Relaxation dynamics of scale-free polymer networks

摘要

We focus on polymer networks with a scale-free topology. In the framework of generalized Gaussian structures,nby making use of the eigenvalue spectrum of the connectivity matrix, we determined numerically the averagednmonomer displacement under external forces and the mechanical relaxation moduli (storage and loss modulus).nFirst, we monitor these physical quantities and additionally the eigenvalue spectrum for structures of differentnsizes, but with the same γ , which is a parameter that measures the connectivity of the structure. Second, we varynthe parameter γ , and we keep constant the size of the structures. This allows us to study in detail the crossovernbehavior from a simple linear chain to a starlike structure. As expected we encounter a more chainlike behaviornfor high values of γ , while for small values of γ a more starlike behavior is observed. In the intermediate timen(frequency) domain, we encounter regions of constant slope for some intermediate values of γ .