Effect of branching on the sedimentation behaviour in moderately concentrated polystyrene solutions

Sedimentation velocity measurements on moderately concentrated solutions of linear and four-branched star polystyrenes at both good (benzene) and theta (cyclohexane) solvent conditions are reported. The branched p′ lystyrenes show a different sedimentation behaviour than the linear ones. If, for instance, $\text{s}{}_0\text{s}$ is plotted versus c[η] the resulting curves for the branched polystyrenes are significantly steeper than the corresponding curves for the linear samples, both at good and theta solvent conditions. The difference in sedimentation behaviour between linear and branched polymers is further elucidated by utilizing the permeability concept and the scaling law hypothesis.     

Gel permeation chromatography: universal calibration for rigid rod and random coil polymers

The g.p.c. behaviour of poly (γ-benzyl-l-glutamate) (PBLG) samples, polystyrene standards and poly(2-vinyl pyridine) has been examined in N,N-dimethylacetamide (DMA) at 80°C. Solution viscosity measurements show that DMA is a good solvent for the flexible random coil polystyrene and that it promotes a helical rigid-rod shaped PBLG. Comparison of polystyrene and poly (2-vinyl pyridine) confirms that polystyrene separates strictly according to steric exclusion and that polymer/gel interactions are not involved. A PBLG calibration curve predicted from the polystyrene calibration by the [η] M universal calibration procedure was used to calculate average molecular weight and M_peak data from the PBLG chromatograms. The calculated $\text{M}\text{?}{}_{\mathrm{v}}$ values are in good agreement with experimental data. Plots of log [η] M_peak against retention volume for PBLG and polystyrene were coincident. These results suggest that the product [η] M is a valid universal calibration parameter for PBLG and polystyrene which have significantly different shapes. Comparison of theoretical equations relating the diameter of polystyrene hydrodynamic spheres to the half-length of PBLG helices suggests that the parallel-plane model may be a useful mathematical representation of pore geometry.     

Effect of molecular weight on the partial specific volume of polystyrenes in solution

The partial specific volume $\text{v}\text{?}{}_2$ of linear and branched polystyrenes has been measured as a function of molecular weight (1300<M_w<9×10⁶). In the low molecular weight range, the effect of end-groups is predominant. In the high molecular weight range (M_w > about 20 000), we have detected small but significant variations due to the intramolecular segment-segment contacts within the coil. We have proposed an empirical relation between $\text{v}\text{?}{}_2$ and the segment density of the macromolecule; this relation has been confirmed using highly branched polystyrenes. These results relative to dissolved polystyrenes are compared to experimental data obtained by different authors on pure liquid polystyrenes at different temperatures. Starting from simple additivity rules and from the known chemical composition of liquid polymers, we have shown that the variation of specific volume with high molecular weights is due to some phenomenon different from an effect of chain-ends.     

Dielectric study on dynamics and conformation of poly(d,l-lactic acid) in dilute and semi-dilute solutions

Fractionated samples of d,l-poly(lactic acid) (PLA) were prepared and the dielectric normal mode relaxation was studied for dilute and semi-dilute solutions of the PLA in a good solvent benzene. Results indicate that in the dilute regime the normal mode relaxation time is proportional to [η]M_w in agreement with the Rouse-Zimm theory, where [η] and M_w denote the intrinsic viscosity and weight average molecular weight, respectively. The dielectric relaxation strength which is proportional to the mean square end-to-end distance 〈r²〉 increases with increasing M_w with the power of 2ν, where ν is the excluded volume parameter determined from [η]. The relaxation time in the semi-dilute regime increases with increasing concentration C due to increases of the entanglement density and the friction coefficient. The relaxation time corrected to the iso-friction state agrees approximately with the dynamic scaling theories. The relaxation strength decreases with increasing concentration indicating that 〈r²〉 decreases on account of the screening of the excluded volume effect. The concentration dependence of 〈r²〉 agrees approximately with the scaling theory proposed by Daoud and Jannink.     

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.     

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.     

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     

Viscosity–temperature relationships for linear and 12-arm star polystyrenes in dilute solution

The actual viscosities (cP) of dilute solutions of linear and 12-arm star polystyrenes were measured in benzene, a good solvent, and cyclohexane, a poor to moderate solvent, as a function of temperature. The equations of Moore, previously established for solutions of linear polymers, were also found to be valid for star polystyrenes. A branching parameter b was defined which is essentially the same as g′ = [η]_br/[η]₁. The values of b found in benzene are close to the value of g′ for 12-arm star polystyrene in toluene, another thermodynamically good solvent. It thus appears that Moore's relationships have at least limited utility in studying branching in polymers.     

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.     

