Polydispersity effects in polymer self-diffusion measured by small-angle neutron scattering

The small-angle neutron scattering (SANS) method for measuring the self-diffusion coefficient D has been analyzed for effects of polydispersity in degree of polymerization for the case of linear polymers diffusing by reptation. Polydispersities corresponding to M_w/M_n = 1.0?10 were considered. It is shown that in all cases a meaningful effective diffusion coefficient D_e can be obtained from the short time recovery of the SANS intensity. This quantity D_e ≤ 1.3 D(M_w), where D(M_w) is the diffusion coefficient of a monodisperse polymer having molecular weight M = M_w. The method relies on SANS intensities extrapolated to zero scattering angle; realistic extrapolation is shown to give rise to quite acceptable errors on the order of 0.05 D_e.     

Rare‐earth‐metal‐initiated polymerizations of (meth)acrylates and block copolymerizations of olefins with polar monomers

The organo‐rare‐earth‐metal‐initiated living polymerization of methyl methacrylate (MMA) was first discovered in 1992 with (C₅Me₅)₂LnR (where R is H or Me and Ln is Sm, Yb, Y, or La) as an initiator. These polymerizations provided highly syndiotactic (>96%) poly(methyl methacrylate) (PMMA) with a high number‐average molecular weight (M_n > 1000 × 10³) and a very narrow molecular weight distribution [weight‐average molecular weight/number‐average molecular weight (M_w/M_n) < 1.04] quantitatively in a short period. Bridged rare‐earth‐metallocene derivatives were used to perform the block copolymerization of ethylene or 1‐hexene with MMA, methyl acrylate, cyclic carbonate, or ?‐caprolactone in a voluntary ratio. Highly isotactic (97%), monodisperse, high molecular weight (M_n > 500 × 10³, M_w/M_n < 1.1) PMMA was first obtained in 1998 with [(Me₃Si)₃C]₂Yb. Stereocomplexes prepared by the mixing of the resulting syndiotactic and isotactic PMMA revealed improved physical properties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 1955–1959, 2001     

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     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

Simple method for determining the critical molecular weight from the loss modulus

The normal concept is that the critical molecular weight (M_C) is about twice as large as the entanglement molecular weight (M_e). However, experimental data have shown considerable deviations from M_C ≈ 2M_e. Furthermore, a determination of M_C requires samples with a wide range of molecular weights, including weights lower than M_C and higher than M_C. In this article, we suggest a simple method for determining M_C from the loss moduli of nearly monodisperse linear polymers with M ? M_C. We consider two characteristic relaxation times, which correspond to the local maximum and minimum of the loss modulus. M_C is determined from the intersection of two phenomenological relaxation times as a function of the molecular weight. The method precisely agrees with M_C ≈ 2M_e, which is not shown by conventional methods. Moreover, our method provides a determination of relaxation time τ_e, at which chain segments first feel the constraints imposed by the conceptual tube, without the measurement of the tube diameter and the monomeric friction coefficient, which may be determined by complicated procedures with a lot of data. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2724–2729, 2004     

Static light scattering from poly(ethylene oxide) in methanol

Static light scattering measurements were performed on dilute solutions of monodisperse poly(ethylene oxide) (PEO) in methanol at 25°C. PEOs of five different molecular weights ranging from nominal M_w = 8.6 × 10⁴ to 9.13 × 10⁵ were used. Linear Zimm plots were obtained for all the PEO samples: no downturn was observed at small angles, indicating that no large aggregates of PEO molecules exist in the solution. From the plots, values of the weight-average molecular weight, M_w, the radius gyration, R_G, and the second virial coefficient, A₂, were successfully determined for respective PEOs. Observed relationship between R_G and M_w indicates that methanol is certainly a good solvent for the polymer. © 1996 John Wiley & Sons, Inc.     

