Kinetic model for tensile deformation of polymers. Part IV: Effect of polydispersity

A previously introduced molecular model for tensile deformation of solid, flexible chain polymers is used to study the effect of the molecular weight distribution on the strain at break, or maximum draw ratio. The parameters in the model are chosen to represent melt-crystallized linear polyethylene. We focus, in particular, on the relation between the maximum draw ratio and two distribution characteristics: theM _t molecular weight average, first introduced by Graessley, and the polydispersity ratioM _z /M _w . For a log-normal molecular weight distribution, an increase in polydispersity at constantM _t leads to a broadening of the optimum rate (or temperature) window for achieving maximum elongation, but is accompanied, however, by a substantial decrease in the maximum attainable draw ratio. Studies on the deformation of systems having a bimodal molecular weight distribution indicate that blends made ofequal weight fractions of long and short chains exhibit an unexpectedly high elongation at break. These results are explained in terms of the model and possible technological implications are discussed.Dedicated to Professor Hans-Henning Kausch on the occasion of his 60th birthday.     

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.     

Structural studies of ultrahigh-modulus linear polyethylene using nitric acid etching and gel permeation chromatography. I. Determination of the crystal size distribution

The technique of nitric acid etching followed by gel permeation chromatography (GPC) has been used to study the structure of ultrahigh-modulus linear polyethylene (LPE) tapes drawn to draw ratio λ of 20. For comparison, lower draw ratio (λ = 11) samples were also examined. The etching was carried out in fuming nitric acid at 60°C and the progress of the reaction was monitored by measuring weight loss and molecular weight distributions as a function of time over a period up to 25 days. Consistent with previous work by us and other workers, notably Porter and Peterlin and co-workers, the ultrahigh-modulus products exhibit an exceptional resistance to the acid attack, i.e., after 3 days their weight loss is still negligible while at lower draw ratios it could be as high as 30%. At longer times, however, the rate of weight loss becomes comparable for the two sets of samples, even if the absolute values are much smaller for the products of λ = 20. During the early stages of the etching treatment a rapid decrease in molecular weight and narrowing of the molecular weight distribution is observed in all cases. Eventually the molecular weight distribution becomes time independent, while the weight loss continues to increase. This stage coincides with the attack of the lateral surfaces of the crystals becoming the dominant process and it is considered that the observed molecular length distribution then reflects the distribution of crystal thicknesses. The values of the weight average crystal thickness derived from the GPC experiments (L?_w) are in very good agreement with those obtained from wide-angle x-ray determinations. Furthermore the ratio of weight-average to number-average crystal thickness (L?_w/L?_n) is about 2 for the high draw (λ = 20) samples, i.e., the value predicted by the simple statistical model proposed by Gibson, Davies, and Ward for the structure of ultrahigh-modulus LPE. It is therefore concluded that the nitric acid etching/GPC technique can be used for reliable measurements of crystal size and crystal size distribution in ultraoriented LPE.     

Copolymerization of ethylene and propylene catalyzed by magnesium chloride supported vanadium/titanium bimetallic Ziegler-Natta catalysts

Magnesium chloride supported vanadium/titanium bimetallic Ziegler-Natta catalysts with di-i-butyl phthalate as internal donor for copolymerization of ethylene and propylene were prepared.The effects of reaction temperature, ethylene/propylene molar ratio,aluminium/vanadium（Al/V）molar ratio and titanium/vanadium molar ratio on the catalytic activity were investigated.The molecular weight,molecular weight distribution,sequence composition and crystallinity of the products were measured by gel permeation chromatography,¹³C-NMR and differential scanning calorimetry analysis, respectively.In comparison to the vanadium and titanium catalysts,the bimetallic catalyst showed higher catalytic activity and better copolymerization performance.The obtained ethylene/propylene copolymers have high molecular weight （10⁵）,broad molecular weight distribution,high propylene content with random or short blocked sequence structures （r_Er_P=1.919）,low melting temperatures and low crystallinities（X_c<20%）.     

