Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Molecular weight dependence of crystal pattern transitions of poly(ethylene oxide)

Crystal patterns in ultrathin films of six poly(ethylene oxide) fractions with molecular weights from 25000 to 932000 g/mol were characterized within crystallization temperature range from 20 ℃ to 60 ℃.Labyrinthine,dendritic and faceted crystal patterns were observed in different temperature ranges,and then labyrinthine-to-dendritic and dendritic-tofaceted transition temperatures T L-D and T D-F were quantitatively identified.Their molecular weight dependences are T L-D(M w) = T L-D(∞) K L-D /M w,where T L-D(∞) = 38.2 ℃ and K L-D = 253000 ℃.g/mol and T D-F(M w) = T D-F(∞) K D-F /M w,where T D-F(∞) = 54.7 ℃ and K D-F = 27000 ℃.g/mol.Quasi two-dimensional blob models were proposed to provide empirical explanations of the molecular weight dependences.The labyrinthine-to-dendritic transition is attributed to a molecular diffusion process change from a local-diffusion to diffusion-limited-aggregation(DLA) and a polymer chain with M w ≈ 253000 g/mol within a blob can join crystals independently.The dendritic-to-faceted transition is attributed to a turnover of the pattern formation mechanism from DLA to crystallization control,and a polymer chain with a M w ≈ 27000 g/mol as an independent blob crosses to a depletion zone to join crystals.These molecular weight dependences reveal a macromolecular effect on the crystal pattern formation and selection of crystalline polymers.     

Cryogenic degradation of polystyrene in solution

An ultra-high molecular weight and narrow distribution polystyrene ($\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{= 7.3 × 10}{}^6$, M_w/M_n = 1.13) was dissolved in a wide range of solvents. Potential degradation by freezing was studied as a function of solvent type, concentration, cooling rate and number of freezing cycles. Cryogenic experiments were conducted in dioxane, tetrahydrofuran, benzene, dichloroethane, cyclohexanone, p-xylene, methyl methacrylate and styrene. The extent of degradation did not relate to a single solvent parameter, but there seemed to be a tendency towards a limited degradation in solvents with low melting points and/or solubility parameters greatly different from that of polystyrene. A low polymer concentration as well as a high cooling rate promoted chain scission, the latter parameter being the most important. In cyclohexanone and p-xylene, linear relationships were observed between the number of scission per molecule and the number of freezing cycles at high polymer concentrations and at high cooling rates. At lower concentrations and slower cooling, the relationships were non-linear suggesting a different degradation mechanism. The most extensive change in molecular weight distribution was observed on freezing in styrene. After 45 freezing cycles, an $\text{M}$_w of only 2.3 × 10⁶ was observed. The results indicate that chain scission occurred together with polymerization and combination reactions. Freezing of suitable solutions of ultra-high molecular weight polymers can thus be used as a new way of initiating polymerizations by cooling rather than heating.     

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     

Preparation of polypseudorotaxane composed of linear and cyclic polyethylene oxides and its application to solid polymer electrolyte

The mixture of linear polyethylene glycol with molecular weight of 20,000 (l-PEG_20K) and cyclic polyethylene glycol with molecular weight of 1,000 (c-PEG_1K) was ultrasonicated in acetonitrile. After evaporating the solvent, the residue was analyzed by DSC to show a remarkable decrease of crystallization temperature. Such a large crystallization suppression was not observed when linear polyethylene glycol with molecular weight of 1,000 (l-PEG_1K) was added instead of c-PEG_1K. Further, the mixture of cyclic polyethylene glycols (c-PEG_6K and c-PEG_1K) did not exhibit a significant crystallization suppression. These experimental results indicated that formation of polypseudorotaxane through ultrasonication-assisted ring penetration played an important role in the crystallization suppression. Ionic conductivities of the polypseudorotaxane-based polymer electrolytes prepared from polyethylene oxide with molecular weight of 600,000 (PEO_600K) and c-PEG_1K showed conductivity enhancement especially at low Li salt concentration.     

Influence of initial polymer concentration in solution and weight-average molecular weight on the drawing behavior of polyethylenes

The influence of initial polymer concentration in solution (c), weight-average molecular weight (M_ω), and drawing temperature on the solid-state drawing behavior of linear polyethylenes was investigated. Optimum conditions, with respect to maximum attainable draw ratio, are observed in isothermal drawing experiments. Moreover, it is shown that high maximum attainable draw ratios can also be obtained upon multistage drawing of UHMW-PE (ultrahigh-molecular-weight polyethylene, M_ω > 10⁶ g/mol) gel films cast from concentrated solutions. The high maximum attainable draw ratio in combination with the high molecular weight (M_ω > 10⁶ g/mol) and polymer concentration (c = 10% w/v) is of particular interest because it results in tapes or fibers with a high Young's modulus (100 GPa) and tensile strength (2.5–3.5 GPa). It is also shown that the maximum attainable draw ratio of polyethylenes scales with the Bueche parameter (c · M_ω) to the ?0.5 power. This experimental observation indicates that intermolecular interactions not only dominate the rheological properties of polyethylene melts and concentrated solutions, but also strongly influence the solid-state drawing behavior of linear polyethylenes.     

