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Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers.

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Title: Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers.
Authors: Barua, Amlan K.1 (AUTHOR) abarua@iitdh.ac.in, Chew, Ray1,2 (AUTHOR), Li, Shuwang3 (AUTHOR), Lowengrub, John4 (AUTHOR), Münch, Andreas5 (AUTHOR), Wagner, Barbara6 (AUTHOR)
Source: Journal of Computational Physics. May2023, Vol. 481, pN.PAG-N.PAG. 1p.
Subjects: Diblock copolymers, Asymptotic expansions, Boundary element methods, Integral equations, Scientific community
Abstract: The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space. • Sharp interface limit of Ohta-Kawasaki model through matched asymptotic formulation. • Boundary integral formulation of the resultant Hele-Shaw type equations. • Spectrally accurate computation in space, second order accurate computation in time. • Numerical simulation of steady-state configurations. • Coarsening type behavior observed. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space. • Sharp interface limit of Ohta-Kawasaki model through matched asymptotic formulation. • Boundary integral formulation of the resultant Hele-Shaw type equations. • Spectrally accurate computation in space, second order accurate computation in time. • Numerical simulation of steady-state configurations. • Coarsening type behavior observed. [ABSTRACT FROM AUTHOR]
ISSN:00219991
DOI:10.1016/j.jcp.2023.112032