Predicting the phase behavior of ABAC tetrablock terpolymers: Sensitivity to Flory–Huggins interaction parameters

Akash Arora, Naveen Pillai, Frank S. Bates, Kevin D. Dorfman

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Self-consistent field theory (SCFT) is a powerful tool for discovering new nanostructures in self-assembling block polymers. However, the reliability of the resulting predictions depend strongly on the Flory-Huggins interaction parameters χij used to quantify the excess free energy of mixing of different blocks i and j arising from segment-segment interactions. The problem is especially significant for multiblock polymers, owing to the multitude of χij parameters and the sensitivity of the resulting phase behavior when the χij do not differ substantially for different block pairs. To illuminate this issue, we examine how the SCFT-predicted phase behavior of a poly(styrene)-b-poly(isoprene)-b-poly(styrene)’-b-poly(ethylene oxide) (SIS'O) tetrablock terpolymer changes depending on the method used to estimate the trio of χij parameters for this chemistry. SIS'O is an ideal model system for our purposes, as it exhibits a large number of poly(ethylene oxide) sphere-forming phases, emerging from the segregation of the poly(ethylene oxide) block due to the relatively high values of χSO and χIO, accompanied by subtle matrix segregation effects arising due to the smaller χIS between poly(isoprene) and poly(styrene). We first use χIS, χIO, and χSO available in the literature that were estimated using mean-field theory order–disorder transitions of the relevant diblock polymers. As this method is expected to lead to significant errors in χij that propagate into the SCFT predictions, we also consider two fluctuation-corrected approaches to extract χij from diblock polymer data, namely (i) fitting the order-disorder transition temperature to that predicted by molecular dynamics simulations and (ii) renormalized one-loop theory predictions for the structure factor of the disordered state. While even the fluctuation-corrected χ parameters do not lead to SCFT phase behavior that exactly matches experiments, the SCFT calculations using the molecular dynamics-fitted χ parameters correctly predict stable Frank–Kasper A15 and σ phases. The results presented here highlight the challenges in predictively modeling the phase behavior of multiblock polymers using SCFT, a critical task for the discovery of new multiblock polymer materials.

Original languageEnglish (US)
Pages (from-to)305-314
Number of pages10
JournalPolymer
Volume154
DOIs
StatePublished - Oct 10 2018

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Terpolymers
Phase behavior
Polymers
Styrene
Polyethylene oxides
Signal filtering and prediction
Isoprene
Molecular dynamics
Mean field theory
Order disorder transitions
Free energy
Superconducting transition temperature
Block copolymers
Nanostructures
Computer simulation
Experiments

Keywords

  • Block polymer
  • Flory-Huggins theory
  • Phase behavior
  • Self-consistent field theory

Cite this

Predicting the phase behavior of ABAC tetrablock terpolymers : Sensitivity to Flory–Huggins interaction parameters. / Arora, Akash; Pillai, Naveen; Bates, Frank S.; Dorfman, Kevin D.

In: Polymer, Vol. 154, 10.10.2018, p. 305-314.

Research output: Contribution to journalArticle

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AU - Dorfman, Kevin D.

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N2 - Self-consistent field theory (SCFT) is a powerful tool for discovering new nanostructures in self-assembling block polymers. However, the reliability of the resulting predictions depend strongly on the Flory-Huggins interaction parameters χij used to quantify the excess free energy of mixing of different blocks i and j arising from segment-segment interactions. The problem is especially significant for multiblock polymers, owing to the multitude of χij parameters and the sensitivity of the resulting phase behavior when the χij do not differ substantially for different block pairs. To illuminate this issue, we examine how the SCFT-predicted phase behavior of a poly(styrene)-b-poly(isoprene)-b-poly(styrene)’-b-poly(ethylene oxide) (SIS'O) tetrablock terpolymer changes depending on the method used to estimate the trio of χij parameters for this chemistry. SIS'O is an ideal model system for our purposes, as it exhibits a large number of poly(ethylene oxide) sphere-forming phases, emerging from the segregation of the poly(ethylene oxide) block due to the relatively high values of χSO and χIO, accompanied by subtle matrix segregation effects arising due to the smaller χIS between poly(isoprene) and poly(styrene). We first use χIS, χIO, and χSO available in the literature that were estimated using mean-field theory order–disorder transitions of the relevant diblock polymers. As this method is expected to lead to significant errors in χij that propagate into the SCFT predictions, we also consider two fluctuation-corrected approaches to extract χij from diblock polymer data, namely (i) fitting the order-disorder transition temperature to that predicted by molecular dynamics simulations and (ii) renormalized one-loop theory predictions for the structure factor of the disordered state. While even the fluctuation-corrected χ parameters do not lead to SCFT phase behavior that exactly matches experiments, the SCFT calculations using the molecular dynamics-fitted χ parameters correctly predict stable Frank–Kasper A15 and σ phases. The results presented here highlight the challenges in predictively modeling the phase behavior of multiblock polymers using SCFT, a critical task for the discovery of new multiblock polymer materials.

AB - Self-consistent field theory (SCFT) is a powerful tool for discovering new nanostructures in self-assembling block polymers. However, the reliability of the resulting predictions depend strongly on the Flory-Huggins interaction parameters χij used to quantify the excess free energy of mixing of different blocks i and j arising from segment-segment interactions. The problem is especially significant for multiblock polymers, owing to the multitude of χij parameters and the sensitivity of the resulting phase behavior when the χij do not differ substantially for different block pairs. To illuminate this issue, we examine how the SCFT-predicted phase behavior of a poly(styrene)-b-poly(isoprene)-b-poly(styrene)’-b-poly(ethylene oxide) (SIS'O) tetrablock terpolymer changes depending on the method used to estimate the trio of χij parameters for this chemistry. SIS'O is an ideal model system for our purposes, as it exhibits a large number of poly(ethylene oxide) sphere-forming phases, emerging from the segregation of the poly(ethylene oxide) block due to the relatively high values of χSO and χIO, accompanied by subtle matrix segregation effects arising due to the smaller χIS between poly(isoprene) and poly(styrene). We first use χIS, χIO, and χSO available in the literature that were estimated using mean-field theory order–disorder transitions of the relevant diblock polymers. As this method is expected to lead to significant errors in χij that propagate into the SCFT predictions, we also consider two fluctuation-corrected approaches to extract χij from diblock polymer data, namely (i) fitting the order-disorder transition temperature to that predicted by molecular dynamics simulations and (ii) renormalized one-loop theory predictions for the structure factor of the disordered state. While even the fluctuation-corrected χ parameters do not lead to SCFT phase behavior that exactly matches experiments, the SCFT calculations using the molecular dynamics-fitted χ parameters correctly predict stable Frank–Kasper A15 and σ phases. The results presented here highlight the challenges in predictively modeling the phase behavior of multiblock polymers using SCFT, a critical task for the discovery of new multiblock polymer materials.

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