Diffusion-limited hyperbranched polymers with substitution effect.

Highly branched structure has the essential influence on macromolecular property and functionality in physics and chemistry. In this work, we proposed a diffusion-limited reaction model with the consideration of macromolecular unit relaxations and substitution effect of monomers to study the structure of hyperbranched polymers prepared by slow monomer addition to a core molecule. The exponential relationship (R(g) ∼ N(λ)) between the radius of gyration R(g) and the degree of polymerization N, was systematically analyzed at various branching degrees. It is shown that the effective exponent λ(eff) decreases at lower N and but increases toward that of diffusion-limited aggregation (DLA) clusters (λ(DLA) = 0.4) with the degree of polymerization increasing. The substitution effect of monomers in reaction strongly influences the evolution pathway of λ(eff). With the static light scattering technique, the fractal property of internal chains was further calculated. A general law about the radial distribution of the units of diffusion-limited hyperbranched polymers was found that, at smaller reactivity ratio k(12), the radial density of all monomer units D(A) declines from the center region to the peripheral layer revealing the dense core structure; however, at larger k(12), the density distribution shows a loose-dense-loose structure. These structural characteristics are helpful to deeply understand the property of hyperbranched polymers.