A STUDY OF LOW-TEMPERATURE CRYSTALLIZATION BEHAVIOR THE cis-1,4 POLYBUTADIENE PREPARED WITH RARE-EARTH CATALYST SYSTEM

The effects of molecular weight and temperature on crystallization processes at low tempera-ture for cis-1,4 polybutadiene prepared with rare-earth catalyst (Ln-PB) have been studied by WAXDmethod. In the range of molecular weight from     

Morphology and modulus–temperature behavior of semicrystalline poly(ethylene terephthalate) (PET)

The influence of the thermal history on the morphology and mechanical behavior of PET was studied. The degree of crystallinity (density measurements) and the morphological structure (electron microscopy and small-angle x-ray diffraction) depend on the crystallization temperature. The viscoelastic parameters obtained from the modulus–temperature curves are mainly determined by the morphology of the samples. The glass-transition temperature, T_i, is a function of the crystallinity and the crystallization temperature. It is maximum for a crystallinity between 0.34 and 0.39 for a sample crystallized isothermally between 120 and 150°C. This dependence on crystallization conditions is ascribed to the conformation of the amorphous chain segments between the crystalline lamellae as well as the concentration and the molecular weight of the polymer material rejected during isothermal crystallization. Both factors are supposed to be temperature-dependent. The value of the rubbery modulus is a function of both the volume concentration of the crystalline lamellae and the structure of the interlamellar amorphous regions (chain folds, tie molecules, chain ends, and segregated low molecular weight material). Annealing above the crystallization temperature of isothermally crystallized samples has a marked influence on their morphology and mechanical behavior. The morphological structure and the viscoelastic properties of annealed PET samples are completely different from those obtained with samples isothermally crystallized at the same temperature.     

Electron-irradiated isotropic polyethylene: Structure and mechanical properties of oriented monofilaments produced by drawing

The structure and properties of oriented (draw ratio 12:1) polyethylene filaments, produced by drawing electron-irradiated isotropic monofilament, have been studied by rubber elasticity measurements, x-ray diffraction, differential scanning calorimetry, and tensile creep behavior. The apparent molecular weight M?_c between network junctions, has been calculated from the Flory and Mooney–Rivlin theories, as a function of dose, and extrapolation back to zero dose gives a value of about 16,000 g mol^?1, which is related to the molecular weight between entanglements in the linear polymer (M?_n 28,000). The WAXS and SAXS patterns of the unirradiated and 6.0 Mrad samples were identical, indicating an equivalent extent of crystallite orientation and a constant long period of about 170Å. Up to a gel dose of 2.4 Mrad, the degree of crystallinity (DC) of the drawn filaments remains constant, but the melting temperature T_m decreases slightly owing to network junctions at the fold surfaces. Above the gel dose, DC drops significantly and T_m falls more sharply, as a result of crystallite distortion. Irradiation dramatically affects the creep behavior, decreasing the equilibrium creep rate by up to four orders of magnitude. For all samples, the constant-flow behavior can be described by a combination of two activated processes in parallel: one associated with the amorphous network and the other with the crystalline regions. Irradiation increases the activation volume of the process occurring in the crystal and is ascribed to an increase in crystallite imperfections.     

Boron trifluoride-catalyzed degradation of poly--caprolactone at ambient temperature

Poly--caprolactone (PCL) can be accelerated to degrade in the presence of boron trifluoride at ambient temperature. The degradation behaviors were studied by using the inherent viscosity measurement, gel permeation chromatography (GPC), infrared analysis (FTIR), nuclear magnetic resonance analysis (NMR), and thermal analysis (DSC). With increasing the addition amount of boron trifluoride, the molecular weight of PCL decreases; the molecular weight distribution is broadened; and the degree of crystallinity of PCL increases at first at low BF₃ level, then decreases when BF₃ content exceeds to 2.64 wt%. The results of IR, ¹HNMR and GPC reveal that -caprolactone monomer does not occur and the main degradation products are the oligomers of PCL with low molecular weight. The mechanism for boron trifluoride-catalyzed degradation of PCL is discussed.     

Mechanical and transport properties of drawn low-density polyethylene

Quenched, quenched and annealed, and slowly cooled branched low-density polyethylene films were drawn at 25, 40, and 60°. The true draw ratio λ^L of the volume element was obtained and used to characterize the dependence on plastic deformation of the density, drawing stress, and work of plastic deformation, and the sorption and diffusion of methylene chloride. The effects observed are similar but less drastic than on linear high-density polyethylene. In particular, the transformation from the original lamellar to the final fibrous structure seems to be fastest for λ^L between 3 and 4. But the changes of vapor transport clearly indicate that the transformation is not yet complete even at the highest draw ratio λ^L = 6, just before the sample breaks. Annealing at 90°C of the drawn samples with free ends restores or even increases the transport properties beyond those of the undrawn sample without causing the fibrous structure to revert to the original lamellar structure.     

