Molecular dynamics results on the pressure tensor of polymer films

Polymeric thin films of various thicknesses, confined between two repulsive walls, have been studied by molecular dynamics simulations. Using the anisotropy of the perpendicular, $PN(z),$ and parallel components, $PT(z),$ of the pressure tensor the surface tension of the system is calculated for a wide range of temperature and for various film thicknesses. Three methods of determining the pressure tensor are compared: the method of Irving and Kirkwood (IK), an approximation thereof (IK1), and the method of Harasima (H). The IK- and the H-methods differ in the expression for $PT(z)$ (z denotes the distance from the wall), but yield the same formula for the normal component $PN(z).$ When evaluated by molecular dynamics (or Monte Carlo)-simulations $PN(z)$ is constant, as required by mechanical stability. Contrary to that, the IK1-method leads to strong oscillations of $PN(z).$ However, all methods give the same expression for the total pressure when integrated over the whole system, and thus the same surface tension, whereas the so-called surface of tension, $zs,$ depends on the applied method. The difference is small for the IK- and H-methods, while the IK1-method leads to values that are in conflict with the interpretation of $zs$ as the effective position of the interface.