99-05E

The quantum - statistical model for the description of polymerization process of uranile complexes $UO_{2}{[(OH)_{2}UO_{2}]}^{2+}_n$ are proposed allowing for the statistical character of distribution protons on the hydrogen bonds. The effective short - range configurational interaction between protons, long - range electrostatic proton - proton interactions as well as boundary effects with the description of all configurations of ionic groups on the ends of polymer complex are considered. At the certain boundary conditions the dependences on the number of ionic groups in polymer chain are investigated. The conditions of complex formations of various lengths are discussed.