Towards entropy-driven interstitial micelles at elevated temperatures from selective $\mathbit{A}\mathbf{1}\mathbit{BA}2$ triblock solutions

Towards entropy-driven interstitial micelles at elevated temperatures from selective $A 1 BA 2$ triblock solutions

S. Wołoszczuk, S. Jurga, and M. Banaszak

Phys. Rev. E 94, 022502 – Published 29 August 2016

Abstract

We simulate selective $A 1 B A 2 − A$ and $A 1 B A 2 − B$ triblock solutions (that is, mixtures of the $A 1 B A 2$ triblock with a solvent of either type $A$ or type $B$ ) using a lattice Monte Carlo method. Although the simulated triblock chains are compositionally symmetric in terms of the $A$ to $B$ volume ratio, the $A 1$ block is significantly shorter than the $A 2$ block. For the pure $A 1 B A 2$ melt the phase behavior is relatively well known, including the existence and stability of the recently discovered interstitial micelles which were found at the very strong segregation limit. In this paper, we investigate the stability of the interstitial micelles as a function of triblock volume fraction in a selective solvent of either type $A$ or type $B$ . The main finding of this paper is that adding a selective solvent of type $A$ shifts the stability of the interstitial micelles into significantly higher temperatures which may provide a pathway towards experimental studies of interstitial micelles in real triblock solutions. We also find that adding selective solvents to the $A 1 B A 2$ melt gives rise to a variety of nonlamellar nanostructures for temperatures and compositions at which the interstitial micelles are stable.

Received 17 April 2016
Revised 30 May 2016

DOI:https://doi.org/10.1103/PhysRevE.94.022502

Physics Subject Headings (PhySH)

Block copolymers

Monte Carlo methods

Polymers & Soft Matter

Authors & Affiliations

S. Wołoszczuk

Faculty of Physics, Adam Mickiewicz University, ulica Umultowska 85, 61-614 Poznan, Poland

S. Jurga

Department of Macromolecular Physics, NanoBioMedical Centre, Adam Mickiewicz University, ulica Umultowska 85, 61-614 Poznan, Poland

M. Banaszak^*

Faculty of Physics, Adam Mickiewicz University, ulica Umultowska 85, 61-614 Poznan, Poland

^*mbanasz@amu.edu.pl

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Vol. 94, Iss. 2 — August 2016

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Figure 1
Snapshot from a simulation of the $A_{2} - B_{48} - A_{46}$ melt at $T^{*} = 1.7$ which shows interstitial micelles. Long $A 2$ blocks are shown in blue (dark gray), short $A 1$ blocks are shown in yellow (medium gray), and selected $B$ blocks are shown in green (light gray); we show only those $B$ blocks that are connected to the upper-right interstitial micelle.
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Figure 2
(a) The interface-domain crossover temperature $T_{IDC}^{*}$ and (b) the reduced interface-domain crossover temperature $T_{IDC}^{*} / x$ as a function of copolymer volume fraction for the $A 1 B A 2 − A$ solution (left-hand side) and the $A 1 B A 2 − B$ solution (right-hand side). The $A_{1} - B_{48} - A_{47}$ triblock is indicated by open squares, the $A_{2} - B_{48} - A_{46}$ triblock is indicated by open circles, and the $A_{3} - B_{48} - A_{45}$ triblock is indicated by open triangles. Similarly, $x = 1$ , 2 or 3 for the $A_{1} - B_{48} - A_{47}$ triblock, the $A_{2} - B_{48} - A_{46}$ triblock, and the $A_{3} - B_{48} - A_{45}$ triblock, respectively.
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Figure 3
Interstitial micelles are stable between the solid lines which are shown as a function of copolymer volume fraction $Φ$ in the selective $A$ solvent and $B$ solvent and the reduced temperature $T^{*}$ (pure melt is at $Φ = 1$ ). Individual figures refer to the following $A 1 B A 2$ triblock copolymer solutions: (a) $A_{1} - B_{48} - A_{47}$ , (b) $A_{2} - B_{48} - A_{46}$ , and (c) $A_{3} - B_{48} - A_{45}$ . The inset snapshots indicate (a) layers, (b) perforated layers, and (c) spatially ordered cylinders with morphologies formed by the $A 2$ block shown in the blue (dark gray) color. The $A 1$ blocks are shown in yellow (light gray) and are visible as interstitial micelles and dangles within the $B$ domain or dangles at the $A / B$ interface. The $B$ blocks and solvent molecules are not shown for clarity.
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Figure 4
Phase diagrams as a function of the triblock copolymer volume fraction $Φ$ in the selective solvent of either type $A$ (on the left-hand side) or type $B$ (on the right-hand side) and temperature $T^{*}$ . Individual figures refer to the following triblock chains: (a) $A_{1} - B_{48} - A_{47}$ , (b) $A_{2} - B_{48} - A_{46}$ , and (c) $A_{3} - B_{48} - A_{45}$ . A logarithmic scale on the $T^{*}$ axis is used for enhanced clarity. Order-disorder and order-order lines are shown as solid and dashed lines, respectively. L indicates layers, C indicates spatially ordered cylinders, PL indicates perforated layers, B represents the bicontinuous nanostructure, and B/PL means that we observed both B and PL structures. In addition, we mark the borders of the region in which the interstitial micelles are stable by red dashed-dotted lines which correspond to the solid lines shown in Fig. 3.
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Figure 5
A fraction of $A 1$ blocks which form the interstitial micelles (squares), which form free dangles (circles), and which are located at the $A / B$ interface (triangles) for the $A 1 B A 2$ solution in the selective $A$ solvent ( $Φ = 0.9$ ) and the following triblock chains: (a) $A_{1} - B_{48} - A_{47}$ , (b) $A_{2} - B_{48} - A_{46}$ , and (c) $A_{3} - B_{48} - A_{45}$ .
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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Towards entropy-driven interstitial micelles at elevated temperatures from selective $A 1 BA 2$ triblock solutions

S. Wołoszczuk, S. Jurga, and M. Banaszak

Phys. Rev. E 94, 022502 – Published 29 August 2016

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Physical Review E

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Towards entropy-driven interstitial micelles at elevated temperatures from selective A1BA2 triblock solutions

S. Wołoszczuk, S. Jurga, and M. Banaszak

Phys. Rev. E 94, 022502 – Published 29 August 2016

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Towards entropy-driven interstitial micelles at elevated temperatures from selective $A 1 BA 2$ triblock solutions