Correlations Based on the Zero-Shear Viscosity

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. 

A caveat that must be kept in mind in evaluating these correlations is that it is often impossible to measure the true zero-shear viscosity of polymers with broad molecular weight distributions or long chain branching. If this parameter is estimated by extrapolation it will reduce the reliability of a correlation. 

The constant A depends on the polymer and the temperature, and the exponent on the last term is related to Mb as follows  

Shroff and Mavridis [ 128] reported that they could estimate the level of long-chain branching in polyethylenes having very low branching levels using the zero-shear viscosity and the intrinsic viscosity of the branched polymer. They also compared their method with several others [129]. To use their method, it is necessary to know the relationship between the zero-shear viscosity of the linear polymer and its intrinsic viscosity, which they described as follows  

Then they propose that the average number of branches per 1000 carbon atoms, which they call the long chain branching index LCBI, is given by  

---