Delaunay-type interface in a screened model of diblock copolymer melts
Abstract
A diblock copolymer is a soft-matter composed of two chemically distinct block of repeating monomers covalently bonded together at an end-to-end junction to form a single polymer chain. In this paper, we establish the existence of infinitely many smooth periodic unbounded domain patterns of Delaunay-type in ℝ3 that optimize the energy distribution in diblock copolymer melts. We emphasize that pattern domains at the equilibrium correspond to stationary sets of the screened Ohta--Kawasaki free energy functional 𝒫γ(Ω) := |∂Ω| + γ∫Ω∫Ω Gκ(|x−y|) dxdy, where γ>0, κ>0 and Gκ(r)=1/r e−κr is the repulisive Yukawa potential. Equivalently, these equilibria satisfy the corresponding Euler--Lagrange equation ℋΩ(x):= H∂Ω(x) + γ∫Ω Gκ(|x−y|) dy = Const on ∂Ω, where H∂Ω denotes the mean curvature of the surface ∂Ω. By analyzing the linearization of Ω↦ ℋΩ around flat cylinders and applying the Crandall--Rabinowitz bifurcation theorem, for any κ> 0 and sufficiently small γ> 0, we prove the existence of non-trivial, 2π-periodic Delaunay-type equilibrium cylinder interfaces with shapes close to a Delaunay unduloid surface of constant mean curvature.
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BibTeX
@misc{foghem2026delaunaytype,
title = {{Delaunay-type interface in a screened model of diblock copolymer melts}},
author = {Guy Foghem and Mouhamed Moustapha Fall},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01333},
eprint = {2609.01333},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01333},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Delaunay-type interface in a screened model of diblock copolymer melts
AU - Guy Foghem
AU - Mouhamed Moustapha Fall
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01333
UR - https://arxiv.org/abs/2609.01333
AB - A diblock copolymer is a soft-matter composed of two chemically distinct block of repeating monomers covalently bonded together at an end-to-end junction to form a single polymer chain. In this paper, we establish the existence of infinitely many smooth periodic unbounded domain patterns of Delaunay-type in ℝ^3 that optimize the energy distribution in diblock copolymer melts. We emphasize that pattern domains at the equilibrium correspond to stationary sets of the screened Ohta--Kawasaki free energy functional 𝒫_γ(Ω) := |∂Ω| + γ∫_Ω∫_Ω G_κ(|x−y|) dxdy, where γ>0, κ>0 and G_κ(r)=1/r e^−κr is the repulisive Yukawa potential. Equivalently, these equilibria satisfy the corresponding Euler--Lagrange equation ℋ_Ω(x):= H_∂Ω(x) + γ∫_Ω G_κ(|x−y|) dy = Const on ∂Ω, where H_∂Ω denotes the mean curvature of the surface ∂Ω. By analyzing the linearization of Ω↦ ℋ_Ω around flat cylinders and applying the Crandall--Rabinowitz bifurcation theorem, for any κ> 0 and sufficiently small γ> 0, we prove the existence of non-trivial, 2π-periodic Delaunay-type equilibrium cylinder interfaces with shapes close to a Delaunay unduloid surface of constant mean curvature.
ER -