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Defects in lamellar diblock copolymers: Chevron-and -shaped tilt boundaries Yoav Tsori and David Andelman

Summary: Defects in lamellar diblock copolymers: Chevron- and -shaped tilt boundaries
Yoav Tsori and David Andelman
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University,
69978 Ramat Aviv, Israel
M. Schick
Department of Physics, Box 351560, University of Washington, Seattle, Washington 98195-1560
Received 24 May 1999; revised manuscript received 27 October 1999
The lamellar phase in diblock copolymer systems appears as a result of a competition between molecular
and entropic forces, which selects a preferred periodicity of the lamellae. Grain boundaries are formed when
two grains of different orientations meet. We investigate the case where the lamellae meet symmetrically with
respect to the interface. The form of the interface strongly depends on the angle, , between the normals of the
grains. When this angle is small, the lamellae transform smoothly from one orientation to the other, creating
the chevron morphology. As increases, a gradual transition is observed to an omega morphology character-
ized by a protrusion of the lamellae along the interface between the two phases. We present a theoretical
approach to find these tilt boundaries in two-dimensional systems, based on a Ginzburg-Landau expansion of
the free energy, which describes the appearance of lamellae. Close to the tips at which lamellae from different
grains meet, these lamellae are distorted. To find this distortion for small angles, we use a phase variation
ansatz in which one assumes that the wave vector of the bulk lamellar phase depends on the distance from the
interface. Minimization of the free energy gives an expression for the order parameter (x,y). The results
describe the chevron morphology very well. For larger angles, a different approach is used. We linearize


Source: Andelman, David - School of Physics and Astronomy, Tel Aviv University


Collections: Materials Science; Physics