The shapes of ideal dendrimers in two and three dimensions

The properties of nine, twelve, twenty-one and thirty-nine branch dendrimers in the ideal regime in both two and three dimensions are investigated. A method based on the Kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers and a scheme originally proposed by Benhamou et al., (2004), are applied to calculate the radii of gyration ratios, the asphericity, shape parameters, and the form factors of these structures. Monte Carlo simulations using a growth algorithm are also employed to determine these properties. It is found that the extrapolated property values obtained by these methods are in excellent agreement with each other and available theory. Dendrimers with a higher generation and a greater number of branches have a more symmetrical shape.