Water-methanol separation with carbon nanotubes and electric fields

Methanol is used in various applications, such as fuel for transportation vehicles, fuel cells, and in chemical industrial processes. Conventionally, separation of methanol from aqueous solution is by distillation. However, this method consumes a large amount of energy; hence development of a new method is needed. In this work, molecular dynamics simulations are performed to investigate the effect of an electric field on water–methanol separation by carbon nanotubes (CNTs) with diameters of 0.81 to 4.07 nm. Without an electric field, methanol molecules fill the CNTs in preference to water molecules. The preference of methanol to occupy the CNTs over water results in a separation effect. This separation effect is strong for small CNT diameters and significantly decreases with increasing diameter. In contrast, under an electric field, water molecules strongly prefer to occupy the CNTs over methanol molecules, resulting in a separation effect for water. More interestingly, the separation effect for water does not decrease with increasing CNT diameter. Formation of water structures in CNTs induced by an electric field has an important role in the separation of water from methanol.

With 0.5 V/nm or stronger fields, χ water in the CNT (8,8) is 1.0, that means only water molecules occupy in the CNT.With an increase of the electric field, the peak width of the radial density becomes narrower and shifted from the CNT axis as shown in Figure S3-A, B for 0.5-and 2 V/nm, respectively.Thus, water molecules form tube-like structures as shown by the snapshots.CNT (6,6), 0.5 V/nm CNT (6,6), 0.25 V/nm CNT (6,6), 0 V/nm CNT (6,6), 2 V/nm CNT (6,6), 1 V/nm

Water molecules vs. methanol molecules in carbon nanotubes under electric field
To compare effect of axial electric field on the water molecules and methanol molecules in carbon nanotubes (CNTs), we performed simulations by filling the reservoir with water molecules only (water-CNT-graphene system) and methanol molecules only (methanol-CNTgraphene system).Then, we compared the dipole moment orientation, occupancy of molecules in CNTs, potential energies, structures, and hydrogen bond network.Dipole moment orientation, occupancy, and structures for the water molecules have been reported in our previous study [1].

Orientation of dipole moment
Figure S5 shows direction of dipole moment for methanol molecules in CNT (6,6) and (8,8) with 0, 1, and 2 V/nm.The direction of dipole moment is represented with angle α, which is the angle between the dipole moment µ and electric field E. The vertical axis denotes probability distribution function (pdf).With 0 V/nm, the peaks are at cos α = −1 and 1 for CNT (6,6) and −0.8 and 0.8 for CNT (8,8).Those mean the dipole moment of methanol molecules in CNTs has two orientations that are opposite to each other.With the electric field, the peak of cos α is shifted to 1 implying the direction of the dipole moment tends to be parallel to that of the field.It is same as for water molecules where the electric field aligns the dipole moment direction parallel to the field.
Figure S5: Effect of electric field on the dipole moment orientation of methanol molecules in CNT (6,6) and (8,8).Direction of dipole moment is indicated with angle α, which is the angle between the dipole moment µ and electric field E. O, H, and Me represent oxygen, hydrogen, and methyl, respectively.The vertical axis shows probability distribution function (pdf).Under the field, direction of dipole moment tends to be parallel to that of the field.

