volume 1 thermodynamics and electrified interfaces

8/4/2019 Volume 1 Thermodynamics and Electrified Interfaces

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1

1

Electrode potentials

Oleg A. Petrii, Galina A. TsirlinaDepartment of Electrochemistry, Moscow State University, Moscow, Russia

1.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 External and Internal Potentials . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Electromotive Force (emf) and Gibbs Energy of Reaction . . . . . . . . 51.4 Diffusion Potential Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Classification of Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6 Membrane Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.7 Standard Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.8 Specific Features of Certain Reference Electrodes . . . . . . . . . . . . . 13

1.9 Values of Redox Potentials. . . . . . . . . . . . . . . . . . . . . . . . . . . .

151.10 Potential Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.11 Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.12 Effects of Ion Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.13 Absolute Electrode Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.14 The Role of Electric Double Layers . . . . . . . . . . . . . . . . . . . . . . . 201.15 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23


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3

1.1

Introductory Remarks

The term electrode potential combinestwo basic notions: electrode and poten-tial. The electrical potential , as knownfrom the physical definition, representsthe electrical energy (work term), whichis necessary for transferring a unit testcharge from infinity in vacuum into thephase under consideration. We call this

charge as probe (sometimes also testor imaginary) in order to emphasizethat it is affected only by the external fieldand does not interact with the mediumvia non-Coulombic forces, and, moreover,is sufficiently small to induce any chargeredistribution inside the phase. In actualpractice, the charges exist only in a com-bination with certain species (elementaryparticles, particularly, electrons, and ions).Hence, the value of appears to be beyondthe reach of experimental determination,

a fact that poses the problems concernedwith interpretation of the electrode po-tential and brings to existence numerouspotential scales. A number of discussionsof various levels can be found in the litera-ture [120].

A system that contains two (or more)contacting phases, which includes at leastone electronic and one ionic conductor,is usually considered as an electrode in

electrochemistry. Electrodes can be basedon metals, alloys, any type of semicon-ductors (namely, oxides and salts withelectronic or mixed conduction, electronconducting polymers, various covalentcompounds of metals), and also on avariety of composite materials. The cor-responding ionic conductors are usuallyelectrolyte solutions or melts, solid elec-trolytes (particularly, amorphous and poly-meric materials), supercritical fluids, and

various quasiliquid systems. In certaincases,the termselectrodeand electrodepotential are applied also to semiperme-able membranes the systems separatingtwo solutions of different composition (al-though these membrane electrodes donot exactly satisfy the definition givenabove).

Real electrodes sometimes represent ex-tremely complicated systems, which caninclude several interfaces, each locatinga certain potential drop. These inter-

faces, together with the phases in contact,take part in the equilibria establishedin the electrochemical system. This iswhy the electrode potential is one ofthe most important notions of electro-chemical thermodynamics (to say nothingabout its role in electrochemical kinetics),which describes the equilibrium phenom-ena in the systems containing chargedcomponents. The term component as


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4 1 Electrode potentials

applied to the charged species does notmean that the ions are considered as thecomponents amenable to Gibbs phaserule.

Consideration of equilibria in the sys-tems of this sort requires the applica-tion of the notion of electrochemicalpotential introduced by Guggengheim[21] on the basis of the relationshipfor the electrochemical Gibbs free en-

ergy

G:

dG = SdT + V dp +

i

i dNi

+ F

i

zi dNi (1)

where S is the entropy, V is the volumeof the system, T and p are its temperatureand pressure, respectively, i is thechemical potential of the ith species,Ni is the number of moles of the

ith component, zi is the charge of theith species taking into consideration itssign, and is the electrical potentialin the location point of the ith species,which is also called the internal (orinner) potentialof the corresponding phase[2226].

According to Eq. (1), the electrochemicalpotentials of the components, i , arecharacteristic values for the ith speciesin any phase under consideration:

i =

i + zi F

= G

Ni

p,T,Nj =i(2)

Only these values or the differencesof electrochemical potentials referred tophases and

i

i = (

i

i ) + zi F (

)

(3)are experimentally available.

1.2

External and Internal Potentials

The electrical state of any phase canbe characterized by its internal potential,which is a sum of the external (or outer)potential induced by free electrostaticcharges of the phase and the surfacepotential [6, 2326]:

= + (4)

When the free electrostatic charge inphase turns to zero, = 0 and = . The surface potential of a liquidphase is dictated by a certain interfacialorientation of solvent dipoles and othermolecules with inherent and induceddipole moments, and also of ions andsurface-active solute molecules. For solidphases, it is associated with the electronicgas, which expands beyond the lattice (andalso causes the formation of a dipolar

layer); other reasons are also possible.A conclusion of fundamental impor-tance, which follows from Eq. (3), statesthat the electrical potential drop canbe measured only between the points,which find themselves in the phases ofone and the same chemical composition.This conclusion was first formulated by

Gibbs. Indeed, in this case, i =

i and

=

=

i

i

zi F. Otherwise,

when the points belong to two different

phases, the experimental determination ofthe potential drop becomes impossible.Furthermore, these arguments imply thatthe difference between the internal poten-

tials at the interface, , cannot be mea-

sured. The quantity is called Galvani

potential and determines the electrostaticcomponent of the work term correspond-ing to the transfer across the interface,whereas the chemical component is


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1.3 Electromotive Force (emf) and Gibbs Energy of Reaction 5

determined by the difference between thechemical potentials. In the literature, theterm Galvani potential is also applied tothe separate value of internal potential.However, it is not significant, because ofthe relative nature of this value, which isdiscussed below.

The electrochemical equilibrium re-quires the equality of electrochemicalpotentials for all components in the con-tacting phases. From this conditionof elec-trochemical equilibrium, the dependenceof Galvani potential on the activities ofpotential-determining ions can be derived,which represents the Nernst equation [27]for a separate Galvani potential. That is,for an interface formed by a metal (M)and solution (S) containing the ions of thismetal Mz+,

MS = M S = const +

RT

zFln aMz+

(5)where M and S are the internal poten-

tials of metal and solution, respectively,and aMz+ is the activity of metal ions insolution.

The impossibility to measure a separateGalvani potential rules out the possibil-ity of establishing a concentration corre-sponding to MS = 0.

A formal consideration of Eq. (5) pre-dicts the infinitely large limiting value ofthe Galvani potential (MS ) whenthe activity of metal ions approaches zero(a hypothetical solution containing no ions

of this sort, or pure solvent). However,this is not the case, because the limitof thermodynamic stability of the solventwill be exceeded. For an ideal thermo-dynamically stable (hypothetical) solution,this uncertainty can be clarified, if theelectronic equilibria between the metaland the solvent are taken into account,which requires the consideration of sol-vated electrons (es) [711]. The latter are

real species present in any solution [27]; inaqueous and certain other media, theirequilibrium concentration is extremelylow, which, however, does not prevent usfrom formally using the thermodynamicconsideration of the electrode potential inthe framework of the concept of electronicequilibria. However, in real systems theexchange current density for Mz+/M pairappears to be so small in the limit underconsideration that equilibrium cannot bemaintained, and Eq. (5) no longer applies.

The equilibrium with participation ofsolvated electrons can be expressed by ascheme

M (solid) M (in solution)

Mz+ + zes (6)

The dissolved metal atoms can be con-sidered as an electrolyte, which dissociatesproducing Mz+ cations and the sim-plest anions, es. Actually, the condition

aMz+ = 0 cannot be achieved, because afinite value for the solubility productof metal exists, and, simultaneously, thecondition of electroneutrality is valid. Byusing the condition of the equality of elec-trochemical potentials of electrons in thesolution and in the metal phases, we ob-tain

MS =Me

Se

F= const

RT

Fln ae

(7)where Me and

Se are the chemical

potentials of electrons in metal andsolution, respectively.

