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Figure 5.6: Excess surface free energy of the copolymer as a function of the effective film
thickness, for symmetric phases of the copolymer. For the diblock copolymer, N = 8 and
ekT = 0.289. For surfaces, ew∕kT = 0.1.

able to attain their bulk equilibrium period, Db. However, there is a slight offset from
the actual value of D;, due to packing near the wall. This offset is accounted by
δ.
Thus the excess surface free energy is at minimum at integer values of Heyʃ when the
film lamellar period is in accord with the bulk equilibrium period. The values of the
excess free energy are the same at all the integer values of Heyy. In any lɪ phase,
the free energy is higher for He∕y < 
n when the lamella are compressed and Heyγ > n
when the lamella are stretched than their preferred lamellar period. For He∫∫ > n, as
the lamella are highly stretched the copolymer undergoes the transition from lɪ to
^2(n+ι) phase to decrease the excess surface free energy.

We can also observe the anti-symmetric ʃɪ-i-i lamellar structures of the diblock
copolymer. Figure 5.7 shows the anti-symmetric segment density profiles of the two

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