BASIC PRINCIPLES OF ELECTRODE PROCESSES I 1. Ag (Ag+ ) Ag+ NO3 solid conductive phase – interface – liquid conductive phase Potential creation on interface   Heterogeneous system  2. Pt ( Pt-Ir, graphite) Fe2+ , Fe3+ ( SO4 2- ) spontaneous ion crossing 1. or electron transfer 2.  spontaneous interface charging: 1. Ag + + e  Ag 2. Fe3+ + e  Fe2+ 0x + z e  Red Structure of the interfacial region Electrode-solution interface Heterogeneous system  bulk electrode bulk solution EDL – electrolyte double layer EDL SCR SCR – space-charge region (thin) interfacial region Chemical potential: i = i o + RT ln ai i * = i + zF = 0 in balance i = /z/ F   = potential difference between solid phase and solution  inner (Galvani) potential, immeasurable! balance stabilization  electrochemical potential equality of ion i in both phases: i * (l) = i * (s) i * (l) = i + zF  chemical work electrical work Energy diagram for a non-charged metal Each chemical species (H2O, Na+, e-….) has an electrochemical potential (a quantity with units of energy) at any given location Contact between two metals having different work functions Measurable  cell potential EMN , made from 2 hemi-cells: standard hydrogen electrode SHE Eo = 0 V measured electrode E = b +  b = constant Ox 0 redoxredox aln zF RT EE  EMN = E - 0 = E Nernst : 1. 2. That was a balance   Ag 0 Ag/AgAg/Ag aln F RT EE red ox0 redoxredox a a ln zF RT EE      2 3 22 Fe Fe0 /FeFe/FeFe a a ln F RT EE 33 From within entered potential on electrode:  charge goes through an interface impossible of charging  impolarizedable interface (impolarizedable electrode, Ag / Ag+ )  charge doesn´t go through an interface possible of charging polarizedable interface (polarizedable electrode, Pt, graphite, Hg, without Hgz+ in solution) ELECTRODE DOUBLE LAYER (EDL) ELECTRODE DOUBLE LAYER electrostatic potential Φ charge density σ surface tension g capacity C adsorption G Electrode Solution φ Solution Solution Electrode Electrode -σM +σS - - - + + + + + + - + + - + - - - - - - - + - G surface tension g a) capillary elevation gρhrπcosΘγrπ2 2  cosΘ2 gρrh γ  b) stalagmometr (also DME) πrγ2gm  r2 gm γ   00 m:mγ:γ  gγ FF  2r Fg Fg h  capacity C adsorption G charge density σ Mσ E γ     Lippman equation d Δ M C E σ    differential capacity Cd integral capacity Ci i Δ M C EE σ     E E E E d z z dE dEC ii aβ -1      G G  Langmuir isotherm adsorption coefficientiβ ia activity of species i in bulk solution fraction of coverage surface or maximum surface excessG, Γ Temkin isotherm Frumkin isotherm )aβln( 2g RT Γ iii  RT 2gΓ exp ΓΓ Γ aβ i i i ii    g …. parameter treating the interaction energy between the adsorbed species Esin-Markov effect M aln )E( RT 1 β z ME            The degree of specific adsorption should vary with electrolyte concentration, just as there should be a change in the point of zero charge ELECTRODE DOUBLE LAYER STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE Electrostatic Models Helmholtz Model (1879) Gouy-Chapman Model (1910-1913) Stern Model (1924) Grahame Model (1947) Bockris, Devanathan, Müller Model (1963) Damaskin and Frumkin Trasatti Parsons Chemical Models Helmholtz Model (1879) H 0r d x εε C  history Electrode (metal) + Electrolyte - - - - - - + + + + + - - - - - - + - + + + + + + + - xH charges - points Cd E about 10-20 F/cm2 φ M φs xxH  = 5-7 Parallel-plate capacitor - neglects interactions - does not take into account any concentration dependence Gouy-Chapman Model (1910-1913) ElectrolyteElectrode (metal) - - - - - - + + + + + - - - - - - + - + + + + + - xxH φ φM φs c2 c1 c1 > c2 Cd EEZ diffuse double layer        Tk2 ze coshKC B 0, GC,d  - neglects interactions - ions are considered as point charges - there is no concentration maximum of ions to the surface Gouy-Chapman Model (1910-1913) distribution of species with distance from electrode Bolztmann´s law        Tk ez expnn B Δi0 ii  s           Tk ez expeznezn)x(ρ B Δi i i 0 i i ii  Poisson´s equation 0r 2 Δ 2 εε ρ(x) x (x)      (xDL = distance characteristic of the diffuse layer) Poisson-Bolztmann equation            Tk ez expzn εε e x (x) B Δi i i 0 i 0r 2 Δ 2  xDL = distance characteristic of the diffuse layer 21 220 i B0r DL ez2n Tkεε x        xDL for water at 298 K is 3.04*10-8 z-1c-1/2 cm if