1.3

Electromotive Force (emf) and GibbsEnergy of Reaction

To study the electrical properties of theM|Sinterface presented schematically in Fig. 1,


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MMS

S

M

MS

MS

Fig. 1 A scheme of potential drops atmetal|solution interface:MS metal/solution Galvani

potential; S and M thesolution/vacuum and metal/vacuumsurface potentials, respectively;MS metal/solution Volta potential.

it is necessary to construct a correctlyconnected circuit (Fig. 2) a galvanic cellsatisfying the condition of identical metalcontacts at both terminals. For the systemunder discussion, it is a circuit of thefollowing type:

M1|S|M|M

1 (8)

in which the electronic conductors M

1 and

M1 consist of the same material, differ-ing only in their electric states (all theinterfaces are assumed to be in equilib-rium). It is assumed that both terminalsof voltmeter used for measurement of thepotential consist of the same metal. It isevident that the measuring device with ter-minals also made of M1 records the totaldifference of electric potentials, or emf,

E = M

1M1

= M

1M +

SM1

+ MS

(9)which corresponds to the route of probe-charge transfer 1 2 3 and consistsof three Galvani potentials. On the otherhand, when going from M1 to M

1 via theroute marked by points 1 2 3 4

(Fig. 2), we obtain

E =

M

1

M1 =

M

S +

S

M1 +

M

1

M (10)Hence, the potential discussed can be

expressed by three values, which are calledVolta potentials (in some cases, contactpotentials). They represent the potentialdifferences between the points just outsidethe phases M and S in vacuum, and aremeasurable quantities. The distances from

M1M1 M1'M1

MM

1

11

22

4

2

3

33

Fig. 2 Illustration of twopossible routes of probe-chargetransfer in a correctly connectedcircuit.


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1.3 Electromotive Force (emf) and Gibbs Energy of Reaction 7

these points to the interface should besufficiently large, as compared with thecharacteristic distance of molecular andimage forces (up to 104 cm), and, at thesame time, not too high to prevent theweakening of interaction with the chargesinside the phases. Volta potential is ameasurable quantity, because the pointsbetween which it is measured are locatedin the same phase and exclusively in thefield of long-range forces. This means thatthe Volta potential does not depend on thecharge of the probe.

For the metal/metal boundary, these po-

tential differences (M

1M ) can be defined

by the difference of work functions [22].The latter can be obtained from the pho-toelectron emission (or thermoelectronemission) and also directly by using a cir-cuit

M1|M|vacuum|M1

where M1 is the reference metal. The main

experimental problems are the surfacepre-treatment (purification) and the elimina-tion of potential drop between the samplesof M1 and M in ultrahigh vacuum.

Volta potential for the interface metal(mercury)/solution can be found by usingthe following cell reference electrode|solu-tion|inert gas|Hg|solution|reference elec-trode when thesolutionflows to the systemthrough the internal walls of a vertical tube,where mercury flows out via a capillaryplaced axially in a vertical tube and is bro-

ken into drops. These mercury drops carryaway the free charges, thus eliminating thepotential difference in inert gas betweenHg and the solution. If a plate of solidmetal is used instead of liquid metal, it isnecessary to eliminate the potential dropmentioned above. A similar technique canbe used for the solution/solution inter-face. There are also other techniques ofVolta potential determination [16, 28].

The interface M

1|M (circuit 1.8) which,in the simplest case, represents a boundaryof two metals, is easy to construct.However,theM1|S contact, whichincludesan additional electrochemical interface, israrely feasible, being usually unstable anddependent on the nature of M1. Generally,in place of M1, a special electrochemicalsystem, the so-called reference electrodeshould be included into cell 1.8. The

electrode potential can be determinedas the emf E of a correctly connectedelectrical circuit formed by the electrifiedinterface under discussion and a referenceelectrode. According to this definition,the potential of any reference electrodeis assumed to be zero.

Thus, electrochemists deal with the val-ues of potentials, which are, actually, thedifferences of potentials. The nature of theemf of a circuit for potential measurementdepends on the type of the electrodes. Ifwe ignore a less frequent situation of ide-ally polarizable electrodes, for the majorityof systems, two half-reactions take placesimultaneously in the cell. For ideally po-larizable electrodes, their contribution toemf can be considered, in the first approx-imation, as the potential drop inside a ca-pacitor formed by the electric double layer.Hence, this drop depends on the electrodefree charge (see Sects. 1.3 and 1.5):

Ox1 + n1e Red1

(on the electrode under study), (11)Ox2 + n2e Red2

(on the reference electrode). (12)

Taken together, Eqs. (11) and (12) corre-spond to the chemical reaction:

1Red1 + 2Ox2 2Red2 + 1Ox1(13)


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the relationship for stoichiometric coeffi-cients being

n11 = n22 = n (14)

where n is the number of electronstransferred across the electrochemical cellin a single act of reaction (13).

From Eq. (3), the emf of the cell,which corresponds to reaction (13), can beexpressed as follows:

E = 1nF

(1Red1 + 2Ox2 2Red2

1Ox1 ) (15)

The right-hand term in parenthesesequals the Gibbs energy of reaction (13)with the opposite sign. Hence, the emfof an electrochemical cell (a cell witheliminated diffusion and thermoelectricpotential drops is implied, see later) corre-sponds to the reaction Gibbs free energy:

E = G

nF(16)

This statement is true also for morecomplicated reactions with the participa-tion ofN reactants and products, and canbe generalized in the form of the Nernstequation:

E = E0 RT

nF

Ni=1

i ln ai (17)

where the stoichiometric numbers i < 0for the reactants and i > 0 for theproducts, ai are their activities, n is the

total number of electrons transferred inthe coupled electrochemical reactions, andE0 is the standard potential, which isexpressed by the standard Gibbs freeenergy G0 as

E0 = G0

nF(18)

Underequilibrium conditions, the meanactivities or the activities of neutral

molecules (salts, acids) in Eq. (17) can besubstituted for partial activities of ions,whichcannot be measured experimentally.

The applications of various types ofelectrochemical cells to chemical thermo-dynamics are considered in Sect. 2.

Experimentally, the emf can be mea-sured either by compensating the circuitvoltage (classical technique which becamerare nowadays) or by using a voltmeterof very high internal resistance. The accu-racy of emf determination of about 1 Vcan be achieved in precise measurements,whereas common devices provide the ac-curacy of about 1 mV. The potential unitnamed Volt, which is used in the modernliterature (particularly, below), is the so-called absolute (abs) Volt; it differs slightlyfrom the international (int) Volt value. Theratio abs/int is 1.00033. To determine thesign of emf, a conventional rule is adopted,which states that the left electrode shouldbe considered as the reference one.

For carrying out the experimental mea-surements of electrode potentials, a systemchosen as the reference electrode shouldbe easy to fabricate, and also stable andreproducible. This means that any pair ofreference electrodes of the same type fabri-catedin any laboratory should demonstratestable zero potential difference within thelimits of experimental error. Additionally,the potential differences between two ref-erence electrodes of different type shouldremain constant for a long time.

Another point is that the transfer ofelectricity (although of very low quan-tity) occurs in the course of emf mea-surements. Thus, the reference electrodeshould comply with the requirement ofnonpolarizability: when the currents (usu-ally in the nanoampere range) flow acrossthe system, the potential of the refer-ence electrode should remain constant.One of the most important features that


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1.4 Diffusion Potential Drop 9

determines this requirement is the ex-change current density i0, which expressesthe rates of direct and reverse processesunder equilibrium conditions. This quan-tity determines the rate of establishmentof equilibrium (the state of the electricdouble layer is established very rapidly ascompared with the total equilibrium).

1.4

Diffusion Potential Drop

The use of reference electrodes frequentlyposes the problem of an additional poten-tial drop between the electrolytes of theelectrode under study and of the referenceone. For liquid electrolytes, this drop arisesat the solution/solution interface (liquid

junction). The symbol ... conventionally de-notes an interface of two solutions witha diffusion potential drop in between; ifthis drop is eliminated (see later), then the

symbol ...... is used. In this case, the equilib-rium is not exact because of the existenceof a diffusion potential drop diff. Thelatter has the meaning of Galvani poten-tial and cannot be measured; however, itcan be estimated by adopting a model ap-proach to the concentration distributionof ions in the interfacial region, the mod-els of Planck [29] and Henderson [30, 31]being the most conventional. The generalexpression for diff at the interface ofliquid solutions (1) and (2) is as follows:

diff = RT

F

(2)(1)

tizi

d ln ai (19)

where ti is the transport number of theith ion, that is, the portion of currenttransferred by this ion through the solu-tion. In the first approximation, diff canbe estimated by substituting correspond-ing concentrations for the partial activities.

