Marcus P. Corrosion mechanisms in theory and practice

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The Hydrogen Surface Reactions in Aqueous Electrolyte

The H entry into a metal from an aqueous electrolyte is believed to involve the same

surface-bulk transfer step as in the gas phase, but the preliminary adsorption step is a

more complex process because more H sources are involved in aqueous solution,

allowing more possible H surface reactions, and also because of the specificity of the

electrolyte-metal interface. Whereas H adsorption in the gas phase occurs by

dissociative adsorption of gaseous H

on the free sites of a bare metallic surface, H

adsorption in aqueous solution may occur either chemically by dissociation of

dissolved H

or electrochemically from solvated (hydrated) protons or water

molecules; it takes place on a hydrated surface and thus implies the displacement of

adsorbed water molecules or specifically adsorbed ions and local reorganization of

the double layer [20]; competition with the adsorption of oxygen species formed from

the dissociation of water may also occur [21–23]. The adsorbed H layer is also in

interaction with surrounding water molecules, i.e., it is hydrated [8c,24,25].

Elementary Surface Reactions

Chemical H

Dissociative Adsorption and H-H Combination (Tafel

Reaction) Under conditions in which there is no specific adsorption of ions or

adsorption of oxygen species, the reaction of adsorption from H

2(g)

in aqueous

electrolyte occurs through the following steps:

Dissolution of H

gas into solution, in equilibrium: H

2(g)

' H

2(aq)

Transport of the dissolved H

molecules to the surface

Direct dissociative adsorption:

56 Protopopoff and Marcus

where H

2(aq)

is a dissolved H

molecule, 2(M)

(hyd)

represents a pair of adjacent

hydrated sites available for adsorption of hydrogen, and H

ads

(M)

(hyd)

represents

an H atom adsorbed in a site (M) and hydrated.

The reverse reaction is the combinative desorption of H atoms, or chemical

combination, also known as the Tafel reaction.

H Electroadsorption/Electrodesorption (Volmer Reaction) In aqueous

electrolyte, because the metal substrate is an electrode with the electric potential

as an additional variable, H adsorption may occur electrochemically (i.e., assisted

by the potential) by reduction of hydrated protons or water molecules, depending

upon the pH [26].

1. Proton discharge in acid medium: it involves:

(a) Fast transport of hydrated protons from the bulk solution to the double

layer between the electrolyte and the cathode surface

(b) H electroadsorption by electron transfer from the electrode to the hydrated

protons in the outer Helmotz plane [26]:

where H

(aq)

represents a hydrated proton, and e

–

(M)

an electron supplied

by the metal M.

2. Reduction of water in neutral or basic medium:

Surface Effects on Hydrogen Entry into Metals 57

Although there is no limitation to the supply of water molecules in not too

concentrated electrolytes (the water activity at the surface is equal to unity), this

reaction has a lower rate constant than proton discharge for a given potential so

that it is predominant only when the proton concentration is very low.

Electrodissociation/Electrocombination (Heyrovsky Reaction) The H atoms

can be desorbed electrochemically by combination with hydrated protons or water

molecules (Heyrovsky reaction or electrocombination). Again, depending upon

the pH, two types of reaction occur:

1. Proton plus H atom reaction in acid medium:

2. Water plus H atom reaction in neutral or basic medium:

H Surface-Bulk Transfer The transfer step from the adsorbed to the absorbed

state is equivalent to the reaction described for the gas phase [Eq. (2)] except that

it occurs from adsorbed H atoms surrounded by water molecules or anions and it

liberates surface sites for hydratation, as follows:

Overall Electrode Reactions

The H sources in solution, i.e., hydrated protons, and water molecules can be

transformed through the preceding elementary adsorption and desorption steps

into H

2(g)

(HER) or H

abs

(HAR).

Hydrogen Evolution Reaction This overall reaction involves the following

two-step pathways proceeding alone or in parallel:

1. Volmer-Tafel pathway: electroadsorption followed by chemical combination

2. Volmer-Heyrovsky pathway: electroadsorption followed by electrocombination

These steps are followed by transport of dissolved H

molecules away from the

electrode via diffusion or gas evolution (formation of nuclei and phase separation).

On a noble metal, equilibrium of the HER (reversible H

electrode) may

be attained provided that the partial H

pressure in solution is high enough because

the kinetics are fast; from thermodynamic arguments, the HER occurs with a net

rate if the potential is cathodic with respect to the equilibrium potential at the

given H

pressure and pH. Conversely, if the overpotential is anodic, the reverse

reaction, i.e., the H

oxidation reaction (HOR), prevails, involving H

dissociation

into adsorbed H followed by H electrodesorption [27].

