Theoretical Insights into the Solvent Polarity Effect on the Quality of Self-Assembled N-Octadecanethiol Monolayers on Cu (111) Surfaces

The effect of solvent polarity on the quality of self-assembled n-octadecanethiol (C18SH) on Cu surfaces was systematically analyzed using first-principles calculations. The results indicate that the adsorption energy for C18SH on a Cu surface is −3.37 eV, which is higher than the adsorption energies of the solvent molecules. The higher adsorption energy of dissociated C18SH makes the monolayer self-assembly easier on a Cu (111) surface through competitive adsorption. Furthermore, the adsorption energy per unit area for C18SH decreases from −3.24 eV·Å−2 to −3.37 eV·Å−2 in solvents with an increased dielectric constant of 1 to 78.54. Detailed energy analysis reveals that the electrostatic energy gradually increases, while the kinetic energy decreases with increasing dielectric constant. The increased electrostatic energies are mainly attributable to the disappearance of electrostatic interactions on the sulfur end of C18SH. The decreased kinetic energy is mainly due to the generated push force in the polar solvent, which limits the mobility of C18SH. A molecular dynamics simulation also confirms that the -CH3 site has a great interaction with CH3(CH2)4CH3 molecules and a weak interaction with CH3CH2OH molecules. The different types of interactions help to explain why the surface coverage of C18SH on Cu in a high-polarity ethanol solution is significantly larger than that in a low-polarity n-hexane solution at the stabilized stage.


Introduction
Copper (Cu) and its alloys have been widely used in many industrial sectors, including electronic, chemical, and ocean engineering [1]. Despite its many outstanding properties, Cu is very chemically active, and is thus prone to corrosion. Serious corrosion not only leads to grave economic loss, it also poses a potential threat to human life [2][3][4]. Various ways to protect metals from corrosion have been developed based on different principles. Self-Assembled Monolayers (SAMs) are one of the most economic, highly efficient, and simple ways to protect metals and alloys from corrosion and oxidization [5][6][7]. Experimental research has been carried out to identify the protection mechanism of SAMs on Cu surfaces. It was generally believed that the densely packed monolayers were formed through chemisorption onto the surface of Cu [8]. Since the properties of the solvent affect the assembly of SAMs, the qualities of the SAMs formed in different solvents are expected to be different. Thus far, many researchers have studied the thiol-SAMs formed on gold surfaces in different solvents. Among them, Bain et al. evaluated the effect of various solvents (dimethylformamide, tetrahydropyranyl, ethanol, carbon tetrachloride, acetonitrile, hexadecane, cyclooctane, and toluene) on the formation of SAMs on gold surfaces. It was found that the hexadecanethiol monolayer adsorbed on gold in a hexadecane solution displays a low contact angle when it reaches certain thickness, which can possibly be attributed to the incorporation of hexadecane into the monolayer [9]. Dai et al. have reported the effects of solvents on the quality of the SAM of dodecanethiol on gold. They revealed that the solvent parameters (such as polarity, solubility, molecular size, octanol-water partition coefficients, and viscosity) affect the quality of the C 12 SH SAMs [10]. Ujjal et al. have also proposed that the nature of the solvent might affect the blocking properties and barrier characteristics of the -CH 3 terminated SAMs [11,12]. Our previous experiments by electrochemical impedance spectroscopy, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy, showed that the qualities of self-assembled n-octadecanethiol (C 18 SH) indeed differ when it is formed in different solvents (n-hexane, toluene, trichloroethylene, chloroform, acetone, acetonitrile, and ethanol) [13]. Based on the experimental results, the assembly is likely to be a competitive adsorption process, containing interactions among the solvent, the solute, and the surface. However, which of these interactions plays an important role during the self-assembly process remains unclear due to the potential complexity of interactions among the different entities.