In Plancks model for a sharp boundary,for a 1,1 electrolyte,

diff =RT

Fln (20)

where function can be found from atranscendent equation in which + and denote the sets, which consist of allcations and of all anions, respectively, and denotes the limiting conductivity of the

corresponding ion:

+

(2)+ c

(2)+

+

(1)+ c

(1)+

(2) c

(2)

(1) c

(1)

=

ln

i

c(2)i

i

c(1)i

ln

ln

i

c(2)i

i

c(1)i

+ ln

i

c(2)i

i

c(1)i

i

c(2)i

i

c(1)i

(21)

TheHendersonequationthat has gainedwider acceptance can be written as followsfor concentrations c having the units ofnormality:

diff =RT

F

i

i

zi

(c

(2)i c

(1)i )

i

i (c(2)i c

(1)i )

ln

i

i c(1)i

i

i c(2)i

(22)


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The solution is given for the case of asmeared out boundary and linear spatialdistributions of concentrations.

Generally, Eqs. (20) (22) yield similarresults; however, for junctions with apronounced difference in ion mobilities

(such as HCl... LiCl), the deviation can

reach about 10 mV. A specific feature ofthe Planck equation is the existence oftwo solutions, the first being close to that

of Henderson, and the second one beingindependent of the solution concentrationand of no physical meaning [32].

In practice, in place of model calcula-tions and corresponding corrections, theelimination of the diffusion potential isconventionally applied. This is achievedby introducing the so-called salt bridgesfilled with concentrated solutions of salts,which contain anions and cations of closetransport numbers. A widely known ex-ample is saturated KCl (4.2 M); in aqueoussolutions, potassium and ammonium ni-

trates are also suitable. However, therequirement of equal transport numbersis less important as compared with that ofhigh concentration of electrolyte solution,which fills the bridge [33, 34]. A suitableversion of the salt bridge can be chosenfor any type of cells, when taking into ac-count the kind of studies and the featuresof chosen electrodes.

In melts, an additional problem ofthermo-emf arises, and the emf correctioncan be calculated from thermoelectric

coefficients of phases in contact [35].

1.5

Classification of Electrodes

No universally adopted general classifica-tion of electrodes exists; however, whendealing with thermodynamic aspects of theelectrode potential notion, we dwell on the

electrode classification based on the natureof species participating in electrochemicalequilibria.

Electrodes of the first kind contain elec-tronic conductors as the reduced forms,and ions (particularly, complex ions) asthe oxidized forms. The equilibrium canbe established with respect to cations andanions; in the absence of ligands, thecations are more typical. The examplesare: Cu|Cu2+ . . . or . . . Au|[Au(CN)

2] . . . .

This group can be supplemented alsoby amalgam electrodes (or other liquidelectrodes) and electrodes fabricated fromnonstoichiometric solids capable of chang-ing their composition reversibly (interca-lation compounds based on carbons, ox-ides, sulfides, and multicomponent salts,particularly, Li-intercalating electrodes ofbatteries).

Electrodes of the second kind contain alayer of a poorly soluble compounds (salt,oxide, hydroxide), which is in contact with

a solution of the same anion. The equi-librium is always established with respectto anions. The most typical examples arebased on poorly soluble compounds ofmercury and silver (Table 1).

The redox polymers, both of organic andinorganic origin (such as polyvinylpyridinemodified by redox-active complexes of met-als; Prussian blue and related materials),can be considered as a version of electrodesof the second kind; however, the equilib-rium is usually established with respect

to cations. Electron conducting polymers(polyanyline, polypyrrol, and so forth) alsopertain, in the first approximation, to theelectrodes of the second kind, which main-tain equilibrium with respect to anion.Ion exchange polymer films on electrodesurfaces form a subgroup of membraneelectrodes.

Rather exotic electrodes of the thirdkind (with simultaneous equilibria with


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1.5 Classification of Electrodes 11

Tab. 1 Conventional reference electrodes [36]

Reference Potential versus Analogs Mediaelectrode SHE (aqueous systems,

recommended valuesfor 25C)

[V]

Calomel electrodes Mercurousbromide, iodide,iodate, acetate,oxalate electrodes

Aqueous andmixed (withalcohols ordioxane)

Saturated (SCE) 0.241(2)Normal (NCE) 0.280(1)decinormal 0.333(7)Silver chloride

electrode(saturated KCl)

0.197(6) Silver cyanide,oxide, bromate,iodate,perchlorate

Aqueous, mixed,abs. alcoholic

Nitrate AproticMercury/mercurous

sulfate electrode0.6151(5) Ag/Ag2SO4,

Pb/Pb2SO4

Aqueous, mixed

Mercury/mercuricoxide electrode

0.098 Aqueous, mixed

Quinhydroneelectrode

Chloranil, 1,4-nap-htoquinhydrone

Any withsufficientsolubility of

components0.01 M HCl 0.586(8)0.1 M HCl 0.641(4)

Note: NCE: Normal calomel electrodes; SCE: saturated calomel electrode.

respect to anions and cations) were alsoproposed for measuring certain specialcharacteristics, such as the solubility prod-uct of poorly soluble salts. The rareexamples are Ag|AgCl|PbCl2|Pb(NO3)2 . . .or M|MOx|CaOx|Ca(NO

3)2

. . . where M =Hg or Pb, and Ox is the oxalateanion.

When the metal does not take part inthe equilibrium and both components ofthe redox pair find themselves in solution,the system is called a redox electrode,for example, a quinhydrone electrodes(Table 1) or electrodes on the basis oftransition metal complexes:

Au|[Fe(CN)6]3, [Fe(CN)6]

4

or Pt|[Co(EDTA)], [Co(EDTA)]2

When equilibrium is established be-tween ions in solution and the gas phase,

we have gaseous electrodes; the inter-mediates of this equilibrium are usuallyadatoms: Pt, H2|H

+ . . ., or Pt, Cl2|Cl . . .

Palladium, hydrogen-sorbing alloys, andintermetallic compounds pertain to gase-ous electrodes. However, at the same time,these systems are example of intercalationprocesses operating under equilibriumconditions, which brings them close toelectrodes of the first kind.


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The various kinds of electrodes consid-ered above can be unified, if we take intoaccount the concept of an electronic equi-librium at metal/solution interface, thatis, bear in mind that a certain activity ofes in solution, which corresponds to anyequilibrium potential, exists.

1.6

Membrane Electrodes

A special comment should be given ofmembrane electrodes. The potential dropacross a membrane consists of the diffu-sion potential (which can be calculatedin a similar manner as that for com-pletely permeable systems) and two so-called Donnan potential drops, namedafter F. G. Donnan who was the first toconsider these systems on the basis ofGibbsthermodynamics [37]; moredetailedconsideration was given latter in Ref. [38].

The Donnan potential can be expressedvia the activities of ions capable of per-meating through the membrane, and itsvalue is independent of the activities ofthe other ions. This fact forms the basisfor the widespread experimental techniqueof measuring the activities in the systemswith eliminated diffusion potentials (ion-selective electrodes [39, 40]). The systembest known among the latter is the pH-sensitive glass electrode, for which themodes of operation, the selectivity, and

microscopic aspects were studied inten-sively [41]. Sensors of this sort are knownfor the vast majority of inorganic cationsand many organic ions. The selectivity ofmembranes can be enhanced by construct-ing enzyme-containing membranes.

The following brief classification ofmembrane electrodes can be used [42]:inert membranes (cellulose, some sorts ofporous glass); ion exchange membranes,

in which charged groups are bound withthe membrane matrix; solid membranesreversible with respect to certain ions (asfor glass electrode); biomembranes. Thesimplest model of a membrane electrodeis the liquid/liquid interface, which isprepared by contacting two immisciblesolutions and usually considered togetherwith liquid electrodes in terms of softelectrochemical interface (see Sect. 3.4).

