Melt fracture of polystyrene

The results of an experimental study of melt fracture using polystyrene samples of narrow and broad molecular weight distribution are presented. The weight average molecular weight (M?_w) ranged from 9.72 × 10⁴ to 1.80 × 10⁶ and the distribution breadth M?_w/M?_η from 1.06 to 9.21. The critical shear stress varies linearly with 1/M?_w, increases slightly with temperature and is independent of the distribution of molecular weights. This type of behavior is satisfactorily explained in terms of Graessley's entanglement theory.     

“SPURT FRACTURE” IN CAPILLARY FLOW

The critical conditions under which flow curves in capillary flow abruptly change their slope to zero (spurt) and the influence of solvent additive and solvent power on this phenomenon have been investigated. Based on a forced high elastic state concept an expression for the so-called spurt phenomenon, i.e. fracture-induced slip at the wall in a capillary of a capillary rheometer, is deduced. It is found that the spurt fracture stress, τ^s _cr, and the spurt fracture shear rate, γ^s _cr, can be represented by the master curve log (τ ^s _crr ((p/M_c)PE(M_c/p))^2/3 against log (a_T γ^s _cr), where a_T is the WLF shift factor, M_c the molecular weight between entanglements and p the density.

Estimation of slip rates at the wall and measurements on slightly crosslinked high density polyethylene supports the assumption that spurt results from melt fracture at the capillary wall.

Only addition of the non-solvent calcium stearate (with high density polyethylene) results in flow behavior which significantly deviates from that found for samples containing good solvents. Gel permeation chromato-graphy indicates that if chain scission resulting in lower molecular weight takes place, it will be limited to thin layers near the capillary wall.

melt fracture in the capillary cannot be reached. The flow behavior is influenced by addition of the non-solvent calcium stearate. The slopes of the flow curves is changed at relatively low shear rates but the high molecular weight polymer DMDS 5140 never the less shows spurt behavior at the same stress as for the pure sample.

This behavior may tentatively be interpreted as being caused by the formation of a boundary layer of non-solvent at low shear rate the thickness of which depends on the polymer and flow field. At stresses corresponding to the critical conditions, fracture in the polymer takes place. The interface between the non-solvent layer and the polymer matrix must according to Han61 be expected to be unstable     

ELASTIC FRACTURE OF POLYMERIC FLUIDS

The elastic fracture of polystyrene solutions and melts was investigated using a plunger driven viscometer. The polymeric extrudate emerging from a circular capillary was photographed to determine the onset of fracture, and an effort was made to relate this information to the shear stress at the capillary wall, the recoverable shear strain, the entanglement density and the geometrical parameters characterizing the system. It was found that narrow molecular weight distribution polystyrenes dissolved in benzene clearly fractured as reported in the literature, but the onset of fracture could not be predicted by available criteria. As opposed to this, highly concentrated (polymer volume fraction up to 0.57) and elastic solutions of a wide molecular weight distribution polystyrene in benzene showed no fracture when judged using similar criteria. Nonetheless, this latter polymer fractured as a melt at a value of the wall shear stress less than that achieved in the solution runs. From an examination of the polymer rheology, it is concluded that the recoverable shear strain is the key quantity influencing the onset of elastic fracture. Also, the recoverable shear-shear rate behavior is different for the melt and the solution and it depends not only on the polymer molecular weight and its distribution but also on the solvent used. The surprising absence of elastic fracture for highly viscoelastic solutions can be understood if one realizes that a critical value of the recoverable shear strain is needed for fracture to occur.     

A study of extrudate distortion in controlled-rheology polypropylenes

The melt fracture characteristics of controlled-rheology polypropylenes (CRPP) were studied by means of capillary rheometry experiments. CRPPs were produced through reactive extrusion of a commodity polypropylene resin using various peroxide concentrations. These materials exhibited lower molecular weights and narrower molecular weight distributions than those of the starting commodity resin. The CRPP materials studied were found to exhibit only gross melt fracture. At extremely high shear rates and relatively low temperatures, a sigmoidal flexure was observed in the flow curve of certain CRPPs. Generally, it was found that the severity of melt fracture decreased with increasing shear rate for a given material and temperature and in some cases, the extrudates exhibited completely smooth surfaces. Also, the severity of surface distortions was reduced when high L/D dies were employed at a given shear rate. The critical shear stress for the melt fracture onset was found to increase with decreasing molecular weight and polydispersity, and correlations have been developed between the critical stress values and the polymer polydispersity and shear compliance.     

