Mobility and diffusivity in a generalized Frenkel-Kontorova model

Abstract

In this work we used a generalized Frenkel-Kontorova model to study the mobility of water molecules inside carbon nanotubes with small radius at low temperatures. Our simulations show that the mobility of the confined water decreases monotonically increasing the amplitude of the substrate potential at fixed commensurations. On the other hand, the mobility of the water molecules shows a non-monotonic behavior when varying the commensuration. This result indicates that the mobility of the confined fluid presents different behavior regimes depending on the amplitude of the water-nanotube interaction. In order to understand qualitatively these results, we study analytically the driven Frenkel-Kontorova model at finite temperatures. This analysis allows us to obtain the curves of the mobility versus commensurations, at fixed substrate potentials. Such curves shows the existence of three regimes of mobility behavior as a function of the commensuration ratio. Additionally, our study indicates a nontrivial and strong dependence of the mobility with a quantity that can be interpreted as an effective amplitude of the substrate potential, depending on the bare amplitude of the substrate potential, the commensuration ratio and temperature.

Nanoscale sliding friction versus commensuration ratio: Molecular dynamics simulations

“…The present results are consistent with those obtained by Braun et al 14 who, using molecular dynamics simulations, studied the mobility and diffusivity of a generalized FrenkelKontorova model taking into account anharmonic interactions. In Fig.…”

Observation of kinks and antikinks in colloidal monolayers driven across ordered surfaces

“…In the Frenkel-Kontorova approach the interface between two solids is described by a monolayer of elastically interacting beads on a periodic substrate potential [5][6][7][8] . In addition to stick-slip motion, the Frenkel-Kontorova model also predicts the formation of topological solitons, so-called kinks and antikinks [9][10][11][12] . These excitations are believed to dominate the frictional properties at atomic length scales because they provide an efficient mechanism for mass transport; so far, such excitations have never been observed in sliding friction experiments 21 .…”

Single-file mobility of water-like fluid in a generalized Frenkel-Kontorova model

“…As a result we obtain numerically the curves of mobility versus commensurations at fixed substrate potentials which as discussed previously shows the existence of three regimes of behavior of such quantity with variations of commensurations. This regimes can be related with the density and dynamic of the defects in our chain of particles in a scenario analogous to the one proposed by Braun et al, 50,51 considering a sort of inverse relation between temperature and amplitude of the substrate potential.…”

“…To understand qualitatively the behavior of the mobility we make use of the picture given by Braun et al 50,51 previously discussed in section III. First it is important to notice that the maximum of the mobility should be reached when the concentration of kinks is maximum as well.…”

“…Additionally, using an analytical analysis we found a relation between the mobility's behavior as a function of temperature (as predicted phenomenologically 50,51 ) and corrugation. This paper is organized as follow: in section II we present the generalized Frenkel-Kontorova model used in the characterization of the mobility of a confined water-like fluid.…”