brushes are the density functional theories (DFTs). McCoy, Ye and Curro applied
the Chandler, McCoy and Singer density functional theory (CMS-DFT) to study
the structure of athermal [225] and attractive [226] grafted polymer chains in the
presence of implicit or explicit solvent. The authors also discuss the approximations
in the SCFTs which are not present in a typical DFT. However, the applicability of
CMS-DFT, which is based on the polymer reference interaction site model (PRISM)
theory [105] for the bulk polymer fluids, is complicated by ambiguities regarding the
closure relations to be used for specific applications [226].
In this work, modified iSAFT density functional theory is used to study the ef-
fective interaction between (flat) grafted monolayers in the presence of free polymer.
Including compressibility, the scaling relation for the boundary between the repul-
sive and attractive domains is expected to be different from the previous theoretical
studies using SCFT. In particular, the interest is in cases where the segment sizes
of the polymer in the monolayers and the free polymer are not identical, which are
not easily accessible to SCFT. These cases have previously not been addressed by
other theoretical models as well. This work will show that a simple scaling relation
accounts for the effect of the difference in the segment sizes of the grafted and free
polymers on the boundary between the repulsive and attractive domains.
The structure of the grafted monolayers plays an important role in determin-
ing the force of interactions between them. Depending upon the number of poly-
mer chains attached to the surface (grafting density) and the quality of the solvent,
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