On the spectra of three-dimensional lamellar solutions of the diblock copolymer problem

SIAM Journal on Mathematical Analysis

Volumn 35, Issue 1, 2004, Pages 1-32

  Ren, Xiaofeng ^a   Wei, Juncheng ^b  

^a UTAH STATE UNIVERSITY   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Diblock copolymer; Lamellar solution; Spectrum; Three dimensional stability

Indexed keywords

EID: 0347431105     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002413348     Document Type: Article

References (16)

1. J.W. CAHN AND J.E. HILLIARD, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys., 28 (1958), pp. 258-267.
2. R. CHOKSI, Scaling laws in microphase separation of diblock copolymers, J. Nonlinear Sci., 11 (2001), pp. 223-236.
3. R. CHOKSI AND X. REN, On the derivation of a density functional theory for microphase separation of diblock copolymers, J. Statist. Phys., to appear.
4. P.C. FIFE AND D. HILHORST, The Nishiura-Ohnishi free boundary problem in the 1D case, SIAM J. Math. Anal., 33 (2001), pp. 589-606.
5. B. HELFFER AND J. SJÖSTRAND, Multiple wells in the semiclassical limit. I, Comm. Partial Differential Equations, 9 (1984), pp. 337-408.
6. M. HENRY, Singular limit of a fourth order problem arising in the micro-phase separation of diblock copolymers, Adv. Differential Equations, 6 (2001), pp. 1049-1114.
7. C.B. MURATOV, Theory of domain patterns in systems with long-range interactions of Coulomb type, Phys. Rev. E, 66 (2002), paper 066108.
8. Y. NISHIURA AND I. OHNISHI, Some mathematical aspects of the microphase separation in diblock copolymers, Phys. D, 84 (1995), pp. 31-39.
9. I. OHNISHI, Y. NISHIURA, M. IMAI, AND Y. MATSUSHITA, Analytical solutions describing the phase separation driven by a free energy functional containing a long-range interaction term, Chaos, 9 (1999), pp. 329-341.
10. T. OHTA AND K. KAWASAKI, Equilibrium morphology of block copolymer melts, Macromolecules, 19 (1986), pp. 2621-2632.
11. X. REN AND J. WEI, On energy minimizers of the di-block copolymer problem, Interfaces Free Bound., to appear.
12. X. REN AND J. WEI, Wriggled Lamellar Solutions and Their Stability in the Diblock Copolymer Problem, preprint.
13. X. REN AND J. WEI, On the multiplicity of solutions of two nonlocal variational problems, SIAM J. Math. Anal., 31 (2000), pp. 909-924.
14. X. REN AND J. WEI, Concentrically layered energy equilibria of the di-block copolymer problem, European J. Appl. Math., 13 (2002), pp. 479-496.
15. X. REN AND J. WEI, Triblock copolymer theory: Free energy, disordered phase and weak segregation, Phys. D, 178 (2003), pp. 103-117.
16. X. REN AND J. WEI, Triblock copolymer theory: Ordered ABC lamellar phase, J. Nonlinear Sci., to appear.