Spontaneous phase separation and pattern formation in a lyotropic nematic mixture

Lyotropic liquid crystals can display rich phase behaviour and self-organisation, yet the physical principles underlying their self-assembly into large scale patterns remains understudied. Here, we combine theory, simulations and experiments on Sunset Yellow-water chromonic mixtures to show that such materials spontaneously phase separate, even without assuming any underlying microscopic attraction between the molecular species. In our minimal model, demixing depends solely on the Onsager-like coupling between local nematogen density and orientational order. If such a coupling is sufficiently strong, nematic defects trigger the nucleation of isotropic droplets, which then coalesce due to elastic or interfacial tensions. We further show that strong anchoring of the director field at the interface arrests this coarsening process, resulting in a stable microphase separated lamellar pattern. This self-assembled smectic phase has striking and unusual features, including spontaneous undulations, heterogeneous layer spacing, long-lived glassy defect patterns and lamellar onions. Our results identify orientational-density coupling and elastocapillarity as fundamental mechanisms to guide self-assembly in lyotropic and chromonic liquid crystals.