Occupancy of molecules in CNTs
The numbers of methanol molecules inside CNTs are shown in Table S1.Same as for the water molecules, the occupancy of methanol molecules in the CNTs increases with the electric field.Although the number of methanol molecules in the CNTs decreases slightly from 1 to 2 V/nm, but it is still larger than that with 0 V/nm.Hence, same as to the water molecules, electric field makes methanol molecules prefer to fill into CNTs.To compare effect of CNT wall on the water and methanol molecules, we calculated Lennard-Jones (LJ) potential energy per molecules in the reservoir and in the CNT (8,8).
Distributions of the LJ potential energy for water and methanol molecules with 0 and 2 V/nm are shown in Figure S6-A and B, respectively.Difference of LJ potential energy in the CNT and in the reservoir (ΔU LJ =U CNT − U res ) indicates van der Waals interaction of water-CNT and methanol-CNT (see Table S2, S3).With 0 V/nm, ΔU LJ for water molecules is higher than that for methanol molecules, which are −10.37 kJ/mol and −18.23 kJ/mol, respectively.This means that van der Waals attraction for methanol-CNT is stronger than that for water-CNT.
With 2 V/nm, ΔU LJ for methanol and water molecules are −12.87kJ/mol and 6.29 kJ/mol, respectively.This means that attraction of methanol-CNT decreases slightly with the field.In contrast, with 2 V/nm, ΔU LJ for water becomes positive denoting repulsive interaction between water and CNT.Thus, we can conclude that the preferential occupancy of water molecules over methanol molecules in the CNT with electric field is not due to the van der Waals interaction between water and CNT.The result suggests that electrostatic interaction (hydrogen bond network) in the water structure is a key factor for the separation effect with electric field.=U CNT − U res ) for methanol is lower than that for water.This implies that van der Waals attraction of methanol-CNT is stronger than that of water-CNT.S2).ΔU coul for methanol decreases as well from 7.51 kJ/mol to −17.97 kJ/mol with 0 and 2 V/nm, respectively (Table S3).Those results reveal that under electric field, electrostatic interaction within structures of molecules in CNT facilitates water and methanol molecules filling CNT.

Coulomb potential energy
Figure S7: Distribution of coulomb potential energy for molecules in the reservoir and in the CNT (8,8) with 0 and 2 V/nm; (A) for water molecules, and (B) for methanol molecules.With electric field, coulomb potential energy in CNT decreases significantly both for water and methanol.This means that under electric field, the coulomb potential energy drives water and methanol to fill in the CNT.

Dipole potential energy
When a dipole is subjected to external electric field, it has the following potential energy where  µ is vector of dipole moment and  E is the electric field.Thus, U dipole will be minimum when the direction of dipole moment is parallel to that of the electric field.Figure S8-A, B show distribution of U dipole in the reservoir and in the CNT (8,8) under 2 V/nm for water and methanol molecules, respectively.Distribution of U dipole in the reservoir is broader than in the CNT.It is because direction of a dipole moment under electric field is not statically parallel to the field but it oscillates around the direction of the field.Amplitude of the oscillation for molecules in the reservoir is larger than that of in the CNT.This is due to the effective electric field working in the reservoir is lower than that in the CNT.As we have discussed in our previous study that graphene sheet induces polarization [1].This means that the polarization induces internal electric field in the direction opposite to the external electric field.Thus, the effective electric field in the reservoir is the external field subtracted by the internal field.Distribution of dipole potential energy in the reservoir for methanol decays faster than that for water (Figure S8-B).It indicates that internal electric field due to the polarization for methanol is lower than that for water.Dipole moment of methanol is lower than that of water, which are 2.22 D and 2.27 D, respectively.That makes charge density for methanol is lower than that for water.As a result, effect of polarization for methanol is weaker.
Because peaks of U dipole distribution in CNT are narrower than those in reservoir, the averages of dipole potential energy in the CNT are lower than those in the reservoir.As a result, differences of dipole potential energy in CNT and in the reservoir (ΔU dipole ) for water and methanol molecules are negative, which are −5.06 kJ/mol and −1.30 kJ/mol, respectively (Table S2, S3).This means the dipole potential energy helps water and methanol molecules to fill CNT.

