The drawing behavior of linear polyethylene. I. Rate of drawing as a function of polymer molecular weight and initial thermal treatment

The drawing behavior of a series of linear polyethylene homopolymers with weight-average molecular weight (M?_w) ranging from 67,800 to ～3,500,000 and variable distribution (M?_w/M?_n = 5.1?20.9) has been studied. Sheets were prepared by two distinct routes: either by quenching the molten polymer into cold water or by slow cooling below the crystallization temperature (～120°C) followed by quenching into cold water. When the samples (2 cm long) were drawn in air at 75°C using a crosshead speed of 10 cm/min it was found that for low M?_w polymers the initial thermal treatment has a dramatic effect on the rate at which the local deformation proceeds in the necked region. At high M?_w such effects are negligible. An important result was that comparatively high draw ratios (λ > 17) and correspondingly high Young's moduli could be obtained for a polymer with M?_w as high as 312,000. It is shown how some of the structural features of the initial materials (mainly studied by optical microscopy, small-angle x-ray scattering and low-frequency laser Raman spectroscopy) can be interpreted in terms of the molecular weight and molecular weight distribution of the polymers. Although crystallization and morphology can be important at low M?_w, it suggested that the concept of a molecular network which embraces both crystalline and noncrystalline material is more helpful in understanding the drawing behavior over the whole range of molecular weights.     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.     

Polymerization by oxidative coupling. IV.. Synthesis and properties of poly(2-methyl-6-phenylphenylene ether)

Copper-amine catalyst systems which polymerize 2-methyl-6-phenylphenol to high molecular weight polymer are described. With CuCl and N,N,N ′,N′-tetramethyl-1,3-butanediamine (TMBD), an intrinsic viscosity of 1.56 dl/g was obtained. Faster rates of polymerization resulted with a CuBr-TMBD catalyst. Catalysts from other tertiary amines and mixtures of tertiary amines also produced high polymer. Pyridine and diethylamine catalyst were less active. Samples of polymer were isolated at different stages of the polymerization. Measurements of viscosity, osmotic pressure, light scattering, gel permeation, hydroxyl groups, nitrogen content, and chemical reactivity were made on the samples. Below a molecular weight value of M?_n 60,000, M?_n/M?_w was 2.0. At higher molecular weights, there was a broadening in molecular weight distribution. No major change in the molar concentration of the “;head” endgroups with increasing molecular weight was detected by infrared analysis. However, nitrogen analyses, chemical reactivity studies, and the M?_n/M?_w ratio suggested the chemical nature of the “head” end had changed. The relationships between intrinsic viscosity in chloroform at 25°C and M?_n and M?_w for unfractionated polymer samples are log [η] = ?4.26 + 0.84 log M?_n and log [η] = ?3.86 + 0.70 log M?_w.     

Non-newtonian behavior of polymers with log-normal molecular weight distribution

By choosing suitable approximations to Bueche's function, it is possible to calculate the viscosity versus shear stress for log-normal molecularly distributed linear polymers. For bulk polymers the mixing rules M?_w, M?_w, M?_z are considered. For values of η/η0 > 0.1 and heterogeneities with M?_w/M?_n > 1.5 the result obtained with any mixing rule is η/η0 = erfc [(1/delta;) log (M₀Q^h/aK)], where a = π²/6_pRT and where the δ and K values are dependent on the heterogeneity ratio Q = M?_w/M?_n and on the type of mixing rule; on the other hand, the h value is independent of the heterogeneity, but depends on the mixing rule. Most experimental data should fit the M?_w mixing rule as one would expect from the zero shear stress mixing rule. Experimental data are compared with the theoretical results.     

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 structure of synthetic rubber. I. Light-scattering properties of styrene–butadiene copolymers

The discrepancy between the values reported for the weight-average molecular weight and molecular weight distribution of cold-type styrene-butadiene rubber is examined. The results obtained indicate that aggregation of the rubber due to hydrogen bonding or cluster formation is not a contributing factor to the high weight-average molecular weights obtained. The very broad molecular weight distributions, the M?_w/M?_n of the order of 10–20, are attributable to the presence of a few per cent of very high molecular weight fraction microgel in samples polymerized to moderate conversions. This microgel has been removed to various degrees by several methods: (1) mastication, (2) treatment with CaSO₄, (3) ultracentrifugation, and (4) ultrafiltration. The nature of this microgel is examined in terms of its light-scattering property, intrinsic viscosity, and concentrated solution viscosity. The weight-average molecular weight obtained by light scattering on these samples after removal of microgel are lower by as much as an order of magnitude. The operational definition of the weight-average molecular weight, M?′_w, is therefore introduced, corresponding to the one obtained after removal of the microgel. It is suggested that the actual and the operational weight-average molecular weights be used in conjunction in the characterization of these copolymers.     

