Viscoelastic relaxation of random scale-free copolymer networks

We study the viscoelastic relaxation dynamics of scale-free copolymer networks in the generalized Gaussian structures framework. We focus on the real and imaginary components of the complex dynamic modulus G^{*}(ω): the storage and loss moduli. Our chosen scale-free network model builds distinct types of hyperbranched copolymers by a careful tuning of the construction parameters, such as γ, which controls the node connectivity, or the minimum allowed degree K_{min} and the maximum allowed degree K_{max}. These parameters, together with the parameters that govern the monomer-type distribution, provide significative distinct behaviors. By only varying γ we change the topology of the copolymers and a local maximum in the region of high frequencies or a constant slope in the intermediate frequency region become more evident. Both K_{min} and K_{max} play an important role, especially in the region of intermediate frequency domain. The ratio σ between the friction coefficients ζ_{A} and ζ_{B} of the A and B beads gives birth to new features, such as, new quasiplateaus or new peaks along with a shift toward lower or higher frequencies depending on the ratio value. The ratio η between the number of A and B monomers influences the size of the constant slope for intermediate frequencies and it is responsible for the symmetry of the two peaks of the loss modulus.