  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.

Soft Condensed Matter;Optimization and Control