The mechanism of diffusion of helical particles in the new screw-like nematic phase is studied by molecular dynamics numerical simulation. Several dynamical indicators are reported that evidence and microscopically characterise the special translo-rotational motion by which helical particles move in this chiral liquid-crystalline phase. Besides mean square displacements and diffusion coefficients resolved parallel and perpendicular to the nematic director, a suitable translo-rotational van Hove self-correlation function and a sequence of translational and rotational velocity, self- and distinct-, time correlation functions are calculated. The analysis of all these correlation functions elicits the operativeness of the aforementioned coupled mechanism and allows its short- and long-time quantitative characterisation.
It was explicitly verified that, in a MD-NVT numerical simulation carried out on the soft repulsive helical particle system at kBT/ϵ = 1 and a value of number density coincident with the average density obtained in the previous MC-NPT numerical simulation on the corresponding hard helical particle system at Pd3/kBT = 0.75, the resulting average dimensionless pressure Pσ3/kBT was 0.77, consistent with the value set in the previous MC-NPT numerical simulation.
It is worth noting that the work by A. Patti et al., Phys. Rev. Lett. 103, 248304 (2009), that postdated Ref. 10, actually claims that chain-like clusters of rod-like particles moving across the layers would contribute to the translational diffusive dynamics along the director in a smectic phase, thus attempting to stretch the analogy between an equilibrium smectic liquid-crystal and a non-equilibrium glass forming fluid. The stringent dynamical criterion adopted in Ref. 10 did not indicate this, however, but rather pointed to the translational diffusive dynamics along the director in a smectic phase essentially remaining an individual process.