Characterization of acrylic dental polymers

The chemical structure and the molecular parameters of four dental acrylic polymer materials (samples P-1 to P-4) and two polyacrylic acids of different molecular weight (relative molecular mass) used as model compounds (samples Paa-1 and Paa-2) were studied and correlated with polymer structure and molecular weight. All polymer samples show low molecular weights, MW, and broad poly-dispersity as obtained by GPC. Samples P-3 and P-4 show the lower MW and bi-modal distribution, one peak corresponding to the polymer and the other to a low molecular weight compound at a lower concentration. The other polymer samples show unimodal distribution. Initially, all samples were soluble in water and dioxane above 99.8%. However, after lyophilization at −50 °C they showed different degrees of solubility because of partial gelation. The FTIR and, ¹H and ¹³C-NMR spectra of Paa-1, Paa-2 in D₂O show the pattern characteristic of poly(acrylic acid). The polymers of P-1 and P-2 are mainly poly(acrylic acid). The P-3 spectra show the peak pattern for an (acrylic acid/methyl acrylate) copolymer of about 2:1 composition as calculated from the NMR spectra. The P-4 is an oligomer derived from 2-hydroxyethyl methacrylate. Solid ¹³C-NMR spectra confirm the above structures and evidence anhydride formation after lyophilization. The MW and the linear expansion coefficient, α, were derived from intrinsic viscosity in theta and perturbed conditions. From this, the steric hindrance parameter, A, the molecular stiffness, σ, and the second virial coefficient, A₂, were calculated using different thermodynamic models. The Flory-Fox-Shafgagen and the Stockmayer-Fixman models fit better the experimental data and can be used to describe the molecular parameters of the acrylic polymers. Light scattering was used to compare results.     

Solid-state coextrusion of poly(ethylene terephthalate). II. Drawing of semicrystalline PET

The drawing of semicrystalline (33 and 50%) poly(ethylene terephthalate) (PET) films has been studied by solid-state coextrusion. Because of its brittleness and opacity, isotropic and semicrystalline PET film is of little practical use. Early attempts to cold-draw crystalline films led to fracture in contrast to deformation of amorphous PET. However, we have succeeded in systematically preparing films with extrusion draw ratios ≤4.4 from semicrystalline PET. In many cases, the properties of the drawn extrudates, as a function of extrusion temperature T_ext and extrusion draw ratio EDR, were similar to those prepared from amorphous PET. However, some remarkable differences have also been found. In the case of coextrudates prepared from isotropic 50% crystalline PET, we found that the larger the deformation, the lower the apparent resulting crystallinity. In the extreme, a 34% reduction in crystallinity after deformation was observed. For the coextrudates drawn from initially 33% crystalline PET, slightly different behavior occurred. For T_ext ≤ 90°C, all extrudates showed crystallinities lower than the original isotropic film, with a minimum at EDR = 3; for T_ext ≥ 110°C, crystallinities were slightly greater than in the original film and increased with EDR. Qualitative measurements of heats of fusion were in agreement with density gradient results for PET crystallinity. In contrast is our previous finding that extrudates from initially amorphous PET always increase in crystallinity with EDR, because of stress-induced crystallization. The results now suggest that in the T_ext range investigated, the initial spherulitic structure is at least in part destroyed on drawing. In addition, the percent crystallinity is revealed to be dependent on T_ext, with lower values at lower temperatures. Mechanical tests show that the extrudates are similar or sometimes higher in tensile modulus when compared to amorphous PET drawn under the same conditions.     

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.     

The role of chain scission in fracture of amorphous polymers

We have investigated the role of chain scission in glassy polymers by monitoring the molecular weight changes induced by microtoming thin slices of monodisperse polystyrenes. The changes in number-average molecular weight allow determination of N_f, the number of bond scissions per unit area. It is found that N_f is independent of initial molecular weight and has the value 6.50 × 10¹³ scissions/cm² at room temperature; N_f decreases with increasing temperature, suggesting that chain pullout increases with temperature. The work required to create unit surface area in polystyrene is several orders of magnitude greater than the energy required to break N_f bonds, indicating that plastic deformation plays a major role in deformation and fracture of glassy polymers.     

