Shear thinning polydispersity

A numerical implementation of this approach can be generalised to include the polydispersity of the polymer. As polydispersity is increased the power law of — 0.8181... reduces. The onset of shear thinning, where Tn y 1 — 1, results in a slightly lower viscosity for polydisperse systems at this rate. So far we have neglected the origin of the characteristic time for the system which we would like to describe in terms of the chemical... 

This can be clearly seen in the comparison of viscosity functions of polystyrene 1 and polystyrene 2. If we add a very high-molecular weight component to polystyrene 2, we obtain polystyrene 3. It is therefore evident that the bimodal molar mass distribution causes the shear thinning to increase further, although not as far as the polydispersity change of the molar mass distribution between polystyrene 1 and polystyrene 2. In the case of higher shear rates, all flow curves proceed to similar viscosity functions. 

Experimentally, melts of low polydispersity that do not overtly spurt, slip, or succumb to other material instabilities will typically show steeply decreasing values of the viscosity and first normal stress coefficient in the shear-thinning region. Menezes and Graessley (1980) reported that t] oc y ° y i- at large y. These dependencies... 

A very recent move to apply the structures emerging from molecular rheology to non-linear models of polydisperse complex-architecture melts has met with considerable success. The simple insight that the stress is a composite, not a structural, variable, with orientational and scalar components of different relaxation times, vastly improves the ability to model LDPE melts quantitatively. It also explains how such melts may be shear thinning yet extension-hardening. 

The quotient (r /r o), which indicates the magnitude of shear thinning effect with increasing y, can be estimated quite well as a function of the Weissenberg number (Nwg) and the polydispersity [7], N yg is the product of a characteristic time scale for the polymer with y, and can be approximated by Equation 13.27 where p is the polymer bulk density at the temperature of calculation. (The density must be expressed in g/m3 rather than g/cc in Equation 13.27 for consistency with the units used for the other quantities entering this equation.) Since the polydispersity Mw/Mn enters Equation 13.27, r depends on the polydispersity both indirectly via the dependence of Ny/g on Mw/Mn and directly. 

The bimodal model has also been applied to polydisperse suspensions (Probstein et al. 1994), which in practice generally have particle sizes ranging from the submicrometer to hundreds of micrometers. In order to apply the bimodal model to a suspension with a continuous size distribution, a rational procedure is required for the separation of the distribution into fine and coarse fractions. Such a procedure has not been developed so that an inverse method had to be used wherein the separating size was selected which resulted in the best agreement with the measured viscosity. Again, however, the relatively small fraction of colloidal size particles was identified as the principal agent that acts independently of the rest of the system and characterizes the shear thinning nature of the suspension viscosity. 

The activation of certain ansa-metallocenes to solid acid supports produces polyethylene with relatively low levels of long-chain branching, which is sufficient to moderately increase the molecular weight distribution of the polyethylene, and improve the polymer processability, but not be detrimental to the properties of the finished fabricated product. Consequently, low levels of LCB improve the shear-thinning behavior of the molten polyethylene, which resolves the processing disadvantage of polyethylene with a polydispersity index of 2. 

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