Tube dilation process in star‐branched cis‐polyisoprenes

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type‐A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]² if the tube actually dilates in the time scale of the star relaxation. For 6‐arm star cis‐polyisoprene (PI) chains (having those type‐A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight M_a. However, in the range of M_a examined, M_a ≤ 8M_e (M_e = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of M_a, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000     

Ethylene/1‐pentene copolymers synthesized using the metaloxycarbene complex catalyst system [(CO)5W=C(Me)OZr(Cp)2Cl]/MAO

Ethylene/1‐pentene copolymers were prepared using a [(CO)₅W= C(Me)OZr(Cp)₂Cl] (1)/MAO catalyst system. 1‐Pentene incorporation in the copolymer was monitored using ¹³C‐NMR spectroscopic methods. The weight average molecular weights (M_w) of the copolymers were between 142,000 and 629,000 g/mol, with polydispersity indexes (PDIs) ranging from ≈ 2 to 90, as analyzed by size exclusion chromatography (SEC). Melting and crystallization temperatures, determined using differential scanning calorimetry (DSC) and crystallization analysis fractionation (CRYSTAF), decreased linearly as the amount of 1‐pentene in the copolymer increased. SEC‐FTIR revealed that the 1‐pentene is predominantly incorporated in the low molecular weight fraction. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5121–5133, 2004     

Synthesis of arborescent styrene homopolymers and copolymers from epoxidized substrates

The synthesis of arborescent styrenic homopolymers and copolymers was achieved by anionic polymerization and grafting. Styrene and p‐(3‐butenyl)styrene were first copolymerized using sec‐butyllithium in toluene, to generate a linear copolymer with a weight‐average molecular weight M_w = 4000 and M_w/M_n = 1.05. The pendant double bonds of the copolymer were then epoxidized with m‐chloroperbenzoic acid. A comb‐branched (or arborescent generation G0) copolymer was obtained by coupling the epoxidized substrate with living styrene‐p‐(3‐butenyl)styrene copolymer chains with M_w ≈ 5000 in a toluene/tetrahydrofuran mixture. Further cycles of epoxidation and coupling reactions while maintaining M_w ≈ 5000 for the side chains yielded arborescent copolymers of generations G1–G3. A series of arborescent styrene homopolymers was also obtained by grafting M_w ≈ 5000 polystyrene side chains onto the linear and G0–G2 copolymer substrates. Size exclusion chromatography measurements showed that the graft polymers have low polydispersity indices (M_w/M_n = 1.02–1.15) and molecular weights increasing geometrically over successive generations. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of perfectly sulfonated sodium polystyrene sulfonate over a wide molar mass range via reversible‐deactivation radical polymerization

An aqueous reversible‐deactivation radical polymerization (RDRP) approach is used to synthesize sodium polystyrene sulfonate directly from functionalized monomers to give uniformly and completely sulfonated materials. Reproducible gram scale syntheses are achieved under simple one pot reaction conditions at ambient temperatures, and full monomer conversions are achieved within approximately 3 h. Reaction variables such as pH, sodium chloride concentration, and methanol cosolvent have a significant effect on the molecular weights (M_n ≈ 20,000–400,000 g·mol^?1) obtained by gel permeation chromatography coupled multiangle light scattering. Observed dispersities were reasonably narrow: Ð ≈ 1.05–1.3. A parametric optimization, rather than direct variation of the monomer to initiator ratio, resulted in some of the highest molecular weight polymers by an RDRP approach. Linear progression between M_n and monomer conversion occurs at a neutral reaction pH, which results in narrow polymer molecular weight distributions, along with high end‐group fidelity as demonstrated with chain extension reactions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1527–1537     

Molecular dimensions and melt rheology of an all‐aromatic liquid crystalline polymer