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     

A technique to infer structural information for low level long chain branched polyethylenes

A technique is proposed to relate the weight average molecular weight of linear chains, M_wBL, in low level long chain branched polyethylenes to their linear viscoelastic data. The new method is based on a previously reported empirical technique [Macromolecules 33 (2000) 7481] and was developed through the use of basic molecular theories. The new technique was applied to model systems whose linear viscoelastic properties were simulated using the molecular model of Milner et al. [Macromolecules 31 (1998) 9345] and to long chain branched metallocene polyethylenes. It is applicable to branched polyethylenes with low levels of long chain branching. In the case of a branched metallocene polyethylene, the structural parameter, M_wBL, inferred from the rheological data together with the GPC data such as M_w or M_n of the sample describes all aspects of the structure of the polymer. In the case of highly branched polymers, a possible modification of the technique is also proposed.     

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.     

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.     

Effects of chain ends and molecular weight on specific volumes of anionic polystyrene melts

Specific volumes of anionic polystyrenes prepared by butyl lithium initiation have been measured at temperatures between 110° and 237°C. Molecular weights of the fractions studied ranged from 2500 to 700 000. Plots of isothermal specific volume against reciprocal molecular weight (M^?1) are fitted by two straight lines intersecting at a molecular weight near 10 000. This parallels the behaviour of thermally initiated polystyrene fractions, which have different end-groups. Volumes attributable to end-groups are greater for the anionic polymers. The specific volume-molecular weight-temperature relations in the M ≤ 10 000 region are explained quite well by the equation of Francois and coworkers, in terms of end-group volumes and a uniform volume contribution from internal repeating units. Restraints on the motion of the butyl end-groups in these polymers by the attached polystyrene chain appear to be temperature dependent in terms of this model. Specific volumes of polymers with M ≥ 10 000 are affected by chain ends and by variation of the volumes of non-end repeating units with molecular weight. The present results parallel those which have been reported for partial specific volumes of polystyrenes in dilute solution and suggest that the same factors operate in both cases.     

Calibration of GPC columns

Abstract

Calibration in gel permeation chromatography is reviewed with special reference to M[η] as the parameter for universal calibration in the case of polymers     

Solution properties and unperturbed dimensions of poly(vinylidene fluoride)

A commercial sample of poly(vinylidene fluoride) (PVF₂) was fractionated and characterized. The following relationships were found: (η) = 1.93 × 10^?4M^0.677 (in dimethylacetamide at 25°C); (η) = 2.13 × 10^?4M^0.62 (in acetophenone at 85°C); (η) = 6.86 × 10^?4M^0.50 (in benzophenone at 190°C), leading to a value of the steric factor: σ = (〈r²〉₀/〈r²〉_0f) = 1.66 ± 0.05, which is in agreement with the crystalline properties of the polymer. The concept of M(η) as a universal parameter for g.p.c. calibration was valid for PVF₂ in dimethylacetamide.     

Partial draining of low-molecular weight polymers with flexible chains

The results of the theory of intrinsic viscosity based on the model of a worm-like chain have been used in analyses of the [η]-M correlation under theta conditions, and of the Stockmayer—Fixman plot for polymers with flexible chains at molecular weights M < 10⁵. Their viscosity behaviour appears to be influenced by the chain thickness d. An analysis of the available data allowed us to obtain reasonable d values for several polymers: polyethylene; poly(ethylene oxide); polystyrene; poly(methyl methacrylate), and poly(vinyl acetate). The effect of solvent on d was ascertained. The analysis shows that the reliability of the results obtained by the Stockmayer—Fixman method is the higher, the larger the proportion of data used which reside in the region M > 10⁵.     

Cohesive-energy density of shellac

The solubility parameter ($\text{δ}$) of shellac has been ascertained by the methods of solubility, structural contributions and intrinsic viscosity [η]. From the solubility method, respective δ ranges for shellac have revealed that shellac is not soluble in poorly H-bonded solvents but dissolves in moderately and strongly H-bonded solvents. The δ value of shellac estimated by the structural contribution technique has been found to be slightly lower. The δ values of shellac computed from [η]_max and related extrapolation are in close agreement with each other and with average value ascertained from the solubility spectra method. The molar volume of shellac from contribution technique has also been estimated. Shellac has been classified as a class III type of material for encapsulation having excessive polar groups.     

Synthesis and characterisation of star branched polyesters with dendritic cores and the effect of structural variations on zero shear rate viscosity

A series of branched polyesters consisting of poly(ε-caprolactone) (PCL) (degree of polymerisation: 5-200) initiated from hydroxy-functional cores and end-capped with methylmethacrylate have been prepared. The cores were third-generation hyperbranched polyester, Boltorn, with approximately 32 hydroxyl groups, a third-generation dendrimer with 24 hydroxyl groups and a third-generation dendron with eight hydroxyl groups. Finally, a linear PCL was synthesised as a reference material. All initiators were based on 2,2-bis(methylol) propionic acid (bis-MPA). ¹³C NMR spectra of the polymers showed that those with shorter arms contained unreacted hydroxyl groups on the core. Rheological measurements of zero shear rate viscosity, η₀, showed that the branched polyesters had a considerably lower η₀ than linear polyester with similar molecular weight. The low melt viscosity and the crystallity produced a rheological behaviour suitable for the film formation process for powder coatings. Measurements of mechanical properties of cured films showed that those with low arm molecular weight, M_a, were amorphous while those of high M_a were crystalline.