Experimental investigation of the concept of molecular migration within sheared polystyrene

Several important aspects of the flow in polymer melts through capillaries remain unexplored. This paper examines experimentally one such effect associated with the radial shear-stress gradient in capillaries. During capillary melt flow of a polymer with a wide molecular weight distribution, migration of the large molecules away from the region of highest shear stress, i.e., at the capillary wall, has been predicted but only modestly investigated. This effect has the potential to produce a molecular weight spectrum over the cross section of extruded polymer. Studies of distribution in shear were conducted on a well-characterized wide-distribution polystyrene (M?_w = 234,000). An Instron Rheometer equipped with a long capillary (length/diameter ratio of 66.7) was used to perform the extrusion at temperatures of 160–250°C. A solvent coring procedure was used to dissolve away concentric layers of polymer from the extrudate for molecular weight analyses. The method has been shown to cut clean sections without selective extraction. Values of M?_w, M?_n and M?_w/M?_n were calculated from complete molecular weight distribution data obtained by calibrated gel permeation chromatography. For a wide range of shear rates and temperatures, no evidence for molecular fractionation was observed. Shear degradation of this polymer was found to be small. However, at high shear rates at 250°C, evidence indicating extensive shear-induced thermal degradation was found. No evidence for oxidative degradation at the extrudate surface was found at either low or high shear rates at this temperature.     

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.     

VISCOSITY BEHAVIOR OF LACQUER POLYSACCHARIDE IN AQUEOUS SOLUTION

The dependence of measured viscosity on NaCl concentration (0.1 to 3.0M), pH (range of 2—13) and cadoxen composition w_(cad) (from 2% to 100%) for the lacquer polysaccharide in NaCl/cadoxen/H_2O mixture containing HCl or without were obtained. All the viscosity exponents γin the Mark-Houwink equations under three different solvent condition arc close to 0.5. The w_(cad) dependence of reduced viscosity ηsp/c confirms the single strand chain of the polysaccharide. As the γvalues close to 0.5 and values of unperturbed dimension _θ/M and [η] much smaller than those for usual linear polymers, these facts suggest that the polysaccharide chains in the aqueous solutions should be dense random coil owing to the highly branched structure.     

Flow properties of poly(methyl methacrylate) solutions

Viscosity and normal stress behavior were measured for poly(methyl methacrylate) samples of various average molecular weights in diethyl phthalate solution at 30 and 60°C. All samples conformed approximately to the most probable distriution (M?_w/M?_n = 2). Concentrations ranged from 0.113 to 0.38 g/ml, and M?_w from 53,800 to 1,620,000. Despite considerable evidence in the literature of unusual linear viscoelastic behavior for this polymer, its nonlinear properties appear to be rather conventional. The viscosity–shear rate master curve was similar to that found earlier for concentrated solutions of polystyrene and poly(vinyl acetate) of comparable molecular-weight distribution. The viscosity time constant τ_o parallels τ_R, the characteristic time of the Rouse model, although the residual dependence of τ_o/τ_R on concentration and molecular weight appears to be slightly different from that for polystyrene and poly(vinyl acetate). Similar conclusions apply to the recoverable compliance J_e,^o estimated from the normal stress behavior of each solution, and its relationship to the Rouse model compliance J_R.     

Molecular weights and molecular weight distribution of polymers by equilibrium ultracentrifugation. Part II. Molecular weight distribution

A method has been developed for determining the molecular weight distribution of a polymer sample from the sedimentation–diffusion equilibrium data for a solution under pseudo-ideal conditions. From some theoretical examples it appears that the method works well and that the molecular weight distribution can be determined with a reasonable degree of resolution. From three polymer samples (polyethylene, polystyrene, and polycaprolactam) the molecular weight distribution was determined in this way. The average molecular weights, M?_n, M?_w, M?_z, and M _z+1, calculated from these distribution functions agree well with those calculated directly from the equilibrium data.     

