Theoretical models of hyperbranched polymers

We have investigated linear, stal branched and hyperbranched XnHm polymers and determined the number of atoms, rotors, internal coordinates, valence a nd HOMO molecular orbitals as well as molecular mass for each generation an d valency. We use the semi-empirical MNDO model to obtain full geometry opt imization for increasingly larger clusters for each generation in order to obtain total relative energies, We then generate analytical functions, whic h correlate the total relative energies with the generation, for each valen cy, for the hyperbranched polymers. We have also generated analytic functio ns, which correlate total relative energies, experimental van der Waals coe fficients and standard enthalpy of combustion with the number of carbon ato ms in each chain of the linear alkanes, These results are used to predict t he enthalpy of combustion for higher generations of alkanes in good agreeme nt with experiment. Due to the exponential increase in size with generation of the hyperbranched polymers alternative analytical models may be of inte rest to theoretical chemists working in this line of research. (C) 2000 Els evier Science B.V. All rights: reserved.