Some phenomenological consequences of the Doi–Edwards theory of viscoelasticity

Doi and Edwards have recently proposed a molecular theory for the dynamics of entangled polymer liquids based on a tube model to represent the mutual constraints on configurational rearrangement of the chains. Expressions for diffusion coefficient, plateau modulus, zero-shear viscosity, steady-state recoverable compliance, and terminal relaxation time can be devloped, and relations among these properties that depend only upon observable quantities can be obtained. Several such relations are derived and are compared with experimental observations.     

Time dependence of shear and normal stresses of polystyrene and poly(ethylene oxide) solutions

The time dependence of shear and normal stresses during constant shearing of some polystyrene and poly(ethylene oxide) solutions in Aroclor 1248 was measured by means of a Weissenberg rheogoniometer. The stresses of the poly(ethylene oxide) solutions first increase rapidly with the increase of strain, then decrease to a value lower than the value in the stationary state, pass another maximum smaller than the first one, and finally reach a steady value. At the end of the shearing of these solutions at high shear rates, the formation of aggregates was clearly evident. The polystyrene solutions became time-dependent only after a certain shear rate and then showed a rheopectic behavior. The difference in behavior is explained qualitatively by the differing tendencies of these polymer chains to form a network.     

Relaxation of shish‐kebab precursor in isotactic polystyrene after short‐term shear flow

We studied the formation and relaxation of precursors of shish‐kebab in isotactic polystyrene after applying pulse shear flow at temperatures above the nominal melting temperatures T_m (=223 °C). It was found that the string‐like objects that were assigned to precursors in a previous article appeared in micrometer scale up to ～285 °C, which was very close to the equilibrium melting temperature T (=289 °C), and the length and the diameter showed two‐step decays consisting of the fast and slow (almost nondecaying) components below ～270 °C, whereas the slow component disappeared above ～270 °C, suggesting that some mechanism stabilizing the string‐like objects disappeared at ～270 °C. It was also found that the two‐step decay was a nature of a single string‐like object, but not an average nature of many precursors, showing heterogeneous inner structure of the precursor. We discussed a possibility that the string‐like object had a fringed micelle type structure including large crystals with a melting temperature of ～270 °C. Within the proposed picture, the highest temperature for the precursor formation (～285 °C) was explained as a melting of the large crystals in oriented melt. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Temperature dependence of viscosity–shear rate behavior in undiluted polystyrene

The time—temperature superposition principle is well-established for linear viscoelastic properties of polymer systems. It is generally supposed that the same principle carries over into nonlinear phenomena, such as the relationship between viscosity η and shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}. Guided by this principle and the forms of various molecular theories, one would expect that η—\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} data on the same polymer at different temperatures would superimpose when plotted as η/η0 versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}η0/ρT, η0 being the limiting viscosity at low shear rates, ρ the polymer density, and T the absolute temperature. Data on polystyrene melts, obtained in a plate-cone viscometer, appear systematically to violate this principle in the range 140–190°. Such anomalies are absent in concentrated solutions of polystyrene. The trends are similar to those reported by Plazek in the steady-state compliance of polystyrene melts near T_g, but they appear to persist to higher temperatures than the compliance anomaly.     

Shear-induced deformation of polystyrene coils in dilute solution from small angle neutron scattering 2. Variation of shear gradient,molecular mass and solvent viscosity

The technique of small angle neutron scattering (SANS) has been used to study the conformation of polystyrene chains in dilute solution under a constant shear gradient. The experiments reveal a distinct anisotropy of the molecular dimensions with regard to the directions parallel and perpendicular to the flow direction on the 2D-multidetector. The deformation ratio of the single polymer chain (R ²/R _iso ² )–1 as a function of the reduced shear gradient=([] · · M _w G)/RT shows a transition from the ideal ²-behaviour for dynamic infinitely flexible coils found at small gradients, to a behaviour with smaller increase at larger. These results are qualitatively consistent with the theory of Cerf for a polymer with finite internal viscosity in a shear gradient. At low(<1), a better agreement with the model of a free-draining coil (Rouse behaviour) than with the Zimm model is observed.     