On a corroding metal surface, a mixed process occurs because the main

reverse reaction is dissolution or oxidation (passivation); consequently, the net

current is a function of the overpotential with respect to the mixed (corrosion) potential

(see Chap. 1). The anodic reaction and the H cathodic reaction proceed simultaneously

close to the corrosion potential, which implies that the HER may occur on a surface

covered by an oxide film (passivated) and that the detrimental effects of anodic

dissolution and H entry may be combined in the embrittlement process.

The mechanisms of the HER on the metals currently studied in H entry

experiments are relatively well known. At high overpotentials they all involve a

coupled electroadsorption-electrocombination mechanism where the reverse steps

are negligible.

On electrodes of noble metals of the Pt group, the mechanism of the HER

involves at low overpotentials electroadsorption in quasi-equilibrium, followed by a

rate-determining step (RDS) of chemical combination, then electrocombination at

higher overpotentials [26,28].

On Ni, the reported mechanisms are electroadsorption in quasi-equilibrium

followed by rate-determining electrocombination [26,29].

On Fe, early experiments indicated coupled mechanisms, with electroadsorption

followed by chemical combination at low overpotential (low θ

) or electrocombination

at high overpotential (higher θ

) [30–32]. However, more recent analyses reported

a parallel pathways mechanism with the chemical and electrochemical combination

steps occurring simultaneously, the former being predominant in 0.1 N H

to high cathodic currents (current densities), whereas in 0.1 N NaOH or neutral

solutions the latter (involving water molecules) already predominates at low

cathodic currents [33,34]. The exact mechanism seems to depend on the structure

and purity of the iron electrode and its surface composition.

Underpotential and Overpotential H Electroadsorption The process of

reversible hydrogen electroadsorption occurs at the surface of metal electrodes of

the platinum group at potentials anodic to the reversible hydrogen electrode at the

given pH and at a pressure of 1 atm (half-standard reversible H

electrode at

1 atm, denoted RHE1 here): H is electroadsorbed at equilibrium at E>0V

(RHE1)

up to a quasi-full monolayer. Because this process occurs, going cathodically, under

the equilibrium potential of the RHE1, by analogy with underpotential metallic

deposition, it is often called H underpotential deposition (UPD) and the adsorbed

H UPD H [35]. Contrary to the HER, which is a steady faradic reaction consuming

the H species electroadsorbed at overpotential, for which a stationary state is reached

when the net rate of electroadsorption of reactants is equal to twice the net rate

of H

formation, H UPD is a pseudocapacitive faradic process; i.e., at a given

potential the adsorption current goes to zero once the equilibrium coverage

is reached,corresponding to equality between the rate of adsorption and the rate

of desorption of H atoms. It can be characterized only by transient techniques such

as cyclic linear sweep voltammetry, giving for cathodic and anodic potential

sweeps the well-known H adsorption/desorption pseudocapacitance peaks

[35–39], symmetrical if the sweep rate is not too high [35]. By integration of a

voltammogram, the electroadsorption/desorption charge flowing through the

interface per unit area during a potential scan is obtained, which allows

determination of the H surface density at a given potential. If the metal atomic

58 Protopopoff and Marcus

density is known (e.g., on a well-ordered single crystal surface), the coverage θ

(number of adsorbed H atoms per metal substrate atom) is obtained as a function

of the potential, giving electroadsorption isotherms [24,37,38,40–42].

UPD H detection is limited cathodically by the onset of the HER, producing a

steady current that is rapidly predominant; UPD is prevented on electrodes covered with

electronegative adorbates (see under Influence of the Surface Modifiers on H Entry),

and even on a clean electrode UP H adsorption may be hindered by competitive

anodic processes such as UP adsorption of O or OH and electrode oxidation

[23,29,43]. This explains why UPD H may be detected only on noble metals where the

anodic preoxidation processes occur at relatively high anodic potentials so that there is

a potential range where H atoms compete only with water molecules forming the metal

hydration layer and the specifically adsorbed anions [23,35,39,59]. However, H UPD

is not detected on Ag and Au, for which H adsorption from H

2(g)

is endothermic (see

later). On Pd, significant H absorption occurs at underpotential in bulk samples [44,45],

so equilibrium UP H adsorption may be characterized by cyclic voltammetry only on Pd

thin films in which the low number of bulk H sites limits the absorption reaction

[46,47]. On corroding or passivated metal electrodes, UPD H detection is impeded by

the metal dissolution and oxidation processes and the voltammograms are not easily

interpreted [43,48]; although some workers claimed that H electroadsorption occurs

in aqueous electrolytes above 0 V (RHE1) on Ni [49], Fe [50], or W [51], at present

there is no strong experimental evidence for this.