The solution phase characterization of poly(ferrocenyldimethylsilane)s by small‐angle neutron scattering

A series of monodisperse (M_w/M_n < 1.1) poly(ferrocenyldimethylsilane)s was prepared with number‐averaged degrees of polymerization, 〈z〉_n, of 9, 33, 206, and 506 ( 2 – 5 , respectively), as determined by gel permeation chromatography (GPC). The polymers were studied by small‐angle neutron scattering (SANS) in solution with the aim of obtaining the radius of gyration, R_g, the weight‐averaged molecular weight, M_w, and the polydispersity index, M_w/M_n. Data were collected over the range 0.008 < Q/Å^?1 < 0.5 and for a series of concentrations (weight fraction, w = 0.0063, 0.0125, 0.025, and 0.05). The scattered intensity, I(Q), was fitted to a model based on a Schultz–Zimm distribution of isolated chains with excluded volume. A comparison of the molecular weight and size data determined by GPC and SANS indicated an acceptable agreement between the values for R_g, M_w and M_w/M_n. The results of this study demonstrate the potential utility of SANS to fully characterize metallopolymers, and other polymer systems where traditional methods cannot be applied. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4011–4020     

Experimental determination of the relationships among various measures of fluid elasticity

The viscoelastic properties of a 4% solution of monodisperse polystyrene (molecular weight 394,000) in Aroclor 1260 were determined by the following techniques: creep recovery, stress relaxation upon cessation of steady flow, dynamic measurements, and normal stress difference and shear stress measurements in steady flow. All measurements were carried out with cone and plate geometry in a Weissenberg rheogoniometer. The modification of this instrument to perform creep and creep recovery experiments by use of an air-bearing suspension and an air-turbine drive is described. A broad range of shear rates and frequencies encompassing both linear and nonlinear behavior was employed. The elastic behavior is described in terms of the recoverable shear strain s or the steady-state compliance J_e°. The first three techniques gave identical results for J_e° in the range of linear viscoelasticity for which it is defined. The normal stress difference measurements confirmed Lodge's relation s = (P₁₁ ? P₂₂)/2σ₂₁. Reasons for previous experimental disagreement with this result are discussed.     

Recent developments in living carbocationic polymerization of alkenes

The recent discovery of living cationic polymerization of alkenes has been followed up in three areas: 1) Demonstration of the validity of the DP_n = [M_o]/[I_o] relationship and the synthesis of high molecular weight polyisobutylenes M_n_>100 000) of narrow molecular weight distribution (M_w/M_n ≈︁1.1) 2) Discovery of electrophilic quenching and the use of this method for the preparation of allyl-telechelic polyisobutylenes by quenching with trimethylallylsilane and 3) Synthesis of novel linear and three-arm star radial thermoplastic elastomers comprising rubbery polyisobutylene central sequences connected to glassy polystyrene or a polystyrene derivative (i.e., p-methylstyrene, p-tert-butylstyrene, indene) outer sequences. Some physical-mechanical properties of these materials have been investigated.     

Swelling of polyacrylamide gels in polyacrylamide solutions

Swelling behavior of polyacrylamide (PAAm) and polyacrylamide-co-polyacrylic acid (PAAm-co-PAAc) gels was investigated in aqueous solutions of monodisperse PAAms with molecular weights (M_w) ranging from 1.5 × 10³ to 5 × 10⁶ g/mol. The volume of the gels decreases as the PAAm concentration in the external solution increases. This decrease becomes more pronounced as the molecular weight of PAAm increases. The classical Flory–Huggins (FH) theory correctly predicts the swelling behavior of nonionic PAAm gels in PAAm solutions. The polymer–polymer interaction parameter χ₂₃ was found to decrease as the molecular weight of PAAm increases. The swelling behavior of PAAm-co-PAAc gels in PAAm solutions deviates from the predictions of the FH theory. This is probably due to the change of the ionization degree of AAc units depending on the polymer concentration in the external solution. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1313–1320, 1998     

The Effect of Polymer Microstructure and Thermal Post-Treatment on Latex-Based Pressure Sensitive Adhesive Performance

