Need Working Electrode - WE Reference Electrode - REF Auxilliary Electrode – AE or Aux

1. How carry out an electrochemical experiment? Lecture 1.1 i(t) Potentiostat i(t) Control Ewk At WE: O + ne- R In this case, minimize by no stirring All are associated with motion due to perturbation • Need • Working Electrode - WE • Reference Electrode - REF • Auxilliary Electrode – AE or Aux • REF is required so that we have a thermodynamic handle on the relative cell voltage • operated at equilibrium • no current flow through the REF Thus, need a current “dump” or alternate path – AE Potentiostat • i(t) is composed of: • i(t)Diffusion • i(t)Migration • i(t)Convection Motion of species to WE, or the Flux of species can be described by (in linear dimensions): mol s-1 cm-2 Nernst-Planck Equation (stirring)

2. Lecture 1.2 A AE Rs l Ref WE We wish to use i(t) to obtain information on the analyte (Di, Ci, etc.). This is difficult to do with the Nernst-Planck Equation. If we make the migration current negligible for the analyte, then we obtain: How is this achieved? Must have another species present that will carry the current, namely, a purposely added supporting electrolyte, SE. Uses of SE: (use ~100x[analyte]) • Eliminate/Reduce Migration • Decrease Rsoln(Rs) L is conductance Aside: - Decrease EiR; EiR = i Rs • Decrease time (t) to charge capacitive layer, known as the double layer Ewk = Eapp- EiR idl(t) = E/Rse-t/RsCdl; t = RsCdl

3. Lecture 1.3 Fick’s Second Law (FSL): For linear diffusion For radial diffusion (See problem 4.5) Back to Diffusion: Fick’s First Law (FFL), for O + ne- R: in e-chem terms Not a function of electrode shape WHOA! How did we do that????!!!! Okay, think of diffusion microscopically: Brownian Motion Random Events Probability Theory - What is probability of finding a molecule at a given distance at a given time? “Drunken Sailor Problem” or 1-D Random Walk

4. Lecture 1.4 p=0.125 +3 l +3 l M +2 l +2 l p=0.5 p=0.375 +1 l +1 l M M 0 l 0 l position position +3 l p=0.375 p=0.5 -1 l -1 l M M p=0.25 +2 l M -2 l -2 l +1 l p=0.125 -3 l -3 l M p=0.5 0 l position M t = t = 1 t 3 t -1 l probability, p probability, p p=0.25 -2 l M -3 l t = 2 t probability, p 1-D Random Walk: +3 l +2 l +1 l p=1 0 l position M -1 l -2 l -3 l t = 0 t probability, p tis the time needed to move l distance. The probability of finding molecule M at a given location after m time intervals (m = t/t, where t is fixed), Binomial Distribution Function Where r is the location in units of l. If r=3l and m=3, then P(3,3) = (3!/(3! 0!))(0.5)3 = 0.125 Mean Square Displacement D, by definition (cm2 s-1) Einstein Equation

5. Lecture 1.5 How far has a molecule moved after 5 sec if D = 10-5 cm2s-1? So, if we reduce O to R at a diffusion-limited rate, then there will be a layer where there “will effectively be no O.” If t = 5 s, then this Diffusion or Depletion Layer is 100 mm thick! At t = 0.5 s, layer is 32 mm thick. @ t = 0.5 s CO @ t = 5 s electrode surface Not truly linear concentration gradients; see Chp. 5, p.164. 32 mm 100 mm Distance from electrode (x) Recall: or