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Khandagale P, Garcia-Cervera C, deBotton G, Breitzman T, Majidi C, Dayal K. Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions. Phys Rev E 2024; 109:044501. [PMID: 38755880 DOI: 10.1103/physreve.109.044501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 02/14/2024] [Indexed: 05/18/2024]
Abstract
The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on three key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution, (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics partial differential equation with the continuous dipole distribution as the forcing, and (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain. The model is applied, using the finite element method, to study the electromechanical response of a polymer chain in the ensemble with fixed far-field applied electric field and fixed chain stretch. The nonlocal dipolar interactions are found to increase, over the case where dipole-dipole interactions are neglected, the magnitudes of the polarization and electric field by orders of magnitude as well as significantly change their spatial distributions. Next, the effect of the relative orientation between the applied field and the chain on the local electric field and polarization is studied. The model predicts that the elastic response of the polymer chain is linear, consistent with the Gaussian approximation, and largely unchanged by the orientation of the applied electric field, though the polarization and local electric field distributions are significantly impacted.
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Affiliation(s)
- Pratik Khandagale
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA
| | - Carlos Garcia-Cervera
- Department of Mathematics, University of California, Santa Barbara CA 93106, USA
- BCAM, Basque Center for Applied Mathematics, E48009 Bilbao, Basque Country, Spain
| | - Gal deBotton
- Department of Mechanical Engineering, Ben Gurion University, 84105 Beer Sheva, Israel
- Department of Biomedical Engineering, Ben Gurion University, 84105 Beer Sheva, Israel
| | | | - Carmel Majidi
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA
- Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA
- Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA
| | - Kaushik Dayal
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA
- Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA
- Center for Nonlinear Analysis, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA 15213, USA
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Spencer RKW, Ha BY, Saeidi N. Interplay between nematic and cholesteric interactions in self-consistent field theory. Phys Rev E 2022; 105:054501. [PMID: 35706232 DOI: 10.1103/physreve.105.054501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2021] [Accepted: 03/29/2022] [Indexed: 06/15/2023]
Abstract
Chirality is a design feature of a number of biomolecules (e.g., collagen). In these molecules, cholesteric (chiral-nematic) behavior emerges from a combination of the tendency for the biopolymers to align (nematic interactions) and for the alignment direction to change with position, rotating around an axis normal to the alignment direction. This paper presents self-consistent field theory (SCFT) of chiral-nematic polymers, which takes into account polymer flexibility and the orientational degrees of freedom of polymer segments. Using the resulting SCFT, we construct a phase diagram showing regions of stability for isotropic, nematic, and cholesteric phases. Furthermore, we find that nematic interactions can stabilize the cholesteric phase, pushing the isotropic-cholesteric phase transition to lower cholesteric interaction strength, until the isotropic-nematic-cholesteric triple point is reached.
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Affiliation(s)
- Russell K W Spencer
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Bae-Yeun Ha
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Nima Saeidi
- Department of Surgery, The Center for Engineering in Medicine, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114, USA
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