Gel-permeation chromatography: X. Molecular weight detection by low-angle laser light scattering

Effluent from a gel-permeation chromatographic column has been simultaneously and continuously monitored with a differential refractometer and a low-angle laser light-scattering (LALLS) photometer. This provides a true and direct determination of molecular weight distribution rather than through a calibration method as obtained by conventional GPC techniques. Computer assisted data reduction provides a rapid determination of M?_w, M?_n, M?_z, M?_w/M?_n, as well as a plot of molecular weight distribution. Samples of very narrow molecular weight distribution (MWD) polystyrene from Pressure Chemicals Co. and relatively wide MWD samples of poly(methyl methacrylate) in chloroform have been characterized.     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Plastic deformation of polypropylene: Effect of molecular weight on drawing behavior and structural characteristics of ultra-high-modulus products

The influence of molecular weight and temperature on the tensile drawing behavior of polypropylene has been studied, with particular reference to the production of ultra-high-modulus oriented materials. It has been shown that the optimum draw temperature is molecular weight independent to a good approximation, and that high-modulus products can be obtained for M?_w in the range 180,000–400,000, the highest modulus being achieved for polymer with M?_w = 181,000. As in the case of linear polyethylene, under optimum drawing conditions the Young's modulus relates only to the draw ratio. Low-temperature moduli as high as 25–27 GPa were recorded, which compare favorably with a previously reported value of 42 GPa for the crystal-lattice modulus. Although the drawing behaviour of the samples studied appeared comparatively insensitive to molecular weight, some of the properties of the draw materials, notably melting point and shrinkage at high temperature, showed a wide range of behavior.     

Structure of gum arabic and its configuration in solution

Gum arabic was found to have an osmotic molecular weight of 250,000, in agreement with earlier determinations. A molecular weight of 365,000 was found by light scattering, somewhat higher than obtained earlier by sedimentation equilibrium analysis but lower than light-scattering values reported by other investigators. The M?_w/M _n ratio, 1.46, is quite low in gum arabic. The angular dependence of light scattering exhibited the upward curvature to be expected of a spherical molecule and a radius of gyration of about 100 A. or less, as estimated from a Zimm plot. Fractionation of the original gum arabic was done by precipitation of a 0.5% solution in aqueous 0.5% NaCl with acetone. Comparison of the curves of viscosity versus molecular weight and the estimated radius of gyration shows that the hydrodynamic volume is less than that of branched dextran of similar molecular weight. The electroviscous effects for gum arabic in aqueous solution were shown by reduced viscosity curves at various acidities and in salt. The degree of dissociation was calculated for each pH level. The minimum intrinsic viscosity was found in 0.04N HCl where the degree of dissociation at pH 1.5 was found to be 0.049. When the acidity was increased, further reduction in viscosity was found to be negligible. Routine determination of the viscosity and molecular weight of the fractions was done in 0.35M NaCl at pH 10 to which 0.25% of the sodium salt of ethylenediaminetetraacetic acid was added as a sequestrant. The intrinsic viscosity in this solvent was nearly as low as in 0.04N HCl. Light-scattering dissymmetries in water and in 0.35M NaCl plus EDTA at pH 10 were similar, 1.13 and 1.09, respectively, which showed that actual expansion of the macroion is not the cause of the large increase in viscosity of gum arabic when the ionic strength of the solvent is reduced. Periodate oxidation of the polymer confirmed the existence of a 1–3-linked backbone of galactose. Subsequent treatment of the oxidized polymer with alkali reduced the osmotic molecular weight to 45,000 but failed to remove oxidized side branches. The oxidized polymer was fractionated by gel permeation chromatography and the intrinsie viscosity–molecular weight relation compared with relations for fractions of the unoxidized polymer and for other branched and crosslinked polymers.     