Flow behavior of well characterized polyethylene melts

A careful characterization and rheological study of low density polyethylene (LDPE) reveals that long-chain branching (LCB) plays a decisive role. At constant molecular weight (M?_w) higher LCB reduces the Newtonian viscosity η_o and the shear sensitivity, increases the activation energy E_o, and finally delays transition to pseudoplastic flow to higher shear rates and the onset of melt fracture to higher shear stresses (τ_d). The flow parameters η_o, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma _{cr} $\end{document}_cr, τ_d, and the derived flow relaxation times are uniquely correlatable by means of a modified molecular weight (gM?_w) incorporating the LCB effect. High density polyethylene are less shear sensitive than their low-density counterparts, have a lower activation energy, fracture at higher shear stress levels and cannot be regarded as branchless LDPE's.     

A model relating the elastic properties of high-density polyethylene melts to the molecular weight distribution

An earlier model relating the variation of the steady-shear melt viscosity of high-density polyethylene to the molecular weight distribution is applied toward predicting the steady-shear elastic compliance, the first normal stress difference, and relaxation spectrum as a function of shear rate from the molecular weight distribution. The model envisions the cutting off of longer relaxation times as the shear rate is raised such that at any shear rate ${\rm \dot \gamma }$ the molecular weights and their corresponding maximum relaxation times τ_m are partitioned into two classes; the relaxation times are partitioned into operative and inoperative states, depending on whether they are less than or greater than τ_c, the maximum relaxation time allowed at ${\rm \dot \gamma }$. Equations relating molecular weight and relaxation time to the steady-shear elastic compliance and viscosity are assumed valid at nonzero shear rates, except for the partitioning effect of shear rate. The shear rate dependence of the first normal stress difference and the steady-shear viscosity for polyethylene melts is successfully predicted over the range covered by the cone-and-plate viscometer. The assumed proportionality constant between τ_c and 1/${\rm \dot \gamma }$ was determined to be 1.7. Using this relation, the maximum relaxation time at 190°C for a polyethylene molecule of molecular weight M is given by τ_m = 1.4 × 10^?19 (M)^3.33. Reasonable agreement has been obtained between the experimentally determined relaxation spectrum of a polyethylene melt and that predicted from the molecular weight distribution. The agreement is best at the longest relaxation times.     

Head to head polymers IX: The rheological behavior of H-H and H-T atactic polystyrenes

The rheological behavior of a sample of H-H polystyrene of M_n of 41,000 and a M_w/M_n of 2 was compared at 160 and 190°C with a sample of H-T atactic polystyrene of similar molecular weight. The melt viscosity of H-H polymer (unlike the H-T polymer) was non-Newtonian at low stresses and decreased more rapidly with stress. This observation seems to indicate a stiffer polymer chain for the H-H polystyrene. The flow activation energy (E*) of H-H polystyrene was found to be dependent on the dynamic shear stress and decreased with increasing dynamic shear stress. The dynamic shear storage modulus of the H-H polymer has a smaller increase of G′ with ω than that of the H-T polystyrene.     

Prediction of high density polyethylene processing behavior from rheological measurements

In order to predict the processing behavior of a high density polyethylene resin one must know the resin flow behavior over a wide range of shear rates. Low shear properties are important in applications where melt strength, sagging, etc. are critical. On the other hand, high shear flow properties are a determining factor in applications where melt instability, melt fracture and heat generation are important. The flow behavior of a resin can be established by measuring the zero shear viscosity, η₀, the maximum relaxation time, τ₀, and the shape of the flow curve. We have measured these basic rheological parameters on a large number of high density polyethylene resins. A shear sensitivity parameter which is independent of molecular weight was derived from a correlation between η₀ and τ₀. This parameter, together with η₀, provide the vital information needed in order to predict the processing behavior of the resin. This method is applicable to other polymer systems provided that the rheological parameters η₀ and τ₀ can be experimentally obtained.     

