Determining molecular weight distributions from viscosity versus shear rate flow curves

Using the theoretical approach of Bersted and Slee, we developed a technique of determining the molecular weight distribution (MWD) from the viscosity vs. shear rate flow curve. Each molecular weight fraction was assumed to have a characteristic deformation rate. Below this rate, the viscosity was equal to the zero shear value. Above this rate, the viscosity was reduced to the zero shear viscosity of the molecular weight characteristic of the higher rate. The relationship between the weight fraction of each component and the viscosity/rate curve was derived from these assumptions. The flow curves of very well-characterized polystyrenes were determined. MWDs were then calculated using the BerstedSlee approach and compared with results from size exclusion chromatography. Comparisons were also made with the results of Malkin and Teishev. They used the same assumptions as Bersted and Slee but chose a different methodology for determining the MWD.     

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride)

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride) has been studied using a capillary rheometer. The elongational viscosity was evaluated based on Cogswell's method with two types of capillaries: capillary length (L)/capillary diameter (D) = 10 mm/1 mm and L/D = 0 mm/1 mm. We used the ratio P₀/P_L that indicates the contribution of elongational flow to the total flow involving both the shear and elongational flows. P_L and P₀ are the pressure losses in the capillary and the converging flows, respectively. P₀/P_L increased with molecular weight and shear rate. This corresponds to decreasing the number of entanglements of molecular chain under a large displacement, especially high shear. Thus, we suggest using P₀/P_L as the parameter of the entanglement interaction on the molecular chain under a large displacement. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2381–2384, 1999     

The effect of shear rate on the molecular weight determination of acrylamide polymers from intrinsic viscosity measurements

The rheological response of dilute solutions of high molecular weight polyacrylamides at low shear rates has been measured using a capillary viscometer that provided for a fivefold variation in shear rate at each concentration. The non-Newtonian effects were found to be significant for polyacrylamides with number-average molecular weights exceeding 10⁶. The molecular weight average–intrinsic viscosity relationship most widely used in the literature, [η] = 6.80 × 10^?4M , was found to be valid when [η] was measured at high shear rates where the polymer solutions approached Newtonian behavior. A new relationship was developed relating M _n to the intrinsic viscosity extrapolated to zero shear rate.     

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.     

Intrinsic viscosity dependence on polymer molecular weight and fluid temperature

Experimental solution intrinsic viscosity responses to temperature and polymer molecular weight variations were used to test the modeling capability of a simplified intrinsic viscosity equation. The multiple linear equation contains three parameters that are related to the thermodynamic properties of a polymer solution. Simple linear regression was used to produce an intrinsic viscosity equation containing unique fitted parameters for each of three solutions. These parameters describe the polymer coil size at unperturbed conditions and the polymer coil expansion capabilities of the solvent as a function of fluid temperature and molecular weight. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2831–2835, 2003     

A generalized correlation for the viscosity of dextrans in aqueous solutions as a function of temperature,concentration, and molecular weight at low shear rates

An expression relating the viscosity of dextran solutions to polymer concentration (c), molecular weight (M), and temperature (T) has been derived from experimental data in the following ranges: 5 < c < 25% (wt/wt), 298.2 < T < 363.2 K, and 71,500 < M < 531,000 g/mol. The experimental work was based on capillary viscosimeters. Thermodynamic data (entropy and energy of activation for the viscous flow of a Newtonian fluid) are also presented as a function of polymer concentration for the three molecular weights studied. This thermodynamic analysis suggests that dextrans in aqueous solutions behave as flexible polymers. Application of our expression to existing viscosity data for ethylene/vinylacetate copolymers in paraffin has resulted in improved goodness of fit with respect to established correlations.     

The viscosity of concentrated polymer solutions containing low molecular weight solvents

The zero shear rate viscosities of polystyrene/ethylbenzene solutions having polymer weight fractions ranging from 0.5 to 1.0 have been measured using a novel sealed rheometer cell over a temperature range of 50 to 200°C. The concentration and temperature dependence of the solution viscosity has been found to be well described by the relation η₀ = K c^aM_w ^3.4ζ(c, T) where the monomeric friction coefficient ζ is determined by the free volume of the solution. Following the procedure of Berry, the free volume parameters, α_f(c)/γ and T_∞ (c), and the fractional free volume, f(c,T)/γ, have been determined. After using these parameters to account for the concentration dependence of the friction coefficient, the concentration exponent a has been evaluated and found to be in reasonable agreement with the value of 3.4 obtained by Berry and Fox for other polymer/solvent systems. A comparison of the relative conributions made by the friction coefficient and the term c^3.4 to the overall concentration dependence of the viscosity of these highly concentrated solutions shows the friction coefficient to be the dominant factor     

Molecular weight and temperature dependence of intrinsic viscosity of polymer solutions

The molecular weight and temperature dependence of the intrinsic viscosity of polymer solutions have been predicted by combining the calculated radius of gyration, R_G, and hydrodynamic radius, R_H, with either the static empirical approach of Mandelkern—Flory or the dynamic argument of Weill—des Cloizeaux. It is found that experimental results can be successfully represented by the dynamic model for a range of five decades of molecular weight and temperature. The discrepancy between the calculated and experimental data at $\text{N ? N}{}_{\mathrm{т}}$ reveals the crudeness of the discontinuity at the temperature cut-off assumed by current temperature blob theory.     