Summary: Butyl acrylate/acrylic acid/2-hydroxyl methacrylate (BA/AA/HEMA, weight ratio: 96/2/2) latexes were produced via starved seeded semi-batch emulsion polymerization. The microstructure of the latex polymers was controlled by varying the amount of chain transfer agent (1-dodecanethiol). The latexes were characterized for gel content, M_c (molecular weight between two adjacent cross-linking points), M_w (molecular weight of sol polymers) and M_e (molecular weight between entanglements). From these latexes, PSA films were cast, dried, conditioned and then thermally post-treated at 120 °C to react the carboxyl and hydroxyl groups from the AA and HEMA units. Tack, peel strength and shear strength of the PSA films were then measured. The thermal post-treatment was shown to be an effective way to improve latex-based PSA performance. The effectiveness of the post-treatment was observed to depend on the polymer microstructure (M_c relative to M_e relative to M_w) of the untreated latex-based PSAs and on the gel content.     

Phase separation induced by shear quenching in polymer blends with a diblock copolymer

The effects of adding A–B diblock copolymer to a polymer blend (A/B) on phase‐separation kinetics and morphology have been investigated in a fixed shallow‐quench condition (ΔT = 1.5 °C) by in situ time‐resolved light scattering and phase‐contrast optical microscopy. A shear‐quench technique was used in this study instead of a conventional temperature‐quench method. Mixtures of nearly monodisperse low relative‐molecular masses of polybutadiene (M_w = 2.8 kg/mol), polystyrene (M_w = 2.6 kg/mol), and a near‐symmetric butadiene–styrene diblock copolymer (M_w = 6.3 kg/mol) as an interfacial modifier were studied. We observed that the addition of the diblock copolymer could either retard or accelerate the phase‐separation kinetics depending on the concentration of the diblock copolymer in the homopolymer blends. In contrast to the conventional temperature quench, we observed complex phase‐separation kinetics in the intermediate and late stages of phase separation by the shear‐quench technique. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 819–830, 2001     

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     

Adiabatic compressibility of solutions of ethylene–propylene copolymers in hydrocarbon solvents

Adiabatic compressibility measurements are reported on solutions in hydrocarbon solvents of a low M_w high ethylene content, and of both high and low M_w low ethylene content ethylene–propylene copolymers. In all solutions the observed adiabatic compressibility was lower than the solvent value by an increment which was a function of the solvent type. Comparison of the data for a high and low molecular weight sample of the same copolymer indicates no molecular weight effects. Changes in the composition of the copolymer, as indicated by NMR spectroscopy, have only a slight effect on the adiabatic compressibility. The dominant feature of these studies is the apparent correlation of the chain length of the alkane solvent with the decrement in the compressibility.     

Anionic dispersion polymerization of styrene. I. Investigation of parameters for preparation of uniform micron-size polystyrene particles with narrow molecular weight distribution

Anionic dispersion polymerization in a hexane medium has been applied to the synthesis of monodisperse polystyrene particles in the size range of 1.41–6.16 μm, and having narrow molecular weight distributions M_w/M_n of 1.02–1.28. sec-Butyllithium was used as the initiator. Polystyrene-block-polybutadiene diblock copolymer containing 23% polystyrene block, (i.e., Stereon 730A) with a molecular weight of 147,000 g/mol and a polydispersity of 1.05, was found to be a suitable steric stabilizer for the preparation of micron-size polystyrene particles with narrow size distribution. Tetrahydrofuran (THF) was used as a promoter for obtaining narrow molecular weight distributions. However, this study revealed that the addition of small amounts of THF as promoter broadened the particle size distribution. High solids content polystyrene dispersions were also prepared without using any promoter by both batch and/or multi-addition monomer processes. © 1996 John Wiley & Sons, Inc.     

Effect of polycondensation methods on molecular weight distribution of nylon 610

Polycondensation methods greatly influence the molecular weight distribution of poly(hexamethylene sebacamide) (nylon 610) as determined by gel permeation chromatography (GPC). The ratio of weight average molecular weight to number average molecular weight (M_w/M_n) was used as a measure for estimating the molecular weight distribution. The M_w/M_n ratios of nylon 610 obtained from melt, solid phase, and high temperature polycondensation methods were 2 to 3.5, which were expected values for the most probable distribution. However, those for polymers obtained from the direct polycondensation in the presence of triphenylphosphine, interfacial polycondensation and low temperature polycondensation using an acid chloride varied over a wide range from 3.5 to 8.5. The effect of the kind of organic solvents in the interfacial method on the M_w/M_n ratios was especially large, and the molecular weight distribution could be controlled to some extent by selecting an appropriate solvent.     

