*3.2. Properties of Surface Hydration Layer*

### 3.2.1. Structural Properties

After the above structural analysis of the antifouling membranes, it was found that the surface hydration ability of the three antifouling membranes was T4-SB > T4-SP > T4-DM. We also noticed that with the increase in surface hydration ability, more water molecules can penetrate into the matrix of membrane from the density profiles in Figure 3. To examine the structure of water molecules near the interface of antifouling membranes, we calculated the cosine of the angle between dipole of water and z-axis at different distances from the surface, as shown in Figure 6. Obviously, for a random distribution, the cos*θ* should be close to 0 [38]. In the T4-DM membrane system, only water molecules close to membrane have a certain orientation, while water molecules farther away are randomly distributed. In the T4-SP system, the dipole orientation of surface water molecules slightly decreased to 0 after 2 nm, while in the T4-SB system, there is still a long-distance arrangement of water molecules even beyond 2 nm away from the surface. This observation is consistent with Leng's experiment [23,24], where ordered water molecules were found at zwitterionic pSBMA surfaces.

### 3.2.2. Dynamic Properties

The antifouling membranes can also affect the hydration layer's dynamic properties beside the structure of surface water molecules. We calculated the distribution of the average residence time of water molecules within 0.5 nm of antifouling membrane surfaces, as shown in Figure 7b. The average residence time means how long water molecules can stay near the surface of the antifouling membrane on average [39]. It reflects the stability of the hydration water layer of the antifouling membrane or, in other words, the hydration ability of antifouling membranes [40]. Figure 7a shows the trajectory of one hydration layer water molecule above T4-SB membrane. The calculated average residence time is shown in Table 2. It can be seen that the average residence time increased from T4-DM and T4-SP to T4-SB, indicating that the binding effect of antifouling membranes on their surface hydration layers increased.

The diffusion behavior of surface hydration layer water molecules above three antifouling membranes was investigated. The mean square displacement (MSD) of surface hydration layer water molecules is shown in Figure 8. Their diffusion coefficients were then calculated according to Einstein's equation and collected in Table 2. It can be seen that the diffusion coefficients of surface hydration layer water molecules above three antifouling membranes gradually decreased from T4-DM and T4-SP to T4-SB, indicating that the mobility of water molecules decreased or the binding effect from the antifouling membranes increased, which is consistent with the previous analysis.


**Table 2.** Dynamic properties of hydration layer water molecules above three antifouling membranes including average residence time and diffusion coefficient.

**Figure 6.** Water dipole orientation profiles of three antifouling membranes. (**a**) T4-DM, (**b**) T4-SP, (**c**) T4-SB. **Figure 6.** Water dipole orientation profiles of three antifouling membranes. (**a**) T4-DM, (**b**) T4-SP, (**c**) T4-SB.

branes increased, which is consistent with the previous analysis.

3.2.2. Dynamic Properties

surface hydration layers increased.

**Figure 7.** Trajectory and residence time of surface hydration layer water molecules. (**a**) Trajectory of one hydration layer water molecule above T4-SB surface (connected blue dots). The antifouling membrane was colored in CPK mode. The surface hydration layer water molecules were modeled **Figure 7.** Trajectory and residence time of surface hydration layer water molecules. (**a**) Trajectory of one hydration layer water molecule above T4-SB surface (connected blue dots). The antifouling membrane was colored in CPK mode. The surface hydration layer water molecules were modeled in VDW mode. (**b**) Residence time distribution of water molecules in the hydration layer of three antifouling membranes. *Molecules* **2022**, *27*, x FOR PEER REVIEW 12 of 18 in VDW mode. (**b**) Residence time distribution of water molecules in the hydration layer of three antifouling membranes.

