Linear response of transient networks

Consider the linear response of the affine network (9.26) to a small oscillatory shear flow defined by the deformation tensor 

The amplitude e is assumed to be sufficiently small, and hence we can expand the chain distribution functions in powers of e. 

The complex modulus is defined by the proportionality constant between the stress and deformation as 

In particular, for a Gaussian chain with a constant recombination rate a, we find [17] 

we find that the slope for the high-frequency region 

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