Computational analysis, on the other hand, is able to overcome the experimental limitations, and thus provides a very useful tool to understand the assembly mechanisms [14][15][16][17]. Benchouk et al. studied the effect of solvents on the 1.3-dipolar cycloaddition of benzonitrile N-oxide with cyclopentene using first-principles calculations. They found that solvent polarity leads to the slow inhibition of the 1,3-dipolar cycloaddition due to the low polarity of the transition state [18]. Sainudeen et al. analyzed the solvent polarity of zwitterionic merocyanine using quantum chemical calculations. They found that solvents play a remarkable role in the structure and in the first hyperpolarizability of merocyanine monomers and aggregates [19]. Thus far, these attempts to elucidate the adsorption process remain at a molecular level, and most of them were carried out in vacuum or water solution conditions.
In this paper, a comprehensive analysis of the effect of solvent polarity is presented from the perspective of interactions among the solvent, the solute, and the surface. First, the electronic structure of C 18 SH, C 18 S, and different solvents are considered. Then, the adsorption of different solvent molecules on the Cu (111) surface is calculated to interpret the interaction between the solvent and the surface. Based on the simulation, the effect of solvent polarity on the quality of C 18 SH SAMs on the Cu surface is explained through the proposed mechanisms. This work helps us to better understand the micro-mechanisms of solvent polarity effects of C 18 SH on pure Cu surfaces. The method can be extended to understand interactions between other SAMs and metal surfaces.

Electronic Structure of C 18 SH, C 18 SH and Different Solvents
The maps of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) are shown in Figure 1. The quantitative results of quantum chemical parameters are as listed in Table 1.
The HOMO and LUMO regions of different molecules are mainly contributed by O, N, and S elements and the benzene ring. This indicates that these are the adsorption sites on the metal surface. As indicated in Table 1, the energy of LUMO, E L , is greatly reduced after C 18 SH dissociates into C 18 S. E L represents the electron acceptability, which is directly related to the electron affinity and characterizes the susceptibility of the molecule against attacks by nucleophiles. The lower value of E L means stronger electron acceptability of the molecules, indicating the strong interaction between the Cu surface and C 18 S. This is also verified through the increased fraction of electron transfer, ∆N, from the Cu surface to C 18 S. Furthermore, it is noted that the difference in ∆N between C 18 SH and different solvent molecules is not very high.  The stable adsorption structures and energies of C18SH and C18S (the dissociated state of C18SH) on the Cu (111) surface in different solvents are shown in Figures 2 and 3, where the stable adsorption energies of solvent molecules are also added and compared. The dominant effect is due to interactions between sulfur group and the Cu surface, based on the well-known hard-soft concept of Pearson.
As shown in Figure 2, H2O adsorbs preferentially at the top site, with its molecular plane parallel to the surface. This result is consistent with a previous STM observation, which indicates an atop adsorption site [20]. Furthermore, the adsorption energy for water on a Cu surface is −0.51 eV, which is also consistent with the reported value of 0.51-0.55 eV [21], 0.54-0.57 eV [22], and 0.42 eV [23]. For the solvent molecules, elements O, N, S, and Cl are easily absorbed by the Cu atoms, because these atoms have many electrons and prefer the acidic Cu sites. Furthermore, it can be seen that only CH3CN is vertically adsorbed to the surface; others molecules are parallel to the surface. The covered area (the dotted black line in Figure 2) for C6H5CH3 and CH3(CH2)4CH3 is larger, due to their bigger molecule sizes. In order to obtain the strength of interaction between the Cu surface and different solvent molecules, the adsorption energy per unit area is plotted and compared, as shown in Figure  3. The adsorption energies are not much different for most solvent molecules and C18SH; this is in accordance with previous quantum chemical parameters, as indicated in Table 1. As we know, C18SH can be dissociated into C18S (after losing one H atom) on the substrate surface. Therefore, the adsorption of C18S is also considered in this paper [24]. As indicated in Figure 3, the adsorption energy

The Adsorption for C 18 SH, C 18 S and Solvent Molecules on Cu Surface
The stable adsorption structures and energies of C 18 SH and C 18 S (the dissociated state of C 18 SH) on the Cu (111) surface in different solvents are shown in Figures 2 and 3, where the stable adsorption energies of solvent molecules are also added and compared. The dominant effect is due to interactions between sulfur group and the Cu surface, based on the well-known hard-soft concept of Pearson.
