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.     

Determination of Polymer Branching with Gel Permeation Chromatography. Abstract of a Review

Abstract

The effect of long- and short-chain branching in polymer molecules on GPC separation is reviewed (1–4). The calculation of branched GPC curves is developed from the uiiiversal calibration techniques, which is based on the concept of hydrodynamic volume (M [η]) and previously established relationships for the effect of branching on molecular dimensions. Typical calibration curves are shown for different branching models and degrees of branching. As the branching level increases, the curves arc shown to approach a limiting value. Methods of characterizing branching level3 and molecular-weight distributions of fractions and whole polymers from GPC and intrinsic viscosity data arc prcsentecl. An iterative computer program is described which was written to calculate the degree of branching in whole polymers. Long-chain branching in beveral low-density polyethylene samples was determined, using both the fraction and the whole polymer methods. Effects of various experimental errors and branching models were investigated. For polyethylene, the data show that the effect of branching in intrinsic viscosity is best described by the relationship (g ₃) _w = [η]_br/[η] whre (g _s is the Zimin-Stockmeyer expression for trifunctional branch points in a polydisperse sample.     

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.     

Gel permeation chromatography in the study of the molecular weight distribution of the copolymer vinyl chloride–vinyl acetate

A sample of the commercial copolymer vinyl chloride–vinyl acetate was fractionated by the GPC method in the preparative scale. The fractions thus obtained were characterized by light scattering, viscometry, GPC in the analytical scale, chemical analysis, and IR spectroscopy. They were compared with those obtained by precipitation fractionation. The M?_w and [η] values from the light scattering and viscometry of fractions of the commercial copolymer were employed for the calculation of the Mark-Houwink equation valid in THF at 25°C for a copolymer with vinyl acetate content of 10–13%. Universal calibration of the [η]·M type was confirmed experimentally for the above polymer. Effects which could change the correct interpretation of the GPC data were discussed in detail. Correct interpretation of the GPC data showed an agreement between the GPC, light scattering, and viscometric data within 6–7%.     

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.     

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.     

D,L-乳酸-肌醇星形聚合物的合成与表征

以廉价易得的D,L-乳酸和无毒的肌醇(Ins)为原料,采用工艺简单、成本低廉的直接熔融聚合法合成了肌醇聚乳酸酯——以肌醇为核的星形聚D,L-乳酸(SPDLLA)。当n(Ins)∶n(LA)=1∶120时,SPDLLA较合适的合成工艺为:140℃预聚8 h后,在w(SnCl2)=0.3%催化下,170℃熔融聚合8 h,可获得最大特性黏数[η]为1.208 dL/g的共聚物。改变投料摩尔比,合成了系列SPDLLA,并用[η]、FTIR、1HNMR、GPC、XRD等手段进行了结构与性能表征,发现不同投料比所得的SPDLLA均为无定形态,它们的Tg(35~42℃)均低于线形聚D,L-乳酸(LPDLLA),最高Mw可达8 600,可望应用于药物缓释等领域。     

Intrinsic viscosity of polymer solutions at high shear rates

Although low-shear intrinsic viscosity is a well-accepted tool for polymer characterization, it often happens (particularly with increasing molecular weights) that it is easier to detect the high-shear (second) Newtonian viscosity η₂ rather than its low shear counterpart. It has also been predicted that because of a higher degree of order, due to disentanglement and orientation, high-shear viscosity data should simplify the prevailing correlations. The possibility of using high-shear viscometric data for polymer characterization was examined by determining intrinsic viscosities for several polyisobutylene samples through extrapolation of the high-shear ultimate viscosity numbers, UVN, to zero concentration: [η]₂ = lim UVN_{C → 0} = lim_{C → 0} (η₂–η_s)/η_sC where η_s is the viscosity of the pure solvent. Five samples of unfractionated polyisobutylene (molecular weights of 1.1 × 10⁶–6.6 × 10⁶) in toluene, kerosene, decalin, and gas oil at concentrations of 0.05–2.4 g./dl. were studied. Higher dilution was avoided because of the problem of onset of turbulence. The absence of shear degradation was ascertained by measuring low-shear intrinsic viscosity data before and after the polymer was exposed to high-shear conditions. The data show two types of behavior: for the lower molecular weight samples in the low-viscosity solvents the UVN decreases linearly with dilution, and for the higher molecular weights and higher solvent viscosities the UVN increases with high dilution, i.e., shows an upturn effect. The first type of data can be successfully correlated with appropriate molecular weights by using a typical Mark-Houwink equation. The exponents in these relationships are in the range of 0.28–0.64, increasing systematically with decrease of solvent viscosity and independent of the “goodness” of the latter. The data that show an upturn effect are not currently amenable to reliable extrapolation techniques. The upturn, however, predicts the conformation of very flexible, isolated polymer chains in viscous solvents under conditions of high shear.     

