Abstract
While Flory theories [J. Isaacson and T. C. Lubensky, J. Physique Lett. 41, 469 (1980); M. Daoud and J. F. Joanny, J. Physique 42, 1359 (1981); A. M. Gutin et al., Macromolecules 26, 1293 (1993)] provide an extremely useful framework for understanding the behavior of interacting, randomly branching polymers, the approach is inherently limited. Here we use a combination of scaling arguments and computer simulations to go beyond a Gaussian description. We analyze distribution functions for a wide variety of quantities characterizing the tree connectivities and conformations for the four different statistical ensembles, which we have studied numerically in [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016) and J. Chem. Phys. 145, 164906 (2016)]: (a) ideal randomly branching polymers, (b) and melts of interacting randomly branching polymers, (c) self-avoiding trees with annealed connectivity, and (d) self-avoiding trees with quenched ideal connectivity. In particular, we investigate the distributions (i) of the weight, , of branches cut from trees of mass by severing randomly chosen bonds; (ii) of the contour distances, , between monomers; (iii) of spatial distances, , between monomers, and (iv) of the end-to-end distance of paths of length . Data for different tree sizes superimpose, when expressed as functions of suitably rescaled observables or . In particular, we observe a generalized Kramers relation for the branch weight distributions (i) and find that all the other distributions (ii–iv) are of Redner-des Cloizeaux type, . We propose a coherent framework, including generalized Fisher-Pincus relations, relating most of the RdC exponents to each other and to the contact and Flory exponents for interacting trees.
- Received 14 October 2016
DOI:https://doi.org/10.1103/PhysRevE.95.012117
©2017 American Physical Society