Long Zero-shear viscosity

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. 

If the molecules are now joined to form chains ti units long, the jump frequency per chain is K0n, while the jump distance (displacement in the direction of the jump) of the center of gravity of the chain is X/ti. The zero shear viscosity... 

Zero shear viscosity (which can be related to weight average molecular weight and long chain branching). 

If rj is independent of the shear rate y a liquid is called Newtonian. Water and other low molecular weight liquids typically are Newtonian. If rj decreases with increasing y, a liquid is termed shear thinning. Examples for shear thinning liquids are entangled polymer solutions or surfactant solutions with long rod-like micelles. The zero shear viscosity is the value of the viscosity for small shear rates ij0 = lim,> o tj y). The inverse case is also sometimes observed rj increases with increasing shear rate. This can be found for suspensions and sometimes for surfactant solutions. In surfactant solutions the viscosity can be a function of time. In this case one speaks of shear induced structures. 

The motion of polymers in concentrated solution and bulk is of major theoretical and practical concern. For example, the strong dependence of zero-shear viscosity on molecular weight (approximately the 3.4 power) and the marked decrease of viscosity 1) with shear rate y not only bespeak some of the unusual properties of long-chain molecules but also are of essential importance in virtually every processing operation. Yet the reasons for these unusual behaviors have become clear only recently. The reptation con-... 

These laws are in very good qualitative agreement with the large number of available experimental data on the dynamic behaviour of linear flexible entangled polymers, but quantitative departures still remain between the experiments and the predictions, as for example the fact that the exponent of the power law which characterises the variation of the zero shear viscosity with the molecular weight is observed to be 3.3 or 3.4 [3, 6] rather than the predicted value 3. These deviations have lead to a long controversy on the validity of the reptation model, and have stimulated a series of experimental and theoretical investigations to try to understand the limitations of this model and to propose the necessary modifications to obtain a better description of the dynamic properties of liquid polymers [7 to 22]. 

According to Doi-Edwards theory, the reptation of the long chains will occur in a tube whose diameter a veuies as Thus the number of monomers between entanglements will scale as < ) . Accordingly, the reptation time x (relation 3-14) should be proportional to (]) as a first approximation, the zero-shear viscosity tio and the steady-state compliance J should respectively scale as [Pg.133]

A frequently encountered behaviour for longer chain surfactants, say Cu or above, is that at low or intermediate concentrations the viscosity starts to increase rapidly with concentration. This is exemplified in a plot of the (zero-shear) viscosity versus concentration in Figure 19.20. Here, the micelles grow with increasing concentration, at first to short prolates or cylinders and then to long cylindrical or thread-like micelles (Figure 19.21). 

For long times the integral corresponds to the zero shear viscosity rjo, i.e.,... 

The zero-shear viscosity t]o of linear polymers scales exponentially with molecular weight [102] above the critical chain length Me, but LCB polymers repeatedly deviate from this dependency. In comparison to linear polymers of similar M, polymers with low levels of LCB exhibit enhanced zero-shear viscosity values and, in a qualitative sense, C-NMR-based LCB content often [85, 92, 93], but not always [100], correlates well with the viscosity increase. For long-chain branched LDPE, the t]q in comparison to linear polyethylene of similar is lower [103, 104]. A zero-shear viscosity t]o value higher than that of the corresponding linear polymers of similar M , is reported to occur at an LCB content of 0.2 LCB/10,000 C but the increase becomes more pronounced as the LCB content grows [85, 91, 92, 105,106]. This feature of low amounts of LCB has also been utilized to explore the extent of metallocene LCB [13, 85, 106, 107]. 

---