The rheology of polysulfone

The viscosity-shear rate functions for polysulfone (PSF) condensates ranging from 0.4RV to 0.95RV were determined using capillary rheometry, The most probable distribution of molecular weights of these resins allowed facile comparison with the polydisperse Bueche theory for viscosity, The agreement in shape of the viscosity function with theory was good but the data were displaced by a factor of 3 to 4 to higher reduced shear rate, a fairly common occurrence for melts. The high absolute value of PSF viscosity was explained with existing empirical correlations as a combination of low critical molecular weight and strong intermolecular interactions. The temperature dependence of viscosity was found to be close to that for polystyrene in the temperature range, T_g + 90 to T_g + 190°C. The die swell, end corrections, and melt fracture characteristics were also determined. The latter was found to occur at a constant wall shear stress of about 6 × 10⁶ dynes/cm² while the die swell and end corrections were found to be small.     

Elastic fracture of polystyrene solutions

Based on the assumption of a constant critical shear strain, an expression for the critical stress at the onset of entrance fracture as a function of polymer concentration has been developed. Experimental results with 10-25 percent narrow distribution, high molecular weight polystyrene-benzene solutions show the critical stress to be much lower than that for the polymer melt and in agreement with predicted values. This result is all the more impressive when the contrast in flow behavior at the capillary entrance for melts and solutions is observed. Instead of the rotating toroidal vortices surrounding a 90-deg material entrance cone observed with polystyrene melt, cine movies of the solution flow birefringence patterns in the capillary entrance region reveal only a stagnant zone surrounding a narrow cone less than 20 deg. At fracture, the cone axis moves in a rotary path circulating about the capillary axis without undergoing the flow discontinuities typical of melt behavior.     

Viscoelastic properties of linear chain macromolecular gels. Growth of stress at the onset of steady shear flow

The growth of stress (shear stress and normal stress) at the onset of steady shear flow was investigated for linear chain macromolecular fluids to determine nonlinear viscoelasticity. The polyacrylamides (PAAm) were dissolved in H₂O, formamide and ethyleneglycol. The polymers were prepared in this laboratory. They were unbranched and free of initiator. The polystyrene (PS) samples from Pressure Chemical Company were studied in decalin solutions. PAAm shows increasingly typical gel character—in all 3 solvents—with increasing molecular weight and polymer concentration. For homogeneous systems gel fracture and undershoot were observed. Further for the first time overshoot due to entangled molecules and overshoot due to energetically associated chains have been distinguished. This behaviour is a strong contrast to the PS/decalin system and demonstrates the strength of the second valence bondings in the PAAm-systems.     

Flow properties of ABS (acrylonitrile–butadiene–styrene) terpolymer

ABS (acrylonitrile–butadiene–styrene) terpolymer is a two-phase thermoplastic with SAN (styrene–acrylonitrile) copolymer constituting the continuous phase (matrix). The flow properties of ABS with varying molecular parameters were studied using a capillary viscometer at the shear rate range encountered in its processing. The viscosity-average molecular weights (M_v) of matrix SAN with 26% acrylonitrile content are in the range of 90,000 to 150,000, and M_v of poly-butadiene-are in the range of 150,000 to 170,000. The weight-average molecular weight of the matrix SAN is the main controlling factor for the flow properties of ABS at low shear rate, while the molecular weight distribution of the matrix SAN becomes increasingly important with the increase of shear rate. The presence of SAN grafted polybutadiene increases the melt viscosity of ABS by 40–60% over comparable free SAN copolymer and also decreases the activation energy at constant shear stress to 24–25 kcal/mole from the 33–36 kcal/mole for free SAN. The die swell of ABS and SAN can be correlated with the dynamic shear modulus G′, and the melt fracture of ABS and SAN starts at G′ equal to 3.6 × 10⁶ dynes/cm².     

