Extensional stresses during polymer flow in ducts

During the flow of high molecular weight, narrow-, and broad-distribution polybutadienes and polyisoprenes rheo-optical measurements were conducted of extensional stresses acting along the flow axis in the preentrance and entrance regions of the duct and of their subsequent relaxation in the duct. The extensional stresses increase in the preentrance region, reach their maximum values at a distance of two or three tenths of the duct width from its edges, and then relax. The position of the maximum extensional stress is independent of polymer characteristics, shear stresses in the duct, and shape of the entrance and dimensions of the rectangular duct. The dependence of the maximum extensional stress on the shear stress of the duct wall can be assumed to be linear for small values. The length of the stress relaxation zone depends on the shear stress at the duct wall and the molecular mass distribution. It is independent of the molecular masses in narrow-distribution polymers. For the polymers investigated, a generalized dependence was obtained for the reduced duct length over which the extensional stresses relax to zero from the reduced deformation rate. This dependence takes into account the characteristic polymer relaxation times and the value of the molecular mass of the chain between the fluctuation entanglement. A considerable decrease in the duct's length-to-width ratio leads to an increase in the maximum values of the extensional stresses. A decreases in the duct entrance angle causes a reduction in the rate of increase of extensional stresses, the maximum values, and the acceleration of the relaxation processes in the duct. A decrease in the ratio of the width of the preentrance region to the duct width leads to a reduction in the maximum in extensional stresses. It is shown that one of the causes for the instability of the polymer flow in the ducts can be the rupture of polymers due to their extension in the preentrance and entrance regions. Calculations were done that describe satisfactorily the relationship between the values of the maximum extensional stresses and the shear rate and stresses on the duct wall.     

Polarization-optical investigation of polymers in fluid and high-elastic states under oscillatory deformation

The relationship was investigated between birefringence and oscillatory shear deformation of linear high molecular mass polymers exemplified by narrow- and broad-distribution polybutadienes and polyisoprenes. Polymer deformation at different frequencies and amplitudes was carried out in an annular gap. The stress field uniformity was not below 95%. It was shown that in oscillatory deformation of polymers in the fluid and high-elastic states, birefringence contains a time-independent steady component and an oscillatory component with a frequency equal to that of the assigned oscillation. A linear interrelation was found to exist between the amplitude of the oscillatory component of birefringence and that of the shear stresses, with a proportionality factor equal to the stress-optical coefficient of the polymers. The phase of the oscillatory component of birefringence coincides with that of the shear stresses. Measurements of the steady component of the birefringence make it possible to find the steady component of the first normal stress difference resulting from the assignment of shear oscillations to the polymer. On the basis of the experimental data obtained for polybutadienes and polyisoprenes, and the literature data for polystyrene solutions, a master curve was constructed that generalizes the dependence of the steady component of the first normal stress difference in the linear and nonlinear deformation regimes on the product of the square of the deformation amplitude and the storage modulus measured at low amplitudes. This dependence is valid in the linear and nonlinear deformation regimes. It is invariant with frequency, amplitude deformation, molecular mass, and molecular mass distribution of the polymers. It is shown by visual observation of deformation that the abrupt drop in resistance of polymer to shear in large-amplitude deformation is due to polymer rupture near the surface of the inner cylinder and is accompanied by a slip-stick process. This is the phenomenon of spurt early observed in capillary viscometers at high shear stresses and recently investigated in coaxial cylinder devices at large amplitude deformation.     

Correlations of the first normal stress difference with shear stress and of the storage modulus with loss modulus for homopolymers

The effects of temperature, molecular weight and its distribution, side chain branching, and the structure of polymers on the elastic behavior of bulk homopolymers were investigated, by using logarithmic plots of first normal stress difference (N₁) against shear stress (σ₁₂) and logarithmic plots of storage modulus (G′) against loss modulus (G″). For the investigation, we have used data from the literature as well as our recent experimental results, covering a very wide range of temperature and shear stress or loss modulus. It has been found that such plots are very weakly sensitive to (or virtually independent of) temperature and to the molecular weight of high molecular weight polymers, but strongly dependent upon the molecular weight distribution and the degree of side chain branching. A theoretical interpretation of the observed correlations is presented, using molecular theories.     

