Triblock copolymer theory: free energy, disordered phase and weak segregation

DOI10.1016/S0167-2789(02)00808-4zbMath1013.82029OpenAlexW2095436347MaRDI QIDQ1860885

Xiaofengg Ren, Wei, Juncheng

Publication date: 4 March 2003

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(02)00808-4

zbMATH Keywords

free energy functionalself-consistent field theoryorder parameter modeltriblock copolymersvariational approximation method

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Statistical thermodynamics (82B30)

Related Items (17)

Droplet solutions in the diblock copolymer problem with skewed monomer composition ⋮ On the ternary Ohta-Kawasaki free energy and its one-dimensional global minimizers ⋮ Periodic patterns for a model involving short-range and long-range interactions ⋮ The soliton-stripe pattern in the Seul--Andelman membrane ⋮ Uniform bound on the number of partitions for optimal configurations of the Ohta–Kawasaki energy in 3D ⋮ MANY DROPLET PATTERN IN THE CYLINDRICAL PHASE OF DIBLOCK COPOLYMER MORPHOLOGY ⋮ A double bubble in a ternary system with inhibitory long range interaction ⋮ Single droplet pattern in the cylindrical phase of diblock copolymer morphology ⋮ Stability of spot and ring solutions of the diblock copolymer equation ⋮ A double bubble assembly as a new phase of a ternary inhibitory system ⋮ Nonhexagonal Lattices From a Two Species Interacting System ⋮ Ring pattern solutions of a free boundary problem in diblock copolymer morphology ⋮ Disc-disc structure in a two-species interacting system on a flat torus ⋮ Stationary disk assemblies in a ternary system with long range interaction ⋮ Energy stable semi-implicit schemes for Allen-Cahn-Ohta-Kawasaki model in binary system ⋮ Periodic minimizers of a ternary non-local isoperimetric problem ⋮ Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem

Cites Work

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• Some mathematical aspects of the micro-phase separation in diblock copolymers
• Triblock copolymer theory: ordered ABC lamellar phase
• The Nishiura--Ohnishi Free Boundary Problem in the 1D Case
• On the Spectra of Three-Dimensional Lamellar Solutions of the Diblock Copolymer Problem
• On the Multiplicity of Solutions of Two Nonlocal Variational Problems
• Analytical solutions describing the phase separation driven by a free energy functional containing a long-range interaction term
• Concentrically layered energy equilibria of the di-block copolymer problem
• Singular limit of a fourth-order problem arising in the microphase separation of diblock copolymers
• Scaling laws in microphase separation of diblock copolymers

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