1 Introduction

Polycrystalline diamond and diamond-like carbon (DLC) provide fully biocompatible, ultra-hard, low-friction, wear-resistant coatings, which make them very attractive for numerous applications ranging from biomedicine to tribology. Recently, a number of studies have been devoted to the incorporation of elements, such as silicon, nitrogen, and metals, into the carbon films to modify their structural and surface properties [1–4]. Silicon, in particular, is incorporated in DLC to improve the adhesion strength on substrates [5, 6], thermal stability [7–10], and biocompatibility [11, 12] and reduce the friction coefficient [13–17].

The microscopic mechanisms that lead to the extremely low friction coefficient of silicon-doped DLC (Si-DLC) are still unclear. It is expected that the presence of Si dopants modifies the surface–water interaction and tribochemistry in humid environments. In fact, silanol groups (Si–OH) have been detected on the surface of as-deposited Si-DLC in ambient air by derivatization X-ray photoelectron spectroscopy [18–20]. This surface termination, resulting from the dissociative adsorption of water molecules, has been suggested to promote the formation of a water boundary layer, which prevents the direct contact of the sliding surfaces and consequently reduces friction [20]. This hypothesis has been confirmed by molecular dynamics (MD) simulations, which showed that water molecules strongly attached to the surface hydroxyl groups via hydrogen bond networks were able to separate the sliding surfaces in shear conditions [21].

A decrease in water contact angle with an increase in Si doping in the DLC coating has been recently reported [22, 23], but the chemical role of the Si dopants has not been elucidated. Understanding the microscopic mechanisms that govern the wettability of doped DLC coatings is of paramount importance not only for tribology, but also for biomedical applications such as contact lens and artificial heart valves [24, 25].

Here, we apply first-principle calculations based on density functional theory (DFT) to investigate the effects of silicon dopants on water adsorption at diamond surfaces. Despite its relevance for lubrication, biological materials application, and microelectronics, the diamond–water interface has been scarcely investigated by ab initio methods [26–29]. The use of a parameter-free approach is particularly important because classical potentials hardly capture the water–surface interaction [30], and chemical reactions such as water dissociation at the surface cannot be accurately described. We consider the diamond (001) surface, which presents a dimer reconstruction composed of carbon double bonds, to resemble the thin DLC layer of sp 2 carbon often detected in tribologial contacts [28]. Silicon atoms are located at substitutional sites identified as most stable at the surface, with a concentration typical for Si-DLC. The simulated crystalline system differs from the amorphous matrix of sp 2 and sp 3 carbon of real Si-DLC coatings [4, 31, 32]; however, it constitutes a minimal model suitable to give insights into the local physical–chemical interactions that promote water adsorption and dissociation at the Si sites. By comparing the adsorption energies and dissociation barriers of Si-doped and clean diamond surfaces, we elucidate the chemical role of Si dopants in modifying the hydrophilic character of the carbon-based films.

2 Method

We model the (001) surface with periodic supercells containing a diamond slab reconstructed on both the sides with 10-layer thickness and 4 × 3 in-plane size. The surface presents a 2 × 1 reconstruction constituted of dimers that give rise to alternating rows and trenches of sp 2- and sp 3-bonded carbon atoms. A vacuum region of 20 Å thickness is included in the supercell to separate each slab from its periodic replicas along the [001] direction. Silicon atoms are located at substitutional sites, consistently with the experimental observation that silicon atoms in Si-DLC are surrounded by carbon atoms, and not by oxygen or other silicon atoms [31, 32]. A 8.3 % Si concentration is realized, which is consistent with that used in the experiments [33].