The antifouling membranes can also affect the hydration layer's dynamic properties beside the structure of surface water molecules. We calculated the distribution of the average residence time of water molecules within 0.5 nm of antifouling membrane surfaces, as shown in Figure 7b. The average residence time means how long water molecules can stay near the surface of the antifouling membrane on average [39]. It reflects the stability of the hydration water layer of the antifouling membrane or, in other words, the hydration ability of antifouling membranes [40]. Figure 7a shows the trajectory of one hydration layer water molecule above T4-SB membrane. The calculated average residence time is shown in Table 2. It can be seen that the average residence time increased from T4-DM and T4-SP to T4-SB, indicating that the binding effect of antifouling membranes on their

The diffusion behavior of surface hydration layer water molecules above three antifouling membranes was investigated. The mean square displacement (MSD) of surface hydration layer water molecules is shown in Figure 8. Their diffusion coefficients were then calculated according to Einstein's equation and collected in Table 2. It can be seen that the diffusion coefficients of surface hydration layer water molecules above three antifouling membranes gradually decreased from T4-DM and T4-SP to T4-SB, indicating that the mobility of water molecules decreased or the binding effect from the antifouling mem-

**Figure 8.** Mean square displacement of water molecules in the hydration layer of nonfouling mem-**Figure 8.** Mean square displacement of water molecules in the hydration layer of nonfouling membrane.

**Diffusion Coefficient D × 10−5 cm<sup>2</sup> /s**

**Table 2.** Dynamic properties of hydration layer water molecules above three antifouling membranes

T4-DM 17.85 2.57 (+/− 0.080) T4-SP 24.98 1.62 (+/− 0.014) T4-SB 27.16 1.54 (+/− 0.043) Bulk water - 4.13(+/− 0.15)

We have analyzed and compared the structural properties of the antifouling membranes and the structural and dynamic properties of their hydration water layers from the overall antifouling membranes' view. The order of surface hydration ability or antifouling ability, T4-SB > T4-SP > T4-DM, was obtained. Next, we analyze the mechanisms for the difference in hydration ability from the monomer's view, which serves as a model for the

Solvation free energies were calculated for three monomers at M05-2X/6-31 g\* level, as collected in Table 3. The negative of solvation free energy indicates all three monomers have a high affinity with water. The order of solvation free energy follows the order of T4-

SB > T4-SP >> T4-DM, which is consistent with previous analysis.

including average residence time and diffusion coefficient.

*3.3. Hydration Mechanisms—From the View of Monomers*

brane.

**Antifouling Mem-**

3.3.1. Solvation Free Energy

antifouling polymer membrane [38].

### *3.3. Hydration Mechanisms—From the View of Monomers*

### 3.3.1. Solvation Free Energy

We have analyzed and compared the structural properties of the antifouling membranes and the structural and dynamic properties of their hydration water layers from the overall antifouling membranes' view. The order of surface hydration ability or antifouling ability, T4-SB > T4-SP > T4-DM, was obtained. Next, we analyze the mechanisms for the difference in hydration ability from the monomer's view, which serves as a model for the antifouling polymer membrane [38].

Solvation free energies were calculated for three monomers at M05-2X/6-31 g\* level, as collected in Table 3. The negative of solvation free energy indicates all three monomers have a high affinity with water. The order of solvation free energy follows the order of T4-SB > T4-SP >> T4-DM, which is consistent with previous analysis.

**Table 3.** Properties of monomer of three antifouling membranes.


### 3.3.2. Electrostatic Potential

Electrostatic potentials of the three monomers were calculated and mapped on their van der Waals surfaces [41], as shown in Figure 9. The molecular polarity, polar, and nonpolar surface area were also calculated, as shown in Table 3 [42]. The surface area with |ESP| <= 10 kcal/mol was considered as nonpolar surface area while the others were considered as polar surface area. It can be seen that the negative charge center of T4-DM monomer is located at the N atom. Since T4-SP monomer has a negative charge, the overall electrostatic surface is negative, and mainly concentrated on the sulfonate group. In the zwitterion T4-SB monomer, the negative charge center is located in the sulfonate group and the positive charge center is located at the N atom. Though the MPI of T4-SP was the largest, the T4-SB has the largest polar surface area, which can combine with more water. Combining with the distribution of areas occupied by different electrostatic potential regions in Figure 9b, it can be seen that the distribution of electrostatic potential on the surface of T4-SB monomer is the broadest, which is conducive to the electrostatic interaction with other polar molecules such as water [43].