Long‐Chain Polyacetals From Plant Oils

Plant oil‐derived α,ω‐diacetals are polycondensated to the novel polyacetals [OCH₂O(CH₂)_y]_n (y = 19 and 23) with molecular weight of ca. M _n = 2 × 10⁴ g mol⁻¹. The long methylene sequences provide substantial melt and crystallization temperatures (T_m = 88 °C and T_c = 68 °C for y = 23), and rates of hydrolytic degradation are dramatically lower for the long‐chain polyacetals versus a shorter chain analogue (y = 12) studied for comparison.     

ESR studies of photosensitized degradation of poly(L‐lactic acid) via photoionization of dopant

The photosensitized degradation of poly(L ‐lactic acid) (PLA) via an anionic reaction process was studied using spectrophotometry, electron spin resonance (ESR), and gel permeation chromatography (GPC) measurements. PLA film doped with N,N,N′,N′‐tetramethyl‐p‐phenylenediamine (TMPD) was irradiated at 77 K using UV light (λ_c = 356 nm) by which the PLA matrix itself cannot be directly excited. After photoirradiation, a new broad absorption band appeared over the original spectrum due to TMPD⁺ ·, which was produced by two‐photon ionization. The ESR spectrum of the irradiated sample indicated the presence of the TMPD⁺ · radical and main‐chain scission radical of PLA. During the thermal annealing at 0 °C, the latter radical changed to another radical species by dehydrogenation of the alpha hydrogen of the PLA main chain. TMPD⁺ · was extremely stable at room temperature for 7 d. However, by thermal annealing at 40 °C, all the radicals decayed due to the enhanced molecular motions near T_g of PLA (58.7 °C). Spectral simulation for the obtained ESR spectra revealed the relative amounts of four radicals: TMPD⁺ ·, a main‐chain scission radical, a main‐chain tertiary radical, and an unknown radical. The last one was tentatively assigned to the PLA radical anion because of its short decay time. GPC measurements clearly indicated a decrease in the molecular weight of PLA after irradiation. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 706–714, 2001     

Polysiloxanes: paradigm or paradox

Spherulitic growth rates and physical properties of polysiloxanes are well correlated for a wide range of molecular weights. Below the zero shear entanglement molecular weight, M_c, chain folding is probably the norm and fractions are brittle, but after M_c is traversed there is a significant decrease in crystallinity, increase in interfacial surface energy and change in lamellar morphology as polymer fractions go from brittle to tough. The chain folded crystallization model with reptation, as a chain folding facilitator, fails to account for this behavior. Appropriate property data for polyethylene and polyisoprene fractions also supports this thesis which now appears to be more of a paradigm than a paradox.     

The effect of network chain-length distribution,specifically bimodality,on strain-induced crystallization

Polyurethane elastomers were prepared from a series of poly(ethylene oxide) samples by end-linking the chains into “model” trifunctional networks. The molecular weight M_c between crosslinks in such networks is simply the number-average molecular weight M_n of the precursor polymer. End-linking samples separately gave networks with unimodal distributions of network chain lengths, whereas end-linking mixtures of two samples having very different values of M_n gave bimodal distributions with average values of M_c equal to the average value of M_n for the two samples. Stress-strain isotherms in elongation were obtained for these networks, both unswollen and swollen to various extents. Strain-induced crystallization was manifested in elastic properties that changed significantly with changes in temperature. Swelling has more complicated effects, since it causes deformation of the network chains as well as melting of some of the crystallites. Comparisons among stress-strain isotherms at constant M_c indicate that bimodality facilitates strain-induced crystallization.     

Modification of poly(vinyl chloride). XIII. Crosslinking of poly(vinyl chloride) with dithiols and properties of the crosslinked products

PVC was crosslinked by immersing PVC–dithiol blends in ethylenediamine at 30°C. Properties of the products depended on the chain length and chemical structure of the crosslinkage and on the molecular weight of the polymer chain between crosslinks M_c. Crosslinking by the agent of soft structure and long molecular chain resulted in high tensile strength at break and impact strength and low brittle temperature. The use of the crosslinking agent of short molecular chain gave high yield strength, Young's modulus, and heat distortion temperature. The relation of M_c and the chemical structure of the crosslinks to the properties of the crosslinked rigid polymer was discussed in regard to the crosslinking effect and plasticizing effect.     

