GPC Analysis of Ethylene-Propylene Copolymers

Abstract

Determination of the values of K and alpha of the Mark-Houwink equation by applying the universal calibration curve and using a trial and error method was performed with samples of ethylene-propylene copolymers with broad MW distributions and different intrinsic viscosities. The following equation was obtained, correlating K with composition of ethylene-propylene copolymer and alpha: logK = log(5.755-4.65C3)-5.75 alpha where C3 is the mole percent of propylene in the copolymer, alpha is a value within the range of 0.73 and 0.755 (i.e., K and alpha are dependent upon each other). Values of intrinsic viscosity or molecular weight determined by means of the universal calibration curve agree well with those determined by solution viscosity, light scattering, and osmometry.     

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).     

SOLUTION PROPERTIES OF LADDER-LIKE POLYMER POLYPHENYLSILSESQUIOXANES

Solution properties of ladder-like polymer polyphenylsilsesquioxane (PPS) were studied by measurement of intrinsic viscosity, small angle laser light scattering and gel permeation chromatography. It was found that PPS can be modeled with a wormlike continuous cylinder rather than a wormlike coil. A plot of (M~2/[η])~(1/3) vs. M~(1/2) was employed in obtaining the persistence length (2λ)~(-1) and effective hydrodynamic diameter. When MW≤5×10~5, Mark-Houwink equation is adequate in describing the relationship between MW and [η] with αabout unity. This implies that PPS chain is semi-stiff. For GPC experiments, it was shown that universal calibration can be applied in PPS. When molecular weights of PPS are sufficiently high, their molecular weight distributions are often very broad.     

Polymerization of vinyl chloride with organolithium compounds. V. Fractionation and solution properties of high molecular weight poly(vinyl chloride)

A sample of high molecular weight poly(vinyl chloride) (PVC) was fractionated by classical precipitation fractionation and gel-permeation chromatography (GPC) on a preparative scale. The fractions thus obtained were characterized by light scattering, viscometry, and by the GPC method. The measured weight-average molecular weights M?_w, intrinsic viscosity [η], and polydispersity index M?_w/M?_n values were used for the determination of the Mark-Houwink equation, [η] = KM^a, for PVC in cyclohexanone (CHX) at 25°C valid for molecular weights from 100,000 to 625,000.     

Molecular chain properties of poly (N-isopropyl acrylamide)

A series of poly( N-isopropyl acrylamide) (PNIPAM) samples with molecular weight ranging from 2.23×10~4 to 130×10~4 and molecular weight distribution M_w/M_n≤1.28 were obtained by free radical polymerization and repeat precipitation fractionation. The molecular weight M_w, second virial coefficient A_2 as well as the mean-square-root radius of gyration 〈S~2〉 for PNIPAM samples in tetrahydrofuran (THF) were determined by light scattering, and the relations were estimated at A_2 ∞ M_w~0.25) and 〈S~2〉~(1/2)=1.56×10~(-9) M_w~(0.56). The intrinsic viscosity for THF solution and methanol solution of PNIPAM samples was measured and the Mark-Houwink equations were obtained as [η]=6.90×10~(-5) M~(0/73) (THF solution) and [η]=1.07×10~(-4) M~(0.71) (methanol solution). The above results indicate that both THF and methanol are good solvents for PNIPAM. The limit characteristic ratio C_∞ for PNIPAM in the two solutions was determined to be 10.6 by using Kurata-Stockmayer equation, indicating that the f     

从特性粘数和GPC图谱获得重均分子量的新方法

本文提出了从未知样品的特性粘数和GPC图谱计算重均分子量的新方法,该方法可用于计算窄分布和宽分布的未知Mark-Houwink 常数的样品的重均分子量。用七个不同分子量和不同分布的实例验证了所提出的方法。结果与已知Mark-Houwink常数用普适校准法得到的结果一致。     

稀土催化聚合的顺式聚丁二烯的单分散粘度方程

对十一个未经分级的多分散稀土顺丁橡胶试样作了渗透压和粘度的测量,计算得到的数均分子量_n及特性粘数[<η>]列于表中。     

从特性粘数和GPC图谱获得数均分子量的新方法

本文提出了从未知K和a的样品的特性粘数和GPC图谱计算数均分子量的新方法。该法对窄分布或宽分布的样品都适用,并用不同分子量和分子量分布的样品进行了验证,和已知K和a的计算值进行比较,得到非常满意的结果。该法是计算M_n的近似解法,但计算简便。     