The molecular dimensions and melt rheology of a thermotropic all‐aromatic liquid crystalline polyester (TLCP) composed of p‐hydroxy benzoic acid, hydroquinone, terephthalic acid, and 2,4‐naphthalenedicarboxylic acid is examined. The Mark–Houwink exponent (α) of 0.95 is estimated for the TLCP. The persistence length estimated from molecular weight (M) and intrinsic viscosity ([η]) data using the Bohdanecky–Bushin equation is about 95 Å, whereas that estimated from light scattering data is 117 Å. These persistence lengths and the observed α value, both higher than those for flexible polymers, suggest that the present TLCP is a semirigid polymer. The zero shear melt viscosity (η₀) varies with approximately M⁶ for molecular weight M > 3 × 10⁴ g/mol; below this molecular weight, η₀ varies almost linearly with M. Widely different entanglement molecular weights (M_e) are predicted, depending on the method used; the plateau modulus estimates M_e of about 8 × 10⁵ g/mol, whereas the ratio of mean square end‐to‐end distance and molecular weight (〈R²〉₀/M) predicts M_e's either too small (0.33 g/mol) or too large (2.5 × 10⁶ g/mol), depending on the theory used. Although the change in the molecular weight dependency of melt viscosity appears to be associated with the onset of entanglement coupling of the semirigid molecules, its origin needs further investigation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2378–2389, 2001     

Effects of chain length distribution on viscoelastic properties of entangled linear polymers: Blending laws for binary blends

The reptation idea of de Gennes and the tube model theory of Doi and Edwards are extended to explain the terminal viscoelastic properties of binary blends in the highly entangled state of two linear monodisperse polymers with different molecular weights M₁ and M₂. A modified tube model is proposed that considers the significance of the constraint release by local tube renewal in accounting for the relaxation process of the higher molecular weight chain. Its relaxation by both reptation and the constraint release is remodeled as the disengagement by pure reptation of an equivalent primitive chain. From knowledge of the longest relaxation times of the blend components, the stress equation is formulated from which blending laws of viscoelastic properties for the binary blends are derived. To force better agreement between theory and experiment at the pure monodisperse limits of the blends, a crude treatment to include the effect of contour-length fluctuation in the equivalent-chain model is also discussed. Theoretical predictions of the zero-shear viscosity and steady-state shear compliance are shown to be in good agreement with literature data on undiluted polystyrenes and polybutadienes over a wide range of the blend composition and M₂/M₁ ratio. The asymptotic of the laws for blends with M₂/M₁ → 1 and 0 are comparable to those from the relaxation spectrum proposed by others earlier on the basis of the tube model.     

Effect of variation of [PMDETA]0/[Cu(I)Br]0 ratio on atom transfer radical polymerization of n‐butyl acrylate

A kinetic study was conducted to examine the effect of varying the ratio of ligand to transition metal in a Cu(I)Br/N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) catalyst system for atom transfer radical polymerization (ATRP) of n‐butyl acrylate (nBA) using methyl 2‐bromopropionate as the initiator. Experimental molecular weights were higher than theoretical when low molecular weight polymers were targeted at low ratios of [PMDETA]₀/[Cu(I)Br]₀ (< 1), indicating inefficient initiation/deactivation. A downward curvature in the plot of M_n versus conversion was observed at high monomer conversion when targeting high molecular weight polymers. This deviation became more significant when an excess of ligand was used, indicating a contribution of chain transfer to ligand. The maximum rate of polymerization was obtained at [PMDETA]₀/[Cu(I)Br]₀ ≈ 0.5 for bulk ATRP of nBA; however for polymerization in the presence of 10 vol% DMF, the maximum appeared at the ratio ≈ 1:1. Addition of acetone or DMF improved solubility of Cu(II) complex, which consequently improved the level of control over the polymerization at low ratios of [PMDETA]₀/[Cu(I)Br]₀, but also reduced the reaction rate. The polymerization rate increased with temperature, but at the expense of increased polydispersities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3285–3292, 2004     

Synthesis and properties of blue light‐emitting,silicon‐containing,regio‐ and stereoregular conjugated polymers

This article concerns the hydrosilylation polyaddition of 1,4‐bis(dimethylsilyl)benzene ( 1 ) with 4,4′‐diethynylbiphenyl, 2,7‐diethynylfluorene ( 2b ), and 2,6‐diethynylnaphthalene with RhI(PPh₃)₃ catalyst. Trans‐rich polymers with weight‐average molecular weights (M_w's) ranging from 19,000 to 25,000 were obtained by polyaddition in o‐Cl₂C₆H₄ at 150–180 °C, whereas cis‐rich polymers with M_w's from 4300 to 34,000 were obtained in toluene at 0 °C–r.t. These polymers emitted blue light in 4–81% quantum yields. The cis polymers isomerized into trans polymers upon UV irradiation, whereas the trans polymers did not. The device having a layer of polymer trans‐ 3b obtained from 1 and 2b demonstrated electroluminescence without any dopant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2774–2783, 2004     

