Self-consistent field theory of twist grain boundaries in block copolymers

Abstract

We apply self-consistent field theory ͑SCFT͒ to twist grain boundaries of block copolymer melts. The distribution of monomers throughout the grain boundary is obtained as well as the grain boundary free energy per unit area as a function of twist angle. We define an intermaterial dividing surface in order to compare it with minimal surfaces which have been proposed. Our calculation shows that the dividing surface is not a minimal one, but the linear stack of dislocations seems to be a better representation of it for most angles than is Scherk's first surface.

Twist grain boundaries in cubic surfactant phases

“…This result is in agreement with previous investigations of twist grain boundaries in the lamellar phase in diblock copolymer systems. 28,29 In the G and D phases the squared-mean-curvature distributions in the grain-boundary regions compared to the corresponding bulk distributions are also consistent with H 2 =0. The distributions in the grain-boundary regions are slightly broader than in the bulk.…”

“…28 based on the explicit expressions for Scherk's minimal surfaces in combination with bending and compression energies, 44 where some parameters such as the compression modulus are determined from self-consistent field theory for a block copolymer system. 28 Interfacial tensions in the G and D phases have similar behavior. There are two maxima at twist angles of about 30°a nd 70°, where the interfacial tension is comparable in magnitude to the interfacial tension in the lamellar phase.…”

“…Twist grain boundaries are interfaces between two grains of the same phase which differ only by a rotation around an axis perpendicular to the grain boundary. Twist grain boundaries in the lamellar phase have been investigated within self-consistent field theory for diblock copolymers 28 and observed experimentally 29 to have a structure similar to Scherk's minimal surface. Tilt grain boundaries in the lamellar phase, where the normals of the lamellae of the two grains define a plane perpendicular to the boundary, have been shown within a Ginzburg-Landau theory to be chevron-shaped at small tilt angles and omega-shaped at large tilt angles, 22,27 in agreement with experimental results.…”

“…In amphiphilic systems many kinds of interfaces occur: between two ordered phases, between ordered and disordered phases, and between two grains of the same ordered phase which differ by their spacial orientation. Recently, interfaces between coexisting lamellar, hexagonal, and disordered phases, [21][22][23] interfaces between lamellar and gyroid phases, 24,25 dislocations in cubic phases, 26 and grain boundaries in the lamellar phase 22,27,28 have been studied. Twist grain boundaries are interfaces between two grains of the same phase which differ only by a rotation around an axis perpendicular to the grain boundary.…”

Studying Amphiphilic Self-assembly with Soft Coarse-Grained Models

“…For controlling the self-assembled structures and improve the material characteristics for applications in nanoscale device manufacturing, one would like to understand the properties of defects and the structure and thermodynamics of grain boundaries [181][182][183][184][185][186], where domains with different orientations of the periodic structure meet, or interfaces between coexisting morphologies.…”