1.7

Standard Potentials

Standard potential values are usually thoseof ideal unimolal solutions at a pres-sure of 1 atm (ignoring the deviations offugacity and activity from pressure andconcentration, respectively). A pressure of1 bar = 105 Pa was recommended as thestandard value to be used in place of1 atm = 101 325 Pa (the difference corre-

sponds to a 0.34-mV shift of potential). Ifa component of the gas phase participatesin the equilibrium, its partial pressure istaken as the standard value; if not, thestandard pressure should be that of theinert gas over the solution or melt. In acertain case, a standard potential can beestablished in a system with nonunity ac-tivities, if the combination of the lattersubstituted in the Nernst equation equalsunity. For any solid component of re-dox systems, the chemical potential does

not change in the course of the reaction,and it remains in its standard state. Incontrast to the common thermodynamicdefinition of the standard state, the tem-perature is ignored, because the potentialof the standard hydrogen (protium) elec-trode is taken to be zero at any temperaturein aqueous and protic media. The zerotemperature coefficient of the SHE corre-sponds to the conventional assumption of


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1.8 Specific Features of Certain Reference Electrodes 13

the zero standard entropy of H+ ions. Thisextrathermodynamic assumption inducesthe impossibility of comparing the valuesreferred to the hydrogen electrodes, in dif-ferent solvents. Of the systems regarded asreference electrodes, platinum hydrogenelectrodes exhibit i0 values ranked amongthe greatest known (103 102 A cm2,at least, in aqueous acidic solutions). Thistype of electrodes is used as the ref-

erence for tabulating universal potentialvalues [43 47].The universal definition of the standard

potential E0 of a redox couple Red/Ox isas follows: the standard potential is thevalue of emf of an electrochemical cell,in which diffusion potential and thermo-emf are eliminated. This cell consists of anelectrode, on which the Red/Ox equilibriaestablish under standard conditions, anda SHE.

1.8Specific Features of Certain ReferenceElectrodes

An important type of reference electrodesis presented by the so-called reversiblehydrogen electrodes (RHE) in the same so-lution, which makes it possible to avoidthe liquid junction. These electrodes arepreferentially used in electrochemical ex-periments when investigating the systemswith H+ and H2 involved in the process

under study (adsorption and electrocataly-sis on hydrogen-adsorbing surfaces, suchas platinum group metals). The RHE canbe produced for a wide range of pH; certainspecial problems associated with neutralsolutions can be solved by using buffer-ing agents. In media containing organiccomponents, the possible catalytic hydro-genation of the latter poses an additionallimitation for hydrogen electrodes.

In general, electrodes of the secondkind are more convenient as referenceelectrodes, because they do not requirea source of gaseous hydrogen. Dynamichydrogen reference electrodes, which rep-resent a wire of platinum metal (or anothermetal with low hydrogen overvoltage) ca-thodically polarized up to the hydrogenevolution, give a possibility of avoidingthe use of gaseous hydrogen. Their sta-ble potential values are determined by theexistence of the currentpotential relation-ship, which is possible for the electrodeprocesses with high degree of stability. Aspecial type of stable hydrogen electrodeis based on Pd hydride (-phase). Anotheradvantage of the electrodes of the secondkind is their applicability in a wider rangeof temperatures, and also suitability for awide range of pressures. Operating at hightemperatures presents a real challenge infinding a suitable reference electrode (al-though there are few examples stable up

to 250300 C). One should never use anyreference electrode containing mercury atelevated temperatures. For other referenceelectrodes (e.g., silver/silver chloride), sta-bility and reproducibility should be testedcarefully before it is used at temperaturesabove 100 C.

For aqueous hydrogen electrodes, thepotentiometric data are now available inboth sub- and supercritical regions, up to723 K and 275 bar [48]. However, their useas the high-temperature reference systems

involves numerous complications.Among reliable systems for high-temperature measurements, gaseous (firstof all, oxygen) electrodes based on solidelectrolytes of the yttria-stabilized zirconia(YSZ) type can be recommended, whichare always applied in the electrochemicalcells with solid electrolytes. Gaseous elec-trodes based on Pt or carbonare also widelyused in high-temperature melts, especially


13/584


those based on oxides (oxygen referenceelectrode) or chlorides (chlorine referenceelectrode).

There are lots of systems, especiallyfor electroplating and electrosynthesis, inwhich electrodes of the first kind can beused, without any liquid junctions (theexample is liquid Al in AlF3-containingmelts). More universal systems for meltsof various kinds are: a chlorine electrode inequimolar NaCl + KCl melt and Ag/Ag+

electrodes with the range of Ag+ con-centrations (0.01 10 mM) correspondingto usual solubility values. Reference elec-trodes of the second kind can hardly beused in melts because of the high solubilityof the majority of inorganic solids.

When studying nonaqueous systems bymeans of galvanic cells with aqueous ormixed reference electrodes, we cannotavoid liquid/liquid junctions and estimatethe corresponding potential drop fromany realistic model. In protic nonaqueous

media (alcohols, dioxane, acetone, etc.),a hydrogen electrode can be used; it isalso suitable for some aqueous/aproticmixtures. However, the i0 values for thehydrogen reaction are much lower ascompared with purely aqueous solutions.When studies are carried out in nonaque-ous media, in order to avoid liquid/liquidjunction preference should be given to thereference electrodes in the same solvent asthe electrode of interest.

In aprotic (as well as in protic and

mixed) media, the two reference sys-tems of choice are ferrocene/ferroceniumand bis(biphenil)chromium(I/0). The pen-tamethylcyclopentadienyl analog of theformer was recently shown to yield higherperformance [49, 50]. Among other typicalelectrodes, Ag/AgNO3 should be men-tioned. We can also mention specialreference systems suitable for certain sol-vents, such as amalgam electrodes based

on Tl and Zn in liquid ammonia and hy-drazine, and also Hg/Hg2F2 electrode inpure HF.

An exhaustive consideration of thespecific features of various reference

electrodes (fabrication, reproducibility andstability, modes of applicability, effectsof impurities, necessary corrections) canbe found in Refs. [36, 5154]. Nowadays,certain new findings in this field are

possible because of the novel approachesto immobilization of redox centers on theelectrode surfaces.

The attempts to interrelate the poten-tial scales in aqueous and nonaqueoussolutions have been undertaken and arestill in progress. Such a relationshipcould have been found if the free en-ergy of transfer was known at least forone type of charged species common tothe solvents. It is evident that ways ofsolving this problem can be based on

the assumptions beyond the scopes ofthermodynamics. Thus, it was mentionedin Ref. [18 20] that the free energy ofsolvation of Rb+ ion is low and approx-imately the same in different solventsbecause of its great size. However, anydirect application of rubidium electrodesis hampered by their corrosion activity aswell as by the fact that their potentiallies in the region of electroreduction ofa number of solvents. Another propositionconcerns the fact that the free energiesof transfer for certain cations and neu-tral molecules of the redox pairs A/A+

are the same in different solvents, whichis also caused by their great sizes [51].Ferrocen/ferrocenium-like systems weretaken as the A/A+ pairs. It is inter-esting that these scales rubidium andA/A+ adequately correlate with one an-other. Different extrathermodynamic as-sumptions are compared in Ref. [54].


14/584

1.9 Values of Redox Potentials 15

Special reference electrodes are intro-duced when considering the thermody-namics of surface phenomena on elec-trodes [55]. That is,when we use a virtualreference electrode potential, which is re-ferred to the electrode reversible withrespect to cation or anion in the same solu-tion, changes by a value of (RT/F) ln a(a is a mean activity coefficient), thenthe thermodynamic relationships can begeneralized for a solution of an arbitraryconcentration without introducing any no-tions on the activity of a separate ion(Sect. 5).

1.9

Values of Redox Potentials

The values of redox potentials were tabu-lated in numerous collections [4347], thelatest collections being critically selected.The potentials of redox systems with par-

ticipation of radicals and species in excitedelectronic states are discussed in Refs. [56,57]. There is no need to measure thepotentials for all redox pairs (and, corre-spondingly, G for all known reactions).If we obtain the partial values for a numberof ions and compounds, the characteristicvalues for any other reactions can be com-puted. The idea of calculation is based onthe fact that the emf value only dependson the initial and final states of the sys-tem, being independent of the existence

of any intermediate states. This fact is ofgreat importance for systems, for whichit is impossible, or extremely difficult, toprepare a reversible electrode (redox cou-ples containing oxygen or active metals).From considerations of the equilibria withparticipation of a solvated electron, theE0 value that determines the value of theconstant in Eq. (7) was estimated: 2.87 V(SHE) [56].

It should be mentioned that no standardelectrode can be experimentally achieved,because the standard conditions are hypo-thetical (no system is ideal at a unimolalconcentration and the atmospheric pres-sure). Hence, the majority of tabulatedvalues were recalculated from the data formore dilute solutions, usually after thepreliminary extrapolation to the zero ionic

strength. When dealing with the reverse

procedure (recalculation of equilibriumpotentials for dilute solutions from tabu-lated standard values), we should take intoaccount that in real systems the time ofequilibrium establishment increases withdecreasing concentration, because of thedecrease in rates of half-cell reactions.Hence, the possibility to prepare a re-versible electrode is limited to a certainconcentration value.