Correction of Doi–Edwards' Green function for a chain in a harmonic potential and its implication for the stress‐optic rule

We show that the stress‐optic rule is violated in a theoretical model of polymer melts that uses a harmonic potential to confine a polymer chain in a tube‐like domain of surrounding entangled polymers. This is the model first proposed by Doi and Edwards (DE) [J. Chem. Soc. Farad. Trans. II 1978, 74, 1802] and later extended by Ianniruberto and Marrucci (IM) [J. Non‐Newton. Fluid Mech. 1998, 79, 225]. We first provide a rigorous Green function for such a chain, which is a correction to that derived by DE. The modification guarantees chain continuity. Second, we show that the stress‐optic rule is violated in the IM model if the modified Green function is used and an unnecessary assumption employed by IM is avoided. Our result contradicts that of IM. The violation is due to the presence of the virtual springs to confine the chain in the tube rather than the anisotropy of the confinement potential. On the other hand, DE used the virtual‐spring model only for estimation of the monomer density along the primitive path where we find just a small correction. As they did not use it for rheological calculations, the stress‐optic rule appears to be safe for the Doi–Edwards model. The result might be useful for extracting tube potentials from atomistic simulations. © 2014 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014 , 52, 460–469     

Dielectric study on copolymers in dilute solution. Relaxation behavior of methyl methacrylate–styrene and methyl methacrylate–α-methylstyrene copolymers

Dielectric measurements were made on some methyl methacrylate (MMA)-related polymers in dilute solution, in the frequency range of 1–150 MHz. Effects of the solvent viscosity upon the relaxation behavior were carefully examined. The dielectric relaxation of MMA–styrene copolymers with a high content of MMA units as well as that of the MMA–α-methylstyrene copolymer was little affected by the solvent viscosity. With the aid of Kramers'rate constant for small friction, it was found that their dipolar relaxation is very similar to that caused by the internal rotation of a flexible side-chain. On the other hand, MMA–styrene copolymer with a low content of MMA units showed a diffusion-controlled relaxation process, which can be interpreted in terms of Kramers' theory for large friction. In the latter case, the dipolar relaxation appears to reflect a molecular motion such as sweeping out solvent molecules. These results indicate that it is not the dipole itself but its environment, or rather the local molecular structure containing dipoles, that principally controls the relaxation process. On this basis, we propose a criterion, for quantitatively distinguishing the two relaxation mechanisms from each other.     

Bulk and shear rheology of a symmetric three‐arm star polystyrene

The bulk and shear rheological properties of a symmetric three‐arm star polystyrene were measured using a self‐built pressurizable dilatometer and a commercial rheometer, respectively. The bulk properties investigated include the pressure–volume–temperature behavior, the pressure‐dependent glass transition temperature (T_g), and the viscoelastic bulk modulus and Poisson's ratio. Comparison with data for a linear polystyrene indicates that the star behaves similarly but with slightly higher T_gs at elevated pressures and slightly higher limiting bulk moduli in glass and rubbery states. The Poisson's ratio shows a minimum at short times similar to what is observed for the linear chain. The horizontal shift factors above T_g obtained from reducing the bulk and shear viscoelastic responses are found to have similar temperature dependence when plotted using T ? T_g scaling; in addition, the shift factors also exhibit a similar temperature dependence to linear polystyrene. The retardation spectra for the bulk and shear responses are compared and show that the long time molecular mechanisms available to the shear response are unavailable to the bulk. At short times, the two spectra have similar slopes, but the short‐time retardation spectrum for the shear response is significantly higher than that for the bulk, a finding that is, as yet, unexplained. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Relaxation theory of the electronic spin of a complexed paramagnetic metal ion in solution beyond the Redfield limit