Static ab initio DFT calculations are performed by means of the pseudopotential/plane-wave computer code included in the QUANTUM ESPRESSO package [34]. The Perdew, Burke, and Ernzerhof generalized gradient approximation (GGA-PBE) is used for the exchange-correlation functional [35], and all the simulations include the spin polarization. The electronic wave functions are expanded on a plane-wave basis set with a cutoff energy of 25 Ry, and the ionic species are described by ultra-soft pseudopotentials [36]. The k points in the Brilliouin zone are sampled by means of a 2 × 3 × 1 Monkhorst–Pack grid [37]. In the geometry optimization procedure, all the atoms except for those belonging to the slab bottom layer are allowed to relax until the forces become lower than 0.001 Ry/Bohr. The adsorption energy of a water molecule on the surface is calculated as \(E_{\mathrm{ad}} = E_{\mathrm{tot}} - E_{\mathrm{surf}} - E_{\mathrm{H_2O}}\), where E tot, E surf and \(E_{\mathrm{H_2O}}\) are the energies of the adsorbate system, the clean surface, and water molecule. E tot and E surf are calculated using the same supercell, while for \(E_{\mathrm{H_2O}},\) we use a cubic cell with edge 16 Å long, being the water molecule assumed as isolated. The reaction path and energy barrier for water dissociation are calculated by means of the nudged elastic band (NEB) method within the “climbing the image” scheme [38, 39]. The NEB method is able to identify the minimum energy path (MEP) for the system transition between two stable configurations. In our case, they correspond to water physisorption and dissociative chemisorption configurations, respectively. In the NEB calculations, we reduce the slab thickness to six layers in order to accelerate the convergence of the method.

3 Results and Discussion

3.1 Effects of Silicon Dopants on the Process of Surface Hydroxylation

In order to construct a realistic model for the Si-incorporating C(001) surface, we identify the most favorable location for the silicon atoms by comparing the stability of different substitutional sites. As shown in Fig. 1, the compared sites are located within the first, second, and third surface layers. The configuration containing the Si–C heterodimer (Fig. 1a) turned out to be the most energetically favored. Indeed, Si dopant surrounded by C-sp 2 atoms has been identified as the prevailing configuration in Si-DLC films by nuclear magnetic resonance experiments [31].

Fig. 1
figure 1

Relative stability of different substitutional sites for the Si dopant. The energy differences are referred to the most stable configuration (a), where the Si atom is located in the first surface layer and forms a Si–C heterodimer. The gray and blue balls indicate Si and C atoms, respectively (Color figure online)

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As a next step, we evaluate the effects of silicon on the dissociative adsorption of water molecules. The considered adsorption configurations are modeled by positioning the two fragments (−H and −OH) of the dissociated molecule on different sites. In particular, we model adsorption processes involving either only one dimer or two adjacent dimers (belonging both to the same row or separated by a trench). The optimized configurations and the corresponding adsorption energies are shown in Fig. 2. As can be seen from the first and second rows, where the Si-doped surface is considered, the adsorption configurations containing a Si–OH group are more stable than those containing a Si–H group by more than 1 eV. The comparison between the adsorption energies for Si-doped and undoped surfaces (first and third rows of Fig. 2) indicates that the stability of a Si–OH group is significantly higher than that of a C–OH group by approximately 1.5 eV. On the contrary, the energy gain for hydrogen adsorption is almost independent from the presence of silicon (second and third rows). These results indicate that the Si dopant selectively stabilizes the hydroxyl group.

Fig. 2
figure 2

Dissociative adsorption configurations for a water molecule on the Si-incorporating and clean C(001) surfaces. The adsorptions energies, E ad, are reported in eV. The red and white balls indicate O and H atoms, respectively (Color figure online)

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To better understand the above-described results, we analyze the electronic charge displacements and the projected density of states (PDOS) of hydroxylated surfaces.

The charge displacement, \(\Delta \rho\), occurring upon adsorption of an OH fragment on the surface is calculated as \(\Delta \rho = \rho _{\mathrm{tot}} - \rho _{\mathrm{surf}} - \rho _{\mathrm{frag}}\), where \(\rho _{\mathrm{tot}}\), \(\rho _{\mathrm{surf}}\) and \(\rho _{\mathrm{frag}}\) are the electronic density of the adsorbed system, the clean surface, and isolated fragment. The charge density of the individual components (surface and adsorbate) has been calculated in the geometry that the components have in the composite system. Figure 3 shows the projected charge displacements occurring upon hydroxyl adsorption on the Si-doped (a) and undoped (b) surfaces. The projection of \(\Delta \rho\) on the (\(\bar{1}\)10) plane is obtained by integration along the perpendicular direction. An accumulation of electrons can be observed both in the O–Si and O–C bond regions, consistently with the covalent character of these bonds. The oxygen bound to the Si site attracts more electrons than the oxygen bound to the C site, as confirmed by the analysis of the L\(\ddot{\text {o}}\)wdin charges displayed in Fig. 3 [40]. The O–Si bond presents, thus, an ionic character more pronounced than the O–C bond.

