The name is absent



the grand free energy,


<5Ω _ Γ∂pa(r) ∙sr~> f∂ua
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'xts2(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)




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