Spontaneous phase separation and pattern formation in a lyotropic nematic mixture

TL;DR

The paper shows that a lyotropic nematic–isotropic mixture can spontaneously demix even without explicit attractive interactions, driven by an Onsager-like coupling between local nematogen density and orientational order. Using a minimal 2D hydrodynamic model (Beris–Edwards Q-tensor coupled to a Cahn–Hilliard composition field with $\gamma(\phi)=\gamma_0+\Delta\phi$) and a hybrid lattice Boltzmann implementation, the authors map phase diagrams and reveal defect-driven droplet nucleation that leads to isotropic domains within a nematic matrix. When anchoring at interfaces is sufficiently strong, coarsening is arrested, giving rise to a self-assembled lamellar or super-smectic phase characterized by undulations, heterogeneous layer spacing, and long-lived defect patterns (e.g., lamellar onions). The study introduces elastocapillarity as a key control parameter ($\text{Ec}=\kappa/K$) for the transition between defect-driven microphase separation and macrophase separation, and demonstrates anchoring-driven microphase separation as a robust mechanism with implications for self-assembly in lyotropic and chromonic systems like Sunset Yellow (SSY). Overall, the work provides a unified framework linking density–orientation coupling, elastocapillarity, and anchoring to explain rich pattern formation and glassy defect states in lyotropic nematic mixtures with potential for tunable soft glasses and biocompatible materials.

Abstract

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.

Figures (8)

• Figure 1: Simulations replicate the isotropic–nematic (I–N) transition and phase separation. (A–C) Experimental images showing the isotropic (A), coexistence (B), and nematic (C) phases as the temperature decreases ($\gamma_0$ increases) and the nematic fluid concentration $\phi_0$ increases. (D–F) Corresponding simulation snapshots illustrating the same sequence of phase behaviour for a 128x128 system. The colour map represents the local compositional phase, $\phi$, while the overlaid lines indicate the nematic director field, with line length proportional to the local degree of orientational order. The cyan and yellow rings represent topological defects of charge +1/2 and -1/2, respectively. Scale bars: 200µm. Vertical and horizontal arrows in panel A show the polariser and analyser orientations, respectively.
• Figure 2: Experimental, simulated, and analytical phase diagrams reveal the isotropic–nematic transition and coexistence regions. (A) Experimental phase diagram of SSY solutions showing isotropic (brown), coexistence (violet), and nematic (beige) regions as functions of concentration and temperature. (B and C) Simulated phase behaviour represented by the average nematic order $\langle q \rangle$ and Binder cumulant, $U_{\phi}$, as functions of bare coupling coefficient $\gamma_0$ and composition $\phi$. (D) Analytical phase diagram derived from the common tangent construction on the free-energy density $f_{\text{hom}}$, showing the binodal and spinodal limits. The pink line denotes $\phi_c$, the nematic fluid concentration marking the transition from a homogeneous to a phase-separated configuration. Inset: Schematic of the common tangent construction, plotting the homogeneous free energy density $f_{\text{hom}}$ (solid line) and its second derivative $\partial^2_{\phi} f_{\text{hom}}$ (dashed lines) as a function of $\phi$. The tangent points (beige circles, $\phi_\pm$) define binodal limits, while regions of negative curvature define spinodal boundaries (bounded by the pink circle, denoting the discontinuity in $\partial^2_{\phi} f_{\text{hom}}$, and the brown circle), indicating that phase-separated states are energetically favoured over homogeneous ones.
• Figure 3: Defect-driven phase separation and droplet coarsening dynamics with and without surface tension. Starting from a random, noisy initial configuration, the nematic field evolves toward macroscopic phase separation through the annihilation of +1/2 (yellow) and -1/2 (blue) topological defects, leading to the formation of isotropic voids that grow and coarsen over time. Panel A shows a simulation without surface tension ($\kappa=0.00$) and panel B includes surface tension ($\kappa=0.01$). The column on the right shows the the average defect distance over time, $\xi_q$ (C) and the average charge density, $q_t$ (D). Both quantities are averaged over three runs with different randomised initial configurations in which the mean compositional phase is fixed at $\phi_0=1$ and the bare coupling coefficient at $\gamma_0=2.1$. Both B and C show magnified views ($40 \times 40$) of the global simulation domain ($128 \times 128$). The full animations are available in Suppl. Movies 1 and 2. A qualitatively similar coarsening is observed experimentally when a mixture of SSY at 28 wt$\%$ undergoes a temperature ramp (Suppl. Fig. 2 and Suppl. Movie 3).
• Figure 4: Anchoring-induced microphase separation and lamellar ordering in the isotropic–nematic mixture. (A) Experimental snapshot showing phase separation into alternating nematic and isotropic layers (see Suppl. Movie 4 for the complete dynamics). (B-C) Corresponding simulations exhibiting similar lamellar structures, albeit more densely packed. Simulation parameters are $\gamma_0=2.0$, $\phi_0=1.0$, and anchoring strength $W=-0.03$ (B), corresponding to normal anchoring, and $W=0.06$ (C), corresponding to planar anchoring. (D-E) Time evolution of two simulations with different initial conditions (same parameters as in B) showing defect dynamics: $+1/2$ (yellow) and $-1/2$ (blue) defects appear, move, and annihilate to relax the lamellar structure (see also Suppl. Movies 5 -6). In some cases, defects reappear transiently (D), while in others, a persistent $+1/2$ defect acts as a source of nematic layers (E). In both cases, complete annihilation is inhibited, leading to arrested, anchoring-stabilised microphase separation. Lower left to top right and top left to lower right arrows in panel A show the polariser and analyser orientations, respectively.
• Figure 5: Critical anchoring for planar and homeotropic cases. The critical anchoring follows the theoretical predictions (dashed lines) for both planar (blue) and homeotropic (orange) anchoring as a function of the surface tension coefficient, $\kappa$. Line brightness increases as a function of the elastic nematic constant, $K$, varied from 0.10 to 0.30. The insets on the top left show typical system configurations at critical anchoring strength $|W_c|$.