Three-dimensional mesoscale dynamics of block copolymers under shear:  The dynamic density-functional approach

Zvelindovsky, Andrei; Sevink, G. J. A.; Vlimmeren, B.A.C. van; Maurits, Natasha M.; Fraaije, J. G. E. M.

doi:10.1103/physreve.57.r4879

Cited by 97 publications

(118 citation statements)

References 31 publications

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“…Since these process is spatially inhomogeneous, such a transition is not compatible with the treatment in the reciprocal lattice space (Fourier space), where spatially periodic lattice structures are assumed. Therefore, dynamical simulations in real space, such as the dynamical SCF simulation, is necessary to correctly investigate this transition 36,37,38,39 . In the present paper, we study the epitaxial OOT G → C using the dynamical SCF theory under shear flows.…”

Section: Introductionmentioning

confidence: 99%

Epitaxial Transition from Gyroid to Cylinder in a Diblock Copolymer Melt

Honda

Kawakatsu

2006

Macromolecules

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An epitaxial transition from a bicontinious double gyroid to a hexagonally packed cylinder structure induced by an external flow is simulated using real-space dynamical self-consistent field technique. In order to simulate the structural change correctly, we introduce a system size optimization technique by which emergence of artificial intermediate structures are suppressed. When a shear flow in [111] direction of the gyroid unit cell is imposed, a nucleation and growth of the cylinder domains is observed. We confirm that the generated cylindrical domains grow epitaxially to the original gyroid domains as gyroid d {220} → cylinder d {10} . In a steady state under the shear flow, the gyroid shows different reconnection processes depending on the direction of the velocity gradient of the shear flow. A kinetic pathway previously predicted using the self-consistent field theory where three fold junctions transform into five fold junctions as an intermediate state is not observed.

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Section: Introductionmentioning

confidence: 99%

Epitaxial Transition from Gyroid to Cylinder in a Diblock Copolymer Melt

Honda

Kawakatsu

2006

Macromolecules

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“…36 The theory was adapted to describe the behavior of block copolymer under shear. 37 Recently, the theory has been extended to study the influence of hard objects on the domain formation process of block copolymers. 38 In fact, our study is a systematic investigation of a block copolymer melt in contact with a specific class of hard objects: infinite parallel surfaces.…”

Section: B This Studymentioning

confidence: 99%

“…38 The influence of the slit is at least twofold. First, it is known that external forces, like electric fields 48 and flow fields, 37 can reduce the time scales connected with long range ordering enormously. The influence of a slit on the ordering process can be thought of in terms of an external force.…”

Section: E Dynamics In a Slitmentioning

confidence: 99%

Asymmetric block copolymers confined in a thin film

Huinink

Brokken-Zijp

Dijk

et al. 2000

The Journal of Chemical Physics

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We have used a dynamic density functional theory ͑DDFT͒ for polymeric systems, to simulate the formation of micro phases in a melt of an asymmetric block copolymer, A n B m ( f A ϭ1/3), both in the bulk and in a thin film. In the DDFT model a polymer is represented as a chain of springs and beads. A spring mimics the stretching behavior of a chain fragment and the spring constant is calculated with the Gaussian chain approximation. Simulations were always started from a homogeneous system. We have mainly investigated the final morphology, adopted by the system. First, we have studied the bulk behavior. The diblock copolymer forms a hexagonal packed array of A-rich cylinders, embedded in a B-rich matrix. Film calculations have been done by confining a polymer melt in a slit. Both the slit width and surface-polymer interactions were varied. With the outcomes a phase diagram for confined films has been constructed. Various phases are predicted: parallel cylinders (C ʈ ), perpendicular cylinders (C Ќ ), parallel lamellae (L ʈ ), and parallel perforated lamellae (CL ʈ ). When the film surfaces are preferentially wet by either the A or the B block, parallel oriented microdomains are preferred. A perpendicular cylindrical phase is stable when neither the A nor B block preferentially wets the surfaces. The predicted phase diagram is in accordance with experimental data in the literature and explains the experimentally observed differences between films of asymmetric block copolymers with only two parameters: the film thickness and the energetic preference of the surface for one of the polymer blocks. We have also observed, that confinement speeds up the process of long range ordering of the microdomains.

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“…Recently we have reported 3D density functional calculations for these two phases 23,24 . Here we report on the effect of shear on more complex phases -bicontinuous gyroid and lamellar/cylinder coexistence in a three component copolymer system.…”

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confidence: 99%

Shear-induced transitions in a ternary polymeric system

2000

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The first three-dimensional simulation of shear-induced phase transitions in a polymeric system has been performed. The method is based on dynamic density-functional theory. The pathways between a bicontinuous phase with developing gyroid mesostructure and a lamellar/cylinder phase coexistence are investigated for a mixture of flexible triblock ABA-copolymer and solvent under simple steady shear.Various self assembly systems such as lyotropic liquid crystals, surfactants, block copolymers can form ordered mesophases (lamellar, cylindrical, spherical, etc). These phases have received much attention because of the fundamental interest to establish universal laws for self-organization phenomena, and also because of the wide range of applications in materials science 1-6 .An interesting issue in the design of new materials is modulation of phase behaviour by external and internal factors such as flows 7 , reactions 8 , temperature inhomogeneity 9 , confinements and surfaces 10 . In particular, externally applied shear flows are found to lead to macroscale order in block copolymer systems. Moreover, shear introduces a new kind of phase behaviour of block copolymer systems, the so-called orientational phase transitions 11-14 .So far, lamellar, hexagonal cylindrical and cubic micellar phases of block copolymers 1

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Three-dimensional mesoscale dynamics of block copolymers under shear: The dynamic density-functional approach

Cited by 97 publications

References 31 publications

Epitaxial Transition from Gyroid to Cylinder in a Diblock Copolymer Melt

Epitaxial Transition from Gyroid to Cylinder in a Diblock Copolymer Melt

Asymmetric block copolymers confined in a thin film

Shear-induced transitions in a ternary polymeric system

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