Shear modulus and shear-stress relaxation in simulated free-standing polymer films

Using molecular dynamics simulations of a coarse-grained model for polymer glasses we examine viscoelastic properties of free-standing (nonentangled) polymer films. We focus on the (in-plane) shear relaxation modulus G(t) and the (in-plane) shear modulus μ, which we analyze as a function of film thickness (h) for temperatures (T) above and below the glass transition temperature T_g(h). The shear modulus is determined via the stress-fluctuation formalism and found to depend, in addition to h and T, also on the time window (Δt) employed for data sampling. This dependence on Δt can related quantitatively to the time dependence of G(t), provided time-translational invariance holds. Therefore, G(t) is the important underlying quantity, which obeys, in good approximation, a time-temperature superposition principle. We determine the viscosity of the films. For a given T the viscosity decreases with film thickness. This effect can be mainly traced back to the decrease of T_g with decreasing h. The presence of the free interfaces also weakens the shear rigidity of the polymer glass relative to the bulk, which can be understood via the relation between μ and G(t) mentioned before.