The application of melt elasticity measurements to polymer processing

In recent years there has been increasing recognition of the importance of melt elasticity in polymer processing. A new instrument has been developed that determines the elastic properties of polymers in the melt state by measuring both the stress relaxation and strain recovery characteristics as a function of applied rate of strain, temperature, and magnitude of applied strain. Data on several different polymers will be presented together with examples of the significance of melt elasticity in such processing operations as thermoforming, blow molding, and film forming. A material parameter that is very important in the processing of polymers such as polystyrene and poly(methylmethacrylate) is the transition above the glass transition, T_g, referred to as the liquid-liquid transition, T_II. At this transition there is an abrupt change in the elasticity of the melt. Processing above or below this transition produces products with very different end use properties.     

Melt fracture behavior of polypropylene‐type resins with narrow molecular weight distribution. I. Temperature dependence

Polypropylene (PP)‐type resins with narrow molecular weight distribution, such as PP‐type thermoplastic elastomer PER and controlled‐rheology PP (CRPP) made by peroxide degradation of high molecular weight PP, have a problem of easy generation of skin roughness at extrusion. To examine the present state, the occurrence of skin roughness in PER and CRPP at extrusion was investigated with a capillary rheometer in a shear rate range of 12–6100 s^?1 and a temperature range of 180–280°C. A homo‐PP (HPP) and a block‐PP (BPP) with usual molecular weight distributions were used for comparison. HPP and BPP with usual molecular weight distributions show smooth extrudates at low shear rates and abruptly generate severe skin roughness “elastic failure” originating at the die entrance at a higher shear rate. PER and CRPP with narrow molecular weight distributions easily generate “sharkskin” melt fracture originating at the die exit, from a shear rate nearly one decade lower than rates of elastic failure of HPP and BPP. The sharkskin becomes more severe, with increasing shear rate, and attains to the elastic failure. The critical shear rate at which sharkskin occurs increases with increasing extrusion temperature. The critical shear rate is about 20 s^?1 at 180°C and about 120 s^?1 at 280°C, which is in the range encountered by the molten resin at extrusion processing. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2111–2119, 2002     

Rheological behavior and flow instability in capillary extrusion of ultrahigh-molecular-weight polyethylene/high-density polyethylene/nano-SiO2 blends

Rheological behaviors of ultrahigh-molecular-weight polyethylene (PE)/high-density PE/SiO₂ blends are investigated using parallel-plate rheometer and capillary rheometer. The molecular chain conformational change mechanism is used to explain flow instabilities during extrusion. The viewpoints are proposed: (1) critical shear rate depends on the relative strength of irreversible viscous loss and reversible elastic orientation for molecular chains in transverse velocity gradient field inside the die and (2) critical shear stress depends on the extent of molecular chain conformational change inside the die, and the ease of conformational recovery after leaving the die. Modified nano-SiO₂ particles are detected a certain interfacial adhesion in PE matrix. The interfacial interaction limits viscous flow inside the die and conformational recovery after leaving the die, thus causing not only the flow instabilities to occur prematurely on shear rate and delaying sharkskin on shear stress, but also an alternate “sharkskin-melt fracture” appearance after global extrusion fracture. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47713.     

Mechanical degradation of high molecular weight polymers in dilute solution

The mechanical shear degradation of polydisperse polyisobutene and monodisperse polystrene in oils of different viscosities in the concentration range of 0.1% to 1% was studied using a high-shear concentric cylinder viscometer under laminar and uniform well-defined shear field conditions. Molecular weight distributions (MWDs) were measured by gel permeation chromatography (GPC). Degradation of polydisperse polyisobutene solutions narrows the distributions principally through the breaking down of large molecules. Degradation of monodisperse polystyrene broadens the distributions at lower shear stress. At higher shear stresses, the distributions do not broaden as much but are still broader than those of the original polymer. The final M_w/M_n ratios are considerably different from the value of 2 expected for random degradation. Hence, the degradation is likely a nonrandom process. It was found that the extent of degradation has a negative concentration dependence coefficient at relatively high molecular weight and a positive concentration dependence at lower molecular weight. Competing mechanisms of “stretching” and “entanglements” for degradation were postulated to explain the results. The degradation data indicate that the shear stress is the controlling parameter, not the shear rate. The shear degradation is independent of initial molecular weight and viscosity of the solvent.     

