Relaxation properties in a diffusive model of k-mers with constrained movements on a triangular lattice.

We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are k-mers that can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean-square displacement, the self-part of the van Hove correlation function, and the self-intermediate scattering function. We observe a considerable slowing of diffusion on a long-time scale when suppressing the rotational motion of k-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self-intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale τ(q(n)) is found to decrease with the wave vector q(n) according to a simple power law. Furthermore, the slowing of the dynamics with density ρ(0) is consistent with the scaling law 1/τ(q(n);ρ(0))∝(ρ(c)-ρ(0))(ϰ), with the same exponent ϰ=3.34±0.12 for all wave vectors q(n). The density ρ(c) is approximately equal to the closest packing limit, θ(CPL)≲1, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient D(s) scales with the same power-law exponent and critical density.