Molecular weight polydispersity effects on the melt viscoelasticity of styrene-acrylonitrile random copolymers

A series of polydisperse SAN (styrene-co-acrylonitrile) random copolymers was studied by means of oscillatory rheometry in the rubbery plateau zone and in the terminal zone. The plateau modulus, the Newtonian viscosity, and the critical frequencies for the onset of non-Newtonian behavior were extracted from the experimental data. All these viscoelastic quantities consistently indicate that the tail of molecular weights below approximately M _e (the entanglement spacing) acts as a solvent for the rest of the polymer with M>M _e .     

Viscoelasticity of low molecular weight polymers and the transition to the entangled regime

The viscoelasticity of unentangled polystyrene melts has been investigated in terms of terminals parameters: zero-shear viscosity, steady-state compliance and relaxation spectrum. The Rouse model applies well for molecular weights lower than the average molecular weight between entanglements, providing that one takes into account the proper variations of the radius of gyration. Moreover, local motions at the scale of Kuhn segments have to be considered in order to describe correctly the relaxation modes intermediate between the terminal zone and the glassy plateau. On the other hand, reptation models are commonly used for describing the entangled regime. We propose an expression of the shear modulus which accounts not only for the terminal modes (reptation, tube length fluctuations and tube renewal), but also for the relaxation modes responsible for the plateau zone and the transition of the glassy plateau. A crossover region between the unentangled and untangled regimes is located around . When the molecular weight increases, a shift transfer of Rouse modes towards reptation modes occurs. That leads to a continuity of the expression of the shear modulus over the entire range of molecular weights. Received: 29 December 1997 Accepted: 27 July 1998     

Mobility anisotropy and nonlinear effects in molecular viscoelasticity theory of linear polymers

Various methods of taking the mobility anisotropy into account in modeling of the behavior of polymer fluids in a simple shear flow are compared. Both the qualitative coincidence of the results of the analysis and the difficulties of quantitatively estimating the anisotropy microparameters on the basis of the available data concerning steady shear are noted. For axial tension the dependence of steady viscosity on tensile stress is considered. This dependence is determined by two independent scalar functions: the slip coefficient and the flow anisotropy coefficient.Barnaul. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–12, July–August, 1995.     

Influence of molecular weight and molecular conformation of polymers on turbulent drag reduction

Summary An investigation was carried out on drag reduction of diluted solutions of four polyisobutylenes of different molecular weight in diversely good and poor solvents in the turbulent region at small (up to 5000) and average (from 19 000 to 42 000) Reynolds numbers, as well as of mixtures of polyisobutylene and polystyrene and of two polyisobutylenes of different molecular weight. Concentration at maximum drag reduction grows, while drag reduction itself decreases with molecular weight going down. The universal curve established byVirk et al. for aqueous solutions of a polyethylene oxide family is also confirmed for a family of polyisobutylenes in an organic solvent. The effect of polymer coils of various dimensions on drag reduction is assessed. PIB coils of various dimensions are produced in two ways — dissolving polyisobutylenes of different molecular weight in a given solvent and dissolving polyisobutylene of a definite molecular weight in diversely good and poor solvent. Coil dimensions in the solution are increasing with the growth of intrinsic viscosity of a polymer by dissolving it in still better solvents, but probably due to impeded orientation and deformation of the larger polymer coils their drag reduction is smaller at low rather than at high shear stresses. Drag reduction of diluted solutions of two PIB differing in molecular weight shows almost no deviation from the additive straight line both when the overall concentration of solutions is equal and when it exceeds the one at maximum drag reduction of PIB of higher molecular weight. Drag reduction of diluted solutions of PIB and PS mixtures at an overall concentration higher than optimum concentration shows a positive deviation from the additive straight line.