Fig. 3
figure 3

Charge displacements projected on the (\(\bar{1}\)10) plane upon adsorption of OH fragments on the a Si-doped and b undoped surfaces. The superscript of each element indicates the partial charge obtained by the Löwdin charge population analysis

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Fig. 4
figure 4

PDOS of the OH-adsorbed on the a Si-doped and b undoped surfaces. The origin of the horizontal axis corresponds to the Fermi energy.

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To establish a connection between the bonding character and the adsorption energy, we analyze the PDOS for hydroxyl adsorptions shown in Fig. 4. On the clean surfaces, the silicon atom in the heterodimer and the carbon atom in the homodimer (dashed lines) have distinctive peaks below their Fermi energies, at about −0.5 eV. The magnitude of the Si surface state is higher than that of the undoped surface. When a hydroxyl adsorbs on the surface, these surface states disappear because new bonds are formed with the oxygen atom. The occupied surface state of the Si dopant before the adsorption (dashed blue line) shifts above the Fermi energy as empty states (solid blue line), which is an evidence that electrons of the Si dopant transfer to the adsorbed oxygen atom and a bond with enhanced ionic character is formed. Although the electron transfer occurs also in the case of the undoped surface, the oxygen peak of the Si–OH group is located in a lower energy region than that of the C–OH group (red lines). This suggests that the transfer of electrons from the dopant to the oxygen stabilizes the hydroxyl adsorbate. Such enhanced electronic transfer is due to the lower electronegativity of silicon: O (3.44) > C (2.55) > Si (1.90), where the numbers in the parentheses are the Pauling values [41]. The lower electronegativity of the Si atoms, which are surrounded by carbon atoms in Si-DLC, thus controls the bond polarization and promotes the surface hydroxylation, as shown by the reaction paths described in the following.

We identify the reaction path and energy barrier for water dissociation both on the clean and Si-incorporating C(001) surfaces, by applying the NEB method. As initial states for the reactions, we consider the most favorable configurations for water adsorption shown in Fig. 5a, b .Footnote 1 The corresponding final states are chosen among the configurations of Fig. 2. In particular, we consider dissociation both on the trench \((a'_1, b'_1)\) and on the dimer \((a'_2, b'_2\)). In the case of Si-doped surface, the minimum energy path (MEP) identified by the NEB algorithm for the \(a \rightarrow a_2'\) transition displays an intermediate minimum corresponding to the \(a'_1\) state. This means that one water molecule physisorbed with the geometry of Fig. 5a hardly reacts with only one dimer to form the \(a'_2\) configuration. The latter is most likely obtained by the dissociation of more than one molecule. Figure 6 summarized the results obtained for the reaction paths and energy barriers for water dissociation on the Si-doped surface (blue line) and the undoped surface (black lines). In the latter case, the comparison between the results obtained for the \(b \rightarrow b_1'\) and \(b \rightarrow b_2'\) transitions indicates that water dissociation occurs most likely within the dimer row rather than within the trench, in agreement with previous calculations [27]. The comparison between the \(a \rightarrow a_1'\) and \(b \rightarrow b_2'\) paths reveals that the Si dopant reduces the energy barrier for the water dissociation by more than 50 %. This significant reduction in the reaction barrier is caused by the stabilization of the hydroxylated configuration by the Si dopant. The reaction energy associated with the \(a \rightarrow a_1'\) transition is, in fact, 0.75 eV higher than the reaction energy of the \(b \rightarrow b_2'\) transition.