Cationic polymerization of L,L‐lactide

Cationic bulk polymerization of L ,L‐ lactide (LA) initiated by trifluromethanesulfonic acid [triflic acid (TfA)] has been studied. At temperatures 120–160 °C, polymerization proceeded to high conversion (>90% within ～8 h) giving polymers with M_n ～ 2 × 10⁴ and relatively high dispersity. Thermogravimetric analysis of resulting polylactide (PLA) indicated that its thermal stability was considerably higher than the thermal stability of linear PLA of comparable molecular weight obtained with ROH/Sn(Oct)₂ initiating system. Also hydrolytic stability of cationically prepared PLA was significantly higher than hydrolytic stability of linear PLA. Because thermal or hydrolytic degradation of PLA starting from end‐groups is considerably faster than random chain scission, both thermal and hydrolytic stability depend on molecular weight of the polymer. High thermal and hydrolytic stability, in spite of moderate molecular weight of cationically prepared PLA, indicate that the fraction of end‐groups is considerably lower than in linear PLA of comparable molecular weight. According to proposed mechanism of cationic LA polymerization growing macromolecules are fitted with terminal ? OH and ? C(O)OSO₂CF₃ end‐groups. The presence of those groups allows efficient end‐to‐end cyclization. Cyclic nature of resulting PLA explains its higher thermal and hydrolytic stability as compared with linear PLA. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2650–2658, 2010     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Molecular geometry and chain entanglement: parameters for the tube model

The tube diameter in the reptation model is the distance between a given chain segment and its nearest segment in adjacent chains. This dimention is thus related to the cross-sectional area of polymer chains and the nearest approach among chains, without effects of thermal fluctuation and steric repulsion. Prior calculated tube diameters are much larger, about 5 times, than the actual chain cross-sectional areas. This is ascribed to the local freedom required for mutual rearrangement among neighboring chain segments. This tube diameter concept seems to us to infer a relationship to the corresponding entanglement spacing. Indeed, we report here that the critical molecular weight, M_c, for the onset of entanglements is found to be M_c = 28 A/(〈R²〉₀/M), where A is the chain cross-sectional area and 〈R²〉₀ the mean-square end-to-end distance of a freely jointed chain of molecular weight M. The new, computed relationship between the critical number of backbone atoms for entanglement and the chain cross-sectional area of polymers, N_c = A^0,44, is concordant with the cross-sectional area of polymer chains being the parameter controlling the critical entanglement number of backbone atoms of flexible polymers.     

Synthesis and characterization of polyoctenamer with WCl6?e−?Al?CH2Cl2 catalyst system via ring‐opening metathesis polymerization

A typical low‐strain monomer, cyclooctene, was polymerized via ring‐opening metathesis polymerization with electrochemically produced active species. The structural properties of the polyoctenamer were determined by NMR, gel‐permeation chromatography and differential scanning calorimetry. Analysis of the polyoctenamer microstructure by ¹H and ¹³C NMR spectroscopy indicates that the polymer contains a highly cis stereoconfiguration of the double bonds (σ_c = 0.75). The resulting polymer is of low molecular weight and has a reasonably broad molecular weight distribution (M_w = 18 000, PDI = 1.9). The glass transition temperature and melting point of the polyoctenamer are ?11.3 °C and 36.5 °C respectively. Copyright © 2005 John Wiley & Sons, Ltd.     

Electron-impact studies—LI: Hydrogen randomization in the stilbene molecular ion

Hydrozen randomization precedes the formation of M^+· ? H· and M^+· ? CH₃· species from the stilbene molecular ion at 15 eV. The carbon atom involved in the M^+· ? CH₃· elimination originates randomly from the whole molecule. The [M ? 15] ion (m/e 165) in the spectra of stilbene and 9,10-dihydrophenanthrene is produced from a common ion.     

