4.3 Results and Discussion
4.3.2 Ion Dynamics
Figure 4-9: Distribution of distance traversed (a) configuration-1 (b) configuration- 2 (c) configuration-3, residence time (d) configuration-1 (e) configuration-2 (f) configuration-3 and velocity (g) configuration-1 (h) configuration-2 (i) configuration- 3, of the water molecules while permeating through the layered GO membranes.
membranes for configuration-1 is 32.15 𝑛𝑚/𝑛𝑠, for configuration-2 is 33.16 𝑛𝑚/𝑛𝑠 and for configuration-3 is 34.76𝑛𝑚/𝑛𝑠.
Figure 4-10: Density of ions along the 𝑍 direction. (a) configuration-1 (b) configuration-2 (c) configuration-3. The positions of the two membranes are shown by two pair of dotted green lines. Please note that simulation time for configuration-1 and configuration-2 is 25 𝑛𝑠, while it is 64 𝑛𝑠 for configuration-3.
Figure 4-11: (a) Trajectory of Mg2+ ion inside the layered GO membrane of configuration-3. (b) Number of water molecules in the hydration shell of Mg2+ ion at various locations while permeating through the membrane. Red color is for oxygen atoms, green color is for hydrogen atoms, cyan color is for carbon atoms and mauve color is for Mg2+ ion.
the Mg2+ ion, Na+ ion and Cl− ion inside the layered GO membrane of configuration- 3. Along with their trajectory inside the membrane the number of water molecules in their hydration shell is also computed. The radius of the hydration shell of Mg2+
ion is 4.25 Å, while for Na+ ion and Cl− ion it is 3.15 Å. Figure 4-11b, Figure 4- 12b and Figure 4-13b show the number of water molecules in the hydration shell of the Mg2+ ion, Na+ ion and Cl− ion respectively at various locations while permeat- ing through the layered GO membrane of configuration-3. Water molecules within
Figure 4-12: (a) Trajectory of Na+ ion inside the layered GO membrane of configuration-3. (b) Number of water molecules in the hydration shell of Na+ ion at various locations while permeating through the membrane. Red color is for oxygen atoms, green color is for hydrogen atoms, cyan color is for carbon atoms and yellow color is for Na+ ion.
Figure 4-13: (a) Trajectory of Cl− ion inside the layered GO membrane of configuration-3. (b) Number of water molecules in the hydration shell of Cl− ion at various locations while permeating through the membrane. Red color is for oxygen atoms, green color is for hydrogen atoms, cyan color is for carbon atoms and blue color is for Cl− ion.
hydration radius from the center of the permeating ion are shown in ball and stick representations (VMD). Atoms of the GO membrane within12.0Å from the center of the permeating ion are shown in VDW representations (VMD). The number of water molecules in the hydration shell of the ions is more outside the membrane (positions 1 and 6 in Figure 4-11, Figure 4-12 and Figure 4-13) as compared to its value inside the membrane (positions 2, 3, 4 and 5 in Figure 4-11, Figure 4-12 and Figure 4-13).
However, inside the membrane, at the locations near the edges of the GO nanosheets (positions 2 and 5 in Figure 4-11, positions 2, 3, 4 in Figure 4-12 and Figure 4-13),
Figure 4-14: Radial distribution function between the ions and oxygen atoms of water inside the layered GO membrane of configuration-3.
the decrease in number of water molecules in the hydration shell of the ions is more prominent as compared to the locations near the basal plane of the GO nanosheets inside the membrane (position 4 in Figure 4-11, position 5 in Figure 4-12 and Figure 4-13). As in the case of water trajectory (Figure 4-4, Figure 4-5 and Figure 4-6) here also the variation of number of water molecules in the hydration shell of ions can be attributed to the interaction between water molecules and the oxygen containing functional groups of the GO nanosheets of the membrane. The carboxyl group has the highest intensity of interaction with the water molecules followed by hydroxyl and epoxy functional group (Figure 4-7). When an ions come closer to the edges of the GO nanosheets during the course of its permeation through the membrane, the carboxyl functional group located at those edges interact strongly with the water molecules in the hydration shell of the ions. As a consequence some water molecules from the hydration shell of the ions shedded away. Similarly, when the permeating ions come closer to the basal plane of the GO nanosheets, the hydroxyl and epoxy functional groups located in the basal plane of the GO nanosheets replaced some of the water molecules in the hydration shell of the ions. But the interaction intensity of hydroxyl and epoxy groups with the water molecules is less as compared to the
interaction intensity between carboxyl functional group and water. As a consequence, the decrease in the number of water molecules in the hydration shell of the ions is more near the edges of the GO nanosheets as compared to the locations near the basal plane of the GO nanosheets.
The functional groups present on the GO nanosheets are negatively charged.
When a cation enters inside the layered GO membrane it experiences an attractive in- teraction from the functional groups. On the other hand when an anion enters inside the layered GO membrane, there is an repulsive interaction between the functional groups and the anion. So the cations are trapped inside the membrane for a longer duration of time as compared to the anions. Higher the magnitude of the charge on the cation, longer it takes to permeate through the membrane. The permeability of the ions through the membrane can also be influenced by its extent of interaction with the water molecules. More intense the interaction of the ion with the water molecules in its hydration shell more difficult for that ion to permeate through the layered GO membrane. Figure 4-14 depicts the radial distribution function between the ions and oxygen atom (OW) of the water molecules. It is evident from Figure 4-14 that the interaction intensity between the ions and the water molecules follows the order Mg2+ > Na+ > Cl−, accordingly the permeation rate of the ions through the layered GO membrane follows the order Mg2+ < Na+ < Cl−.