Cooperative chain relaxation in miscible polymer blends

Orientation relaxation of dissimilar chains in the molten miscible blends, poly(methyl methacrylate)/poly(vinylidene fluoride) and poly(methyl methacrylate)/poly(vinylidene fluoride-co-trifluoroethylene), were investigated by measuring (1) the change of infrared dichroic ratio with time after the uniaxial stretching of film specimens, (2) the shear stress relaxation spectrum, and (3) birefringence relaxation in shear. The dissimilar polymers showed an identical time variation of the normalized Hermans orientation function. The blend showed a relaxation spectrum with a single characteristic relaxation time τ_c, depending on the blend composition. The birefringence relaxed monotonically, remaining positive. These results suggest that the dissimilar polymers do not relax independently but cooperatively. This behavior may be induced by a constraint due to the specific interactions between the dissimilar polymers, e.g., weak hydrogen bonding. For the cooperative chain relaxation, a third power relationship was found; τ_c/τ_e vprop; (M/M_e),³ where τ_e and M_e are the relaxation time and molecular weight of entanglement strand, respectively, and M is the number average molecular weight in the blend.     

Effect of Molecular Weight on Enthalpy Relaxation in Syndiotactic Poly(Methyl-Methacrylate)

The structural relaxation behaviour of narrow fractions (M_w/M_n < 1.1) of syndiotactic poly(methyl methacrylate) with molecular masses ranging from 2,000 to 200,000 Daltons have been studied by DSC with two classical procedures, namely: the rate of cooling and the isothermal approaches. The apparent activation energy (Δh*) of enthalpy relaxation was evaluated from the dependence of the glass transition temperature on the cooling rate while a comparison of the apparent relaxation rates was appraised from the enthalpy loss by annealing the different samples at the same level of undercooling (T_a = T_g − 10 °C). As expected, the increase of molecular weights gives rise to both a continuous increase of Δh* and a decrease of the apparent isothermal relaxation rate. More interestingly, both Δh* and the apparent isothermal relaxation rate showed abrupt changes around the syndiotactic PMMA entanglement mass (M_e ).     

Chemical composition effects on the fracture of polystyrene-block-poly(methyl methacrylate)block copolymers

The crazing and fracture behaviors of glassy–glassy block copolymers were investigated for polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymers that had similar overall molecular weights but different poly(methyl methacrylate) (PMMA) molar fractions. A liquid chromatography technique was applied to separate as-synthesized PS-b-PMMA [(1) weight-average molecular weight (M_w) = 94,000 g/mol and PMMA molar fraction = 0.35 and (2) M_w = 65,000 g/mol and PMMA molar fraction = 0.28] into three fractions with different chemical compositions. With a copper-grid technique, the fracture behaviors of 0.5-μm-thick PS-b-PMMA films were studied as a function of the applied strain. For the higher M_w PS-b-PMMA samples, the median strains at crazing and fibril breakdown increased with an increase in the PMMA molar fraction from 0.24 to 0.46, corresponding to an increase in the chain entanglements in the PMMA domains. In contrast, for the lower M_w samples, the two values were not significantly changed even when the PMMA molar fraction was varied from 0.16 to 0.35. M_w of the minor component in PS-b-PMMA played a critical role in controlling the fracture behaviors of the block copolymers. Specifically, M_w/M_e of the minor component (where M_e is the molecular weight between entanglements) had to be roughly larger than 2 for the block copolymers to sustain sufficient strains before fracture. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3612–3620, 2006     

Entanglement properties of cellulose and amylose in an ionic liquid

Concentrated solutions of cellulose and amylose were prepared with an ionic liquid 1‐butyl‐3‐methylimidazolium chloride (BmimCl), which was chosen as a good solvent for these polysaccharides. Dynamic viscoelasticity of the concentrated solutions was examined to obtain the molecular weight between entanglements, M_e. The value of M_e in the molten state (M_e,melt), a material constant that reflecting the entanglement properties, was determined for cellulose and amylose by extrapolating M_e to the “melt.” A marked difference in M_e,melt was found: 3.2 × 10³ for cellulose and 2.5 × 10⁴ for amylose. The value of M_e,melt for cellulose, which is composed of β‐(1,4) bonding of D ‐glucose units, is very close to those for polysaccharides with a random‐coil conformation such as agarose and gellan in BmimCl. The much larger M_e,melt for amylose can be attributed to the helical nature of the amylose chain, α‐(1,4)‐linked D ‐glucose units. The effect of concentration on the zero‐shear viscosity for the solutions of cellulose and amylose was also examined. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Effects of tris(pentafluorophenyl)borane on the activation of a metal alkyl‐free Ni‐based catalyst in the polymerization of 1,3‐butadiene

