Evolution in off-critical diblock copolymer melts

Michael Helmers; Barbara Niethammer; Xiaofeng Ren; Michael Helmers; Barbara Niethammer; Xiaofeng Ren

doi:10.3934/nhm.2008.3.615

Networks and Heterogeneous Media

2008, Volume 3, Issue 3: 615-632. doi: 10.3934/nhm.2008.3.615

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Evolution in off-critical diblock copolymer melts

1.
Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB
2.
Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB
3.
Department of Mathematics, The George Washington University, 2115 G Street, Washington, DC 20052

Received: 01 May 2008
82C26, 82D60, 37M05.

We study the evolution of diblock copolymer melts in which one component has small volume fraction. In this case one observes phase morphologies which consist of small spheres of the minority component embedded in the other component. Based on the Ohta-Kawasaki free energy one can set up an evolution equation which has the interpretation of a gradient flow. We restrict this gradient flow to morphologies in which the minority phase consists of spheres and derive monopole approximations for different parameter regimes. We use these approximations for simulations of large particle systems.
- Diblock copolymers,
- gradient flow,
- monopole approximation
Citation: Michael Helmers, Barbara Niethammer, Xiaofeng Ren. Evolution in off-critical diblock copolymer melts[J]. Networks and Heterogeneous Media, 2008, 3(3): 615-632. doi: 10.3934/nhm.2008.3.615

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Abstract

We study the evolution of diblock copolymer melts in which one component has small volume fraction. In this case one observes phase morphologies which consist of small spheres of the minority component embedded in the other component. Based on the Ohta-Kawasaki free energy one can set up an evolution equation which has the interpretation of a gradient flow. We restrict this gradient flow to morphologies in which the minority phase consists of spheres and derive monopole approximations for different parameter regimes. We use these approximations for simulations of large particle systems.
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