One-, Two-, and Three-Dimensional Hopping Dynamics

Hopping dynamics in glass has been known for quite a long time. In contrast, hopping dynamics in smectic-A (SmA) and hexatic smectic-B (HexB) liquid crystals (LC) has been observed only recently. The hopping in SmA phase occurs among the smectic layers (one-dimensionally), while hopping in HexB phase occurs inside the layers (two-dimensionally). The hopping dynamics in SmA and HexB liquid crystal phases is investigated by parallel soft-core spherocylinders, while three-dimensional hopping dynamics in inherent glassy states is investigated by systems of Weeks–Chandler–Andersen (WCA) spheres. The temperature dependence of diffusion coefficients of hopping in SmA phase can be described by the Arrhenius equation characteristic of activation process. In HexB LC phase, the diffusion coefficients saturate at higher temperatures. In a system of WCA spheres, the values and temperature dependence of diffusion coefficients depend on the observed states.