Critical regimes of oscillatory deformation of polymeric systems above glass transition and melting temperatures

High molecular weight linear polymers and their concentrated solutions were investigated over a wide range of frequencies and amplitudes of oscillatory deformation. At definite critical deformation and stress amplitudes, the resistance to deformation drops abruptly as a result of the rupture of continuity of polymer specimens in the region of action of the highest shear stresses. The lowest critical values of deformation rate amplitudes are inversely proportional to the initial viscosity and correspond quantitatively to the critical shear rates at which the spurt occurs during the flow of polymeric systems in ducts. The spurt effect is due to the transition of the polymer systems to the forced high-elastic state, in which they behave like quasi-cured polymers whose deformability is always limited. Up to the critical values of the stress amplitudes, narrow-distribution high molecular weight linear flexible-chain polymers behave like Hookean bodies, whereas the broad-distribution polymers show a sharply defined nonlinear behavior which asymptotically passes to a spurt. The amplitude dependence of the dynamic characteristics of the high molecular weight linear polymers, as well as their non-Newtonian behavior, is due to polymolecularity. An increase in deformation amplitudes reduces the frequency at which the spurt, and hence the transition of the polymer systems to the high-elastic state, is observed. Therefore, under conditions of oscillatory deformation the physical state (fluid or high-elastic) is determined not only by the frequency but also by the value of deformation. In the high-elastic state region (estimated at low amplitude deformation), the critical deformation amplitude is frequency independent and has an unambiguous relationship with the molecular mass of the chain (M_e) between the entanglements. For the bulk polymers studied, the spurt in the high-elastic state occurs at stress amplitudes of the order of 10⁵ N/m² irrespective of frequency, molecular mass, or polymolecularity. In concentrated polymer solutions, in the high-elastic state the critical stress amplitudes decrease with reducing polymer content, whereas the critical deformation amplitudes increase.     

Wall slip of molten polymers

There is considerable experimental evidence that the classical no-slip boundary condition of fluid mechanics is not always a valid assumption for the flow of high molecular weight molten polymers. In fact, molten polymers slip macroscopically at solid surfaces when the wall shear stress exceeds a critical value. Moreover, for linear polymers there exists a second critical wall shear stress value at which a transition from a weak to a strong slip occurs. These two modes of slip (weak and strong) are due to flow-induced chain detachment/desorption at the polymer/wall interface and to chain disentanglement of the polymer chains in the bulk from a monolayer of polymer chains adsorbed at the interface. In this review, the two physical mechanisms of slip are discussed and validated on the basis of published experimental data. The slip velocity of molten polymers is a complex function and has been reported to depend on wall shear and normal stresses, temperature, and molecular characteristics of polymers (molecular weight and its distribution). Proposed slip models, static and dynamic, are also reviewed and their significance on the rheology and flow simulations of molten polymers is discussed.     

Polydispersity effect on transient flow behavior of polystyrene solution

Summary The transient flow behavior of the binary blend of monodisperse polystyrene fractions is measured by a flow birefringence method. Both of the shear stress and first normal stress difference are obtained simultaneously in time by using a PMFB technique. The entanglements of the polymer chains significantly affect the rheological property of the binary blend in flow region. Especially, the entanglements of the high molecular weight fractions with themselves is proven to be the main source to the growth of first normal stress differences.     

Model suspensions with rheological additives: Systems with plastic flow behavior

Model suspensions with different concentrations of the rheological additives Aerosil 380 in silicone oil M20 000 and Bentone 27 in epoxy resin Araldite GY260 were researched. The shear stress and the first normal stress difference were measured simultaneously with shear flow start‐up experiments followed by stress relaxation. At higher concentrations, the rheological additives build a strong three‐dimensional (3D) structure that leads to systems with plastic flow behavior. It was established that the structure of 7.5% Aerosil 380 in silicone oil M20 000 is strong and stiff due to the big difference between shear stress and normal stress at small shear rates. This solid‐like system exhibits only one yield stress region. It was found that the suspensions with a strong 3D structure and comparable values of shear stress and first normal stress difference at small shear rates have a first and a so‐called second yield stress regions. In the transition section, between the two yield stress regions, there occurs a break of the distortion and a rearrangement of the structure. The decrease and increase of the first normal stress difference also belongs to the rearrangement of the structure. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Viscoelastic properties of linear polymers in the fluid state and their transition to the high-elastic state