Randomly branched bisphenol A polycarbonates. I. Molecular weight distribution modeling,interfacial synthesis,and characterization

Randomly branched bisphenol A polycarbonates (PCs) were prepared by interfacial polymerization methods to explore the limits of gel‐free compositions available by the adjustment of various composition and process variables. A molecular weight distribution (MWD) model was devised to predict the MWD, G, and weight‐average molecular weight per arm (M_w /arm) values based on the composition variables. The amounts of the monomer, branching agent, and chain terminator must be adjusted such that the weight‐average functionality of the phenolic monomers (F_OH ) was less than 2 to preclude gel formation in both the long‐ and short‐chain branched (SCB) PCs. Several series of SCB and long‐chain branched PCs were prepared, and those lacking gels showed molecular weights measured by gel permeation chromatography–UV and gel permeation chromatography–LS consistent with model calculations. In SCB PCs, the minimum M_w /arm that could be realized without gel formation depended on both composition (molecular weight, terminator type) and process (terminator addition point, coupling catalyst) variables. The minimum M_w /arm achieved in the low molecular weight series studied ranged from ∼3300 to ∼1000. The use of long chain alkyl phenol terminators gave branched PCs with lower glass‐transition temperatures but a higher gel‐free minimum M_w /arm. SCB PCs where M_w /arm was less than ∼M_c spontaneously cracked after compression molding, a result attributed to their lack of polymer chain entanglements. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 560–570, 2000     

Molecular weight analysis of pitches and polymeric pitches by gel-permeation chromatography

The technique of gel-permeation chromatography (GPC) has been developed as a method for measuring molecular weight distribution in pitch materials. Molecular weight calibration data were obtained from measurements made on GPC fractions collected from a standard pitch. By solubilization of the polymeric portion of pitch through a reduction with lithium in ethylenediamine, the molecular weight range for analysis was extended to in excess of 3000. Mass spectroscopy has been used to further analyze some of the GPC fractions. The GPC calibration data can be employed, with the aid of computer analysis, to determine quantitatively number-average molecular weights M?_n weight-average molecular weights M?_w, and molecular weight distribution D (= M?_w/M?_n) in pitch materials.     

Excluded volume study of a sulfonate-containing polyelectrolyte in salt solutions

Chain characteristics of a linear sulfonate-containing homopolymer, sodium poly(3-methacryloyloxypropane-1-sulfonate), in aqueous salt solutions (ionic strength, C_s = 0.01N to 5N NaCl) have been investigated by light scattering and intrinsic viscosity. The molecular weight (M?_w)–viscosity relation can be well described by the Mark–Houwink and the Stockmayer–Fixman equations. The coil is highly expanded even in the most concentrated NaCl solution (6N), and no 1:1 electrolyte was found to precipitate this polymer. A linear relation was observed between the viscosity expansion factor, α^3η, and (M?_w/C_s)^1/2. Examination of the data in terms of theories for excluded volume and hydrodynamic interaction suggests that the coil experiences dominant hydrodynamic interaction, corresponding to a nondraining coil, and the second virial coefficient and coil expansion at high C^s can be correlated by the Flory–Krigbaum–Orofino equation. Results for this polymer are compared with those for other polyelectrolytes, and are discussed in terms of chain structure, flexibility, and hydrophobicity.     

Drawing behavior of linear polyethylene. II. Effect of draw temperature and molecular weight on draw ratio and modulus

The drawing behavior of linear polyethylene homopolymers with weight-average molecular weights (M?_w) from 101,450 to ca. 3,500,000 has been studied over the temperature range 75°C to the melting point. In all cases 1-cm gauge length samples were drawn in an Instron tensile testing machine at a constant cross-head speed of 10 cm/min. With the exception of the lowest molecular weight polymer, it was found that increasing the draw temperature led to substantial increases in the maximum draw ratio which could be achieved, and that this increased monotonically with increasing draw temperature. Measurements of the Young's modulus of the drawn materials showed, however, that the unique relationship between modulus and draw ratio previously established for drawing at 75°C was not maintained to the highest draw temperatures. The highest draw temperature at which this relation held was found to be strongly molecular weight dependent, increasing from ca. 80 to ca. 125°C when M?_w increased from 101,450 to 800,000. In all cases conditions could be found for drawing samples to draw ratios of 20 or more with correspondingly large values of the Young's modulus.     

Flow birefringence and polydispersity

Flow birefringence data for dilute solutions of various linear and branched polymers of different degrees of polydispersity are discussed. The polymers considered are polystyrene, polypropylene, and polyethylene. By making use of a well-known stress-optical relation, reduced elastic normal stresses, which can also be interpreted as coil expansions, are plotted against reduced shear stresses. As elastic normal stresses are rather sensitive to the shape of the molecular weight distribution at high molecular weight, a characteristic, p, related to the skewness of the distribution, is obtained. Experimental values of p are compared with theoretical ones based on special types of distribution functions. Attention is paid to the method of extrapolating experimental results to zero shear stress and concentration.