A famous collection of calculated poten-tials was presented by Pourbaix [46] for

aqueous solutions of simplest compoundsof elements with oxygen and hydrogen.Although this collection ignores the non-stoichiometry phenomena, which are ofgreat importance for many oxides and hy-droxides, it remains helpful for makingrough estimates and also predicting thecorrosion peculiarities. It should be notedthat these predictions cannot be observedin some systems under pronounced ki-netic limitations.

The shifts of reversible potentials of ox-

ide electrodes with composition were firstconsidered in Ref. [12] using the exampleof hydrated MnO2x , which demonstratesa wide region of inhomogeneity. Later, theconsiderations of this sort were carried outalso for other systems [58].

There are lots of empirical and semiem-pirical correlations of redox potentials withmolecular characteristics of substances,especially for the sequences of related


15/584


compounds, which can be used for semi-quantitative estimates of potentials ofnovel systems. The most advanced ap-proaches known from coordination chem-istry take into account -donating and -accepting abilities of the ligands, whichcan be expressed, for example, in termsof Hammett or Taft, and also other effec-tive parameters [59]. For the sequences ofcomplexes with different central ions andrelated ligands, the steric factors (namely,chelating ability) are knownto significantlyaffect the redox potentials.

A separate field deals with correlatingthe redox potentials with spectroscopicparameters, such as the energy of thefirst allowed dd transition in a complex,the energy of the metal-to-ligand charge-transfer band (i.e., the separation betweenthe HOMO (highest occupied molecularorbital) on the metal and LUMO (lowestunoccupied molecular orbital) on theligand), and nuclear magnetic resonance

(NMR) chemical shifts. The problemof extending these correlations over awider range of reactions, including thoseirreversible (for which the kinetics makesa substantial contribution to the formalpotential value, the latter being evidentlynonthermodynamic) was considered alongtime ago [60]. Advanced spectroscopictechniques are widely used for solving thereverse problem of determining the redoxpotentials of irreversible couples [61].

1.10

Potential Windows

The feasibility of determining the redoxpotential depends strongly on the solvent,the electrolyte, and the electrode material:all of them should remain inert in po-tential ranges as wide as possible. In thisconnection, the term potential window

is usually used, which characterizes thewidth of the interval between the poten-tials of cathodic and anodic backgroundprocesses. The narrow potential window

of water (about 1.31.4 V on platinumgroup metals, and up to 2 V on mercury-like metals, which do not catalyze thehydrogen evolution reaction) stimulatesthe potentiometric studies in nonaqueoussolvents. Aprotic solvents usually demon-

strate windows of about 33.5 V, if theoptimal supporting electrolyte is chosen.

An extremely wide window is known, forexample,forliquidSO2,whichisofhighestinterest for measuring extremely positiveredox potentials (up to +6.0 V (SCE)) [62].Low-temperature haloaluminate melts arehighly promising systems [63]. Finally, a

number of unique mixed solvents withextremely wide windows were found inrecent studies of lithium batteries [64].

Among electrode materials, the widest

windows are known for transition metaloxides, borides, nitrides, and some spe-

cially fabricated carbon-based materials. Itshould be mentioned that, if the nature

of electrode material can affect the formalpotential value by changing the mecha-nism and kinetic parameters, the solventfrequently has a pronounced effect on theequilibrium potential, because of the sol-vation contribution to free Gibbs energy.

1.11

Experimental Techniques

Direct potentiometry (emf measurements)requires the potentialof indicator electrodeto be determined by the potential of the re-dox pair under study. Sometimes this is

impossible, because of the low exchangecurrent densities and/or concentrations(particularly, at low solubilities or limited


16/584

1.12 Effects of Ion Pairing 17

stabilities of the components), when extra-neous redox pairs contribute significantlyto the measured potential. The sensitivityof direct potentiometry canbe enhanced byusing preconcentration procedures, partic-ularly in polymeric films on the electrodesurfaces [65]. However, it is common touse voltammetry, polarography, and otherrelated techniques in place of potentiom-etry. The formal potential (determined asthe potential between anodic and cathodiccurrent peaks on voltammograms) doesnot generally coincide with the equilib-rium redox potential, the accuracy depend-ing on the reaction mechanism [6668].For reversibleand simplest quasireversibleelectrode reactions, the exact determina-tion of standard potentials from the data ofstationary voltammetry and polarographyis possible. Only these dynamic techniquesare suitable for the studies of equilibriawith participation of long-living radicalsand other excited species, which can be

introduced into solution only by in situelectrochemical generating.

If voltammetric and related techniquesare used, the ohmic drop should be eithercompensated (now this is usually done bythe software or hardware of electrochem-ical devices [69]), or reduced by using, forexample, a Luggin (Luggin-Gaber) capil-lary (see in Ref. [12]). Another importanttechnical detail is that the componentsof reference redox systems (such as fer-rocene/ferrocenium) are frequently added

immediately into the working compart-ment when voltammetry-like techniquesare applied.

Applications of potentiometry are ratherwidespread, and its efficiency is highenough when operating with relative po-tential values. A mention should be made,first of all, of the determination of ba-sic thermodynamic quantities, such asthe equilibrium constants for coordination

chemistry and the activity coefficients. Thelatter task covers a wide field of pH-metricapplications, and also the analytical tech-niques based on ion-selective electrodes.

1.12

Effects of Ion Pairing

An important factor affecting redox po-

tentials is also ion pairing, which isconventionally taken into account in termsof activity coefficients. For redox potentialsof coordination compounds, the followingequation is known [70]:

E = E0 +RT

Fln

Kred

Kox(23)

where Kred and Kox denote the equilib-

rium constants of a complex (particularly,ion pair) formation. In as much as outer

sphere ionic association is highly sensitiveto the ionic charge, Kred appears to behigher than Kox, and the potential shiftsto more positive values with the ionicstrength. That is, for usual concentrationsof hexacyanoferrates in aqueous solutions,the shift induced by the association withK+ ions reaches 0.1 V and higher at usualconcentrations.

In electroanalysis, Eq. (23) forms the

basis of highly sensitive techniquesof potentiometric titration. The practi-cal applications are presented by numer-ous potentiometric sensors, particularlybiosensors [7174]. The potential mea-surements in microheterogeneous media(microemulsions; anionic, cationic andnonionic micelles) were worked out re-cently [75]. A separate field is the potentio-metric studies of liquid/liquid junctionsdirected to the determination of ionictransport numbers.


17/584


1.13

Absolute Electrode Potential

Although it has long been known that onlyrelative electrode potentials can be mea-sured experimentally, numerous attemptswere undertaken to determine the valueof potential of an isolated electrode with-

out referring it to any reference system(absolute electrode potential). Exhaus-tive and more particular considerations ofthe problem of absolute potential canbe found in Refs. [120, 7686]. Theseattempts were concentrated around thedetermination of a separate Galvani po-tential, MS (which was named initiallyas the absolute electrode potential) and also

included the search for a reference elec-trode, for which the maximum possiblework of any imaginary electrode processequals zero. Sometimes, the problem wasformulated as a search for the hypotheti-cal reference state determined as reckonedfrom the ground state of electron in vac-uum (a physical scale of energy with

the opposite sign). In this connection, therequirement for the reference electrodeunder discussion was formulated in theabsence of any additional electrochemicalinterfaces.

Finally, these studies have transformedinto a reasonable separation of the mea-sured emf for a cell, which consists ofan electrode under consideration and astandard reference electrode, in order to

determine two electrode potentials re-ferred to individual interfaces (or to theseparate half-reactions) by using only theexperimentally measurable values.

