Randomly hyperbranched polymers

We describe a model for the structures of randomly hyperbranched polymers in solution, and find a logarithmic growth of radius with polymer mass. We include segmental overcrowding, which puts an upper limit on the density. The model is tested against simulations, against data on amylopectin, a major component of starch, on glycogen, and on polyglycerols. For samples of synthetic polyglycerol and glycogen, our model holds well for all the available data. The model reveals higher-level scaling structure in glycogen, related to the beta particles seen in electron microscopy.