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
§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
10-6 ~ 10-7 m W1 e W2 + e e + + + + Vacuum, infinite charged sphere (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. This process can be divided into two separated steps.
W2 + 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. Moving unit charge from vicinity (10 –6 ~10-7 m) into inner of the sphere overcomes surface potential (). Short-distance force takes effect . 10-6 ~ 10-7 m Outer potential also termed as Volta Potential () is the potential measured just outside a phase. W1 For hollow ball, can be excluded. W2 arises due to the change in environment experienced by the charge (redistribution of charges and dipoles at the interface) (3) Inner, outer and surface potential
10-6 ~ 10-7 m W1 W2 The total work done for moving unit charge to inner of the charged sphere is W1 + W2 = (W1+ W2) / ze0 = + 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 work function 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
No potential difference between well contacting metals can be detected Conclusion Galvanic and voltaic potential can not be measured using voltmeter.
n n 1 1 Fermi level 1’ Fermi level (2) Measurement of inner potential difference If electrons can not exchange freely among the pile, i.e., poor electrical conducting between phases.
n 1 1’ Fermi level (3) Correct connection Knowing V, can be only measured when
I S2 II I’ S1 (4) Analysis of real system Consider the cell: Cu|Cu2+||Zn2+|Zn/Cu’ 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 IS is unmeasurable but the change of is [ (IS )] can be measured. absolute potential
Chapter 2 Electrode/electrolyte interface: structure and properties
Zn Zn2+ Zn2+ Zn2+ Zn2+ Zn2+ e- e- e- e- e- e- e- e- Cu 2.4 origination of surface potential 1) Transfer of electrons
e- Cu2+ Cu2+ e- Cu2+(aq) e- Cu2+ e- Cu Cu e- Cu2+ e- e- Cu2+ e- 2) Transfer of charged species
+ + I¯ + I¯ + I¯ + I¯ + I¯ + I¯ + I¯ 3) Unequal dissolution / ionization AgI AgI AgI
+ I¯ + I¯ + I¯ + I¯ + I¯ + I¯ + I¯ 4) specific adsorption of ions
+ + – – + – + – – + – + – – + – – + – – + – – + – – + – + – Electron atmosphere 5) orientation of dipole molecules
H+ Cl- HCl KCl KCl HCl Cl- H+ K+ H+ Cl- H+ H+ Cl- 6) Liquid-liquid interfacial charge Different transference number
1), 2), 3) and 6): interphase potential 4), 5) surface potential.
e- Cu2+ e- e- – + Cu2+ – e- + – + Cu – + e- – + Cu2+ – + e- – + e- Cu2+ e- Electric double layer capacitor Electroneutrality: qm = -qs Holmholtz double layer (1853)
iec icharge 2.5 Ideal polarizable electrode and Ideal non-polarizable electrode equivalent circuit i = ich+ iec Electrochemical rxn Charge of electric double layer Faradaic process and non-Faradaic process
I 0 E 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. no electrochemical current: i = ich
Electrode Solution Hg Virtual ideal polarizable electrode 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 0 E ideal non-polarizable electrode an electrode whose potential does not change upon passage of current (electrode with fixed potential) 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?
a’ a S’ S b b’ The Gibbs adsorption isotherm 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.
Cdl Rs Rct Differential capacitance 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
KI 60 Cd / F·cm-2 KBr KCl 40 K2SO4 20 KF 0.0 0.4 1.6 1.2 0.8 / V Differential capacitance curves Dependence of differential capacitance on potential of different electrolytes.
-12 q/ C·cm-2 -8 -4 0 NaF 4 KI 8 Na2SO4 12 0.4 0.0 -1.2 -0.8 -0.4 / V Charge density on potential
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
q qs + c0 Surface excess
For R.E. in equilibrium with cation For any electrolyte
Surface excess curves KBr 6 cation excess KCl q/ C·cm-2 4 KAc 2 KF 0 Anion excess -2 KF -4 KCl KBr -6 KAc 0.4 0.0 -1.2 -0.8 -0.4 / V
E 0 d 2.7 Models for electric double layer 1) Helmholtz model (1853) 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)
E 0 d 2) Gouy-Chappman layer (1910, 1913) Plane of shear 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.
Gouy and Chapman quantitatively described the charge stored in the diffuse layer, qd (per unit area of electrode:) Boltzmann distribution Poisson equation