Gel permeation chromatography on branched polymers

In gel permeation chromatography on long-chain branched polymers, calibration with linear samples leads to incorrect results. There are, however, several ways in which the data can be treated correctly. All of them call for the use of extra experimental information, such as viscosity or light scattering data of the whole polymer or the GPC eluent. The Drott—Mendelson method, using [η] of the whole polymer and GPC data, has been employed for analysing three low density polyethylene samples. The potentialities of viscometry and light-scattering measurements in the GPC effluent have also been examined. From [η], M_w and GPC data the long-chain branching index g′ can be derived in three ways, although it should be stated that the average g′-values so found for polydisperse samples are different.     

Evaluation of different branching functions used in the determination of random branching by GPC

Three branching functions are evaluated for use in the measurement of random branching by GPC. Initial evaluations of the functions g^1/2, g^3/2, and h³ were made by computer simulations of GPC experiments using published data of lightly and highly randomly branched polymers. Actual GPC experiments were then performed on characterized samples of lightly and highly branched styrene–divinylbenzene copolymers. The results indicate that h³ adequately predicts branching and molecular weight at all branching densities, whileg^1/2 is accurate only for lightly branched polymers and g^3/2 is accurate only for highly branched polymers. A means for predicting the M–[η] curve for branched polymers from the M–[η] calibration curve for linear polymer is proposed.     

Gel permeation chromatography of polyethylene. I. Calibration

An accurate GPC calibration is essential if computer techniques are to be utilized in obtaining the molecular weight distribution and degree of long-chain branching from an intrinsic viscosity and GPC trace of a polymer. The use of the National Bureau of Standards Linear Polyethylene Standard Reference Material, SRM 1475, to calibrate GPC is described. Employing this calibration, the Mark–Houwink relationship for linear polyethylene in 1,2,4-trichlorobenzene was established utilizing narrow molecular weight fractions derived through fractionation of SRM 1475 and other polymers. This Mark–Houwink equation was subsequently employed for the evaluation of high molecular weight fractions which were then used to extend the GPC calibration to the high molecular weight region not covered by SRM 1475. An iterative technique was used to obtain coincidence of the measured intrinsic viscosity and the viscosity calculated from the GPC data. The accuracy of the GPC calibration was demonstrated by obtaining coincidence of the measured and calculated viscosity of high and low molecular weight polymers of both narrow and broad polydispersity.     

GPC determination of molecular weights for EPM,EPDM, and polybutadienes

Molecular weights from GPC curves are determined for EPM, EPDM, and some polybutadienes. The determinations make use of a Benoit factor, B, which is defined and tabulated for the polymers studied. The use of this factor provides a convenient method of employing the Benoit hypothesis. The M _n from the GPC curves are compared with osmotic molecular weights to provide additional confirmation of the Benoit hypothesis. The M _v from the GPC curves are used with intrinsic viscosity data to establish [η]–versus–M relations.     

Branching and molecular weight distribution of polyethylene SRM 1476

A method of determining the distribution of branching in a polymer is developed employing limiting viscosity numbers (intrinsic viscosity), gel permeation chromatography (GPC), and absolute molecular weight determinations of fractions of the whole polymer. A molecular weight calibration of the GPC column set is first determined empolying these fractions. From the limiting viscosity number measurements of these fractions and their molecular weight distribution determined from the GPC chromatogram, the viscosity–molecular weight relationship is determined by a nonlinear least-squares fitting procedure. For the same molecular weight, the limiting viscosity number of the branched polymer is less than the limiting viscosity number of the linear polymer. From the ratio of the two, the number of branches per unit molecular weight of the branched polymer is calculated. The method was applied to SRM 1476, the standard reference branched polyethylene issued by the National Bureau of Standards. The branching density for the constituents of SRM 1476 rise from zero at molecular weights less than 10,000 to about 6 to 8×10^?5 at molecular weights of 50,000 and above. The branching of SRM 1476 was also determined by the method of Drott and Mendelson, giving a result in fair agreement with the above method.     

Evaluation of GPC methods for estimation of Mark–Houwink–Sakurada constants

Constants for the Mark–Houwink–Sakurada relation can be established in principle from GPC measurements on broad distribution polymers. The method requires use of two samples with different intrinsic viscosities or a single polymer for which [η] and M ⁿ M ^w are known. The [η]–M ^w combination is not reliable because M ^v and M ^w are often very similar in magnitude. The [η]M _n method is likewise not recommended because of the influence of skewing and axial dispersion effects on the GPC measurement of M _n. The simplest and safest way to use GPC data to estimate the MHS constants involves the measurement of GPC chromatograms of two polymer samples with different intrinsic viscosities. The method is not confined to the solvent used as the GPC eluant. The MHS constants derived from GPC appear to reflect the molecular weight range of the calibration samples and may not be as widely applicable as those from the more tedious classical methods which employ a series of fractionated samples.     

