Force is zero at large separations, it becomes attractive at intermediate separations
before turning repulsive at lower separations. The attraction roughly begins when the
free ends of the two grafted monolayers come in contact with each other. The mutual
overlap of these free ends of the monolayers is entropically more favorable than the
overlap of the two monolayers with the free polymer, hence the monolayers attract
each other and push the free polymer out. At lower separations when almost all the
free polymer has been expelled, the monolayers overlap extensively and compress each
other which leads to repulsion.
Figure 6.11b shows the effect of changing the bulk free polymer density on the
interaction force between the grafted monolayers at fixed grafting density and chain
lengths of the grafted and free polymers. The unperturbed brush height (when the
two grafted monolayers are far apart) decreases as the bulk free polymer density
increases. The attractive region also decreases with the increase in the bulk free
polymer density such that it completely disappears for pj∙σ3 = 0.75. For this case,
the interaction force is purely repulsive. At such high bulk free polymer density, the
grafted monolayers are already highly compressed and therefore they Sterically hinder
themselves from approaching towards each other.
Similar behavior for the interaction force is observed on changing the chain length
of the free polymer while keeping its bulk density fixed, as shown in fig. 6.12. The in-
teraction force is purely repulsive for smaller chain length while at larger free polymer
chain lengths, the force is attractive at intermediate separations and repulsive at lower
168
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