Branching Zero-shear viscosity, effect

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. 

Similar results are obtained for linear, four and six-branched polyisoprenes at a concentration of 0.145 g/ml. In this case, however, at hi r concentrations more serious deviations occur from theory. The higher molecular weight samples can have zero shear viscosities higher than linear polymers of the same molecular wei t Such behavior was first noted in a study of melt viscosity of regular star-branched polybutadienesViscosities of the order of one hundred times that of a linear equivalent could be observed, but the effect decreased rapidly on dilution with solvents i.e. the viscosities of branched polymers were more sensitive to concentration than those of linear polymers. Star-branched polyisoprenes show viscosity enhance-... 

Chapter 5 is a fairly detailed discussion of the linear viscoelastic behavior of melts. The most used linear properties are the zero-shear viscosity and the storage and loss moduli, and the effects of molecular weight, molecular weight distribution, and branching on these properties are described. While the approach is primarily phenomenological, melt behavior is interpreted qualitatively in terms of the molecular models that are presented in mathematical detail in later chapters. 

The effects of long-chain branching on the zero-shear viscosity are discussed in Section 5.11. 

Arnett and Thomas [78] used hydrogenated polybutadiene to study the effect of ethyl branches on the zero-shear viscosity. The data did not obey either of the standard expressions for the effect of temperature, but data at the highest temperatures were fitted to the Arrhenius expression (Eq. 4.68), and log(E3) was found to be linear in the number of ethyl branches per total carbon atoms, n. They correlated all of their data by use of Eq. 5.41. 

The exponential increase of viscosity with M is consistent with the picture in which relaxation occurs primarily by means of primitive path fluctuations (sometimes called arm retraction). In Chapter 9 we will see that this effect can be explained quantitatively by a tube model. The exp onential increase of t]q with M results from the fact that the branch point prevents reptation, so that the principal mechanism of relaxation is primitive path fluctuation, which becomes exponentially slower with increasing arm length. The energy of activation for the zero-shear viscosity is little affected by star branching, except in the case of polyethylene and its close relative, hydrogenated polyisobutylene. 

Levels of long-chain branching as low as 0.1 branch per 1,000 carbon atoms can have an important effect on viscosity but are quite difficult to detect using non-rheological techniques. This makes it important to be able to detect such levels, and at the same time it provides a means for doing this. The zero-shear viscosity is particularly sensitive to large molecular structures and is the property used in several correlations. 

The effect of branching on the zero-shear-rate intrinsic viscosity is often expressed in terms of branching index, g, defined as the ratio of the zero-shear-rate intrinsic viscosities of a branched to a linear polymer of the same composition and molecular weight. 

Flow properties are very strongly dependent on molecular architecture, i.e. molar mass and chain branching. Figures 6.13 and 6.14 illustrate the effect of molar mass on the zero-shear-rate viscosity (//q) and on the steady-state recoverable shear compliance. 

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