Monte Carlo computer investigations of higher generation ideal dendrimers

The properties of ideal tri-functional dendrimers with forty-five, ninety-three and one hundred and eighty-nine branches are investigated. Three methods are employed to calculate the mean-square radius of gyration, $g$-ratios, asphericity, shape parameters and form factor. These methods include a Kirchhoff matrix eigenvalue technique, the graph theory approach of Benhamou et al. (2004), and Monte Carlo simulations using a growth algorithm. A novel technique for counting paths in the graph representation of the dendrimers is presented. All the methods are in excellent agreement with each other and with available theoretical predictions. Dendrimers become more symmetrical as the generation and the number of branches increase.