High-temperature coupling of high-speed GPC with continuous viscometry. I. Long-chain branching in polyethylene

The coupling of a high-temperature liquid chromatograph (Waters 150C) with a home-made continuous capillary viscometer is described. This detector is the only one suitable for high-speed GPC when the small volume of the mobile phase prohibits the coupling with a classical viscometer. The pressure drop of the GPC effluent through the capillary is continuously measured along with the refractive index change. This dual detection leads to the determination of the intrinsic viscosity as a function of the elution volume, thus allowing a precise use of Benoit's universal calibration. The accuracy of our system is demonstrated in the case of the characterization of linear and branched polyethylene samples. The results concerning the average molecular weights as well as the branching factors (structure parameter g′ and long-chain branching frequencyλ) are in close agreement with those obtained by the classical way (coupling traditional GPC and discontinuous viscometry). It is well known that an estimate of the λ coefficient is extremely dependent on several hypotheses. However, for a set of commercial low-density polyethylenes, we obtained λ values about 0.5 × 10_?4, with no marked change along the molecular weight range.     

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

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

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     

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.     

Long-chain branching in low-density polyethylene

A sample of a commercial low-density polyethylene was fractionated and values of number ? M_n and weight-average M_w, molecular weights obtained together with intrinsic viscosities [η], measured in decalin at 135° and in a theta-solvent, diphenyl at 118°. Results are compared with those obtained using samples of high-density polyethylene, of narrow molecular weight distribution, in decalin at 135° and in diphenyl at 125°. Values of the z-average mean square radius of gyration (S^?2)_z, are converted to the weight-average unperturbed state. The branching parameters g and g¹ thus obtained, indicate that long-chain branching increases with increasing molecular weight. Intrinsic ivscosities under theta-conditions for the low-density polyethylene fractions lead to a relationship [η]_θ = K _w^0·20, agreeing with the treatment of Zimm and Kilb. Some of the approximations involved in the estimation of long-chain branching are discussed.     

Untersuchungen zur Langkettenverzweigung in Polyäthylenen

Polyethylene samples of various densities and melt flow indices resulting from different polymerization processes have been investigated with respect to long chain branching (LKV). For that purpose several polymer fractions have been characterized by measurement of weight average molecular weights M_w and intrinsic viscosities [η], the latter ranging from 0,2 to 3,2 with high pressure samples and from 0,2 to 10 with low pressure material. The intrinsic viscosity difference of branched (high pressure) polyethylene compared to linear (low pressure) polyethylene is used as a measure of LKV. With high pressure polyethylene LKV increases with decreasing density. This dependence is strongest within the medium molecular weight range. Samples with varying LKV but constant density can be obtained by appropriate change of polymerization conditions. No LKV has been observed with low pressure polyethylene. This means a marked difference compared to high pressure material of equal density. Branching with low pressure polymers can therefore be ascribed to the short chain type only, which in particular results from copolymerization. Several mathematical approaches have been checked whether or not they can yield suitable information about n, the number of long chain branches per molecule. The best fit with our experimental data is obtained using the expression [η]v/[η]₁ = g^1,3 (n = f(g)) and assuming, that the average concentration of long chain branch points does not depend on molecular weight for fractions of the same sample (n/M = const.). If LKV ist taken into consideration, logarithmic normal molecular weight distributions are obtained for many high pressure polyethylenes (similar to low pressure material). Data are reported in support of the view, that performance characteristics are dependent on LKV. There is some evidence, that melt flow properties of polyethylene are improved with increasing LKV.     

Synthesis and characterization of branched polymers by a free radical approach using a novel ‘macroiniferter’

Free radical bulk polymerization of styrene and methyl methacrylate (MMA) was carried out using a novel ‘macroiniferter’ which resulted in branched polymers with relatively narrow molecular weight distribution. This approach involving the novel macroiniferter; poly[3-(t-butylperoxy)propyl disulfide] (PBPPDS) that has side chain peroxide groups and main chain disulfide linkages was developed to prepare soluble branched polymers as well as to control the extent of branching in vinyl polymers synthesized via a free radical route. The synthesis, characterization and thermal degradation studies of PBPPDS are reported here for the first time. The resulting polystyrene (PS) and poly(methyl methacrylate) (PMMA) polymers were characterized using gel permeation chromatography (GPC), intrinsic viscosity [η] measurements and the degree of branching was studied by the determination of g′ factor.     

