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We study the collective elastic behavior of semiflexible polymer solutions in a nematic liquid-crystalline state using polymer field theory. Our polymer field-theoretic model of semiflexible polymer solutions is extended to include second-order fluctuation corrections to the free energy, permitting the evaluation of the Frank elastic constants based on orientational order fluctuations in the nematic state. Our exact treatment of wormlike chain statistics permits the evaluation of behavior from the nematic state, thus accurately capturing the impact of single-chain behavior on collective elastic response. Results for the Frank elastic constants are presented as a function of aligning field strength and chain length, and we explore the impact of conformation fluctuations and hairpin defects on the twist, splay, and bend moduli. Our results indicate that the twist elastic constant Ktwist is smaller than both bend and splay constants (Kbend and Ksplay, respectively) for the entire range of polymer rigidity. Splay and bend elastic constants exhibit regimes of dominance over the range of chain stiffness, where Ksplay > Kbend for flexible polymers (large-N limit) while the opposite is true for rigid polymers. Theoretical analysis also suggests the splay modulus tracks exactly to that of the end-to-end distance in the transverse direction for semiflexible polymers at intermediate to large-N. These results provide insight into the role of conformation fluctuations and hairpin defects on the collective response of polymer solutions.
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This content will become publicly available on July 1, 2026
A critical and constructive analysis of nonstretching approximations in a family of Rolie-Poly models
Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. During processing, deformation introduces elastic stresses due to a combination of polymer orientation and polymer stretching. For many flows, however, the elastic contribution from chain stretching is not significant, and so-called “nonstretching” approximations have been developed to help explain and interpret experimental observations. Unfortunately, these nonstretching models tend to be limited to simple polymer formulations (linear and monodisperse) and are not useful for understanding any effects from marginal chain stretching that may be present. In this paper, we show that nonstretching approximations can be formally constructed as a perturbation expansion starting from a fully stretching constitutive equation. We apply this framework to the Rolie-Poly model, deriving the existing nonstretching variation and expanding to the second order. The second-order continuation provides quantitatively improved accuracy for both steady and unsteady flows and prevents a pathological/nonphysical blowup that can occur when effects from marginal chain stretching are ignored. We also derive and discuss leading order nonstretching approximations for more complex models of entangled polymers, accounting for disentanglement dynamics, polydispersity, and reversible scission reactions. Alternatives to the formal perturbation framework are also discussed, with potential trade-offs between accuracy, versatility, and computational cost.
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- Award ID(s):
- 2442896
- PAR ID:
- 10639869
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Journal of Rheology
- Volume:
- 69
- Issue:
- 4
- ISSN:
- 0148-6055
- Page Range / eLocation ID:
- 387 to 407
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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