Size dependence of hydrophobic hydration at electrified gold/water interfaces

Significance

The optimization of “green” electrochemical processes is one of the most important challenges in the transition toward renewable energy technologies. In many of these processes, including, e.g., ${\mathrm{C}\mathrm{O}}_2$ and ${\mathrm{N}}_2$ reduction, small hydrophobic molecules are formed and react at the interface, and their hydration free energy modulates the associated thermodynamics. Here, we use molecular dynamics simulations to elucidate the mechanisms and energetics of hydrophobic hydration at an electrified gold/water interface. We propose an adaptation of the Lum–Chandler–Weeks theory that maps the changes in hydration free energies at the interface as a function of solute size and applied potential.

Abstract

Hydrophobic hydration at metal/water interfaces actively contributes to the energetics of electrochemical reactions, e.g. ${\mathrm{C}\mathrm{O}}_2$ and ${\mathrm{N}}_2$ reduction, where small hydrophobic molecules are involved. In this work, constant applied potential molecular dynamics is employed to study hydrophobic hydration at a gold/water interface. We propose an adaptation of the Lum–Chandler–Weeks (LCW) theory to describe the free energy of hydrophobic hydration at the interface as a function of solute size and applied voltage. Based on this model we are able to predict the free energy cost of cavity formation at the interface directly from the free energy cost in the bulk plus an interface-dependent correction term. The interfacial water network contributes significantly to the free energy, yielding a preference for outer-sphere adsorption at the gold surface for ideal hydrophobes. We predict an accumulation of small hydrophobic solutes of sizes comparable to CO or ${\mathrm{N}}_2$, while the free energy cost to hydrate larger hydrophobes, above 2.5-Å radius, is shown to be greater at the interface than in the bulk. Interestingly, the transition from the volume dominated to the surface dominated regimes predicted by the LCW theory in the bulk is also found to take place for hydrophobes at the Au/water interface but occurs at smaller cavity radii. By applying the adapted LCW theory to a simple model addition reaction, we illustrate some implications of our findings for electrochemical reactions.

Small hydrophobic species are often present at metal/water interfaces, as reactants, intermediates, and products in a large variety of electrochemical processes, such as ${\mathrm{C}\mathrm{O}}_2$ (1, 2) and ${\mathrm{N}}_2$ reduction (3, 4). The development of models able to describe hydrophobic hydration at the interface with a metal is therefore a key step in the optimization of these reactions.

The structure and the dynamics of water molecules adsorbed at metallic surfaces is now well understood thanks to the combination of advanced experimental (e.g., surface specific in situ vibrational spectroscopies and synchrotron-based techniques) (5–8) and computational (8–16) methods. A very interesting result arising from these studies is the existence of hydrophobic effects at the interface due to the peculiar organization of the hydrogen bond (HB) network of the adsorbed water molecules (17). Hydrophobic hydration is a key phenomenon in bulk water (18, 19), and its understanding has led to important progress in, e.g., our comprehension of biological processes where it is ubiquitous (19–25). A molecular description of hydrophobicity is still a challenge for theory and experiments (20, 26–29).

As described by the Lum–Chandler–Weeks (LCW) theory (18), the free energy cost of solvating a hydrophobic solute in bulk water is well approximated by the free energy cost to form a cavity in the liquid and primarily depends on the cavity size. In particular, for small solutes (<7-Å radius), the water HB network responds elastically to accommodate the cavity, but a reduced number of intact network configurations results in an entropy decrease proportional to the volume. On the other hand, interfacial thermodynamics applies for larger solutes, involving the breaking of water–water HBs and a corresponding change in enthalpy that scales with the cavity surface area (19). When moving from the bulk to the interface, the hydration of hydrophobic species is further modulated by specific water–water and water–surface interactions, and deviations from the bulk behavior are often observed (17, 20, 23, 30). For instance, large density fluctuations of the water surface in contact with hydrophobic media were shown to promote the solvation of hydrophobic solutes, while a more bulk-like behavior has been reported for hydrophilic interfaces, where density fluctuations are suppressed by water–surface interactions (20, 31).