As shown in Figure 2, H 2 O adsorbs preferentially at the top site, with its molecular plane parallel to the surface. This result is consistent with a previous STM observation, which indicates an atop adsorption site [20]. Furthermore, the adsorption energy for water on a Cu surface is −0.51 eV, which is also consistent with the reported value of 0.51-0.55 eV [21], 0.54-0.57 eV [22], and 0.42 eV [23]. For the solvent molecules, elements O, N, S, and Cl are easily absorbed by the Cu atoms, because these atoms have many electrons and prefer the acidic Cu sites. Furthermore, it can be seen that only CH 3 CN is vertically adsorbed to the surface; others molecules are parallel to the surface. The covered area (the dotted black line in Figure 2) for C 6 H 5 CH 3 and CH 3 (CH 2 ) 4 CH 3 is larger, due to their bigger molecule sizes. In order to obtain the strength of interaction between the Cu surface and different solvent molecules, the adsorption energy per unit area is plotted and compared, as shown in Figure 3. The adsorption energies are not much different for most solvent molecules and C 18 SH; this is in accordance with previous quantum chemical parameters, as indicated in Table 1. As we know, C 18 SH can be dissociated into C 18 S (after losing one H atom) on the substrate surface. Therefore, the adsorption of C 18 S is also considered in this paper [24]. As indicated in Figure 3, the adsorption energy per unit area of C 18 S decreases from −3.24 eV·Å −2 to −3.37 eV·Å −2 in solvents with an increased dielectric constant of 1 to 78.54. Therefore, the adsorption energy per unit area for C 18 S is much smaller than that for C 18 SH; this applies to the different solvent molecules as well. This indicates that C 18 S can be easily self-assembled on the Cu surface through competitive adsorption. Furthermore, the adsorption energy of C 18 S decreases in solvents with increased dielectric constant, which can well explain the previous experimental phenomenon that the C 18 S coverage on the Cu surface in the CH 3 CH 2 OH solution was higher than in the CH 3 (CH 2 ) 4 CH 3 solution at the assembly stage [13], as indicated in Figure S1. per unit area of C18S decreases from −3.24 eV·Å −2 to −3.37 eV·Å −2 in solvents with an increased dielectric constant of 1 to 78.54. Therefore, the adsorption energy per unit area for C18S is much smaller than that for C18SH; this applies to the different solvent molecules as well. This indicates that C18S can be easily self-assembled on the Cu surface through competitive adsorption. Furthermore, the adsorption energy of C18S decreases in solvents with increased dielectric constant, which can well explain the previous experimental phenomenon that the C18S coverage on the Cu surface in the CH3CH2OH solution was higher than in the CH3(CH2)4CH3 solution at the assembly stage [13], as indicated in Figure S1.  Table S1.   Table S1.
Molecules 2018, 23, x 4 of 11 per unit area of C18S decreases from −3.24 eV·Å −2 to −3.37 eV·Å −2 in solvents with an increased dielectric constant of 1 to 78.54. Therefore, the adsorption energy per unit area for C18S is much smaller than that for C18SH; this applies to the different solvent molecules as well. This indicates that C18S can be easily self-assembled on the Cu surface through competitive adsorption. Furthermore, the adsorption energy of C18S decreases in solvents with increased dielectric constant, which can well explain the previous experimental phenomenon that the C18S coverage on the Cu surface in the CH3CH2OH solution was higher than in the CH3(CH2)4CH3 solution at the assembly stage [13], as indicated in Figure S1.  Table S1.

The Interaction between C18SH and Solvent Molecules
In order to understand the reason for the adsorption energy changes in different solvents, we compare the different energies, as shown in Figure 4.

The Interaction between C18SH and Solvent Molecules
In order to understand the reason for the adsorption energy changes in different solvents, we compare the different energies, as shown in Figure 4. Based on Figure 4, the atomic energy, exchange-correlation energy, spin polarization and DFT-D correction energy are not greatly changed in different solvents. The electrostatic energies gradually increase while the kinetic energies decrease with increasing dielectric constant. Furthermore, the energies are not greatly changed if we sum the corresponding energy before adsorption, illustrating that the change is caused by the interaction between Cu (111) and C18SH (or C18S).
