Page 73 - ILL Annual Report 2019

SCIENTIFIC HIGHLIGHTS
70-71
Figure 2
Profiles evaluated using the location of the centre of mass of the chains within the film of:
a) Bulk normalised and temporal-averaged components of the radii of gyration Gxx, Gyy and Gzz; and
b) The cosine director of the most important direction in which the chain is elongated with respect to the surface of confinement. These observables were evaluated for two film thicknesses: heff = 22.16 (in blue) and heff = 44.32 (in red).
c) Snapshot of the polymer melts simulated here in bulk (left) and
thin films (right). In the centre, a sketch illustrates the idea of how the volume pervaded is compressed by the confinement in thin films while remaining isotropic in bulk.
A spatially resolved profile of the entanglement density across the film for three different films are compared with their associated monomer density profile in figure 1a. Note that the entanglements do not sample all the volume available in the film, as is evident in figure 1a where the two density profiles do not match exactly.
The integrated contribution of this surface effect is summarised in figure 1b, which shows the total number of entanglements per chain compared with its bulk value, for thin films of various thicknesses. The film thickness is normalised here using the average end-to-end distance
in bulk conditions for the same chain length. Overall, we find that confinement leads to a decrease in the average number of entanglements per chain. Qualitatively, these results are in good agreement with those observed
in experiments using thin films and nanocomposites.
It is interesting to note that this trend of ‘confinement disentangles the chains’ is valid for all the cases studied here; however, the decrease is not dramatic, being 30 % at most for a strong confinement strength.
In order to understand the fundamental reasons for this outcome we performed several statistical analyses, one
of which provided us with a clear picture. This arose from studying how confinement alters the overall shape of the chains. To do this, we used the gyration tensor (G), whose three diagonal components, Gxx, Gyy and Gzz, account well for the spatial conformations of the chains.
Figure 2a shows the averaged value of these components normalised with the corresponding bulk value as a function of the chain position within the film.
The figure shows that for both thicknesses (continuous lines) the component Gzz, associated with the direction of confinement, tends to induce a noticeable shrinking of the chains in that direction, i.e. the chains break their spatial isotropy and tend to adopt a flat shape near the free surface. Conversely, the components Gxx and Gyy experience a slight change in their values in terms of increasing by as much as 10 % with respect to the bulk state (dashed lines in figure 2a).
By diagonalising the G tensor and studying the cosine director of the eigenvector associated with the minimum eigenvalue (which represents the most important direction in which the chain is elongated), it was possible to determine the main direction of the flatness. Figure 2b illustrates how the average orientation of this vector is dictated by
the position of the chains within the film. Independently of the molecular weight, all chains are flat at the edges of the film; this effect then decreases monotonically as the chains enter the film.
This anisotropic compression seems not to be wholly compensated for in the other directions, leading to an effective decrease in the volume pervaded by the chain. This decrease reduces the number of neighbour chains inside the shared space, lowering the potential inter-chains contacts and resulting chiefly in the effective reduction of entanglements. This idea is illustrated in figure 2c.
The assumption that the number of entanglements is proportional to the volume pervaded by the chain is supported by the chain packing model [4], which unequivocally links both quantities.
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