In this respect, metal/water interfaces represent a special case, where strong water–surface interactions lead to very ordered water adlayers on top of the metal, with a soft liquid interface being, however, formed between the adlayer and the adjacent water layer (10, 17, 32). In the case of platinum, this water–water interface was shown to exhibit density fluctuations typical of hydrophobic environments, promoting the formation of cavities that can accommodate small solutes (17). In the present work, we investigate hydrophobic hydration at the electrified interface between water and a gold (100) surface by classical molecular dynamics (MD) simulations. By focusing on a range of solute size and surface potential relevant for electrochemical applications, we provide a surface-dependent correction to the LCW theory that accounts for the modifications imposed by the gold surface on the cavity formation mechanism, and we shed light on its dependence on the applied voltage.

Results

Hydrophobic Hydration at the Interface.

Fig. 1 reports the solvation free energy profiles $\delta {\mu }_v\left(z\right)$, obtained as the difference in the solvation free energy at a distance $z$ from the surface and in the bulk, for small spherical hydrophobic solutes with increasing radius (from $r$ = 2.0 Å to $r$ = 3.5 Å). The profiles are obtained by monitoring the probability to form spherical cavities of the chosen radius as a function of $z$ (Eq. 5). The applied voltage ($\mathrm{\Delta }V$) is set to 0 V, which corresponds to the point of zero charge (PZC) of the model. A characteristic snapshot illustrating this methodology is provided in Fig. 1A, where the interfacial organization of water molecules is also highlighted. This latter resembles the one previously shown by Limmer et al. for Pt/water interfaces (17): Strong, favorable interactions between the water molecules and the metal surface lead to peculiar interactions with adjacent water molecules. As illustrated in the top view of Fig. 1B, water molecules within the first adsorbed layer (the adlayer, with on average 12 waters per ${\mathrm{n}\mathrm{m}}^2$) preferentially lie flat on the surface in a distance of $\sim$3 Å. The global arrangement exhibits a square symmetry with, however, some vacancies left, which position is dynamic in time. Similar vacancies were observed in the monolayer structures of water absorbed on many face-centered cubic metals (33). The ordered water structure above the Au surface leads to a maximization of the number of HBs formed between adlayer water molecules (18 HBs per ${\mathrm{n}\mathrm{m}}^2$ on average, corresponding to 2.9 HBs per molecule; see Computational Methods for the definition of HBs). As a consequence, few spots remain available for forming HBs between the adlayer and the second water layer, resulting in only four interlayer HBs per ${\mathrm{n}\mathrm{m}}^2$ (0.4 HBs per molecule). For this reason, the second layer resembles in some aspects the layer formed by water in contact with hydrophobic media (17), e.g., air, and we refer to it as the air/water-like layer, even though the composite Au(100)+adlayer surface is macroscopically hydrophilic (SI Appendix, Fig. S1). In particular, four interlayer HBs per ${\mathrm{n}\mathrm{m}}^2$ is in between 0 HBs per ${\mathrm{n}\mathrm{m}}^2$, for water above a purely hydrophobic surface, and 9.3 HBs per ${\mathrm{n}\mathrm{m}}^2$ for a uniform hydrophilic surface such as $\alpha$-001-quartz (34). As a consequence, one out of every five water molecules in the air/water-like layer carries a dangling OH pointing to the adlayer, which is a signature of local hydrophobicity, such as experimentally detected by sum frequency generation spectroscopy at gold/water interfaces (7). Such a local hydrophobic character enhances water density fluctuations, increasing the probability to form small cavities. This appears clearly on the hydration free energy profiles in Fig. 1C, Left, which show a minimum at $z$ < 5 Å for all of the investigated cavity radii. The minima represent stable locations for hydrophobic solutes at the interface.

Fig. 1.

