Thermodynamic Analysis of the Hydrolysis of Borate-Based Lithium Salts by Density Functional Theory

The electronic structure of neutral molecules, either radical with odd electrons or closed shell, ions and atoms were modeled by DFT. All species and their optimized structures were computed using the Spartan20 ²⁹ software. The Range Separated meta-GGA ωB97M-V ³⁰ functional was adopted with a 6–31++G** basis set. ³¹ Singlet or doublet spin states were assumed for all closed shell and radical species, respectively: spin contamination has been checked in preliminary tests. The choice of ωB97M-V/6–31++G** is a good compromise between computational costs and accuracy (see below). Geometrical conformers were identified using the molecular mechanics algorithm inbuilt in Spartan20. Equilibrium geometries were computed by structural relaxations of the atomic positions and verified by vibrational frequencies calculations. Electronic energies and vibrational contributions were evaluated assuming an implicit solvation model (Polarizable Continuum Model, PCM ³² ), to simulate a polar environment (ε = 37.22). Free Gibbs energy was computed for each chemical species by evaluating the partition functions and considering the zero-point energies. Free Gibbs Energy, ${{\rm{\Delta }}}_{r}{G}_{T}^{0},$ of reactions were calculated as stoichiometrically-weighed algebraic sums between the Gibbs Free Energy of products and reactants.

The computational accuracy of ωB97M-V/6–31++G** was evaluated comparing the thermodynamics of a set of reactions with similar calculations carried out by B3LYP ³³ and the benchmarks MP2 and CCSD(T) methods, using the same basis set (see the Supporting Info). The relative errors in terms of Gibbs energy of reaction accuracy compared to MP2 calculations are 11.6% in the case of ωB97M-V/6–31++G** and 14.3% for B3LYP/6–31++G** and thus the ωB97M-V functional outperforms the popular B3LYP. Turning to the relative errors in terms of total energy of reaction at 0 K calculated by comparing the DFT total electron energies with the corresponding CCSD(T) data are 4.1% in the case of ωB97M-V/6–31++G** and 16.1% for B3LYP/6–31++G**. Again, the ωB97M-V functional outperforms the popular B3LYP. The stoichiometry of all reactions, energies and relative errors are summarized in Tables SI–SV in Supplementary Information (SI)(available online at stacks.iop.org/JES/169/070523/mmedia). Cartesian coordinates of the relaxed structures of all relevant reagents, intermediates and products are reported in the SI (Table SVI).

In order to evaluate the possible occurrence of heterogeneous reactions, we coupled DFT-based thermodynamics in solvents with the thermodynamic cycles shown in Fig. 2. In fact, a direct computation of the thermodynamics of heterogeneous reactions is not feasible using our computational approach but can be achieved by exploiting the thermochemical methodology already proposed by us, ²⁸ consisting in a general approach to calculate the effect of the precipitation based on thermochemical cycles, as described in Fig. 2. In this framework, the precipitation thermodynamics of a generic compound A_aB_bC_c is described combining the DFT data on molecules with assessed literature thermodynamic quantities obtained from standard thermodynamic database. ³⁴ Here we extended the use of thermochemical cycles to the description of the precipitation of boric acid and oxalic acid. Assuming the notation in Fig. 2, the precipitation of the solvated A_aB_bC_c(sol) species is driven by the thermodynamics of reaction R. On the other hand, the Gibbs energy of reaction R is also given by the following set of thermochemical equations:

$$\begin{eqnarray}&&{{\rm{\Delta }}}_{r}{G}_{T}^{0}\left(R\right)={{\rm{\Delta }}}_{r}{G}_{T}^{0}\left({R}^{a}\right)+\,{{\rm{\Delta }}}_{r}{G}_{T}^{0}\left({R}^{b}\right)+{{\rm{\Delta }}}_{r}{G}_{T}^{0}\left({R}^{c}\right)\end{eqnarray} \tag{ R }$$

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Atomization of A_aB_bC_c (solvated):

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{\Delta }}}_{r}{G}_{T}^{0}\left({R}^{a}\right)=a{\rm{\Delta }}{G}_{T}^{tot,DFT}\left(A\left(g\right)\right)\\ \,+\,b{\rm{\Delta }}{G}_{T}^{tot,DFT}\left(B\left(g\right)\right)+\,c{\rm{\Delta }}{G}_{T}^{tot,DFT}\left(C(g)\right)-\left({A}_{a}{B}_{b}{C}_{c}(sol)\right)\end{array}\end{eqnarray} \tag{ Ra }$$

Formation of the monoatomic gas:

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{\Delta }}}_{r}{G}_{T}^{0}\left({R}^{b}\right)=a{{\rm{\Delta }}}_{f}{G}_{T}^{0}\left(A\left(g\right)\right)\\ \,+\,\,b{{\rm{\Delta }}}_{f}{G}_{T}^{0}\left(B\left(g\right)\right)+\,c{{\rm{\Delta }}}_{f}{G}_{T}^{0}\left(C\left(g\right)\right)\end{array}\end{eqnarray} \tag{ Rb }$$

Formation of A_aB_bC_c (solid):

$$\begin{eqnarray}&&{{\rm{\Delta }}}_{r}{G}_{T}^{0}\left({R}^{b}\right)={{\rm{\Delta }}}_{f}{G}_{T}^{0}\left({A}_{a}{B}_{b}{C}_{c}(s)\right)\end{eqnarray} \tag{ Rc }$$

Where s stands for solid phase, g for gas phase and sol for solution phase.

Examples of thermochemical cycle to derive the precipitation thermodynamics of LiOH, LiF, H₃BO₃ and H₂C₂O₄ are shown in Figs. 2B–2E.

LiBF₄ hydrolysis in simulated aprotic solvent

The Potential Energy Surface (PES) calculated to mimic the hydrolysis of LiBF₄ is shown in Fig. 3. It is important to underline that all steps where solid phases are present have been computed by combining firsts principle computations in simulated solvents with thermodynamic cycles whereas all reactions in the homogeneous simulated solvent are predicted uniquely from the computational modeling results.

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In aprotic solvents Li⁺ is strongly coordinated to the BF₄ ^- anion by a direct coulombic ionic interaction. This ionic couple can unlikely undergo to the ionic dissociation R1:

$$\begin{eqnarray}&&LiB{F}_{4}\rightleftarrows \,L{i}^{+}+B{F}_{4}^{-}\end{eqnarray} \tag{ R1 }$$

being the computed ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R1 = 74 kJ mol⁻¹. Other simple reactions involving LiBF₄ are the Lewis acid/base equilibria R2:

$$\begin{eqnarray}&&LiB{F}_{4}\rightleftarrows LiF(s)+B{F}_{3}\end{eqnarray} \tag{ R2a }$$

$$\begin{eqnarray}&&LiB{F}_{4}\rightleftarrows LiF(sol)+B{F}_{3}\end{eqnarray} \tag{ R2b }$$

The dissociation of lithium tetrafluoroborate leads to the formation of trifluoroborane (BF₃) and lithium fluoride. The thermodynamic of R2 is strongly altered by the precipitation of LiF; in fact, the computed ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R2a is −25 kJ mol⁻¹, whereas ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R2b is strongly positive (120 kJ mol⁻¹). Turning to the direct reaction with water, lithium tetrafluoroborate can follow two competitive mechanisms:

$$\begin{eqnarray}&&LiB{F}_{4}+{H}_{2}O\rightleftarrows \displaystyle \frac{1}{3}{B}_{3}{O}_{3}{F}_{3}+2HF+LiF(s)\end{eqnarray} \tag{ R3a }$$

$$\begin{eqnarray}&&LiB{F}_{4}+{H}_{2}O\rightleftarrows BOF+2HF+LiF(s)\end{eqnarray} \tag{ R3b }$$

