Hyperbranched polymers have many short chains linked together to form a large polymer; their average branch length is much smaller than the overall degree of polymerisation. For example, the hyperbranched polymer glycogen is an energy storage material in animals; and amylopectin is hyperbranched and a major component of starch, it provides a great deal of the energy in many people’s diets. Synthetic polyglycerols can also be hyperbranched. They are biocompatible, and likely to find application in pharmaceutical and medical technologies.
We discovered that randomly branched models accurately reproduce the sizes and shapes of a remarkable variety of synthetic and natural, regularly and randomly, branched polymers. Random Branching Theory (see tab above) is important because it can accurately predict the behaviour of the full range of highly branched structures. Prediction and understanding of these properties is needed for the design of new polymers, which have applications in drug delivery, and as viscosity modifiers, among many others. We're also using the theory to extract information on the structure of glycogen from the size-exclusion chromatography experiments, as a new approach to the study of metabolic disease.
Random Branching Theory (RBT) is a simple, mean-field theory of the structures of highly branched polymers. Its basic assumption is that a highly branched structure is built from simple units, attached to each other at random by branch points. These simple units may be linear, oligomeric chains, or larger structures. Previous theories of highly branched polymer structure have followed the approach of de Gennes and Hervet in analysing a chain of monomers out from the centre of a dendrimer, or near-dendritic structure. Many highly branched polymers of practical use as viscosity modifiers and drug-delivery vehicles are not at all dendritic, and so RBT fills the need for a simple theory that can describe the shape, size-mass scaling and distribution of functional groups of these polymers. Surprisingly, RBT predicts the conformations of both real and simulated dendrimers extremely well, providing a more detailed and more accurate picture than treatments in the tradition of the de Gennes-Hervet approach. This is strong evidence that applications of dendrimers, which are often prohibitively expensive to synthesise, may be equally served by their synthetically straightforward and randomly branched cousins.
RBT is a general theory of highly branched polymer structure. It accurately describes the structures of glycogen α-particles, of simulated dendrimer structures (see tab above), of the structures of real dendrimers obtained by Small Angle X-ray Scattering, of simulated hyperbranched polymers, and of real hyperbranched polyglycerols, and is used by food scientists at the Centre for Nutrition and Food Science at the University of Queensland in the interpretation of data on starch.
A dendrimer is a tree-like molecule with monomers arranged regularly into generations, with all potential branch points occupied. A comparison between the density profiles of simulated dendrimers at various temperatures and the predictions of RBT. Not only is the fit very good, but the fit parameters give the correct size for the units from which the polymer is built, the correct temperature dependence and correctly predict the strength of solvent-mediated interactions between the monomers in the dendrimer.
Similar agreement is obtained on comparison to the form factors of real dendrimers obtained by SAXS. These results show that the regular branching structure of a dendrimer may be regarded as a perturbation around the randomly branched state. This is in stark contrast to the more natural approach taken by de Gennes in perturbing the regular structure.