Electrode/electrolyte interface: ----structure and properties Chapter 2 Electrode/electrolyte interface: ----structure and properties Electrochemical reactions are interfacial reactions, the structure and properties of electrode / electrolytic solution interface greatly influences the reaction. Influential factors: 1) Chemistry factor: chemical composition and surface structure of the electrode: reaction mechanism 2) Electrical factor: potential distribution: activation energy of electrochemical reaction

dG = -SdT + VdP + W’+idni §2.1 Interfacial potential and Electrode Potential 1) Electrochemical potential For process involving useful work, W’ should be incorporated in the following thermodynamic expression. dG = -SdT + VdP + W’+idni For electrochemical system, the useful work is: W’ = zie Under constant temperature and pressure, for process A  B:

1) Definition: Electrochemical potential zi is the charge on species i, , the inner potential, is the potential of phase . In electrochemical system, problems should be considered using electrochemical potential instead of chemical potential.

2) Properties: 1) If z = 0 (species uncharged) 2) for a pure phase at unit activity 3) for species i in equilibrium between  and . 3) Effect on reactions 1) Reactions in a single phase:  is constant, no effect 2) Reactions involving two phases: a) without charge transfer: no effect b) with charge transfer: strong effect

2) Inner, outer and surface potential (1) Potential in vacuum: the potential of certain point is the work done by transfer unite positive charge from infinite to this point. (Only coulomb force is concerned).  - strength of electric field

 (2) Potential of solid phase Electrochemical reaction can be simplified as the transfer of electron from species in solution to inner part of an electrode.  Vacuum, infinite charged sphere + This process can be divided into two separated steps. W2 +   10-6 ~ 10-7 m W1

(3) Inner, outer and surface potential Moving unit charge from vicinity (10 –6 ~10-7 m) into inner of the sphere overcomes surface potential (). Short-distance force takes effect . W2 +  (3) Inner, outer and surface potential The work (W1) done by moving a test charge from infinite to 10-6 ~ 10-7 m vicinity to the solid surface (only related to long-distance force) is outer potential. Outer potential also termed as Volta Potential () is the potential measured just outside a phase.  10-6 ~ 10-7 m W1 W2 For hollow ball,  can be excluded.  arises due to the change in environment experienced by the charge (redistribution of charges and dipoles at the interface)

W2  10-6 ~ 10-7 m W1 The total work done for moving unit charge to inner of the charged sphere is W1 + W2  = (W1+ W2) / z e0 =  +  The electrostatic potential within a phase termed the Galvani potential or inner potential (). If short-distance interaction, i.e., chemical interaction, is taken into consideration, the total energy change during moving unite test charge from infinite to inside the sphere:

distance infinite 10-6~10-7 hollow inner workfunction

(4) Work function and surface potential the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface or energy needed to move an electron from the Fermi energy level into vacuum.

3) Measurability of inner potential (1) potential difference For two conductors contacting with each other at equilibrium, their electrochemical potential is equal.   =

different metal with different Therefore

Galvanic and voltaic potential can not be measured using voltmeter.   No potential difference between well contacting metals can be detected Conclusion Galvanic and voltaic potential can not be measured using voltmeter.

(2) Measurement of inner potential difference 1 Fermi level 1’ If electrons can not exchange freely among the pile, i.e., poor electrical conducting between phases.

(3) Correct connection n 1 1’ Fermi level 1’ Knowing V,  can be only measured when

(4) Analysis of real system Consider the cell: Cu|Cu2+||Zn2+|Zn/Cu’ I S1 S2 II I’ For homogeneous solution without liquid junction potential the potential between I and II depends on outer potential difference between metal and solution.

