Useful Relations for Material Functions

4 power dependence has been observed experimentally and predicted theoretically. Furthermore, the primary normal stress difference coefficient in the limit as y goes to zero, 4 1,0, is observed to be proportional to M raised to the 7.0 power that is. 

Usually M is replaced by Afw which is the weight average molecular weight (which is the second moment of the molecular weight distribution). In the case of 4/i,o there is not as much experimental confirmation as there is for t]o. For rod-like molecules there is some evidence that the following relations hold (Baird and Ballman, 1979)  

The change in the linear dependence of jjq on M to the 3.4 power dependence for flexible chain polymers is believed to be due to the formation of an entanglement network or temporary physical junctions between the polymer chains. In the case of rod-like molecules, the hindrance of free rotation of the rod-like molecule by neighboring molecules serves as the entanglements. 

In addition to the dependence of the magnitude of rfo and 4/1,0 on M, the onset of shear-thinning behavior is affected by M. In particular, as M increases, the shear rate at which shearthinning behavior starts, yo, decreases. The relation between 

In this section three topics are discussed (1) the molecular weight dependence of the rheological properties (2) the interrelation between steady shear and dynamic oscillatory shear measurements and (3) the effect of branching. The importance of the second topic rests on the fact that dynamic oscillatory properties are easier to measure and can be obtained at higher equivalent shear rates than are possible for the steady shear flow properties obtained by means of rotary rheometers. 

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