The MD models in this study can also be used to gain physical insight into the origin of the size effect. It is well known that crystalline [27–29] and amorphous materials [30–33] have molecular structures at the surface (or bi-material interface) that differ substantially than in the bulk. In fact, the CG potential used for the research described herein was developed specifically to accurately predict the bulk and surface structure of PE [15]. For amorphous

polymers, the above-cited references show that the mass density of the polymer is higher on the surface than in the bulk. This high-density layer has a thickness on the order of 1 nm. The cause of the densification of polymer molecules on a surface is classically explained by the concept ICG-001 cost of surface tension. Segments of polymer molecules in the bulk have a relatively low energy PD0325901 datasheet state because of the balance of attractive short-range (e.g., covalent bonds) and long-range (e.g., van der Waals bonds) interactions in every direction. Segments of polymer molecules on a free surface (or a non-bonded bi-material interface of two dissimilar materials) do not have these strong attractive interactions

in the direction normal to the surface and are thus pulled by the attractive forces in the opposite direction towards the bulk. As a result, there is a densification of the top layer of polymer molecules on a surface. This densified surface layer of material has a constant thickness regardless of the size and geometry of the overall material structure. For polymer particles, this means that the surface layer will have the same finite thickness for any particle

size. For decreasing particle sizes, the relative volume fraction of the densified material increases. Therefore, it follows that the smaller polymer particles studied herein are expected to have stiffer mechanical responses than the larger particles, as observed experimentally Chloroambucil [5–7] and discussed in ‘Simulated compression loading’ and ‘Simulated compression unloading’ sections. In order to quantify the influence of the surface layer on the mechanical response of the polymer particles, the surface energy has been determined for each diameter. The total internal energy associated with the presence of the surface (i.e., surface energy) in a molecular system can be determined by (8) where U particle is the total energy (kinetic plus potential) of a polymer particle, and U b is the total energy in a bulk sample of material with the same number of CG beads. These potential energies were calculated using the potential shown in Table  1 using the procedures outlined in ‘Spherical particle molecular models’ section. Figure  9 shows a plot of the ratio U sur/U b over the ratio of the surface area to volume for each of the five particles.