title: Flory theory of randomly branched polymers.
abstract: Randomly branched polymer chains (or trees) are a classical subject of polymer physics with connections to the theory of magnetic systems, percolation and critical phenomena. More recently, the model has been reconsidered for RNA, supercoiled DNA and the crumpling of topologically-constrained polymers. While solvable in the ideal case, little is known exactly about randomly branched polymers with volume interactions. Flory theory provides a simple, unifying description for a wide range of branched systems, including isolated trees in good and θ-solvent, and tree melts. In particular, the approach provides a common framework for the description of randomly branched polymers with quenched connectivity and for randomly branching polymers with annealed connectivity. Here we review the Flory theory for interacting trees in the asymptotic limit of very large polymerization degree for good solvent, θ-solutions and melts, and report its predictions for annealed connectivity in θ-solvents. We compare the predictions of Flory theory for randomly branched polymers to a wide range of available analytical and numerical results and conclude that they are qualitatively excellent and quantitatively good in most cases.
authors.affiliation: Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique and Centre Blaise Pascal, F-69342 Lyon, France. ralf.everaers@ens-lyon.fr.
authors.forename: Ralf
authors.initials: R
authors.lastname: Everaers
authors.affiliation: Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, NY 10003, USA. ayg1@nyu.edu.
authors.forename: Alexander Y
authors.identifier: http://orcid.org/0000-0002-4230-8690
authors.initials: AY
authors.lastname: Grosberg
authors.affiliation: Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599, USA. mr@unc.edu.
authors.forename: Michael
authors.initials: M
authors.lastname: Rubinstein
authors.affiliation: SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy. anrosa@sissa.it.
authors.forename: Angelo
authors.identifier: http://orcid.org/0000-0002-9627-2486
authors.initials: A
authors.lastname: Rosa