The experimental results of the Viscoelastic properties of linear polymers of narrow molecular weight distribution (MWD) and of their mixtures have been analyzed and generalized. Based on the study of the properties of polymers of narrow MWD, we propose a classification of high molecular weight compounds. It specifies a distinct boundary between oligomers and polymers, assuming that the most important feature of polymers is the manifestation of large high-elastic recoverable deformations of entropy character. For polymers to be characterized, not the absolute molecular weight is essential, but the molecular weight referred to the boundary values. The corresponding state for polymers is attained at temperatures 100°C away from the glass temperature. The transition from the fluid to the high-elastic state with increasing deformation rate (or frequency for cyclic deformation) has been studied. Transition to the high-elastic state takes place over a narrow stress range (0.1-1.0 dynes/cm²), independent of molecular weight, whereas the critical deformation rates (frequencies), like viscosity, depend greatly on molecular weight. An increase in the amount of deformation shifts, to u certain extent, this transition to lower Kites of deformation (frequencies). In the region of deformation rates (frequencies) corresponding to the high-elastic state, the effect of large deformations during shear manifests itself largely in the tear-off of polymers Iron, the confining surfaces and in specimen rupture. Polydispersity has a strong effect on the properties of polymeric systems. As the rate of deformation is increased, the transition proceeds successively from the higher molecular weight components. This relaxational transition is tantamount to a change of the structure for polymeric systems. It is responsible for non-linear, particularly, non-Newtonian behavior of such systems. The transition to the high-elastic state and all the related phenomena are observed also in concentrated solutions of high molecular weight polymers. The long-term durability of un-cured rubbers in the high-elastic state is described by the same relationships.     

Rheology of polymers containing carbon black

In order to elucidate the flow behavior of electrophotographic toner systems, shear stress was measured as a function of shear rate in a cone and plate rheometer for polymer melts containing carbon blacks of surface area 24 and 625 m²/g at several concentrations and temperatures. Polymers included high and low molecular weight polystyrene and poly(butyl methacrylate). The addition of carbon black to the polymers caused a large increase in viscosity, especially at low shear rates and shear stresses. As the concentration of carbon black was increased, the viscosity at low shear rates became unbounded below a value of the shear stress designated the yield stress. The absolute magnitude of the yield stress depended primarily on the concentration and surface area of the carbon black and was independent of the polymer and temperature. Apparently, carbon black forms an independent network within the polymer at low shear rates which precludes flow. In some cases, the viscosity of polymers filled with carbon black was lower than that of the pure polymer. This effect was favored for polystyrene compared to poly(butyl methacrylate) and was facilitated by increasing the molecular weight of polystyrene, reducing the surface area and concentration of carbon black, and by increasing the temperature and shear rate.     

Rheological characterisation of hydroxyapatite filled polyethylene composites. Part 2 – Isothermal compressibility and wall slip

Abstract

Rheological characterisation of hydroxyapatite–high density polyethylene (HA–HDPE) composites has been performed in terms of isothermal compressibility and wall slip. Addition of HA to the polymer melt decreases the compressibility of the melt. The unfilled HDPE was found to exhibit wall slip at shear stresses as low as 0·10 MPa. The flow curves of the composites showed three distinct regions: a gradient at low shear rates; a plateau region; and a gradient at higher shear rate. An increase in rheometer pressure seems to suppress the slip in composites. The 40 vol.-% HA–HDPE composite exhibited two critical shear stresses, one corresponding to wall slip, which occurs in the lower shear rate region of the flow curve, and the other corresponding to a plateau, which is identified with the stick–slip behaviour of unfilled HDPE reported in the literature. The plateau shear stress increased with filler volume fraction and this effect is attributed to the decreased compressibility of the melt. A good correlation with a negative correlation coefficient was found to exist between compressibility and shear stress in the plateau region. The slip observed in unfilled HDPE and at low shear rates in the 40 vol.-% HA–HDPE systems has been explained in terms of a low molecular weight polymer layer formed at the melt/wall interface. The large interfacial slip observed in the plateau region is attributed to complete disentanglement of adsorbed chains from free chains at the melt/wall interface at and beyond the plateau region.     