Reaction R3a is exergonic, i.e. ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R3a is −15 kJ mol⁻¹. In this reaction two factors push the equilibrium in favor of the products: the precipitation of LiF(s) and the formation of trifluoroborexine (B₃O₃F₃), as already described in previous works. ^35–37 The trimerization of BFO to give B₃O₃F₃:

$$\begin{eqnarray}&&BFO\rightleftarrows \displaystyle \frac{1}{3}{B}_{3}{O}_{3}{F}_{3}\end{eqnarray} \tag{ R4 }$$

is strongly exergonic, with ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R4 = −170 kJ mol⁻¹. As a consequence, R3b unlikely occurs, because the computed ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R3b equals 155 kJ mol⁻¹.

The hydrolysis mechanism of BF₃ is well known from a previous work. ³⁸ BF₃ can easily react with water forming hydrofluoric acid and BF₂OH:

$$\begin{eqnarray}&&B{F}_{3}+{H}_{2}O\rightleftarrows B{F}_{2}OH+HF\end{eqnarray} \tag{ R5 }$$

Reaction R5 is a nucleophilic addition, and it is weekly exergonic, with ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R5 = −8 kJ mol⁻¹. Considering a similar mechanism described for LiBF_4, boron trifluoride can also follow a parallel reactive channel as described in R6:

$$\begin{eqnarray}&&B{F}_{3}+{H}_{2}O\rightleftarrows \displaystyle \frac{1}{3}{B}_{3}{O}_{3}{F}_{3}+2HF\end{eqnarray} \tag{ R6 }$$

However, R6 reaction is slightly endergonic (${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R6 = 10 k J mol⁻¹). Once formed, BF₂OH can further hydrolyze by another water addition:

$$\begin{eqnarray}&&B{F}_{2}OH+{H}_{2}O\rightleftarrows BF{(OH)}_{2}+HF\end{eqnarray} \tag{ R7 }$$

Reaction R7 is moderately endergonic, as ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R7 = 8 kJ mol⁻¹. Also in this case, an additional competitive path leads to the formation of B₃O₃F₃:

$$\begin{eqnarray}&&B{F}_{2}OH+{H}_{2}O\rightleftarrows \displaystyle \frac{1}{3}{B}_{3}{O}_{3}{F}_{3}+HF\end{eqnarray} \tag{ R8 }$$

However, reaction R8 is thermodynamically unfavorable, because ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R8 = 18 kJ mol⁻¹. Starting from BF(OH)₂ also a third water addition may occur leading to the formation of boric acid and the release of hydrofluoric acid:

$$\begin{eqnarray}&&BF{(OH)}_{2}+{H}_{2}O\rightleftarrows {H}_{3}B{O}_{3}+HF\end{eqnarray} \tag{ R9 }$$

This reaction is endergonic, with a moderate change of the Gibbs Free energy ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R9 = 16 kJ mol⁻¹.

All these reactions occur in solution without precipitation of by-products apart from LiF(s) in reaction R2a. In fact, the precipitation of boric acid R10 is endergonic, ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R10 = 22 kJ mol⁻¹:

$$\begin{eqnarray}&&{H}_{3}B{O}_{3}(sol)\rightleftarrows {H}_{3}B{O}_{3}(s)\end{eqnarray} \tag{ R10 }$$

BF(OH)₂ can also react with a molecule of water, forming a molecule of B₃O₃F₃, through the endergonic reaction R11:

$$\begin{eqnarray}&&BF{(OH)}_{2}\rightleftarrows \displaystyle \frac{1}{3}{B}_{3}{O}_{3}{F}_{3}+{H}_{2}O\end{eqnarray} \tag{ R11 }$$

Being ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R11 equal to 10 kJ mol⁻¹. Besides these mechanisms, LiBF₄ can react with water leading to the release of lithium hydroxide via an acid/base equilibrium, as described in R12:

$$\begin{eqnarray}&&LiB{F}_{4}+{H}_{2}O\rightleftarrows B{F}_{3}+\,LiOH(s)+HF\end{eqnarray} \tag{ R12 }$$

However, the formation of LiOH can be excluded since the thermodynamics of R12 is strongly endergonic, both in solution and in heterogeneous phase, given that ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R12 = 84 kJ mol⁻¹.

