High-functionality star-branched macromolecules: Polymer size and virial coefficients

Abstract

We perform high-statistics Monte Carlo simulations of a lattice model to compute the radius of gyration Rg, the center-to-end distance, the monomer distribution, and the second and third virial coefficients of star polymers for a wide range of functionalities f, 6 ≤ f ≤ 120. We consider systems with a large number L of monomers per arm (100 is approximately < L is approximately < 1000 for f ≤ 40 and 100 is approximately < L is approximately < 400 for f = 80, 120), which allows us to determine accurately all quantities in the scaling regime. Results are extrapolated to determine the behavior of the different quantities in the limit f → ∞. Structural results are finally compared with the predictions of the Daoud-Cotton model. It turns out that the blob picture of a star polymer is essentially correct up to the corona radius Rc, which depends on f and which varies from 0.7Rg for f = 6 to 1.0Rg for f = 40. The outer region (r > Rc), in which the monomer distribution decays exponentially, shrinks as f increases, but it does not disappear in the scaling regime even in the limit f → ∞. We also consider the Daoud-Cotton scaling relation Rg (2)~f(1-ν)L(2ν), which is found to hold only for f >> 100.