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

TLDR

Star‑shaped polymers exhibit a radial monomer concentration profile that depends on branch number, monomer count, excluded volume, and monomer length. The study proposes a model that predicts star‑shaped polymer conformation by incorporating radial monomer concentration variation. The model employs two characteristic lengths—χ(c), the radius within which branches of other stars do not penetrate, and ξ(c), a screening length similar to that in semi‑dilute linear polymers—to describe star conformation beyond the overlap concentration. The model predicts that each branch is larger than an equivalent linear polymer and that the overall star size varies with monomer number, branch count, excluded volume, and concentration.

Abstract

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 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.