Triblock Copolymer Theory: Ordered ABC Lamellar Phase |
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Authors: | Ren and Wei |
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Institution: | (1) Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA e-mail: ren@math.usu.edu, US;(2) Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China, HK |
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Abstract: | Summary. The ABC lamellar phase of a triblock copolymer in the strong segregation region is studied on periodic and bounded intervals. In
the periodic case we find a family of local minimizers of the free energy functional all with a fine lamellar structure. Among
these local minimizers we identify the one most favored by the free energy, and hence determine the thickness of lamellar
microdomains. In the bounded interval case we show that perfect lamellar structure does not exist due to the boundary effect.
We view the strong segregation limit as a Γ -limit of the free energy by a proper choice of the material sample size. The key step is the spectral analysis of a large
matrix resulting from the second derivative of the Γ -limit. |
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Keywords: | , Triblock copolymer, local minimizer, global minimizer, Γ, -convergence |
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