Phase behavior of disk-coil block copolymers under cylindrical confinement: Curvature-induced structural frustrations

Min Young Ha, Ji Ho Ryu, Eugene N. Cho, Junwon Choi, YongJoo Kim, and Won Bo Lee

Phys. Rev. E 100, 052502 – Published 15 November 2019

Abstract

In this paper, we explore the self-assembly behavior of disk-coil block copolymers (BCPs) confined within a cylinder using molecular dynamics simulations. As functions of the diameter of the confining cylinder and the number of coil beads, concentric lamellar structures are obtained with a different number of alternating disk-rich and coil-rich bilayers. Our paper focuses on the curvature-induced structural behavior in the disk-rich domain of a self-assembled structure, which is investigated by calculating the local density distribution $P (r)$ and the orientational distribution $G (r, θ)$ . In the inner layers of cylinder-confined disk-coil BCPs, both $P (r)$ and $G (r, θ)$ show characteristic asymmetry within a bilayer which is directly contrasted with the bulk and slab-confined disk-coil BCPs. We successfully explain the structural frustration of disks arising from the curved structure due to packing frustration of disks and asymmetric stretching of coils to the regions with different curvatures in a bilayer. Our results are important to understand the self-assembly behavior of BCPs containing a rigid motif in a confined structure, such as a self-assembled structure of bacteriochlorophyll molecules confined by a lipid layer to form a chlorosome, the photosynthetic antennae complex found in nature.

Received 14 June 2019

DOI:https://doi.org/10.1103/PhysRevE.100.052502

Physics Subject Headings (PhySH)

Biomimetic & bio-inspired materials Confinement Polymer behavior Self-assembly

Polymers & Soft Matter

Authors & Affiliations

Min Young Ha^1,*, Ji Ho Ryu^1,*, Eugene N. Cho², Junwon Choi^3,4, YongJoo Kim^2,†, and Won Bo Lee ^1,‡

¹School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea
²KAIST Institute for NanoCentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
³Chemical Kinomics Research Center, Korea Institute of Science and Technology (KIST), Seoul 02792, Republic of Korea
⁴Bio-Med Division, KIST-School UST, Seoul 02792, Republic of Korea

^*These authors contributed equally to this paper.
^†cjyjee@kaist.ac.kr
^‡wblee@snu.ac.kr

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Vol. 100, Iss. 5 — November 2019

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Images

Figure 1
(a) Modeled disk-coil BCPs. The blue beads represent the peripheral beads of the disk block, and the purple beads represent the coil block. The central bead of the disk block is highlighted in pink. The black lines show three extra harmonic springs, introduced for the rigidity of the disk. (b) Simulated disk-coil BCPs within cylindrical wall with diameter $D$ composed of gray beads.
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Figure 2
(a) A snapshot of the self-assembled structure of disk-coil BCPs with $N_{c} = 3$ and $D = 58.90 σ$ , showing three alternating layered structures. The disk center and coil beads are represented as pink and purple beads, respectively. Peripheral beads of the disks are not shown to emphasize the bilayer structure of the disk-rich layers. (b)–(d) Snapshots of half-concentric lamella highlighted with a blue dashed line in (a) of disk-coil BCPs with (b) $N_{c} = 3, D = 58.90 σ$ , (c) $N_{c} = 4, D = 61.20 σ$ , and (d) $N_{c} = 5, D = 63.68 σ$ where disk-center and disk periphery beads are represented as pink and blue beads, respectively. In (b)–(d), coil beads are removed for visual purpose.
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Figure 3
Structures of disk-coil BCPs in cylindrical confinement as functions of the number of beads of coil $N_{c}$ and the diameter of cylindrical wall $D$ . Dots denote the simulation results, and dashed lines denote hypothetical boundaries. The inset figures are representative snapshots of each structure described by parameter $S$ where the disk-center and coil beads are represented as pink and purple beads, respectively. Peripheral beads of disks are not shown to emphasize the bilayer structure of the disk-rich layers. Note that inset figures are not shown on the same length scale: Snapshots for larger $S$ are obtained from simulations with larger $D$ .
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Figure 4
Local density distribution function $P (r)$ (in units of $σ^{- 3}$ ) of central beads of the disk for $S = 3.0$ , acquired from simulations with (a) $N_{c} = 3, D = 58.90 σ$ , (b) $N_{c} = 4, D = 61.20 σ$ , and (c) $N_{c} = 5, D = 63.68 σ$ , plotted as a function of $r / D$ where $r$ is the radial distance from the cylinder core. Corresponding simulation results of slab-confined disk-coil BCPs are acquired under conditions from Fig. S3 of the Supplemental Material [45]. For the case of slab confinement, $r$ and $D$ denotes the distance from the center of the two confining slabs and the distance between slabs, respectively.
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Figure 5
The orientational distribution function $G (r, θ)$ of disks for $S = 3.0$ , acquired from simulations with (a) $N_{c} = 3, D = 58.90 σ$ , (b) $N_{c} = 4, D = 61.20 σ$ , and (c) $N_{c} = 5, D = 63.68 σ$ , plotted as a function of $r / D$ and $θ$ , where $θ$ is the relative angle between the director vector of the disk and the radial vector from the cylinder axis.
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