Review: Fermi level Electrochemical potential Inner, outer, surface potential, work function Inner potential difference, correct connection, absolute potential, relative potential (standard potential)

§2.2 Structure of Electrolyte/electrode surface 2.2.1 Surface charge Review: §2.2 Structure of Electrolyte/electrode surface 2.2.1 Surface charge 2) Transfer of charged species 1) Transfer of electrons Cu2+(aq) Cu Cu2+ e- Cu Zn Zn2+ e-

Review: 3) Unequal dissolution / ionization + AgI I¯ + 3) Unequal dissolution / ionization 4) specific adsorption of ions –  + + Electron atmosphere KCl HCl H+ K+ Cl- 6) Liquid-liquid interfacial charge 5) orientation of dipole molecules

Electroneutrality: qm = -qs Review: 2.2.2 Electric double layer – + Cu Cu2+ e- capacitor Electroneutrality: qm = -qs Holmholtz double layer (1853)

Review: 1) Ideal polarizable electrode E I E I

2.2.4 Interfacial structure: experimental Review: 2.2.4 Interfacial structure: experimental 1) Experimental methods: (1) electrocapillary curve measurement (2) differential capacitance measurement Lippman equation

2) Experiment equipment Review: 2) Experiment equipment When the composition of solution keeps constant

Electrocapillary curve Review: 3) Experiment results 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.

2.6.3 differential capacitance oscillograph 1) Measurement method Rs Rct Cdl Cd = C()

3) Experimental results Differential capacitance curves Review: 3) Experimental results Differential capacitance curves NaF Na2SO4 KI 0.0 -0.4 -0.8 -1.2 0.4  / V q / C·cm-2 4 8 12 -4 -8 -12 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

Review: 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

§2.3 Models for electric double layer Review: §2.3 Models for electric double layer 1) Helmholtz model (1853) d E

2) Gouy-Chappman layer (1910, 1913) Review: 2) Gouy-Chappman layer (1910, 1913) d E Plane of shear

Review: Gouy and Chapman quantitatively described the charge stored in the diffuse layer, qd (per unit area of electrode:) Boltzmann distribution Poisson equation  +  q qs c0

Review:

Review: 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

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

At low c0 At high c0 Cd dominant Ci dominant Cd  Ct Ci  Ct Inner layer + diffuse layer This may be seen as 2 capacitors in series: 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 model: what have been solved, what have not? Review: experimental calculation Fitting result of Gouy-Chapman Stern Fitting of 0.0001 mol·L-1 HCl Stern model: what have been solved, what have not?

The progress of Model for electric double layer Helmholtz model Gouy-Chappman model Stern model what have been solved, what have not? At higher negative polarization, the differential capacitance, approximately 18-20 F·cm-2, is independent of the radius of cations. At higher positive polarization, differential capacitance approximates to be 36 F·cm-2.

4) BDM model Bockris-Devanathan-Muller, 1963 Nom-electrostatic adsorption Electrostatic adsorption

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

Dielectric saturation di i =5-6 do i =40 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.

What have been solved, what have not? 0.0 -0.4 -0.8 -1.2 0.4 M / C·cm-2 -2 -4 -6 2 4 6 0.8 K+ F E-EPZC / V What have been solved, what have not? d E 0.0 -0.4 -0.8 -1.2 0.4 -5 -10 -15 5 10 15 0.8 K+ Br E-EPZC / V M / C·cm-2

Surface excess curves For R.E. in equilibrium with cation KF 0.0 -0.4 -0.8 -1.2 0.4  / V q / C·cm-2 -2 -4 -6 2 4 6 KAc KCl KBr Anion excess cation excess For R.E. in equilibrium with cation For any electrolyte

5) Gramham Model-specific adsorption Normal adsorption due to electrostatic attraction of cations  = 0  1  + Specific adsorption due to chemical adsorption of anions +  Overload adsorption

Triple layer Specifically adsorbed anions d E Triple layer Specifically adsorbed anions Helmholtz (inner / outer) plane

Summary: For electric double layer 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

1 = 0 validate only at high concentration or larger polarization §2.4 1 potential 1 = 0 validate only at high concentration or larger polarization 1  -1 x 1 potential at outer Helmholtz plane

GCS model When electrode bear negative charge Discussion: When c0 and are very small When c0 and are very large Influential factors: concentration and potential

Dependence of 1 on c -0.1 -0.2 0.0 -0.5 -1.0 -1.5 1 / V  / V 0.001 0.01 0.1 1.0

Dependence of 1 on  IHP OHP  / V d / Å Hg in NaCl solution 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 0.2 0.4 IHP OHP  / V d / Å Hg in NaCl solution

effect of 1 1. on concentration 2. on reaction rate x 1 -1 2. on reaction rate  3. on polarization

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

§2.3 Models for electric double layer 1) Helmholtz model (1853) 2) Gouy-Chappman model Primary water layer Secondary water layer Inner Helmholtz plane IHP 1 Outer Helmholtz plane, OHP, 2 3) Stern double layer (1924) 4) BDM model 5) Gramham Model §2.4 1 potential

