Search Advanced

Networks and Heterogeneous Media

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

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.

    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

    Related Papers:

    [1] Michael Helmers, Barbara Niethammer, Xiaofeng Ren . Evolution in off-critical diblock copolymer melts. Networks and Heterogeneous Media, 2008, 3(3): 615-632. doi: 10.3934/nhm.2008.3.615
    [2] Karoline Disser, Matthias Liero . On gradient structures for Markov chains and the passage to Wasserstein gradient flows. Networks and Heterogeneous Media, 2015, 10(2): 233-253. doi: 10.3934/nhm.2015.10.233
    [3] Felisia Angela Chiarello, Harold Deivi Contreras, Luis Miguel Villada . Nonlocal reaction traffic flow model with on-off ramps. Networks and Heterogeneous Media, 2022, 17(2): 203-226. doi: 10.3934/nhm.2022003
    [4] Fabian Rüffler, Volker Mehrmann, Falk M. Hante . Optimal model switching for gas flow in pipe networks. Networks and Heterogeneous Media, 2018, 13(4): 641-661. doi: 10.3934/nhm.2018029
    [5] Luis Almeida, Federica Bubba, Benoît Perthame, Camille Pouchol . Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations. Networks and Heterogeneous Media, 2019, 14(1): 23-41. doi: 10.3934/nhm.2019002
    [6] Gabriella Bretti, Roberto Natalini, Benedetto Piccoli . Numerical approximations of a traffic flow model on networks. Networks and Heterogeneous Media, 2006, 1(1): 57-84. doi: 10.3934/nhm.2006.1.57
    [7] Gianni Dal Maso, Francesco Solombrino . Quasistatic evolution for Cam-Clay plasticity: The spatially homogeneous case. Networks and Heterogeneous Media, 2010, 5(1): 97-132. doi: 10.3934/nhm.2010.5.97
    [8] Ioannis Markou . Hydrodynamic limit for a Fokker-Planck equation with coefficients in Sobolev spaces. Networks and Heterogeneous Media, 2017, 12(4): 683-705. doi: 10.3934/nhm.2017028
    [9] Matthias Erbar, Dominik Forkert, Jan Maas, Delio Mugnolo . Gradient flow formulation of diffusion equations in the Wasserstein space over a Metric graph. Networks and Heterogeneous Media, 2022, 17(5): 687-717. doi: 10.3934/nhm.2022023
    [10] Olli-Pekka Tossavainen, Daniel B. Work . Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data. Networks and Heterogeneous Media, 2013, 8(3): 803-824. doi: 10.3934/nhm.2013.8.803
  • 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.


  • This article has been cited by:

    1. Barbara Niethammer, Yoshihito Oshita, A rigorous derivation of mean-field models for diblock copolymer melts, 2010, 39, 0944-2669, 273, 10.1007/s00526-010-0310-x
    2. Nam Q. Le, On the Convergence of the Ohta–Kawasaki Equation to Motion by Nonlocal Mullins–Sekerka Law, 2010, 42, 0036-1410, 1602, 10.1137/090768643
    3. Barbara Niethammer, Yoshihito Oshita, A rigorous derivation of mean-field models describing 2D micro phase separation, 2020, 59, 0944-2669, 10.1007/s00526-020-1706-x
    4. Rustum Choksi, Mark A. Peletier, Small Volume-Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional, 2011, 43, 0036-1410, 739, 10.1137/10079330X
    5. Karl Glasner, Rustum Choksi, Coarsening and self-organization in dilute diblock copolymer melts and mixtures, 2009, 238, 01672789, 1241, 10.1016/j.physd.2009.04.006
    6. Lisa J. Larsson, Rustum Choksi, Jean-Christophe Nave, Geometric Self-Assembly of Rigid Shapes: A Simple Voronoi Approach, 2016, 76, 0036-1399, 1101, 10.1137/15M1034167
    7. Barbara Niethammer, Evolution in dilute diblock-copolymer melts, 2011, 34, 09367195, 130, 10.1002/gamm.201110021
    8. Rustum Choksi, Mark A. Peletier, Small Volume Fraction Limit of the Diblock Copolymer Problem: I. Sharp-Interface Functional, 2010, 42, 0036-1410, 1334, 10.1137/090764888
    9. Stanley Alama, Lia Bronsard, Xinyang Lu, Chong Wang, On a quaternary nonlocal isoperimetric problem, 2023, 82, 0033-569X, 97, 10.1090/qam/1675
  • Reader Comments
  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.9

Metrics

Article views(4267) PDF downloads(85) Cited by(9)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog