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.

💡 Research Summary

This paper investigates the origin of the broad nematic–isotropic coexistence region observed in Sunset Yellow (SSY)–water chromonic mixtures, a class of lyotropic liquid crystals. Contrary to the common assumption that attractive interactions between SSY stacks drive demixing, the authors propose a minimal theoretical model that contains no explicit inter‑species attraction. Instead, the free energy includes an Onsager‑like coupling term linking the local nematogen concentration φ to the nematic order parameter q. When the coupling strength Δ exceeds a threshold, the homogeneous free‑energy surface becomes non‑convex, generating a spinodal region where the mixture is thermodynamically unstable. By applying a common‑tangent construction to the homogeneous free‑energy density f_hom(q,φ), the authors analytically determine binodal limits φ⁻ and φ⁺ that delineate the coexistence region. The resulting phase diagram displays nearly linear phase boundaries, in excellent agreement with both experimental measurements and numerical simulations.

To explore the dynamics of phase separation, the authors perform two‑dimensional lattice‑Boltzmann simulations of the coupled concentration‑director field equations. In the absence of interfacial tension (σ=0), topological defects of charge ±½ nucleate spontaneously in the nematic background. Each defect locally perturbs φ, nucleating isotropic droplets. Elastic stresses associated with the director field drive the coalescence of droplets bearing opposite topological charge. The defect density decays as t⁻¹/², and the average defect spacing grows as ξ∝t¹/², mirroring the coarsening law of a single‑phase nematic. However, once most defects have annihilated, droplet coalescence slows dramatically, leading to kinetic arrest and a stable microphase‑separated lamellar morphology. This elastically driven arrest is governed by the dimensionless elasto‑capillary number Ec=κ/K, where κ is related to interfacial energy and K is the Frank elastic constant. For Ec≪1, elasticity dominates and arrest occurs; for Ec≫1, surface tension dominates and the system proceeds to macroscopic phase separation.

When a finite interfacial tension is introduced (σ>0), the coarsening dynamics change qualitatively. Both elastic and capillary forces now drive droplet growth, and the system exhibits unbounded coarsening, ultimately yielding macroscopic phase separation. The authors thus identify Ec as the control parameter that selects between elastically driven, arrested microphase separation and tension‑driven macrophase separation.

A further layer of complexity arises when anchoring of the nematic director at the isotropic–nematic interface is incorporated. Strong normal or tangential anchoring imposes a fixed orientation at the interface, suppressing the formation of simple lamellar stacks and instead stabilizing a “super‑smectic” phase. This phase is characterized by spontaneous undulations of the layers, heterogeneous layer spacing, and the emergence of lamellar onions. The layer compression modulus appears unusually low, allowing the layers to bend easily and to form onion‑like structures even without external shear. Defect patterns become long‑lived and history‑dependent, suggesting a glassy, multistable state with potential bio‑compatible applications.

Experimentally, the authors map the phase behavior of SSY–water mixtures over concentrations of 26–32 wt % and temperatures of 20–45 °C. They observe three regimes—pure isotropic, pure nematic, and a coexistence region—mirroring the theoretical predictions. Within the coexistence region, nematic “rafts” appear non‑circular, indicating anisotropic effective surface tension arising from elastic stresses. Introducing surfactants to increase interfacial tension in the experiments yields more rounded domains, consistent with simulation outcomes.

In summary, the study makes three major contributions: (1) it reveals that Onsager‑type density‑order coupling alone can drive phase separation in lyotropic nematics, eliminating the need for explicit attractive forces; (2) it demonstrates that the balance between elastic stresses, interfacial tension, and anchoring—quantified by the elasto‑capillary number and anchoring strength—determines whether the system undergoes macroscopic demixing, arrested microphase separation, or forms a super‑smectic pattern; and (3) it validates the theoretical framework through quantitative agreement with both simulations and experiments on SSY–water systems. These insights open new avenues for designing self‑assembled, tunable soft materials for sensors, metamaterials, and bio‑compatible glassy states.