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

We perform high-statistics Monte Carlo simulations of a lattice model to compute the radius of gyration R-g, 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 less than or similar to L less than or similar to 1000 for f <= 40 and 100 less than or similar to L less than or similar to 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 -> infinity. 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 R-c, which depends on f and which varies from 0.7R(g) for f = 6 to 1.0R(g) for f = 40. The outer region (r > R-c), 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 -> infinity. We also consider the Daoud-Cotton scaling relation R-g(2) similar to f(1-nu)L(2 nu), which is found to hold only for f >> 100. (C) 2013 AIP Publishing LLC.