Aggregation phenomena in lyotropic chromonic liquid crystals

Lidia Mrad; Longhua Zhao; Malena I. Español; Ling Xu; M. Carme Calderer

doi:10.1016/j.cnsns.2023.107139

Aggregation phenomena in lyotropic chromonic liquid crystals

Lidia Mrad, Longhua Zhao, Malena I. Español, Ling Xu, M. Carme Calderer

School of Mathematics

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Abstract

We study the aggregation phenomenon in lyotropic chromonic liquid crystals as the molecular concentration changes and condensing agents are added into the system. Using properties of the critical points of the Oseen–Frank energy of a nematic liquid crystal, combined with the geometric constraints of the hexagonal columnar chromonic phases, we show that the minimizers of the total energy are topologically equivalent to tori, in agreement with available experimental evidence on chromonic liquid crystals and DNA condensates, in viral capsids as well as in free solution. We model the system as bi-phasic, consisting of liquid crystal molecules and water, and postulate the total energy as the sum of the Flory–Huggins energy of mixing together with the bending and surface tension contributions of the liquid crystal. Two types of problems are considered, one related to finding the optimal shape of a torus, once the phase separation has occurred, and the second one that models the conditions leading to molecular aggregation. This work follows recent experimental investigations, but without addressing the topological properties of the toroidal nuclei observed and focusing on how the liquid crystal order competes with the aggregation phenomenon.

Original language	English (US)
Article number	107139
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	120
DOIs	https://doi.org/10.1016/j.cnsns.2023.107139
State	Published - Jun 2023

Bibliographical note

Funding Information:
M. Carme Calderer acknowledges the support from the National Science Foundation, USA , grant number DMS-DMREF 1729589 and DMS-1816740 . The authors are grateful to the support of the Michigan Center for Applied and Interdisciplinary Mathematics at the University of Michigan, USA , for hosting the Women in Mathematics of Materials (WIMM) Workshop that allowed this research to get underway and the partial support provided by the Association for Women in Mathematics (AWM), USA through the AWM-ADVANCE grant NSF-HRD 1500481 . The authors thank Runa Koizumi for helpful discussions regarding the experimental data, and the reviewers for their thoughtful comments and effort towards improving the manuscript.

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

Chromonic liquid crystals
Flory–Huggins energy
Oseen–Frank energy
Toroidal nuclei

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10.1016/j.cnsns.2023.107139

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title = "Aggregation phenomena in lyotropic chromonic liquid crystals",

abstract = "We study the aggregation phenomenon in lyotropic chromonic liquid crystals as the molecular concentration changes and condensing agents are added into the system. Using properties of the critical points of the Oseen–Frank energy of a nematic liquid crystal, combined with the geometric constraints of the hexagonal columnar chromonic phases, we show that the minimizers of the total energy are topologically equivalent to tori, in agreement with available experimental evidence on chromonic liquid crystals and DNA condensates, in viral capsids as well as in free solution. We model the system as bi-phasic, consisting of liquid crystal molecules and water, and postulate the total energy as the sum of the Flory–Huggins energy of mixing together with the bending and surface tension contributions of the liquid crystal. Two types of problems are considered, one related to finding the optimal shape of a torus, once the phase separation has occurred, and the second one that models the conditions leading to molecular aggregation. This work follows recent experimental investigations, but without addressing the topological properties of the toroidal nuclei observed and focusing on how the liquid crystal order competes with the aggregation phenomenon.",

keywords = "Chromonic liquid crystals, Flory–Huggins energy, Oseen–Frank energy, Toroidal nuclei",

author = "Lidia Mrad and Longhua Zhao and Espa{\~n}ol, {Malena I.} and Ling Xu and Calderer, {M. Carme}",

note = "Funding Information: M. Carme Calderer acknowledges the support from the National Science Foundation, USA , grant number DMS-DMREF 1729589 and DMS-1816740 . The authors are grateful to the support of the Michigan Center for Applied and Interdisciplinary Mathematics at the University of Michigan, USA , for hosting the Women in Mathematics of Materials (WIMM) Workshop that allowed this research to get underway and the partial support provided by the Association for Women in Mathematics (AWM), USA through the AWM-ADVANCE grant NSF-HRD 1500481 . The authors thank Runa Koizumi for helpful discussions regarding the experimental data, and the reviewers for their thoughtful comments and effort towards improving the manuscript. Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

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AU - Mrad, Lidia

AU - Zhao, Longhua

AU - Español, Malena I.

AU - Xu, Ling

AU - Calderer, M. Carme

N1 - Funding Information: M. Carme Calderer acknowledges the support from the National Science Foundation, USA , grant number DMS-DMREF 1729589 and DMS-1816740 . The authors are grateful to the support of the Michigan Center for Applied and Interdisciplinary Mathematics at the University of Michigan, USA , for hosting the Women in Mathematics of Materials (WIMM) Workshop that allowed this research to get underway and the partial support provided by the Association for Women in Mathematics (AWM), USA through the AWM-ADVANCE grant NSF-HRD 1500481 . The authors thank Runa Koizumi for helpful discussions regarding the experimental data, and the reviewers for their thoughtful comments and effort towards improving the manuscript. Publisher Copyright: © 2023 Elsevier B.V.

PY - 2023/6

Y1 - 2023/6

N2 - We study the aggregation phenomenon in lyotropic chromonic liquid crystals as the molecular concentration changes and condensing agents are added into the system. Using properties of the critical points of the Oseen–Frank energy of a nematic liquid crystal, combined with the geometric constraints of the hexagonal columnar chromonic phases, we show that the minimizers of the total energy are topologically equivalent to tori, in agreement with available experimental evidence on chromonic liquid crystals and DNA condensates, in viral capsids as well as in free solution. We model the system as bi-phasic, consisting of liquid crystal molecules and water, and postulate the total energy as the sum of the Flory–Huggins energy of mixing together with the bending and surface tension contributions of the liquid crystal. Two types of problems are considered, one related to finding the optimal shape of a torus, once the phase separation has occurred, and the second one that models the conditions leading to molecular aggregation. This work follows recent experimental investigations, but without addressing the topological properties of the toroidal nuclei observed and focusing on how the liquid crystal order competes with the aggregation phenomenon.

AB - We study the aggregation phenomenon in lyotropic chromonic liquid crystals as the molecular concentration changes and condensing agents are added into the system. Using properties of the critical points of the Oseen–Frank energy of a nematic liquid crystal, combined with the geometric constraints of the hexagonal columnar chromonic phases, we show that the minimizers of the total energy are topologically equivalent to tori, in agreement with available experimental evidence on chromonic liquid crystals and DNA condensates, in viral capsids as well as in free solution. We model the system as bi-phasic, consisting of liquid crystal molecules and water, and postulate the total energy as the sum of the Flory–Huggins energy of mixing together with the bending and surface tension contributions of the liquid crystal. Two types of problems are considered, one related to finding the optimal shape of a torus, once the phase separation has occurred, and the second one that models the conditions leading to molecular aggregation. This work follows recent experimental investigations, but without addressing the topological properties of the toroidal nuclei observed and focusing on how the liquid crystal order competes with the aggregation phenomenon.

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KW - Flory–Huggins energy

KW - Oseen–Frank energy

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Aggregation phenomena in lyotropic chromonic liquid crystals

Abstract

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