Block Copolymer Theory. II. Statistical Thermodynamics of the Microphases

  • Eugene Helfand
Part of the Polymer Science and Technology book series (POLS, volume 4)


A theory of block copolymers has been developed based on an earlier mean-field approach to inhomogeneous macromolecular materials. Domains form in block copolymer systems. Then, as a result of the tendency of the block joints to stay in the interfacial regions, there is a loss of entropy in two ways. One is due to the confinement of the joints to a smaller region than when the system is homogeneous. The other has its origin in the vast number of polymer conformations which are suppressed because they create excessive density inhomogeneity. As domains grow, these two conformational free energy terms increase and must be balanced against the decrease of interfacial free energy to determine the equilibrium domain size and shape. The necessary statistics of the molecules are embodied in the solutions of modified diffusion equations. There are no adjustable parameters. Some numerical results for lamellar systems are presented. The paper concludes with a critique of prior theories, and a list of the type of experimental investigations which will shed light on block copolymer systems and other polymer blends.


Free Energy Block Copolymer Surface Free Energy Graft Copolymer Uniform Density 
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Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • Eugene Helfand
    • 1
  1. 1.Bell LaboratoriesMurray HillUSA

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