To illustrate the technique of Galvanipotential calculation, we return to the M|Sinterface. According to scheme in Fig. 1,

MS = MS

S + M (24)

and the problem reduces to the determi-nation of S and M, because the Voltapotential MS can be measured. The es-

timates of H2O for the water/air interfacewere made by considering the adsorptioneffects that inorganic acids, HClO4, andHBr [87, 88] and aliphatic compounds [89]exert on the Volta potential of water/airinterface, and also by measuring the tem-perature coefficient of H2O [90]. In this

connection, the measured real hydrationenergies of ions, G(real)hydr

, were compared

with the calculated chemical hydration en-

ergies, G(chem)hydr . The real (total or free)

energies were considered as the energychanges, which accompany the transferof ions from air to solution. This valuecan be divided into the chemical hydrationenergy, which is caused by the interac-tion of an ion with surrounding watermolecules, and the change of electric en-ergy that equals zi F H2O (where zi is the

charge of the ion of the correspondingsign):

G(real)hydr = G

(chem)hydr + zi F

H2O (25)

On the other hand, the real solvationenergy can be written as

G(real)hydr = Gsubl Gion

+ zi F MH2O

zi F We (26)

where Gsubl is the free energy of metalsublimation (atomization), Gion is thefree energy of ionization of a metal atom,We is the electron work function of M,and MH2O is the Volta potential of theinterface corresponding to the equilibriumpotential in a solution, in which theconcentration of metal ions is unity. The

most reliable values of G(real)hydr

were

reported in Ref. [91].


18/584

1.13 Absolute Electrode Potential 19

The value of G(chem)hydr

cannot be mea-

sured directly;however,it can be estimatedon the basis of information on the liq-

uid structure of water and the structure

of its molecule. Having G(chem)hydr

and

G(real)hydr

, we can find H2O from Eq. (24).

The estimates of this value given in the

literature for water/air interface disagree

with one another significantly (from 0.48up to +0.29 V). A critical comparative con-

sideration of various studies leads to a

conclusion about a low positive value of

H2O, namely, 0.13 V [1 9]. This value

corresponds to the infinite dilution and

can be changed by changing the solutionconcentration.

The estimation of M is an even

more complicated problem. Figure 3

schematically illustrates a metal boxcorresponding to the jellium model.According to this figure,

We = V F = e0M + Vex F (27)

the notations are given in the figurecaption. In the framework of the jelliummodel, we can calculate M by twotechniques: directly from the distributionof the electronic gas outside the metal, and

also by calculating Vex and F with thesubsequent use of Eq. (26). Unfortunately,the jellium model has a serious limitation;the estimates of M will be improved infuture as the theory of electronic structureof metals and their surfaces becomes moreadvanced.

As was correctly reasoned in Ref. [10,11], the scale of absolute potential

eF

We

V= Vex+ Vel

Fermi level

e0yM

electron in vacuum

(at infinity)

electron in vacuum(near the metal surface)

mMe/NA

Fig. 3 A scheme of electron energy levels for a model of metal box (according toC. Kittel, Elementary Solid State Physics, Wiley, New York, 1962): Me electrochemicalpotential of electron in metal, NA Avogadro number, F Fermi energy,

M outerpotential of metal, We electron work function, V electron potential energy in metal(V = Vex + Vel, Vex energy of electron exchange, which corresponds to the electroninteraction with positively charged jellium, Vel = e0

M the surface component ofelectron potential energy).


19/584


constructed in accordance with Ref. [7]and recommended in Ref. [9] is, in fact,equivalent to the EK scale first proposedin Refs. [7681], which should be namedafter Kanevskii:

EK = [Gsubl + Gion + G

(real)hydr

]

zi F(28)

By introducing this scale, we can sep-

arate the total emf of the cell into twoquantities, for which the contributions

Gsubl, Gion, and G(real)hydr

can be ex-

perimentally determined. For a hydrogenelectrode,

(EK)H+,H2

=

12 Gdiss + Gion + G

(real)hydr

F

(29)which gives the possibility to recommend

the value 4.44 0.02 V for the abso-lute potential of hydrogen electrode (at298.15 K). For other temperatures, the cal-culations of this sort are limited by thelack of information on the temperaturecoefficient of work function. It shouldbe mentioned that the uncertainty ofabsolute potential calculation is substan-tially higher than the accuracy of directpotential measurements with respect toa reference electrode. The useful com-ments to Kanevskiis scale can be foundin Refs. [1620, 84]. In the absolutescale, the absolute potential of anyaqueous electrode at 298.15 K can be de-termined as

EK = (EK)H+,H2 + E 4.44 + E(30)

where E is the potential referred tothe SHE. Two scales are combined forcomparison in Fig. 4.

The absolute potentials of the hydro-gen electrode in a number of nonaqueoussolvents are reported in Ref. [9].

The value of EK can be expressed viametal/vacuum electron work function andVolta potential [10, 11]:

EK = We + MS (31)

The majority of electrochemical prob-lems can be solved without separating

the emf into absolute potentials. How-ever, it should be mentioned that theproblem concerning the structure of theinterfacial potential drop becomes the top-ical problem for the modern studies ofelectrified interfaces on the microscopiclevel, particularly, in attempts of test-ing the electrified interfaces by probetechniques [92 94]. The absolute scalesare also of interest for electrochemistryof semiconductors in the context of cal-ibrating the energy levels of materials.This problem is related to another generalproblem of physical chemistry the de-termination of activity coefficient of anindividual charged species.

1.14

The Role of Electric Double Layers

Later, a more detailed consideration of theM|S interface is given, which takes intoaccount the formation of electric doublelayer. Figure 1 shows the potential drops

at the metal/solution interface. It followsfrom this figure that

MS = S + MS

M (32)

The value of the Galvani potential MS can be represented as the sum of thepotential drop inside the ionic double layer and the surface potentials of solutionand metal, which have changed as a result


20/584

1.14 The Role of Electric Double Layers 21

4.44

4

3.052.87

2.37

1.66

0.19

0.24

0.80

1.23

1.70

0.76

0.69

1.391.57

2.07

2.78

4.25

4.68

5.24

5.67

6.14

3.68

3.75

3

2

1

0

1

2

2

1

3

4

5

6

4.44

0 electrons at restin a vacuum

E

0

(Li+

/Li)

E0(Mg2+/Mg)

E0(Al3+/Al)

E0(Zn2+/Zn)

E0(Ag+/Ag)

E0(MnO4

/MnO2)

Hydrated electron

Potential of zero charge of gallium

Potential of zero charge of mercuryStandard hydrogen electrode (SHE)

Saturated calomel electrode (SCE)

Standard oxygen electrode (aH+ = 1)

Electrochemical

scale[V]

Physical

scale[eV]

(Absolute potential scale) = (Physical scale)E(abs) / V =E(SHE) / V + 4.44

Fig. 4 Comparison of SHE and absolute scales, as reported in Ref. [9].

of mutual contact:

MS = S(M) + M(S) (33)

where S(M) and M(S) are the sur-face potentials of solution and metal

at their common interface, respectively.Hence,

MS = S S(M) + + M(S) M

= + M S (34)


21/584


0 0.2 0.4 0.6

0

0.2

0.4

0.6

WeH

gWeM

e

[eV]

2

Sn

Sn

Ga

Tl

InIn

Cd

Pb

Cd

Ga

BiBi

1

Sb

EHg EMe ,EHg EMe

[V]s= 0 s= 0 s= 18 s= 18

Fig. 5 Correlation of work function differences and the differences ofpotentials at constant electrode charge for = 0 (1) and18 C cm2 (2), as reported in Ref. [5].

By writing such relationships for twointerfaces, M1|S and M2|S and substitut-ing corresponding M1S and

M2S into

Eq. (10), we obtain

E = MM1 + (1 2)

+ ( M1 M2 +

S2

S1 ) (35)

If the metals M1 and M2 interact veryweakly with the solvent molecules, we canassume that, in the first approximation,the last right-hand term in parentheses is

zero, and

E = MM1

+ (1 2) (36)

When both metals, M1 and M2, arezero charged (their excess surface chargedensity M = 0), and the ionic doublelayers are absent on their surfaces,

EM=0 M2M1

(37)

Eq. (36) and (37) obtained by Frum-kin [15] can be classified as the solutionof the famous Volta problem of the natureof emf of electrochemical circuit. Equa-tion (37) demonstrates that the differenceof potentials of zero charge (pzc) of twometalsis approximately equal to their Voltapotential. In as much as the Volta poten-

tial M2M1 is equal to the difference of

work functions of the metals (WM2e and

WM1e ), the verification of Eq. (37) can be

carried out by comparing the differencesboth in pzc and in work functions (Fig. 5).The data of Fig. 5 confirm Eq. (37) and, si-multaneously, demonstrate the possibilityof substantial deviations from this rela-tionship for the systems with pronouncedsolvent/metal interaction (as, for example,for the Ga/water interface).

