Dual modes of self-assembly in superstrongly segregated bicomponent triblock copolymer melts

While $ABC$ triblock copolymers are known to form a plethora of dual-mode (i.e., order-on-order) nanostructures, bicomponent $ABA$ triblock copolymers normally self-assemble into single morphologies at thermodynamic incompatibility levels up to the strong-segregation regime. In this study, we employ on-lattice Monte Carlo simulations to examine the phase behavior of molecularly asymmetric $A_{1}B{A}_2$ copolymers possessing chemically identical endblocks differing significantly in length. In the limit of superstrong segregation, interstitial micelles composed of the minority $A_2$ endblock are observed to arrange into two-dimensional hexagonal arrays along the midplane of $B$-rich lamellae in compositionally symmetric $(50:50 A:B)$ copolymers. Simulations performed here establish the coupled molecular-asymmetry and incompatibility conditions under which such micelles form, as well as the temperature dependence of their aggregation number. Beyond an optimal length of the $A_2$ endblock, the propensity for interstitial micelles to develop decreases, and the likelihood for colocation of both endblocks in the $A_1$-rich lamellae increases. Interestingly, the strong-segregation theory of Semenov developed to explain the formation of free micelles by diblock copolymers accurately predicts the onset of interstitial micelles confined at nanoscale dimensions between parallel lamellae.

Figure 1

Snapshots of MC simulations of molecularly asymmetric $A_{1}B{A}_2$ triblock copolymers in the SSS regime revealing the existence of interstitial micelles between lamellae [(a) edge view] and perforated lamellae [(b) parallel view through perforation]. Included in (a) is an inset showing the lateral hexagonal packing of the micelles in (a). The schematic illustration in (c) depicts the placement of the blocks (not drawn to scale). In (a)–(c), shades of blue and green refer to $A_1$ and $A_2$ features, respectively, whereas red signifies individual $B$ midblocks in (c).

Figure 2

Values of the $A_2$ block fractions extracted from MC simulations of SSS $A_{1}B{A}_2$ triblock copolymers—(a) 39-40-1, (b) 38-40-2, (c) 37-40-3, (d) 47-48-1, (e) 46-48-2, and (f) 45-48-3—provided as functions of reduced temperature $\left(T^{*}\right)$. The fractions shown include micelle-forming bridges (${\upsilon }_M$, red circles), double-anchored chains (${\upsilon }_L$, blue triangles), and dangling ends (${\upsilon }_D$, black squares). The solid lines connect the data, and the sizes of the simulation boxes employed here are (a)–(c) $80\times 40\times 40$ and (d)–(f) $96\times 48\times 48$ to explore size effects.

Figure 3

Dependence of the micelle aggregation number $\left(Q\right)$ on $T^{*}$ for copolymers designated as $\left(40\text{−}x\right)\text{−}40\text{−}x$ (black squares), $\left(48\text{−}x\right)\text{−}48\text{−}x$ (red circles), and $\left(56\text{−}x\right)\text{−}56\text{−}x$ (blue triangles) for the cases of $x=1$ (solid symbols) and $x=2$ (open symbols). The solid lines connect the data.

Figure 4

The upper and lower stability limits (open and solid circles, respectively) for interstitial micelles in $A_{1}B{A}_2$ triblock copolymers with short $A_2$ blocks compiled from MC simulation results for copolymers varying in chain length $\left(N\right)$: 80 (black squares), 96 (red circles), and 112 (blue triangles). The solid lines are guides for the eye, and the dashed line corresponds to Eq. (3) in the text (evaluated under the specified conditions). The inset displays the dimensionless free energy as a function of $\chi N$ from Eq. (2) for dangling ends (${\upsilon }_L=0$, black curves) and double-anchored chains $({\upsilon }_L=1$, red curve) at different $f_{A_2}$ (labeled).