The activation of a metal alkyl‐free Ni‐based catalyst with B(C₆F₅)₃ was investigated in the polymerization of 1,3‐butadiene. A catalyst of bis(1,5‐cyclooctadiene)nickel (Ni(COD)₂)/B(C₆F₅)₃ was found to have high catalytic activity and 1,4‐cis stereoregularity. The catalyst was also found to provide polybutadiene having a molecular weight (M_w) of up to 117,000, even in the absence of AlR₃ and MAO. Variations in the mol ratio of B(C₆F₅)₃ to Ni affected catalytic activity, 1,4‐cis stereoregularity, and the M_w of polybutadiene, while the molecular weight distribution (MWD) of polybutadiene showed little correlation with the mol ratio of B(C₆F₅)₃ to Ni. The use of other borane compounds such as B(C₆H₅)₃, BEt₃, and BF₃ etherate in place of B(C₆F₅)₃ clearly showed the two main functions of B(C₆F₅)₃ in the present catalyst. The high Lewis acidity of B(C₆F₅)₃ enabled it to activate catalytic complexes, thus inducing the polymerization. The steric bulkiness of B(C₆F₅)₃ suppressed chain transfer reactions, contributing to the production of polybutadiene with a high M_w. Kinetic studies showed that the catalyst had an induction period, possibly due to the time needed for the formation of catalytic complexes starting from Ni(COD)₂. A plot of ?ln (1?X), where X is the fractional conversion, as a function of time resulted in a linear relationship, showing that the present catalyst system followed first‐order kinetics with respect to monomer concentration. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1164–1173, 2004     

Using apparent molecular weight from SEC in controlled/living polymerization and kinetics of polymerization

Apparent molecular weights from size exclusion chromatography, that is molecular weights relative to standards of a nature different to that of the polymer sample being studied, are frequently used. We use calculations corresponding to realistic cases to provide guidelines for situations when, and to what extent, apparent molecular weights (MWs) can be meaningful. In controlled polymerization, we show how, without due care, use of apparent MW, could lead to the incorrect conclusion that the reaction was not controlled, whereas the true MWs would be close to theoretical values. We show here that the quality of the eluent as a solvent for the standard and the polymer sample is a good indication of the accuracy and the significance of the apparent polydispersity index. Accurate Mark–Houwink–Sakurada parameters are of limited availability, but the data about solvent quality available in handbooks or available from static light scattering measurements. Apparent M_n is of no use in controlled polymerization if simple simulations as performed in this work do not validate their use. The determination of transfer constants by the Mayo plot can be performed using apparent M_n without introducing any significant error, contrary to apparent weight‐average molecular weight M_w or apparent ln number distribution. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 897–911, 2008     

Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model

The viscosity η₀(M) of polymeric liquids of molecular weight M is calculated on the basis of the tube model formulated by Doi and Edwards (ref. 3). The contour length fluctuation of polymers along the tube, which was neglected in ref. 3, is now explicitly taken into account. The result is where M_c = 2M_e, and M_e is the molecular weight between the entanglement points. This result is numerically close to the empirical 3.4-power law, η₀(M) = η₀(M_c)(M/M_c)^3.4, for 10M_c ? M ? 100M_c but approaches the result in ref. 3 for very high molecular weight. We thus conclude that the 3.4-power law is actually an approximate expression for the real curve which slowly approaches the asymptotic form calculated in ref. 3.     

Behavior of cellulose in NaOH/Urea aqueous solution characterized by light scattering and viscometry