The relaxation of the electronic spin S of a paramagnetic metal ion with fully quenched orbital angular momentum in its ground state is investigated in an external magnetic field through a systematic study of the time correlation functions governing the evolution of the statistical operator (density matrix). Let omega0 be the Larmor angular frequency of S. When the relaxation is induced by a time-fluctuating perturbing Hamiltonian hH1(t) of time correlation tauc, it is demonstrated that after a transient period the standard Redfield approximation is relevant to calculate the evolution of the populations of the spin states if parallelH1 parallel2tauc2/(1+omega0(2)tauc2)<1 and that this transient period becomes shorter than tauc at sufficiently high field for a zero-field splitting perturbing Hamiltonian. This property, proven analytically and confirmed by numerical simulation, explains the surprising success of several simple expressions of the longitudinal electronic relaxation rate 1/T1e derived from the Redfield approximation well beyond its expected validity range parallelH1 paralleltauc<1. It has favorable practical consequences on the interpretation of the paramagnetic relaxation enhancement of nuclei used for structural and dynamic studies.     

Rheology of polystyrene solutions around the coil overlapping concentration: A phenomenological description of stresses in simple shear flow

Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τ_RZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τ_L > τ_RZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ₁) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ²)^?1/2, where γ is the magnitude of shear. Contributions to η and Ψ₁ from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τ_st = τ + (τ_RZ ? τ)/(1 + 0.35τ_RZ γ˙) instead of τ_RZ. Here, γ˙ is the rate of shear, and τ is the τ_RZ value at the infinite dilution limit. η and Ψ₁ at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol^?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002     

Relaxation of excited Franck–Condon states of molecular electron donor–acceptor complexes in liquid solution: the role of orientational isomers

The direct consequences of the presence of ground state orientational isomers of molecular complexes are discussed in terms of the adiabatic potential energy surfaces calculated for the ground and excited states of electron donor–acceptor complexes of tetracyanobenzene with toluene and with mesitylene. Some earlier experimental results that confirm the presence of orientational isomers are also recalled and reviewed, together with the recent results for molecular exciplexes under supersonic molecular beam conditions. Exploration of potential energy surfaces shows that the relaxation pathways of excited Franck–Condon states of the ground state isomers may differ considerably and in liquid solution may be sensitive to physical conditions, which in fact is observed in time-resolved fluorescence spectra of the electron donor–acceptor systems under consideration, upon excitation of high-energy Van der Waals orientational isomers. It is concluded that, in weak electron donor–acceptor complexes in liquid solutions, the role of such isomers may be limited, but it may become crucial for the kinetics and dynamics of excited states if the system is simultaneously capable of forming an exciplex.     

Investigation of the micromechanical deformation behavior of styrene–butadiene star block copolymer/polystyrene blends with high‐voltage electron microscopy

The deformation behavior of blends consisting of a styrene–butadiene star block copolymer and a polystyrene homopolymer was studied by high‐voltage electron microscopy with a tensile device. The mechanical properties and micromechanical deformation mechanisms in the star block copolymer/polystyrene blends were directly influenced by their morphology. Although the pure block copolymer deformed in a very unequal manner (because of a thin‐layer‐yielding mechanism) and revealed no local deformation zones, a transition to the formation of crazelike zones was observed in the blends. This transition in the deformation mechanisms was correlated to the abrupt change in the macroscopic strain at break of the injection‐molded specimens. At lower contents of added polystyrene, a craze‐stopping mechanism was observed, whereas the blends with higher polystyrene contents demonstrated crazing like that in pure polystyrene. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1157–1167, 2003     

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.     

