Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique and Centre Blaise Pascal, F-69342 Lyon, France.
Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, NY 10003, USA.
Soft Matter. 2017 Feb 8;13(6):1223-1234. doi: 10.1039/c6sm02756c.
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.
无规支化聚合物链（或树）是聚合物物理的一个经典主题，与磁系统理论、渗流和临界现象有关。最近，该模型被重新考虑用于 RNA、超螺旋 DNA 和拓扑约束聚合物的褶皱。虽然在理想情况下可以求解，但对于具有体积相互作用的无规支化聚合物，人们知之甚少。弗洛里理论为包括良好和θ溶剂中的孤立树以及树熔体在内的广泛支化系统提供了一个简单而统一的描述。特别是，该方法为淬火连接性的无规支化聚合物和退火连接性的无规支化聚合物提供了一个共同的描述框架。在这里，我们综述了在良溶剂、θ溶液和熔体中聚合度非常大的渐近极限下的相互作用树的弗洛里理论，并报告了它对θ溶剂中退火连接性的预测。我们将弗洛里理论对无规支化聚合物的预测与广泛的可用分析和数值结果进行了比较，并得出结论，在大多数情况下，它们在定性上是极好的，在定量上也是良好的。
