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

A bead and spring model is considered for the Brownian dynamics simulation of the behavior of cyclic polymer chains (rings) in a dilute solution under shear or elongational flow. Finite extensibility, excluded volume, and hydrodynamic interaction are taken into account to make the polymer model as realistic as possible. In shear flow, the deformation of the chain and the shear rate viscosity dependence (the flow curve), are studied and characterized. In elongational flow, the coil-stretch phenomenon is described and the relationship between the critical elongational rate and the molecular weight is given. The qualitative behavior obtained for ring polymers is analogous to that of linear polymers.     

Modified bead-spring theory of polymer solutions. IV. Extension to polymer melts

A constitutive equation which has proven quite successful in describing the nonlinear viscoelastic behavior of dilute polymer solutions is extended to the case of molten polymers. The techniques utilized and similar to those discussed by Ferry in a similar adaptation of the Rouse–Zimm Theory. The resulting model is found to quantitatively portray the shear rate dependence of the non-Newtonian viscosity and primary normal stress functions and the frequency dependence of the storage and loss moduli. Extensional flow data reported by Spearot and Metzner for two polyethylenes are well described, using parameters calculated from steady shearing measurements. Of major significance is the ability of the model to account for influences of molecular weight, molecular weight distribution, and temperature.     

Experimental investigation of the influence of molecular weight distribution on the rheological properties of polypropylene melts

An experimental study of steady shear and elongational flow Theological properties of a series of polypropylene melts of varying molecular weight and distribution is reported. Broadening the molecular weight distribution increases the non-Newtonian character of the shear viscosity function and increases the principal normal stress differences at fixed shear stress. The behavior is compared to earlier rheological property-molecular weight studies. Correlations are developed for these properties in terms of molecular structure. Elongational flow studies indicate that for commercial and broader molecular weight distribution samples, ready failure by neck development occurs and the elongational viscosity appears to decrease with increasing elongation rate. For narrower molecular weight distribution samples, the elongational viscosity is an increasing function of elongation rate, The implication of these experimental results to viscoelastic fluid constitutive equations and polymer melt processing is developed.     

An experimental study of threadline dynamics with emphasis on the effect of molecular weight on the elongational viscosity of melt-spun poly(ethylene terephthalate)

A study of a melt-spun threadline has been carried out to determine the effect of molecular weight on the elongational viscosity of the polymer being spun. Polymer chosen for this study was poly(ethylene terephthalate) having different molecular weights. Conventional nonisothermal spinning of the polymers was carried out with cooling by free convection. Threadline surface temperatures were measured by a null-balance technique. Threadline tension at the take-up device was measured, and samples of the threadline were taken to obtain linear density profiles. Nonlinear least-squares fits were applied to the linear density data to obtain equations for velocity and elongation rate. These measurements were then used to determine the threadline elongational viscosity. Least-squares fits were made to a polynomial relating absolute temperature and elongation rate to the elengational viscosity. These results were then used to determine an activation energy of elongational flow which was found to decrease with elongation rate. Elongational viscosity was found to increase with molecular weight.     

Equibiaxial elongational viscosity measurements of commercial polymer melts

The equibiaxial elongational viscosity of six commercially available polymer melts is measured using a novel technique known as continuous lubricated squeezing flow. This technique is a modification of simple lubricated squeezing flow. The systems were chosen in order to investigate the dependence of equibiaxial elongational viscosity on molecular structure. Three of the melts are polyethylene with long chain branching, two are polyethylene with short chain branching, and one is polyisobutylene with linear chains. Each polymer was subjected to strain rates ranging from 0.003 to 0.1 s^?1 and compared to the linear viscoelastic prediction so that the degree of strain hardening could be determined. For a modestly branched polymer, comparison of rheological behavior in both uniaxial and equibiaxial deformations was possible. POLYM. ENG. SCI., 55:1012–1017, 2015. © 2014 Society of Plastics Engineers     

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.     

Validation of cogswell's convergent flow analysis

The behavior of two polymers, namely, low-density and linear low-density polyethylenes, was studied in transient and steady-state shear and elongational flows. The predictions of Wagner's model with a damping function using a generalized invariant were calculated. The model appears to be suitable for predictions of the shear and elongational transient flows on the range of strains experimentally tested. The shear flow curves can also be recovered by the model on a very broad range of shear rates. The model is then used to assess extensional data obtained with the convergent flow analysis proposed by Cogswell. © 1996 John Wiley & Sons, Inc.     