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Zusammenfassung Untersucht wurde die Verringerung des Reibungswiderstandes (VRW) fließender, verdünnter Lösungen von vier Polyisobutylenen mit verschiedenem Molekulargewicht in unterschiedlich guten und schlechten Lösungsmitteln im turbulenten Bereich bei kleinen (bis 5000) und bei mittleren (von 19 000 bis 42 000) Reynoldsschen Zahlen, sowie von Mischungen aus Polyisobutylen und Polystyrol und aus zwei Polyisobutylenen mit verschiedenem Molekulargewicht. Die Konzentration bei maximalem VRW-Effekt nimmt zu, und der maximale VRW-Effekt selbst vermindert sich mit abnehmendem Molekulargewicht. Die vonVirk und Mitarbeitern für wäßrige Lösungen einer Reihe von Polyäthylenen festgestellte universale Kurve wird auch für die Polyisobutylenfamilie in einem organischen Lösungsmittel bestätigt. Der Einfluß der nach ihren Dimensionen unterschiedlichen Polymerknäuel auf die Verringerung des Reibungswiderstandes wurde ausgewertet. Polyisobutylen-Knäuel mit verschiedenen Dimensionen werden auf zwei Weisen realisiert, durch Auflösung von Polyisobutylenen mit verschiedenem Molekulargewicht in einem gegebenen Lösungsmittel und durch Auflösung von Polyisobutylen mit einem gegebenen Molekulargewicht in unterschiedlich guten und schlechten Lösungsmitteln. Mit der durch seine Auflösung in immer besseren Lösungsmitteln steigenden Grenzviskosität eines Polymeren nehmen die Knäueldimensionen in den Lösungen zu. Jedoch ist, wahrscheinlich wegen der damit verbundenen Behinderung der Orientierung und Deformierung der größeren Polymerknäuel, ihr VRW-Effekt bei den niedrigen Scherspannungen kleiner als bei den höheren. Der VRW-Effekt der verdünnten Lösungen aus zwei Polyisobutylenen mit verschiedenem Molekulargewicht weist fast keine Abweichung von der additiven Geraden auf, sowohl wenn die Gesamtkonzentration der Lösungen gleich als auch wenn sie größer als die Konzentration beim maximalen VRW-Effekt des Polyisobutylens mit höherem Molekulargewicht ist. Der VRW-Effekt der verdünnten Lösungen von Mischungen aus Polyisobutylen und Polystyrol mit einer über der optimalen liegenden Gesamtkonzentration zeigt eine positive Abweichung von der additiven Geraden.

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D diameter of capillary - [DR] intrinsic drag reduction - DR _F fractional drag reduction - DR _{F, max} maximum fractional drag reduction - DR_sp specific drag reduction - K constant - L length of capillary - M _v molecular weight of polymer, determined by the viscosimetric method - flow rate - c concentration - [c] intrinsic concentration - _equiv. equivalent sphere density - _{w, p} wall shear stress of polymer solution - _{w, s} wall shear stress of solvent - CMC carboxymethylcellulose - PAA polyacrylamide - PEO polyethylene oxide - PIB polyisobutylene - PS polystyrene - DR drag reduction With 8 figures and 2 tables     

Predicting the nonlinear hereditary viscoelasticity of polymers

A mathematical model for the nonlinear hereditary viscoelasticity of polymer materials is proposed to predict deformation processes of various complexity — from simple relaxation and simple creep to complex deformation-relaxation and reverse relaxation processes with alternative loading and unloading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 147–157, November–December, 2007.     

The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

Influence of molecular weight upon drag reduction by polymers

Summary Drag reduction measurements have been made with samples of polyethyleneoxide and polyacrylamide with relatively narrow molecular weight distributions obtained by fractionation of commercial polymers. Relationships between the polymer molecular weight and the concentration required to give the same drag reduction have been determined. The influence of polymer degradation upon these relationships has been investigated.Molecular weight distributions of commercial polymers have been determined and their influence upon the drag-reducing properties is noted.The influence of wall shear stress has been investigated over the range 1.0 × 10² - 4.5 × 10³ dyn/cm². The results with unfractionated polymers were found to be consistent with other results in the literature.     