Experimental arguments on the conformation of molecules in molten and glassy polymers

In molten non-crystallising polymers we find normal random coil conformations of the molecules. This is inferred from the theoretically predicted and experimentally observed relationships between the properties of solutions (relaxational modulus, viscosity, osmotic pressure and specific volume) and melts. It is also derived from the intrinsic viscosities (η) and the diffusion constants of molecules with a very high molecular weight in polymeric solvents (M = 10⁴?10⁵) of the same chemical constitution. Moreover the properties of melts (relaxational modulus, flow curve, viscosity) depend on chemical structure and long chain branching in the manner predicted assuming a random coil conformation. At the glass temperature T_g the conformation resembles that in the melt as the temperature dependence of the conformation at T > T_g shows ((η) in polymeric solvents, diameters of the domains in block copolymers). However, on cooling below T_g an irreversible volume shrinking process may lead to an inhomogeneous distribution of densities and possibly to an extended conformation of molecules in grain boundaries. Experiments show that only strong deviations from random coil conformations decrease the ultimate strength of a glass.     

New method for MWD determination in branched polymers

GPC data for long-chain branched polymers (low-density polyethylene) are interpreted with the aid of a polynomial expression for intrinsic viscosity in terms of the molecular weight. The resulting molecular weight distribution curves agree well with those derived in an earlier work based on certain assumptions regarding the degree of long-chain branching.     

Predictors of glass transition in the biodegradable poly‐lactide and poly‐lactide‐co‐glycolide polymers

The biodegradable polylactide (PLA) and polylactide‐co‐glycolides (PLGAs) are being widely investigated for use as scaffolds in bone and ligament reconstruction. The glass transition temperatures (T_g) for these polymers are generally greater than 37°C, causing PLA and PLGA devices to possess brittle characteristics in physiological conditions. To evaluate the possibility of obtaining PLGA polymers with T_g values below 37°C, we evaluated the determinants of T_g in PLA and PLGA copolymers. The T_g, changes in specific heat capacity (ΔC_p), and enthalpic relaxation (ΔH_g) in two consecutive heating cycles were correlated with lactide/glycolide content and intrinsic viscosity [η] for PLA, PLGAs 90:10, 75:25, 65:35, and 50:50. A linear correlation was observed between T_g and intrinsic viscosity, with 0.1 dL/g increase in viscosity resulting in an increase in T_g by about 3.55°C. The selection of PLA and PLGA copolymers with [η] values <0.19 dL/g, corresponding to a viscosity average molecular weight of <70 kDa, will obtain PLA/PLGA polymers with T_g values below 37°C. The lowest attainable T_g values were found to be 28–30°C. Intrinsic viscosity also correlated with ΔC_p differences between aged and rapidly cooled polymers, and is therefore important in predicting free volume changes within these polymers upon aging. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 1983–1987, 2006     

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.     

Solution properties of polyaniline

Solution properties of polyaniline (PANI) synthesized at various temperatures were studied using static light scattering (SLS), intrinsic viscosity, and dynamic light scattering (DLS). We demonstrated that average radius of gyration 〈R_g〉, intrinsic viscosity [η], and average hydrodynamic radius 〈R_H〉, of polyaniline molecules in dilute N‐methyl‐2‐pyrrolidinone (NMP) solutions increased with decreasing synthesis temperatures, i.e.; increasing molecular weight. SLS data demonstrate that second virial coefficient (A₂) decreased with increasing particle sizes suggesting that solubility of PANI in NMP decreased with increasing particle sizes. We also find that the polymers extend as the polymer concentration is lowered and that the increase in the hydrodynamic radius can be expressed by a power law of the electrostatic screening length. This behavior is typical of polyelectrolytes in dilute solution, providing a basis for understanding the conformation changes of this metallic polymer in solution. Copyright © 2009 Society of Chemical Industry     

Characterization of Anadenanthera macrocarpa exudate polysaccharide

Exudate gum from Anadenanthera macrocarpa Benth. trees was purified and fractionated using 0·1M aq. NaCl/ethanol as a solvent/non-solvent system. The composition of the polysaccharide was determined as 67% arabinose, 24% galactose, 2% rhamnose and 7% glucuronic acid, by a combination of high performance liquid chromatography of fully hydrolysed gum and colorimetric analysis of uronic acid. Molecular characteristics of the polysaccharide and its fractions were investigated by light scattering intensity, dilute solution visco-metry and gel permeation chromatography (GPC). The whole gum was shown to possess a broad molar mass distribution with Mw = 3·7×10⁶ g mol^-1 and [η] = 11cm³ g^-1. Hydrodynamic properties indicated a highly branched structure. Fractions were obtained covering a range of molar masses. The intrinsic viscosity in 1·0 M aq. NaCl at 25°C was found to depend on molar mass according to: [η]/cm³ g^-1 =0 ·0145 M^0·44. The hydrodynamic volume parameter [η]M gave a common GPC calibration for branched polysaccharide fractions and linear poly(oxyethylene) standards. ©1997 SCI