Effect of the $\pi$-$\pi$ interactions on the Glass Transition Temperature of Nanometer Thin Polystyrene Films

The glass transition in free-standing films of linear and cyclic polystyrene (PS) was studied to identify a potential relationship between glass transition temperature (T$_{g}$) and film thickness. United-atom molecular-dynamic simulations were performed on free-standing films of varying thicknesses. Data revealed a positive correlation between T$_{g}$ and film thickness, i.e. T$_{g}$ decreases as film thickness decreases. At 20 nm the difference is less than 1$\%$, while at 2.5 nm the difference is 13$\%$ for linear and 9$\%$ for cyclic chains. Recent studies show that a larger number of end groups inhabit the interface rather than the middle of the film and that a deficit of phenyl groups exists in the interfacial film layers nearly 1 nm below the surface. The large number of end groups would increase interfacial layer mobility while the deficit of phenyl groups would weaken the phenyl-phenyl aromatic ($\pi$-$\pi$) interaction. Through comparing the linear and cyclic PS, it was shown that cyclic chains lack end groups but the cyclic PS has an observed deficit of phenyl rings comparable to that in linear polymers. Therefore, the ($\pi$-$\pi$) interaction seems to be the reason for the observed T$_{g}$ dependence on the thickness of thin PS films.