Excess solvation free energy for ideal hydrophobes at the Au(100)/water interface at PZC. (A) Schematic illustrating how the excess solvation free energy, $\delta {\mu }_v\left(z\right)$, with v the volume of the ideal hydrophobe (white sphere) and z the vertical distance from the adlayer, is calculated from MD simulations. The water molecules belonging to the adlayer (in direct contact with Au, at z $\sim$0 Å) and to the adjacent air/water-like layer (at z $\sim$3 Å) are highlighted. The white spheres identify the hydrophobe solvated in the bulk and in its most stable position at the interface, i.e., with one side contacting the adlayer. (B) Top view of the ordered water arrangement within the adlayer, showing a square symmetry with some vacancies (see black circle for one example). (C, Left) $\delta {\mu }_v\left(z\right)$ vs. $z$ profiles for ideal hydrophobes with increasing radius (r), obtained as the difference in the solvation free energy at a distance $z$ from the surface and in the bulk. (C, Right) Same profiles plotted as a function of $z-r$. The vertical dashed lines identify the location of the adlayer and the air/water-like layer.

When the cavity radius increases, the free energy minimum is located further away from the surface and its value increases. To rationalize this result, we should consider not only the distance between the center of the cavity and the Au surface but also the minimum distance between the cavity surface and Au, $z-r$, as reported in Fig. 1C, Right. For all cavities, the most stable location at the interface is at $z-r=$ 0 Å, i.e., when the cavity surface contacts the adlayer in one point, as illustrated in the inset. This corresponds to an outer-sphere adsorption of the hydrophobes, which are separated from the metal by the adlayer. In contrast, inner-sphere adsorption, which would require the formation of a cavity within the adlayer, is largely disfavored, as measured by the sharp increase of $\delta {\mu }_v\left(z\right)$ for $z-r$ < 0 Å. This can be understood by considering that replacing a water molecule in the adlayer with an empty patch has a high free energy cost, which has been estimated in ref. 10 to be on the order of 10 ${\mathrm{k}}_B$T. More details regarding the features in the $\delta {\mu }_v\left(z\right)$ profiles can be found in SI Appendix, Fig. S2 and related discussion).

Adapted LCW Theory for the Metal–Water Interface.

The value of $\delta {\mu }_v\left(z\right)$ at the minimum ($z-r=$ 0 Å) is denoted hereafter $\delta {\mu }_v\left(z^{*}\right)$. This term corresponds to the difference in the free energy cost to form the same cavity in the most stable position at the interface and in the bulk:

$$\delta {\mu }_v\left(z^{*}\right)=\mathrm{\Delta }{\mu }_v^{int}-\mathrm{\Delta }{\mu }_v^{bulk}.$$ [1]

Therefore, it provides a correction term that allows us to adapt the LCW theory, which describes the hydration free energy of ideal hydrophobes in the bulk (18, 19), to the Au/water interface. Fig. 2A shows the variations of $\delta {\mu }_v\left(z^{*}\right)$ normalized by the cavity surface area with respect to the cavity radius. This representation allows to establish a proportional increase of the free energy to the cavity volume, as it is the case in the bulk (18, 19) for cavity radii smaller than 7 Å (Fig. 2A, Inset). A similar volume-dominated regime is observed for the additional interfacial contribution, as shown by the linear dependence of $\delta {\mu }_v\left(z^{*}\right)/r^2$ on $r$. However, the linear behavior is strictly valid for a more limited radii range, i.e., until $r$ = 3.0 Å, in contrast to the bulk case. The deviation from linearity is much less pronounced in the $\mathrm{\Delta }{\mu }_v^{int}$ term, since it is a combination of $\delta {\mu }_v\left(z^{*}\right)$ and $\mathrm{\Delta }{\mu }_v^{bulk}$ (SI Appendix, Fig. S3A).

Fig. 2.

Hydrophobic hydration at the Au(100)/water interface vs. bulk. (A) Excess solvation free energy for ideal hydrophobes as a function of their radius, $r$, normalized by the cavity surface area. The reported $\delta {\mu }_v$ values are differences between the solvation free energy of the hydrophobe located at the interface (z = z*, first minimum in Fig. 1C) and in the bulk. The black solid line is a linear fit, highlighting the volume-dominated regime strictly valid until r = 3.0 Å. (Inset) The plot obtained from the LCW theory (18) for bulk water, adapted from ref. 19. (B) $\delta {\mu }_v\left(z^{*}\right)$ provides the means to obtain the free energy cost of cavity formation at the interface, $\mathrm{\Delta }{\mu }_v^{int}$, directly from the well-known values in the bulk, $\mathrm{\Delta }{\mu }_v^{bulk}$. (C) The adsorption profile of a CO molecule at the Au(100)/water interface, as obtained from umbrella sampling technique, is compared to the profile for a 2.5-Å cavity (same as in Fig. 1C, Left).

Moreover, as observed in the plot, $\delta {\mu }_v\left(z^{*}\right)/r^2$ is equal to zero at about $r$ = 2.5 Å, which according to Eq. 1 corresponds to the case when the cavity formation at the interface and in the bulk are isoenergetic, while it becomes less than 0 for $r$ < 2.5 Å. Therefore, the formation of small cavities, that can accommodate the smallest hydrophobic molecules such as ${\mathrm{N}}_2$ or CO, is favored at the interface with respect to the bulk, promoting their accumulation near the Au surface. In order to check this result, the adsorption free energy profile of CO at the Au(100)/water interface was obtained from umbrella sampling technique. As shown in Fig. 2C, the CO behavior is well approximated by a 2.5-Å cavity, with the most stable location in the outer layer ($z=r=2.5$ Å), a high free energy barrier to enter the adlayer ($z<2$ Å), and a maximum at $z=4$ Å.

In contrast, $\delta {\mu }_v\left(z^{*}\right)$ becomes positive for cavities with $r$ > 2.5 Å, representative of larger hydrophobic molecules such as ${\mathrm{C}\mathrm{O}}_2$ or ${\mathrm{C}\mathrm{H}}_4$. Thus, a substantial accumulation of these molecules at the interface is not promoted by the water network, even though the well-defined minimum at $z-r=$ 0 Å in Fig. 1C demonstrates that they are metastable at the metal–water interface. Interestingly, the cross-over from negative to positive $\delta {\mu }_v\left(z^{*}\right)/r^2$ values goes beyond what is expected for canonical hydrophobic interfaces, where density fluctuations are enhanced with respect to bulk in both small and large observation volumes (20, 31). The water–water interface formed between the adlayer and the air/water-like layer hence plays a dual role: On the one hand, it creates a hydrophobic environment where short-range density fluctuations that can accommodate small hydrophobic solutes are enhanced; on the other hand, it constrains long-range density fluctuations, so that the formation of large cavities is hindered.