In the context of concept of zero chargepotential [15], a specific scale of electrodepotentials should be mentioned, a reduced


22/584

1.15 Conclusion 23

scale, in which the potential of electrodereferred to its pzc for given solutioncomposition. It was used actively in thestudies of theelectric doublelayeras theso-called Grahame rational scale (see Sect. 5).

1.15

Conclusion

As mentionedearlier,the role played by theelectrode potential in electrochemistry andsurface science is not limited to thermody-namic aspects. The electrode potential isthe factor that governs (directly or via theelectrode charge) the surface reconstruc-tion and phase transitions in adsorbedlayers. It is also the key factor, which de-termines the Gibbs free energy of reactionand, correspondingly, the FrankCondonbarrier. In electrochemical kinetics, thecharacteristic value is not the potentialitself, but the overvoltage, which is the de-

viation of the potential from its reversiblevalue in the same solution when thecurrent flows across the electrochemicalinterface. The potential plays an impor-tant role in electrosynthesis, because thecontrolled potential electrolysis can be per-formedwith high selectivity,in theabsenceof foreign reagents (oxidizers or reduc-ers). The concept of membrane potentialis one of the basic concepts in biophysics.All these wide fields of science demon-strate the interplay with electrochemical

thermodynamics and provide the basis forfurther interpenetration of chemistry, bi-ology, and physics, which was pioneeredtwo centuries ago by the studies on theproblem of electrode potential.

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33

2.1

Electrochemical Interfaces: At the BorderLine

Alexei A. KornyshevResearch Center J

..ulich, J

..ulich, Germany and

Imperial College of Science, Technology andMedicine, London, UK

Eckhard SpohrResearch Center J

..ulich, J

..ulich, Germany

Michael A. VorotyntsevUniversite de Bourgogne, Dijon, France

2.1.1

Introduction

Most of the events in electrochemistry takeplace at an interface, and that is whyinterfacial electrochemistry constitutes themajor part of electrochemical science. Rel-evant interfaces here are the metalliquidelectrolyte (LE), metalsolid electrolyte(SE), semiconductorelectrolyte, and the

interface between two immiscible elec-trolyte solutions (ITIES). These interfacesare chargeable, that is, when the exter-nal potential is applied, charge separationof positive and negative charges on thetwo sides of the contact occurs. Suchan interface can accumulate energy andbe characterized by electric capacitance,within the range of ideal polarizability be-yond which Faraday processes turn on.

The interfaces dielectric electrolyte areless important in classical electrochem-istry, but are central for bioelectro-chemistry and colloid science. Theseare, e.g., ionic crystalelectrolyte, lipid-bilayer electrolyte, and protein elec-trolyte interfaces. Such interfaces are notchargeable, but they may contain chargesattached to surfaces. All these interfaces,chargeable or containing fixed charges,zwitter-ions or dipoles, are called electrified

interfaces.Properties of the interface play a crucial

role in electrochemical energy conversion,electrolysis, electrocatalysis, and electro-chemical devices. On the other hand, thechargeable interface can and has beenwidely used to probe various surface prop-erties. Indeed, due to Debye screening inelectrolyte, the electric field at the electro-chemical interface is localized in a narrowinterfacial region and the interface canbe easily charged to tens of C cm2 at

quite modest potentials. Physicists calledelectrochemistry a surface science with ajoystick. The potentiostat is the joystick,which allows to vary the electric field atthe interface from zero to 10 V A1. Mea-suring the given signal dependence onthe potential modulation makes it possi-ble to distinguish the terms related to theinterface, since the electric field in equi-librium is zero in the bulk. That joystick


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34 2 Electrochemical Double Layers

was not available in surface science, andthus physicists started to immerse solidsurfaces into the electrolyte environmentin order to probe the interface response tocharging.

Distribution of potential near a chargedinterface is crucial in electrode kinetics,since the potential drop plays the role ofa variable driving force of reaction. Thereactions take place at the interface andwith participation of adsorbed reactants.However, not only reactants but otherspecies as well can adsorb at the interface.Competitive adsorption of these species,ions or dipoles can play, depending on thesituation, a catalyzing or inhibiting role onthe reaction rates.

On the whole, understanding the struc-ture of the interface and its response tocharging is most essential for electrochem-istry andits implicationsfor colloid scienceand biophysics.

The electrochemical interface is com-

posed of molecules (solvent, adsorbedmolecular species) and ions (of electrolyte),which can be partially discharged whenchemisorbed, electrons and skeleton ionsin the case of metal electrodes, electronsand holes in the case of semiconductorelectrodes, mobile conducting and im-mobile skeleton ions in SEs. Moleculesand ions are classical objects but elec-trons, holes with small effective mass,and protons are quantum objects. Inter-action between molecules and surfaces

is quantum-mechanical in nature in thecase of chemisorption. Thus, microscopicdescription of the interface requires acombination of quantum and classicalmethods. One can benefit, however, fromsimple or more involved phenomenologi-cal descriptions of the interface.

In this chapter we will focus on charge-able interfaces: metal LE interface andITIES. Although similar in concepts and

methods, the extensive research area ofsemiconductor/electrolyte and metal/SEinterfaces will not be considered here.We will start with phenomenology, andthen move, where possible, to a micro-scopic theory and simulations. Without asolidphenomenological basis one may riskcalculating things from the scratch manytimes, whereas the calculation of one pa-rameter of the phenomenological theorymight be all that is actually needed from amicroscopic model! On the other hand, thephenomenology often receives its justifica-tion and validity criteria from microscopictheories.

2.1.2

Basic Concepts

Electrified interfaces represent the princi-pal object of interfacial electrochemistry.Various aspects of this area are describedin monographs and textbooks on this

subject [111]. A brief outline of this in-formation is given in the following text.

Electrified interfaces represent a spe-cific quasi two-dimensional object in thevicinity of the geometrical boundary oftwo phases containing, in general, mo-bile electronic and/or ionic charges, and,correspondingly, an electric-field distribu-tion generated by these charges. Practicallyat least one of these media in contact isconducting, while the second one maybe either a conductor of another kind

(metalelectrolyte interface, semiconduc-torelectrolyte interface), or of the samekind (interface of two immiscible elec-trolytes), or an insulator. As importantexceptions, one can point out pure sol-vent/air or pure solvent/insulator (e.g.silica-water) boundaries where a signifi-cant potential drop may be created by theformation of a dipole layer, without thegeneration of a space-charge region.


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2.1 Electrochemical Interfaces: At the Border Line 35

The simplest example is given by thefree metal surface. Owing to the Pauliprinciple the metal electrons at the highestoccupation levels possess a significantkinetic energy so that their density extendsoutside the ionic skeleton of the electrode.It results in the formation of a structurecharacteristic for numerous electrifiedinterfaces; two oppositely charged spatialregions (with zero overall charge), this timea positively charged region inside the ionskeleton due to the depletion of electronsand a negatively charged region formedby the electronic tail. Because of thisnanocondenser, the bulk metal has gota high positive potential of several Voltswith respect to the vacuum. This manifestsitself in the value of the electron workfunction the work needed to withdrawan electron from the metal across itsuncharged surface.

A more complicated example is providedby the contact of two electronic conductors,

metals or semiconductors. At equilibriumthe electrochemical potentials of electrons(i.e. their Fermi energies) must be equalin both bulk phases. The Galvani potentialdifference between them is determined bythe bulk properties of the media in contact,i.e. by the difference between the chemicalpotentials of electrons:

m1/m2 = m1e m2e

e(1)

where e is the elementary charge, since

the right-hand-side termsare constant,onecannot change the interfacial Galvani po-tential in equilibrium conditions withoutchanging the chemical composition of thephases. The difference between the bulkpotentials required by Eq. (1) has to be es-tablished by the formation of an electricaldouble layer (EDL) owing to the electronexchange between the surface layers of thephases. Finally, one of the surface layers

acquires an extra electronic charge, whilethe adjacent layer of another phase con-tains an excessive positive charge formedby the uncompensated ionic skeleton. Thethickness of each charged layer dependson the screening properties of the corre-sponding medium (their ThomasFermior Debye screening lengths) so that thewhole space-charge region is very thin fora contact of two metals (within 0.1nm),while it may be much more extended inthe case of semiconductors, depending ontheir bulk properties.

