Molecular Dynamics Simulations of Hyperbranched PAMAM Vicsek Fractals

Abstract

Within the broad class of hyperbranched polymers, highly symmetrical objects (such as dendrimers and Vicsek fractals) are of special theoretical interest. Here we study, using the MARTINI force-field, polyamidoamine Vicsek fractals (PVF) in silico, focusing on their structure and dynamics in dilute solution. Our extensive microsecond-long simulations show that the radius of gyration of PVF scales with the molecular weight as N 0.54 , behavior rather close to that of stars and considerably distinct from that of dendrimers. The study of the radial density profiles indicates that different parts of the PVF interpenetrate significantly, fact which stresses the soft and sparse character of PVF. These results are also supported by our findings for the rotational autocorrelation functions.

Exploring the applications of fractional calculus: Hierarchically built semiflexible polymers

“…(25) it follows immediately that for chemically reasonable f values the VF have d frac ≤ 3, i.e., that they can readily be embedded in the three-dimensional space, regardless of their generation g [38]. In addition, it follows that by changing f it is possible to investigate VF of varying fractal dimension.…”