Viscosity coefficient zero shear

The empirical equation relating viscosity at zero-shear rate (t]o) to molecular weight for linear amorphous polymers is used to compare PLLA melts with those of conventional polymers. The form of this equation has been applied to the elasticity coefficient, Aq, to further quantify the effect of molecular weight on the elasticity (Cooper-White and Mackay 1999) ... 

As a result, we find for sols that the divergence of the above zero shear viscosity rj0 and of two other linear viscoelastic material functions, first normal stress coefficient and equilibrium compliance 7°, depends on the divergence... 

We can also calculate other viscoelastic properties in the limit of low shear rate (linear viscoelastic limit) near the LST. The above simple spectrum can be integrated to obtain the zero shear viscosity 0, the first normal stress coefficient if/1 at vanishing shear rate, and the equilibrium compliance J... 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

In Sect. 6.3, we have neglected the intermolecular hydrodynamic interaction in formulating the diffusion coefficients of stiff-chain polymers. Here we use the same approximation by neglecting the concentration dependence of qoV), and apply Eq. (73) even at finite concentrations. Then, the total zero-shear viscosity t 0 is represented by [19]... 

Another often used representation of the viscoelastic flow behavior utilizes normal stress coefficients P/ = Ni/y. Figure 10 depicts flow curves of a family of PAA/water solutions differing in concentrations and therefore in their viscosities. Normalized by the zero-shear viscosity fiQ and by a constant shear rate /q shear stress value of to= 1 N/m they produce master curves for viscosity and the normal stress coefficient. The preparation... 

Although shear rate effects are more pronounced in good solvents, the intrinsic viscosity decreases with shear rate even in 0-solvents, where excluded volume is zero (317,318). The Zimm model employs the hydrodynamic interaction coefficients in the mean equilibrium configuration for all shear rates, despite the fact that the mean segment spacings change with coil deformation. Fixman has allowed the interaction matrix to vary in an appropriate way with coil deformation (334). The initial departure from [ ]0 was calculated by a perturbation scheme, and a decrease with increasing shear rate in 0-systems was predicted to take place in the vicinity of / = 1. 

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). 

The use of effective friction coefficient Qe for M > Mc implies that all relaxation times contributing essentially to the zero shear viscosity [cf. eq. (3.37)], are increased by the same factor Qe. One can also say that for M > M friction factor f is replaced by an effective friction factor CQe-... 

Here we have three parameters r/o the zero-shear-rate viscosity, Ai the relaxation time and A2 the retardation time. In the case of A2 = 0 the model reduces to the convected Maxwell model, for Ai = 0 the model simplifies to a second-order fluid with a vanishing second normal stress coefficient [6], and for Ai = A2 the model reduces to a Newtonian fluid with viscosity r/o. If we impose a shear flow,... 

Here are the components of the stress tensor as defined in rheology Tn—T22 is the first normal stress difference and T21 the shear stress, equal to Nt and rxsh, respectively. Hence, from dynamic mechanical measurements it is possible to determine the zero shear first normal stress coefficient Fq0 and zero shear viscosity y0. 

Due to difficulties in measuring the zero-shear viscosity of such high molecular weight polymers, and thus deducing the monomeric friction coefficient from Graessley s uncorrelated drag model [43], the following equation adapted from the modified Rouse theory has been applied [8]. 

These coefficients, along with the shear viscosity rj = cyii/y, often approach constant values at low shear rates these are called the zero-shear values, rjo, 4>i,o, and 4 2,o- Figure 1-9 shows for a polyethylene melt that the zero-shear constant values of rj r]o and 4 1 — 4/1,0 are approached at low shear rates. For a viscoelastic simple liquid with fading memory, the zero-shear values of the viscosity and first normal stress coefficient are related to the zero-frequency values of the dynamic moduli by... 

Figure 7.10 The effect of poly-isobutylene (PIB) concentration on the zero-shear viscosity of the suspensions described in Fig. 7-9. The lines were calculated assuming / r,o(0) = K exp(—atTniin/A er), with values of the second virial coefficient A2 of 6 X 10 8 X 10 and 10 ". (From Buscall et al. 1993, with permission from the Journal of Rheology.)...

It seems that Chappelear [1964] was the first who applied this technique to measure the interfacial tension coefficient of polymer blends. Further refinements have been published [Elemans, 1989 Elemans et al., 1990 Elmendorp, 1986]. The method is simple, not requiring special equipment, but the zero-shear viscosity of the investigated polymers at the processing temperature must be known. Typical results obtained this method are shown in Table 4.3. 

Vrc y,y r 11 o - volume fraction of dispersed and matrix phase, respectively - volume fraction of the crosslinked monomer units - volume fraction of phase i at phase inversion - maximum packing volume fraction - percolation threshold - shear strain and rate of shearing, respectively - viscosity - zero-shear viscosity - hrst and second normal stress difference coefficient, respectively... 

Ohshima, A., Yamagata, A., Sato, T, and Teramoto, A., Entanglement effects in semiflexible polymer solutions 3. Zero-shear viscosity and mutual diffusion coefficient of poly(n-hexyl isocyanate) solutions. Macromolecules, 32, 8645-8654 (1999). 

Phillies, G. D. J., Self-consistency of hydrodynamic models for the zero-shear viscosity and the self-diffusion coefficient. Macromolecules, 35, 7414—7418 (2002a). 

---