Continuum theory Oseen-Zocher-Frank elasticity

There are two basic theories to describe the LC state, the continuum theory mainly proposed by Oseen, Zocher, and Frank and the swarm theory supported by researchers such as Bose, Bom, Omstein, Maier, and Saupe [10,11]. The continuum theory models the liquid crystal as an anisotropic elastic medium with properties varying as a function of position. The swarm theory emphasizes molecular interactions and interprets the LC state as the result of a statistically driven thermodynamic equilibrium. In the recent work of de Gennes, Leslie and Ericksen, LC theories integrate aspects of both the continuum theory and the swarm theory [11]. 

The foundations of continuum theory were first established by Oseen [61] and Zocher [107] and significantly developed by Frank [65], who introduced the concept of curvature elasticity. Erickson [17, 18] and Leslie [15, 16] then formulated the general laws and constitutive equations describing the mechanical behavior of the nematic and chiral nematic phases. 

As discussed in Sec. 2.2.2.1, the foundations of the continuum model were laid by Oseen [61] and Zocher [107] some seventy years ago, and this model was reexamined by Frank [65], who introduced the concept of curvature elasticity to describe the equilibrium free energy. This theory is used, to this day, to determine splay, twist, and bend distortions in nematic materials. The dynamic models or how the director field behaves in changing from one equilibrium state to another have taken much longer to evolve. This is primarily due to the interdependency of the director it (r, t) and v (r, /) fields, which in the case of chiral nematics is made much more complex due to the long-range, spiraling structural correlations. The most widely used dynamic theory for chiral... 

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