Conversely, the electroadsorption step involved in the HER at cathodic

overpotentials on all electrodes is called H overpotential deposition (OPD) and the

ads

intermediate involved in the HER is called OPD H [35]. Because overpotential

adsorption does not occur alone but is only a step in the steady HER process, it is

much more difficult to characterize. A technique of measurements of potential

relaxation transients (potential decay) could allow determining pseudocapacitance

versus potential curves and obtaining the OPD H coverage by integration [29], but

this is not straightforward. The OPD H fractional coverage is usually estimated from

analysis of the kinetics of the HER and HAR. OPD H is also likely to be the

intermediate of the HOR on Pt, in an anodic potential range overlapping that of UPD

H [27]. In principle, the electroadsorption of OPD H can occur under true

equilibrium only at the H

equilibrium potential, and the OPD H coverage

versus potential variation depends upon the HER or the HOR mechanism (see later).

It seems likely that the OPD H atoms reacting in the HER on Pt are adsorbed on top

of Pt atoms, while the UPD H atoms are adsorbed in high coordination sites [52,53]

(see later). There are no similar data for non-noble metals.

Hydrogen Electroabsorption Reaction (HEAR) In aqueous solution, the

hydrogen absorption reaction occurs mainly by electrochemical reduction of pro-

tons or water molecules (electroabsorption). The overall H electroabsorption reac-

tion from protons is:

It was demonstrated for iron, from the analysis of the relation between the

Surface Effects on Hydrogen Entry into Metals 59

stationary cathodic and anodic currents measured on each side of a permeation

membrane, that the HER and the HEAR share a common adsorbed H intermediate

ads

) and a common first step of electroadsorption [see Eqs. (4) and (5)] [31]; then H

enters the metal lattice by the surface-bulk transfer step [Eq. (8)], assumed to be in

quasi-equilibrium because in most cases the permeation rate is found to be limited

only by H diffusion through the bulk. This mechanism has been verified to be valid

for permeation through iron and nickel and their alloys and it is the generally

accepted one [28].

However, it has been suggested by Russian workers [54,55] for explaining the

effects of adsorbed I

–

ions on H permeation into Pd membranes that the process of H

electroadsorption in the HER and the process of electroabsorption “should be

regarded as occurring simultaneously and to a certain extent independently of each

other” [55]. Thus, on Pd the HAR would not occur by the pathway described before,

but by what has been interpreted since as direct H entry from protons [31,56]; this

mechanism was invoked for explaining Pd membrane permeation data showing an

anomalous relationship between steady-state cathodic and permeation currents [57].

Actually, because a direct entry would involve a quantum tunneling effect not likely

at room temperature (see section on gas phase), a classical activation mechanism of

H entry through a surface intermediate state different from the adsorbed state

involved in the HER (OPD H) is more rational and has to be considered as a

possible alternative to the preceding mechanism, at least on Pd. The observation that

significant H electroabsorption into bulk Pd already occurs at positive potentials

versus RHE1, before the HER takes place, and is likely to involve H UPD [44,58,59]

could be consistent with the so-called direct entry mechanism as UPD H is an inter-

mediate surface state different from the HER intermediate (see following section).

THERMODYNAMICS OF METAL-HYDROGEN SYSTEMS

Thermodynamics of H Adsorption and Absorption in the Gas Phase

Isotherms of the Metal-Hydrogen Equilibria

Isotherm of H

Dissociative Adsorption The equation of the isotherm of

equilibrium adsorption from H

2(g)

[see Eq. (1)] is

60 Protopopoff and Marcus

where θ

is the H surface fractional coverage in the sites (M), f

is the fugacity of

hydrogen gas expressed in atm, and ΔG

Hads

is the half-standard free energy of H

adsorption referred to ½H

2(g)

(ΔG

Hads

(θ

) = μ

Hads

(θ

)–½μ°

Η2

). ΔG

Hads

is in the

general case a function of the coverage θ

[60]. θ

is equal to the ratio Γ

/Γ

Hsat

the H

ads

surface density to the surface density at saturation. Γ

Hsat

is not necessarily

equal to the surface density of H sites on the given face because of H–H repulsive

interactions [8].

