The name is absent



and for other segments,

PjH = г r∩V qn exp[nX2)ljljWj2j(^), for z>⅛.

(6.21)


Clearly, this derivation is only for the polymer chains grafted to the wall at z =
0. For the case of two grafted monolayers, similar results can be obtained for the
polymer chains grafted to the wall at z = H, where H is the separation between
the two surfaces. The force of interaction between the two grafted surfaces (in the
absence∕presence of free polymer) at separation H, is given by [246]
where Ω is the equilibrium grand free energy, A is the surface area of the two surfaces,
and H → ∞ implies the limit when the separation between the two surfaces is large
enough that the monolayers do not interact with each other. If
f is positive, the
surfaces repel each other and if
f is negative, they attract. In the current work, the
two hard surfaces are grafted with same polymer chains at the same grafting density.
Hence, the density profiles of the two grafted monolayers are symmetric. For such a
symmetric system, the functional derivative of the grand free energy can be simplified
as [246]

/(Я) _ (

A AδH


1 5Ω
AδH


H→<x>


(6.22)


≡φ∕⅛¾    <-)

a

where λTjrt,s is the external field on segment a due to a single surface at z = 0. For

154



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