### 3.3.3. Radial Distribution Function

To further understand the hydration ability of antifouling polymers' monomers, another molecular dynamics simulation was conducted. Three monomers were solvated in <sup>4</sup> <sup>×</sup> <sup>4</sup> <sup>×</sup> 4 nm<sup>3</sup> water box, respectively; then, 50 ns NPT simulations were performed. After that, the radial distribution functions (RDFs) of the water molecules or Na<sup>+</sup> around the polar groups of three monomers and their coordination number were calculated, respectively, as shown in Figure 10. The RDFs can reflect the intermolecular structure and interactions between center atoms and surrounding water molecules. Two peaks were found in the RDF curve, indicating that two hydration layers were formed, which corresponded to the first hydration layer that consisted of bound water and the second hydration layer made up of trapped water; this agrees with Paul's experiment [25]. According to Figure 10a,b, SO<sup>3</sup> − groups in T4-SP and T4-SB have similar hydration ability and are stronger than the N group in T4-DM and T4-SB. Meanwhile, the peaks of g(r)N-OW in T4-DM were lower than those in T4-SB and also the coordination number of the first hydration shell from Figure 11c,d, indicating a better packed hydration shell around N in T4-SB. The number of water molecules tightly bonded to three monomers were also calculated and collected

*Molecules* **2022**, *27*, x FOR PEER REVIEW 13 of 18

**Table 3.** Properties of monomer of three antifouling membranes.

**Nonpolar Surface Area** (**Å<sup>2</sup>**

)

T4-DM −6.16 203.59 63.16 8.58 10.02 T4-SP −71.68 0.00 283.56 67.07 15.43 T4-SB −73.46 24.60 339.35 43.54 18.43

Electrostatic potentials of the three monomers were calculated and mapped on their van der Waals surfaces [41], as shown in Figure 9. The molecular polarity, polar, and nonpolar surface area were also calculated, as shown in Table 3 [42]. The surface area with |ESP| <= 10 kcal/mol was considered as nonpolar surface area while the others were considered as polar surface area. It can be seen that the negative charge center of T4-DM monomer is located at the N atom. Since T4-SP monomer has a negative charge, the overall electrostatic surface is negative, and mainly concentrated on the sulfonate group. In the zwitterion T4-SB monomer, the negative charge center is located in the sulfonate group and the positive charge center is located at the N atom. Though the MPI of T4-SP was the largest, the T4-SB has the largest polar surface area, which can combine with more water. Combining with the distribution of areas occupied by different electrostatic potential regions in Figure 9b, it can be seen that the distribution of electrostatic potential on the sur-

**Polar Surface Area**  (**Å<sup>2</sup>** )

**Molecular Polarity Index**  (**kcal/mol**)

**Number of Bonded Water Molecules**

**Solvation Free Energy** (**kcal/mol**)

**Monomer of Antifouling Membranes**

3.3.2. Electrostatic Potential

in Table 3. Consequently, the T4-SB antifouling membrane presents a more hydrophilic behavior than T4-SP and T4-DM. face of T4-SB monomer is the broadest, which is conducive to the electrostatic interaction with other polar molecules such as water [43].

**Figure 9.** Electrostatic potential of monomers of three antifouling polymers' monomers. (**a**) Electrostatic potential mapped on vdW surface; (**b**) distribution of surface area percentage of different electrostatic potentials. **Figure 9.** Electrostatic potential of monomers of three antifouling polymers' monomers. (**a**) Electrostatic potential mapped on vdW surface; (**b**) distribution of surface area percentage of different electrostatic potentials. SB. The number of water molecules tightly bonded to three monomers were also calculated and collected in Table 3. Consequently, the T4-SB antifouling membrane presents a more hydrophilic behavior than T4-SP and T4-DM.

**Figure 10.** Radial distribution functions (RDFs), g(r) of hydration groups on antifouling membrane surface, and the cumulative number. (**a**) RDF of SO<sup>3</sup> <sup>−</sup>\_O-OW and SO<sup>3</sup> <sup>−</sup>\_O-Na<sup>+</sup> , oxygens in SO<sup>3</sup> groups as referenced atoms. (**b**) RDF of N-OW, nitrogen atoms as referenced atoms. (**c**) Cumulative number of SO3-\_O-OW and SO<sup>3</sup> <sup>−</sup>\_O-Na<sup>+</sup> . (**d**) Cumulative number of N-OW. **Figure 10.** Radial distribution functions (RDFs), g(r) of hydration groups on antifouling membrane surface, and the cumulative number. (**a**) RDF of SO<sup>3</sup> −\_O-OW and SO<sup>3</sup> <sup>−</sup>\_O-Na<sup>+</sup> , oxygens in SO<sup>3</sup> − groups as referenced atoms. (**b**) RDF of N-OW, nitrogen atoms as referenced atoms. (**c**) Cumulative number of SO<sup>3</sup> −\_O-OW and SO<sup>3</sup> <sup>−</sup>\_O-Na<sup>+</sup> . (**d**) Cumulative number of N-OW.

