The influence of molecular weight distribution on some properties of polystyrene melt

At high shear rates a steady state of shear flow with constant shear rate, constant shear stress, and constant recoverable shear strain is observed in the short-time sandwich rheometer after some few shear units already. The melt exhibits rather high elastic shear deformations and the recovery occurs at much higher speed than it is observed in the newtonian range. The ratio of first normal stress difference and twice the shear stress, being equal to the recoverable strain in the second-order fluid limit, significantly underestimates the true elastic shear strains at high shear rates. The observed shear rate dependence of shear stress and first normal stress difference as well as of the (constrained) elastic shear strain is correctly described on the basis of a discrete relaxation time spectrum. In simple shear a stick-slip transition at the metal walls is found. Necessary for the onset of slip is a critical value of shear stress and a certain amount of elastic shear deformation or orientation of the melt.

The melt viscosities of three low density polyethylenes of widely varying melt indices were studied as a function of temperature over a broad range of shear rates and shear stresses. Apparent viscosities at constant shear stress could be fitted adequately to a simple Arrhenius equation over the entire temperature range studied. However, pronounced curvature of the log ηa–1/T curves was observed for apparent viscosities at constant shear rate. The apparent activation energies for viscous flow at constant shear stress were found to decrease slowly with increasing shear stress and also to decrease with decreasing molecular weight. A temperature‐shear rate superposition was demonstrated to hold, and the shift factor dependence on temperature was determined.

The rate of breakage of duplex DNA molecules by laminar flow through a capillary has been studied. For λb2b5c DNA (molecular wt., M = 25 × 106) the point at which breakage occurs is normally distributed around the center of the molecule with a standard deviation of 12.5% of the molecular length. At constant shear stress or shear rate, the breakage rate is independent of ionic strength. Thus, shear induced local denaturation is not a rate limiting, preliminary step in breakage. In experiments at constant temperature with varying solvent viscosity (controlled by added sucrose) the breakage rate is a function of shear rate, not of shear stress. The rate of opening of hydrogenbonded circles into linear molecules by hydrodynamic shear is also shown to be a function of shear rate and not of shear stress. The breakage rate at constant shear rate is not greatly dependent on temperature. The shear rate required to achieve breakage is inversely proportional to M1,2. The breakage rate constant, k varies as a very high power of the shear rate; at 25°C, d In k/d In Gm ∼ 15; at 10°C, d In k/d In Gm ∼ 26, where Gm is the maximum shear rate at the capillary wall. The unexpected result that breakage rate is mainly dependent on shear rate, not shear stress, supports a model in which the DNA molecule is distorted with a driving force which depends on the hydrodynamic shear stress, ηG, but the rate limiting step is segment diffusion into a highly extended configuration. The characteristic time to achieve this configuration is proportional to solvent viscosity, η, hence the breakage rate is dependent on ηG/η or G, the shear rate.

Monodisperse and polydisperse polystyrenes of equal weight average molecular weight (Mw) are evaluated for melt flow behavior in an Instron capillary rheometer and for injection molding behavior in a 12 ounce in‐line reciprocationg screw injection molding machine. The influence of molecular weight distribution on the shape of the flow curves is deconstrated over a wide range of shear rate and temperature. The influence is also reflected in injection molding behavior as defined by pressure to fill or flash the mold at a given melt temperature. Studies of capillary rheometer data for correlation with injection moling beghavior indicate poor agreement when low shear rate viscosity data are used. Good agrement is foun using high shear rate viscosity data in the range 103 to 104 sec−1 Striking crossover points on melt rheology and injection colding area diagram curvs are found with the monodisperse and polydisperse polystyrenes of the same M These crossovers shift with melt temperature and make possible the determination of a “controlling shear rate” for the injection molding process. This is found to be 3500 sec−1 for short shot and 6200 sec−1 for flash with the ASTM test specimen mold used in this study.

Vinyl ester resins with varied acid values (11, 22, 32, 38, and 48 mg KOH/g solid) were prepared by reacting epoxy-novolac resin with methacrylic acid. The rheological behavior of these synthesized vinyl ester resin (VER) samples containing styrene as reactive diluent was studied using a Haake Rotovisco RV 20 viscometer. The apparent viscosity was found to be inversely proportional to the square root of the acid value in the temperature range of 25–40°C and at shear rates ranging from 100–800 sec−1. The zero-shear viscosity of these VER samples containing styrene (40% w/w) as reactive diluent decreased linearly with temperature. The activation energies for flow at constant shear stress (25–100 Pa) for a particular sample were found to be constant. The activation energy at constant shear rate decreases with the increase in the shear rate (50–400 sec−1). The activation energy at constant shear rate and shear stress decreased with the increase in the acid value. The viscosity of vinyl ester resin containing styrene as reactive diluent decreased almost 50 times with the increase in the concentration of reactive diluent from 30% to 100% (w/w of the resin).