LiODBF hydrolysis in simulated aprotic solvent

The thermodynamic landscape computed for the hydrolysis of LiODBF is shown in the Fig. 4, where the stoichiometry of two competitive paths is also reported.

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Li⁺is strongly coordinated to ODBF^-via a delocalized Coulombic interaction, as the partial negative charges are sitting on the carbonylic oxygens of the counter anion. In this respect the binding between anion and cation is strong being the ionic dissociation of LiODBF R13 endergonic:

$$\begin{eqnarray}&&LiODBF\rightleftarrows L{i}^{+}+ODB{F}^{-}\end{eqnarray} \tag{ R13 }$$

In fac the ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R13 = 83 kJ mol⁻¹ a value that suggest a close interaction between anion and cation in the solvent and a very limited ionization. The second reaction is a Lewis acid/base equilibrium R14 similar to R3 for LiBF₄:

$$\begin{eqnarray}&&LiODBF\rightleftarrows LiF(s)+ODBF\end{eqnarray} \tag{ R14 }$$

This reaction is slightly endergonic, with ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R14 equal to 19 kJ mol⁻¹.

Starting from the electron poor ODBF molecule the hydrolysis degradation onsets from the nucleophilic attack to form the intermediate product M₁ (see Fig. 2a) thought reaction R15:

$$\begin{eqnarray}&&ODBF+{H}_{2}O\rightleftarrows {M}_{1}+HF\end{eqnarray} \tag{ R15 }$$

Reaction R15 is exergonic being ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R15 = −14 kJ mol⁻¹. The addition of another molecule of water leads to the formation of M₂ (see Fig. 2a):

$$\begin{eqnarray}&&{M}_{1}+{H}_{2}O\rightleftarrows {M}_{2}\end{eqnarray} \tag{ R16 }$$

The ring-opening mechanism is weakly exergonic, with a Gibbs Free energy variation ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R16 = −1 kJ mol⁻¹. The heterolytic cleavage of the boron-oxygen bond in M₂ can easily release boric acid and oxalic acid following reaction R17:

$$\begin{eqnarray}&&{M}_{2}+{H}_{2}O\rightleftarrows {H}_{3}B{O}_{3}(sol)+{H}_{2}{C}_{2}{O}_{4}(sol)\end{eqnarray} \tag{ R17 }$$

Reaction R17 is exergonic (${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R17 = −27 kJ mol⁻¹). Once formed, H₂C₂O₄ does not precipitate, because the corresponding thermodynamics is endergonic, i.e. ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R18 = 11 kJ mol⁻¹:

$$\begin{eqnarray}&&{H}_{2}{C}_{2}{O}_{4}(sol)\rightleftarrows {H}_{2}{C}_{2}{O}_{4}(s)\end{eqnarray} \tag{ R18 }$$

Keeping in mind the reaction energies of R18 and R10, we can exclude massive precipitations of boric acid and oxalic acid through this hydrolysis path.