Isotherm of H

Dissociative Absorption (Dissolution) The equation of the

isotherm of equilibrium absorption (or dissolution) from H

2(g)

[see Eqs. (1) and

(2)] is the following:

where X

is the H bulk fractional solubility in the sites [M] and ΔG

Hdiss

is the

half-standard free energy of H dissolution from ½ H

2(g)

. ΔG

Hdiss

is the general

case a function of the fractional solubility X

, the fractional solubility of H in the metal or fraction of the intersticial sites

occupied by H, may be expressed as the ratio c

Hsat

of the H volumic concentration

to the concentration at saturation, or as r

Hsat

where r

is the hydrogen/metal (H/M)

atomic ratio and r

Hsat

is the ratio at saturation. In a particular lattice, only one kind of

interstitial sites is populated by H at moderate pressures. In the ideal case where there

were no H–H interactions, r

Hsat

would be equal to the number of those interstitial sites

per metal atom ( = 1 for octahedral sites in face-centered cubic (fcc) metals, 2 for

tetrahedral sites in hexagonal close-packed (hcp) metals, 6 for tetrahedral sites in

body-centered cubic (bcc) metals) [5].

Isotherm of H Surface-Bulk Transfer The equation of the equilibrium

isotherm for the surface-bulk transfer step [Eq. (2)] is [53,61,62]

Surface Effects on Hydrogen Entry into Metals 61

where E

dH2

is the dissociation energy of H

, equal to 436 kJ mol

–1

at 25°C. In

consequence, the values of the M–H

ads

bond energy at zero coverage fall in the

range 240–290 kJ mol

–1

, i.e., 2.5 to 3.0 eV [8c] (see Chapter 2).

Experimental heats of adsorption of H obtained on polycrystalline transition

metal surfaces are shown in Figure 2a [63]. Calculated and experimental adsorption

bond energies for H on the most close-packed surfaces of the transition metals

are given in Figure 2b [64]. A diminution of the chemisorption bond strength is

observed from center left to the right in each metal series (3d, 4d, and 5d).

Experimental data obtained on single crystals for the three low-index faces of

Pd, Ni, and Fe are shown in Table 1 of Chapter 2. It is deduced that the initial heat

of adsorption and adsorption bond energy depend slightly on the nature of the metal

and the surface orientation.

H Absorption The solubility of H in metals varies over a great range, from

–10

to 10

–1

mol cm

–3

[28]. According to the sign of the enthalpy of dissolution from

(g), metals are exothermic H absorbers (ΔH

Hdiss

< 0; the H solubility decreases

with increasing temperature) or endothermic absorbers (ΔH

Hdiss

> 0; the H solubility

increases with temperature). Among the transition metals, the exothermic absorbers

most often undergo a transition to a hydride phase when the bulk H/M ratio

increases. These are metals of columns 3 to 5 [65]. Most other transition metals are

endothermic absorbers and have very low H solubility at 25°C and 1 atm, especially

Cu, Ag, and Au in column 11 [66]. The well-known exception is Pd, which is an

exothermic absorber. When the H

pressure (or cathodic overpotential) increases, Pd

forms with H an α solid solution up to the terminal solubility 0.03 H/Pd at 25°C,

above which a β hydride phase with 0.55 H/Pd precipitates; then the H-saturated

Thermochemical Data

H Adsorption All transition metals from column 3 to 10, plus Cu, are

exothermic H adsorbers (ΔH

Hads

< 0; θ

decreases when the temperature increases).

For these metals, the values of the initial H adsorption heat on single crystal faces

[–ΔH

Hads

(θ

= 0) = ½H°

– H

Hads

(θH = θ)] fall in the range between 20 and

70 kJ mol

–1

[8]. The M–H

ads

bond energy at any coverage may be obtained from

the relation:

metal and the H-deficient hydride coexist until the ratio H/Pd = 0.55 is passed;

for very high pressures or overpotentials, the hydride may be enriched in H up to

the stoichiometric compound PdH. Also a special case is Ni: (fcc), which exhibits

the highest H absorption capacity of any purely endothermic absorber (solubility

at 25°C and 1 atm: ~ 10

–6

mol cm

–3

[28], 1–5 × 10

–5

H/Ni [67]; it may form a

hydride out of equilibrium, i.e., under very high pressures or overpotentials, up

to NiH [68]; Cr (bcc) also forms hydrides in these conditions. Both Mn and Cr

exhibit a minimum in solubility as a function of temperature, which means that

they change from exothermic absorbers at low temperatures to endothermic at

high temperatures [68]. Fe (bcc) has low H solubility (about 3 × 10

–9

mol cm

–3

2–3 × 10

–8

H/Fe [67] at 25°C and 1 atm).