Tensile strength of highly oriented polyethylene. II. Effect of molecular weight distribution

The tensile strength of oriented polyethylene filaments is discussed in relation to molecular weight. Short-term tensile properties at room temperature were obtained in our laboratory and from the literature for polymer samples covering the molecular weight (M _w) range from 54 × 10³ to 4 × 10⁶, and polydispersities ranging from 1.1 to 15.6, oriented by solid-state extrusion, melt spinning/drawing, solution spinning/drawing, and “surface growth.” It was found that both the molecular weight and its distribution markedly affected tensile strength. The breaking stress σ of highly oriented fibers varied with molecular weight roughly as σ ∝, M^0.4, at constant M _w/M _n over the entire range studied. Reduction of polydispersity from 8 to 1.1 by an increase of M _n with M _w approximately constant at 10⁵ increased tensile strength of oriented polyethylene filaments by a factor of nearly 2.     

Studies on Macromolecular Complexing Agents. II. Effects of Polypropylene Oxide on the Copolymerization Reaction between Butadiene and Styrene

ABSTRACT

Ultra-high-molecular-weight poly[(R)-3-hydroxybutyrate](P(3HB)) was biosynthesized from glucose by a recombinant Escherichia coli XL-1 Blue (pSYL105) harboring Alcaligenes eutrophus PHB biosynthesis phbCAB genes. Six kinds of P(3HB) samples with differ-ent weight-average molecular weight (M_w ) from 1.1 × 10⁶ to 11 × 10⁶ measured by multi-angle laser light scattering were respectively produced at pH values of 7.0 to 6.5 in culture media. Solvent-cast P(3HB) films of high-molecular-weights over M_w of 3.3 × 10⁶ were stretched easily and reproducibly at 160°C to a draw ratio of 400-650%. Mechanical properties of the stretched P(3HB) films were markedly improved relative to those of solvent-cast film. The elongation to break, Young's modulus, and tensile- strength of stretched film (M_w = 11 × 10⁶) were 58%, 1.1 GPa, and 62 MPa, respectively. X-ray diffraction patterns indicated that the stretched film was highly oriented and had a high crystallinity over 80%. When the stretched film was annealed at 160°C for 2 hours, the mechanical properties were further improved (elongation to break = 67%, Young's modulus = 1.8 GPa and tensile strength = 77 MPa). The mechanical properties of the stretched-annealed film remained almost unchanged for 6 months at room temperature, suggesting that a high crystallinity of the stretched-annealed film avoids a progress of secondary crystallization.

     

Morphology of uniaxially oriented poly(ethylene terephthalate)

The morphological character of uniaxially oriented poly(ethylene terephthalate) (PET) films was investigated as a function of draw ratio. Dynamic mechanical, infrared, and crystallite-size measurements were made on the samples. In addition, selective degradation experiments and molecular weight determinations were employed. The dynamic mechanical measurements indicated a sharp decrease in irregular folds for draw ratios of 3.0 and higher, which also coincided with the essentially complete disappearence of regular folds (from the 988 cm^?1 band in the infrared spectra) in unannealed samples. Infrared studies of drawn samples annealed under different conditions gave evidence in support of a structure in which the chains are stretched out. Apparent crystallite-size measurements showed a sudden increase in length of the crystals in the direction of the draw beyond a draw ratio of 3.0. Molecular weight measurements showed a large increase in average chain length in the residue after selective degradation of amorphous material and folds; undrawn and slightly drawn samples gave a much lower M _n. Based on these observations, it is postulated that for higher draw ratios and present drawing conditions, the crystals are of the straight chain type, somewhat similar to the fringed-micelle crystal concept.     

