Large scale Monte Carlo simulations of center-adsorbed star polymers

Abstract

A star‐shaped polymer whose center unit is adsorbed on a surface offers a peculiar example of surface‐grafted polymers. When it is isolated in a good solvent, it has been conjectured that several distinct scaling relations hold for the monomer and end‐point density profiles. Especially, the density decay in a direction parallel to the surface is described by a new critical exponent λ(f) as ρ(r,z=0)∼r^−d+λ(f). However, the precise values of the exponent as a function of the number of arms were still unclear. Another interesting quantity is the total number of configurations behaving as N∼l^γ_s(f)−1μ^fl. Here, l is the length of the arm, μ the effective coordination number for a single chain, and λ_s(f) a new surface critical exponent yet to be known. We perform large scale Monte Carlo simulations of such an adsorbed star with the number of arms, f, ranging from 2 to 15, to verify the predicted scaling theory and to calculate various static properties and exponents. Estimates of γ_s(f ) are presented. The validity of the scaling relations is clearly shown, and the first estimation of the value of λ(f ) is given also. Furthermore, an empirical form of the exponent λ(f ) as a function of f is proposed.