Using reference with the same the exact value  of unknown electrode can not be detected. The value of IS is unmeasurable but the change of is [ (IS )] can be measured. absolute potential

Electrode/electrolyte interface: structure and properties Chapter 2 Electrode/electrolyte interface: structure and properties

2.4 origination of surface potential 1) Transfer of electrons Cu Zn Zn2+ e-

2) Transfer of charged species Cu Cu2+ Cu2+(aq) e-

3) Unequal dissolution / ionization + + AgI AgI AgI

4) specific adsorption of ions +

5) orientation of dipole molecules –  + + – Electron atmosphere

KCl HCl H+ K+ KCl HCl H+ Cl- 6) Liquid-liquid interfacial charge Different transference number

2) Transfer of charged species 3) Unequal dissolution 1) Transfer of electron 2) Transfer of charged species 3) Unequal dissolution 4) specific adsorption of ions 5) orientation of dipole molecules 6) liquid-liquid interfacial charge 1), 2), 3) and 6): interphase potential 4), 5) surface potential.

Electroneutrality: qm = -qs Electric double layer Cu Cu2+ e- – + capacitor Electroneutrality: qm = -qs Holmholtz double layer (1853)

Faradaic process and non-Faradaic process 2.5 Ideal polarizable electrode and Ideal non-polarizable electrode icharge iec equivalent circuit i = ich + iec Electrochemical rxn Charge of electric double layer Faradaic process and non-Faradaic process

i = ich ideal polarizable electrode an electrode at which no charge transfer across the metal-solution interface occur regardless of the potential imposed by an outside source of voltage. E I no electrochemical current: i = ich

Virtual ideal polarizable electrode Solution Hg K+ + 1e = K -1.6 V 2Hg + 2Cl- - 2e- = Hg2Cl2 +0.1 V Hg electrode in KCl aqueous solution: no reaction takes place between +0.1 ~ -1.6 V

i = iec ideal non-polarizable electrode an electrode whose potential does not change upon passage of current (electrode with fixed potential) E I i = iec no charge current: Virtual nonpolarizable electrode Ag(s)|AgCl(s)|Cl (aq.) Ag(s) + Cl  AgCl(s) + 1e

For measuring the electrode/electrolyte interface, which kind of electrode is preferred, ideal polarizable electrode or ideal non-polarizable electrode?

2.6 interfacial structure Experimental methods: 1) electrocapillary curve measurement 2) differential capacitance measurement surface charge-dependence of surface tension: 1) Why does surface tension change with increasing of surface charge density? 2) Through which way can we notice the change of surface tension?

The Gibbs adsorption isotherm   S S’ a a’ b b’ Interphase Interfacial region interface When T is fixed

Integration gives Gibbs adsorption isotherm

Lippman equation When the composition of solution keeps constant Electrocapillary curve measurement

Electrocapillary curve Zero charge potential: 0 (pzc: potential at which the electrode has zero charge) Electrocapillary curves for mercury and different electrolytes at 18 oC.

Theoretical deduction of

Differential capacitance Rs Rct Cdl Differential capacitance

Measurement of interfacial capacitance – + capacitor The double layer capacitance can be measured with ease using electrochemical impedance spectroscopy (EIS) through data fitting process.

Differential capacitance curves Cd = C() Integration of capacitance for charge density

Differential capacitance curves KF K2SO4 KCl KBr KI 0.4 0.8 1.2 1.6 0.0  / V Cd / F·cm-2 20 40 60 Dependence of differential capacitance on potential of different electrolytes.

Charge density on potential NaF Na2SO4 KI 0.0 -0.4 -0.8 -1.2 0.4  / V q / C·cm-2 4 8 12 -4 -8 -12

Dependence of differential capacitance on concentration Potential-dependent Concentration-dependent Minimum capacitance at potential of zero charge (Epzc) 36 F cm-2; 18 F cm-2; differential capacitance curves for an Hg electrode in NaF aqueous solution

Surface excess  +  q qs c0

For R.E. in equilibrium with cation For any electrolyte

Surface excess curves cation excess Anion excess KBr q / C·cm-2 KCl 6 KCl cation excess q / C·cm-2 4 KAc 2 KF Anion excess -2 KF -4 KCl KBr -6 KAc 0.4 0.0 -0.8 -1.2 -0.4  / V

2.7 Models for electric double layer 1) Helmholtz model (1853) d E Electrode possesses a charge density resulted from excess charge at the electrode surface (qm), this must be balanced by an excess charge in the electrolyte (-qs)

q charge on electrode (in Coulomb)

2) Gouy-Chappman layer (1910, 1913) Plane of shear d E Charge on the electrode is confined to surface but same is not true for the solution. Due to interplay between electrostatic forces and thermal randomizing force particularly at low concentrations, it may take a finite thickness to accumulate necessary counter charge in solution.

Boltzmann distribution Gouy and Chapman quantitatively described the charge stored in the diffuse layer, qd (per unit area of electrode:) Boltzmann distribution Poisson equation

Integrate from x = d to x = 

For 1:1 electrolyte For Z:Z electrolyte

Experimentally, it is easier to measure the differential capacitance: Hyperbolic functions

2) Gouy-Chappman layer (1910, 1913) For a 1:1 electrolyte at 25 oC in water, the predicted capacitance from Gouy-Chapman Theory. 1) Minimum in capacitance at the potential of zero charge 2) dependence of Cd on concentration

3) Stern double layer (1924) Combination of Helmholtz and Guoy-Chapman Models The potential drop may be broken into 2:

Inner layer + diffuse layer This may be seen as 2 capacitors in series: Ci Cd M S Ci: inner layer capacitance Cd: diffuse layer capacitance-given by Gouy-Chapman

At low c0 At high c0 Cd dominant Ci dominant Cd  Ct Ci  Ct Ci Cd M S Total capacitance (Ct) dominated by the smaller of the two. At low c0 At high c0 Cd dominant Ci dominant Cd  Ct Ci  Ct

Stern equation for double layer Discussion: When c0 and are very small

Discussion: When c0 and are very large Cd plays a role at low potential near to the p. z. c.

Fitting of Gouy-Chapman model to the experimental results Fitting result of Stern Model.

4) Gramham Model-specific adsorption Triple layer E d Specifically adsorbed anions Helmholtz (inner / outer) plane

5) BDM fine model Bockris-Devanathan-Muller, 1963

do i =40 di i =5-6 If rH2O = 2.7 10-10 m, i=6

The progress of Model for electric double layer Helmholtz model Gouy-Chappman model Stern model Graham model BDM model What experimental phenomenon can they explain?

of the electric double layer 2.8 Fine structure of the electric double layer Without specific adsorption – BDM model With specific adsorption – Graham model

Models of electric double layer Who can satisfactorily explain all the experimental phenomena in differential capacitance curve?

Stern model: what have solved, what not? As demonstrated last time, Stern Model can give the most satisfactory explanation to the differential capacitance curve, but this model can not give any suggest about the value of the constant differential capacitances at high polarization.

At higher negative polarization, the differential capacitance, approximately 18-20 F cm2, is independent of the radius of cations. At higher positive polarization, differential capacitance approximates to be 36 F cm2. As pointed out by Stern, at higher polarization, the structure of the double layer can be described using Helmholtz Model. This means that the distance between the two plates of the “capacitor” are different, anions can approach much closer to the metal surface than cations.

i = 5-6 i = 40 Capacitance of compact layer mainly depends on inner layer of water molecules. d i d o

If the diameter of adsorbed water molecules was assumed as 2 If the diameter of adsorbed water molecules was assumed as 2.7 10-10 m, i = 6, then The theoretical estimation is close to the experimental results, 18-20 F cm-2, which suggests the reasonability of the BDM model.

Inner Helmholtz plane 1 Outer Helmholtz plane 2 Specially adsorbed anion Solvated cation Weak Solvation and strong interaction let anions approach electrode and become specifically adsorbed. Primary water layer Secondary water layer

4. BDM model – Bockris, Devanathan and Muller, 1963

Summary: For electric double layer without specific adsorption 1. A unambiguous physical image of electric double layer 2. The change of compact layer and diffusion layer with concentration 3. The fine structure of compact layer