The shapes of simple three and four junction comb polymers

A scheme originally proposed by G. Wei [Physica A 222, 152 (1995); Physica A 222, 155 (1995)] is redesigned to produce numerical shape parameters of arbitrary tree-branched polymers based on the Kirchhoff matrix eigenvalue spectrum. This method and two different Monte Carlo techniques (pivot and growth) are employed to investigate the asphericity of three and four junction comb polymers in both the ideal and excluded volume regimes. It is found that the extrapolated g-ratio and asphericity values obtained by all of these methods are in excellent agreement with each other and the available theory in the ideal regime and that polymers with a complete set of interior branches display a more sphere-like shape.