In order to better elucidate the microscopic origin of such dual role, a direct visualization of the cavities formed during the simulation is provided in Fig. 3. For the smallest cavities, represented in the figure by the $r=2.0$ Å panel, most of the empty volume occupies the interlayer space in between the adlayer and the air/water-like layer (which are separated by $\sim$3 Å) and the HB network within the air/water-like layer (orange bonds in the figure) is virtually unperturbed around the cavity. Since the density of HBs between the adlayer and the air/water-like layer is extremely low (only four HBs per ${\mathrm{n}\mathrm{m}}^2$), the free energy cost of cavity formation is minimized in the interlayer space, thus $\delta {\mu }_v\left(z^{*}\right)/r^2<0$. However, when the size of the cavity increases above 2.5 Å, i.e., when we enter in the size range where $\delta {\mu }_v\left(z^{*}\right)/r^2>0$ and still scales linearly with the cavity volume, the distortion imposed on the HB network in the air/water-like layer becomes more severe (see orange bonds in Fig. 3, Middle). As can be seen in the snapshot, this distortion arises from an elastic response of the water network, which is wrapped around the cavity. According to the LCW theory (18), this process has an entropic cost, which is found to be larger at the interface than in bulk water since $\delta {\mu }_v\left(z^{*}\right)/r^2>0$. Thus, the “flexibility” of the hydrophobic air/water-like layer is reduced in presence of the adlayer, as this latter can provide some HBs, even if few, that locally pin water density fluctuations. This is not the case for purely hydrophobic interfaces, which accordingly promote the accommodation of both small and large hydrophobic solutes (20, 31). The effect of the adlayer becomes more pronounced when increasing the cavity radius up to 3.5 Å (Fig. 3, Right), where the HB network within the air/water-like layer is locally broken (missing orange bonds in Fig. 3) in proximity of the cavity. The breaking of some HBs introduces an enthalpic component to the free energy cost of cavity formation, which according to the LCW theory is expected to scale with the cavity surface area (see SI Appendix, Fig. S3B for an estimation of the corresponding change in entropy). This is the reason why deviations from the volume-dominated regime in Fig. 2 are observed beyond 3.0-Å radius. Our results therefore demonstrate that the transition from the volume-dominated (entropic) to the surface-dominated (enthalpic) regimes predicted by the LCW theory in the bulk also takes place at the Au/water interface, but it is anticipated to smaller cavity radii due to the constraints imposed by the adlayer on the fluctuations of the interfacial water network.

Fig. 3.

Hydrophobic hydration mechanism at the Au(100)/water interface at PZC. MD snapshots illustrating the mechanism for the solvation of small ideal hydrophobes (i.e., small cavities, gray spheres) in their most stable position at the interface (first minimum in Fig. 1C). The HBs between water molecules in the air/water-like layer are materialized in orange to better appreciate the distortion (for 2.5 Å in radius cavities) and the local breaking (for 3.5 Å in radius cavities) of the interfacial water network.

Effect of Applied Potential.

In Fig. 4 we now evaluate the effect of an applied voltage by varying the Au slab potential from −2 V to +2 V. Since interfacial chemical reactions are not included in our classical simulations, only the potential-induced structural changes within the adlayer and the air/water-like layer will affect density fluctuations and cavity formation at the interface. Fig. 4A demonstrates that the effect of the surface potential on the free energy cost of cavity formation is negligible in the investigated range, with the free energy profiles obtained at all potential values being almost superimposed. Therefore, all of the previous results obtained for PZC conditions can be extended to a wide range of working electrochemical conditions, as long as no reactions occur.

Fig. 4.

Effect of the applied potential. (A) Excess solvation free energy, $\delta {\mu }_v\left(z\right)$, for a 2.0-Å radius ideal hydrophobe at negative and positive electrodes. Similar trends for a larger cavity are shown in SI Appendix, Fig. S4. (B) Adlayer water structure as a function of the applied voltage, as quantified by the variation in the number of HBs ($\mathrm{\Delta }H{B}^{//}$) formed between adlayer water molecules with respect to PZC. (Inset) The probability for adlayer waters to orient their hydrogen atoms toward the Au surface (H-up, red), away from the Au surface (H-down, cyan), or parallel to it (H-//, green). Water density profiles are shown in SI Appendix, Fig. S5.