Stress relaxation of elongated strip of poly(vinylidene fluoride) in ethyl acetate vapor

Poly(vinylidene fluoride) films in ethyl acetate vapor were studied at 30°C for vapor pressures of p = 0, 12, 30, 40, 66, 85 torr and elongations ε = 4.5%, 7%, 9.5%, 19%, 29%, and 44%. A cyclic experiment was also performed at ε = 7% and p = 40 torr for three sorption/desorption cycles. Assuming, as a first approximation, that the stress relaxation of the “dry” and “wet” polymers is proportional to the elastic strain, ε_el, empirical calculations were performed and compared to experimental results. In general, the presence of a vapor or gas in a polymer matrix enhances the stress relaxation by softening or plasticizing the polymer and transforming a portion of the elastic strain, ε_el, into the plastic strain, ε_pl. As the transformation continues, the sorption and stress of the wetted elongated sample change simultaneously with time until an optical “overshoot” and a mechanical or stress “undershoot” is observed. This result seems to be the consequence of the differential change of the stress of the “dry” and “wetted” samples with sorption time, τ = t ? t_o(t = time; t_o = initial sorption time), which depends on the differential time dependencies of the transformations of the elastic and plastic strains.     

The degradation of polystyrene during extrusion

An investigation was made of the magnitude and mechanism of shear degradation of a narrow distribution, high molecular weight (M_w = 670,000) polystyrene. An Instron rheometer was used to perform the extrusion at temperatures from 164° to 250°C. The change in molecular weight distribution was studied by gel permeation chromatography. The maximum shear stress employed was 5.83 kg/cm². It was found that degradation could be induced at high stress at temperatures of 50°C lower than degradation of polystyrene would occur exclusively due to thermal forces. An activation energy for the degradation, calculated at constant shear rate, was +20.2 kcal/mole. The direction and magnitude of this value are consistent with degradation induced through a mechanical reduced activation for thermal degradation.     

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.     

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.     

Maxwell Fluid Model for Generation of Stress–Strain Curves of Viscoelastic Solid Rocket Propellants

Solid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–strain curve is generated for case‐bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different strain rate. It is observed that change in spring constant, representing elastic part is very small with strain rate but damping constant varies significantly with variation in strain rate. For a typical propellant formulation, when strain rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all strain rates, stress–strain curve is generated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case‐bonded solid propellant formulations. It is observed that with increases in strain rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher strain rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with strain rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any strain rate from that at a reference strain rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K₂=(K₁‐H)×{ln(dε₂/dt)/ln(dε₁/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D₂=D₁×{(dε₂/dt)/(dε₁/dt)}^S. Evaluating constants “H” and “S” at different strain rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–strain curves, which are not attempted by any other researchers.     

Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data

Improvements to the Weissenberg rheogoniometer are necessary in order to measure the transient rheological properties of polymer melts correctly. The improvements reported concern the mechanical design, a new heating system, a new normal force measuring system, and additional equipment for the relaxation test. Reliable short-time results require sufficiently stiff torque and normal force springs, and a small radius and relatively large angles of the cone-and-plate gap. The behavior of the LDPE melt under test is “linear viscoelastic,” if shear rate or total shear are small: The relaxation modulus, the stress growth at the onset of constant shear rate, the stress relaxation after cessation of steady shear flow, and, in addition, dynamic shear data (from an oscillation viscometer) all show consistent results when correlated by means of formulae from the theory of linear viscoelasticity. Shearing in the nonlinear range with constant shear rate leads to pronounced maxima of the shear stress p₁₂ and of the first normal stress difference p₁₁ ? p₂₂ which occur at constant total shear, almost independent of shear rate. Comparison of shear and tensile data (from extensional rheometer) confirms the Trouton relation in the linear-viscoelastic case. In the nonlinear case, there is a “work softening” in shear and a “work hardening” in extension.     

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.     

Diffuse shear banded zones of blends of polystyrene and poly(2,6-dimethyl-1,4-phenylene oxide)

The formation, mechanical properties, thermal characteristics, and density of diffuse shear banded zones of polystyrene, poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), and their miscible blends were studied. A significant increase in density of 0.2 to 0.3 percent was found for the diffuse shear banded zones. Differential scanning calorimetry results revealed a volume recovery process that occurs below T_g for the diffuse shear banded zones. The post-yield-stress drop, anelastic shear strain within the zone, and anelastic tensile strain were all found to decrease with increasing PPO content in an identical manner. The sharp shear band to diffuse shear banded zone transition was related to chain mobility, molecular packing, and free energy as manifested in the post-yield-stress drop. The decrease in anelastic shear strain with increasing PPO content for the blends is possibly related to the beta transition and length between entanglements.     