the water molecules around the hydrophilic group, which neglects the spatial distribution of the water molecules. Therefore, the spatial distribution function (SDF) of water molecules around hydrophilic groups was calculated, shown in Figure 11. From this, we can see that there is only a ribbonlike distribution around the carbonyl oxygen in DM monomer, while the distribution of water molecules around the N atom cannot be shown under current isosurface. In the SP monomer, there are three spherical crown water molecule distribution areas in the direction of three S–O bonds, which is obviously caused by the

3.3.4. Spatial Distribution Function

hydrogen bond formed between the O atom in SO<sup>3</sup>

tion of water molecules around the N atom.

**Figure 11.** Spatial distribution function of water molecules around three different antifouling monomers. (**a**) DM, (**b**) SP, (**c**) SB. **Figure 11.** Spatial distribution function of water molecules around three different antifouling monomers. (**a**) DM, (**b**) SP, (**c**) SB. *Molecules* **2022**, *27*, x FOR PEER REVIEW 15 of 18

ilar structures were also found in SB monomer. Besides this, there is a ribbonlike distribu-

<sup>−</sup> group and the water molecules. Sim-

### 3.3.5. Noncovalent Interactions To fundamentally understand the different hydration ability of three antifouling 3.3.4. Spatial Distribution Function

monomers, aNCI (averaged noncovalent interaction) analysis [44,45] was conducted, shown in Figure 12. The green area in the figure indicates that van der Waals interaction is dominant. Blue area indicates that there is a strong hydrogen bond interaction. The red area indicates that there is a strong steric hindrance effect. In DM monomer, as the negative charge center N atom was shielded by surrounding methyl groups, it can only interact with water molecules through weak vdW interactions. In T4-SP and T4-SB monomers, water molecules can directly form hydrogen bonds with the exposed O atoms, which plays a key role in their strong hydration ability. Besides that, the extra positive charge center N atom can also interact with water molecules through weak vdW interactions such as N in the T4-DM monomer. Therefore, the hydration abilities of three antifouling polymers are in the order of T4-SB > T4-SP > T4-DM. Though the RDFs can reflect the hydration effect of hydrophilic groups in three monomers on water molecules, the calculation of RDFs is based on the spherical averaging of the water molecules around the hydrophilic group, which neglects the spatial distribution of the water molecules. Therefore, the spatial distribution function (SDF) of water molecules around hydrophilic groups was calculated, shown in Figure 11. From this, we can see that there is only a ribbonlike distribution around the carbonyl oxygen in DM monomer, while the distribution of water molecules around the N atom cannot be shown under current isosurface. In the SP monomer, there are three spherical crown water molecule distribution areas in the direction of three S–O bonds, which is obviously caused by the hydrogen bond formed between the O atom in SO<sup>3</sup> − group and the water molecules. Similar structures were also found in SB monomer. Besides this, there is a ribbonlike distribution of water molecules around the N atom. hydrogen bond formed between the O atom in SO<sup>3</sup> <sup>−</sup> group and the water molecules. Similar structures were also found in SB monomer. Besides this, there is a ribbonlike distribution of water molecules around the N atom.

#### 3.3.5. Noncovalent Interactions **Figure 11.** Spatial distribution function of water molecules around three different antifouling mon-