Polymer welding relations investigated by a lap shear joint method

A lap shear joint method was used to study strength development during welding of polystyrene surfaces- The surfaces previously had not been in contact and care was taken to insure rapid wetting of the interface. The shear stress at failure, τ_f was measured at room temperature as a function of contact time, t, at constant welding temperatures up no 20°C above the glass transition temperature, T_g. The time dependence of welding could be well described by τ_fαt^1/4. This result is in agreement with predictions of the reptation molecular dynamics model applied to inter-diffusion at a symmetric amorphous polymer-polymer interface. The activation energy for the thermally activated increase in strength development was determined as E = 96 kcal/mol at T = 113.5°C, which compares with E = 93,2 kcal/mole as predicted by the W-L-F theory using C₁ = 13.7, C₂ = 50 and T_g = 100°C. The polystyrene samples had molecular weights, M_n = 143,000 and M_w = 262.000. The time to achieve complete healing, t_∞ ≈? 256 min at 118°C, was found to be of the same order of magnitude as the viscoelastic relaxation time and also with the time required for a polymer chain to diffuse a distance equal to its root mean square end-to-end vector.     

Shear stress at polymer/metal interface during melting in extrusion

Prediction of the screw horsepower requirement involves, among many others, the calculation of the shear stress (τ_s) between the solid polymer and the barrel surface during melting. Prediction of the solid bed down-channel velocity also requires the calculation of τ_s. However, the pseudoplastic nature and strong temperature dependence of melt viscosity make the mathematics of calculating τ_s extremely difficult. As a first step of developing a reasonable mathematical model for calculating τ_s, experimental measurements of τ_s were made over a wide range of metal temperature and sliding speed for five commercial polymers using molded, block samples. Although dependences of τ_s on metal temperature and sliding speed were found to have similar functionality to those of the dependences of melt viscosity on melt temperature and shear rate, this study showed that τ_s could not be expressed as a sole function of the melt rheological properties. Our subsequent study, to be reported in a follow up paper, will show that τ_s must be expressed as a function of the thermodynamic properties and melt density of the polymer as well as the melt rheological properties and the melting conditions.     

Fluorine-containing arborescent polystyrene-graft-polyisoprene copolymers as polymer processing additives

Linear low density polyethylene (LLDPE) can suffer from melt extrusion defects including sharkskin, cyclic melt fracture, and gross melt fracture during processing. Arborescent polymers are dendritic macromolecules with characteristics, such as a compact structure and a rigid spherical topology, making them potentially useful as polymer processing additives (PPA) to alleviate melt extrusion defects. Arborescent polystyrene-graft-polyisoprene copolymer samples were synthesized from polystyrene substrates of linear and branched architectures functionalized with acetyl groups, and coupled with polyisoprene macroanions. A linear polyisoprene sample was also investigated for comparison. The polymers were hydrosilylated with (tridecafluoro-1,1,2,2-tetrahydrooctyl)dimethylsilane on 17-52% of the isoprene units and blended with LLDPE at 0.1 and 0.5% w/w to evaluate their performance as PPA by extrusion at different shear rates. All the samples led to some degree of improvement in the extrusion of LLDPE, albeit the performance of the branched additives was inferior to a commercial fluoroelastomer PPA. The lower molecular weight and more compact (G0 or comb-branched) PPA generally performed better than those with a high molecular weight. Several PPA samples induced the early onset of cyclic melt fracture but glossy, defect-free surfaces were obtained at higher shear rates. This suggests that a minimum shear rate is required for these additives to coat the extrusion die under the experimental conditions used.     

Deformation behavior of polystyrene as a function of molecular weight parameters

The mechanical deformation of polystyrene as it relates to molecular weight parameters was investigated. Mechanical testing consisted of uniaxial tension and compression experiments on a variety of polystyrenes. Such quantities as modulus, proportional limit, and various yield stress measurements were determined on polystyrene samples of controlled number-average molecular weight and molecular weight distribution. A basic tool for the mechanical behavior analysis was the use of a power law equation σ = K?ⁿ to examine the initial nonlinear region of each experimentally determined stress–strain curve. Correlations between mechanical deformation and molecular weight parameters were determined using statistical linear regression analysis. It was generally found for uniaxial tension that mechanical parameters in or near the elastic region were independent of M?_n and MWD, while at larger strains correlations were found. For uniaxial compression, stress maxima and the strain where this occurred increased with increasing MWD. Otherwise, mechanical parameter changes in uniaxial compression did not occur with changing M?_n and MWD. Finally, a direct comparison of tension versus compression showed only the initial moduli to be the same. All other mechanical parameters showed significantly differing values, indicating different deformation mechanisms operating in tension verus compression. The analysis of this behavior from both a mechanics and molecular weight viewpoint provides some insight about glassy polymer deformation processes on the microscopic level.     

