“lamellae” at the two surfaces is oscillatory due to pronounced packing effects in
agreement with the simulation results [141]. There are two A-B interfaces, hence
these are designated as L2 phases. The actual film thickness of the copolymer is (H -
σ), as the segments cannot penetrate the surfaces. Therefore, at H = 9σ, the lamella
are compressed and at H = 13σ the lamella are stretched compared to their bulk
equilibrium period, Db — 10.2σ. At H = 15σ, we observe the L4 phase. Again, two
half-lamellae of A are at the two surfaces. The lamellar period is less than D⅛ or
the lamella are compressed. The excess surface free energy Ω,s of the copolymer at a
separation H is calculated as the difference of the free energy Ω of the copolymer in the
confinement (at separation H) and the free energy Ωb of the bulk ordered copolymer
in the absence of confining surfaces.
n'(ʃʃ) = (s.i6)
Tl /1 -*-^b
where A is area of the surfaces.
Figure 5.6 shows the excess surface free energy as a function of the effective film
thickness of the copolymer, He∕∕∙
_H-a + S
(5.17)
h'" - ~~dΓ~
where δ accounts for the offset in the lamellar period from D6. Intuitively, the excess
surface free energy should be at minimum when the lamella in the copolymer film are
131
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