Rheological Properties of Different Film Blowing Polyethylene Samples Under Shear and Elongational Flow

Summary: The rheological behavior of polyethylenes is mainly dominated by the molecular weight, the molecular weight distribution and by the type, the amount and the distribution of the chain branches. In this work a linear metallocene catalyzed polyethylene (m‐PE), a branched metallocene catalyzed polyethylene (m‐bPE), a conventional linear low density polyethylene (LLDPE) and a low density polyethylene (LDPE) have been investigated in order to compare their rheological behavior in shear and in elongational flow. The four samples have similar melt flow index and in particular a value typical of film blowing grade. The melt viscosity has been studied both in shear and in isothermal and non‐isothermal elongational flow. The most important features of the results are that in shear flow the m‐PE sample shows less pronounced non Newtonian behavior while in the elongational flow the behavior of m‐PE is very similar to that of the linear low density polyethylene: the narrower molecular weight distribution and the better homogeneity of the branching distribution are reasonably responsible for this behavior. Of course the most pronounced non‐linear behavior is shown, as expected, by the LDPE sample and by the branched metallocene sample. This similar behavior has to be attributed to the presence of branching. Similar comments hold in non‐isothermal elongational flow; the LDPE sample shows the highest values of the melt strength and the other two samples show very similar values. As for the breaking stretching ratio the opposite is true for LDPE while m‐PE and LLDPE show higher values. The transient isothermal elongational viscosity curves show that the branched samples show a strain hardening effect, while LLDPE and m‐PE samples present a linear behavior.

Dimensionless flow curves of different polyethylene samples.     

Orientation development in thermotropic liquid crystal polymers

Thermotropic liquid crystal polymers are a new class of polymeric materials that consist of rigid backbone molecules and thus, even in the quiescent condition, take extended chain conformation to form optically anisotropic melts. A systematic investigation was carried out on how this type of material responds to two basic flow fields: shear and elongation. Rheological properties of the polymer in these flow fields have also been measured. It was found that a high level of molecular orientation was readily obtained by elongational flow but not with shear flow. Specifically, extraordinarily high orientation was obtained when the melt was subjected to small elongational strains, whiel shear strain or shear rate had little effect. A possible mechanism to explain these behaviors is illustrated based on the existing observations or theories of rodlike molecules. This finding was used to interpret the orientation distribution in the extruded and injection-molded articles.     

Apparent elongational viscosity of dilute polymer solutions

Apparent elongational viscosity studies were made on dilute solutions of high molecular weight polymers using a fiber spinning apparatus designed for low shear viscosity liquids with substantial elongational effects. The experimental method involved the flow of solutions of polyacrylamide and poly(ethylene oxide) from a tube into an evacuated vessel. Experimental results showed that the apparent elongational viscosity obtained from the jet shape increased linearly with the stretch rate.     

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.     

High shear rheology and shear degradation of aqueous polymer solutions

We have investigated the possibility of replacing hydraulic oils with aqueous polymer solutions having the same rheological properties. We measured the low and high shear rate viscosities of polymer solutions at several moderate concentrations and compared the results to the predictions of a molecular model. We found that viscosities measured at shear rates near 1 million reciprocal seconds are in good agreement with those calculated using the model of Mochimaru.⁶ Shear degradation studies were also conducted using higher molecular weight versions of some of the polymers. Exposure of these to very high shear rate caused a permanent decrease in viscosity and a corresponding change in the molecular weight and molecular weight distribution. Taken together, these results show that very low molecular weight polymers at moderate concentrations are necessary to formulate an aqueous hydraulic fluid with approximately Newtonian behavior at shear rates near 1 million reciprocal seconds, and without long-term polymer degradation.     

PVC melt rheology III: The effect of order and molecular weight on the shear rate dependence

The effect of polymerization temperature on the melt flow behavior of PVC of varying molecular weights has been studied over a wide shear rate range. For the same molecular weight, higher melt viscosities are observed for polymers prepared at lower temperatures. The shear rate dependence of the viscosity vs molecular weight plot is shown to be nonlinear over the shear rates examined. The inability to achieve a limiting zero-shear viscosity is discussed.     

Polarization-optical investigation of normal and shear stresses in flow of polymers

A method has been suggested for calculating the first difference of normal stresses characterizing the flow of polymers at high shear stresses. The calculations are based on the results of rheooptical measurements in a slit of rectangular cross section. It has been found, for several samples of high molecular weight polybutadienes and polyisoprenes, that the flow behavior of the representatives of the given polymer homologous series having different molecular weights is characterized by a general relationship between the first normal stress differences and the shear stresses in those cases where the polymers are characterized by narrow molecular weight distributions. It has also been established that the first normal stress difference sharply increases in the region of shear stresses which immediately precedes the spurt—a jumpwise increase of the flow rate at a certain critical value of shear stress; while for polymers of wide molecular weight distribution the increase of the normal stress difference in the region of high values of shear stresses is retarded. Equilibrium swell of the extrudate has been measured and the first normal stress difference determined by the rheo-optical method has been found to agree satisfactorily with the values calculated from the swelling ratios according to theoretical models.     