**Figure 12.** Noncovalent interaction around three different nonfouling repeat units. (**a**) DM, (**b**) SP, (**c**) SB. **4. Conclusions** To fundamentally understand the different hydration ability of three antifouling monomers, aNCI (averaged noncovalent interaction) analysis [44,45] was conducted, shown in Figure 12. The green area in the figure indicates that van der Waals interaction is dominant. Blue area indicates that there is a strong hydrogen bond interaction. The red area indicates that there is a strong steric hindrance effect. In DM monomer, as the negative charge center N atom was shielded by surrounding methyl groups, it can only interact with water molecules through weak vdW interactions. In T4-SP and T4-SB monomers, water molecules can directly form hydrogen bonds with the exposed O atoms, which plays a key role in their strong hydration ability. Besides that, the extra positive charge center N atom can also interact with water molecules through weak vdW interactions such as N in the T4-DM monomer. Therefore, the hydration abilities of three antifouling polymers are in the order of T4-SB > T4-SP > T4-DM. omers. (**a**) DM, (**b**) SP, (**c**) SB. 3.3.5. Noncovalent Interactions To fundamentally understand the different hydration ability of three antifouling monomers, aNCI (averaged noncovalent interaction) analysis [44,45] was conducted, shown in Figure 12. The green area in the figure indicates that van der Waals interaction is dominant. Blue area indicates that there is a strong hydrogen bond interaction. The red area indicates that there is a strong steric hindrance effect. In DM monomer, as the negative charge center N atom was shielded by surrounding methyl groups, it can only interact with water molecules through weak vdW interactions. In T4-SP and T4-SB monomers, water molecules can directly form hydrogen bonds with the exposed O atoms, which plays a key role in their strong hydration ability. Besides that, the extra positive charge center N atom can also interact with water molecules through weak vdW interactions such as N in the T4-DM monomer. Therefore, the hydration abilities of three antifouling polymers are in the order of T4-SB > T4-SP > T4-DM.

In this work, we investigated the surface hydration of three antifouling membranes—

**Figure 12.** Noncovalent interaction around three different nonfouling repeat units. (**a**) DM, (**b**) SP, (**c**) SB. **Figure 12.** Noncovalent interaction around three different nonfouling repeat units. (**a**) DM, (**b**) SP, (**c**) SB.

In this work, we investigated the surface hydration of three antifouling membranes—

**4. Conclusions**

### **4. Conclusions**

In this work, we investigated the surface hydration of three antifouling membranes—T4-DM, T4-SP, and T4-SB—by a series of molecular dynamics simulations. Dipole orientation distribution, diffusion coefficient, and average residence time revealed an orderly, packed, and tightly bound surface hydration layer above T4-SP and T4-SB antifouling membranes. The surface structure, density profile, surface roughness, and area percentage of hydrophilic surface provide further details regarding the strong surface hydration of T4-SP and T4-SB from the membranes' aspect. The side chains of T4-SP and T4-SB were more stretched in hydrated state due to their high hydration ability, which can cause steric repulsion and prevent adsorption. Their surfaces are relatively rough, which can bind much more water or even let water penetrate into the internal voids of the membrane.

To further understand the surface hydration ability of three antifouling membranes, solvation free energy, electrostatic potential, RDFs, SDFs, and noncovalent interactions of three monomers were analyzed. T4-SB monomer has the broadest distribution of electrostatic potential on the surface, resulting from the separated negatively and positively charge center and largest water coordination number for its zwitterionic architecture. Its exposed negative charge center SO<sup>3</sup> − group can form hydrogen bonds with surrounding water molecules and the shielded positive charge center N can also bind water molecules through weak vdW interaction.

The simulation data suggest the hydration ability of monomers ranks in terms of T4-SB > T4-SP > T4-DM. Since the surface hydration layer serves as a physical and energy barrier during the prevention of protein adsorption, we believe their antifouling ability ranks in terms of T4-SB > T4-SP > T4-DM, which is consistent with experiments.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules27103074/s1, Figure S1: Final simulation configuration of three antifouling membranes under dry and hydrated states; Table S1: 21-step MD compression and relaxation schemes.

**Author Contributions:** Conceptualization, H.Z., J.Z. and S.Y.; methodology, H.Z.; software, H.Z.; validation, H.Z.; formal analysis, H.Z.; investigation, H.Z.; writing—original draft preparation, H.Z.; writing—review and editing, S.Y.; supervision, S.Y.; project administration, S.Y.; funding acquisition, S.Y. and C.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the open fund of State Key Laboratory of Marine Corrosion and Protection grant number 6142901190402, and Natural Science Foundation of Shandong Province grant number ZR2021MB055.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We gratefully appreciate the financial support from the open fund of State Key Laboratory of Marine Corrosion and Protection (6142901190402) and Natural Science Foundation of Shandong Province (ZR2021MB055).

**Conflicts of Interest:** The authors declare no conflict of interest.

**Sample Availability:** Samples of the compounds are not available from the authors.

### **References**