c = 1M and z = 1, then xDL is 0.3 nm diffuse layer thickness Gouy-Chapman Model (1910-1913)                   Tk2 ze sinhnεεTk8 x εε B 0,210 i0rB 0x 0rM    Gouy-Chapman Model (1910-1913)                   Tk2 ze sinhnεεTk8 x εε B 0,210 i0rB 0x 0rM                           Tk2 ze cosh Tk nεεez2 C B 0, 21 B 0 i0r 22 0, M GC,d        2 0, 21 GC,d cm.Fz5.19coshzc228C           Tk2 ze coshKC B 0, GC,d  Stern Model (1924) Electrolyte - - - - - - + + + + + - - - - - + - + + + + + + + -Electrode (metal) Compact Layer φ φM φs xxH Diffuse Layer C d EZ E OHP Stern Model (1924) GCHd C 1 C 1 C 1    )Tk2zecosh(Tknezε2ε 1 εε x B0 21 B 2 i 22 0r0r H   close to EZ, CH >> CGC and so Cd ~ CGC far from EZ, CH  CGC and so Cd ~ CH separation plane between the two zones is called the outer Helmholtz plane (OHP) Grahame Model (1947) Electrolyte - - - - - - + + + + + - - - - - + - + + + + + + + -Electrode (metal) - - - IHP - Inner Helmholtz Plane OHP IHP OHP - Outer Helmholtz Plane C d EZ -E E > EZ φ xxH Diffuse Layer OHP IHP E = EZ E < EZ Layer of oriented molecules of supporting electrolytes or solvents IHP OHP Electrolyte Electrode (metal) + + - + - + - + - + - + - + + - + + - + - - - - - - - + - - - - - - Bockris, Devanathan, Müller Model (1963) BDM Model - + + + Water concentration IHP - Inner Helmholtz Plane the first sovation layer OHP - Outer Helmholtz Plane the second solvation layer zeta or electrokinetic potential OHP  2 0 x2  x x2 2   x OHP adsorption CHARACTERISTIC OF ELECTRODE POTENTIAL IN DOUBLE LAYER Chemical Model (Damaskin and Frumkin) (Trasatti) (Parsons) ELECTRODE DOUBLE LAYER STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE - the electronic distribution of the atoms in electrodes (not only electrostatic forces) - difference between (sp) metals and transition (d)metals - IHP as an electronic molecular capacitor - jellium model Raman spectra, EXAFS:Extended X-Ray Absorption Fine Structure Variation of the electrostatic potentials with distance from a metallic electrode φM φs Classical representation φM φs The jellium model Chemical Models ELECTRODE DOUBLE LAYER STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE Electron spill-over at the surface of a metal according to the Jellium model. ELECTRODE DOUBLE LAYER STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE Radial distribution of potential for a metal sphere of radius R carrying a positive charge Q, illustrating the contributions of the outer potential and the surface potential. The inner potential is constant inside the sphere. ELECTRODE DOUBLE LAYER STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE Surface potential, the Volta potential and the Galvani potential differences for two phases in contact. Solid metallic electrodes φM (Galvani potential)  (Volta potential)  (surface potential) Electrode Solution φ x Solid metallic electrodes mercury solid electrode pc (polycrystal) mc (monocrystal) a well defined structure kBTe pc mc dislocation adsorption applied potential The orientation of a surface or a crystal plane may be defined by considering how the plane (or indeed any parallel plane) intersects the main crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices , (hkl) ; a set of numbers which quantify the intercepts and thus may be used to uniquely identify the plane or surface. The following treatment of the procedure used to assign the Miller Indices is a simplified one (it may be best if you simply regard it as a "recipe") and only a cubic crystal system (one having a cubic unit cell with dimensions a x a x a ) will be considered. Miller Index (hkl) Solid metallic electrodes (monocrystals) The Miller indices are found by determining the points at which a given crystal plane intersects the three axes, say at (a,0,0), (0,b,0), and (0,0,c). If the plane is parallel an axis, it is given an intersection . The Miller index for the face is then specified by ( 1/a, 1/b, 1/c), where the three numbers are expressed as the smallest integers, and negative quantities are indicated with an overbar. A face, when given with the crystal class, determines a set of faces known as a form and is denoted {a,b,c}. The vector normal to a face is specified as [a,b,c]. http://onsager.bd.psu.edu/~jircitano/Miller.html Surface