Table 1 Model parameters

From: Disentangling the Janus-faced effects of cations in electrocatalysis

Category

Item

Value

EDL parameters

Thickness of IHL, \({\delta }_{1}\)

\(2\,\mathring{\rm A}\)

Thickness of OHL, \({\delta }_{2}\)

\({d}_{i}/2\)

Permittivity of IHL, \({\epsilon }_{1}\)

\(8{\epsilon }_{0}\)

Permittivity of OHL, \({\epsilon }_{2}\)

\(30{\epsilon }_{0}\)

Permittivity of bulk solution, \({\epsilon }_{{{\rm{s}}}}\)

\(78{\epsilon }_{0}\)

Potential of zero charge, \({E}_{{{\rm{pzc}}}}\)

0.5 V vs. SHE for Au(111)

Cation properties

Effective diameter of Li+, \({d}_{{{{\rm{Li}}}}^{+}}\)

\(8\,\mathring{\rm A}\)

Effective diameter of Na+, \({d}_{{{{\rm{Na}}}}^{+}}\)

\(7\,\mathring{\rm A}\)

Effective diameter of K+, \({d}_{{{{\rm{K}}}}^{+}}\)

\(6\,\mathring{\rm A}\)

Charge number of per adsorbed cation, \({\xi }_{i}\)

0.85 for Li+, Na+, K+

Lateral interaction coefficient, \({\gamma }_{i}\)

3 for Li+, Na+, K+

Adsorption equilibrium potential, \({E}_{{{\rm{L}}}{{{\rm{i}}}}^{+}}^{0}\)

\(-1.65\,{{\rm{V}}}\) versus SHE

Adsorption equilibrium potential, \({E}_{{{{\rm{Na}}}}^{+}}^{0}\)

\(-1.27\,{{\rm{V}}}\) versus SHE

Adsorption equilibrium potential, \({E}_{{{{\rm{K}}}}^{+}}^{0}\)

\(-1.19\,{{\rm{V}}}\) versus SHE

Maximum coverage, \({\theta }_{\max }\)

0.5

Kinetic parameters

Solvent reorganization energy, \(\lambda\)

\(3\,{{\rm{eV}}}\)

Field-free H-OH bond strength, \({D}_{0}\)

\(4.7\,{{\rm{eV}}}\)

Coefficient for electric field effects, \(B\)

\(1.7\times {10}^{-9}\,{e}_{0}{{\rm{m}}}\)

Equilibrium potential of Volmer step, \({E}_{{{\rm{eq}}}}\)

\(-1.24\,{{\rm{V}}}\) versus SHE

Electronic interaction strength, \(\varDelta\)

\(3\,{{\rm{eV}}}\)

Active site density, \(\rho\)

\(0.14\,{\mathring{\rm A} }^{-2}\)

Transmission coefficient, \({\kappa }_{{{\rm{el}}}}\)

1

Nuclear barrier-crossing frequency, \({v}_{{{\rm{n}}}}\)

\(\frac{{k}_{{{\rm{B}}}}T}{h}\)