The variation with shear of the concentration dependence of the reduced viscosity was studied in the system polystyrene‐toluene at 20, 40, and 60°C. The slope constant k′ was determined at constant shear stress k′T and at constant shear rate k′D; k′T was found to increase, k′D to decrease, with increasing shear. Alternatively, the concentration dependence was expressed in terms of Peterlin's effective viscosity. For this system the effective viscosity at constant shear stress was independent of shear but the effective viscosity at constant shear rate decreased with shear. The decrease in k′D, and in effective viscosity at constant shear rate with shear are attributed to molecular entanglement and an explanation is proposed for the observed differences in behaviour at constant shear stress and constant shear rate. In appendices a new formula for the calculation of viscosity ratios from the relative flow times is derived, and a procedure is outlined to compute intrinsic viscosities and limiting slope constants that will be free from absorption effects.

Melt rheology and extrudate swell properties of talc filled polyethylene compounds

The influence of molecular weight and molecular weight distribution on the melt rheological behavior of two polystrenes of approximately the same weight average molecular weight, but of widely different molecular weight distribution, was determined. Then, using a series of capillaries with different length‐to‐diameter ratios in an Instron Capillary Rheometer, the entrance correction methods of E. B. Bagley and the relationships of W. Philippoff and F. H. Gaskins, the recoverable shear strain (SR) in the melt at the capillary wall for these mono‐ and polydisperse polystyrenes was determined. Shear modulus (G) and normal stress (PN) were calculated using the relationships: G = τRC/SR and PN = 2τRC SR, where τRC is the corrected shear stress at the capillary wall. These are compared to values obtained using a Weissenberg Rheogonimeter. These two polystyrenes were also injection molded into an ASTM specimen mold over a wide range of stock temperature, using a 12 OZ. in‐line reciprocating screw injection press, and evaluated for mechanical property values. The effects of the elasticity parameters (SR G & PN) and their magnitude on the rheology, processability and mechanical properties of these polystyrenes are discussed.

Properties modification by blending polymers has been an area of immense interest. In this work, rheological and mechanical properties of poly(lactic acid)/polystyrene (PLA/PS) blends were investigated. PLA/PS blends in different ratios were prepared using a laboratory scale single screw extruder to obtain (3 mm) granules. Rheological properties were studied using a capillary rheometer and the Bagley’s correction was performed. True shear rate (γr), true shear stress (τr), and true viscosity (ηr) were determined, the relationship between true viscosity and (1/T) was studied for PLA70 blend and the flow activation energy at a constant shear stress (Eτ) and a constant shear rate (Eγ) was determined. The mechanical property measurements were performed at room temperature. Stress at break and strain at break were determined. The results showed that PLA/PS blend exhibited a typical shear-thinning behavior over the range of the studied shear rates, and the viscosity of the blend decreased with increasing PLA content. Also it was found that no equal-viscosity temperature exists between PLA and PS. The mechanical results showed immiscibility between PLA and PS in the blend.

A low-density polyethylene (LDPE) sample and an isotactic polypropylene (PP) sample were chemically cross-linked in molten state with dicumyl peroxide using liquid 1,2-polybutadiene (L-PB) as an auxiliary for PP. The effects of the degree of cross linking on their capillary flow properties have been studied. The apparent viscosity ηa of LDPE system at a constant shear rate rapidly increases until a gel content of 1.1 wt%, which is due to the increase in molecular weight, and after that log ηa linearly increases with the gel fraction, which is due to an action of gel particles as filler. The dependence of ηa on the gel fraction is more notable at lower shear rate. The value of ηa at a constant shear rate of PP system with an L-PB content of 5 phr drops until a gel content of about 15 wt%, and after that shows a maximum at a gel fraction of about 25 wt%, and gradually decreases with the gel content. For the system of an L-PB content of 20 phr, ηa gradually increases with the gel fraction. The end correction coefficient ν shows a maximum in a range of gel fractions from 15 to 40wt%. The flow activation energy at a constant shear rate, ΔHγ, of LDPE system decreases with the gel fraction and the flow activation energy at a constant shear stress, ΔHτ, shows a maximum at a gel fraction of about 70wt%.

A low-density polyethylene (LDPE) sample and an isotactic polypropylene (PP) sample were chemically cross linked in molten state with dicumyl peroxide using liquid 1,2-polybutadiene (L-PB) as an auxiliary for PP. The effects of the degree of cross linking on their capillary flow properties have been studied. The apparent viscosity ηa of LDPE system at a constant shear rate rapidly increases until a gel content of 1.1 wt. %, which is due to the increase in molecular weight, and after that log ηa linearly increases with the gel fraction, which is due to an action of gel particles as filler. The dependence of ηa on the gel fraction is more notable at lower shear rate. The value of ηa at a constant shear rate of PP system with an L-PB content of 5 phr drops until a gel content of about 15 wt. %, and after that shows a maximum at a gel fraction of about 25 wt. %, and gradually decreases with the gel content. For the system of an L-PB content of 20 phr, ηa gradually increases with the gel fraction. The end-correction coefficient ν shows a maximum in a range of gel fractions from 15 to 40 wt. %. The flow activation energy at a constant shear rate, ΔHγ̇, of LDPE system decreases with the gel fraction and the flow activation energy at a constant shear stress, ΔHτ, shows a maximum at a gel fraction of about 70 wt. %.

