Aggregation phenomena in lyotropic chromonic liquid crystals

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number107139
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - 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.


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


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