Viscosity measurements zero-shear

We studied the dependence of spin modes on viscosity in the HDDA/persulfate system. Determining the viscosity is complicated by the shear-thinning behavior of silica gel suspensions. Figure 6 shows the apparent viscosity vs. shear rate for different percentages of silica gel in HDDA. The linear stability analysis assumes Newtonian behavior so we need to estimate the viscosity at zero shear, which is something we can not reliably estimate with our viscometer. We used the viscosities at the lowest shear rate we could measure and recognize that we are underestimating the true value. Fortunately, this does not affect the qualitative trends. 

A viscoelastic shift factor, as, can be found from the ratio of the experimentally measured zero shear rate viscosity (at test conditions of P, T, and SCF cOTicentratiOTi), to the experimentally measured zero shear rate viscosity (at some reference conditions of Fref> Iref, and reference SCF concentration). Once as is determined experimentally, a master curve can be constmcted by plotting ij/as vs. as 7 where tj is the measured viscosity and y is the measured shear rate. If the fractional free volume, /, is estimated from an equation of state as/ = 1 — pjp, where p is the mixture density and p is the mixture close-packed density, then the shift factor due to the presence of the SCF can be calculated from Eq. (18.3), provided the constant B is known. Experimentally, B for SCF-swoUen polymers has been found to be near unity [130,131], in agreement the universal constants of the WLF equation [132] for the temperature dependence of pure polymers. 

These data are presented in Table 3. What is immediately evident from these data is that the closest correlation occurred when particle settling rates were compared to the apparent viscosity measured at shear rates of 1 sec . The xanthan polymer solution showed a greater ability to suspend the solids and had a higher apparent viscosity in the low shear rate range. In contrast the HEC solution had higher apparent viscosities at shear rates above 10 sec but exhibited lower particle suspension properties. The dependence on low shear rate apparent viscosity is not entirely unexpected. Roodhart has shown emperically that the zero shear viscosity must be factored into a Stokes law type calculation before settling velocities can be calculated for HPG solutions. Thus, reliance on viscosity measurements at the customary shear rates would not have selected the more efficient fluid for particle suspension. 

Zero Shear Viscosity (ZSV) is the viscosity measured in shear deformation at a shear rate approaching zero. This parameter is an indicator of two polymer characteristics (Phillips and Robertus 1996) ... 

The viscosity of all thermoplastic melts is non-Newtonian, i.e., the viscosity is a function of the shear rate at which it is tested. For this reason great care must be taken to define deformational conditions when discnssing viscosities. For purposes of comparison the viscosities of polymers are Irequently quoted in terms of their apparent viscosity at zero shear rate. Zero shear viscosity is not a directly measurable value, but it can be obtained by extrapolation Irom observed viscosities over a range of finite shear rates. 

We are interested in viscosity and elastic modulus which are stationary quantities. Let us call T, the longest relaxation time of the polymeric system. In order to measure zero shear viscosity and stationary elastic modulus, the experiment must be performed at oTr < 1 and wTr < 1, where a is the shear rate and m the frequency. 

This real difficulty of measuring zero shear viscosity near the gel point was taken into consideration by Gordon and Roberts . In this work (p. 686), the Tc value obtained by extrapolation of the modulus and the one obtained by extrapolation of the viscosity are compared Tc from back-extrapolation of the modulus is generally lower than the value from viscosity. This small discrepancy is significant and intelligible because shear rate effects will raise the viscometric gel point but lower the gel point from modulus data . ... 

Rheological determinations are destructive of the structures they measure for this reason they do not portray the actual structure of the dispersion at rest. Accordingly, various methods have been devised for extrapolating to zero the results of measurements at various shear rates. The most useful one has been the conversion of viscosities to fluidities at various shear rates and the extrapolation of the resulting nearly linear relationship to zero shear, as shown in Figure 7. Sometimes a power of the shear rate, D, provides a better distinction between a sol (essentially a liquid) and a gel (essentially a solid), as shown in the figure, but the difference between a finite intercept (sol) and zero fluidity (gel) is largely fictitious because of the dependence of the intercept on the exponent n. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The zero-shear viscosities measured in toluene solution are listed in Table 1 together with the values of r 0(theor) calculated from Eq. (14). The percentage deviation of the theoretical from the measured viscosities is given in column 8. 

