Optimizing Chain Bridging in Complex Block Copolymers

Abstract

Recent experiments by Ryu, Hermel, and co-workers have demonstrated a correlation between the presence of bridging A-blocks and practical toughness in themoplastic ABABA pentablock copolymers. Building on this observation, we develop a computational tool for evaluating average bridging fractions of internal blocks in complex block copolymers and apply the tool to the optimization of bridging fractions in mesophase structures computed with self-consistent-field theory. We identify optimal molecular designs for ABABA pentablock copolymers that could provide the useful combination of high modulus and high toughness. Further applications of the approach to property screening in complex mesophases formed by ABC and ABCA block copolymers are discussed.

Elastic moduli of multiblock copolymers in the lamellar phase

“…Such increases in moduli are usually associated with an increase in the bridging fraction of intermediate blocks. [8][9][10][11] Although there exists a corresponding increase of bridging fraction in multiblock copolymers with block number, 10 our results indicate that it is not the cause of the increase in tensile modulus. Rather, the increase of modulus with block number is shown to be due to an increase of mixing between repulsive A and B monomers upon deformation.…”

“…With the qualitative agreement with experiment in mind, we can analyze the source of the increase of modulus with diblock number p. According to the bridging hypothesis for the strengthening of multiblock copolymers, the conformational entropy contribution to the free energy of the system should increase as the bridging blocks stretch, [8][9][10] and so we should have a positive curvature. In Table I, the reverse is seen.…”

“…The ability of intermediate blocks of multiblock copolymers to bridge between different chemical domains means that pseudo-''cross links'' can form, which may be expected to have a profound effect on the elastic moduli. 8,9 SCFT calculations have shown that the fraction of blocks that bridge between domains increases as a function of the number of blocks in a multiblock. 10 Experimentally, increases in the elastic moduli as a function of block number have also been found in multiblock systems.…”

Position transitions of polymer-grafted nanoparticles in diblock-copolymer nanocomposites

“…To obtain the equilibrium nanostructure, we solve these equations by using the combinatorial screening technique of Drolet and Fredrickson [30,42] implemented with a highly stable and accurate numerical algorithm [43,44]. All the simulations are performed in a two-dimensional square lattice with periodic boundary conditions.…”

“…The system is thought to have reached equilibrium when the relative difference between the free energies of the system at two neighboring iteration steps has been smaller than 0.0001%. More details on the numerical implementation of SCFT can be found in the literature [30,[42][43][44].…”