Cellulose was dissolved in 6 wt % NaOH/4 wt % urea aqueous solution, which was proven by a ¹³C NMR spectrum to be a direct solvent of cellulose rather than a derivative aqueous solution system. Dilute solution behavior of cellulose in a NaOH/urea aqueous solution system was examined by laser light scattering and viscometry. The Mark–Houwink equation for cellulose in 6 wt % NaOH/4 wt % urea aqueous solution at 25 °C was [η] = 2.45 × 10^?2 weight‐average molecular weight (M_w)^0.815 (mL g^?1) in the M_w region from 3.2 × 10⁴ to 12.9 × 10⁴. The persistence length (q), molar mass per unit contour length (M_L), and characteristic ratio (C_∞) of cellulose in the dilute solution were 6.0 nm, 350 nm^?1, and 20.9, respectively, which agreed with the Yamakawa–Fujii theory of the wormlike chain. The results indicated that the cellulose molecules exist as semiflexible chains in the aqueous solution and were more extended than in cadoxen. This work provided a novel, simple, and nonpollution solvent system that can be used to investigate the dilute solution properties and molecular weight of cellulose. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 347–353, 2004     

Semi‐perfluoroalkylated perylene diimides for conjugated polymers with high molecular weight and high electron mobility

Perylene diimides (PDIs) and their derivatives are excellent semiconductors, while conjugated polymers based on PDIs have limited applications because of their low electron mobility (μ_e) derived from low molecular weight. The reported maximum number‐average molecular weight (M_n) of related polymers is only 21 kDa because PDIs have very poor solubility due to strong π–π stacking of their big planar conjugated cores. Herein, it is found that suitable semi‐perfluoroalkyl groups could enhance the solubility of PDIs significantly, and a series of semi‐perfluoroalkyl modified conjugated polymers with high molecular weight and electron mobility were synthesized. The maximum M_n reaches 94.8 kDa [P(4C_F8C_H‐PDI‐T2)_HW]. In their space‐charge‐limited current (SCLC) devices, all polymers exhibit typical characters of electron transporting semiconductors, and the highest μ_e is up to 8.40 × 10⁻³ cm² V⁻¹ s⁻¹ [P(4C_F8C_H‐PDI‐T2)_HW], which is similar as that of widely used electron transporting semiconductor PC₆₁BM (6.41 × 10⁻³ cm² V⁻¹ s⁻¹). © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 116–124     

A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes

We report measurements of the nonlinear relaxation moduli after a step-shear strain of polystyrene solutions with nearly monodisperse and with bidisperse distributions of molecular weight. We find, as have others, that for monodisperse solutions with M/M_e > 60, there are anomalies, such as an unusually low nonlinear modulus and a kink in a plot of shear stress versus time after the step strain. Here M is the polymer molecular weight and M_e is the entanglement molecular weight. We find that in the bidisperse solutions the anomalies persist as long as M_w/M_e > 60, where M_w is the weight-averaged molecular weight of the bidisperse solution. The persistence of the anomalies in bidisperse solutions disagrees with a theory of Marrucci and Grizzuti that attributes the anomalies to strain inhomogeneities similar to shear banding. The Marrucci-Grizzuti theory predicts that as little as 10% short chains in the bidisperse mix should eliminate the anomalies, whereas in the experiments reported here at least 30% is required. Nevertheless the way in which the anomalies disappear at high strains when one increases the fraction of low-molecular-weight component is qualitatively similar to the theoretical predictions and supports the notion that strain inhomogeneities occur in these systems. © 1992 John Wiley & Sons, Inc.     

Preparation and characterization of graft terpolymers with controlled molecular structure

Segmented terpolymers, poly(alkyl methacrylate)‐g‐poly(D ‐lactide)/poly(dimethylsiloxane) (PLA/PDMS), were prepared with a combination of the “grafting through” technique (macromonomer method) and controlled/living radical polymerization (atom transfer radical polymerization or reversible addition–fragmentation transfer polymerization). Two synthetic pathways were used. The first was a single‐step approach in which a low‐molecular‐weight methacrylate monomer (methyl methacrylate or butyl methacrylate) was copolymerized with a PLA macromonomer and a PDMS macromonomer. The second strategy was a two‐step approach in which a graft copolymer containing one macromonomer was chain‐extended by a copolymerization of the second macromonomer and the low‐molecular‐weight methacrylate. The kinetics of both synthetic approaches were investigated, showing that the polymerizations exhibited a controlled/living behavior. Furthermore, the molecular structure of the terpolymers (composition, molecular weight distribution, and microstructure) was investigated by two‐dimensional liquid chromatography. Well‐defined terpolymers with controlled branch distribution, composition (F_w,PMMA/F_w,PLA/F_w,PDMS ～ 50/30/20) molecular weight (M_n ～ 50,000 g · mol^?1), and a narrow molecular weight distribution (M_w/M_n ～ 1.3) were prepared via both pathways. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1939–1952, 2004