Previous class. Today RMA. Mass Transfer Effects. Non-Langmuir examples Summary of RMA. Accounting for diffusion

Transcription

1 Previous class Toay RM Non-Langmuir eamples Summary of RM Mass Transfer Effects ccounting for iffusion

2 Mass Transfer Only Simple Electron Transfer Reaction i k k No stirring. L - semi infinite thick With rotation. L finite thickness () Electroe. Reaction is + e - iffusion In ounary layer X=0 X= ulk Electrolyte Oiize Reuce k k 10 bulk 10 bulk k i k e i0 be i b b 1 1, RT 1 RT

3 Mass Transfer Steay State Solution pply potential Species (,), consume or prouce ick s law of iffusion t t i 2 2, 2 2 be 1 k10e 0, t b1e k10e 0, t Steay State. /t = 0 ounary onitions. t =0 i n 0, t 0, t t =, bulk bulk

4 Mass Transfer ounary onitions. t =0 Steay State Solution i n 0, t 0, t t =, a b S bulk bulk S k k bulk 1c bulk 1c bulk k k 1c 1c S bulk bulk S i k k

5 Mass Transfer t = 50 m. Steay State Solution Levich iffusion layer thickness equation 1.61 r

6 Mass Transfer E E E E E t c ac c ac k k 1 b E, 1 1c 1 k k 1b E ac 1 1c 1 ac sin i i i c ac Impeance calculation i k k nrze Lasia, Univ e Sherbrooke, anaa 0 0 i k1 c 1 b1 Eac E , ss ac k c b Eac E 0, ss ac E E onsier E, an as 3 inepenent variables (e.g. vary rpm an hence ()) i i i i i E ac E, E, E, i E, E bk b k 1 1c 0 1 1c 0 ac E i i k, 1c 1c E, E, k To fin an, solve ick s Eqn.

7 Mass Transfer in magnitue an phase of =0 as a function of t, an E ac0 (or i ac0 an f i ) We convert PE to OE by assuming the form of solution in time e ac ac0 tf s long as E ac0 is small enough, -ac0 can vary with an, an is proportional to E ac0 f can vary with an, an is inepenent of E ac0 We nee -ac at =0 2 ac ac SS SS 2 t 2 ac t ac 2 is a function of, an E ac0, but not t

8 Mass Transfer in magnitue an phase of =0 as a function of t, an E ac0 (or i ac0 an f i ).

9 Mass Transfer 2 y 2 my 0 2 m ounary onitions t = 0 i 0 0 t = or as tens to infinity, bulk bulk

10 Mass Transfer s tens to infinity t = 0, bulk bulk onvert to bounary conitions in i

11 Mass Transfer

12 Mass Transfer i i i i i i E ac E, E, E, 0 0 i E, i E bk b k 1 1c 0 1 1c 0 ac E i i k, 1c 1c E, E, b1k1 c 0 E b 1k 1c 0 i i k1c i k1c Y k ac i b1k 1c b 0 1k 1c 0 Eac 1 1 1k1c k1c

13 Mass Transfer i b1k 1c b 1k 1 0 c 0 Z Y 1 k 1c k 1c 1 b k b k 1 1c 0 1 1c 0 Y Eac k 1c k 1c 1 Z R Z Z t W, W, k 1c k1c 1 b k b k 1 1c 0 1 1c 0 Note. 1. R t epens on an at =0. i.e. R t is not inepenent of mass transfer. 2. Z W, an Z W, epen on k 1 an k -1, i.e. They are not inepenent of kinetics

14 Mass Transfer. Special case of E c =0 Z R Z Z t W, W, k 1c k1c 1 b k b k 1 1c 0 1 1c 0 When E c = 0,, 0 0 k k, k k 1c 10 1c 10 bulk bulk b k b k 1 1c 0 1 1c 0 1 k k RT RT k10bulk RT 10 bulk 10 bulk Z R Z Z t W, W, RT RT k RT bulk bulk bulk

15 Mass Transfer. Special case of E c =0 R Z t W, RT k Let 2 W, 2 10bulk 2 RT bulk 1 RT RT, Z, bulk bulk bulk Z R Z Z R Z t W, W, t W Z W 2 1 Remember: 1. These are vali only at equilibrium. 2. In general, kinetic an mass transfer effects cannot be separate. 3. lean separate epressions only in special cases. There are other methos to erive Z in mass transfer limite cases

16 Mass Transfer. Special case of E c =0 l 1 2 R t Z W / Z W k 10 = k -10 = 10-4 m s -1, E c =0 V vs. OP, bulk = bulk = 5 mm, = 0.5, T = 300 K, l = 20 m cm -2

17 Mass transfer effects in reactions with asorbe intermeiates? Very comple mathematical epressions Written in elegant form, 1960s! One paper in 2013 S.K. Rangaraan, former ERI irector k R 1 O e k 2 sol k as e 2 ssume that only P an Q are limite by iffusion, - sol iffusion is rapi araaic impeance stuy of E-ER reaction, M.. Molina oncha, M.hatenet,.Montella, J.-P.iar, Journal of Electroanalytical hemistry 696 (2013)24 37

18 Mass Transfer. oune Warburg Impeance ounary onitions t = 0 i t = 0 0, bulk bulk e 1 i e e e

19 Mass Transfer. oune Warburg Impeance i e e e e sinh cosh i sinh cosh i

20 Mass Transfer. oune Warburg Impeance i i i i i E ac E, E, E, i i k, 1c 1c E, E, k i E, E bk b k 1 1c 0 1 1c 0 ac E t i sinh e i tanh e 0 cosh sinh t i e b1k 1c b 0 1k1c 0 k 1c cosh t i i ac ie i sinh e t k 1c cosh t

21 Mass Transfer. oune Warburg Impeance i i i i i E ac E, E, E, i i k, 1c 1c E, E, k i E, E bk b k 1 1c 0 1 1c 0 ac E Y i b1k 1c b 0 1k1c ac 0 Eac tanh tanh 1 k1 c k 1c

22 Mass Transfer. oune Warburg Impeance tanh tanh 1 c c ac ac c c k k i Y E k b b k , 1 1, ta ta h 1 nh n W t W W c c t c c Z R Z b k Z k Z k b R k When tens to infinity, tan 1 i lim 1 c c c c Z b k b k k k

23 Mass Transfer. Special case of E c =0 k 10 = k -10 = 10-4 m s -1, E c =0 V vs. OP, bulk = bulk = 5 mm, = 0.5, T = 300 K, l = 20 m cm -2 oe plot, = 20 m l 1 2 R t Z W / Z W

24 Mass Transfer. Effect of changing E c k 10 = k -10 = 10-4 m s -1, = 20 m, bulk = bulk = 5 mm, = 0.5, T = 300 K, l = 20 m cm -2 oe plot, E c = 0.1 V vs. OP l 1 2 R t Z W / Z W