The two dimensional shapes of simple three and four junction ideal comb polymers

• Mixed numeric and analytic methods are applied to determine polymer shape parameters.
• Semi-analytic and simulational results compare favorably.
• The method may easily be applied to other branched polymer structures.

We redesign and apply a scheme originally proposed by Wei (1995) [2,3] to produce numerical shape parameters with high precision for arbitrary tree-branched polymers based on their Kirchhoff matrix eigenvalue spectrum. This algorithm and a Monte Carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers. We find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory. We confirm that polymers with a complete set of interior branches display a more circular shape.