Presentation on theme: "Lecture 9.1 The Electrochemical Double Layer Gouy – Chapman Model ---------- + electrostatics k T (Boltzman) Thermal Randomization The number of carriers."— Presentation transcript:
Lecture 9.1 The Electrochemical Double Layer Gouy – Chapman Model electrostatics k T (Boltzman) Thermal Randomization The number of carriers in a given energy plane (distance away from electrode) is found to be: electrostatic thermal Bulk carrier # concentration charge on e - The potential profile is: In all cases For a 1:1 electrolyte (~e.g. NaF, CaSO 4 ) is potential at electrode inverse thickness of diffuse layer mol/L
Lecture 9.2 The Electrochemical Double Layer Use unsimplified equation effectively linear exponential Ah, the outer Helmholtz Plane! −1 is often called the Debye Length
Lecture 9.3 The Electrochemical Double Layer ***Figure *** ***Figure *** 1:1 electrolyte Too large a C d and too fast a change! Why does Gouy – Chapman Fail? The model assumes that the ions are point charges. As increases, the separation between the metal and charged electrolyte decreases to 0. Not Realistic! Stern’s Modification Accounts for 1. Finite ionic size 2. Additional radial increase due to solvation of ions Chem. Rev , 441
Lecture 9.4 The Electrochemical Double Layer Thus, must have plane of closest approach! For diffuse layer only!!! “x 2 ” OHP This is the compact layer. Get linear drop of. 1.0 compact OHP Diffuse Layer Recall capacitance is inversely additive! Exactly what we saw from Helmholtz.
Lecture 9.5 The Electrochemical Double Layer Effects of Double Layer on ET Reactions O + C + O + O + O + O + C + O + O + O + O + C + O + C + O + O + O vs. x 2 OHP C+O-C+O-C+O-C+O-C+O-C+O-C+O-C+O- O - O - attracts repels Thus apparent concentration of O z is “similar” to that of the electrolyte. That is to say we have an electrostatic driving force attracting the cationic O or repelling anionic O. If is +, then cationic O repelled and anionic O attracted. So, So, we will see changes in i 0 and k 0 at different [SE] and [O z ] *, which is what prompted this study/theory. Note NO absolute value of charge. z is the signed charge on O.
Lecture 9.6 The Electrochemical Double Layer OHP Linear Decay of, à là Helmholtz Diffuse Layer, exponential decay of So, O z does not experience, but. So, must correct for: 1. electrostatic effects on 2. electrostatic effects on E in rate equations from Chp. 3. Recalling: Totally irreversible reaction of O R k f >>> k b +ne corrections This is the apparent rate constant. Frumkin Correction so mV
Lecture 9.7 The Electrochemical Double Layer Examples: Mg(ClO 4 ) 2 and “An” Of course, x 2, and thus,, vary with electrolyte size/type. Also, we have assumed NO specific adsorption of SE anions, O, or R. Thus, the Frumkin Correction is limited, but it works well in most cases. The [ ] at x 2 is being depleted due to - - interactions. means delocalized