The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts

Fraaije, J. G. E. M.; Vlimmeren, B.A.C. van; Maurits, Natasha M.; Postma, Maarten J.; Evers, O. A.; Hoffmann, Christian; Altevogt, Peter; Goldbeck, Gerhard

doi:10.1063/1.473129

Cited by 354 publications

(422 citation statements)

References 42 publications

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“…account for the entropy of a system of n ideal Gaussian chains in an external field U I (r). 35 In the next section we will come back to these external fields. In Eq.…”

Section: B Free Energy Modelmentioning

confidence: 99%

“…The model has previously been used to study the diffusive dynamics of the domain formation process of a symmetric diblock copolymer. 35,44 A detailed validation has been carried out on ͑PO͒ n ͑EO͒ m ͑PO͒ n block copolymer surfactants. 36 The theory was adapted to describe the behavior of block copolymer under shear.…”

Section: B This Studymentioning

confidence: 99%

“…In the DDFT model the following free energy functional is used to model the behavior of an one-component polymer melt. 35,38 F͓͕ ͖͔ϭϪkT ln ⌽Љ…”

Section: B Free Energy Modelmentioning

confidence: 99%

“…35,36,38,39 In the DDFT model a box with periodic boundaries is filled with fixed amounts of beads of different types, ͕N I ͖. A polymer is represented as a string of beads.…”

Section: A Dynamicsmentioning

confidence: 99%

“…34͒ and a dynamic density functional theory ͑DDFT͒. 35 We have used the DDFT approach. The DDFT model combines the Langevin equation, which handles the dynamics on a mesoscopic scale, and a free energy functional for polymers, based on the Gaussian chain model.…”

Section: B This Studymentioning

confidence: 99%

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Asymmetric block copolymers confined in a thin film

Huinink

Brokken-Zijp

Dijk

et al. 2000

The Journal of Chemical Physics

186

318

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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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“…account for the entropy of a system of n ideal Gaussian chains in an external field U I (r). 35 In the next section we will come back to these external fields. In Eq.…”

Section: B Free Energy Modelmentioning

confidence: 99%

Section: B This Studymentioning

confidence: 99%

“…In the DDFT model the following free energy functional is used to model the behavior of an one-component polymer melt. 35,38 F͓͕ ͖͔ϭϪkT ln ⌽Љ…”

Section: B Free Energy Modelmentioning

confidence: 99%

“…35,36,38,39 In the DDFT model a box with periodic boundaries is filled with fixed amounts of beads of different types, ͕N I ͖. A polymer is represented as a string of beads.…”

Section: A Dynamicsmentioning

confidence: 99%

Section: B This Studymentioning

confidence: 99%

See 3 more Smart Citations

Asymmetric block copolymers confined in a thin film

Huinink

Brokken-Zijp

Dijk

et al. 2000

The Journal of Chemical Physics

186

318

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Molecular Modeling

Eichinger¹,

Khare²

2002

Encyclopedia of Polymer Science and Technology

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The application of the methods of computational chemistry and physics to polymeric systems within the last two decades has generated an arsenal of techniques that are designed to analyze and predict the properties of this important class of materials. Much effort has been devoted to solving the length and timescale problems that polymers present. Concurrently, accurate force field descriptions of condensed phases, including efforts to treat reacting systems, is enabling significant predictions of properties to be made reliably. Many of these techniques are discussed, as is an array of results that have been obtained by a variety of methods.

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Coarse-Graining in Polymer Simulation: From the Atomistic to the Mesoscopic Scale and Back

2002

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Polymers can be theoretically and computationally described by models pertaining to different length scales and corresponding time scales. These models have traditionally been used independently of each other. Recently, considerable progress has been made in systematically linking models of different scales. This Review focuses on the generation of lattice and off‐lattice coarse‐grained polymer models, whose “monomers” correspond to roughly a chemical repeat unit, from chemically detailed atomistic simulations of the same polymers. Computational methods are described as well as applications to polymers in the melt and in solution. The success of multiscale simulations in solving real‐world polymer problems that could not be solved in any other way suggests that they will have an important role to play in the future.

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The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts

Cited by 354 publications

References 42 publications

Asymmetric block copolymers confined in a thin film

Asymmetric block copolymers confined in a thin film

Molecular Modeling

Coarse-Graining in Polymer Simulation: From the Atomistic to the Mesoscopic Scale and Back

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