Effect of Composition on the Phase Behavior of Ion-Containing Block Copolymers Studied by a Minimal Lattice Model

Abstract

We performed Monte Carlo simulations using a minimal lattice model with short-range interactions modeled using Flory−Huggins interactions parameters, χ, to investigate morphology of ioncontaining A−B diblock copolymers. A fraction of the segments in the A block, p, were ionic (labeled S) while the B block segments were nonionic (p was held fixed at 0.588). The dielectric constants of the polymers is assumed to be low, and thus charge dissociation effects are negligible. The magnitude of the χ between ion and nonionic species, determined in previous experiments on poly(styrenesulfonate)-bpoly(methyl butylene), PSS−PMB, is an order of magnitude larger than that between the nonionic segments. Simulations indicate that complex morphologies such as gyroid and perforated lamellae are obtained in symmetric block copolymers wherein the volume fraction of the B block, ϕ B , is about 0.5, while simple unperforated lamellae are obtained in asymmetric block copolymers wherein ϕ B is about 0.25. This result is very different from the well-established phase behavior of nonionic block copolymers but consistent with experimental results of Wang et al. [Macromolecules 2010, 43, 5306]. We also make a number of additional predictions, still awaiting an experimental verification, such as the emergence of the hexagonal phase in the weak segregation limit, and a remarkable insensitivity of the product p 2 χN (N is the total number of segments in a copolymer chain) at the order−disorder transition to ϕ B .

Self‐Assembly of Poly(vinylpyridine‐b‐oligo(ethylene glycol) methyl ether methacrylate) Diblock Copolymers

“…Brownian dynamics simulations of a block copolymer where the charged block accounts for 25% of the component monomers match the results of the field theory simulations when the dielectric constant is low; however, for high dielectric constant materials, increased charge promotes phase mixing . Lattice Monte Carlo simulations for symmetric diblocks show the presence of cylindrical, gyroid, hexagonally perforated lamellar, and lamellar phases depending on the degree of charge, the value of χ , and the overall chain length …”

“…There have been several different approaches to modeling the phase behavior of low dielectric constant block copolymers with salt or charge, which have resulted in different predictions for the expected phase behavior. Knychala et al 33,34 used a Monte Carlo simulation approach where six v parameters were defined between three different monomers (two uncharged, one charged) with the highest values of v between the charged and uncharged monomers; they found that the effective interaction depended on the square of the fraction of charged monomers (p) and that the strong segregation regime was dominated by lamellar phases caused by a high degree of chain stretching (p 2 vN values of 40 and above for the compositions studied here), FULL PAPER inconsistent with our experimental observations. Goswami et al 32 and Sing et al 30,31 both developed approaches that account for Coulombic interactions: Goswami using an explicit Coulomb potential in a Brownian dynamics simulation and Sing by using a coupled liquid state and selfconsistent field theory simulation.…”

“…32 Lattice Monte Carlo simulations for symmetric diblocks show the presence of cylindrical, gyroid, hexagonally perforated lamellar, and lamellar phases depending on the degree of charge, the value of v, and the overall chain length. 33,34 Testing these predictions has proven challenging because it is difficult to find charge asymmetric block copolymers that are close to their ODT, and because many polyelectrolytes have a very high glass temperature in the absence of a solvent. In previous work, we have shown that poly(oligoethylene glycol methyl ether methacrylate)-poly(2-vinylpyridine) (POEGMA-P2VP) block copolymers have a protonation-induced order-disorder transition, making them ideal materials to test the phase behavior of charge-asymmetric block copolymer systems.…”

Effects of Blockiness and Polydispersity on the Phase Behavior of Random Block Copolymers

“…One example would be poly(styrenesulfonate‐ block ‐polymethylbutylene) in which a random selection of the polystyrene monomers are sulfonated. Experimental studies as well as Monte Carlo simulations have shown that this system displays interesting phase behaviors . It would be interesting to explore the phase behavior of random copolymers with a non‐Markovian sequence distribution.…”

“…Experimental studies as well as Monte Carlo simulations have shown that this system displays interesting phase behaviors. [5][6][7] It would be interesting to explore the phase behavior of random copolymers with a non-Markovian sequence distribution.…”