Construction And Properties Of Models Of Thin Films

Construction of the thin films commences with an equilibrated model of the melt at bulk density, contained in a three-dimensional box of dimensions LxLyLz, measured along the three axes of the periodic cell. The angle between any two axes is 60o. Periodic boundary conditions are applied in all directions. The number and degree of polymerization of the parent chains are chosen so that the system will have bulk density, pbulk, at the temperature of the simulation. The construction, equilibration, analysis, and reverse mapping of these models of polyethylene melts have been reviewed recently,111 and will receive no additional mention here.

The equilibrated model of the melt is converted to a model of the free-standmg thin film using the approach described by Misra et al. 19 The value of Lz is increased sufficiently so that a parent chain cannot interact with its image along the z direction. When the perturbed system is re-equilibrated, with the same procedure employed for the initial equilibration of the bulk, it now settles down into a free-standmg thin film, with both surfaces exposed to a vacuum.20 If the initial model was large enough, the freestanding film retains pbulk in its interior. Films have been constructed and analyzed with thickness up to 12 nm. The density profiles, p(z), near both surfaces are described by a hyperbolic tangent function.

The width parameter, E, has a value close to 0.5-0.6 nm, corresponding to a surface region of thickness 1.0-1.2 nm.21 A larger thickness for the surface region is obtained if it is defined in terms of a property of the entire chain, such as the distribution of the centers of mass of the chains.21 These results are similar to the ones obtained earlier in thin films of atactic polypropylene that were constructed by a different method.2223

The anisotropy of the local environment is assessed using an order parameter S, defined using the angle, 0z, between the z axis and a bond in the coarse-grained representation of the system.

This order parameter is applied to individual bonds of length 0.25 nm in the coarsegrained representation (which become chord vectors in the fully atomistic representation of the same system).20 The order parameter shows that the local environment is isotropic in the middle of the film (assuming the film is sufficiently thick), but the local environment becomes anisotropic near the surfaces. The nature of the anisotropy at the surface depends on whether the chains are linear or cyclic. For cyclic chains, S becomes negative near the surface, and remains negative, due to the tendency for internal bonds in the surface region to be oriented parallel to the surface.21 For linear chains, S initially becomes negative as one approaches the surface from the interior, but S eventually turns positive when the density is very small, due to the tendency for the ends to be segregated at the surface, with an orientation perpendicular to the surface.20

The contribution made by the internal energy to the surface energy, y, is in the range 21-22 erg/cm2 20 21 The surface energy is dominated by the contributions from the

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