Using molecular dynamics simulation of a polymer glass model we investigate free-standing polymer films focusing on the in-plane shear modulus $\mu$, defined by means of the stress-fluctuation formula, as a function of temperature $T$, film thickness $H$ (tuned by means of the lateral box size $L$), and sampling time $\mathrm{\Delta }t$. Various observables are seen to vary linearly with $1/H$, demonstrating thus the (to leading order) linear superposition of bulk and surface properties. Confirming the time-translational invariance of our systems, $\mu \left(\mathrm{\Delta }t\right)$ is shown to be numerically equivalent to a second integral over the shear-stress relaxation modulus $G\left(t\right)$. It is thus a natural smoothing function statistically better behaved as $G\left(t\right)$. As shown from the standard deviations $\delta \mu$ and $\delta G$, this is especially important for large times and for temperatures around the glass transition. $\mu$ and $G$ are found to decrease continuously with $T$ and a jump-singularity is not observed. Using the Einstein-Helfand relation for $\mu \left(\mathrm{\Delta }t\right)$ and the successful time-temperature superposition scaling of $\mu \left(\mathrm{\Delta }t\right)$ and $G\left(t\right)$, the shear viscosity $\eta \left(T\right)$ can be estimated for a broad range of temperatures.

• Received 7 September 2018
• Revised 25 October 2018

DOI:https://doi.org/10.1103/PhysRevE.98.062502