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September  2008, 3(3): 615-632. doi: 10.3934/nhm.2008.3.615

Evolution in off-critical diblock copolymer melts

Michael Helmers 1, , Barbara Niethammer 2, and  Xiaofeng Ren 3,

1. 

Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, United Kingdom
2. 

Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom
3. 

Department of Mathematics, The George Washington University, 2115 G Street, Washington, DC 20052, United States

Received  May 2008 Published  June 2008

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.
Keywords: monopole approximation, Diblock copolymers, gradient flow.
Mathematics Subject Classification: 82C26, 82D60, 37M0.
Citation: Michael Helmers, Barbara Niethammer, Xiaofeng Ren. Evolution in off-critical diblock copolymer melts. Networks & Heterogeneous Media, 2008, 3 (3) : 615-632. doi: 10.3934/nhm.2008.3.615
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