of a monocrystal (110) and (100) Surface of a monocrystal (111) Cyclic voltammogram of a Pt(111) electrode having just been polished,flametreated and cooled in air. Solution: 0.5 M H2SO4. Sweep rate 50 mV·s–1 [Clavilier, J. Electroanal. Chem., 107(1980)205]. CV curve for Au(100) in 0.1 M H2SO4, starting with a freshly prepared reconstruction surface at – 0.2 V vs. SCE. Scan rate: 50 mV·s–1. Lifting of the (hex) reconstruction during the positive scan is seen by a pronounced current peak. The subsequent scan in negative direction reflects the electrochemical behaviour of Au(100)-(1×1). [Dakkouri& Kolb, in Interfacial Electrochemistry, Marcel Dekker, 1999] Cyclic Voltammetry I = f (E) i = f (E) Solid metallic electrodes Electrons Fermions valence band, valence energy, Fermi energy level the highest occupied molecular orbital in the valence band at 0 K „Fermi sea“ Solid metallic electrodes Copper Cu (Ar) 3d10, 4s1 The density of states occupied by electrons in a metal in the region of the Fermi level EF at different T Band Theory Copper Cu (Ar) 3d10, 4s1 Cu Cu 4s1 4s1 Cu2 Based on Quantum Molecular Orbital Theory E 4s 4s CuA CuB Cu2 σ* - antibonding σ - bonding BA SS  BA SS  CuA CuB CuA CuB + + - - node Band Theory Copper Cu (Ar) 3d10, 4s1 Based on Quantum Molecular Orbital Theory E Cu Cu4Cu2 Cu8 …. CuN filled empty from Cu2 to Cu(s) valence band conduction band S - bands Band Theory Zinc (Ar) 3d10, 4s2 Based on Quantum Molecular Orbital Theory E Zn2 Zn4 …. Znn filled empty from Zn2 to Zn(s) conduction band valence band Zn 4s 4p virtual orbitals T=0 T=T2 T=T1 E T=T2 T= T1 EF P0 1 T2 > T1 Fermi energy is the electrochemical potential of the electrons in the metal electrode kBTe pc mc dislocation adsorption applied potential Solid metallic electrodes P …. probability of occupation of a level of energy E EF …. energy of the Fermi level (electrochemical potential) E = EF - kBT…. P = 0.73E = EF + kBT…. P = 0.27E = EF ……. P = 0.50 E …. energy of electron   T/kEEexp1 1 P BF  EF Fermi energy level smeared occupationT Solid metallic electrodes P …. probability of occupation of a level of energy E   T/kEEexp1 1 P BF  E = EF - kBT…. P = 0.73 E = EF + kBT…. P = 0.27 E = EF ……. P = 0.50 E …. energy of electron EF ….Fermi energy level smeared occupationT Chemical Model (Damaskin and Frumkin) (Trasatti) (Parsons) ELECTRODE DOUBLE LAYER STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE - the electronic distribution of the atoms in electrodes (not only electrostatic forces) - difference between (sp) metals and transition (d)metals - IHP as an electronic molecular capacitor - jellium model Raman spectra, EXAFS:Extended X-Ray Absorption Fine Structure Variation of the electrostatic potentials with distance from a metallic electrode φM φs Classical representation φM φs The jellium model Chemical Models Conductor, semiconductor, insulator E conduction band valence band small band gap large band gap B, Si, Ge. As metalloids, conduct electricity – but not well overlap or no band gap yes or not, 0 or 1 Eg Eg> 3eVEg˂ 3eV Semiconductor electrodes  accessible electronic levels are more restricted  separation between the occupied valence band and the unoccupied conduction (smaller than 3 eV) (greater than 4 eV - insulator, for example diamond 5.4 eV) EV EF EC band model for a semiconductor The valency band is totally filled and the conduction band is empty Variation of density of available states with energy Conductivity – movement of electrons or holes in the valence band. Electron promotion to conductivity band – T, h excitation The Fermi energy – EF (EV+EC)/2 = EV+Eg/2 Eg         Tk2 expn B gE The number of excited electrons n Other electronic levels (surface states) can exist on the semiconductor surface due to adsorbed species or surface reorganization. n - type semiconductor (Si doped P, As) p - type semiconductor (Si doped B) semiconductor Eg/eV  /nm SnO2 3.5 350 TiO2 3.0 410 Si 1.1 1130 (considering the case Eg>>kBT) Semiconductor electrodes (SemiCEs) The major interest in semiCEs is due to: 1) the photoelectrochemical properties of the semiCE/electrolyte interface, 2) the generation of currents following exposure to elmg radiation (e.g., solar energy conversion), 3) optically transparent semiCEs are