^{1,a)}and Johannes G. E. M. (Hans) Fraaije

^{2}

### Abstract

The dynamics of alignment of microstructure in confined films of diblock copolymer melts in the presence of an external electric field was studied numerically. We consider in detail a symmetric diblock copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory. The time evolution of concentration variables and therefore the alignment kinetics of the morphologies are described by a set of stochastic equations of a diffusion form with Gaussian noise. We investigated the effect of an electric field on block copolymers under the assumption that the long-range dipolar interaction induced by the fluctuations of composition pattern is a dominant mechanism of electric-field-induced domain alignment. The interactions with bounding electrodesurfaces were taken into account as short-range interactions resulting in an additional term in the free energy of the sample. This term contributes only in the vicinity of the surfaces. The surfaces and the electric field compete with each other and align the microstructure in perpendicular directions. Depending on the ratio between electric field and interfacial interactions, parallel or perpendicular lamellar orientations were observed. The time scale of the electric-field-induced alignment is much larger than the time scale of the surface-induced alignment and microphase separation.

I. INTRODUCTION

II. THEORY: THERMODYNAMICS AND EQUATIONS OF BLOCK COPOLYMER MORPHOLOGY DYNAMICS IN AN EXTERNAL ELECTRIC FIELD

III. NUMERICAL PROCEDURE AND CHARACTERISTICS OF AN ORIENTATIONAL ORDER

IV. RESULTS AND DISCUSSION

V. CONCLUDING REMARKS

### Key Topics

- Electric fields
- 116.0
- Lamellae
- 103.0
- Block copolymers
- 81.0
- Surface morphology
- 36.0
- Free energy
- 26.0

## Figures

Isosurface representation of a symmetric diblock copolymer melt for and the projection of the 3D structure factor at different dimensionless times . The surface related interaction parameter is , corresponding to the adsorption energy per statistical unit.

Isosurface representation of a symmetric diblock copolymer melt for and the projection of the 3D structure factor at different dimensionless times . The surface related interaction parameter is , corresponding to the adsorption energy per statistical unit.

The part of the total free energy of a diblock copolymer as a function of time for the surface related interaction parameter .

The part of the total free energy of a diblock copolymer as a function of time for the surface related interaction parameter .

The enlarged part of the two-cluster morphology shown in Fig. 1(e) containing the region of cluster dividing surface (the position ranges between and ). The region exhibits a doubly periodic array of saddle surfaces.

The enlarged part of the two-cluster morphology shown in Fig. 1(e) containing the region of cluster dividing surface (the position ranges between and ). The region exhibits a doubly periodic array of saddle surfaces.

The morphology scans through the region of cluster dividing surface in the same ranges, as shown in Fig. 3. The morphologies shown are orthoslices of two-cluster morphology from Fig. 1(e) at different positions. The regions containing more blocks are colored black with linear gray scale of the density from 0.0 (black) to 1.0 (white).

The morphology scans through the region of cluster dividing surface in the same ranges, as shown in Fig. 3. The morphologies shown are orthoslices of two-cluster morphology from Fig. 1(e) at different positions. The regions containing more blocks are colored black with linear gray scale of the density from 0.0 (black) to 1.0 (white).

Evolution of the orientational order parameter corresponding to the morphological transformations shown in Fig. 1. The surface related interaction parameter is .

Evolution of the orientational order parameter corresponding to the morphological transformations shown in Fig. 1. The surface related interaction parameter is .

The time evolution of stresses in the morphology due to domains (curve 1), (curve 2), and (curve 3).

The time evolution of stresses in the morphology due to domains (curve 1), (curve 2), and (curve 3).

An intermediate structure of two coexisting lamellae clusters of parallel to the electric field lamellae and the final morphology for the surface related interaction parameters (a) , (b) 0.7, and (c) 0.8. The -axis projections in the direction of the applied electric field of the morphologies are shown.

An intermediate structure of two coexisting lamellae clusters of parallel to the electric field lamellae and the final morphology for the surface related interaction parameters (a) , (b) 0.7, and (c) 0.8. The -axis projections in the direction of the applied electric field of the morphologies are shown.

Isosurface representation of an diblock copolymer melt for and the projections of the lamellar morphology for the surface related interaction parameter , corresponding to the adsorption energy per statistical unit.

Isosurface representation of an diblock copolymer melt for and the projections of the lamellar morphology for the surface related interaction parameter , corresponding to the adsorption energy per statistical unit.

Time evolution of the orientational order parameter in the presence (solid line) and in the absence (dashed line) of an external electric field. The surface related interaction parameter is the same for both cases.

Time evolution of the orientational order parameter in the presence (solid line) and in the absence (dashed line) of an external electric field. The surface related interaction parameter is the same for both cases.

Time evolution of stresses in the subjected to the electric field sample, , due to domain transformations: (curve 1), (curve 2), and (curve 3). The transformations in stresses are related to morphological evolution shown in Fig. 8.

Time evolution of stresses in the subjected to the electric field sample, , due to domain transformations: (curve 1), (curve 2), and (curve 3). The transformations in stresses are related to morphological evolution shown in Fig. 8.

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