Interstitial micelles in binary blends of $ABA$ triblock copolymers and homopolymers

We investigate triblock-homopolymer blends of types A1BA2/A and A1BA2/B, using a lattice Monte Carlo method. While the simulated triblock chains are compositionally symmetric in terms of the A-to-B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt and the A1BA2 solutions in selective solvent the phase behavior is relatively well known, including existence and stability of the interstitial micelles which were discovered in previous Monte Carlo simulations. In this paper we study the stability of the interstitial micelles as a function of triblock volume fraction in selective homopolymers of either type A or type B, using two significantly different homopolymer chain lengths. We found that adding selective homopolymer of type A shifts the stability of the interstitial micelles into significantly higher temperatures. We also obtained, via self-assembly, intriguing new nanostructures which can be identified as ordered truncated octahedra. Finally, we established that the phase behavior of the triblock-homopolymer blends depends relatively weakly on the chain length of the added homopolymer.

Figure 1

Selected snapshots: (a) lamellar structure for the $A_1\text{−}{B}_{48}\text{−}{A}_{47}/A$ blend, $\varphi =0.7$, $N_H=N_C$, $T^{*}=1.0$; (b) cubically packed cylinders for the $A_1\text{−}{B}_{48}\text{−}{A}_{47}/A$ blend, $\varphi =0.7$, $N_H=N_C/4$, $T^{*}=2.5$; (c) truncated octahedra for the $A_1\text{−}{B}_{48}\text{−}{A}_{47}/B$ blend, $\varphi =0.9$, $N_H=N_C$, $T^{*}=1.3$; (d) truncated octahedra for the $A_2\text{−}{B}_{48}\text{−}{A}_{46}/A$ blend, $\varphi =0.8$, $N_H=N_C/4$, $T^{*}=3.3$. $A_2$ blocks are indicated in dark gray (blue in the online version), $A_1$-blocks in very light gray (yellow in the online version), $B$-blocks in medium gray (red in the online version), and $A$-homopolymer in light gray (green in the online version). The $B$-blocks and $A$-homopolymers are not shown in (a), (b), and (c) for clarity.

Figure 2

(a) The interface-domain crossover temperature, $T_{\mathrm{IDC}}^{*}$, and (b) the reduced interface-domain crossover temperature $T_{\mathrm{IDC}/x}^{*}$ as a function of copolymer volume fraction for the $A_{1}B{A}_2/A$ blend (left-hand side) and the $A_{1}B{A}_2/B$ blend (right-hand side) for $N_H=N_C/4$. The $A_1\text{−}{B}_{48}\text{−}{A}_{47}$ triblock is indicated by open squares, the $A_2\text{−}{B}_{48}\text{−}{A}_{46}$ triblock by open circles, and the $A_3\text{−}{B}_{48}\text{−}{A}_{45}$ triblock by open triangles; $x=1,2$, or 3.

Figure 3

(a) The interface-domain crossover temperature, $T_{\mathrm{IDC}}^{*}$, and (b) the reduced interface-domain crossover temperature $T_{\mathrm{IDC}/x}^{*}$ as a function of copolymer volume fraction for the $A_{1}B{A}_2/A$ blend (left-hand side) and the $A_{1}B{A}_2/B$ blend (right-hand side) for $N_H=N_C$. The $A_1\text{−}{B}_{48}\text{−}{A}_{47}$ triblock is indicated by open squares, the $A_2\text{−}{B}_{48}\text{−}{A}_{46}$ triblock by open circles, and the $A_3\text{−}{B}_{48}\text{−}{A}_{45}$ triblock by open triangles; $x=1,2$, or 3.

Figure 4

Region of stability of the interstitial micelles for the copolymer-homopolymer blend for $N_H=N_C/4$. This region lies between the solid lines which are shown as a function of copolymer volume fraction, $\varphi$, in a selective $A$ homopolymer and $B$ homopolymer and the reduced temperature $T^{*}$ (pure melt is at $\varphi =1$). Panel figures refer to the following $A_{1}B{A}_2$ triblock copolymer blends: (a) $A_1\text{−}{B}_{48}\text{−}{A}_{47}$, (b) $A_2\text{−}{B}_{48}\text{−}{A}_{46}$, and (c) $A_3\text{−}{B}_{48}\text{−}{A}_{45}$.

Figure 5

Region of stability of the interstitial micelles for the copolymer-homopolymer blend for $N_H=N_C$. This region lies between the solid lines which are shown as a function of copolymer volume fraction, $\varphi$, in a selective $A$ homopolymer and $B$ homopolymer and the reduced temperature $T^{*}$ (pure melt is at $\varphi =1$). Panel figures refer to the following $A_{1}B{A}_2$ triblock copolymer blends: (a) $A_1\text{−}{B}_{48}\text{−}{A}_{47}$, (b) $A_2\text{−}{B}_{48}\text{−}{A}_{46}$, and (c) $A_3\text{−}{B}_{48}\text{−}{A}_{45}$.

Figure 6

Phase diagrams as a function of a triblock copolymer volume fraction and temperature in a selective homopolymer of either type $A$ (on the left-hand side) or type $B$ (on the right-hand side) and the temperature $T^{*}$ for $N_H=N_C/4$. Panel figures refer to the following triblock chains: (a) $A_1\text{−}{B}_{48}\text{−}{A}_{47}$, (b) $A_2\text{−}{B}_{48}\text{−}{A}_{46}$, and (c) $A_3\text{−}{B}_{48}\text{−}{A}_{45}$. Order-disorder and order-order lines are shown as solid and dashed lines, respectively.

Figure 7

Phase diagrams as a function of a triblock copolymer volume fraction and temperature in a selective homopolymer of either type $A$ (on the left-hand side) or type $B$ (on the right-hand side) and the temperature $T^{*}$ for $N_H=N_C$. Panel figures refer to the following triblock chains: (a) $A_1\text{−}{B}_{48}\text{−}{A}_{47}$, (b) $A_2\text{−}{B}_{48}\text{−}{A}_{46}$, and (c) $A_3\text{−}{B}_{48}\text{−}{A}_{45}$. Order-disorder and order-order lines are shown as solid and dashed lines, respectively.

Figure 8

Looping fraction as a function of the reduced temperature, $T^{*}$, for $A_1\text{−}{B}_{48}\text{−}{A}_{47}/A$ blend for $N_H=N_C$).