available for electrochromic displays and spectroelectrochemistry. The properties of semiCEs - their differences from those of metallic electrodes (the electronic structures) - energy bands, which are made up of the atomic orbitals of the individual atoms Semiconductor electrodes (SemiCEs) the energy gap between the upper edge of the valence band and the lower edge of the conduction band) that determines the properties of the material Electrons can be excited to the conduction band either thermally or photochemically. Semiconductor electrodes (SemiCEs) n-type: negative (electrons) p-type: positive (holes) Holes are considered to be mobile the vacancy Doping involves the addition of a different element into the semiconductor (group V element, e.g., P or a group III element,e.g., Al) into a group IV element, e.g., Si). The addition of P (V) into Si (IV) introduces occupied energy levels into the band gap close to the lower edge of the conduction band, thereby allowing facile promotion of electrons into the conduction band. The addition of Al (III) introduces vacant energy levels into the band gap close to the upper edge of the valence band, which allows facile promotion of electrons from the valence band. Semiconductor electrodes (SemiCEs) Another important concept in discussion of solid state materials is the Fermi level. This is defined as the energy level at which the probability of occupation by an electron is ½; for an instrinsic semiconductor the Fermi level lies at the mid-point of the band gap. Doping changes the distribution of electrons within the solid, and hence changes the Fermi level. For a n-type semiconductor, the Fermi level lies just below the conduction band, whereas for a p-type semiconductor it lies just above the valence band . 1) The Fermi level of a semicCE varies with the applied potential 2) The redox potential of a semicCEis determined by the Fermi level 3) In order for the two phases to be in equilibrium, their electrochemical potential must be the same The excess charge that is now located on the semiconductor does not lie at the surface, as it would for a metallic electrode, but extends into the electrode for a significant distance (100-10,000 Å). This region is referred to as the space charge region, and has an associated electrical field. Hence,there are two double layers to consider: 1) the interfacial (electrode/electrolyte) double layer 2) the space charge double layer. Semiconductor electrodes (SemiCEs) Semiconductor electrodes (SemiCEs) For an n-type semiCE at open circuit, the Fermi level is typically higher than the redox potential of the electrolyte, and hence electrons will be transferred from the electrode into the solution. Therefore, there is a positive charge associated with the space charge region, and this is reflected in an upward bending of the band edges For a p-type semiconductor, the Fermi layer is generally lower than the redox potential, and hence electrons must transfer from the solution to the electrode to attain equilibrium. This generates a negative charge in the space charge region, which causes a downward bending in the band edges Semiconductor electrodes (SemiCEs) Semiconductor electrodes (SemiCEs) Since the holes in the space charge region are removed by this process, this region is again a depletion layer. As for metallic electrodes, changing the potential applied to the electrode shifts the Fermi level. The band edges in the interior of the semiconductor (i.e., away from the depletion region) also vary with the applied potential in the same way as the Fermi level. The charge transfer abilities of a semiconductor electrode depend on whether there is an accumulation layer or a depletion layer. If there is an accumulation layer, the behavior of a semiconductor electrode is similar to that of a metallic electrode, since there is an excess of the majority of charge carrier available for charge transfer. In contrast, if there is a depletion layer, then there are few charge carriers available for charge transfer, and electron transfer reactions occur slowly, if at all. However, if the electrode is exposed to radiation of sufficient energy, electrons can now be promoted to the conduction band. If this process occurs in the interior