Birefringence of polyethylene melt in transient elongational flow at constant strain rate

Simultaneous birefringence and elongational viscosity measurements were carried out on molten commercial grade, low-density polyethylenes during simple elongational flow at constant strain rate and constant temperature. The birefringence increased with time during constant strain rate elongation. The increase in birefringence was a linear function of elongational stress throughout whole elongation, but the elongational viscosity increased in two stages. The increase in elongational viscosity can be divided into linear viscoelastic and nonlnear viscoelastic regions. The linear region appeared at small strain and the nonlinear region appeared at strain greater than 0.7. The elongational viscosity in the nonlinear region increased much more rapidly than that in the linear region. The Gaussian approximation, which is commonly used in molecular models, could be used for the transient elongational flow. A constant stress-optical coefficient C = 1.3 × 10^?10 cm²/dyn was obtained for all the elongational experiments, independent of strain rate (0.002-0.2s^?1). The stress-optical coefficients were weakly dependent on temperature, as predicted by the theory of rubber elasticity.     

Melt rheology of hyperbranched‐polystyrene synthesized with multisite macromonomer

Melt rheological behaviors of hyperbranched‐polystyrene (PS) copolymerized by dendric macromonomer technique are presented. The time–temperature superposition principle was applicable to the hyperbranched‐PS. The branched‐PS showed slightly lower zero‐shear viscosity in comparison with linear PS regardless of a presence of a number of branches expected from the dendric macromonomer technique. Although the influence of use of multimethacryloyl macromonomer in the polymerization process was marginal for linear viscoelastic regime, nonlinear shear and uniaxial elongational flows showed distinct differences between linear and branched‐PS. The strain dependence of the damping function became weak as increase of macromonomer content. The branched‐PS exhibited the growing elongational viscosity function comparing with linear PS. This prominent effect on the elongational flow behavior can be explained by the molecular architecture of the branched‐PS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2226–2237, 2009     

A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow

In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.     

Interfacial tension of blends containing thermotropic liquid crystalline polymers

A method is proposed to determine the interfacial tension of immiscible blends containing a liquid crystalline polymer (LCP) and a flexible-molecule polymer, under flow conditions. The method is based on Taylor's theorem for immiscible fluids, i.e., that a suspended drop of liquid A in liquid matrix B is deformed in shear or elongational flow in proportion to the ratio of interfacial to viscous stresses. Taylor's theorem, as originally derived, applies to low concentrations, Newtonian fluids and small deformations. Thus, the theorem was modified to account for “Power Law” fluids in elongational flow and large deformations, more applicable to the system under investigation. The elongational viscosities of the LCP and the flexible polymer (polycarbonate) as a function of elongational rate were determined using converging type flow. The two polymers exhibited a Power-Law behavior in elongational flow and, hence, the experimental constitutive equations of state were used to quantify the viscous stresses. The interfacial stresses were modified for large deformations by taking into consideration the deformed shape and hence increased surface area of the elongated LCP particle. Using the modified expression, the interfacial tension of LCP and PC was determined to be in the range of 5–6.6 dyne/cm.     

刚性聚合物稀溶液流变性质的计算 Ⅰ.定常流动

本文采用多棒刚杆分子模型,用Galerkin法计算了聚合物稀溶液在定常剪切流、平面拉伸流、单轴拉伸流、单轴拉伸与剪切流相组合的复杂流动的流变学性质。计算结果表明,多棒刚杆分子模型有希望成为描述聚合物稀溶液流变性质的较为完善的分子模型。本文的研究不仅可使人们用分子模型来代替连续介质本构方程进行粘弹性流体复杂流动的数值模拟,而且也为探讨描述聚合物浓溶液的分子模型提供了一种新的途径。     

Planar mixed flow and chaos: Lyapunov exponents and the conjugate-pairing rule

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.     

Fluid vesicles in flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.     

Phenomenological analysis of elongational flow birefringence in semidilute solutions of hydroxypropylcellulose

The relaxation time of a polymer chain in an elongational flow field was investigated for hydroxypropylcellulose (HPC) semidilute solution systems by two methods: phenomenological analysis of elongational flow-induced birefringence, and dynamic light scattering (DLS) and rheological measurements. To understand the relaxation time of an entangled semiflexible polymer solution in an elongational flow field, scaling analysis of the elongational flow-induced birefringence curve was performed. The results of both temperature and concentration scaling analyses showed that birefringence curves at different temperatures and at several HPC concentrations were described well by a universal birefringence–strain rate curve. This scaling behavior was compared with the "fuzzy cylinder" model. The critical strain rate corresponded to the correlation time of the slow relaxation mode determined by DLS measurement and the relaxation spectrum obtained by dynamic viscoelasticity measurement. The elongational flow-induced birefringence observed in an HPC semidilute solution was concluded to be attributed to the orientation of the HPC segment in the entangled molecular system, because the dominant relaxation mode is found to be the concentration fluctuation of an entangled molecular cluster in a quiescent state.     