A concentric cyclinder dilatometer was designed and built to study the influence of shear on the crystallization kinetics of polymers. This instrument allows crystallization to be followed at both constant temperature and shear rate. Several samples of polyethylene oxide (Carbowax 4000, Carbowax 20‐M, and WSR‐205) were used. A low molecular weight fraction of the Carbowax 20‐M, as well as the unfractionated material, was crystallized under shear. The WSR‐205 was studied only in a mixture with Carbowax 4000. It was shown that the kinetics of crystallization of uncrosslinked melts of polyethylene oxide are altered by shear. The induction times for the appearance of crystallinity are shorter in the sheared systems than in the quiescent melts. The Avrami exponents are also higher for crystallization in sheared melts than in quiescent systems and increase with decreasing supercooling. The high values of the Avrami exponent are attributed to the disruption of crystalline aggregates into particles larger than the critical sized nucleus. These particles will persist in the melt and continue to grow spontaneously. A continuous infusion of growing particles into the melt occurs.At constant temperature and shear rate, the induction time of the crystallization curve is influenced by polymer molecular weight. In moderate to high molecular weight samples, the effect of shear becomes saturated at very low shear rates. Decreasing the molecular weight separates the crystallization curves. The curves from the higher shear rates appear at the shorter induction times. However, decreasing the molecular weight below that at the critical entanglement molecular weight allows the nucleation rate, strongly dependent upon the supercooling, to influence the relative positions of the sheared crystallization curves.

A concentric cylinder viscometer was used to measure high shear viscosities of polyisobutene solutions. Data were obtained in laminar flow from 20–100°C. and at shear rates from 5 × 102 to 8 × 105 sec.−1. Three polymer molecular weights, 4.0 × 104−2.2 × 106, in three concentrations from 11.5–49.2 wt.-% polymer were tested in cetane. The viscosity of cetane at all test temperatures was low and independent of shear rate up to 106 sec.−1. Therefore, variations in viscosity with shear were due totally to the effect of polymer. Viscosities of 11.5% solutions of low molecular weight polyisobutene, 4–6 × 104, approached limiting viscosities at both high and low rates of shear. Viscosity changed markedly between the limiting values as did the flow activation energy at constant shear rate, ΔE. At extremes of both high and low shear rate ΔE appeared to be insensitive to polymer molecular weight. Solutions containing the highest molecular weight and concentration of polyisobutene reached shear stresses for polymer degradation before a limiting high shear viscosity could be observed. For all solutions, ΔE was independent of temperature form 20–100°C. At low shear, ΔE increased with polymer concentration. At high shear, the concentration dependence was reversed, with the highest concentration having the lowest ΔE. A simple shear correlation was found to superimpose all data for which reduced viscosities could be derived. Reduced specific viscosities superimposed on a master curve when plotted against log (shear stress/T°K). The correlation covered data at all temperatures and concentrations for the two lower molecular weight polymer solutions.

The pressure dependence of viscosity of two nanocomposites with a polystyrene (PS) matrix that contains, respectively, multiwalled carbon nanotubes (MWCNTs) and graphene, was investigated. Two procedures were used: (a) Pressure-volume-temperature (PVT) results to obtain the pressure coefficient β0 for Newtonian viscosity and (b) measurements in a pressure chamber in a capillary rheometer, to obtain the pressure coefficient at constant shear rate, β′ and the pressure coefficient at constant shear stress, β″. PVT results revealed that the most significant differences between the samples concerned the variation of the glass transition with pressure, dTg/dP, which was concomitant with the number of polymer chains fixed on the surface of the nanofillers. Pressure chamber results showed that the pressure coefficient β″ was similar for PS and the nanocomposites, at the shear rates involved in processing. For the first time, the piezorheological complexity of nanocomposites was analyzed, together with the thermorheological complexity. PS/MWCNT nanocomposite was thermorheologically complex in the linear viscoelastic regime, but thermorheologically and piezorheologically simple in the shear thinning flow region. Nevertheless, PS/graphene nanocomposite was thermorheologically and piezorheologically complex in the linear viscoelastic regime and the shear thinning regime. This was due to the high capacity of graphene 2D platelets to retain polymer chains anchored to its surface.

Apparent flow activation energies evaluated from viscosity changes with temperature can be calculated in the non‐Newtonian region at either constant shear rate, E, or at constant shear stress, E. For many linear, amorphous polymere, it can be shown that E is independent of stress over the full range for which shear stress data tire reported. This conclusion also holds for solutions of several polymer types. Anomalous results are documented only for branched polyethylene. E decreases with shear in the non‐Newtonian region approaching a lower limit corresponding to the “power law” region. The relative changes in E with shear rate can be expressed in terms of reduced variables. The absolute change in E with shear rate can he used as a measure of polymer molecular weight distribution.