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29
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85033180409
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note
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To induce the parallel morphology to appear, we force the self-consistent potential U to be translationally invariant in the x-direction. Then, the converged solution also displays this invariance, so there is a composition modulation only in the z-direction.
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30
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85033172016
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note
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To determine the properties of the bulk lamellar phase, we replace the confining substrates with periodic boundaries and apply eq 2. The free energy given in eq 2 takes a uniformly mixed state as its zero.
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31
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85033160349
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note
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To induce the perpendicualar morphology of the lamellae, we implement periodic boundary conditions in both the x- and z-directions and choose the self-consistent potential to be invariant in the z-direction. Once we have a converged solution in these circumstances, we relax the constraint on U, thus allowing variations in the z-direction. Also, we impose hard wall boundary conditions at z = 0 and z = L + 1. We then recalculate the self-consistent potential, U, thus arriving at a state in which the lamellae are perpendicular to the substrates.
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32
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85033168468
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note
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With χ = 0, and with hard wall conditions in the z-direction, the free energy given by eq 2 is calculated. The appropriate reference state in this case is not the lamellar microphase but rather an ideal melt of homopolymers. Then, γ = F/L is calculated.
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35
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85033170270
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note
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The stabilization of the perpendicular orientation is explained here by the orientation of rigid statistical segments in the vicinity of a hard wall. Interestingly, when the chains are completely flexible, as in the calculation of ref 25, the perpendicular orientation is still stabilized. The AB interfacial tension is lowered near the contact line with a neutral substrate by a factor of order unity. The effect contributes to Δ with the same power in N as the nematic stabilization discussed here.
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