Mechanisms for the different scaling behaviour

The viscosities above c increase abruptly following the power law (Eq. 8) with an exponent X 3.5, while the exponent of the power law for the shear modulus is always about 2.3. This behaviour has been treated in detail by Cates et al. [33]. The structural relaxation times are affected by both, reptation and bond breaking processes. Cates treats three different kinetic mechanisms. The first consists of the break of a rod with the formation of two new end caps. In the recombination step the rods have to collide at the ends in order to fuse into a new rod. In the second mechanism the end cap of one rod collides with a second rod and in a three-armed transition state a new rod and a new end cap is formed. In the third mechanism two rods collide and form two new rods through a four armed transition state. It is obvious that stress can release all three mechanisms. These mechanisms lead to somewhat different power laws for the kinetic time constant t according to 

But in all cases x is between 1 and 2. Mechanism 3 is less likely in systems with low c values and stiff rods. For this argument it is likely that mechanism 2 or 3 is effective in the more concentrated region of the pure CxDMAO solutions. 

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