Despite hydrophobic hydration remaining unaltered, structural changes within the adlayer are detected upon voltage application. In Fig. 4B they are evaluated by quantifying the variation in the number of HBs formed between adlayer water molecules, denoted HBs^// due to their orientation parallel to the Au surface, as well as by the changes in the orientation of adlayer water OH-groups (Fig. 4B, Inset). At 0 V (PZC), adlayer water molecules preferentially lie parallel to the Au surface (>70% of the OH-groups with parallel orientation, green curve in the inset) and form 18 HBs^///${\mathrm{n}\mathrm{m}}^2$. Once a negative potential is applied, some adlayer waters reorient with one OH-group pointing toward the surface (red curve in the inset) and the adlayer structure is partially disordered, with a loss of 0.5 HBs// per ${\mathrm{n}\mathrm{m}}^2$ (2% of the total) at −1 V and of 1.2 HBs// per ${\mathrm{n}\mathrm{m}}^2$ (6% of the total) at −2 V. These structural changes are consistent with a previous study employing ab initio simulations in combination with surface enhanced Raman spectroscopy (8). By contrast, the water reorientation at positive potentials (Fig. 4B, Inset) is not accompanied by a disordering within the adlayer, as shown by $\mathrm{\Delta }H{B}^{//}$ per ${\mathrm{n}\mathrm{m}}^2$, that is larger for potentials of +1 V and +2 V than for 0 V. In agreement with what previously observed at Pt/water interfaces (10), we hence find an asymmetry in the response of the adlayer structure at positive/negative electrodes. However, the changes within the adlayer structure do not significantly alter its hydrophobicity toward the adjacent air/water-like layer, and therefore the cavity formation process. This is measured by the number of interlayer HBs per ${\mathrm{n}\mathrm{m}}^2$ formed between adlayer and air/water-like layer, which remains constant around the value of 4 with a variance of $\pm$0.1 in the whole potential range.

It should be noted that in case of metals such as platinum that strongly interact with water an additional degree of complexity will be provided by the presence of chemisorbed water molecules within the adlayer, as recently shown by Le et al. (12) from ab initio MD simulations. How much chemisorbed waters can affect the cavity formation mechanism described here, as well as its dependence upon voltage application, is an intriguing question that still remains to be addressed.

Implications for Outer-Sphere Electrochemical Reactions.

We now apply our adaptation of the LCW theory to a simple model addition reaction:

$$R_1+R_2=P,$$ [2]

where $R_1$ and $R_2$ are small hydrophobic molecules that react to form a larger molecule $P$. Such addition reactions are key steps for electrochemical routes reducing ${\mathrm{C}\mathrm{O}}_2$ to multicarbon products, such as ethanol and ethylene (35–37), which are obtained with sufficient faradaic efficiencies on copper electrodes but not on other metals such as gold (37–39). In the bulk, the hydrophobic hydration contribution ($\mathrm{\Delta }{F}_{reax}$) to the total free energy of the addition reaction 2 is given by

$$\mathrm{\Delta }{F}_{reax}=\mathrm{\Delta }{\mu }_v^{bulk}\left(P\right)-\mathrm{\Delta }{\mu }_v^{bulk}\left(R_1\right)-\mathrm{\Delta }{\mu }_v^{bulk}\left(R_2\right).$$ [3]

For example, assuming a similar radius of 2.5 Å for the cavity of both $R_1$ and $R_2$ (which corresponds to the case of a CO molecule) would lead to a product with an approximate radius of 3.25 Å, yielding a contribution $\mathrm{\Delta }{F}_{reax}=45.0$ meV in the bulk according to the LCW theory. In order to determine whether this reaction would become favored or hindered at the interface (in the absence of chemisorption effects for the molecules), it is necessary to add the corresponding free energy contributions for bringing $R_1$, $R_2$, and $P$ to the $z$ position at which the reaction occurs. If we assume the latter to be equal to the most favorable position in the outer-layer ($z=z^{*}$, as illustrated in the scheme of Fig. 5), the hydrophobic hydration contribution to the reaction free energy is now

$$\mathrm{\Delta }{F}_{reax}^{int}=\mathrm{\Delta }{F}_{reax}+\delta {\mu }_v\left(z_P^{*}\right)-2\delta {\mu }_v\left(z_{R1}^{*}=z_{R2}^{*}\right).$$ [4]

