The project explored the problem of morphogenesis during first-order phase transitions in liquid crystals (LCs). The focus was on experimental characterization and theoretical description of the structure of soft LC nuclei shaped by bulk elasticity and anisotropic surface tension.

The intellectual merit of the project is that the elasticity of LCs was treated with different elastic constants describing the splay, twist, and bend of the molecular orientation. The project demonstrated that the widely used one-constant approximation does not adequately describe the complex world of LCs. Explored examples represented (i) droplets of the nematic and columnar LC in an isotropic melt, (ii) isotropic droplets nucleating at the cores of topological defects in a nematic LC, (iii) thin films of ferroelectric nematic LCs. In the columnar phase, the molecules form a two-dimensional periodic lattice; the requirement of a constant period of this lattice prohibits twists and splays but allows bend. As a result, the research established that a columnar droplet is shaped as a doughnut-like torus rather than a sphere. The hole size is controlled by the ratio of the bend elastic constant and the surface tension. In a conventional nematic, all three types of deformations are allowed. The research uncovered that a nematic droplet changes its equilibrium shape from a simply-connected tactoid, which is topologically equivalent to a sphere, to a torus, which is not simply connected. The topological shape transformation is triggered by minute changes in the temperature or concentration and is caused by the interplay of nematic elastic constants, which facilitates splay and bend in tactoids but hinders splay in the toroids. The topological transformation of a droplet from a sphere into a torus is the first example of such a morphogenetic change in an inanimate system. Disparity of the elastic constants also dictates the position of isotropic droplets formed at the cores of topological defects upon heating. These droplets appear at the centers of the defects but as heating progresses, they shift away. The direction of the shift is dictated by the ratio of the splay to bend moduli. Finally, the project demonstrated that the disparity of elastic constants is of prime importance in the equilibrium states of recently discovered ferroelectric nematic LCs, in which the splay is difficult because of the formation of space charge. As a result, their domain structure supports twist and bend but avoids splay.  

Mathematical analysis of the experimental observations that the balance of strongly anisotropic elastic bulk and interfacial forces yields intricate inner structure and shape of confined LCs represents a major step forward in intellectual insight as compared to the current level of modeling that is hindered by limitations such as the one-constant approximation or a shape fixed by the surface tension insensitive to the bulk elasticity. The disparity of elastic constants represents a significant challenge for analysis in mathematics and materials science; successful modeling of it promises new and interesting applications in materials design. The comprehensive plan of attack included interconnected theoretical and experimental components that validated and informed each other for the duration of the project.

Broader Impacts: The chosen objects of the research represented tractable models of more complex formations, such as condensed strands of DNA, red blood cells, and developing embryos. For example, DNA condensates in viral capsids show toroidal morphology similar to the columnar droplets but these DNA condensates are only 50 nm wide, which makes them very difficult to visualize and explore. In contrast, the columnar droplets are thousands of times larger, which allowed the team to use optical microscopy for the detailed analysis of shapes and inner structure. The elastic anisotropy mechanism might be helpful in understanding topology transformations in morphogenesis and pave the way to control and transform shapes of droplets of liquid crystals and related soft materials. The results will be important in various fields of mathematics, physics, and materials science, since the development of various morphologies in coexisting phases is a ubiquitous natural phenomenon. The acquired knowledge will bring about new and powerful tools to experimentally control the geometry and topology of coexisting phases. The project engaged and educated a new, diverse generation of multi-lingual scientists, including women, with fundamental and technological cross-disciplinary backgrounds in physics, mathematics, engineering, and materials science. Participating male and female graduate students successfully defended their PhD theses and continued research careers in academia and industry. 

Last Modified: 08/11/2024
Modified by: Oleg D Lavrentovich