Fig. 5
figure 5

Most stable configurations identified for molecular adsorption on a Si-doped and b undoped surfaces

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Fig. 6
figure 6

Reaction paths and the energy barriers \(\Delta E\) for water dissociations obtained by NEB calculations. The blue and black plots indicate the NEB images for the Si-doped and undoped surfaces, respectively. The initial (final) states of the reaction paths correspond to the configurations shown in Fig. 5 (Fig. 2), which are labeled in the same way

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Fig. 7
figure 7

Water physisorption at OH- and H-terminated surface sites. In the first case, both Si-doped and undoped surfaces are considered

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3.2 Effects of Surface Hydroxylation on Water Adsorption

As last step in our analysis, we clarify the effects of surface hydroxylation on the physisorption of further water molecules, i.e., on the surface wettability. We focus on the effects of hydroxylation because several studies have highlighted the important role of −OH groups in enhancing the surface hydrophilicity and frictional performances [17–20, 25]. Moreover, according to the phase diagram of the C(001) surface that we presented in a previous work [42], the full hydroxyl termination is more favorable than the termination containing both −OH and −H adsorbates, for a wide range of the oxygen and hydrogen chemical potentials and especially when the condition \(2\mu _{\mathrm{H}} + \mu _{\mathrm{O}} = \mu _{\mathrm{H_2O}}\) is satisfied, i.e., when the adsorbates are in thermodynamic equilibrium with water vapor. We compare the energy for molecular adsorption on OH-terminated, H-terminated, and clean surfaces. In the first case, we consider both Si-doped and undoped surfaces. The calculated adsorption energies, which are reported in Figs. 5 and 7, indicate that the surface hydroxylation highly enhances water attraction: The physisorption energy in the presence of adsorbed hydroxyl groups is three times higher than in the absence. Furthermore, the distance between the physisorbed molecule on the hydroxylated surface (calculated as the distance between the O atom of the physisorbed molecule and the H atom of the adsorbed −OH group) ia of about 1.8 Å. This value is lower than that obtained for the hydrogenated surface of Fig. 7c and is very close to 1.9 Å, which is the typical length of hydrogen bonds in bulk water. These results indicate that the surface hydroxylation enhances the attraction of water molecules toward the surface thanks to the formation of hydrogen bond networks that involve the chemisorbed −OH groups. This increases the diamond/DLC hydrophilicity.

It should be kept in mind that the GGA functional in DFT fails in the exact prediction of adsorption energies because of the inadequate description of the van der Waals (VdW) interactions [27, 43–45]. However, the qualitative conclusions derived from this study should hold on the basis of a comparative analysis of the result present in the literature: In our previous DFT study, the energies for water physisorption and dissociation on the diamond surface were calculated both with and without the inclusion of VdW interactions. The results indicate that VdW inclusion increases the water physisorption energy approximately by 0.1 eV on average and decreases the energy barrier for water dissociation by 30 % [27]. Even if we take into account of the errors maximally, the conclusions on the effects of Si dopants here derived will not be altered because they are based on estimated energy differences that are much higher than these errors.

Finally, by comparing the adsorption energies reported in Fig. 7a, b, we observe that water adsorption on hydroxylated surfaces is not significantly affected by the presence of Si dopants. Therefore, the main effect of Si dopants is to favor water dissociation. The consequent hydroxyl termination enhances the hydrophilic character of the surface.

4 Conclusions

To shed light into the effects of Si dopants in increasing the hydrophilicity of carbon-based coatings, we study the interaction of water molecules with Si-doped and undoped C(001) surfaces by means of ab initio calculations. We find that the energy gain for water dissociative adsorption increases by approximately 1.5 times in the presence of substitutional Si atoms at the surface. The analysis of the electronic charge displacements occurring upon adsorption reveals that this stabilization effect is due to the larger polarization of Si–OH bonds with respect to C–OH bonds. We apply the NEB method to identify the reaction paths for water dissociation and find that the energy barrier on the Si-incorporating surface is 50 % lower than on the clean surface. The process of surface hydroxylation is, thus, highly favored by Si dopants.

Once hydroxylated, the surface is able to attract further water molecules more strongly than the clean surface by hydrogen bond formation (the energy is more than three times higher on the OH-terminated surface than on the clean surface). This two-step tribochemical process is consistent with and can explain the enhancements of hydrophilic character and the consequent friction reduction observed in carbon films doped by silicon.