Geometric modeling of phase ordering for the isotropic–smectic A phase transition - Zamora Cisneros, David Uriel; Wang, Ziheng; Dorval Courchesne, Noémie-Manuelle; Harrington, Matthew J.; Rey, Alejandro D. (Frontiers in Soft Matter, 2024)
1) Background: Liquid Crystal mesophases have orientational and positional order that can be found in both synthetic and biological materials. These orders are maintained until some parameter, mainly temperature or concentration, is changed inducing a phase transition. Among these transitions, a special sequence of mesophases has been observed, in which priority is given to the direct smectic liquid crystal transition. The description of these transitions is carried out with the Landau-de Gennes (LdG) model, which correlates the free energy of the system with orientational and positional order. (2) Methodology: This work explored the direct isotropic-to-smectic A transition studying the free energy landscape constructed with the LdG model and its relation to three curve families -(I) level-set curves, steepest descent and critical points; (II) lines of curvature and geodesics, which are directly connected to the principal curvatures; and (III) the Casorati curvature and shape coefficient that describe the local surface geometries resemblance (sphere, cylinder, saddle). (3) Results: 12-cyanobyphenil experimental data was used to study the three curve families. The presence of unstable nematic and metastable plastic crystal information was found to add information to the already developed smectic A phase diagram. The lines of curvature and geodesics were calculated and laid out on the energy landscape, which highlighted energetic pathways connecting critical points. The Casorati curvature and shape coefficient were computed, and in addition to the previous family, they framed a geometric region that describes the phase transition zone. (4) Conclusions and significance: A direct link of the energy landscape topological geometry with phase transitions and relevant critical points was established. The shape coefficient delineates a stability zone in which the phase transition develops. The methodology significantly reduces the impact of unknown parametric data. Symmetry breaking with two order parameters may lead to novel phase transformation kinetics and droplets with partially ordered surface structures.