62 Protopopoff and Marcus

Figure 2 (a) Experimental heats of adsorption of hydrogen on polycnstalune transition metal

surfaces. (From Fig. 2a in Ref. 63.) (b) Calculated and experimental chemisorption bond

energies for H on the most close-packed surfaces of transitions metals (1 eV ≡ 96.5 kJ mol

–1

(From Fig. 2 in Ref. 64, with permission from Elsevier Science.)

Table 1 Diagnostic Parameters for Various HER Mechanisms

Derivatives expressing the dependency of the H coverage, the HER current and the H bulk fractional concentration beneath the surface/steady permeation

current, on the potential and on the HER current, at given ΔG

ads

(given surface conditions), for the main HER mechanisms, and different values of the surface

coverage. The Tafel slope is related to the transfer coefficient α by the relation: ∂E/∂log i

= –RT ln 10/αF. Rigorously, the last two derivatives are to the

multiplied by the factor (1 – X

)/[1 + hX

(1 – X

)], which takes into account the limitation of bulk population due to possible interactions between dissolved

H atoms and saturation of the bulk sites. This factor drops to zero when θ

reaches unity. For endothermically absorbing metals, it can be considered as

practically equal to unity for moderate coverages (θ

≤ 1/2).

Figure 3 shows ΔH

Hdiss

at infinite dilution plotted for most metals [69].

Figure 4 shows an approximately linear correlation between values of –ΔS

Hdiss

(cal mol

–1

) and ΔH

Hdiss

for a given crystal structure [70], that is rather classic

(–ΔS

Hdiss

increases with –ΔH

Hdiss

): the larger the value of –ΔH

Hdiss

, the more tightly

bound the interstitial H and the lower its vibration frequency, hence the greater the

value of –ΔS

Hdiss,

the reduction in entropy from the gaseous state to the dissolved state.

The fcc and hcp metals give one correlation line and the bcc metals another one [70].

Thermodynamics of the M-H Equilibria in Aqueous Electrolyte

Isotherms of the Metal-Hydrogen Equilibria

Isotherm of H

Dissociative Adsorption/H-H Combination Under conditions

in which there is no competitive specific adsorption of ions or adsorption of oxygen

species in the H

ads

potential range, the equilibrium of the dissociative adsorption

from H

2(g)

in aqueous solution (or its reverse reaction, the chemical combination)

[see Eq. (3)] leads to the same adsorption isotherm as Eq. (10):

64 Protopopoff and Marcus

Figure 3 Enthalpies of solution of H at infinite dilution in metals; ΔH

∞

≡ΔH

Hdiss

in our

conventions. (From Fig. 6.3 in Ref. 69.)

where θ

, and f

have already been defined and ΔG

Hads(aq)

is the half-standard

free energy of adsorption in aqueous solution from ½H

2(g)

[60] (which is a priori

different from ΔG

Hads

in the gas phase because adsorption in aqueous solution

implies displacement of asorbed water molecules and reorganization of the

double layer) [20,23].

Isotherm of H Electroadsorption/Electrodesorption The equation of the

equilibrium H electroadsorption isotherm [see Eqs. (4) and (5)] is [53,58,61,71]:

where E

(SHE)

is the electrode potential referred to the reversible standard

hydrogen electrode; ΔG

Hads(aq)

has been defined. If the equation is rearranged to

involve the potential referred to the half-standard reversible hydrogen electrode in

the same electrolyte (a

, p

= 1 atm)(RHE1), E

(RHE1)

= E

(SHE)

– RT/F ln a

H+

We obtain the simpler expression [41,53,58,71]:

Surface Effects on Hydrogen Entry into Metals 65

Figure 4 Correlation between excess entropy and enthalpy of solution of H in metals;

ΔS

≡ΔS

Hdiss

= S

Hdiss

+ R ln X

/(1 – X

) – ½S°

. (From Fig. 3 in Ref. 70, with

permission from Elsevier Science.)

Isotherm of Electrodissociation / Electrocombination Similarly, the isotherm of

equilibrium electrodissociation of H

2(g)

[see Eqs. (6) and (7)] can be expressed as [61]

Isotherm of H electroabsorption (HEAR) The equation of the equilibrium

electroabsorption isotherm [Eq. (9)] is [53,61,62]:

with ΔG

Hdiss

as defined before for the gas-phase reaction [Eq. (11)].