Structure and deformation of an elastomeric propylene–ethylene copolymer

The elastic behavior of a propylene–ethylene copolymer was investigated. An initial “conditioning” tensile extension up to 800% strain resulted in an elastomer with low initial modulus, strong strain hardening, and complete recovery over many cycles. Structural changes that occurred in the low crystallinity propylene–ethylene copolymer during conditioning, and that subsequently imparted elastomeric properties to the conditioned material, were investigated. Thermal analysis, wide and small angle X‐ray diffraction, and atomic force microscopy measurements were performed at various strains during the conditioning process. Conditioning transformed crystalline lamellae into shish‐kebab fibers by melting and recrystallization. The fibers, accounting for only 5% of the bulk, were interconnected by a matrix of entangled, amorphous chains that constituted the remaining 95%. It was proposed that the shish‐kebab fibers acted as a scaffold to anchor the amorphous rubbery network. Entanglements of the amorphous chain segments acted as network junctions and provided the elastic response. The stress–strain response of materials conditioned to 400% strain or more was described by the classical rubber theory with strain hardening. The extracted value of M_c, the molecular weight between network junctions, was intermediate between the entanglement molecular weights of polypropylene and polyethylene. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 489–499, 2007     

Cold milling of polyisobutylene—A molecular weight distribution study

High molecular weight polyisobutylene samples were degraded by milling at 320 K. The degradation process was followed by determining the course of the changes in molecular weight distributions (MWD) that were obtained by gel permeation chromatography. After long milling times degradation stops or at least the rate of rupture becomes extremely small, the molecular weight approaching an apparent minimum value (M_m) of 0.4 × 10⁶. The rate of degradation decreases in the course of the first ½ to 1 hr from an initial value to one constant up to at least 3 hr if the maximum shear rate is higher than about 6 s^?1. At lower shear rates the rate of scission is constant from the start. When milling is stopped for 24 hr, high initial rupture rate is observed on resumption of milling at high shear rate, again followed by a drop in rate to the same value as before the interruption. The initial rates are independent of shear rate, whereas the subsequent constant rates are proportional to the rate of shear. These observations are discussed in terms of an equilibrium between the formation of multimolecular “rheological units” and the tendency, due to thermal motion, to form a homogeneous entanglement network. The MWDs are compared with those calculated from a model based on a given relation between probability of scission (P) and molecular weight and an assumed probability distribution (Q) of rupture site along the length of the polymer moelecules. The observed MWDs are incompatible with those calculated from models in which M_m = 0 or in which breakage near the center of the molecule is favored. They agree rather well with computed MWDs based on the assumptions that P ∞ MW and Q is the symmetrical beta function between points along the molecule M_m removed from the ends, where M_m is (0.4–0.5) × 10⁶. The mechanism of rupture appears to be the same for low and for high shear rates.     

A study on the dissolution rate of irradiated poly(methyl methacrylate)

A detailed study of the factors affecting the dissolution rate of poly(methyl methacrylate), PMMA, showed that the magnitude of the increase in the dissolution rate of irradiated PMMA could not be entirely attributed to the reduction in the molecular weight, MW. The formation of non-polymeric volatile fragments by radiation exposure, i.e., CO, CO₂H₂, CH₃OH and CH₄ causes a large increase in the solvent flux into the polymer matrix, thereby causing a large increase in the dissolution rate of exposed PMMA. The volatilization of these low molecular weight fragments cause an increase in the “excess free volume” (microporosity) of the glassy PMMA. The relative magnitudes of the contribution of the MW reduction and the formation of volatile matter on the increase in the solubility rate of the irradiated polymer were found to depend on the molecular size of the solvent, and also on the enthalpy of mixing.     

Ultradrawing behavior of one- and two-stage drawn gel films of ultrahigh molecular weight polyethylene and low molecular weight polyethylene blends

The ultradrawing behavior of gel films of plain ultrahigh molecular weight polyethylene (UHMWPE) and UHMWPE/low molecular weight polyethylene (LMWPE) blends was investigated using one- and two-stage drawing processes. The drawability of these gel films were found to depend significantly on the temperatures used in the one- and two-stage drawing processes. The critical draw ratio (λ_c) of each gel film prepared near its critical concentration was found to approach a maximum value, when the gel film was drawn at an “optimum” temperature ranging from 95 to 105°C. At each drawing temperature, the one-stage drawn gel films exhibited an abrupt change in their birefringence and thermal properties as their draw ratios reached about 40. In contrast, the critical draw ratios of the two-stage drawn gel films can be further improved to be higher than those of the corresponding single-stage drawn gel films, in which the two-stage drawn gel films were drawn at another “optimum” temperature in the second drawing stage after they had been drawn at 95°C to a draw ratio of 40 in the first drawing stage. These interesting phenomena were investigated in terms of the reduced viscosities of the solutions, thermal analysis, birefringence, and tensile properties of the drawn and undrawn gel films. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 149–159, 1998     