Effect of short-chain polymer on scission of long-chain polymer in solution by high-speed stirring

The effect of short-chain poly(methyl methacrylate) (PMMA) (P?_v = 950) on scission of longchain PMMA (P?_v = 6150) in solution by high-speed stirring was investigated by measuring changes in [η] and GPC, stirring at 30,000 ± 500 rpm at 30° ± 5°C benzene solutions containing the above two polymers at several concentrations and at various mixing ratios. It was found that the scission of long-chain PMMA was small or a little suppressed by addition of short-chain PMMA. The scission-suppressing effect of the coexisting polymers depended on the chain length. The longer the chain, the larger the effect. It was also found that the rate constant of scission, k, in Ovenall's equation had a certain significance in polymer systems with the same MWD but no significance in those with different MWDs.     

Viscosity and molecular weight distribution of ultrahigh molecular weight polyethylene using a high temperature low shear rate rotational viscometer

To obtain accurate measurements of the limiting viscosity number (LVN) or the intrinsic viscosity [η] of solutions of ultrahigh molecular weight polyethylene (UHMWPE), a low shear floating-rotor viscometer of the Zimm-Crothers type was constructed to measure viscosities at elevated temperatures (135°C) and near zero shear rate. The zero shear rate measurements for UHMWPE whole polymer and UHMWPE fractionated by hydrodynamic crystallization were compared with viscosity measurements at moderate and high shear rates (up to 2000 _s^?1) carried out in a capillary viscometer. The limiting viscosity number of UHMWPE decreases, as expected, with shear rate. The higher shear rate data could not be extrapolated to yield the correct zero-shear rate viscosities. Fractionation of UHMWPE gave 10 fractions ranging in LVN from 9 to 50 dL/g. A tentative integral molecular weight distribution for the whole polymer was calculated on the basis of the Mark-Houwink equation, but because it had been previously established only for lower molecular weight polyethylenes, it may not be accurate. A correlation was found between the LVNs for the fractions in the two types of viscometers.     

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.     

Rheological properties of concentrated polymer solution: Polybutadiene in good and θ solvents

