the grand free energy,
<5Ω _ Γ JΩ ∂pa(r) ∙sr~> f 5Ω ∂ua(ι
δH = ½-'J δpa(r) ∂H dr + ^J δua(r) ∂H
a ∣x∕ gi ∖ /
(6.33)
or
dV∞t(r)
~4H~dr-
(6.34)
In one dimension
dVSκ‰)
dH ’
(6.35)
where
Vaat(z) = V^l"sβz') + V'xt∙s2(H - z
(6.36)
V^xt'sl is the external potential on segment a due to the surface at z = 0 and
ɪ/eæt,s2 jue to tjιe 0t]ιer surface at z = H. If both these surfaces are similar, i.e.
V^≈rf,sl (z) = veχt>s2(}/ — zj and density profiles of the grafted chains at the two sur-
faces are symmetric, then this functional derivative can be expressed as [246]
g-ΛΣA(√*⅛‰.
α
(6.37)
For the polymer chains grafted at the surface at z — 0, the external potential
acting on the segments are: for the tethered segment,
exp(-βVfxt,sl (z∖) = exp(-βv}δ(z)
177
(6.38)