Optimizing the network topology of block copolymer liquid crystal elastomers for enhanced extensibility and toughness

Molecular simulations are used to study the effect of synthesis conditions on the tensile response of liquid-crystalline elastomers formed by block copolymer chains. Remarkably, it is found that despite the significant presence of trapped entanglements, these networks can exhibit the sawtooth tensile response previously predicted for ideal unentangled networks. It is also found that the monomer concentration during crosslinking can be tuned to limit the extent of entanglements and inhomogeneities while also maximizing network extensibility. It is predicted that networks synthesized at a “critical” concentration will have the greatest toughness.

Figure 1

(a) Depiction of unfolding mechanism for semiflexible chains (colored as block copolymer for clarity). Unequal pull on the ends of the hairpin aids to the release of bending energy by unfolding. (b) Cartoon of the stress built-up and release mechanism in T-LCE with block copolymer chains, describing states around a representative tooth in the stress-strain curve (c). From left to right: The applied strain first removes any “slack” in the system, and begins to deform the llamella, increasing the interfacial energy and the stress. After a greater amount of strain, the hairpins begin to unfold, breaking the parent layer into two daughter layers, and relaxing the stress.

Figure 2

Schematic of ABTAM reaction. Each monomer consists of a tetra-functional crosslink (black), connected by the A block (blue) of an AB block copolymer (B block is purple). There are two monomer types differentiated by the end-group on the chains (type 1 is red, type 2 is green). Only end-beads of different colors can bond.

Figure 3

Tensile plots of various ${\varphi }_0$ for $l_{\mathrm{a}}=11$(a) and $l_{\mathrm{a}}=20$ (b). (c) Snapshots from the deformation of a network synthesized from 4096 monomers at ${\varphi }_0=0.0133$, for $\alpha =1$, 4.7, 5.9, and 6.9 counterclockwise from the top left. Color scheme follows Fig. 1. For high α the B block is removed for clarity.

Figure 4

The number of topological loops (a), $\mathit{SR}$ (b), solid lines, and $\mathit{CR}$ (b), dashed lines, for different $l_{\mathrm{a}}$. In (a), $l_{\mathrm{a}}=5$, 11, 15, 20, 40, 60, 80, and 100 are represented by the open diamonds, filled circles, filled squares, filled triangles, filled diamonds, filled hexagons, open circles, and open triangles, respectively. In (b), $l_{\mathrm{a}}=11$, 15, 20, and 40 are colored blue, green, black, and red, respectively. In the inset, $l_{\mathrm{a}}=5$, 20 (for reference), 60, 80, and 100 are colored purple, black, cyan, brown, and pink, respectively. Black dashed lines outside of inset are used as guides to show that when $\mathit{SR}$ $=1$, there is an inflection point in $\mathit{CR}$.

Figure 5

Cartoons (top) of synthesis environment (red circles depict monomer coils of radius $r_{\mathrm{ee}}$), and representative simulation snapshots after applying the chain ratio algorithm (bottom) for networks with $l_{\mathrm{a}}=11$ synthesized at ${\varphi }_0=0.107$ (a), 0.045 (b), and 0.023 (c).

Figure 6

Plot of the scaled extensibility against the $r_{\mathrm{sep}}$ normalized by $r_{\mathrm{ee}}$. Circle cartoons represent the monomer spheres and their interacting regions (spherical caps in red).

Figure 7

The tensile response of synthesized flexible block copolymer networks with $l_a=11$ for different ${\varphi }_0$.

Figure 8

(a) The tensile response of FF, ESF, and SF networks. “FF” and “ESF” (“equilibrated as SF”) have identical network topologies. Note: the tensile response of the FF network is the same as that shown in Fig. 7 (for ${\varphi }_0=0.107$). (b) Plot of the absolute change in $r_{\mathrm{ee}}$ normalized by $l_c$ for all chains in the FF and ESF networks. The two values of $\alpha$ from which the configurations were sampled are marked by arrow in (a).