Rheological properties of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

Steady-state shear rheological properties of liquid crystalline solutions of four ethyl celluloses (ECs) were determined at a low shear rate (1 s^?1) and at relatively high shear rates by using two rheometers (cone-plate and capillary types), and were compared with those of liquid crystalline hydroxypropyl cellulose (HPC). The effect of molecular weight (MW) on the viscoelastic behavior was also determined. The viscoelastic behavior was also determined. The viscometric behavior of EC solutions was similar to that of HPC solutions: (1) with respect to temperature, the shear viscosity (η) at shear rate of 1 s^?1 exhibited a minimum (η_min) and a maximum (η_max), and the concentration–temperature superposition for η could be applied; (2) the behavior of η at relatively high shear rates as a function of shear rate or polymer concentration was typical of lyotropic liquid crystals. The MW dependence of η_min was greater than that of η_max for EC solutions. The behavior of the elastic parameters such as Bagley correction factor (v), entrance pressure drop (ΔP_ent), and die swell (B) at relatively high shear rates for EC solutions was essentially similar to that for HPC solutions: (1) the shear rate or stress dependence of the elastic parameters was greatly dependent on whether the polymer solution was in a single phase or biphase; (2) with respect to concentration the elastic parameters showed a maximum and a minimum and the maximum or minimum point for each parameter was not always identical to each other. η for the isotropic or fully anisotropic solutions at a given concentration (C) increased, whereas η for the solutions in the vicinity of the biphasic region showed a minimum, with respect to MW. The slope of η at a given shear rate vs. CM _w depended on shear rate, and this slope for the isotropic solutions appeared to be greater than that for fully anisotropic solutions. ΔP_ent and v at a given concentration showed either a monotonical increase or a maximum or minimum with MW, and this behavior was not fully consistent with that of η. B for the isotropic solutions increased and B's for both biphasic and fully anisotropic solutions were almost constant, with MW.     

Transition in deformation mechanism of aluminosilicate glass at high pressure and room temperature

Deformation experiments for 20(MgO or Na₂O)-20Al₂O₃-60SiO₂ glasses were performed in simple shear geometry at 1.5-5 GPa and room temperature. An abrupt change in the thinning rate and the turning of the birefringence azimuth at a shear strain of γ = 1-2 indicate a transition of deformation mechanism from uniaxial compression aided by densification to shear flow in the glasses. The high-dense magnesium aluminosilicate glass showed strain softening controlled by the rearrangement of the tetrahedral network. On the other hand, low-dense sodium aluminosilicate glass deformed by packing-induced flow associated with densification and via the rearrangement of the tetrahedral network at lower and higher strains, respectively. The transition of the deformation mechanism was triggered by the limitations of the densification of the tetrahedral network. The difference of deformation mechanism brought about higher strain in magnesium aluminosilicate glass than sodium aluminosilicate glass at the same stress condition. Easiness of remarkable deformation, which relaxed residual stress, and high deformability contributed to the high ductility of the MgO-aluminosilicate glass.     

Fracture toughness of adhesive joints. II. Temperature and rate dependencies of mode I fracture toughness and adhesive tensile strength

It has been known that adhesive strength shows temperature and rate dependencies reflecting visoelastic properties of an adhesive. Similarly, a critical strain energy release rate is expected to show temperature and time dependencies deformation and fracture of the adhesive occurs at the time of measurement of the critical strain energy release rate, which is a kind of fracture mechanical parameter for adhesive joints. The term “critical strain energy release rate” has usually been called “fracture toughness.” In this study, the critical strain energy release rate (G_IC) of the opening mode was called mode I fracture toughness. G_IC was measured over a wide range of temperatures and rates, and then a master curve was obtained by applying the temperature–rate superposition principle to the obtained data. Also, on the relation between G_IC and adhesive tensile strength is discussed. © 1995 John Wiley & Sons, Inc.     

An empirical model relating the molecular weight distribution of high-density polyethylene to the shear dependence of the steady shear melt viscosity

An empirical model has been developed to relate molecular weight distribution to the shear dependence of the steady shear viscosity in high-density polyethylene melts. It uses a molecular weight, M_c, which partitions molecular weights into two classes; those below M_c contribute to the viscosity as they do at zero shear, and those above M_c contribute to the viscosity as though they were of molecular weight M_c at zero shear. Each individual molecular weight species contributes on the basis of its weight fraction. M_c is proposed to be a unique function of the shear rate. Using this method of treating the molecular weight distribution, and the zero shear relation for relating η0 to molecular weight, the calculated steady shear viscosities at various shear rates for polyethylene samples of widely varying polydispersities agree well with experimental results. The model makes no judgment on the existence or importance of entanglements in non-Newtonian behavior since it has no specific parameters involving an entanglement concept. Use of the model suggests that for the samples studied, only the upper portion of the molecular weight distribution contributes toward the experimentally observed decrease of steady shear viscosity with shear rate for shear rates of up to 10,000 sec^?1. The lower molecular weight species are assumed to behave in a Newtonian manner.