The additional free energy cost to move a 2.5-Å radius cavity from the bulk to the stable outer-layer position is equal to 2.2 meV, while it amounts to 22.1 meV for the larger 3.25-Å radius cavity. Therefore, $\mathrm{\Delta }{F}_{reax}^{int}$ equals 62.7 meV. The unfavorable hydration of large hydrophobic molecules at the Au/water interface thus imposes a free energy penalty to outer-sphere addition reaction steps, while it can promote elimination reactions (which follow the opposite path: $P=R_1+R_2$). Such energetic penalty is not negligible, since the $\mathrm{\Delta }{F}_{reax}^{int}$ of our model reaction is of the same order of magnitude as the reaction free energies theoretically determined for common addition reaction steps (35, 36). Therefore, our results suggest that hydrophobic hydration could actively contribute to the preferential formation of monocarbon over multicarbon products from ${\mathrm{C}\mathrm{O}}_2$ reduction at gold electrodes.

Fig. 5.

Hydrophobic hydration contribution to electrochemical processes. Scheme of a model outer-sphere addition reaction, where two cavities (${\mathrm{R}}_1$ and ${\mathrm{R}}_2$) of 2.5-Å radii form a larger cavity (P) of 3.25-Å radius.

Discussion and Conclusions

The hydration of small hydrophobic solutes forming cavities of 2.0- to 3.5-Å radius at an electrified Au(100)/water interface has been investigated from classical MD simulations. In a wide potential range relevant for electrochemical applications, the most stable position for the hydrophobes at the interface is found to correspond to an outer-sphere adsorption, i.e., occupying an interlayer region separated from the metal by the water adlayer. By contrast, inner-sphere adsorption is hindered by the high free energy cost to form a cavity within the adlayer, where the density of HBs is five times higher than in the interlayer region. Subnanometric heterogeneity hence exists for the adsorption of hydrophobic species at the metal/water interface, with an unfavorable spot within the adlayer and a favorable position in the interlayer region.

The interfacial water network is proposed to play a crucial role: While it promotes the accumulation of small hydrophobic solutes of sizes comparable to CO or ${\mathrm{N}}_2$, the free energy cost to hydrate larger hydrophobes, above 2.5-Å radius, is greater at the interface than in the bulk. In stark contrast with the Au(100) case, even cavities of 3-Å radius were shown to be enriched at Pt/water interfaces, as a result of the stronger chemisorption of water on the platinum surface (9, 17). Therefore, the more a metal surface interacts strongly with water, inducing a very ordered adlayer structure with a low density of interlayer HBs, the more hydrophobic hydration is promoted, increasing the limit size for accumulation of solutes at the interface. In the limit scenario where a purely hydrophobic interface is formed between the adlayer and the air/water-like layer, i.e., with zero interlayer HBs, the enrichment of both small and large solutes will be favored at the interface with respect to bulk (20, 31). Interesting perspectives are opened by the possibility to trigger the adsorption of hydrophobic species at the metal/water interface as a function of the degree of ordering within the adlayer. Moreover, since density fluctuations in liquid water can deviate significantly from the canonical spherical shapes (22, 40), the subnanometric heterogeneity observed in the direction normal to the surface at the gold/water interface suggests that not only the volume but also the shape of the cavity could affect hydration free energies.

In summary, when evaluating the free energy cost for hydrophobic hydration in the interlayer region as a function of the cavity size, the volume-dominated and surface-dominated regimes as described by the LCW theory (18) for the bulk can be identified. At the interface, however, the transition from the first to the second regime occurs for hydrophobes of $\sim$3-Å radius, smaller than in the bulk. For such radius, corresponding to the distance between the adlayer and the air/water-like layer, half of the cavity extends in the interlayer region, while the other half protrudes into the air/water-like layer, inducing the breaking of some HBs. Here, we propose a framework that allows to adapt the LCW theory to metal/water interfaces, by rewriting the free energy cost of hydrophobic hydration at the interface as the free energy cost in the bulk plus a size-dependent correction term. While the values for the correction term are specific for a given interface, the approach can be generalized to any other metal/water interface.