Rheological studies on the phase separation of hydroxypropylcellulose solution systems

Phase behavior of hydroxypropylcellulose (HPC) in a mixed solvent of glycerol and water was investigated by two different rheological methods: rheooptical birefringence measurement in an elongational flow field and viscometric measurement in a shear flow field. The association process of the HPC chain during phase separation observed by the elongational flow birefringence method was also investigated by the shear viscometric method. The temperature dependence of chain rigidity was determined by measuring the intrinsic viscosity, and change in the conformation was investigated by observing elongational flow birefringence over the temperature range from the one‐phase to inside a phase boundary. The results focus on the molecular process of phase separation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1976–1986, 2001     

Nanostructural modifications of polyamide/MMT hybrids under isothermal and nonisothermal elongational flow

The aim of this work is to investigate the effects of elongational flow on the nanoscale arrangement of the silicate inside polyamide‐based nanocomposites. Hybrids, at different loadings of a commercial organoclay, were produced by melt compounding using two polyamide matrices, a nylon‐6, and a copolyamide with similar molecular weight and rheological properties. The elongational flow characterization was performed under both isothermal and nonisothermal conditions by using, respectively, an elongational rheometer (SER) and a fiber‐spinning technique. The extensional rheological response of melt‐compounded nanocomposites, correlated to TEM and X‐ray analyses, was used to probe the nanostructural modifications developed during the uniaxial stretching. The results demonstrated that isothermal and nonisothermal elongational flow can modify the nanomorphology of the nanocomposite hybrids affecting the degree of silicate exfoliation as well as the extent of silicate orientation upon the stretching direction. The entity of structural modifications induced by the stretching were highly dependent on the initial nanomorphological state and on the polymer‐clay affinity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 981–993, 2009     

Some aspects of theory and simulations of polymers in steady flows

We present a study of various properties of bead spring chains in steady flows. The Langevin equation of the normal modes of the chain is solved by Fourier transformation. From the resulting power spectrum, the autocorrelation functions of all configuration-dependent quantities can be calculated. In equilibrium, the influence of the bead masses on the short-time dynamics is discussed. The influence of different flow fields (shear, elongational and Kramers potential flow) on the mean-square chain dimension is calculated. A comparison with results obtained from non-equilibrium molecular dynamics and Monte Carlo calculations is made. Finally, the influence of shear flow on the configurational and rheological properties of cyclic polymers and on the excluded volume behavior of linear chains is examined.     

Brownian dynamics simulation of polyelectrolyte dilute solutions: Relaxation time and elongational flow

The authors used the bead‐and‐spring model and the Brownian dynamics simulation technique including hydrodynamic interaction to study the behavior of dilute polyelectrolyte solutions under elongational flow. First they carried out simulations to determine the longest relaxation time of a polyelectrolyte, finding that the relaxation time depends on the ionic strength of the solution. Then, they studied the coil‐stretch transition of polyelectrolyte molecules in elongational flow and determined the critical value of the elongational rate necessary in order this transition to occur. In this way, they could compute the value of the Deborah number at which coil‐stretch transition sets in for polyelectrolyte dilute solutions. Finally, they studied the power law relationship that relates the critical elongational rate with the molecular weight of the polyelectrolyte. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 714–722, 2007     

Effect of different matrices and nanofillers on the rheological behavior of polymer‐clay nanocomposites

In this work, a comprehensive study of the rheological behavior under shear and isothermal and nonisothermal elongational flow of low density polyethylene (LDPE) and ethylene‐vinyl acetate copolymer (EVA) based nanocomposites was reported to evaluate their “filmability”, that is, the ability of these material to be processed for film forming applications. The influence of two different kinds of organoclay – namely Cloisite 15A and Cloisite 30B – and their concentration was evaluated. The presence of filler clearly affects the rheological behavior in oscillatory state of polyolefin‐based nanocomposites but the increase of complex viscosity and the shear thinning are not dramatic. A larger strain‐hardening effect in isothermal elongational flow is shown by the nanocomposites compared to that of the pure matrix, particularly for EVA based nanocomposites. The melt strength measured under nonisothermal elongational flow increases in the presence of the nanofiller, while the drawability is only slightly lower than that measured for the neat matrix. Moreover, the rheological behavior under nonisothermal elongational flow of EVA‐based nanocomposites is similar for both nanoclays used. Differently, LDPE‐based nanocomposites show a strong dependence on the type of organoclay. Finally, the mechanical properties of the materials were measured by tensile tests. They revealed that the presence of the filler provokes, in all the cases, an increase of the rigidity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 344–355, 2010     

Predictive/fitting capabilities of differential constitutive models for polymer melts—reduction of nonlinear parameters in the eXtended Pom-Pom model

A phenomenological modification of the eXtended Pom-Pom (XPP) model is proposed with the aim to reduce the number of free nonlinear parameters. The modified XPP model includes three parameters per mode in total (two linear viscoelastic parameters—linear relaxation time λ and shear modulus G, and one nonlinear parameter). The original XPP model contains five parameters (two linear viscoelastic parameters and three nonlinear ones, one nonlinear parameter participates in the second normal stress difference prediction). The predictive/fitting capabilities of the modified model are compared with the Giesekus, eXtended Pom-Pom, and modified Leonov models using various low-density PE materials in steady and transient shear and uniaxial elongational flows. It has been found that the modified model is capable of predicting/fitting the rheological properties, with the exception of the second normal stress difference, for studied LDPE materials with sufficient accuracy, including strain hardening in uniaxial elongational flow.     

