doi:10.11777/j.issn1000-3304.2018.18097

引用本文: 宋俊清, 刘一新, 张红东. 软受限条件下嵌段共聚物薄膜缺陷消除的理论研究[J]. 高分子学报, 2018, (12): 1548-1557. doi: 10.11777/j.issn1000-3304.2018.18097 shu

Citation: Jun-qing Song, Yi-xin Liu and Hong-dong Zhang. Theoretical Study on Defect Removal in Block Copolymer Thin Films under Soft Confinement[J]. Acta Polymerica Sinica, 2018, (12): 1548-1557. doi: 10.11777/j.issn1000-3304.2018.18097 shu

软受限条件下嵌段共聚物薄膜缺陷消除的理论研究

聚合物分子工程国家重点实验室复旦大学高分子科学系　上海 200438

通讯作者: 刘一新, E-mail: lyx@fudan.edu.cn

基金项目: 上海市浦江人才计划(项目号 18PJ1401200)、国家自然科学基金(基金号 21004013)和国家重点基础研究发展计划项目(项目号 2011CB605701)资助

摘要: 理解缺陷消除机理对于制备无缺陷的长程有序嵌段共聚物薄膜至关重要. 本文利用弦方法结合自洽平均场理论研究了接枝均聚物高分子刷在AB两嵌段共聚物垂直层薄膜的偶极位错缺陷消除中发挥的作用. 研究发现，高分子刷的“浸润效应”和“重排效应”能够降低χ_AB的有效值，增大跳跃扩散的扩散系数，进而促进“桥连”结构的形成. 并且，接枝高分子刷的基底表面的“硬度”越小，以上2种效应越显著，越能进一步降低缺陷消除过程中形成“桥连”结构这一关键步骤的能垒.

关键词:

English

Theoretical Study on Defect Removal in Block Copolymer Thin Films under Soft Confinement

State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200438

Corresponding author: Yi-xin Liu, E-mail: lyx@fudan.edu.cn

Received Date: 2018-03-29
Accepted Date: 2018-04-24
Available Online: 2018-12-01

Abstract: Understanding the defect removal process is crucial for the fabrication of defect-free self-assembled structures in block copolymer thin films. In this study, the removal of the dislocation dipole defect in thin films of perpendicular lamellar block copolymers on substrates modified by grafting polymers has been extensively studied. As revealed in previous studies, the " bridge” structure, which converts the slow hopping diffusion of block copolymer chains to fast interfacial diffusion, is a key factor to understand the mechanism of the defect removal process. Polymer grafting onto substrates is a widely accepted way to control domain orientation and fabricate surface pattern for directed self-assembly (DSA). However, the role of the grafted polymers on defect removal is unclear. In this study, the string method coupled with the self-consistent field theory (SCFT) is used to explore the influence of grafted polymers on the removal of a dislocation dipole in lamellar-froming thin films assembled by symmetric AB diblock copoymers. It is found that the " immersion effect” and the " rearrangement effect” introduced by the grafted polymers can facilitate the hopping diffusion of the block copolymer chains through reducing the effective χ_AB, thus making the formation of the bridge structure easier. The decrease of the softness of the brush layer (γ) will enhance these two effects and reduce the energy barrier of the transition state of the defect removal process. In the limit of γ = 0, the bridge structure is found to already exist in the dislocation dipole near the brush layer, leading to a diminishing energy barrier of the removal process. Using the symmetric PS-b-PMMA with a number-average molecular weight of ≈ 5.1 × 10⁴ at 195 °C as an example, we estimated the annealing time required to eliminate the dislocation dipole by assuming the diffusion coefficient of the hopping diffusion of block copolymers being D_⊥ ≈ 10⁻¹³ cm²/s. The annealing time are estimated to be τ = 91.4 s and 150.9 s for extremely soft confinement (γ = 0) and intermediate soft confinement (γ = 30), respectively. During the defect removal process, the brush layer will redistribute its density along the normal and the lateral directions of the substrate in response to the structural evolution of the thin film due to the " rearrangement effect”. Thus, the morphology of the brush layer reflects the microstructure of the thin film near the bottom substrate.

Key words:

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Figure 1. Free energy difference (ΔF_d) between a dislocation dipole and perfect lamellae as a function of physical size in x direction across the layers (a), and y direction along the layers (b). The simulations are conducted in a two-dimensional AB diblock copolymer system.

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Figure 2. MEP for the transition between the defective (α = 0) and the perfect lamellae obtained using the string method associated with SCFT. No energy barrier is found along the MEP. Blue: the brush layer; red: A-rich domains; green: B-rich domains. The softness of the brush layer is γ = 0 and the length of brush chain is ϵ = 0.2.

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Figure 3. Density distribution of component A in Fig. 2 as a function of the film depth parameterized by z: (a) three-dimensional morphology of the thin film; two-dimensional morphology of component A at (b) z = 0R_g, (c) z = 2.9R_g and (d) z = 3.4R_g. (e): Density distribution of A component along the yellow dotted line with different film depths. The thickness of AB block copolymer film is ${\bar \phi _{{\rm{AB}}}}d$ = 3.51R_g.

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Figure 4. Density amplitude ϕ_C,max − ϕ_C,min of grafted brush in xy plane as a function of film depth d − z from bottom substrate: (a) defect-free lamellae, (b) dislocation dipole, (c) rearrancement degree of brush ${κ} = 1/A \!\!\displaystyle\mathop {\text{\rotatebox[origin=t]{12}{\scalebox{0.95}[1]{\int}}}} \limits \!\! \sqrt {{{\left[ {{ϕ} \left( z \right) - 1} \right]}^2}} {\rm d}A$ with ${ϕ} \left( z \right) = {{ϕ} _{\rm{C}}}\left( z \right)/{\bar {ϕ} _{\rm{C}}}\left( z \right)$

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Figure 5. Responsive density rearrangement of the grafted brush by morphology of ϕ(z) with d – z = 1 R_g during the defect removal process in Fig. 2

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Figure 6. (a) MEP for the transition between a dislocation dipole and perfert lamellae on grafted brush with different γ (The online version is colorful.); (b) Corresponding free energy difference $\Delta {f_{\rm{d}}} = {(}{{F_{\rm{d}}} - {F_{\rm{p}}}} {)}/{(}{{d}{{\bar {ϕ} }_{{\rm{AB}}}}} {)}$ ; (c) Energy barrier of the transition state over defect $\Delta {f_{\rm{b}}} = \left( {{F_{{\rm{tran}}}} - {F_{\rm{d}}}} \right)/{(} {{d}{{\bar {ϕ} }_{{\rm{AB}}}}} {)}$

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Figure 7. (a) MEP for the transition between a dislocation dipole and perfert lamellae on grafted brush with different ϵ (The online version is colorful.); (b) Corresponding free energy difference Δ f_d; (c) Energy barrier Δ f _b

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Table 1. Annealing time estimated from kinetic barriers at different softness parameters for PS-b-PMMA system