Vinylic polymerization of norbornene by Pd(II)-catalysis in the presence of ethylene

Pd(II) catalysts with nitrilo ligands and BF₄⁻ counter ions give the best results in vinylic polymerization of norbornene. Absolute molecular weight determination of polynorbornene (PN) by means of light scattering and the three-dimensional shape of PN were also investigated. By correlation of molecular weights M̄_w with intrinsic viscosity (Staudinger-index) [η], yield a close to 0.5 exponent for the Mark-Houwink equation with solvents chlorobenzene and cyclohexane at 25°C expected for polymer molecules with confined conformation. The vinylic polymerization of norbornene with [(CH₃CN)₄Pd][BF₄]₂ ( I ) in nitromethane in the presence of ethylene results in PN with narrow molecular weight distribution. No termination and transfer reactions were found, nor any incorporation of ethylene could be detected.     

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.     

Solution properties of poly(dimethyl siloxane)

The solution properties of poly(dimethyl siloxane) (PDMS) were studied with light scattering (LS), gel permeation chromatography/light scattering (GPC/LS), and viscometry methods. PDMS samples were fractionated, and the weight‐average molecular weights, second virial coefficient, and the z‐average radius of gyration of each fraction were found according to the Zimm method with the LS technique. In this work, the molecular weight range studied was 7.5 × 10⁴ to 8.0 × 10⁵. Molecular weights and molecular weight distributions were determined by GPC/LS. The intrinsic viscosities of these fractions were studied in toluene at 30 °C, in methyl ethyl ketone (MEK) at 20 °C, and in bromocyclohexane (BCH) at 26 °C and 28 °C. The Mark–Houwink–Sakurada relationship showed that toluene was a good solvent, and MEK at 20 °C and BCH at 28 °C were θ solvents for PDMS. The unperturbed dimensions were calculated with LS and intrinsic viscosity data. The unperturbed dimensions, expressed in terms of the characteristic ratio, were found to be 6.66 with different extrapolation methods in toluene at 30 °C. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2678–2686, 2000     

On the validity of the Mark-Houwink relationship at very high molecular weights

Adsorption-entanglement layers have been shown to interfere with the measurement of intrinsic viscosity of high-molecular weight (M _w10⁶) atactic polystyrene solutions. Values of the intrinsic viscosity, corrected for the pressure of any such layers are reported. The Mark-Houwink relationship is thus shown to fail at high molecular weights.     

Dilute solution properties of a polyurethane. I. Linear polymers

A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10^?4M^0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions.     

Relaxation characteristics and intrinsic birefringence and viscosity of polystyrene solutions for a wide range of molecular weights

A comparison is made between measurements on polystyrene solutions and the relaxation characteristics and intrinsic birefringence and viscosity given by the theory for the flexible Gaussian chain of variable number of segments and with internal viscosity and internal hydrodynamic interaction. This is done in order to determine the applicability of the theory to polymers over a wide range of molecular weights, including the low molecular weight range in which there may be conflict with the theoretical assumption of chains having a large number of segments. The longest, terminal relaxation time and the number of chain segments are determined from measurements of the frequency dependence of oscillatory flow birefringence while the intrinsic birefringence and viscosity are determined from steady flow measurements. The range of molecular weights studied is from approximately 900 at 10⁶. It is found that the segment weight is approximately 1000 and the number of segments is in direct proportion to the molecular weight for the range from 1 to 1000 segments. The terminal relaxation time has a molecular weight dependence of the type given by the theory but with better agreement for higher molecular weights. While the measured dependences of the intrinsic viscosity and birefringence are in agreement with theory for molecular weights greater than 5 × 10⁴, they deviate significantly for molecular weights below 1 × 10⁴. The ratio of the intrinsic birefringence to intrinsic viscosity, which in theory is a constant independent of molecular weight, is found to change at the lower molecular weights.     

Molecular weight distribution by stirring-induced fractional precipitation

Ultrahigh molecular weight polyethylenes GUR, UTEC 2540, and UTEC 3540 were fractionated by precipitation from cooling of solutions with stirring [stirring-induced fractional precipitation (SIFP)]. The samples were dissolved in decalin and precipitated over the temperature range of 100-78°C. Three types of procedures were investigated. From fractionation data, the integral and differential molecular weight distribution (MWD) of the polymer were calculated. The MWD and average molecular weights, and , by size exclusion chromatography (SEC) and the limiting viscosity number of the fractions and whole polymer were determined. From these data, the Mark-Houwink constants were calculated. The ‘K’ and ‘a_η’ values obtained were 6.70 × 10^?4 and 0.69, respectively. The MWD curves calculated from SIFP technique by using these constants are in accordance with the MWD by SEC. Fractionation depended on the chemical nature of the stirrer and the cooling rate of the solution during precipitation. The methodology is reproducible. Faster fractionation was observed compared with other methods. © 1995 John Wiley & Sons, Inc.     