The zero shear viscosity, η° of three polybutadiene samples having different molecular weights over a wide range of concentration (1.0–35.0% polymer) in good and θ solvents has been studied. Superposition of viscosity data has been made to give a single composite curve for each solvent by shifting them vertically by a factor (M°/M)^3.4, where M° represents the molecular weight of the reference sample. The shift factor is found to be proportional to M^3.4 in the region of higher concentration, which indicates that the 3.4-power law is valid for the data of polybutadiene. The double-logarithmic plots of relative viscosity η°_r as a function of c⁵M^3.4 yielded a single composite curve approximating a straight line with slope of unity at the higher values of the variables. The results indicate that over a considerable range of the variables (molecular weight and concentration) at a constant temperature, the relative viscosity is a single function of c⁵M^3.4. The results for double-logarithmic plots of zero shear specific viscosity η°_csp as a function of concentration confirmed those observed in polycholoroprene samples studied earlier that the η0_sp values in θ solvents at higher concentration region are found to be higher than those found in good solvents, whereas in the moderately concentrated region the values are just opposite in θ and good solvents. The viscosity crossover in θ solvents is not as sharp as is found in case of polychloroprene samples and that crossover, too, has taken place in the range of concentration of 11.7–31.6% polymer, which is comparatively higher than that of polychloroprene samples (6.06–21.0% polymer). The results indicate some relation between viscosity crossover and polymer polarity, supporting the idea of enhanced intermolecular association in poor solvents. To correlatethe viscosity data obtained in good and poor solvents, two methods, one given by Graessley and the other given by Dreval and coworkers involving the correlating variable c[η], were considered. The plots of relative viscosity η°, versus the correlating variable c[η] in benzene (good solvent) yielded one curve, but in the case of θ solvents (dioxane and isobutyl acetate), the same plots yielded three separate curves instead of a single curve, which is rather unusual. The appropriate correction on the correlating variable for chain contraction in the concentrated region in a good solvent moved the data to a common curve, especially in lower concentration region, but at the higher concentration region a slight overestimation of data seems to have been effected. On the other hand, the plots of log η as a function of correlating variable c[η] yielded a single curve for three samples in the good solvent benzene, but in poor solvents (diozane and isobutyl acetate) the same plots yielded three separate curves for three samples instead of a single curve, the reason for which is not known at present. However, the normalization of the correlating variable c[η] with Martin constant K_M reduced all experimental data of the polymer samples to a common curve. The correlation of the viscosity data by either of the two methods seems to be possible in the case of the nonpolar flexible polymer, polybutadiene.     

Triple-detector GPC characterization and processing behavior of long-chain-branched polyethylene prepared by solution polymerization with constrained geometry catalyst

Fourteen long-chain branched (LCB) polyethylene (PE) samples were prepared by a constrained geometry catalyst. The PE samples had average branching frequencies of 0.06-0.98 branches per polymer chain, as determined by the nuclear magnetic resonance spectroscopy (¹³C NMR). These samples, as well as five linear PEs were characterized using a gel permeation chromatography (GPC) coupled with online three-angle laser light scattering (LS), differential refractive index (DRI), and viscosity (CV) detectors. The root mean-square radius of gyration intrinsic viscosity ([η]), and molecular mass (M) of the PEs were measured for each elution fraction. Based on the comparison of the long-chain branching (LCB) PEs with their linear counterparts and the Zimm-Stockmayer equation, the distributions of long-chain branch frequency (LCBF) and density (LCBD) as function of molecular mass were estimated. It was found that although the LCBF increased with the increase of molecular mass, the LCBD showed a maximum value in the medium molecular mass range for most of the PE samples. The average LCBD data from the GPC analysis were in good agreement with the ¹³C NMR measurements. The rheological properties and processing behavior of these samples were also assessed. While the long chain branching showed significant effects on the modulus and viscosity, it did not improve the processing. Compared to linear PE, polymer melt flow instabilities such as sharkskin, stick-slip and gross melt fracture developed in extrusion of LCB PEs occurred at lower wall shear stresses and apparent shear rates.     

Preparative GPC in fundamental polymer synthesis

Summary A simple efficient preparative gel permeation chromatography assembly (prep GPC) has been built using largely commercially available components, (i.e., pump, columns, all glass solvent recirculating system) and its usefulness in fundamental polymer synthesis was demonstrated. The operating cost of prep GPC has been reduced and the safety much improved by the use of n-hexane as the mobile phase. Rapid one-recycle narrow fractionation (M_w/M_n=1.1–1.2) and purification of relatively large quantities (up to 20 g/loading) of polyisobutylene (PIB) samples is described. Operating parameters and efficiency are illustrated by examples. By the use of this equipment sufficient quantities of narrow MWD polyhydrocarbons can be conveniently and rapidly obtained for meaningful structure/property research.     