Molecular theories of nonlinear viscoelasticity of polymers

It is emphasized that considerable advances have been made recently in the development of the molecular theories of nonlinear viscoelasticity of concentrated solutions and melts of linear polymers. The new ideas in this exceptionally important field of the rheology of polymers are analysed. The methods by which the constraints (entanglements) imposed on the motion of macromolecules by the polymer environment are taken into account are also considered in the paper. The most detailed discussion is devoted to the model of topological constraints in the form of a tube and to the self-consistent theory of anisotropic micro-viscoelasticity which takes into account the relaxation nature of the interaction of macromolecules with their surrounding medium as well as the anisotropy of their mobility.Invited paper, presented at the XII-th All-Union Symposium on Rheology held in Riga (USSR), December 7–9, 1982.     

Finite viscoelasticity and viscoplasticity of semicrystalline polymers

Observations are reported on low-density polyethylene in uniaxial tensile and compressive tests with various strain rates and in tensile and compressive relaxation tests with various strains. A constitutive model is developed for the time-dependent response of a semicrystalline polymer at arbitrary three-dimensional deformations with finite strains. A polymer is treated as an equivalent network of chains bridged by junctions (entanglements between chains in the amorphous phase and physical cross-links at the lamellar surfaces). Its viscoelastic behavior is associated with separation of active strands from temporary junctions and merging of dangling strands with the inhomogeneous network. The viscoplastic response is attributed to sliding of junctions between chains with respect to their reference positions. Constitutive equations are derived by using the laws of thermodynamics. The stress–strain relations involve 6 material constants that are found by matching the observations.      

Turbulent expansion flow of low molecular weight shear-thinning solutions

A Laser-Doppler anemometer and a pressure transducer were used to carry out detailed measurements of the mean and root mean square of the velocity and wall-pressure in an axisymmetric sudden expansion flow, with 0.4 and 0.5% by weight shear-thinning aqueous solutions of a low molecular weight polymer (6,000), after appropriate rheological characterisation. In spite of their very low molecular weight, these solutions still exhibited elongational elastic effects through drag reduction of up to 35% relative to Newtonian turbulent pipe flow, as shown by Pereira and Pinho (1994). The results showed small variations of the recirculation bubble length with polymer concentration and Reynolds number and reductions of the normal Reynolds stresses of up to 30%, especially in the tangential and radial directions. The reduction in normal Reynolds stresses within the shear layer is an elongational elastic effect, but this elasticity needs to be considerably more intense, such as with high molecular weight polymers, in order to strongly affect the mean flow characteristics. The observed mean flow patterns with these low molecular weight polymer solutions were indeed similar to those exhibited by Newtonian and inelastic fluids.     

Rheo-Dielectric behavior of low molecular weight liquid crystals.

Dielectric relaxation behavior was examined for 4-4′-n-pentyl-cyanobiphenyl (5CB) and 4-4′-n-heptyl-cyanobiphenyl (7CB) under flow. In quiescent states at all temperatures examined, both 5CB and 7CB exhibited dispersions in their complex dielectric constant ε*(ω) at characteristic frequencies ω _c above 10⁶ rad s^–1. This dispersion reflected orientational fluctuation of individual 5CB and 7CB molecules having large dipoles parallel to their principal axis (in the direction of C≡N bond). In the isotropic state at high temperatures, these molecules exhibited no detectable changes of ε*(ω) under flow at shear rates . In contrast, in the nematic state at lower temperatures the terminal relaxation intensity of ε*(ω) as well as the static dielectric constant ε′(0) decreased under flow at . This rheo-dielectric change was discussed in relation to the flow effects on the nematic texture (director distribution) and anisotropy in motion of individual molecules with respect to the director. Received: 14 April 1998 Accepted: 29 July 1998     

Molecular origin of viscoelasticity and chain orientation of glassy polymers

Dynamic birefringence and dynamic viscoelasticity of poly(4-methyl styrene) and poly(4-t-butyl styrene) were measured to investigate the molecular origin of viscoelasticity around the glass transition zone. The data were analyzed with a modified stress-optical rule: The birefringence and the stress were separated into two component functions of different molecular origins. One component is related to the orientation of the main chain axis and the other one to the rotation of the repeating units about the main chain axis. The strain dependence of the two characteristic orientation functions in the glassy zone was estimated and the orientation mechanism of repeating units was discussed.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities

The method presented in this paper allows to calculate the molecular weight distribution (MWD) of linear homopolymer melts from the complex shear modulus data measured in a wide frequency domain. An empirical blending law on complex viscosities is first developed; as a consequence, the variations of the storage and loss modulus as a function of MWD are presented. This simulation demonstrates also the role of the shape of the MWD itself, and shows that one should not postulate a priori the shape of the MWD. An efficient numerical approach based on a Tikhonov regularization method with constraint is used to solve this ill-posed problem; the MWD is hence derived without any assumption on its shape. This method is first applied on simulated data to prove its numerical efficiency. Then the inversion method is applied on complex moduli data of various commercial polymers (polypropylene, polyethylene and polystyrene) and on an artificial mixture of polystyrene that have been presented in the literature. For amorphous polymers, the coupling of the terminal relaxation domains with the transition region at higher frequency leads to errors in the low molecular weight tail: one way to solve this problem is to cut off the experimental data at the high frequencies. This general method needs only a few physical parameters, namely the scaling law for the Newtonian viscosity η₀=f(M _w ) and the plateau modulus G _N ⁰, and leads to reasonable results with respect to the simplicity of the viscoelastic model used. Received: 27 October 1997 Accepted: 24 February 1998     

Rheology of polydisperse polymers: relationship between intermolecular interactions and molecular weight distribution

An expression of the relaxation function of linear polydisperse polymers is proposed in terms of intermolecular couplings of reptative chains. The relaxation times of each molecular weight are assumed to be shifted according to a tube renewal mechanism accounting for the diffusion of the surrounding chains. The subsequent shift is applied to the relaxation function of each molecular weight obtained from an analytical expression of the complex compliance J ^*(). Therefore the complex shear modulus G ^*() is derived from the overall relaxation function using the probability density accounting for the molecular weight distribution and four species-dependent parameters: a front factor A for zero-shear viscosity, plateau modulus G _N ⁰ , activation energy E and characteristic temperature T . All the main features of the theology of polydisperse polymers are described by the proposed model.     

Linear viscoelasticity of ZrO 2 nanoparticle dispersions with associative polymers

ZrO₂ nanoparticle dispersions containing associative polymers exhibit two relaxation modes: Maxwellian behavior at high frequency imparted by the associating polymers and a power law spectrum at low frequency generated by the particle dynamics. The timescales and volume fraction dependence of the dispersions reflect weak attractions between particles with adsorbed polymer layers dispersed in a percolated network of associative polymer. The Baxter stickiness parameter extracted from the high frequency viscosity data indicates strong attractions, whereas the high frequency modulus reveals three sources of elasticity: micelle–micelle associations in the solution, rigidity of the particles and adsorbed layer, and adsorbed layer–adsorbed layer interactions. The sol-gel transition of the dispersions occurs around 12–14% particle loading. Comparison with latex dispersions suggests a slower relaxation mode and greater rigidity with the ZrO₂ particles.     

Effects of viscoelasticity on the retraction of a sheared drop

Effects of drop and matrix viscoelasticity on the retraction of a sheared drop are numerically investigated. Retraction of an Oldroyd-B drop in a Newtonian matrix is initially faster and later slower with increasing drop Deborah number. The observed behavior is explained using an ordinary differential equation model representing the dominant balance between various forces during retraction. The initial faster relaxation of viscoelastic drops is due to viscoelastic stresses pulling the drop interface at the tips inward. The later slower retraction is due to the slowly-relaxing viscoelastic forces at the equator, where they act against the capillary force. The drop inclination decreases substantially during retraction unlike in a Newtonian case. Matrix viscoelasticity slows the relaxation of a Newtonian drop because of the increasingly slow relaxation of highly stretched polymers near the drop tip with increasing Deborah number. Increasing the ratio of polymeric to total viscosity further accentuates the viscoelastic effects in both cases. For an Oldroyd-B drop in an Oldroyd-B matrix, a competition between the dispersed and the continuous phase elasticities, represented by their ratio, determines the dynamics; larger values of the ratio leads again to initial faster and later slower retraction.