Melt viscosity zero shear

From the correspondence between the calculated and experimental curves we can extract other information. For example the temperature (ca. 72 °C) at which x = 1/2 is shown on Fig. 14b. Above this temperature no more chains break at this temperature and higher, the craze growth is disentanglement dominated. We can use the fact that = 1/2 and Eq. (19) to extract a value for the corresponding to disentanglement of chains at the void interface under these conditions this value is 1.5 x 10" N-s/m, a value that is only reached for polystyrene melts (from zero shear viscosity or diffusion measurements) at a temperature of about 120 °C, or 20° above T. ... 

Figure 9.29 Behavior of melt viscosity and shear modulus near the gel point in a cross-linking polymerization as a tunction of reaction time. The steady shear viscosity goes to infinity, while the equilibrium shear modulus rises from zero, eventually reaching a plateau for the fully reacted material.

The viscosity of polymer melts at zero shear is a function of the weight average molecular weight, M, where the molecular weight distribution (MWD) is narrow ... 

Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight. 

Figure 8.6. Relationship between molecular weight and zero shear rate viscosity for melts of linear...

Typical of thermoplastics (see Chapter 8) the melts are pseudoplastic and also in common with most thermoplastics the zero shear rate apparent viscosity of linear polyethylene is related to the weight average molecular weight by the relationship... 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

The results of Equation (3.56) are plotted in Figure 3.14. It can be seen that shear thinning will become apparent experimentally at (p > 0.3 and that at values of q> > 0.5 no zero shear viscosity will be accessible. This means that solid-like behaviour should be observed with shear melting of the structure once the yield stress has been exceeded with a stress controlled instrument, or a critical strain if the instrumentation is a controlled strain rheometer. The most recent data24,25 on model systems of nearly hard spheres gives values of maximum packing close to those used in Equation (3.56). 

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]. 

For the unfilled polystyrene melt at low elongational rates a constant value of Tjg is achieved given by three times the zero shear viscosity according to Trou-... 

Mendelson and co-workers (56) have studied the extrapolated zero shear-rate melt viscosities of linear HDPE and branched LDPE found that while the LDPE fractions could have either lower or higher viscosities than linear polymers of the same MW, results for the LDPE fractions could be reduced to the same curve by taking not Mw but gMw as the independent variable, where... 

Mendelson (169) studied the effect of LCB on the flow properties of polyethylene melts, using two LDPE samples of closely similar M and Mw plus two blends of these. Both zero-shear viscosity and melt elasticity (elastic storage modulus and recoverable shear strain) decreased with increasing LCB, in this series. Non-Newtonian behaviour was studied and the shear rate at which the viscosity falls to 95% of the zero shear-rate value is given this increases with LCB from 0.3 sec"1 for the least branched to 20 sec"1 for the most branched (the text says that shear sensitivity increases with branching, but the numerical data show that it is this shear rate that increases). This comparison, unlike that made by Guillet, is at constant Mw, not at constant low shear-rate viscosity. 

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). 

Originally, Fox and Flory (121) found that the zero shear viscosity of polymer melts increases with the 3.4-th power of the molecular weight. Bueche (122) has shown that this relationship holds only above a certain critical molecular weight Mc which depends on the structure of the polymer chain. Below Mc the zero shear viscosity is found to depend on a significantly lower power of molecular weight. A theoretical interpretation of these facts has been given by the latter author on the basis of the free-draining model (Section 3.4.1.). 

---