We focus on treelike generalized scale-free polymer networks, whose geometries depend on a parameter, γ, that controls their connectivity and on two modularity parameters: the minimum allowed degree, Kmin, and the maximum allowed degree, Kmax. We monitor the influence of these parameters on the static and dynamic properties of the achieved generalized scale-free polymer networks. The relaxation dynamics is studied in the framework of generalized Gaussian structures model by employing the Rouse-type approach. The dynamical quantities on which we focus are the average monomer displacement under external forces and the mechanical relaxation moduli (storage and loss modulus), while for the static and structure properties of these networks we concentrate on the eigenvalue spectrum, diameter, and degree correlations. Depending on the values of network’s parameters we were able to switch between distinct hyperbranched structures: networks with more linearlike segments or with a predominant star or dendrimerlike topology. We have observed a stronger influence on Kmin than on Kmax. In the intermediate time (frequency) domain, all physical quantities obey power-laws for polymer networks with γ = 2.5 and Kmin = 2 and we prove additionally that for networks with γ ≥ 2.5 new regions with constant slope emerge by a proper choice of Kmin. Remarkably, we show that for certain values of the parameter set one may obtain self-similar networks.
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