Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers

Jeong, Darae; Shin, Jeeyoung; Li, Yibao; Choi, Yongho; Jung, Jae Hun; Lee, Seunggyu; Kim, Junseok

doi:10.1016/j.cap.2014.06.016

Cited by 26 publications

(18 citation statements)

References 54 publications

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“…There have been some efforts on developing energy stable schemes for the PF-BCP model recently (cf. [1,23,44]). These schemes are essentially based on either the nonlinear convex splitting approach (cf.…”

Section: Introductionmentioning

confidence: 99%

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

Cheng

Yang

Shen

2017

Journal of Computational Physics

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Abstract. In this paper, we consider numerical approximations of a hydrodynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

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Section: Introductionmentioning

confidence: 99%

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

Cheng

Yang

Shen

2017

Journal of Computational Physics

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“…The numerical scheme is based on a linearly gradient stable method, and the resulting discrete system of equations is solved by a Fourier-spectral method. To find the optimal wavelength that has the global minimum of the energy, we use the algorithm in a previous paper [21]. We run the computation until the system reaches a numerical equilibrium state.…”

Section: Discussionmentioning

confidence: 99%

“…is the most fastest growth wavelength obtained by a linear stability analysis [21]. Next, we compute the slope of the discrete energy at L x ¼L using the centered difference.…”

Section: Optimal Wavelength Having Minimum Discrete Total Energymentioning

confidence: 99%

Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase

Jeong

Lee

Choi

et al. 2015

Current Applied Physics

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“…Various numerical methods for solving the Ohta-Kawasaki model have been studied [1,7,16]. For the other numerical approach to simulate the block copolymer, we can refer the dynamic mean field theory [9], based on the selfconsistent field theory.…”

Section: Introductionmentioning

confidence: 99%

An Unconditionally Gradient Stable Numerical Method for the Ohta-Kawasaki Model

Kim¹,

Shin²

2017

Bulletin of the Korean Mathematical Society

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Abstract. We present a finite difference method for solving the OhtaKawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the OhtaKawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.

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Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers

Cited by 26 publications

References 54 publications

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase

An Unconditionally Gradient Stable Numerical Method for the Ohta-Kawasaki Model

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