Structural and rheological investigation of low density polyethylenes

Some low density polyethylenes (LDPE) with different melt flow index (MFI) or produced by different producers have been examined in detail by solvent gradient fractionation, ¹³C NMR analysis, FTIR spectroscopy and melt rheological measurements. It was found that the distribution curves of the samples resemble Wesslau's logarithmic-normal model. From branching analyses it can be concluded that the branching content in the analyzed LDPEs is independent from the molecular weight. Relations between viscosity curve parameters and molecular structure have been investigated. It has been found that the dependence of the first normal stress difference on the shear stress is influenced by polydispersity as well as by the character of samples branching.     

Molecular weight distribution and rheological properties of polyisobutylene solutions

The molecular weight distribution of a series of polyisobutylenes was determined using osmotic pressure measurements, gel permeation chromatography, and intrinsic viscosity. All of the polymers except for one, a blend of the highest and lowest molecular weight constituents, had similar moderate molecular weight distributions. The “extended chain length” method of calibrating the gel permeation chromatograph for polyisobutylenes was found to be effective. Steady state and transient shear stresses and normal stresses were measured on 5% decalin solutions of these polymers. The zero shear viscosity increased with the 3.3 power of molecular weight, and the zero shear normal stress coefficient (σ₁₁ ? σ₂₂)/Γ² varied with the 7.5 power. Relative elastic memory as measured by (σ₁₁ ? σ₂₂)/σ₁₂ or stress relaxation increased with increasing molecular weight (and at constant number- or weight-average molecular weight) with breadth of distribution. Stress overshoot also correlated with this tendency.     

Melt rheology of some aliphatic polyamides

The melt rheology of nylon-6, nylon-6,6, nylon-6,10 and nylon-11, has been investigated by different techniques. It has been found that their behaviour is quite similar and almost Newtonian regarding both the flow curves and the elastic and instability properties. The samples show rather different viscous flow activation energies, although their values approach each other at high shear rate. The critical shear stresses of such materials are compared with those of other known polymers.     

A theoretical analysis of non-isothermal flow in wire-coating co-extrusion dies

A theoretical study of non-isothermal superimposed flow of two polymer melts in wire coating co-extrusion dies has been carried out. Numerical methods have been employed to solve the coupled momentum- and energy-balance equations. Various combinations of three polymers—namely, high density polyethylene (HDPE), polystyrene (PS) and low density polyethylene (LDPE) have been studied and least squares curve fitted quadratic polynomials have been used for constitutive equations for all three polymers in non-Newtonian high shear rate regions. A multitude of thermal and mechanical boundary conditions can be treated by this algorithm. It was found that temperature and velocity profiles in the die depend significantly on the arrangement of the polymers. Maximum temperature rise has been noted to increase sharply with wire velocity but it can be reduced by increasing the die radius. When the thickness of the outer layer is increased from zero, the shear stress at the wall undergoes a dramatic change (if the viscosities of the polymers are different) at small values of the flow rate ratio and it reaches an asymptotic value at large values of flow rate ratio. It was also found that viscosity ratio at the interface can be reduced by changing the initial temperatures of the liquids. It was observed in some cases that large errors in the calculation of rheological and thermal variables for this problem can be made if temperature rise due to viscous dissipation is not considered.     

Limiting regimes of deformation of polymers

The relaxation transition of polymers under the influence of deformation from the fluid to the forced high-elastic (rubbery) and leathery states has been studied. It has been shown that the investigation of the polymers in question under the conditions of uniaxial extension allows one to estimate the properties of polymers at deformation rates exceeding by 4-5 decades the rates of deformation at which simple shear can be realized. A set of critical parameters has been found for the polymers investigated which determines the regimes of their transition from the fluid to the forced rubbery and leathery states and also their fracture properties. These parameters are subdivided into two groups. The parameters of the first group refer to critical values of stress and deformation. They are invariant to temperature and molecular mass. For different polymer-homologous series the critical stresses vary by more than 10-20 times; as regards the values of strains, they vary by more than several times. The parameters of the second group define the rates of strain which bear a simple relation to the initial viscosity and can be changed within many decades. This determines the success of the procedure of reduction of fracture properties to temperature and molecular mass.     