As we know, the C18SH is inherently non-polar and predominantly hydrophobic in nature, although the SH group provides a weakly polar character. When the C18SH solute molecule is surrounded by solvent molecules with different dielectric constants, the C18SH can generate a strong pull force with polar molecules and a weak compressive force with polar solvents. Although the increased polarizability of S compared to C provides a subtly greater polar character, SH groups are far less polarized than OH groups. Thus, a weak push force is generated in non-polar solvents, while a strong pull force is generated in nonpolar solvents. When the C18SH is absorbed on the Cu (111) surface, the electrostatic interactions on the sulfur end disappears, but the electrostatic interactions on the other position still exist. As a result, the electrostatic interaction is quickly reduced in a polar solution (higher electrostatic energy means low interaction). The force on the hydrophobic end still exists after the adsorption, and it generates both a pull force in the non-polar solvent, and a compressive force in the polar solvent. The generated push force in the polar solvent limits the mobility of C18SH. Therefore, the kinetic energies for the adsorption of C18SH on Cu (111) decrease with increasing dielectric constant (more polar molecules). Based on Figure 4, the atomic energy, exchange-correlation energy, spin polarization and DFT-D correction energy are not greatly changed in different solvents. The electrostatic energies gradually increase while the kinetic energies decrease with increasing dielectric constant. Furthermore, the energies are not greatly changed if we sum the corresponding energy before adsorption, illustrating that the change is caused by the interaction between Cu (111) and C 18 SH (or C 18 S).
As we know, the C 18 SH is inherently non-polar and predominantly hydrophobic in nature, although the SH group provides a weakly polar character. When the C 18 SH solute molecule is surrounded by solvent molecules with different dielectric constants, the C 18 SH can generate a strong pull force with polar molecules and a weak compressive force with polar solvents. Although the increased polarizability of S compared to C provides a subtly greater polar character, SH groups are far less polarized than OH groups. Thus, a weak push force is generated in non-polar solvents, while a strong pull force is generated in non-polar solvents. When the C 18 SH is absorbed on the Cu (111) surface, the electrostatic interactions on the sulfur end disappears, but the electrostatic interactions on the other position still exist. As a result, the electrostatic interaction is quickly reduced in a polar solution (higher electrostatic energy means low interaction). The force on the hydrophobic end still exists after the adsorption, and it generates both a pull force in the non-polar solvent, and a compressive force in the polar solvent. The generated push force in the polar solvent limits the mobility of C 18 SH. Therefore, the kinetic energies for the adsorption of C 18 SH on Cu (111) decrease with increasing dielectric constant (more polar molecules).
In order to understand the interaction between C 18 SH and solvent molecules, the radial distribution function between C 18 SH and the solvent was analyzed based on a molecular dynamics (MD) simulation, as shown in Figure 5. There is a strong peak at 1.2 Å in the CH 3 (CH 2 ) 4 CH 3 solution, and no obvious peak in CH 3 CH 2 OH solution. This indicates that there is a high probability for CH 3 (CH 2 ) 4 CH 3 to be distributed on the -CH 3 site. This confirms that the -CH 3 site has indeed a great interaction with CH 3 (CH 2 ) 4 CH 3 molecules and a weak interaction with CH 3 CH 2 OH molecules.
Molecules 2018, 23, x 6 of 11 In order to understand the interaction between C18SH and solvent molecules, the radial distribution function between C18SH and the solvent was analyzed based on a molecular dynamics (MD) simulation, as shown in Figure 5. There is a strong peak at 1.2 Å in the CH3(CH2)4CH3 solution, and no obvious peak in CH3CH2OH solution. This indicates that there is a high probability for CH3(CH2)4CH3 to be distributed on the -CH3 site. This confirms that the -CH3 site has indeed a great interaction with CH3(CH2)4CH3 molecules and a weak interaction with CH3CH2OH molecules. Figure 5 The radial distribution between the -CH3 site of C18SH and solvent molecules in a 24.3-CH3CH2OH and 1.89-CH3(CH2)4CH3 solution.

