Analytical model of critical buckling transition for smectic liquid crystal based on the viscoelastic scaling of coarse-grained molecular dynamics.

The buckling transition of smectic liquid crystals (LCs) is important not only as fundamental physics but also for the rational design of devices to make use of their optical and mechanical properties. However, there exists a huge gap between the specific knowledge and universal analytical formulation. We have conducted coarse-grained molecular dynamics (CGMD) simulations with the force field optimized for the description of buckling phenomena including topological defects to link the molecular nature and continuum formulation. The simulations reveal the viscoelastic characteristics where the critical strain and the compression modulus highly depend on the strain rate as well as the number of layers. Therefore, we formulate the scaling model whose coupling constants depend on both strain rate and domain size. The model reproduces the CGMD results as well as experimental and theoretical values in existing literature. Furthermore, we elucidate from this model that the critical buckling behavior is determined by the competition between the suppression of compression-induced flow and the undulation fluctuation of layers. The framework consisting of the CGMD simulation and the scaling model enables us to estimate the buckling characteristics of smectic LCs reflecting their molecular structures in a wide range from the low-frequency regime that can be verified by experiments to the high-frequency regime beyond the reach of it.