Structures and hydrogen bond network
Figure S9 shows structure of methanol molecules in CNT (8,8) with 2 V/nm.The molecules form two line-structures.The methyl groups from each line-structure are close to each other implying that each line-structure is not hydrogen bonded to one another.Similar structure is shown for methanol molecules in CNT (8,8) with 1 V/nm.The structures of methanol molecules differ from those of water molecules, which are helical structures in CNT (8,8) with 1 and 2 V/nm.
For analyzing hydrogen bond (HB), we employed the following geometrical criteria.For water molecules: R OO < 0.36 nm, R OH < 0.24 nm, and angle of HO---O < 30° [2] and for methanol molecules: R OO < 0.35 nm, R OH < 0.26 nm, and angle of HO---O < 30° [3].Average numbers of HB per molecule for water in CNT (8,8) are 2.84, 2.93 and 2.77 with 0, 1 and 2 V/nm, respectively.Those for methanol in CNT (8,8) are 1.70, 1.89 and 1.83 with 0, 1 and 2 V/nm, respectively.Because the methyls cannot form HB, the number of HB of methanol is lower than that of water.Electric field does not affect the number of HB per molecules significantly both for water and methanol molecules.However, the field makes lifetime of HBs in the water structure becomes very long.The electric field strengthens the HBs in the water structure [1].We determined dynamics of HBs with the HB autocorrelation function [4]: (2) where h(t)=1 if a pair of molecules is bonded at time t and h(t)=0 otherwise.The denominator is for normalization, which is the number of HBs tagged at t=0.Same as to the water molecules, HB autocorrelation function for methanol with electric field slightly decreases and then constant (Figure S10).It indicates that the lifetime of HBs is very long.The field strengthens HBs of methanol structure in CNT as well.To clarify the HB network in the water and methanol structures, we calculated distribution of HB direction.The pairs of molecules bonded with HB were determined from the three-dimensional (3D) structures.Then, the structures were unrolled to obtained 2D structures as shown in Figure S11-A and B for water and methanol molecules in CNT (8,8) with 2 V/nm, respectively.Direction of HB in 2D structure is indicated with angle α, which is measured from the z-axis to the clockwise direction.As an example, for the molecule i-th in Figures S11-A, we identified all HBs from the i-th to all other molecules at z ≥ 0. Position of the chosen molecules i-th was set to z = 0 at the time, and i-th was applied all molecules in the CNT.We calculated from 22 ns of simulation time.The result is shown in Figure S11-C for water (red line) and methanol (dotted blue-line).There are two main-peaks at α w1 = 23˚,  S2, S3).Those data indicate that electrostatic interaction in the water structure is stronger than that in the methanol structure.

Figure S1 :Figure
Figure S1: Snapshots of water molecules in CNTs under 2 V/nm of electric filed.The simulation condition is χ water = 0.81 in reservoirs.(A) in CNT (7,7) with orthographic and perspective projections for the left and the right figures, respectively.Water molecules form helical structure.(B) in CNT (9,9), water molecules have outer and inner structures.The outer structure is helical and the inner one is single-file structure as shown with orange and blue colors in the right figure.(C) in CNT (10,10), water molecules form double-walls structure.The outer structure is not helical (the right figure).(D) in CNT (12,12), the outer structure is not helical (the right figure).(E) to (H) in CNT (15,15), (20,20), (25,25) and (30,30), respectively.Water molecules form multi-walls structures.

Figure S2 :Figure S3 :
Figure S2: Radial density distribution of atoms in CNT (8,8) with 0 V/nm, (A) for water molecules, and (B) for methanol molecules.Simulation was performed with χ water = 0.81 in reservoirs.Snapshot in figure B shows structure of water and methanol molecules in the CNT.

FigureFigure S4 :
FigureS4represents the molecules structures inCNT (6,6).With 0 to 0.5 V/nm, methanol molecules prefer to occupy in the CNT where their structure is single-file.With an increase of the electric field, 1 V/nm or stronger fields, water molecules prefer to fill in the CNT instead of the methanol molecules.Under this field, the water molecules form zig-zag structures where every molecule is bonded to each other by hydrogen bond.It makes the water molecules structure more stable.