In all cases such interfaces are non-polarizable, since the only way to changethe interfacial potential difference is tomodify the bulk properties of the phase(s),for example, the degree of doping orstoichiometry for semiconductors.

Analogousionic systems are representedby a contact of two electrolyte solutions inimmiscible liquids, which contain a com-mon ion. Owing to its interfacial exchange

the electrochemical potential of this ion isto be constant throughout the system, andit leads again to a relation for the interfa-cial potential difference similar to Eq. (1)(called Donnan equation this time), that is,the interface is nonpolarizable without achange of the bulk media properties.

The same process of interfacial ion ex-change determines the potential differencefor other ion conductors, like membranesor SEs. The existence of this potential dif-ference again leads to the formation of the

EDL, but this time it is formed by exces-sive ionic charges in the surface layers ofboth solutions. Since this EDL is createdby the ion transfer across the interface,without charge transport across the bulkmedia, the Donnan potential drop corre-sponding to the composition of the phasesis established very rapidly.

Similar to the contact of two elec-tronic conductors, the imposition of a


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nonequilibrium potential difference bet-ween two ion conductors (having a com-mon ion) from the external circuit resultsin a dc current passage. Subsequent pro-cesses depend on the type of electrodereactions at the reversible electrodes im-mersed into the ion-conducting phases. Ifboth reactions generate or consume thesame exchangeable ion, even a long-termrealization of the process does not changethe bulk composition of the phases. Inthe case of the electrode reactions gener-ating or consuming different species, thelongtime application of this potential dif-ference will lead to electrolysis, that is, tothe gradual change of the composition ofthe bulk phases. The latter is accompaniedby the change of the equilibrium valuesof all interfacial potential drops (betweenion conductors and at both reversible elec-trodes), with the approach to a differentequilibrium potential difference.

The contact of solutions that possess

more than one common ion, in particularall contacts of solutions with identicalor miscible solvents, exhibits a morecomplicated phenomenon. At the initialstage, all exchangeable ions are transferredacross the boundary generating a long-living nonequilibrium structure, liquidjunction (LJ), which retains its diffusionpotential difference for an extended time,despite the absence of the thermodynamicequilibrium (different compositions) bet-ween the interphase and two bulk phases.

If the solutions in contact have the samesolvent, this potential drop is usuallyrelatively small, mostly within a fewdozen mV or less (but it may sometimesreach a much larger value for dilutesolutions even in the same solvent).Elaborated procedures for its calculationas a function of the solutions compositionexist [12]. For nonidentical solvents, thispotential difference may be much larger,

being primarily dependent on the solventproperties.

The principal object of electrochemicalinterest is given by another type of elec-trified interface, contacts of an electronic(liquid or solid metal, semiconductor) andan ionic (liquid solution, SEs, membranes,etc) conductor. For numerous contacts ofthis kind, one can ensure such ionic com-position of the latter that there is practicallyno dc current across the interface within acertain interval of the externally appliedpotential. Within this potential intervalthe system is close to the model of anideally polarizable interface; the change ofthe potential is accompanied by the relax-ation current acrossthe external circuit andthe bulk media that vanishes after a cer-tain period. For sufficiently small potentialchanges, dE, the ratio of the integratedrelaxation current, dQ, to dE is indepen-dent of theamplitude andit determines theprincipal electrochemicalcharacteristics of

the interface, its differential capacitanceper unit surface area, C:

C = S1 dQdE

(2)

S being the surface area. Its value canbe measured for each potential within theideal polarizability interval, and it variesgenerally as a function of this potentialas well as of the nature of the electrodeand the solution composition. The EDLfor such systems contains an excess

(positive or negative) electronic chargeat the electrode surface and the ioniccountercharge at the solution side. Thepossibility to freely change the interfacialpotential difference implies a qualitativeanalogy to a condenser whose separatedcharge is directly related to the above-mentioned quantity, dQ.

This simple picture gives a reasonableidealization of the interface in the case of


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2.1 Electrochemical Interfaces: At the Border Line 37

when the electronic and ionic charges ofthe EDL are separated by a layer of thesolvent molecules, as it is in the case of asurface-inactive electrolyte discussed inthe following text. The specific adsorptionof the ionic-solution components, that is,their significant accumulation in the im-mediate contact with the metal surface,is usually accompanied by the strong re-distribution of the electronic charge neareach adsorbed species. As a result theymay possess a much lower charge, com-pared to the one in the bulk solution(it is termed as adsorption with a par-tial or complete charge transfer). Underthese conditions the charge dQ suppliedvia the external circuit is not equal to thechange of the free electronic charge dis-tributed along the surface of the metal.Such perfectly polarizable electrodes re-quire a more elaborated description; seeChapter 3.1 of this book [13].

At approaching the limits of the ideal-

polarizability interval, the rate of faradaicprocesses at the interface increases rapidly(discharge of the solvent or solute compo-nents), with a dc current passing throughthe system.

The existence of this ideal-polariz-ability range of potentials is of greatpractical importance, since it allows oneto study an individual faradaic process ofthe added electroactive species in the pres-ence of the background electrolyte, whosepresence provides important advantages

(diminished Ohmic potential drop, rapidcharging of the EDL, etc).A specific type of the electrified interface

is given by the contact of an insulatingphase with electrolyte solutions. Since thecharged species cannot cross the insulator,the EDL formation originates from the ion-ization process of surface groups (most fre-quently, the proton-based dissociation orassociation) or/and the adsorption of ionic

components of the solution. As a resultthe EDL includes this fixed charge at thesurface and the counterions in the solutionpart. For a further discussion, see Ref. [14].

Such charged interfaces are typical forvarious ionic or polar solids, for ionexchange, lipid or biological membranes,or for any insulating surface in thepresence of amphiphilic solute species.Even though one cannot polarize thisinterface from the external source, thepotential difference and the separatedcharge can change as a function of thesolution composition, in particular its pHand ionic strength.

In many cases the solvent moleculesand solutes penetrate into the surfacelayer of the insulator, thus forming a gellayer composed of the components ofboth phases. Its thickness is sometimessignificant. Then the charge distributionacross such interphase is quite differentfrom the simple condenser idealization,

in particular the overall potential differ-ence between the bulk phases is composedof two contributions for the insulator gellayer and gel layer solution interfaces,with a plateau between them, if the gellayer is sufficiently thick [15].

This two-step profile of the potentialacross the interphase is also characteris-tic for certain types ofmodified electrodes inwhich the metal surface is coated with afilm, whose thickness significantly exceedsthe atomic scale. Such systems represent

a much more complicated type of electri-fied interfaces, since the distribution ofcharged species depends crucially on thespecific properties of the film. In mostcases of sufficiently thick films, the pro-file of the Galvani potential across theinterphase possesses a plateau inside thebulk film separating two potential dropsat its interfaces with the electrode and thesolution [16].


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Traditionally, special attention inelectrochemistry has been paid to themetalsolution interfaces. The interfacialpotential drop and the correspondingelectrode charge within the interval of theideal polarizability can be regulated by theimposed external voltage. The change ofthis voltage requires a supply of extraelectron and ion charges to both sidesof the interface across the correspondingbulk media. This charging process ismostly limited by the transport in thesolution (as well as inside the electrodein certain cases), since the relaxationtime inside the interfacial region itself(DebyeFalkenhagen time determined bythe double-layer thickness and the ion-diffusion coefficient, L2D/D) is extremelyshort. Generally the current distributionalong the electrode surface is nonuniformdue to geometrical reasons (shape andpositions of electrodes), hydrodynamicstructure, electrode surface properties, and

so on. If the effect of these factors issufficiently small, the charging processcan be described by a simple RC circuitcomposed of the Ohmic resistance of thesolution and the interfacial capacitance(multiplied by the surface area, S) definedin Eq. (2). This result is widely usedfor the measurement of this importantinterfacial characteristic, with the useof chronoamperometry or electrochemicalimpedance.

For liquid metals (mercury, gallium) ortheir alloys, one can measure another in-terfacial quantity, interfacial tension equalto the specific energy of the interfaceformation, , at different values of the elec-trode potential, E [1, 17]. At equilibriumthe Lippmann equation relates it to theelectrode-charge density , that is, to thecharge Q in Eq. (2) per

volume 1 thermodynamics and electrified interfaces

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