Combinatorics and Modelling of Highly Branched Polymers

Abstract

Highly branched polymers such as dendrimers and hyperbranched polymers have a found a variety of chemical applications owing to their unique structural and functional properties, but in many cases are still lacking sufficient theoretical characterization. This thesis takes marginal steps toward addressing this by firstly studying a combinatorial analog of the Degree of Branching – a quantity used by chemists to classify the extent of branching in polymers -- in the mathematically convenient setting of lattice models of polymers. Next the adsorption behaviour of dendrimers is studied by adapting the Monte Carlo method of Random Sequential Adsorption to dendrimers and applying the model to experimental results of a novel synthetic dendrimer of interest (dendritic Polyglycerol Amine).