of the semiconductor, recombination of the promoted electron and the resulting hole typically occurs, together with the production of heat. However, if it occurs in the space charge region, the electric field in this region will cause the separation of the charge. For example, for an n-type semiconductor at positive potentials, the band edges curve upwards, and hence the hole moves towards the interface, and the electron moves to the interior of the semiconductor. The hole is a high energy species that can extract an electron from a solution species; that is, the n-type semicoductor electrode acts as a photoanode. Semiconductor electrodes (SemiCEs) Ideal behavior for an n-type semiconductor electrode in the dark and under irradiation is shown in F7. At the flatband potential (Efb), there is no current, either in the dark or upon irradiation (Region II), since there is no electric field to separate any generated charge carriers. At potentials negative of the flatband potential (Region I), an accumulation layer exists, and the electrode can act as a cathode, both in the dark and upon irradiation (the electrode is referred to as a dark cathode under these conditions). At potentials positive of the Efb (Region III), a depletion layer exists, so there can be no oxidative current in the dark. However, upon irradiation, a photocurrent can be observed at potentials negative of the redox potential of the analyte (which lies at Eo ), since some of the energy required for the oxidation is provided by the radiation (via the high energy hole). Using similar reasoning, it can be shown that p-type semiconductor electrodes are dark anodes and photocathodes. There are a number of experiments used to measure the various parameters discussed above. The Efb can be determined by measuring the photopotential as a function of radiation intensity, the onset of the photocurrent, or the capacitance of the space charge region. The simplest method is to measure the open-circuit potential (photopotential) of the electrochemical cell under radiation of varying intensity. For a system under equilibrium, the photopotential is the change in the Fermi level due to the promotion of electrons to the conduction band, and it reaches a maximum at the Efb . Therefore, a plot of photopotential versus light intensity will attain a limiting plateau at the flatband potential. For the second method, although the onset of the photocurrent might be simplistically considered to be the flatband potential, it is actually the potential at which the dark current and photocurrents are equal. Therefore, such measurements should be used with caution. The third method involves measuring the apparent capacitance as a function of potential under depletion condition and is based on the Mott-Schottky relationship: Semiconductor electrodes (SemiCEs) Mott-Schottky plots (1/C2vs. E) are shown for a p-type silicon semiconductor and an n-type silicon semiconductor in F8 and F9, respectively (2). The donor density can be calculated from the slope, and the flatband potential can be determined by extrapolation to C = 0. The capacitance values are calculated from impedance measurements. The model required for the calculation is based on two assumptions: 1. There are two capacitances to be considered, that of the space charge region and that of the double layer. Since these capacitances are in series, the total capacitance is the sum of their reciprocals. As the space charge capacitance is much smaller than double layer capacitance (2-3 orders of magnitude), the contribution of the double layer capacitance to the total capacitance is negligible. Therefore, the capacitance value calculated from this model is assumed to be the value of the space charge capacitance. 2. The equivalent circuit used in this model is a series combination of a resistor and a capacitance (the space charge capacitance). The capacitance is calculated from the imaginary component of the impedance (Z") using the relationship Z" = 1/2 π fC. The model is adequate provided the frequency is high enough (on the order of kHz). Semiconductor electrodes (SemiCEs) Ideal behavior of n-type conductor on the dark and under irradiation Mott-Shottky plot n-type semiconductor p-type semiconductor