Nanofluidic Osmotic Diodes: Theory and Molecular Dynamics Simulations

Osmosis describes the flow of water across semipermeable membranes powered by the chemical free energy extracted from salinity gradients. While osmosis can be expressed in simple terms via the van ’t Hoff ideal gas formula for the osmotic pressure, it is a complex phenomenon taking its roots in the subtle interactions occurring at the scale of the membrane nanopores. Here we use new opportunities offered by nanofluidic systems to create an osmotic diode exhibiting asymmetric water flow under reversal of osmotic driving. We show that a surface charge asymmetry built on a nanochannel surface leads to nonlinear couplings between water flow and the ion dynamics, which are capable of water flow rectification. This phenomenon opens new opportunities for water purification and complex flow control in nanochannels.

Figure 1

Sketch of the system showing the asymmetry of surface charge in the nanochannel, and the different salt concentrations in the left and right reservoirs.

Figure 2

Apparent osmotic pressure $\Delta {\Pi }_{\mathrm{app}}$ versus the salinity gradient $\Delta n=n_R-n_L$ (left) and applied voltage $\Delta V=V_R-V_L$ (right) obtained from Eq. (6). Note that the water flux $Q$, which is the measurable flux, is directly proportional to $\Delta {\Pi }_{\mathrm{app}}$ for vanishing $\Delta P$, see Eq. (3). All the quantities are depicted in reduced units of $k_{B}T$, $k_{B}T/e$, and $n_0$ (average salt concentration); $\delta =3$, $\alpha =5$.

Figure 3

Comparison of the theoretical apparent osmotic pressure and the MD simulations results versus the osmotic gradient (left) and the applied voltage (right). As in Fig. 2, the water flux is expected to be proportional to $\Delta {\Pi }_{\mathrm{app}}$ according to Eq. (3). Surface charges are chosen such that the surface-to-bulk-charge ratios are ${\delta }_L=5$ and ${\delta }_R=\alpha {\delta }_L$, with $\alpha =10$. Same units as in Fig. 2.

Figure 4

(a) View of the simulation system using VMD [33], where parallel graphenelike sheets with asymmetric surface charges act as a membrane. (b) Evolution of the amount of water molecules after 20 ns for various $\Delta V$, with salt concentration $n_R=n_L=0.15\mathrm{M}$; the surface-to-bulk-charge ratios are ${\delta }_L=3$, ${\delta }_R=12$. All curves are the average over five realizations of the simulations with duration 20 ns. $\Delta V$ is in units of $k_{B}T/e$. Inset: Flux $Q=\Delta N_{{\mathrm{H}}_2\mathrm{O}}/\Delta t$ versus the applied voltage drop. The dashed line is an adjustment using the expression $Q=Q_s(\exp [eV/k_{B}T]-1)$ with $Q_s=9\times {10}^{-4}{\mathrm{ns}}^{-1}$.