Modeling and Mass-Distance Scaling of a Nanometer Starburst Polymer

摘要

We report numerical scaling of cumulative mass with intramolecular distance of a model of one of the four segments of the hyperbranched poly(propylene-imine)-dendr-DAB(CN)_(64) molecule. Assuming prevalent repulsive link-link forces gives a power law relation with non-Euclidian exponent d = 2.12 +- 0.10, in close agreement with the known exact value d = 2 of the universality class of isolated branched polymers with negligible loops. This outcome implies that the dendrimer molecule DAB(CN)_(64) under good solvent conditions can be considered a mass fractal (non-compact structural pattern) with considerable open spacing, causing delayed diffusion of trapped species and a range of fracton modes in its low-frequency spectra.