- Gouy – Chapman Model + electrostatics k T (Boltzman) Thermal

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Presentation transcript:

- 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 charge on e- Bulk carrier # concentration The potential profile is: In all cases For a 1:1 electrolyte (~e.g. NaF, CaSO4) is potential at electrode mol/L inverse thickness of diffuse layer

Use unsimplified equation k−1 is often called the Debye Length 1.0 effectively linear exponential Ah, the outer Helmholtz Plane!

Too large a Cd and too fast a change! Why does Gouy – Chapman Fail? 1:1 electrolyte ***Figure 12.3.5*** Chem. Rev. 1947 41, 441 ***Figure 12.3.1*** Too large a Cd 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

- Thus, must have plane of closest approach! + For diffuse layer only!!! “x2” OHP 1.0 This is the compact layer. Get linear drop of . Diffuse Layer Recall capacitance is inversely additive! compact OHP Exactly what we saw from Helmholtz.

- - Effects of Double Layer on ET Reactions O+ C+ O- C+ O+ O- O+ O+ O+ attracts repels - - O+ C+ O+ O+ O+ O+ C+ O+ O+ C+ O+ O+ C+ O- O- vs. x2 OHP Thus apparent concentration of Oz 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 i0 and k0 at different [SE] and [Oz]*, which is what prompted this study/theory. Note NO absolute value of charge. z is the signed charge on O.

So, Oz does not experience , but . Linear Decay of , à là Helmholtz OHP 140 120 100 80 60 40 20 10 20 30 40 50 60 70 80 Diffuse Layer, exponential decay of mV OHP So, Oz 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 kf >>> kb +ne corrections so Frumkin Correction This is the apparent rate constant.

Of course, x2, and thus, , vary with electrolyte size/type. Examples: Mg(ClO4)2 0.025 -63.0 12 0.40 0.25 -41.1 2.7 0.38 means delocalized and “An” The [ ] at x2 is being depleted due to - - interactions. Of course, x2, 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.