Molecular Dynamics Simulation of Ratchet Motion in an Asymmetric Nanochannel

The persistence of ratchet effects, i.e., nonzero mass flux under a zero-mean time-dependent drive, when many-body interactions are present, is studied via molecular dynamics (MD) simulations of a simple liquid flowing in an asymmetric nanopore. The results show that (i) ratchet effects persist under many-body density correlations induced by the forcing; (ii) two distinct linear responses (flux proportional to the drive amplitude) appear under strong loads. One regime has the same conductivity of linear response theory up to a forcing of about 10 kT, while the second displays a smaller conductivity, the difference in responses is due to geometric effects alone. (iii) Langevin simulations based on a naive mapping of the many-body equilibrium bulk diffusivity, $D$, onto the damping rate, $\gamma$ are also found to yield two distinct linear responses. However, in both regimes, the flux is significantly smaller than the one of MD simulations.

Figure 1

Sketch of $xz$ section of the simulation box at $y=0$, (the origin of axes $O$ is taken in the center of the channel). The solid line is the wall surface, the dashed one is the isosurface [$V_w(\mathbf{r})=k_b\theta$] of argon-wall potential. The effective radii of the pore ($r_1$ and $r_2$) are also indicated.

Figure 2

Particle flux ($\mathrm{\text{atoms}}/\mathrm{ps}$) vs the static forcing amplitude $A_s$. Black triangles $1\to 1$ geometry, squares $2\to 2$ geometry, circles conical pore geometry, dot-dashed line linear response prediction.

Figure 3

Density profiles on a symmetry plane: equilibrium (a), static forcing, $A_s=-4.15\mathrm{pN}$ (b) and $A_s=4.15\mathrm{pN}$ (c).

Figure 4

(a) Particle flux $\Phi$ ($\mathrm{\text{atoms}}/\mathrm{ps}$) as function of the period $T$ [Eq. (3)] at different amplitudes $A_d$. Squares $A_d=1.66\mathrm{pN}$, triangles $A_d=4.15\mathrm{pN}$, circles $A_d=8.3\mathrm{pN}$. The three horizontal lines are the adiabatic plateaux obtained by numerical integration of (4). (b) $\Phi$ as a function of the dynamic forcing amplitude $A_d$ for different periods $T$. Squares $T=200\mathrm{ps}$, circles $T=50\mathrm{ps}$, upper triangles $T=25\mathrm{ps}$, lower triangles $T=12.5\mathrm{ps}$. Filled circles: adiabatic values.