the scaling relations of Alexander [51] and de Gennes [52]. The presence of a solvent
in the case of ‘wet brush’, compresses the brush due to entropie effects. The increase
in the number of segments in the free polymer solvent at the same monomer density
decreases the brush height. Again the theoretical results are in good quantitative
agreement with the simulation results.
The force of interaction between the two grafted monolayers in the absence∕presence
of free polymer is also investigated. In case of no free polymer, the interaction force
is always repulsive due to the steric hindrance of the monolayers. The detailed seg-
ment density profiles of the two monolayers show that as the monolayers approach,
they compress each other. The interaction force for different grafting densities and
chain lengths of the grafted polymer follows the scaling relation, f pig2 F(H ∕2H0),
previously proposed by Alexander [51] and confirmed using molecular dynamics sim-
ulations by Murat and Grest [247] and Chandler McCoy Singer (CMS) DFT by
McCoy and Curro [248]. However, the interpretation of the arguments to the func-
tion, F(H∕Ho), is different in the two studies. McCoy and Curro defined an average
layer thickness of the grafted monolayers, L as 2 ∙ From their DFT results,
they developed an empirical expression for L∕2H0 as a function of H∕2Ho and showed
that f ~ p3g2F(L∕2H0). On the contrary, simulation results from Murat and Grest
show that f pg^2F{H∕2Ho) which is in agreement with our results using modified
iSAFT.
The situation is more complicated when free polymer is present between the two
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