| Issue |
J. Phys. II France
Volume 7, Number 2, February 1997
|
|
|---|---|---|
| Page(s) | 249 - 255 | |
| DOI | https://doi.org/10.1051/jp2:1997122 | |
J. Phys. II France 7 (1997) 249-255
Analytical Weak-Segregation Theory of Bicontinuous Phases in Diblock Copolymers
Scott T. Milner and Peter D. OlmstedExxon Research & Engineering Company, Corporate Research Science Laboratories, Annandale NJ 08801, USA
(Received 26 July 1996, received in final form 21 October 1996, accepted 7 November 1996)
Abstract
We compute phase diagrams for diblock copolymers in the mean-field weak
segregation regime as a function of the fraction
f of A-monomers and the repulsive interaction
. We include the ordered bicontinuous double-diamond (OBDD) phase [space group Pn3m]
and the gyroid phase [space group Ia3d] as well as lamellae, hexagonal cylinders, and BCC
spheres. We find a stable region of gyroid phase between cylinders and lamellae just above the
mean-field critical point, in agreement with numerical mean-field calculations. The stability
of gyroid depends on the presence of the next higher [220] reflections in addition to the [211]
fundamental. The gyroid free energy is favored by terms of the form
![$\psi_{[211]}^3 \psi_{[220]}$](/articles/jp2/abs/1997/02/jp2v7p249/img2.gif){kind=small}
and
![$\psi_{[211]}^2\psi_{[220]}$](/articles/jp2/abs/1997/02/jp2v7p249/img3.gif){kind=small}
;
the analogous terms are not permitted for OBDD.
© Les Editions de Physique 1997