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

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

doi:10.1016/j.polymer.2018.08.070

Cited by 17 publications

(31 citation statements)

References 60 publications

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“…Overall, the SCFT calculations capture the salient aspects of the experimental phase behavior, namely the sequence of the Frank-Kasper phases as the volume fraction of homopolymer increases and the transition from Frank-Kasper particle phases to a cylindrical phase as the homopolymer degree of polymerization decreases. SCFT does not provide a quantitative prediction of the stability windows for Frank-Kasper phases due to their nearly degenerate free energies (SI Appendix, Tables S1-S10), consistent with prior work (9,12,13,27,39,40).…”

Section: Resultssupporting

confidence: 72%

Symmetry breaking in particle-forming diblock polymer/homopolymer blends

Cheong

Bates

Dorfman

2020

Proc. Natl. Acad. Sci. U.S.A.

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Compositionally asymmetric diblock copolymers provide an attractive platform for understanding the emergence of tetragonally close-packed, Frank–Kasper phases in soft matter. Block-polymer phase behavior is governed by a straightforward competition between chain stretching and interfacial tension under the constraint of filling space at uniform density. Experiments have revealed that diblock copolymers with insufficient conformational asymmetry to form Frank–Kasper phases in the neat-melt state undergo an interconversion from body-centered cubic (bcc) close-packed micelles to a succession of Frank–Kasper phases (σ to C14 to C15) upon the addition of minority-block homopolymer in the dry-brush regime, accompanied by the expected transition from bcc to hexagonally packed cylinders in the wet-brush regime. Self-consistent field theory data presented here qualitatively reproduce the salient features of the experimental phase behavior. A particle-by-particle analysis of homopolymer partitioning furnishes a basis for understanding the symmetry breaking from the high-symmetry bcc phase to the lower-symmetry Frank–Kasper phases, wherein the reconfiguration of the system into polyhedra of increasing volume asymmetry delays the onset of macroscopic phase separation.

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Section: Resultssupporting

confidence: 72%

Symmetry breaking in particle-forming diblock polymer/homopolymer blends

Cheong

Bates

Dorfman

2020

Proc. Natl. Acad. Sci. U.S.A.

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“…A direct comparison between calibrations based on ODTs and the Morse calibration has been performed previously by Arora et al [63,30,65]. This calibration used predictions for symmetric and monodisperse melts, decreasing its accuracy compared to our method.…”

Section: Calibration Of Experimental Systemsmentioning

confidence: 98%

“…This mapping requires a calibration of the Flory-Huggins parameter χ. There are numerous strategies used to calibrate the χ parameter, but this has lead to a discrepancy between the values found using different methods [25,26,27,28,29,30]. This has caused many to propose that χ depends not only on temperature, T , but also on architecture, composition, molecular weight, and polydispersity.…”

Section: Universalitymentioning

confidence: 99%

Simple and Accurate Calibration of the Flory–Huggins Interaction Parameter

2020

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This paper improves upon a standard method of determining the Flory–Huggins χ parameter, whereby experimental order–disorder transitions (ODTs) of symmetric diblock polymer melts are fit to the mean-field prediction, (χN)ODT = 10.495. The improvement is achieved by switching to an accurate prediction of (χN)ODT from Glaser et al. (Phys. Rev. Lett. 2014, 113, 068302), supplemented with corrections for the small degrees of polydispersity and compositional asymmetry that inevitably exist in real diblock polymers. The first correction is evaluated by simulating polydisperse diblocks over a wide range of invariant polymerization indices, and the second correction is extracted from analogous simulations for compositionally asymmetric diblocks by Ghasimakbari and Morse (Macromolecules 2020, 53, 7399). The resulting calibration method is then demonstrated on 19 different chemical pairs, using previously published experimental data. It provides a considerable increase in accuracy, but yet is nearly as simple to apply as the original version.

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“…These models are influential due to their elegance, simplicity of the input parameters, and ability to reproduce key scaling dependencies of experimental systems. − The Flory–Rehner theory has been extended to anisotropic and charged , polymer networks. However, the Flory–Huggins χ parameter is challenging to measure accurately and is often used as a fitting parameter in these theories due to complex functional relationships that depend on temperature, concentration, and chemistry, making quantitative evaluation difficult. − Beyond covalently cross-linked chemistries and the Flory–Rehner equation, other scaling relations for swelling behavior have been developed for systems like Olympic gels …”

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confidence: 99%

“…To use this experimental data to compare the accuracy of swelling models, χ must be accurately determined for each polymer–solvent pair, a measurement which may introduce substantial error. − Therefore, the Bray–Merrill and REST equations are modified to isolate χ and the partial molar solvent volume V 1 under the assumption that the polymer volume fraction during swelling remains <0.20 (all gels in this study were <0.10 at equilibrium). The REST equations are converted into the following model that isolates χ and V 1 : where C is the elastic effectiveness per strand of the gel, a proportionality constant related to the unentangled shear modulus as G ′ = C ϕ r ( v̅M c ) −1 RT , or the right-hand side of eq 5 .…”

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confidence: 99%

Adding the Effect of Topological Defects to the Flory–Rehner and Bray–Merrill Swelling Theories

2021

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The Flory–Rehner and Bray–Merrill swelling theories are venerable theories for calculating the swelling of polymer networks and are widely applied across polymer materials. Here, these theories are revised to include cyclic topological defects present in polymer networks by using a modified phantom network model. These closed-form equations assume defect contributions to the swelling elasticity to be linear and additive and allow different assumptions regarding prestrain of larger loops to be incorporated. To compare to the theories, swelling experiments are performed on end-linked poly(ethylene glycol) gels in which the topological defects (primary and secondary loops) have been previously measured. Gels with higher loop densities exhibit higher swelling ratios. An equation is derived to compare swelling models independent of knowledge of the Flory–Huggins χ parameter, showing that the revised swelling models for loop defects are more accurate than both the phantom network model that neglects loops and the Bray–Merrill equation.

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

Cited by 17 publications

References 60 publications

Symmetry breaking in particle-forming diblock polymer/homopolymer blends

Symmetry breaking in particle-forming diblock polymer/homopolymer blends

Simple and Accurate Calibration of the Flory–Huggins Interaction Parameter

Adding the Effect of Topological Defects to the Flory–Rehner and Bray–Merrill Swelling Theories

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