Rheological properties of linear and crosslinked polymer blends: Relation between crosslink density and enhancement of elongational viscosity

Strain‐hardening behavior in the elongational viscosity of binary blends composed of a linear polymer and a crosslinked polymer, in which the molecular chains of the linear polymer were incorporated into the network chains of the crosslinked polymer, was studied. Blending the crosslinked polymer characterized as the gel just beyond the sol–gel transition point greatly enhanced the strain‐hardening behavior in the elongational viscosity, even though the amount of the crosslinked polymer was only 0.3 wt %. However, the crosslinked polymer, which was far beyond or below the sol–gel transition point, had little influence on the elongational viscosity as well as the shear viscosity. The stretching of the chain sections between the crosslink points was responsible for the strain‐hardening behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 228–235, 2001     

A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow

We present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. Non-Newtonian, Fluid Mech. 96, 163 (2001)], which we shall call the proper-SLLOD algorithm, or p-SLLOD for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the so-called SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] boundary conditions. Using the p-SLLOD algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the p-SLLOD algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.     

Effect of the flow field on the mechanical degradation of molten polystyrene

Degradation tests have been carried out on a polystyrene sample using various capillaries of different length (L) to diameter (D) ratio and entrance angle. The extent of degradation depends on the length to diameter ratio becoming larger and larger with increasing length of the capillary. However, even when L/D approaches zero degradation still occurs to some extent.It may thus be inferred that degradation occurs both in the capillary and in the converging flow preceding the entrance of the melt to the capillary. Runs with a conical die lubricated to eliminate any shearing effects show that the elongational flow is mainly responsible for the mechanical degradation in the converging flow.On the basis of an approximate analysis, one may say that the breakage of C-C links is possible in elongational flow.     

Supermolecular structures and flow birefringence in polymer solutions

Experimental studies of supermolecular structures and localized flow birefringence in solutions of high-molecular weight polymer are described. Advantage is taken of poly(ethylene oxide) and polyisobutylene. Supermolecular structures are examined with the aid of optical microscopy using freeze-dried samples of the polymer solutions. Birefringence is investigated that arises in planar elongational flow in a cross-slot cell. Flow velocities at which the onset of the localized birefringence occurs are determined. Then these velocities are correlated with viscoelastic characteristics of the solutions. The presence of a liquid-crystalline fibrillar network in the polymer solutions exhibiting flow birefringence is ascertained. The fibrils are birefringent objects. The fibrils are birefringent objects. The localized birefringence phenomenon is explained in term of the orientation of the fibrils in elongational flow. It has been shown that the onset of localized birefringence occurs at a critical Weissenberg number, the value of which is close to unity.     

Conductive polyethylene-carbon black composites by elongational-flow injection molding Part 3. Study of the structure and morphology

The morphology and structure of high molecular weight linear polyethylene (M _w 450000) filled with carbon black and processed using molds that introduce an elongational flow component during injection molding has been examined using electron microscopy and x-ray diffraction techniques. The study of fracture surfaces reveals the display of shish-kebabs oriented along the injection direction with segregated longitudinal channels of carbon black particles. Molecular and lamellar changes in orientation are, furthermore, studied across the thickness of the moldings. It is shown that addition of carbon black particles to injection-molded polyethylene induces significant changes in lamellar orientation. Thus, while lamellar overgrowth proceeds perpendicular to the fiber axes within carbon free channels, lamellae grow randomly within carbon-enriched regions where flow is less pronounced.     

The influence of various deformation histories on elongational properties of low density polyethylene

Summary The elongational viscosity of low density polyethylenes depends on the mechanical history as is demonstrated on the samples IUPAC A and IUPAC C and some other specimens. IUPAC C which stems from the same batch as IUPAC A but has undergone an additional extrusion shows a significantly lower elongational viscosity whereas the shear viscosity remains nearly unchanged. The elastic behaviour measured by the recoverable strain is not influenced by a mechanical pretreatment. The viscosity decrease is found to be canceled to its greatest extent after dissolving the sample in xylene and evaporating the solvent. Pure elongation seems to be more effective in creating the viscosity decrease than pure shear. A similar effect could not be found for linear polyethylene and polystyrene. This result leads to the assumption that the branched molecules give rise to a mechanically induced change of the entanglement structure which can be reverted by dissolving. The evidence of the elongational behaviour for film blowing is discussed.Dedicated to Professor Dr. Reif on the occasion of his 60th birthday.