Molecular weight dependence of mechanical properties of poly(p,p′-oxydiphenylene pyromellitimide) films

The mechanical properties, i.e., Young's modulus, elongation, and tensile stress, were determined as functions of the molecular weight for films of poly(oxydi-p-phenylene pyromellitimide) prepared by thermal cyclization of the precursor poly(amic acid). The molecular weights of the samples were controlled by the monomer stoichiometry employed for the solution condensation of pyromellitic dianhydride and p,p′-oxydianiline. Weight-average molecular weights were determined by light scattering of the precursor poly(amic acid) as well as the fully cyclized polyimide. The elongation-at-break is most sensitive to the molecular weight, undergoing a rapid increase at M _w ? 8000 and reaching a limiting value of about 60% for M _w > 20,000.     

Synthesis of high molecular weight polystyrene using AGET ATRP under high pressure

High molecular weight polystyrene (PS) was synthesized by ATRP. Under atmospheric pressure (1 bar), PS with M_n up to 200,000 was prepared using either ARGET or ICAR ATRP. Under high pressure (6 kbar), higher molecular weight PS could be obtained due to accelerated radical propagation and diminished radical termination in polymerization of styrene. Therefore, it was possible to synthesize PS with M_n > 1,000,000 and M_w/M_n < 1.25 using AGET ATRP under a pressure of 6 kbar at room temperature. This is the highest molecular weight linear PS prepared by a controlled radical polymerization.     

Click Functionalization of a Dibenzocyclooctyne‐Containing Conjugated Polyimine

A conjugated poly(phenyl‐co‐dibenzocyclooctyne) Schiff‐base polymer, prepared through polycondensation of dibenzocyclooctyne bisamine (DIBO‐(NH₂)₂) with bis(hexadecyloxy)phenyldialdehyde, is reported. The resulting polymer, which has a high molecular weight (M_n>30 kDa, M_w>60 kDa), undergoes efficient strain‐promoted alkyne–azide cycloaddition reactions with a series of azides. This enables quantitative modification of each repeat unit within the polymer backbone and the rapid synthesis of a conjugated polymer library with widely different substituents but a consistent degree of polymerization (DP). Kinetic studies show a second‐order reaction rate constant that is consistent with monomeric dibenzocyclooctynes. Grafting with azide‐terminated polystyrene and polyethylene glycol monomethyl ether chains of varying molecular weight resulted in the efficient syntheses of a series of graft copolymers with a conjugated backbone and maximal graft density.     

Dependence of Polymer Chain Entanglements on the Solution Concentration

For the viscometric determination of molecular weights of polymers, sufficiently dilute solutions have to be used so that entanglements of the polymer chain are absent. The concentration of the polymer should be such that the relative viscosity (η_r) lies in the range 1.1–1.5 [1]. Similarly, for molecular weight determination by light scattering, the suggested concentration for polymer with weight-average molecular weight ( M _w ) > 10⁵ is 0.5 wt%; for those with M _w < 10⁵, up to 1% may be used [2].

The limits of polymer concentration for such measurements are not clearly known. On dissolution, the polymer molecules adopt a more or less extended configuration whose shape depends on the structure and molecular weight of the polymer, the properties of the solvent, and the temperature

[3]. The molecules of flexible linear polymers acquire a coiled configuration due to free rotation about the C-C bonds. When a dilute solution satisfies theta conditions, the polymer molecules are free from all kinds of interaction and move freely. Then their solution properties could possibly be related to their end-to-end distance. Based on this concept, our attempt to establish the permissible limits of polymer concentration for dilute solutions of several polymers of different molecular weights is reported here.