An alternative pathway of the hydrolysis of LiODBF has been also considered starting from a direct nucleophilic addition of water to give LiOH and ${M}_{1}^{a}$ (see Fig. 2a):

$$\begin{eqnarray}&&LiODBF+{H}_{2}O\rightleftarrows {M}_{1}^{a}+LiOH\left(s\right)\end{eqnarray} \tag{ R19 }$$

Reaction R19 is strongly endergonic, being ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R19 = 117 kJ mol⁻¹. ${M}_{1}^{a}$ can react again with water: in this case the formation of BF₂OH and the release of oxalic acid is favored, given that ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R20 = −55 kJ mol⁻¹:

$$\begin{eqnarray}&&{M}_{1}^{a}+{H}_{2}O\rightleftarrows B{F}_{2}OH+{H}_{2}{C}_{2}{O}_{4}\end{eqnarray} \tag{ R20 }$$

Once formed BF₂OH may follow the degradation path described in the previous section (R7 and

R9). Overall, despite the large exergonicity of R20, the remarkable positive energy difference between reagents and products of reaction R19 likely hinders this chemical hydrolyzation path.

LiBOB hydrolysis in simulated aprotic solvent

The PES of the hydrolysis of LiBOB is shown in Fig. 5.

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In aprotic solvents Li⁺ is strongly coordinated to BOB^-. This ionic couple can dissociate following reaction R21:

$$\begin{eqnarray}&&LiBOB\rightleftarrows L{i}^{+}+BO{B}^{-}\end{eqnarray} \tag{ R21 }$$

This reaction is endergonic with a ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R21 = 77 kJ mol⁻¹. LiBOB can undergo a nucleophilic water addition R22, forming the intermediate product P₁ (see Fig. 5a):

$$\begin{eqnarray}&&LiBOB+{H}_{2}O\rightleftarrows {P}_{1}+LiOH(s)\end{eqnarray} \tag{ R22 }$$

Reaction R22 is strongly endergonic (${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R22 = 133 kJ mol⁻¹) and, therefore, this reaction unlikely occurs. Once formed P₁ can undergo a nucleophilic attack by a second water molecule, forming the intermediate P₂ (see Fig. 5a):

$$\begin{eqnarray}&&{P}_{1}+{H}_{2}O\rightleftarrows {P}_{2}\end{eqnarray} \tag{ R23 }$$

This reaction is exergonic being ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R23 = −15 kJ mol⁻¹. The addition of another water molecule leads to the loss of oxalic acid and the formation of P₃ (see Fig. 5a). This reaction is strongly exergonic and ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R24 = −49 kJ mol⁻¹:

$$\begin{eqnarray}&&{P}_{2}+{H}_{2}O\rightleftarrows {P}_{3}+\,{H}_{2}{C}_{2}{O}_{4}(sol)\,\end{eqnarray} \tag{ R24 }$$

The hydrolysis degradation proceeds with the loss of a second molecule of oxalic acid and the formation of boric acid R25:

$$\begin{eqnarray}&&{P}_{3}+{H}_{2}O\rightleftarrows {H}_{3}B{O}_{3}(sol)+\,{H}_{2}{C}_{2}{O}_{4}(sol)\,\end{eqnarray} \tag{ R25 }$$

The last step is exergonic given that ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R25 = −27 kJ⁻¹ mol. Although R23, R24 and R25 are widely exergonic, the large positive energy difference observed in R22 hinders this hydrolysis path.

The comparison between the hydrolysis mechanisms of LiBF₄, LiODBF and LiBOB (see Fig. 6) allows to identify two possible reaction paths:

• 1.  
  LiF(s) precipitation and HF release;
• 2.  
  LiOH(s) precipitation.

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The first type mechanism is thermodynamically viable at room temperature; in fact, the hydrolytic path for fluorine-containing salts is exergonic or weakly endergonic. LiBF₄ can easily hydrolyze, whereas LiODBF shows a small Gibbs energy difference between reagents and products (${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ = 19 kJ mol⁻¹). This barrier is only slightly altered by the temperature, being ${{\rm{\Delta }}}_{r}{G}_{248K}^{o}$ = 15 kJ mol⁻¹, ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ = 19 kJ mol⁻¹ and ${{\rm{\Delta }}}_{r}{G}_{348K}^{o}$ = 23 kJ mol⁻¹. The second path, i.e. the LiOH(s) precipitation, is thermodynamically irrelevant at room temperature for all salts, due to the extremely high positive Gibbs energy variations. It is of interest to underline that apparently all the coordination of lithium ions in the solution to form chelating adducts with intermediate species are unlikely to occur being endergonic the corresponding Gibbs energy of reactions at 298 K (see Table SVII in the SI).