Partitioning of polystyrene between incompatible phases and distributional effects in the system polystyrene–polybutadiene–toluene

The average molecular weights and the molecular weight distributions of polystyrene (PS) in the conjugate incompatible phases of the ternary system of PS and polybutadiene with toluene as solvent were studied at 23°C. Gelpermeation chromatography, with ultraviolet and differential refractive index detectors, was used for analyzing the compositions of the conjugate phases and for obtaining the molecular weight averages of PS in the phases. Both narrow and broad molecular weight distribution (MWD) polymer samples were used. The effect of broad MWD polymers is seen as one of narrowing the shape of the binodal, thus effectively increasing the compatible region. The molecular weight averages of PS in the two conjugate phases do not vary significantly in the case of the narrow MWD PS sample while for broad MWD samples the average molecular weight of PS is found to be higher in the PS-rich phase than in the polybutadiene-rich phase for tie lines closer to the plait point indicating a partitioning or redistribution of the molecular weight species of PS between the incompatible phases.     

Effect of shear flow on the phase‐separation behavior in a blend of polystyrene and polyvinyl methyl ether

The phase behavior and phase‐separation dynamics of polystyrene/polyvinyl methyl ether (PS/PVME) blend with a critical composition of 70 vol % PVME were examined with a light scattering technique under a shear‐rate range of 0.1–40 s^?1. If the shear rates were less than 8 s^?1 and the starting temperatures of the measurement were 343 and 383 K, respectively, two cloud points were observed, whereas after the shear rate was higher than 8 s^?1, only one cloud point existed, 20 K higher than that of the static state of the blend. Investigation of the phase‐separation dynamics at 443 K suggested that in the vorticity direction the phase‐separation behavior at the early stage and the later stage can be explained by Cahn–Hilliard linearized theory and the exponent growth law, respectively. Phase separation occurs after a shearing time, which was called a delay time τ_d. The delayed time τ_d, the apparent diffusion coefficient, and the exponent term of the blend show strong dependence on shear rates. A theoretical prediction of the phase behavior of PS/PVME under a shear flow field by introducing an elastic energy term into Flory's equation‐of‐state theory was made, and the prediction was consistent with the experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 661–669, 2003     

Block copolymers derived from azobiscyanopentanoic acid. IV. Synthesis of a polyamide–polystyrene block copolymer

Polyamides 6.10 and 6.6 (PA^* 6.10 and 6.6) containing small amounts of ? N?N? units in the main chains were prepared by interfacial polycondensation between hexamethylenediamine and sebacoyl chloride or adipoyl chloride with addition of azobiscyanopentanoyl chloride. Polyamide–polystyrene block copolymers (PA-b-PSt) were then prepared by decomposition of the ? N?N? units of PA^*, initiating radical polymerization of styrene in m-cresol. The average PA block length of PA-b-PSt thus formed was longer than that expected from the initially present PA segments between the ? N?N? units. This is probably due to recombination of PA radicals whose initiation efficiency is as low as 15%. The PSt blocks also had higher molecular weight (7000–79,000) in comparison with homopolystyrene produced from monomeric azobiscyanopentanoic acid used as an initiator due to higher viscosity of polymerization system. Variation of intrinsic viscosity and turbidimetric titration behavior along with the change in composition were also discussed.     

Block copolymers derived from azobiscyanopentanoic acid. VI. Synthesis of a polyethyleneglycol–polystyrene block copolymer

Polycondensations were carried out between azobiscyanopentanoly chloride (ACPC) and polyethyleneglycols (PEG) having average molecular weight of 600, 2000, 8400, and 21,500, resulting in the chain extended PEG of several times the original polymer chain length and containing scissile ? N?N? units of azobiscyanopentanoic acid (ACPA). The poly(polyethyleneglycol-azobiscyanopentanoate), designated as \documentclass{article}\pagestyle{empty}\begin{document}$\rlap{--} (PEG\rlap{--} )_n^*$\end{document} were thermally decomposed in the presence of styrene (St) to obtain PEG–PSt block copolymers. The amount of St consumed was proportional to [? N?N? ]^0.5 and [St]^1.2, whereas the chain length of the PSt segment was proportional to [? N? N? ]^?0.5 and [St]^0.8.