potential cut-off distance and
1
5
f ^wa
∖ Z
)9
3 ∕rτ ∖3
° t υwa ∖
2 ∖-Γ )
(5.6)
All the interaction diameters are the same, σwa = σw = σ. Furthermore, the surfaces
are symmetric, that is both the surfaces preferentially attract the segments in the A
block with εwA = εw and repel the segments in the B block with ewβ — 0.
The general formulation of modified iSAFT as a DFT was presented in the previ-
ous chapter. As mentioned, the basis of a DFT is the energy minimum principle or
mathematically,
<5Ω[{pα,4(r)} , {pq,b(γ)}]
= 0 Va = l,m, (5.7)
[{pα,Λ }, {pα,s }] equilibrium
where Ω is the grand free energy of the open system at fixed chemical potential (μ),
volume (V), and temperature (T), ра,д is the density of a segment a of type A, {pa,д}
is the set of densities of all the segments in the A block of the copolymer, and m (=
2N) is the total number of segments in the copolymer chain. Since a segment-based
DFT like modified iSAFT treats every segment individually, let {pα} denote the set
of densities of all the segments of the copolymer that are enumerated from 1 to m, 1
being the first segment of the copolymer and m being the last one. It is to be noted
that 1 to N are the segments in the A block and (N+l) to m are the segments in the
B block of the copolymer. The set of eqs. 5.7 can be reformulated in terms of the
120
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