The Effect of Solvent Polarity on the Quality of Self-Assembled C18SH
Based on our previous results, the effect of solvent polarity on the quality of self-assembled C18SH on a Cu (111) plane can be illustrated in Figure 6. Figure 6. The adsorption of C18SH on the Cu (111) surface in polar and non-polar solvents, where the columnar chart represents the adsorption energies per unit area. The inward arrows present a push force, the outward arrows present a pull force, the solid line stands for a strong interaction, and the dash lines stand for a weak interaction.
As shown, the C18SH is embedded in the solute molecules, forming a cavity within the dielectric layer. The polarization charge distribution is determined by the generation of the charges on the cavity surface. The polarity can generate interaction forces between the molecules of solvent and the solute. Because of the predominantly hydrophobic property of C18SH in nature, C18SH generates a strong pull force with non-polar molecules and a weak compressive force with polar solvents. The solvent polarity effect is manifested through the interaction between SAMs and solvent molecules. When the C18SH adsorbs on the Cu (111) surface, the interaction between the -SH group and the

The Effect of Solvent Polarity on the Quality of Self-Assembled C 18 SH
Based on our previous results, the effect of solvent polarity on the quality of self-assembled C 18 SH on a Cu (111) plane can be illustrated in Figure 6. In order to understand the interaction between C18SH and solvent molecules, the radial distribution function between C18SH and the solvent was analyzed based on a molecular dynamics (MD) simulation, as shown in Figure 5. There is a strong peak at 1.2 Å in the CH3(CH2)4CH3 solution, and no obvious peak in CH3CH2OH solution. This indicates that there is a high probability for CH3(CH2)4CH3 to be distributed on the -CH3 site. This confirms that the -CH3 site has indeed a great interaction with CH3(CH2)4CH3 molecules and a weak interaction with CH3CH2OH molecules. Figure 5 The radial distribution between the -CH3 site of C18SH and solvent molecules in a 24.3-CH3CH2OH and 1.89-CH3(CH2)4CH3 solution.

The Effect of Solvent Polarity on the Quality of Self-Assembled C18SH
Based on our previous results, the effect of solvent polarity on the quality of self-assembled C18SH on a Cu (111) plane can be illustrated in Figure 6. Figure 6. The adsorption of C18SH on the Cu (111) surface in polar and non-polar solvents, where the columnar chart represents the adsorption energies per unit area. The inward arrows present a push force, the outward arrows present a pull force, the solid line stands for a strong interaction, and the dash lines stand for a weak interaction.
As shown, the C18SH is embedded in the solute molecules, forming a cavity within the dielectric layer. The polarization charge distribution is determined by the generation of the charges on the cavity surface. The polarity can generate interaction forces between the molecules of solvent and the solute. Because of the predominantly hydrophobic property of C18SH in nature, C18SH generates a strong pull force with non-polar molecules and a weak compressive force with polar solvents. The solvent polarity effect is manifested through the interaction between SAMs and solvent molecules. When the C18SH adsorbs on the Cu (111) surface, the interaction between the -SH group and the Figure 6. The adsorption of C 18 SH on the Cu (111) surface in polar and non-polar solvents, where the columnar chart represents the adsorption energies per unit area. The inward arrows present a push force, the outward arrows present a pull force, the solid line stands for a strong interaction, and the dash lines stand for a weak interaction.
As shown, the C 18 SH is embedded in the solute molecules, forming a cavity within the dielectric layer. The polarization charge distribution is determined by the generation of the charges on the cavity surface. The polarity can generate interaction forces between the molecules of solvent and the solute. Because of the predominantly hydrophobic property of C 18 SH in nature, C 18 SH generates a strong pull force with non-polar molecules and a weak compressive force with polar solvents. The solvent polarity effect is manifested through the interaction between SAMs and solvent molecules. When the C 18 SH adsorbs on the Cu (111) surface, the interaction between the -SH group and the solute disappears due to an intense chemical adsorption, while interactions between other positions of the C 18 SH and the solute still exists. The hydrophobic end mainly consists of CH groups, and it generates a great pull interaction with non-polar solvents. The generated pull interaction makes the adsorption unstable. Therefore, the kinetic energies of Cu (111) adsorbed by C 18 SH decrease along with increasing dielectric constant. A further MD simulation confirm that the -CH 3 site does indeed have a great interaction with CH 3 (CH 2 ) 4 CH 3 molecules and a weak interaction with CH 3 CH 2 OH molecules. The above effect significantly increases the surface coverage of C 18 SH on Cu in an ethanol solution, compared with that in an n-hexane solution at the late stabilized stage.