Finally, we have shown that outer-sphere addition reaction steps suffer from an energetic penalty imposed by the high cost of large cavities formation, while elimination reactions, where a large molecule is decomposed in smaller cavities, are promoted. Since hydration free energies sizably vary within few angstroms at the interface, it will be interesting to go beyond the simplification that reactants and products are ultimately confined in the outer layer and evaluate how the hydrophobic hydration contribution to the reaction changes as a function of their distance from the surface. Our preliminary results pave the way to a fine-tuning of hydration free energies at the interface as an efficient strategy to manipulate the energetics and mechanisms of electrochemical reactions.

Computational Methods

A liquid slab composed by 3,481 water molecules between two planar Au(100) surfaces (each electrode made of five layers, 162 Au atoms each) was simulated using the MetalWalls code (41). Three simulations were performed at fixed applied potentials of 0, 1, and 2 V between the electrodes, respectively. Two-dimensional (2D) periodic boundary conditions were employed, with no periodicity on the direction normal to the Au surface. Box dimensions along the $x$ and $y$ directions are of $L_x=L_y=36.63$ Å. The SPC/E (42) model was chosen for water, while Lennard-Jones parameters introduced by Heinz et al. (43) were adopted for Au(100). Lorentz–Berthelot mixing rules were used to model the interactions between all atoms and a cutoff of 15 Å was used. Electrostatic interactions were computed using a 2D Ewald summation method, with a cutoff of 12 Å for the short-range part. The simulation boxes were equilibrated at constant atmospheric pressure by applying a constant pressure force to the electrodes. The electrode separation was then fixed to the equilibrium value of 78.6 Å (for which the water density in the middle of box corresponds to the bulk value). A second equilibration step of 5 ns has been performed for all simulations in the NVT ensemble with $T=298$ K. After equilibration, production runs of 80 ns each have been collected with a timestep of 2 fs (NVT, $T=298$ K) and used for the analysis. We have checked that the simulation time is sufficient to converge vacancies concentration in the adlayer.

The water–water HBs were computed using the definition of White et al. (44) with $O\left(-H\right)\cdots O$ distance $\le 3.2$ Å and $O-H\cdots O$ angle in the range $\left[140-220\right]°$. A second criterion (45) has been tested to ensure that the results are not biased by the adopted HB definition. The number of dangling OH groups carried by a water molecule is then estimated as 2 minus the average number of HBs it forms as donor. For the OH-orientation analysis (Fig. 4B, Inset), an OH-group is considered parallel to the Au surface (H-$//$) if it forms an angle of $\mathrm{90}°\pm 30°$ with respect to the normal $z$-direction (oriented from solid to liquid), H-down if < $\mathrm{60}°$, and H-up otherwise.

The free energy cost of cavity formation as a function of the vertical distance from the Au surface has been calculated by sampling the probability ($P_v\left(0,z\right)$) to find zero water oxygen centers in a spherical probing volume of the chosen radius (17):

$$P_v\left(0,z\right)=e^{-\beta \mathrm{\Delta }{\mu }_v\left(z\right)},$$ [5]

where $\beta =1/k_{B}T$, $k_B$ being the Boltzmann constant.

The umbrella sampling calculation of the CO adsorption profile along the $z$ coordinate, i.e., the vertical distance between the CO center of mass and the water adlayer, was accomplished using the open-source PLUMED library, version 2.5 (46). Six calculations were performed at z values of 0.5, 2.5, 4.5, 6.5, 8.5, and 10.5 Å, with a spring constant of 250 kJ ${\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}\hspace{0.17em}{\mathrm{n}\mathrm{m}}^{-2}$. The force field parameters from ref. 47 were used for CO.

Data Availability

Input files and raw data used for the figures have been deposited in Zenodo (https://doi.org/10.5281/zenodo.4467959) and GitLab https://gitlab.com/ampere2/serva_-arxiv_2011.08825_2020).