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

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 < 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

Conformation of Arborescent Polymers in Solution by Small-Angle Neutron Scattering: Segment Density and Core−Shell Morphology

“…The blob theory of branched polymers predicts a similar increase in R s with the number of arms (R s ∝ f 1/5 ). 26 Candau et al likewise suggested that R s should increase with the segmental density for branched polymers. 27 In contrast to the predictions of these theories for branched polymers, the relative independence of R s on generation number for arborescent 30K polymers is attributed to their hard spherelike behavior.…”

Chemical analysis and aqueous solution properties of charged amphiphilic block copolymers PBA-b-PAA synthesized by MADIX®

“…For aqueous dispersions of spherical micelles, which include almost all the solutions considered in this work, different models have been applied. In the case of low pH (around 2), where the PAA is mostly neutral, the Daoud Cotton model [17] was applied to fit the data. It is based on a dense core and a corona whose radial concentration decreases with a power law.…”

Formation of Block Copolymer Micelles in Solution: A Monte Carlo Study of Chain Length Dependence

“…N A and star polymers. 73,74 This analogy is particularly obvious for the extreme case N A ) 1. Bug et al 24 find that in this limit eq 2.29 again holds although n j does not increase with N but rather is a decreasing function of…”

“…Finally, Halperin et al 23,25,26 again exploit the analogy with star polymers 73,74 but for the case of N A , N B at finite f. They obtain a power law Unlike in eqs 2.22, 2.25, and 2.30 n j decreases with a logarithm of N B . The cmc is…”