Materials and Methods
Quantum chemical calculations can provide insights into the design of inhibitor systems with superior properties and elucidate the adsorption process at a molecular level [25]. The Dmol 3+ module of the Materials Studio software (Accelrys Inc., San Diego, CA, USA) was employed for the quantum chemistry calculations. For the calculations, the Cu (111) facet has been widely chosen as an ideal model system to investigate the structure, stability, and adsorption properties, since it is the most stable surface under realistic conditions [26]. A supercell (4 × 4) was built with the following dimensions: 7.75 × 7.75 × 6.32 Å 3 (as indicated in Figure S2). The Cu (111) lattice structure was divided into four layers, and the two bottom layers were constrained. The top site (above the Cu atom of the central plane), the bridge site (between the two Cu atoms, above the contact location), the face centered cubic (fcc) site (above the triangle of the Cu atoms on the plane, or directly above a Cu atom in the next layer below the plane), and the hexagonal close packing (hcp) site (above the triangle of Cu atoms on the plane, or directly above a Cu atom in the third layer below the plane) were considered during the adsorption study. The most stable adsorption site was determined based on the minimum energy of the system. During the calculations, the self-consistent periodic Density Functional Theory (DFT) was used to study the relative stability and reactivity of the surface species on the Cu (111) surface. The Gradient-Corrected Functionals (GGA), in the form of the Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy, and the double-numerical quality basis, which was set with Double Numerical plus Polarization (DNP) functions, were employed. The Effective Core Potential (ECP) was used to handle the core electrons of the metallic atoms. Standard Kohn-Sham Density Functional Theory Dispersion (DFT-D) correction was used for the corrective calculation of van der Waals dispersion. A thermal smearing was adopted at 0.002 hartree, with a real-space cutoff at 4.4 Å. The k-point separation was at 0.04 Å −1 . The solvent effect was considered by using a conductor-like screening model (COSMO) with different dielectric constant values [27]. The dielectric constants of water (H 2 O), acetonitrile (CH 3 CN), ethanol (CH 3 CH 2 OH), acetone (CH 3 COCH 3 ), chloroform (CH 3 Cl 3 ), trichloroethylene (C 2 HCl 3 ), toluene (C 6 H 5 CH 3 ), n-hexane (CH 3 (CH 2 ) 4 CH 3 ) and vacuum are 78. 5, 37.5, 24.3, 20.7, 4.81, 3.42, 2.40, 1.89 and 1, respectively. The calculated lattice constants of Cu was consisted with the experimental result, as indicated in Table S2.
A Molecular Dynamics (MD) simulation was carried out with 1 C 18 SH and 100 solvent molecules in an amorphous cell. A COMPASS force field was used during the optimization as indicated in Figure S3. The initial models with 3D periodic boundary conditions were optimized via the smart minimizing method until the energy gradient reaches less than 0.1 kcal·mol −1 . Moreover, the operating temperature was set at 298 K and controlled by means of the Nose thermostat method to match the real experiment procedure. Then, NVT (constant molecule numbers, volume and temperature) were used for the dynamic calculation. The van der Waals interaction was calculated using an atom-based method with a cutoff radius of 18.5 Å, while the long-range corrections were adopted outside 15 Å. The electrostatic summation method was calculated using the Ewald method with an accuracy of 10 −5 kcal·mol −1 for the computation of long-range non-bond energies in periodic systems. The details of the coordinates of atoms before C 18 SH was adsorbed and after C 18 SH was adsorbed on the Cu surface in vacuum are indicated in Tables S3 and S4, respectively. Some parameters of molecular orbitals, such as absolute electronegativity (χ), the global hardness (η), and the fraction of electron transfer (∆N), were also calculated using Equations (1)- (3).
