Date: 24 Oct 2005

Droplet solutions in the diblock copolymer problem with skewed monomer composition

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A droplet solution characterizes the lamellar phase of a diblock copolymer when the two composing monomers maintain a skewed ratio. We study the threshold case where the free energy of a droplet solution is comparable to the free energy of the constant solution. Using a Lyapunov-Schmidt reduction approach, adapted to calculus of variations, we prove the existence of a free energy local minimizer with a given number of droplets. Also determined are the free energy, the droplet location, and the droplet size.

Supported in part by a Direct Grant from CUHK and an earmarked Grant of RGC of Hong Kong.