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In this work, we present a simple and efficient generator of polymeric linear chains, based on a random self-avoiding walk process. The chains are generated using a discrete process of growth, in cubic networks and in a finite time, without border limits and without exploring all the configurational space. First, we thoroughly describe the chains morphology exploring the statistics of two characteristic distances, the radius of gyration and the end-to-end distance. Moreover, we examine the dependence of mean characteristic distances with the number of steps (N). Despite the simplicity of our procedure, we obtain universal critical exponents, which are in very good agreement with previous values reported in the literature. Moreover, studying the balance between the monomer-monomer interaction and the bending energy, we find that initially, the chains develop by multiple doubling, forming a cluster and increasing its energy. After reaching a given number of steps, the chains stretch and flee from the cluster, which results in a reduction of its interaction energy. However, the behaviour of the bending energy reveals that the chains follow the same folding pathway in both regimes. Additionally, we also characterize the energy of the obtained chains, combining the local interaction energy with its corresponding bending energy but in a discrete version. This analysis is relevant because it allows differentiating between chains of equal interaction energy but with different structures.