Star shaped polymers : a model for the conformation and its concentration dependence

We propose a model giving the conformation of a star shaped polymer by taking into account the radial variation of the monomer concentration ϕ( r). For an isolated star when increasing r (at the centre of the star r = 0), the variation of ϕ (r) is first given by a constant value (r < f 1/2 l) then has a (r/l)-1 variation (for f1/2 / < r < f1/2 ν-1 /) and finally a (r/l)-4/3 variation (for r > f1/2 ν-1 l); wh ere f is the number of branches, N the number of monomers in a branch and ν and l are the excluded volume and the length associated to a monomer. For all these cases, it is shown that the size of a branch is always larger than that of a linear polymer made of N monomers. Beyond the overlapping concentration the star conformation is obtained from two characteristic lengths essentially : χ(c ) a radius inside which the branches of the other stars do not penetrate, this radius defines a domain where the conformation of a star is similar to that of an isolated one. Beyond χ(c) the interpenetration of branches is characterized by a screening length ξ(c) very similar to that found for semi-dilute solutions of linear polymers. For all these regimes the variation of the size of a star is predicted as a function of N, f, v and c.