on a single intrinsic viscosity value. The notion of the chromatographic mass of a polymer is advanced and is employed for determining other molecular mass parameters.     

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.     

Size Exclusion Chromatography of Polymers With Random Tetrafunctional Branching

Abstract

The behaviour of polydisperse branched copolymers of methyl methacrylate with a small amount of randomly situated tetrafunctional ethylenedimethacrylate units was investigated by means of size exclusion chromatography (SEC). A procedure has been suggested for the conversion of apparent values of molecular parameters of real polymer branched systems (M_{n, app}; M_{w, app} obtained from SEC data by calibration of the separation system using a linear polymer) into actual values. This was made possible by off-line coupling of SEC and viscometry. The branching was characterized by the weight average number of branching sites in the macro-molecule, m_w, and the branching index, y.     

Modification of the universal calibration of gel permeation chromatography to include macromolecules presenting a draining effect

A new universal calibration for gel permeation chromatography is proposed in which the hydrodynamic volume of the macromolecular chains is expressed by the quantity [η]M/Φ instead of the commonly used quantity [η]M (where [η] is the intrinsic viscosity, M is the molecular mass, and Φ is Flory's parameter). Introducing Φ into the hydrodynamic volume is necessary because its value changes from one polymer to another when the polymers present a certain draining effect. The proposed procedure also allows the determination of Φ of any wormlike polymer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 707–710, 2003     

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.     

Treating the polyelectrolytes as polymers with a draining effect. II. The behavior in the gel permeation chromatography

The behavior of the polyelectrolytes in the gel permeation chromatography (GPC) can be better understood if the modified universal calibration (log([η]M/Φ) vs. elution volume) is used instead of the “classical” universal calibration (log[η]M vs. elution volume). The value of Flory's parameter Φ is obtained from an equation established for nonionic polymers presenting a draining effect, considering that polyelectrolytes also behave as polymers with a draining effect. The modified universal calibration does not apply as successfully to polyelectrolytes as to nonionic polymers, because of their electrostatic exclusion in the pore surface of the GPC columns. Nevertheless, when polyelectrolytes are found in a high salt concentration solution, the modified universal calibration can be used to obtain their molecular mass, using nonionic hydrosoluble polymers as standard polymers. Moreover, considering polyelectrolytes as polymers presenting a draining effect and applying the modified universal calibration provides a better explanation for the electrostatic exclusion of these polymers from the pores of the GPC columns, using the Dubin–Tecklenburg model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1106–1113, 2006     

An Experimental Evaluation of a New Commercial Viscometric Detector for Size-Exclusion Chromatography (SEC) Using Linear and Branched Polymers

Abstract

Herein are reported some findings on the application of a new type of continuous automatic viscometer, in parallel with a differential refractometer, as a detector system for SEC. A universal calibration is required for the instrument and two methods of construction are applicable. The first is the customary peak-position calibration using polymer standards of narrow molecular-weight distribution and the second uses a single broad standard of known [Mbar]_w and [Mbar]_n. The two types of calibration are shown to give nearly-identical values of molecular weight when used to process chromatograms obtained from various linear homopolymer standards of varying chemical composition. These values compare favourably with those quoted by the suppliers of the polymer standards. One of the more powerful features of this instrumentation, namely its potential for estimating accurate molecular weights of branched polymers, is demonstrated by analysis of a series of branched polyvinylacetates prepared by a conventional bulk, free-radical polymerisation procedure. The calculation of the degree of chain branching is discussed. Another particular feature of the viscometer detector, its ability to indicate the presence of low concentrations of high-molecular-weight impurity in polymer samples, is also shown.     

GPC-[η]测定聚碳酸酯的长支链

本文的目的在于,在没有相同化学组成的线型待测聚合物试样的情况下,以普适标定线为基础,得到试样的 log[η]～logM 曲线,或从实验直接得到log[η]～V_e曲线,由此计算出G和G_v。 实验说明,支化对M[η]有影响,经修正之后,由GPC-[η]数据计算的?和[η]_b更接近光散射法和经典法测得的和[η]_b值。     

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.     

Determination of composition of ethylene–propylene copolymers by intrinsic viscosity

Intrinsic viscosities have been measured at 25° on five ethylene–propylene copolymer samples ranging in composition from 33 to 75 mole-% ethylene. The solvents used were n-C₈ and n-C₁₆ linear alkanes and two branched alkanes, 2,2,4-trimethylpentane and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). This choice was based on the supposition that the branched solvent would prefer the propylene segments and the linear solvent the ethylene segments, due to similarity in shape and possibly in orientational order. It was found that [η]_n ? [η]_br ≡ Δ[η] is indeed negative for propylene-rich copolymers, zero for a 56% ethylene copolymer, and positive for ethylene-rich copolymers. The Stockmayer–Fixman relation was used to obtain from Δ[η] a molecular-weight independent function of composition. The quantities (Δ[η]/[η])(1 + aM^?1/2) and Δ[η]/M are linear with the mole percent ethylene in the range investigated with 200 ≤ a ≤ 2000. The possibility of using these results for composition determination in ethylene–propylene copolymers is discussed. Intrinsic viscosities in the same solvents are reported for two samples of a terpolymer with ethylidene norbornene.     

Gel permeation chromatography: Examination of column efficiency

Gel permeation chromatographic (GPC) separations have been performed with several commercially available column packing materials. The results have been analyzed in the conventional manner to obtain the ratio of weight average to number-average molecular weight, M_w/M_n, for solutes with narrow molecular weight distribution. Various other parameters proposed to measure the efficiency of GPC columns have been evaluated and compared. It is proposed that the experimentally determined value of M_w/M_n for a series of different molecular weight samples with similar, narrow distribution for a given set of columns is a convenient parameter for comparing column efficiency in GPC. This parameter may be calculated from a single chromatogram unlike resolution, R, resolution index, RI, or specific resolution, RS, which require a pair of chromatograms. Results from the M_w/M_n method are usually in agreement with those from the R, RI, and RS calculations but one exception has been found. The number of theoretical plates calculated from the elution of a small molecule or from the polymer peak bears little relation to efficiencies predicted from the proposed M_w/M_n method or from R, RI, or RS.