*2.2. Computational Methods*

All molecular dynamics simulations were carried out by using the open-source software DL POLY 4.08 [14,15]. For visualization, VMD 1.9.4a12 software [16] was used. All simulations were carried out by using the non-equilibrium molecular dynamics (NEMD) method to derive the motion of the

molecules. LJ-potential is used to describe the interactions between the water molecules and the interaction between the CNT and water molecules. The LJ-potential is given by the following equation:

$$\mathbf{U}(\mathbf{r}\_{ij}) = 4\epsilon \left[ (\sigma \langle \mathbf{r}\_{ij} \rangle^{12} - (\sigma \langle \mathbf{r}\_{ij} \rangle^{6}) \right]$$

where <sup>r</sup>*ij*, σ, and are the interatomic bond vector, the balance distance where the interaction of particles is zero, and the depth of the potential well, respectively.

In this study, to model the flow, an external force field method is used. In this method, a constant force f is added to all water molecules along +Z direction to mimic the pressure-driven flow, whereas the pressure di fference between the two sides of a membrane is as follows:

> ΔP = nf/A

where f is the applied force on each water molecule, n is the number of water molecules, and A is the membrane area. This is one of the widely accepted methods in molecular dynamics (MD) to simulate the pressure-driven flow [17]. Force is applied to the molecules, using the external force field known as the gravitational field in the DL POLY software, where the force is given by the following equation:

$$\underline{F} = m\underline{G}$$

where *G* is the gravitational field which is given as input, *F* is the force, and *m* is the mass of the water molecule.

All simulations were carried out with a gravitational field of 0.0185G applied to the molecules. The SPC/E water model used in this simulation has a contact angle θ = 95.3◦ [18]. The LJ cross-interaction between the water molecules and carbon atoms are σC-O = 0.319 nm and εC-O = 0.392 kJ/mol [18], which were determined by using the Lorentz-Berthelot mixing rules [19]. For water–water interactions, the default value of LJ parameter of SPC/E water model σO-O = 0.3169 nm and εO-O = 0.6498 kJ/mol is used [20]. The LJ parameters of σB-O = 0.331 nm, εB-O = 0.5079 kJ/mol, σN-O = 0.326 nm, and εN-O = 0.6276 kJ/mol were used for the boron nitride interactions with water [21]. The bond lengths and angle degrees of the water molecule are constrained by SHAKE algorithm [22]. The canonical ensemble NVT is used for all the simulations, to update the velocity and position, along with Noosé-Hoover thermostat coupling, to maintain a constant temperature. A cut-o ff distance of 10 Å is used for LJ interactions.
