Previous class. Today. Porous Electrodes. Impedance of a film on electrode surface. Cylindrical pore

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1 Previous class Today Porous lectrodes ylindrical pore Impedance of a film on electrode surface Insulating or conducting film Point efect odel Surface harge pproach

2 Film on electrode surface R.. rmstrong, K. dmonson, lectrochimica cta, 97, 8, 97-9 Films may be an insulator or an electronic conductor lectrode Film lectrolyte m/f TL/FIL Z m/f Z f Z f/s R m/f f FIL ONUTOR f INSULTOR R f R FIL/SOLUTION R In film, movement of cation interstitial, electron and hole movement were considered Not analyzed in detail and was descriptive in nature If conc. of interstitial varies with distance, space charge has to be considered

3 Soft Film on electrode surface. acdonald, H.. ndreas, lectrochimica cta, 0, 9, lectrode Insulating Non- Porous Film lectrolyte lectrode Insulating Porous Film lectrolyte ouble Layer Film f dl R sol f dl R sol R f R t W lectrode onducting Film lectrolyte Film ouble Layer If f is a P, then film is porous f dl R sol R f R t W

4 Point efect odel (P), 98 onward Passive metals, anodic dissolution igby acdonald s group Film formation and dissolution are continuous processes Film has defects (vacancies, interstitials) Interstitial movements

5 Point efect odel Vacancy diffusion

6 P Seven reactions are considered m V e - v m k m V v e m. etal atoms goes into the film and fills a cation vacancy location. i.e. cation vacancy is consumed. etal-film interface does not move. Lattice conserving reaction

7 P m e - v m i k m v e i m. etal atom goes into the film as interstitial ion. etal-film interface does not move. Lattice conserving reaction. Interstitial is formed

8 P k m V ' e O m e - V O k m ' e O V ' e O. etal atom becomes metal ion, but does not move. Instead, we say film grows into the metal and an anion vacancy is created. Lattice non-conserving reaction

9 . nother way to visualize this is to think that when metal atom near the m/f interface is ionized, oxygen anions move from existing film to cation s neighborhood and form film; this generates anion vacancies in the film (near the m/f interface). Lattice nonconserving reaction P k m V ' e O m e - O O V O k m ' e O V ' e O

10 P V? e - k V e sol. etal ion in film (lattice) moves into solution. It may have a different charge ( > ) or same charge (=). Film /solution interface does not move. Instead, we say a cation vacancy is created in film. Lattice conserving reaction

11 P i? e - k 5 i e sol 5. etal ion interstitial in film moves into solution. It may have a different charge ( > ) or same charge (=). Film /solution interface does not move. Lattice conserving reaction

12 P V O H O O O H V H O O H O k6 O 6. n oxygen vacancy is filled (consumed) by reaction with water. Film/solution interface does not move. Lattice conserving reaction

13 P O H? e - H O O H H O e k 7 7. Film dissolves into solution. Lattice non-conserving reaction

14 P Salient points ations vacancies are created at solution side and consumed at metal side. They diffuse from solution side to metal side nion vacancies are created at metal side and consumed at solution side. They diffuse from metal side to solution side ation vacancies inside the metal are quickly moved very much into the metal ation vacancies, anion vacancies and cation interstitial movements can be rate limiting. Resulting impedance has the signature of Warburg e - impedance nions are large unlikely to be present as interstitial and diffuse If film is a good electrical conductor, electron and hole movements should also be considered Resulting impedance has signature of resistor

15 P Steady state conditions Film formation rate = film dissolution rate i i i i i i Total e h V V O i If anion vacancy transmission is dominant mechanism, then film is n-type semiconductor (e.g. W/WO ) If cation vacancy transmission is dominant mechanism, then film is p-type semiconductor (Ni/NiO) If cation interstitial movement is dominant, then film is n-type semiconductor e - (Fe/FeO x ) Z Z Z Z Z Z film e h V V O i

16 P oncentration of oxygen (anion) vacancies V O m/ f N W e F a q RT V O f / s N W e Fa q RT N - vogadro number, W- molar volume of oxide, a polarizability of film/solution interface, q = constant = dc + ac0 sin(wt) e - Use Fick s law, but account for movement due to electric field (Nernst Planck qn) F q t x RT x field strength q charge of vacancy /interstitial

17 P Potential drop across f/s interfaces depend on ph Potential drop across m/f interface depends on ph and film thickness L Lengthy derivation and complex expression, for anion and cation vacancies, interstitials Results some what similar to Warburg Impedance epending on material properties, it may appear similar to semi-infinite e - Warburg impedance odel predicts film thickness as a function of potential, impedance response of passive film, breakdown by pitting corrosion

18 P-II INNR, RRIR LYR TL OUTR LYR LTROLYT FIL should be viewed as bi-layer Inner barrier layer offers protection Inner layer grows into the metal Outer layer is formed when metal ion reacts with solution species and precipitates Outer layer may be porous, may contain solution Outer layer may be very thick compared to inner layer Note: ation interstitial was not used in P-I, although we have shown them in the earlier slides

19 P-III INNR LYR TL OUTR LYR LTROLYT FIL should be viewed as bi-layer In some materials, outer layer is very resistive and offers protection (e.g. valve metals like Ta) odel development so far restricted to pure metal and their films lloys not analyzed

20 P Zr immersed in (OH) + LiOH at high pressure and temperature acdonald, Russ. J. lectrochem. 0, 8(),5-58 Low frequency impedance in tens of kw-cm (or larger)

21 Surface harge pproach Proposed by artin ojinov, Univ. hem. Tech. et., ulgaria P uses Nernst Plank qn. escribes movement of ions in solution S uses Fromhold & ook qn. escribes movement of ions in discrete lattice ccumulation of ions or vacancies near the interfaces included Leads to a mid frequency inductive loop

22 Surface harge pproach S. attarin,. usiani,. Tribollet, J. lectrochem. Soc, (00), 9, 57-6 b R sol 0 R b R S L S b barrier film capacitance R b resistance to migration 0 faradaic pseudo capacitance R W electrolyte resistance R sc, L sc elements to represent ve surface charge near oxide solution interface

23 Surface harge pproach Nb in 5 NaOH, 60. ojinov, S. attarin,. usiani,. Tribollet, lectrochim. cta, (00), 8, 07-7

24 nion concentration nion incorporation within oxide film e-sheng Kong, Qufu Normal University, hina R sol b.s. Kong, Langmuir, 00, 6, b R sol 0 R b S model R b Z R S L S Not drawn to scale R S L S etal Oxide lectrolyte r F r O r r O r r O

25 Summary When a film is present on electrode surface, developing a suitable expression to describe the impedance is challenging In case of passive films and their breakdown, P appears to be the most successful model Variants of P such as S and I may be suitable to describe certain cases