Mechanical stability of high‐molecular‐weight polyacrylamides and an (acrylamido tert‐butyl sulfonic acid)–acrylamide copolymer used in enhanced oil recovery

High‐molecular‐weight partially hydrolyzed and sulfonated polyacrylamides are widely used in enhanced oil recovery (EOR). Nonionic polyacrylamide and polyacrylamide‐based microgels are also used in water shut‐off treatments for gas and oil wells. A comparative study of the mechanical degradation for three linear polyacrylamides and a microgel is presented. Mechanical degradation is quantified from the loss of the viscosity of the polymer solution as it passes through a stainless steel capillary with a length of 10 cm and an internal diameter of 125 µm. The critical shear rate above which degradation increases exponentially was found to depend on the chemical structure of the polymer, molecular weight, and electrolyte strength. The nonionic polyacrylamide shows higher degradation and lower critical shear rate compared with a sulfonated polyacrylamide with similar molecular weight. Moreover, the nonionic polyacrylamide with a higher molecular weight results in lower mechanical degradation. The higher mechanical stability of the sulfonated polymer is attributed to the higher rigidity of its molecules in solution. On the other hand, the ability of the high‐molecular‐weight polymers to form transient, flow‐induced microgels boost their mechanical stability. This ability increases with the increase in the molecular weight of the polymer. Indeed, the microgel solution used in this study demonstrates exceptional mechanical stability. In general, mechanical stability of linear polymers used in chemical enhanced oil recovery can be enhanced by tailoring a polymer that has large side groups similar to the sulfonated polyacrylamide. Also, polyacrylamide‐based microgels can be applied if high mechanical stability is required. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40921.     

The effect of random branching on the balance between flow and mechanical properties of polyamide-6

The rheological and mechanical properties of a series of linear and randomly branched polyamide 6 samples, with varying molar mass and varying degree of moderate branching, have been investigated.As expected, it was found that random long-chain branching has a pronounced effect on the rheological behaviour of the materials in both shear and extensional flow. The zero shear viscosity increases with branching while the flow curve becomes more shear thinning. Randomly branched materials have an enhanced melt strength in elongational flow. Although branched, the materials show perfect melt stability in their rheology.The mechanical properties show minor differences between the linear and the moderately branched samples and are mainly dependent on the weight average molar mass. A small increase in modulus, yield stress and failure stress and a decrease in the strain at break are found, which is probably due to increased molecular orientation in the plane of injection moulding. The IZOD impact strength is similar to what is normally found for linear polyamide-6, and independent of branching. Also the fracture toughness K_IC is not affected by the incorporation of random branching. However, it is clearly dependent on the weight average molar mass.By using random branched polyamide-6, molecular weights and related mechanical properties can be obtained that are out of reach for linear polyamide-6.     

Effect of chain structure on the melt rheology of modified polypropylene

The effect of molecular structure of polypropylene (PP) on the melt rheological properties were investigated for electron irradiated polymer and di-2-ethylhexyl peroxy dicarbonate (EHPC)-treated polymer. The modifications were examined in terms of the rheological behaviors, molecular weight distribution, and the degree of branching. The high melt strength PP was obtained by irradiating with 50 and 80 kGy and adding EHPC. The modified PPs showed the strain hardening in the uniaxial elongational viscosity, though the linear elongational viscosity was lower than that of the unmodified PP. Low angle laser light-scattering measurements of the modified PPs showed the interesting results; high irradiation doses such as 50 and 80 kGy caused higher molecular weight chains branching. Nevertheless, the long branching chains were not detected for the EHPC modified PP, which also showed the strain hardening in uniaxial elongational flow. In this article, the relation between chain structure and rheological properties is discussed. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1493–1500, 1999     

Nonlinear rheological behavior of a novel oil displacing agent

In this work, the shear and elongational rheologies have been investigated for a newly developed oil displacing agent, polymeric surfactant‐PSf. It was found that the PSf solutions exhibited Newtonian, shear‐thinning, and shear‐thickening behavior, respectively, depending on the polymer concentration and shear rate, and Cox–Merz rule was not applicable to these systems. The first normal stress difference (N₁) versus shear rate plots for PSf were complicated, which varied with the composition of the solutions. The uniaxial elongation in capillary breakup experimental results indicated that Exponential model could be used to fit the experimental data of the PSf solutions at lower polymer concentrations. In addition, it was found that PSf was more effective in improving shear viscosity than partially hydrolyzed polyacrylamide, but not in the case of elongational viscosity. The experimental results indicated that the microstructural mechanisms are responsible for the rheological behavior of the polymers. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40813.     

Capillary breakup extensional rheometry of associative and hydrolyzed polyacrylamide polymers for oil recovery applications

High molecular weight polymers used for heavy oil recovery exhibit viscoelasticity that can influence the oil recovery during chemical enhanced oil recovery. Different polymers having similar molecular weight and shear rheology may have different elongation flow behavior depending on their extensional properties. Displacing slugs are more likely to stretch than shear in tortuous porous media. Therefore, it is critical to seek an analytical tool that can characterize extensional parameters to improve polymer selection criteria. This article focuses on the extensional characterization of two polymers (hydrolyzed polyacrylamide and associative polymer) having identical shear behavior using capillary breakup extensional rheometer to explain their different porous media behavior. Maximum extensional viscosity at the critical Deborah number and Deborah number in porous media classified the associative polymer as the one having high elastic‐limit. Extensional characterization results were complemented by significantly higher pressure drop, marginally increased oil recovery of associative polymer in porous media. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46253.