Overall, the precipitation of lithium fluoride and the release of hydrofluoric acid is the driving force of the hydrolysis of these fluorinated salts, leading to BF₂OH as the main degradation byproduct. In fact, the formation of BF₂OH in the pathway of hydrolysis of LiBF₄ is the possible thermodynamic endpoint of the fluoroborate hydrolysis. LiBOB does not contain fluorine atoms: thus the direct reaction with water exhibits only an insurmountable thermodynamic energy difference at room temperature to precipitate LiOH(s). From a kinetic point of view the energy barrier is even higher in consideration to the inevitable additional activation energy to initiate the reaction. This means that LiBOB is stable in presence of traces of water and the degradation of this salt likely occurs through more complex mechanisms, probably driven by electrochemical reduction/oxidation processes.

As a final point, we must consider the possible driving force to form solid lithium borate or lithium oxalate. In fact, the formation of boric acid, although in traces, can feed another reaction, R26, between H₃BO₃ and LiBF₄, to form LiBO₂(s):

$$\begin{eqnarray}&&\begin{array}{l}{H}_{3}B{O}_{3}(sol)+LiB{F}_{4}(sol)\rightleftarrows LiB{O}_{2}(s)\\ \,+\,B{F}_{3}+HF+{H}_{2}O\,\end{array}\end{eqnarray} \tag{ R26 }$$

Similarly, the formation of solid lithium oxalate must be considered in view of the reaction between H₂C₂O₄(sol) and LiODBF, R27:

$$\begin{eqnarray}&&{H}_{2}{C}_{2}{O}_{4}(sol)+LiODBF\rightleftarrows L{i}_{2}{C}_{2}{O}_{4}\left(s\right)+2ODBF+2HF\,\end{eqnarray} \tag{ R27 }$$

However, both R26 and R27 are endergonic, being ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R26 = 46 kJ mol⁻¹ and ${{\rm{\Delta }}}_{r}{G}_{298K}^{o}$ R27 = 291 kJ mol⁻¹, respectively, and it is, therefore, unlikely that LiBO₂ and Li₂C₂O₄ nucleate as final byproducts of borate-based salt hydrolysis.

In this work we studied the thermodynamics of hydrolysis of LiBF₄, LiODBF and LiBOB, as these salts are commonly used in lithium-ion batteries. We performed density functional theory calculations to compute the thermodynamic stability of reagents, reaction intermediates and products. We exploited thermochemical cycles to describe the realistic thermodynamic landscape of hydrolysis mechanisms, coupling literature assessed values for solid compounds (LiOH(s), LiF(s), H₃BO₃(s) and H₂C₂O₄(s)) with the quantities obtained by DFT calculations. We investigated the direct reaction of salts with water, observing two general reaction paths. The first is driven by the precipitation of lithium fluoride and the release of hydrofluoric acid, while the second one by the formation of lithium hydroxide. LiBF₄ and LiODBF likely react with water following both pathways; however, the degradation through the LiF(s)/HF channel is strongly favored. On the other hand, the F-free LiBOB salt is much more stable and apparently does not react with water following a simple chemical path. The degradation of LiBOB in LIBs electrolytes is probably driven by other more complex mechanisms, involving oxidation/reduction processes and will be the object of a future focused work.

The authors would like to acknowledge the financial support from the European Union Horizon 2020 research and innovation program within the Si-DRIVE project; grant agreement No. 814464. This manuscript is dedicated to Prof. Guido Gigli for his mentoring, tutoring and extraordinary teachings in the field of physical chemistry.