Steady shear and dynamic properties of biodegradable polyesters

The rheological properties of three biodegradable partially crystalline alipathic polyesters—poly ε carolactone (PCL), polylactic acid (PLA), and polyhydroxybutyrate-co-hydroxyvalerate (PHBV)—were investigated. Low shear viscosity (η), first normal stress difference (N₁), and dynamic properties (G′ and G″), were measured for each polymer using rotational instruments. High shear viscosity data was obtained using a capillary rheometer. Gel permeation chromatography indicates that both PLA and PHBV undergo degradation during processing. Thermal degradation rate constants for PLA and PHBV were determined from the time-sweep data. Data indicates that material functions are proportional to the molecular weight for PCL and PLA samples, and directly related to the HV content in the PHBV samples. The relaxation spectra were calculated from the G′ and G″ data using the regularization method and the applicability of the nonlinear Wagner equation was checked on these materials. Results are discussed in terms of variations in the molecular characteristics on rheological properties and their possible influence on the processability.     

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.     

Degradation and in situ reaction of polyolefin elastomers in the melt state induced by ultrasonic irradiation

The degradation and in situ reaction with polystyrene (PS) of polyolefin elastomers in the melt state induced through high intensity ultrasonic wave were investigated. The effects of initial molecular weight of polyolefin elastomers, irradiation time, ultrasonic intensity, as well as reaction temperature on the ultrasonic degradation of polyolefin elastomers melt were studied using a “static” ultrasonic vibration system. The results show that the degradation occurs mostly at the tip of the ultrasonic probe, and little or no degradation was observed at the distance of 5 mm or greater from the tip of the probe. The intrinsic viscosity [η] of polyolefin elastomers near the tip of ultrasound probe significantly decreases with irradiation time in the first 100 s and tends toward a limiting value for all samples. The degradation rates increased with an increase in ultrasonic intensity and decrease in reaction temperature. The ultrasonic degradation kinetics of polyolefin elastomers in melt state follows the equation: [η]_t = [η]_∞ + Ae^?kt. The fitting results by this equation accord well with the experimental data. The feasible ultrasonic degradation mechanism is proposed based on the viscoelastic characteristic of polymer melt. FTIR analysis confirms that the copolymer forms under ultrasonic irradiation for PS/POE mixtures and in situ reaction of polymer in melt state can be induced by ultrasonic irradiation. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Investigation of the interpolymer association between poly(vinyl alcohol) and poly(sodium styrene sulfonate) in aqueous solution

A viscosimetric method has been used to study the interpolymer association between poly(vinyl alcohol) (PVA) and poly(sodium styrene sulfonate) (PSSNa) in aqueous solution. At constant molecular weight of PSSNa, it was found that, the PVA and PSSNa associations were improved with the decrease of molecular weight of PVA and the decrease of its hydrolysis degree. The measurement of intrinsic viscosity [η] and the determination of Huggins associative coefficient K_H of different PVA samples were used to select the most appropriate PVA sample, which leads to homogeneous polymer–polymer mixtures (PVA with hydrolysis degree 87–89%, molecular weight 124,000–186,000 g/mol, intrinsic viscosity [η] = 1.02 dL/g, and Huggins associative coefficient K_h.ass = 0.76). The obtained results show that the interpolymer association between PVA and PSSNa, in aqueous solution, is mainly due to intermolecular hydrogen bonds between hydroxyl groups of PVA and sulfonate groups of PSSNa. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

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.     

两亲性苯乙烯嵌段共聚物的合成及结构表征

以α,α'-二甲基-α-乙酸-三硫代碳酸酯(BDATC)为链转移剂,采用可逆-加成-断裂链转移(RAFT)自由基聚合方法合成了末端带有—COOH官能团的两亲性嵌段共聚物聚苯乙烯-b-聚甲基丙烯酸聚乙二醇单甲醚-b-聚苯乙烯(PSt-b-POEOMA-b-PSt),这种含有亲水性端基的嵌段共聚物可以自组装成核-壳结构的纳米微粒,用于载药高分子的模板研究。利用FTIR、1HNMR、GPC对产物结构进行表征,用热失重(TG)和差示扫描量热(DSC)的方法研究了3种不同比例的嵌段共聚物的热性能。实验结果表明,通过RAFT聚合方法得到了所设计的嵌段共聚物,相对分子质量(简称分子量,下同)分布1.35左右;嵌段共聚物的热稳定性较好,通过玻璃化转变温度(Tg)的变化推测出嵌段共聚物中两种嵌段比例对两嵌段相容性的影响。