where E H and E L are, respectively, the energies of the HOMO and the LUMO for the corresponding molecules. In order to calculate the fraction of electron transfer, a theoretical value for the absolute electronegativity of Cu is taken as 4.48 eV, and a global hardness as 0 eV·mol −1 , assuming the Cu atoms are softer than the neutral metallic atoms [28,29]. The interaction energy E ads between the Cu (111) surface and the molecules is computed by: where E total is the total energy of the system in different solutions, including the energy of water molecules and the metal plane; E molecule is the molecules energy in different solutions; E surface is the energy of the metal surface in different solutions. In the current definition, the higher negative value of E ads indicates a more stable adsorption on the surface [30,31]. E atom (atomic energies) is obtained from atomic reference data for electronic structure calculations. The E elst (Electrostatic energy), E kine (kinetic energy), E XC (exchange-correlation energy), E spin (Spin-polarization energy), and E DFT− (DFT-D correction energy) can be calculated by Equations (5)-(9), respectively [32].
In the above equations, Z is the nuclear charges, D = BA −1 B, B and A are Coulomb matrices, ρ is the electron density, ρ is the auxiliary density to solve the Poisson equation for the electrostatic potential of the solute, and N f is the number of degrees of freedom. k B is the Boltzmann constant, T is the absolute temperature, n(r) is the number of the particles, ε XC [n(r)] is the exchange-correlation energy per particle in a uniform electron gas, E(M 0 ) is the energy for the ground-state magnetic moment in the absence of an external field, and E(0) is the energy when the ground-state magnetic moment is equal to zero. S i is the XC-functional dependent factor where S R = 1 and S 6 ≡ 1, f (S R R 0 ij , R ij ) f S R R 0 ij , R ij is the damping function to express short range S R R 0 ij by long-range R ij . C 6,ij R −6 ij is a long range isotropic potential.

Conclusions
Based on the previous experimental findings, solvent polarity plays an important role in the adsorption of C 18 SH SAMs on Cu surfaces. The effect of solvent polarity on the quality of self-assembled C 18 SH on Cu (111) surfaces has been systematically analyzed using first-principles calculations. The results have revealed the molecular mechanisms behind the effect of solvent polarity. C 18 SH is inherently non-polar and predominantly hydrophobic in nature, although the SH group provides a weakly polar character. In a non-polar molecule solution, there is a great pull interaction between C 18 SH and non-polar molecules. However, in a polar molecule solution, there is a weak interaction between C 18 SH and polar molecules. Due to the great interaction between C 18 S and the Cu surface, C 18 SH can self-assemble on the Cu surface (E ads = −3.37 eV and ∆N = 312.7). After this, the electrostatic interactions on the sulfur end disappears, but the electrostatic interactions on the other positions still exist. The adsorption energy decreases greatly with increasing dielectric constant (or polarity). This is mainly caused by the change of electrostatic energies and kinetic energies in different solutions, attributable to the different types of interaction. The electrostatic interaction is quickly reduced in polar solutions due to the disappearance of electrostatic interactions on the sulfur end, and the reduced kinetic energies are due to the solvophobic cage-type effects which limit the mobility of C 18 SH. A further MD simulation also verifies that the -CH 3 site has indeed a strong interaction with CH 3 (CH 2 ) 4 CH 3 molecules and a weak interaction with CH 3 CH 2 OH molecules. This study helps us to better understand the micro-mechanisms of solvent polarity effects for C 18 SH adsorption on Cu surfaces.

Supplementary Materials:
The following is available online. Figure S1: Impedance plots of C18SH SAMs on Cu surfaces in different solvents in 0.1 mol·L −1 KCl as the supporting electrolyte. Figure S2: Top and side view of the Cu (111) surface. Figure S3: MD model in different solutions. Table S1: Stable adsorption energies of different species on the Cu (111) surface. Table S2: The calculated lattice constants of Cu, as compared with experimental results of reference. Table S3: The coordinates of atoms on a Cu (111) surface after the optimization in vacuum conditions. Table S4: The coordinates of atoms when C 18 SH is adsorbed on the top site of the Cu (111) surface after the optimization in vacuum conditions.