Viscosity–molecular weight relationship for fractionated poly(ethylene terephthalate)

Poly(ethylene terephthalate) was separated into 12 fractions of equal size by a stepwise increase in the amount of solvent in the two-phase liquid fractionation system of phenol-tetrachloroethane (PTCE) (1:1) and n-heptane. Various molecular weight parameters of the fractions were measured by osmotic pressure and gel-permeation chromatography. Intrinsic viscosity-molecular weight plots were made for three different solvents at 25°C. Mark-Houwink constants for viscosity-average molecular weight were measured and gave values of K of 2.50, 2.37, and 2.25 × 10^?4 dl/g and values of a of 0.73 for 1:1 PTCE, 3:2 PTCE, and o-chlorophenol, respectively. A comparison with the literature values for this polyester was made, and application of the Mark-Houwink equation to the determination of number-average (M _n) and weight-average (M _w) molecular weight of whole polymers is considered.     

INVESTIGATIONS ON VINYLENE CARBONATE Ⅰ. PREPARATION AND PROPERTIES OF POLY-(VINYLENEC ARBONATE)

Bulk polymerization of vinylene carbonate using t-butylperoxypivalate at 40℃gave colourless, high molecular weight poly(vinylene carbonate) (PVCA). Solutions of PVCA in acetone and DMF are not stable at 25℃and this degradation was studied. From measurements in DMF with unfractionated PVCA a Mark-Houwink equation was obtained:     

Dilute Solution Properties of Poly(Vinyl Chloride)

Light scattering and viscosity studies were made on dilute solutions of poly(vinyl chloride) (PVC) in three solvents: cyclo-hexanone, cyclopentanone, and tetrahydrofuran. Eight samples of PVC (M_w = 25,400 to 145,000) were used to determine the intrinsic viscosities, molecular weights, and the polymer-solvent interaction parameters over a range of temperatures. The solutions were found to behave normally and to exhibit no evidence of aggregate formation. The molecular weights obtained in all three solvents were independent of temperature and agreed well within the experimental errors. The interaction parameters observed were independent of concentration and molecular weight, and functions only of temperature. The intrinsic viscosities were related to molecular weight by the Mark-Houwink equation between 20 and 50°C. The temperature coefficient of the interaction parameter obtained by light scattering agrees well with that found by viscometry. Cyclohexanone, cyclopentanone, and tetrahydrofuran are all good solvents for PVC, and the order of solvent quality is cyclohexanone > cyclopentanone > tetrahydrofuran.     

Universal calibration in GPC: A new approach for the calculation of molecular weights

A method has been developed for determining simultaneously the molecular weight of a broad-distribution polymer and the Mark-Houwink coefficients for that polymer type by using only GPC and intrinsic viscosity data. Standardized samples of poly(vinyl chloride), polystyrene, polybutadiene, and an experimental cycloolefin polymer were analyzed by this method. Shear-corrected intrinsic viscosities were used in all cases because of the high molecular weights involved. Molecular weight data for all samples were found to be in good agreement with molecular weight data obtained by membrane osmometry and from other GPC techniques. The proposed technique provides a means for calculating the molecular weight of a single polymer sample through universal calibration of GPC without knowledge of the Mark-Houwink coefficients for that polymer type.     

Diffusion and equilibrium swelling of macromolecular networks by their linear homologs

Polydimethylsiloxane (PDMS) networks having strands of molecular weight in the range 11,000–36,000 have been prepared by endlinking linear PDMS molecules of these molecular weights with a tetrafunctional linking agent. Absorption of a series of homologous linear PDMS molecules by the resulting PDMS networks has been investigated. The diffusion coefficients at 70°C were found to be rather large, 1 × 10^?12–6 × 10^?12 m²/s, and approximately inversely proportional to the molecular weight of the diffusing liquid, over the range 5000–38,000. The amount of liquid absorbed at equilibrium was relatively small, 10–80%, in good agreement in all cases with an especially simple version of the Flory–Huggins theory when the heat of mixing is made vanishingly small and only entropic terms are retained.