Recent studies have shown the possibility of water transport across carbon nanotubes, even in the case of nanotubes with small diameter (0.822 nm). In this case, water shows subcontinuum transport following an ordered 1D structure stabilized by hydrogen bonds. In this work, we report MD simulations describing the effect of a perpendicular electric field in this single-file water transport in carbon nanotubes. We show that water permeation is substantially reduced for field intensities of 2-3 V/nm and it is no longer possible under perpendicular fields of 4 V/nm.
Despite its strong hydrophobic character, single walled carbon nanotubes (SWCNTs) are spontaneously filled by water [1,2]. Transport of water in these systems has novel and promising properties which have been extensively studied by Molecular Dynamics (MD) simulations (see for example [3] for a review). Quite interestingly, the water transport trough a carbon nanotube depends strongly on its radius and MD simulations predict a transition between continuum to subcontinuum transport as the radius decreases [4], as recently confirmed experimentally [5] . In the case of the nanotubes with small radius, the nanotubes are filled by a one-dimensional ordered chain of water molecules which maintain 2 hydrogen bonds per molecule inside the CNT [6]. This effective 1D water system has extremely interesting properties and it has been studied experimentally [5], by MD simulations [1][2][3][4][6][7][8] and analytical treatments based on the 1D Ising model [9]. Interestingly, this system has been analyzed as a model for water transport in biological pores [10].
A recent MD simulation study has shown the strong response of this single-file water system inside CNTs to electric fields parallel to the axis of the nanotube [8], due to the peculiarities of the 1D hydrogen bonding network. Motivated by this previous study, in this work we consider a related but different question, namely the effect of applying an electric field perpendicular to the single file water transport across carbon nanotubes. In this case, a competition arises between the hydrogen bonding network (which tends to maintain the alignment of the chain of water molecules in the nanotube axis direction) and the perpendicular electric field (which tends to align the water dipole in the perpendicular direction). A simple numerical calculation proposed in [11] suggests that this effect will appear for field intensities between 2-3 V/nm. Noting that a single water-water hydrogen bond has a free energy of about 5k B T and the dipole of the water molecule in liquid phase is about 2.5 D we can say that H-bonding will compete with external fields with intensities up to E ∼ 2.4 V/nm. Albeit high, these field intensities can be studied in simulations and experiments. In this work, we report a preliminary set of MD simulations in order to study the effect on water transport of this competition between hydrogen bonding and electric field.
We have performed a total of 33 molecular dynamics (MD) simulations of water transport across carbon nanotubes in both equilibrium and nonequilibrium conditions in presence and in absence of an electric field perpendicular to the axis of the nanotubes.
All simulations described here were performed using the 2.7 version of the NAMD program [12]. The preparation of the system and analysis of the results were made using the Visual Molecular Dynamics (VMD) software [13]. The simulated system is shown in Figure 1. It consisted of a periodic simulation box of dimensions 23.0×19.9×30.4 Å3 containing 248 water molecules and a porous membrane made of four carbon nanotubes with their axis aligned in the z direction. Each carbon nanotubes has 144 carbon atoms and has a radius of 0.411 nm and length 1.34 nm. Water molecules were modelled using the TIP3P model as implemented in the CHARMM force field and carbon atoms from nanotubes were modelled as Lennard-Jones spheres with parameters = 0.07 kcal/mol and σ = 3.9848 Å . Carbon atoms were maintained fixed during all the simulation as in previous works [4,6]. Lennard-Jones interactions were computed using a smooth (10-12 Å) cutoff, as it is customary done in NAMD2 simulations. The electrostatic interactions were calculated using the particle-mesh Ewald (PME) method. We employ a multiple time step. The equations of motion are solved with a 1 fs time step, nonbonded interactions are updated each 2 time steps and electrostatic interactions are updated each 4 time steps. The temperature was maintained at 300 K in all simulations employing a Langevin thermostat with a 5 ps -1 dumping constant. The Langevin thermostat is applied to the water oxygen atoms only. Some of our simulations were performed in presence of an external pressure difference. This external pressure was applied in NAMD2 as a Tcl force (as implemented in [14]) which acts on oxygen atoms in a slab of 5.4 Å thickness (all oxygen atoms with coordinates z > 12.5 Å or z < -12.5 Å). This methodology is also described in detail in Ref [15]. The applied pressure ∆P is computed from the force f by ∆P = nf /A where n is the number of water molecules in the slab and A its transversal area.
In most of our simulation runs, we applied an uniform electric field E y , perpendicular to the axis of the nanotubes, a feature which is implemented in NAMD2. The field is acting in all the simulation box.
In all simulations, we compute the number of permeation events, defined as the number of water molecules observed to completely cross the nanotube (entering
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