Rigidity percolation model of polymer fracture

A theory of the fracture of polymers with network microstructure was developed that was based on the vector, or rigidity percolation (RP) model of Kantor and Webman, in which the modulus, E, is related to the lattice bond fraction p, via E ～ [p ? p_c]^τ. The Hamiltonian for the lattice was replaced by the strain energy density function of the bulk polymer, U = σ²/2E, where σ is the applied stress and p was expressed in terms of the lattice perfection via the bond density ν, with the entanglement molecular weight, ν = ρ/M_e and appropriate measures of crosslink density for rubber, thermosets, and carbon nanotubes. The stored mechanical energy, U, was released by the random fracture of νD_o[p ? p_c] over stressed hot bonds of energy D_o ≈ 330 kJ/mol. The polymer fractured critically when p approached the percolation threshold p_c, and the net solution was obtained as σ = (2EνD_o [p ? p_c])^1/2 with a fracture energy, G_1c ～ [p ? p_c]. The fracture strength of amorphous and semicrystalline polymers in the bulk was well described by, σ = [ED_oρ/16 M_e]^1/2, or σ ≈ 4.6 GPa/M_e^1/2. Fracture by disentanglement was found to occur in a finite molecular weight range, M_c < M < M*, where M*/M_c ≈ 8, such that the critical draw ratio, λ_c = (M/M_c)^1/2, gave the molecular weight dependence of the fracture as G_1c ～ [(M/M_c)^1/2 ? 1]². The critical entanglement molecular weight, M_c, is related to the percolation threshold, p_c, via M_c = M_e/(1 ? p_c). Fracture by bond rupture was in accord with Flory's suggestion, G/G* = [1 ? M_c/M], where G* is the maximum fracture energy. Fracture of an ideal rubber with p = 1 was determined not to occur without strain hardening at λ > 4, such that the maximum stress, σ = E (λ ? 1/λ) = 3.75E. The fracture properties of rubber were found to behave as σ ～ ν, σ ～ E, and G_1c ～ ν. For highly crosslinked thermosets, it was predicted that σ ～ (Eν)^1/2, σ ～ (X ? X_c)^1/2, and G_1c ～ ν^?1/2, where X is the degree of reaction of the crosslinking groups and X_c defines the gelation point. When applied to carbon nanotubes (SWNT and MWNT) of diameter d and hexagonal bond density ν = j/b², the nominal stress as a function of diameter is σ(d) = [16 ED_o(p ? p_c) j/b]^1/2/d ≈ 211/d (GPa.nm) and the critical force, F_c(d) ≈ 166 d (nN/nm), in which j = 1.15, b = 0.142 nm, E ≈ 1 Tpa, and D_o = 518 kJ/mol. For polymer interfaces with Σ chains per unit area of length L and width X ～ L^1/2, G_1c is then ～ [p ? p_c], where p ～ ΣL/X. The results predicted by the RP fracture model were in good agreement with a considerable body of fracture data for linear polymers, rubbers, thermosets, and carbon nanotubes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 168–183, 2005     

Microstructure and rheological properties of polybutadienes

The viscosities, rubbery deformations, densities, and their dependence on temperature have been measured for several series of polybutadienes with molecular weights ranging from 5,000 to 400,000 and differing in proportions of cis and trans structures (cis content from 40 to 95%). On the basis of the viscosity measurements the critical molecular weight M_c has been determined, corresponding to a sharp change in the nature of the viscosity versus molecular weight dependence. Rubbery deformations are displayed pronouncedly in specimens with M > M_c and are closely related to the appearance of non-Newtonian flow. The value of M_c depends on the relative content of cis and trans forms. When M > M_c, the initial viscosity is a parameter sensitive to the microstructure of polybutadienes, so that with at a single molecular weight, depending on the ratio of cis and trans units, the viscosity may vary over a more than tenfold range. The glass transition temperature and activation energy of viscous flow rise regularly with increasing trans content in the polymer chain, these parameters becoming independent of the molecular weight for specimens with M > M_c within a series of polybutadienes of equal microtacticity. Thermomechanical investigations of polybutadienes also made it possible to define more accurately the boundaries of the crystallization region and the dependence of the melting point on the microtacticity. The results obtained are discussed on the basis of modern ideas of polymer structure.     

Copolymerization of propylene with 1,3‐butadiene using isospecific zirconocene catalysts

Poly(propylene‐ran‐1,3‐butadiene) was synthesized using isospecific zirconocene catalysts and converted to telechelic isotactic polypropylene by metathesis degradation with ethylene. The copolymers obtained with isospecific C₂‐symmetric zirconocene catalysts activated with modified methylaluminoxane (MMAO) had 1,4‐inserted butadiene units ( 1,4‐BD ) and 1,2‐inserted units ( 1,2‐BD ) in the isotactic polypropylene chain. The selectivity of butadiene towards 1,4‐BD incorporation was high up to 95% using rac‐dimethylsilylbis(1‐indenyl)zirconium dichloride (Cat‐A)/MMAO. The molar ratio of propylene to butadiene in the feed regulated the number‐average molecular weight (M_n) and the butadiene contents of the polymer produced. Metathesis degradations of the copolymer with ethylene were conducted with a WCI₆/SnMe₄/propyl acetate catalyst system. The ¹H NMR spectra before and after the degradation indicated that the polymers degraded by ethylene had vinyl groups at both chain ends in high selectivity. The analysis of the chain scission products clarified the chain end structures of the poly(propylene‐ran‐1,3‐butadiene). © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5731–5740, 2007