An examination of the shear‐thickening behavior of high molecular weight polymers dissolved in low‐viscosity Newtonian solvents

The anomaly of shear thickening at high shear rates can be observed under certain conditions for high molecular weight polymers dissolved in low‐viscosity Newtonian solvents despite the fact that shear‐thinning behavior is considered the norm for these fluids. The nature of the shear‐thickening region of the flow curve is examined herein through the application of a recent rheological model that has the capability of quantifying not only the rheological properties of the material, but its internal microstructural state as well. The results of this examination provide a self‐consistent explanation of the full flow characterization of this anomalous behavior, including both rheological and optical experimental measurements. The results presented herein suggest that the shear‐thickening behavior is actually caused by the destruction of structures formed during shear at lower shear rates, not by their formation, as previously assumed. The linear birefringence and linear dichroism observed experimentally in correlation with the shear‐thickening behavior are well described by the rheological model and give predictions in line with experimental measurements. Furthermore, quantitative predictions are made for rheological characteristic functions, such as the first and second normal‐stress coefficients, for which experimental measurements for these solutions have not yet been made. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1714–1735, 2002     

Steady-state behavior of star polymers in dilute flowing solutions via Brownian dynamics

A bead and spring model is considered for the Brownian dynamics simulation of the behavior of regular star polymer chains in a dilute solution under both shear flow and extensional (or elongational) flow. Finite extensibility, excluded volume, and hydrodynamic interaction are taken into account to make the polymer model as realistic as possible. The behavior of star-like chains in flow is similar to that of linear and ring polymers. Thus, dependence of a given property with the arm molecular weight is analogous to that found for linear polymers when using the total molecular weight. In shear flow, the deformation of the chain and the shear rate viscosity dependence (the flow curve), are studied. We find a slope for the shear-thinning region of the flow curve close to −2/3. In elongational flow the coil-stretch transition is characterized by giving the relationship between the critical elongational rate and the arm molecular weight, which turns out to be similar to the power law found in linear chains.     

A rheological study of the low molecular weight butyl polymer

A rheological study has been performed to characterize the low molecular weight butyl polymers using a couette coni-cylindrical viscometer. The bulk viscosity was determined as a function of temperature, weight-average molecular weight, viscosity-average molecular weight, and shear rate. The temperature dependence of the viscosity, while adequately represented by the Williams, Landel, and Ferry equation, is best described by an Arrhenius equation for the temperature range investigated. The viscosity is shown to vary with the 3.5th power of the weight-average molecular weight above a critical molecular weight and to the 1st power below this molecular weight. Although the ratio of the weight-average molecular weight to the number-average molecular weight usually affects the flow properties of polymers, this was not true for the polymers investigated. The bulk viscosity was found to be independent of the molecular weight distribution for the temperature and shear rate range studied. It has been shown that a definite relationship exists between the bulk viscosity and the viscosity-average molecular weight as determined by dilute solution viscosity. A mathematical model has been developed to relate these two parameters as a function of temperature and shear rate.     

Stable flow regions for highly concentrated solutions of polyacrylonitrile in dimethyl sulfoxide

Conclusions Conclusions about the decrease in critical values of shear stress and shear rate with increase in the ratio of capillary length to capillary diameter at constant flow rates, and about the increase in critical values of shear stress and shear rate on the use of spinnerets with a conical inlet have been confirmed on polyacrylonitrile solutions having a high concentration.A second region of stable flow of polyacrylonitrile solutions having concentrations of 17.7% by wt. has been found in short capillaries (with a length of 3 or 10 mm).Translated from Khimicheskie Volokna, No. 2, pp. 23–24, March–April, 1990.     

The viscosity of monomolecular melts of poly(vinyl chloride)

PVC melts are predicted to be homogeneous with single molecules as the stable flow units (monomolecular melts) at corresponding values of high temperatures and/or high shear stresses. Under these conditions, it is found that the zero shear viscosity in simple shearing flow of rigid compounds depends on the average molecular weight by weight to the 3.5 power for molecular weights between 24,000 and 100,000. All data measured under conditions where monomolecular melts are predicted fall on a master curve of reduced viscosity versus reduced shear rate when a relaxation time proportional to η0/c²T is used. It is, therefore, concluded that monomolecular melts of PVC compounds follow the same structure–viscosity relations as found for other linear melts in viscometric flow.