A 'phantom bubble' model for the distribution of free volume in polymers

摘要

A new approach to investigate free volume in atomistic simulation was devised. The atoms in the structure are represented by hard spheres. A phantom bubble is defined as an empty sphere, which contacts four or more hard spheres of atoms simultaneously in 3 dimensional space and does not overlap with any atom in the structure. Phantom bubbles are only allowed to overlap with other phantom bubbles. For the purpose of illustration, phantom bubbles were constructed in a fully atomistic structure. An amorphous polyethylene was prepared in a periodic box having the dimension of 28.2 * 28.2 * 28.2 Anstrom at 293 K and a density of 0.83 g/cm~3. There were two fully atomistic polymeric chains (each C_(400)H_(802)) in the box. All the atoms in the system were assumed to be hard spheres, usually with 89% of their van der Waals radii. Larger and smaller radii were also considered. The size distribution of phantom bubbles in this system was calculated and the bubbles had a median radius of 0.8 Anstrom. Small changes in the radii used for the atoms have little effect on the shape of the distribution function.