Shear rate dependence of the viscosity of cellulose nitrate solutions in the dilute concentration regime revisited

A detailed rheological study of cellulose nitrate in ethylacetate had been carried out in the dilute concentration (c) regime, covering a degree of polymerization (DP) range between 300 < DP_η < 7000 and shear rates ($ \dot \gamma $) between 100 s^?1 < $ \dot \gamma $ < 2000 s^?1. The results show a strong dependence of the transition Newtonian to non-Newtonian behavior on the three variables $ \dot \gamma $, DP, and c, similar to that found recently on solutions of synthetic polymers. Emphasis has been put on the critical concentrations corresponding to the standard shear rate 1000 s^?1 to correspond to the standard conditions ($ \dot \gamma $ ? 1000 s^?1; 0.3 < [η] · c < 0.6; DS = 2.90 ± 0.02) proposed for the determination of the intrinsic viscosity [η] of cellulose nitrates. It is shown that solutions with concentrations adjusted according to the above given conditions still exhibit Newtonian behavior, up to the highest range of DP. It follows, therefore, that applying the standard conditions, an extrapolation to $ \dot \gamma $ = 0 as has been proposed often for the intrinsic viscosity determination of cellulose nitrate is not advisable and results in considerable error. Considering the relationship between [η] and DP, the present results indicate that the decrease of the exponent ( a ) from a = 1.0 to a = 0.76, taking place above a DP ? 1000, is not a consequence of the applied shear rate but rather of the molecular properties of the solutes themselves.     

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.     

Polymer molecular weight,zero shear viscosity,steady state compliance and binary blending law

Viscoelastic properties of binary blends of polystyrenes with a narrow distribution of low and high molecular weights (M₂ > M₁ > M_c) were examined. By combining the theoretical work of Montfort et al., Kurata, and Schausberger, a binary blending law was developed and was used to calculate the zero shear viscosity and steady state compliance of the blend of two monodisperse polymers. The blending law was also used to calculate the molecular weight distribution of a polydisperse polymer. The calculated results were compared with those obtained from viscoelastic ] and GPC measurements, with good agreement.     

Relationship of intrinsic viscosity of polymer solutions to molecular weight

An equation derived by Han relating intrinsic visocity to molecular weight of a polymer has been fitted to experimental data over a large range of molecular weight. Excellent fits were obtained although the Mark-Houwink equation did not fit the data over the complete molecular weight range. Han's equation may be fit to intrinsic viscosity data over a moderate range of molecular weight, and is shown to then accurately predict the intrinsic viscosities for molecular weights outside this range. A method is given to compute the two parameters of Han's equation from the Mark-Houwink parameters of a polymer in a solvent.     

Low shear viscosity and crystallization in dilute solutions of polymers at high pressures: Falling body viscometry of high molecular weight polyethylene solutions

A specially designed falling body viscometer has been used to obtain low shear viscosities of dilute solutions of high molecular weight polyethylene in decalin and for detecting phase transitions at high pressures. The method provides valuable rheological data at pressures that correspond to those I lubrication and some extrusion processes. In addition, the method enables detection of phase transitions, such as crystallization, that result in detectable changes in rheology. The influence of pressure as high as 0.6 GPa ( ～ 80.000 psi) is illustrated here through a study of crystallization, with verification from light scattering and calorimetry.     

Comments on the accuracy of zero shear intrinsic viscosity of high molecular weight polyacrylamide

The intrinsic viscosity of a polymer is traditionally measured with a capillary tube viscometer where the shear rate range is moderately high. Such method is valid when the polymers are non-ionic and have low to moderate molecular weight. The viscosity-shear rate curves obtained for dilute aqueous solutions of two high molecular weight polyacrylamides using two rotational viscometers indicate a strong shear-dependent viscosity in the medium to high shear rate regions. The zero shear intrinsic viscosity of the polymers determined by extrapolation from the high shear rate region to the zero shear condition may result in large errors. Its implication in predicting the molecular weight of polymers using the Mark-Houwink-Sakurada equation is discussed. A rheological equation for intrinsic viscosity as a function of shear rate is proposed.     

Coal-derived asphaltenes: effect of phenol content and molecular weight on viscosity of solutions

Phenol contents and molecular weights of coal-derived asphaltenes are shown to affect the viscosity of their solutions. Phenol contents were determined by non-aqueous titrimetry. Intermolecular aggregation probably involving hydrogen bonding is a prime factor in the increase in viscosity found with increased asphaltene concentration in a reference solvent system composed of an $\text{88}\text{12}$ ($\text{wt}\text{wt}$) mixture of 1-methylnaphthalene and o-cresol. Aggregation effects are greater for those asphaltenes with relatively higher phenol contents. Asphaltenes were separated into fractions of different polarity by adsorption chromatography. The more polar subfraction was found to increase viscosity in the reference solvent to a greater extent than the less polar subfraction. The logarithmic viscosity numbers of solutions of the asphaltenes and their subfractions are correlated by a linear combination of molecular weights and phenol contents. It is concluded that an effective means of reducing the viscosity of coal-derived liquids would be to reduce the phenol content of the asphaltene fraction.