The power of this technique is two-fold. Firstly, the viscosity can be measured over a wide range of shear rates. At the tube center, symmetry considerations require that the velocity gradient be zero and hence the shear rate. The shear rate increases as r increases until a maximum is reached at the tube wall. On a theoretical basis alone, the viscosity variation with shear rate can be determined from very low shear rates, theoretically zero, to a maximum shear rate at the wall, yw. The corresponding variation in the viscosity was described above for the power-law model, where it was shown that over the tube radius, the viscosity can vary by several orders of magnitude. The wall shear rate can be found using the Weissen-berg-Rabinowitsch equation ... 

Measurement of the equilibrium properties near the LST is difficult because long relaxation times make it impossible to reach equilibrium flow conditions without disruption of the network structure. The fact that some of those properties diverge (e.g. zero-shear viscosity or equilibrium compliance) or equal zero (equilibrium modulus) complicates their determination even more. More promising are time-cure superposition techniques [15] which determine the exponents from the entire relaxation spectrum and not only from the diverging longest mode. 

The melt flow index is a useful indication of the molar mass, since it is a reciprocal measure of the melt viscosity p. p depends very strongly on 77 ( ) (doubling of results in a 10.6 times higher 77 ). This relation is valid for the zero-shear viscosity the melt index is measured at a shear stress where the non-Newtonian behaviour, and thus the width of the molar mass distribution, is already playing a part (see MT 5.3.2). The melt index is a functional measure for the molar mass, because for a producer of end products the processability is often of primary importance. 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The structure can be established from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often in a Newtonian region. This zero-shear viscosity, T 0, is related direcdy to the molecular weight of polymer melts and concentrated polymer solutions. 

Yield stress values can depend strongly on filler concentration, the size and shape of the particles and the nature of the polymer medium. However, in filled polymer melts yield stress is generally considered to be independent of temperature and polymer molecular mass [1]. The method of determining yield stress from flow curves, for example from dynamic characterization undertaken at low frequency, or extrapolation of shear viscosity measurements to zero shear rate, may lead to differences in the magnitude of yield stress determined [35]. 

The rheological properties of gum and carbon black compounds of an ethylene-propylene terpolymer elastomer have been investigated at very low shear stresses and shear rates, using a sandwich rheometer [50]. Emphasis was given to measurements of creep and strain recovery at low stresses, at carbon black flller contents ranging between 20 and 50% by volume. The EPDM-carbon black compounds did not exhibit a zero shear rate viscosity, which tended towards in-Anity at zero shear stress or at a finite shear stress (Fig. 13). This was explained... 

The intimate contact data shown in Figure 7.16 were obtained from three-ply, APC-2, [0°/90o/0o]7- cross-ply laminates that were compression molded in a 76.2 mm (3 in.) square steel mold. The degree of intimate contact of the ply interfaces was measured using scanning acoustic microscopy and image analysis software (Section 7.4). The surface characterization parameters for APC-2 Batch II prepreg in Table 7.2 and the zero-shear-rate viscosity for PEEK resin were input into the intimate contact model for the cross-ply interface. Additional details of the experimental procedures and the viscosity data for PEEK resin are given in Reference 22. 

The zero-shear viscosity r 0 has been measured for isotropic solutions of various liquid-crystalline polymers over wide ranges of polymer concentration and molecular weight [70,128,132-139]. This quantity is convenient for studying the stiff-chain dynamics in concentrated solution, because its measurement is relatively easy and it is less sensitive to the molecular weight distribution (see below). Here we deal with four stiff-chain polymers well characterized molecu-larly schizophyllan (a triple-helical polysaccharide), xanthan (double-helical ionic polysaccharide), PBLG, and poly (p-phenylene terephthalamide) (PPTA Kevlar). The wormlike chain parameters of these polymers are listed in Tables... 

Fox,T.G., Allen, V.R. Dependence of the zero-shear melt viscosity and the related friction coefficient and critical chain length on measurable characteristics of chain polymers. J. Chem. Phys. 41, 344-352 (1964). 

As pointed out in the paragraph after eq. (3.43), the dimensionless quantity / can be interpreted as a reduced shear stress or also, when the measured ("Newtonian ) zero shear viscosity r]y of the solution is used in eq. (3.43), as a reduced shear rate. 

In dynamic oscillatory measurements, however, higher order relaxation times (i.e. shorter times), which do not noticeably contribute to the zero shear viscosity, can become of importance when the frequency is increased. For this purpose, Ferry and co-operators 123, 14) proposed the following, rather crude approximation of the relaxation times [cf. eq. (3.50)] ... 

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