Complexes of Block Copolymers in Solution: Tree Approximation

We determine the statistical properties of block copolymer complexes in solution. These complexes are assumed to have the topological structure of (i) a tree or of (ii) a line-dressed tree. In case the structure is that of a tree, the system is shown to undergo a gelation transition at sufficiently high polymer concentration. However, if the structure is that of a line-dressed tree, this transition is absent. Hence, we show the assumption about the topological structure to be relevant for the statistical properties of the system. We determine the average size of the complexes and calculate the viscosity of the system under the assumption that the complexes geometrically can be treated as porous spheres.