2.5 Potential at zero charge (PZC, PZC) Definition: potential at which the electrode bears no charge. 2.4.1 Determination of PZC 1) Experimental method (1) electrocapillary curve (2) differential capacitance curve (most accurate ) (3) contact angle of gas bubble on the metal surface (4) surface hardness (5) wetting of surface

0.5 0.5 1.0  / Nm-1 0.3 0.4 q / Cm-2 0.3 E / V vs. SCE

2) Some experimental results of PZC Metals Electrolyte PZC Hg NaF -0.193 Bi (multicrystal) KF (0.002) -0.39 Bi (111 surface) KF (0.01) -0.42 Ag (111) -0.46 Ag(100) NaF (0.005) -0.61 Ag (110) -0.77 Cd NaF (0.001) -0.75 When the electrode potential is more positive than potential at zero charge, how is the electrode charged, positive or negative?

3) Difficulties in measuring PZC 1) purification of electrolyte and metal (why do we usually use mercury? ) 2) specific adsorption (includes adsorption of hydrogen) Hg-like metal: Cd, Sn, Pb, As, Sb, Bi; Ga, In, Tl Pt-like metal: Ni, Pt, Pd; Co; Rh, Ir; Ru. Os 3) crystal facet and multi-crystal

Differential capacitance curves of different crystal facets of Ag in 0 Differential capacitance curves of different crystal facets of Ag in 0.01 mol dm-1 NaF solution. 1. (100); 2. (100), 3. (111). Different crystalline facet has different differential capacitance and thus different potential of zero charge Ag (111) 0.001 moldm-3 KF -0.46 (100) 0.005 moldm-3 NaF -0.61 (110) -0.77 (MC) 0.005 moldm-3 Na2SO4 -0.7 Au +0.19 +0.50 +0.38 MC +0.25 For multi-crystal, its differential capacitance is the sum of all the differential capacitance of the surface of single crystal times their fraction.

4) Application of PZC Therefore: Surface potential () still exists due to the specific adsorption, orientation of dipoles, polarization of surface atoms in metal electrode, etc. Therefore: PZC can not be taken as the absolute zero point for the interphase potential.

Potential standard: 1) potential versus reference electrode (0); 2) potential versus PZC (PZC) Potentials refereed to PZC as zero point (E-EPZC) are named as rational potential standard.

5) Relationship between PZC and We For mercury-like metals: -1.0 -0.5 0.0 4.0 4.5 5.0 Ti Cd In Ga Zn Ag Sn Bi Hg Sb Cu Au

Theoretical calculation of electrochemical potential Vacuum +  M +  +  SHE

2.6 Interface adsorption and Graham Model The former four models for electric double layer are all electrostatic models without consideration of non-electrostatic interaction between species and electrode surface. influential factors: 1) valence type; 2) concentration; 3) size of solvated ions; 4) potential related to PZC Electrocapillary curve and differential capacitance curve in electrolytes with same valence type and concentration should be similar and neutral molecules have little effect on the curves.

2.6.1 Some experimental phenomena (1) Effect of ion on PZC NaF NaCl KBr KI K+ Ta+ N(C3H7)4+ Special adsorption of cations: Capillary curves of Hg in 0.01 mol dm-3 NaCl, NaBr and KI solution. Dependence of PZC on anion and concentration HS¯ > I¯ > Br¯ > Cl¯ > OH¯ > SO4¯ > F¯

(2) Effect of surface active agent on PZC C- curve for n-pentanol at a dropping Hg electrode in 0.1 M KCl Capillary curves of Hg in 0.01 mol dm-3 NaCl containing t-C5H11OH of different concentration.

(1) Adsorption of organic molecules 2.6.2 discussion (1) Adsorption of organic molecules At PZC, surface tension decrease dramatically, but at higher polarization, no significant change can be observed. Effect of potential on surface adsorption: around PZC, the adsorption attain maximum. At high potential, water may replace organic molecules already adsorbed on the electrode surface. And the arrangement of water molecules on the electrode surface may change accordingly.

As concentration of surface active reagent increases, the surface tension decreases, and finally attains a limiting value. Adsorption peaks appearing in differential capacitance curve Where Ci is integration capacitance When adsorption/desorption occurs, d(Ci)/d becomes astonishingly large – false capacitance. The peak of false capacitance marks the adsorption/desorption of the surface active reagent.

(2) Degree of coverage  can be used to characterize the formation of self-assembled monolayer, to evaluate the defect in polymeric coatings and determine the wetted area on substrate metal surface or water sorption of polymer materials.

S-Y ZHANG, et al., "Evaluation of thin defect-free epoxy coatings using electrochemical impedance spectroscopy", Journal of Applied Electrochemistry, 1998，28(11): 1277~1281

2.6.3 Other ways to measure adsorption Concentration change in solution; Electrochemical oxidation or reduction of adsorbed species (coulomb); Radioactive marks (radiation counter) EQCM: Electrochemical quartz crystal micro-balance (gravimetric method)