Theoretical models of hyperbranched polymers

We have investigated linear, starbranched and hyperbranched X_nH_m polymers and determined the number of atoms, rotors, internal coordinates, valence and HOMO molecular orbitals as well as molecular mass for each generation and valency. We use the semi-empirical MNDO model to obtain full geometry optimization for increasingly larger clusters for each generation in order to obtain total relative energies. We then generate analytical functions, which correlate the total relative energies with the generation, for each valency, for the hyperbranched polymers. We have also generated analytic functions, which correlate total relative energies, experimental van der Waals coefficients and standard enthalpy of combustion with the number of carbon atoms in each chain of the linear alkanes. These results are used to predict the enthalpy of combustion for higher generations of alkanes in good agreement with experiment. Due to the exponential increase in size with generation of the hyperbranched polymers alternative analytical models may be of interest to theoretical chemists working in this line of research.