Melt drawing of ultra‐high molecular weight polyethylene: Comparison of Ziegler‐ and metallocene‐catalyzed reactor powders

The drawing behavior of the ultra‐high molecular weight polyethylene (UHMW‐PE) melts has been studied by comparing the stress/strain curves for two types of samples as polymerized using conventional Ziegler and newer metallocene catalyst systems. Two UHMW‐PE samples, having the same viscosity average molecular weight of 3.3 × 10⁶, but different molecular weight distribution, have been drawn from melt at special conditions. The sample films for drawing were prepared by compression molding of reactor powders at 180°C in the melt. Differences in the structural changes during drawing and resultant properties, ascribable to their broad or narrow molecular weight distribution, were estimated from tensile tests, SEM observations, X‐ray measurements and thermal analyses. The metallocene‐catalyzed sample having narrower molecular weight distribution, could be effectively drawn from the melt up to a maximum draw ratio (DR) of 20, significantly lower than that obtained for the Ziegler‐catalyzed sample, ∼ 50. The stress/strain curves on drawing were remarkably influenced by draw conditions, including draw temperature and rate. However, the most effective draw for both was achieved at 150°C and a strain rate of 5 min⁻¹, independent of sample molecular weight distribution. The efficiency of drawing, as evaluated by the resultant tensile properties as a function of DR, was higher for the metallocene‐catalyzed sample having narrower molecular weight distribution. Nevertheless, the maximum achieved tensile modulus and strength for the Ziegler sample, 50–55 and 0.90 GPa, respectively, were significantly higher than those for the metallocene sample, 20 and 0.65 GPa, respectively, reflecting the markedly higher drawability for the former than the latter. The stress/strain behavior indicated that the origin of differences during drawing from the melt could be attributed to the ease of chain relaxation for the lower molecular weight chains in the melt. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1921–1930, 1999     

Synthesis and properties of high‐molecular‐weight stereo di‐block polylactides with nonequivalent D/L ratios

Di‐stereoblock polylactides (di‐sb‐PLA: PLLA‐b‐PDLA) having high molecular weight (M_n > 100 kDa) were successfully synthesized by two‐step ring‐opening polymerization (ROP) of L ‐ and D ‐lactides using tin(2‐ethylhexanoate) as a catalyst. By optimizing the polymerization conditions, the block sequences were well regulated at non‐equivalent feed ratios of PLLA and PDLA. This synthetic method consisted of three stages: (1) polymerization of either L ‐ or D ‐lactide to obtain a PLLA or PDLA prepolymer with a molecular weight less than 50 kDa, (2) purification of the obtained prepolymer to remove residual lactide, and (3) polymerization of the enantiomeric lactide in the presence of the purified prepolymer. Their ¹³C and ³¹P NMR spectra of the resultant di‐sb‐PLAs strongly supported their di‐stereo block structure. These di‐sb‐PLAs, having weight‐average molecular weights higher than 150 kDa, were fabricated into polymer films by solution casting and showed exclusive stereocomplexation. The thermomechanical analysis of the films revealed that their heat deformation temperature was limited probably because of their low crystallinity owing to the non‐equivalent PLLA/PDLA ratio. The blend systems of the di‐sb‐PLAs having complementary stereo‐sequences (the one with a long PLLA block and the other with long PDLA block) were also prepared and characterized to enhance the sc crystallinity. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 794–801, 2010     

Cationic polymerization of styrene by acetyl perchlorate. II. Steric structure of the polymer and nature of the propagating species

Cationic polymerization of styrene initiated by acetyl perchlorate in CH₂Cl₂ yields a polymer having a bimodal molecular weight distribution. The high molecular weight and the low molecular weight portions of the polymer were separated by thin-layer chromatography, and the steric structure of these separated polymers was investigated by ¹³C NMR spectra. The high molecular weight polymer had a larger racemic dyad content than the low molecular weight material. From the dependence of the steric structure of the polymer on the polarity of a solvent, it was estimated that the propagating species producing the high molecular weight material was a loose ion pair or a free ion, and that producing the high molecular weight material was a loose ion pair or a free ion, and that producing the low one was a nondissociated species.     

Copolymer synthesis of poly(L-lactide-b-DMS-L-lactide) via the ring opening polymerization of L-lactide in the presence of α,ω-hydroxylpropyl-terminated PDMS macroinitiator

Various amounts of hydroxy terminated PDMS were linked into PLLA chains via in-situ ring opening polymerization at a very low content of SnOt₂. The ¹H and FTIR spectra provided evidence for the incorporation of the PDMS in the PLLA chains. The molecular weights, T_g, T_m, crystallinity and the heats of fusion decreased as the feed mole ratio of PDMS/LLA in the block copolymer increased. The molecular weight distribution broadened as the content of the PDMS increased, due the occurrence of two initiation and propagation mechanisms. Linking PDMS into the PLLA chains improved its thermal stability. © 1996 John Wiley & Sons, Inc.