Figure S6 :
Figure S6: Distribution of Lennard-Jones (LJ) potential energy for molecules in the reservoir and in the CNT (8,8) with 0 and 2 V/nm; (A) for water molecules, and (B) for methanol molecules.Difference of LJ potential energy in the reservoir and in the CNT indicates van der Waals interaction of water-CNT and methanol-CNT.The difference of LJ potential in CNT and in reservoir (ΔU LJ

Figure
FigureS7-A, Bshow distribution of coulomb potential energy in reservoir and in CNT (8,8) for water and methanol molecules, respectively.Coulomb potential energy for water and methanol in CNT decreases significantly with the electric field.Difference of coulomb potential energy in the CNT and in the reservoir (ΔU coul =U CNT − U res ) for water decreases from 12.13 kJ/mol to −31.55 kJ/mol with 0 and 2 V/nm, respectively (TableS2).ΔU coul for

Figure S9 :
Figure S9: Structure of methanol molecules in CNT (8,8) with 2 V/nm.The molecules form two linestructures where the methyl groups from each line-structure are close to each other.This indicates that each line-structure is not bonded to one another.

Figure S10 :
Figure S10: HB autocorrelation function for methanol molecules in CNT (8,8) under 0, 1, and 2 V/nm.With the electric field, the lifetime of HBs of methanol molecules is very long.
and a low peak at α w3 = 75˚ for HBs in water molecules structure.The angle α w1 and α w2 are related to the column direction (magenta dashed-line) and the row direction (green dashed-line).That means the HB network is composed of a group of parallel lines in the column direction and a group of parallel lines in the row direction.In other word, water molecules structure consists of some line-structures that are hydrogen bonded to each other such as a net structure.In addition, few molecules make HB in the direction of α w3 (orange arrow-line).The 2D structure in FigureS11-B confirms the explanation before that methanol molecules have two line-structures.There are two peaks of HB direction, which are at α m1 = 25˚ and α m2 = 334˚ (FigureS11-C).The angle α m1 and α m2 are related to the directions of magenta line and green line (FigureS11-B), respectively.There are two directions of HB within a line-structure because methanol molecules form zig-zag configuration.There is no hydrogen bond from a line-structure to the other line-structure.Hence, the two line-structures are independent.They are not hydrogen bonded to each other.Consequently, the methanol structure in the CNT is weaker than the water structure.With 2 V/nm, ΔU of coulomb potential energy per molecule for water molecules is lower than that for methanol molecules, which are −31.55kJ/mol and −17.97 kJ/mol, respectively (Table

Figure
Figure S11: (A) Two-dimensional (2D) structure of water molecules in CNT (8,8) with 2 V/nm.(B) 2D structure of methanol molecules in CNT (8,8) with 2 V/nm.(C) Distribution of hydrogen bond direction in the water and the methanol structures.The direction is indicated with angle α, which is measured from the z-axis to the clockwise direction.

Table SI :
Average numbers of methanol molecules in CNTs.(with standard deviation)

Table S2 :
TableS2and S3 decreases with electric field.For water, total of ΔU per molecule decreases from 1.76 kJ/mol to −30.32 kJ/mol with 0 and 2 V/nm, respectively.For methanol, those values are −10.72 kJ/mol to −32.14 kJ/mol with 0 and 2 V/nm, respectively.Decreasing of total ΔU per molecule support the notion that under the electric field, water and methanol molecules prefer to fill CNT.Those results confirm the occupancy data where the number of molecules in CNTs increases with electric field.With 2 V/nm, those values are −77.92kJ/mol and −32.14 kJ/mol for water and methanol, respectively.The ΔU for water is much lower than that for methanol.It suggests that water molecules strongly prefer to occupy in the CNT over methanol molecules.Average potential energies per molecule in reservoir and in CNT (8,8) for water.ΔU is the difference between potential energy in CNT (U CNT ) and in reservoir (U res ).
V/nm, respectively.Thus, with 0 V/nm, ΔUs for all molecules in CNT (8,8) are 3.78 kJ/mol and −10.72 kJ/mol for water and methanol, respectively.The ΔU for methanol is lower than that for water.It suggests that methanol molecules prefer to fill in the CNT over water molecules.FigureS8: Distribution of dipole potential energy for molecules in the reservoir and in the CNT (8,8) with 2 V/nm; (A) for water molecules, and (B) for methanol molecules.

Table S3 :
Average potential energies per molecule in reservoir and in CNT (8,8) for methanol.ΔU is the difference between potential energy in CNT (U CNT ) and in reservoir (U res ).