The source of degradation during extrusion of polystyrene

The nature and magnitude of mechanical reactions of polystyrene in capillary flow has been examined in a model extrusion process. Studies on polystyrene quantify the sensitive increase in shear degradation tendency with increasing polymer molecular weight. A molecular weight spectrum caused by the shear stress profile was measured across the extrudate radius by the new technique of solvent coring. It was further determined that an appreciable fraction of the mechanical reaction is shear induced in the capillary reservoir. This is confirmed by precision determinations of molecular weights and distributions by gel permeation chromatography on samples taken from concentric layers in the capillary reservoir after 50% sample extrusion. These results, involving traces of oxygen as a chemical probe, describe the stress profile in the reservoir and in the capillary during the pressure extrusion of high molecular weight polystyrene. Thus, changes in molecular weight and distribution may be attributable to changes in different portions of the shear geometry rather than the uniform changes generally considered. Clear evidence is also presented showing the dramatic effects of oxygen on these shear-induced changes in molecular weight and distribution.     

Effects of extrusion conditions on rheological behavior of acrylonitrile–butadiene–styrene terpolymer melt

The influence of temperatures and flow rates on the rheological behavior during extrusion of acrylonitrile–butadiene–styrene (ABS) terpolymer melt was investigated by using a Rosand capillary rheometer. It was found that the wall shear stress (τ_w) increased nonlinearly with increasing apparent shear rates and the slope of the curves changed suddenly at a shear rate of about 10³ s^?1, whereas the melt‐shear viscosity decreased quickly at a τ_w of about 200 kPa. When the temperature was fixed, the entry‐pressure drop and extensional stress increased nonlinearly with increasing τ_w, whereas it decreased with a rise of temperature at a constant level of τ_w. The relationship between the melt‐shear viscosity and temperature was consistent with an Arrhenius expression. The results showed that the effects of extrusion operation conditions on the rheological behavior of the ABS resin melt were significant and were attributable to the change of morphology of the rubber phase over a wide range of shear rates. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 606–611, 2002     

Shear degradation of polyisobutene

A polyisobutene of M?_w 1.98 × 10⁶, M?_w/M?_n 1.8, was extruded in an Instron capillary rheometer. Shear degradation occurred at high shear stresses, approaching melt fracture, and was more prominent at lower extrusion temperatures for tests at 60–140°C. The capillary was 2.0 in. long with a length/diameter ratio of 66.7 and a 90° entrance angle. Repetitive extrusions at constant shear rate caused a decrease in a molecular weight and a simultaneous narrowing of the molecular weight distribution. Extrudate expansion was measured after each successive capillary pass for tests at 80°C. Extrudate swelling correlated well with (M?_z+1) M?_z/M?_w, except for the two first passes, where melt fracture was pronounced. The correlation with equilibrium extrudate expansion was almost as good for (M?_z/M?_w)^3.7 (Mill's correlation) and for M?_z+1 alone. The efficiency of bond rupture is low, with the energy required to rupture 1 mole of bonds being about 200,000 kcal at 80°C.     

Effects of drawing conditions on the properties of optical fibers made from polystyrene and poly(methyl methacrylate)

Monofilaments possessing various degrees of birefringence were obtained by changing the drawing rate, the molten polymer temperature, and the molecular weight of polystyrene (PS) and poly(methyl methacrylate) (PMMA). The “brittle-toductile” transition point of optically pure PS was found in the range of birefringences of ?0.6 · 10^?3 to ?2.6 · 10^?3. Both the height and position of this point are influenced by M?_w, molecular weight distribution, and polymer melt temperature. The birefringence of PS is higher by two orders of magnitude than that of PMMA in which this transition point has not been observed. The mechanical and optical properties depend not only on the average amount of orientation characterized by the birefringence but on what portion of the relaxation spectrum of the polymer is preferentially oriented. During the drawing of PS and PMMA monofilaments crazes are formed in the centre of the fibers and do not reach the surface.