Presentation on theme: "- Gouy – Chapman Model + electrostatics k T (Boltzman) Thermal"— Presentation transcript:
1- Gouy – Chapman Model + electrostatics k T (Boltzman) Thermal RandomizationThe number of carriers in a given energy plane (distance awayfrom electrode) is found to be:electrostaticthermalcharge on e-Bulk carrier # concentrationThe potential profile is:In allcasesFor a 1:1 electrolyte (~e.g. NaF, CaSO4)is potentialat electrodemol/Linverse thickness of diffuse layer
2Use unsimplified equation k−1 is often called the Debye Length 1.0effectively linearexponentialAh, the outer Helmholtz Plane!
3Too large a Cd and too fast a change! Why does Gouy – Chapman Fail? 1:1 electrolyte***Figure ***Chem. Rev , 441***Figure ***Too large a Cd and too fast a change!Why does Gouy – Chapman Fail?The model assumes that the ions are pointcharges. As increases, the separation betweenthe metal and charged electrolyte decreases to 0.Not Realistic!Stern’s Modification Accounts for1. Finite ionic size2. Additional radial increase due tosolvation of ions
4- Thus, must have plane of closest approach! + For diffuse layer only!!!“x2” OHP1.0This is the compact layer.Get linear drop ofDiffuse LayerRecall capacitanceis inversely additive!compactOHPExactly what we saw from Helmholtz.
5- - Effects of Double Layer on ET Reactions O+ C+ O- C+ O+ O- O+ O+ O+ attractsrepels--O+C+ O+O+ O+ O+C+O+ O+C+ O+ O+C+O-O-vs.x2OHPThus apparent concentration of Oz is “similar” to that of theelectrolyte. That is to say we have an electrostatic drivingforce attracting the cationic O or repelling anionic O.If is + , then cationic O repelled and anionic O attracted.So,So, we will see changes ini0 and k0 at different [SE]and [Oz]*, which is whatprompted this study/theory.Note NO absolutevalue of charge.z is the signedcharge on O.
6So, Oz does not experience , but . Linear Decay of , à là HelmholtzOHP14012010080604020Diffuse Layer,exponential decay ofmVOHPSo, Oz does not experience , butSo, must correct for:1. electrostatic effects on2. electrostatic effects on E in rate equations from Chp. 3.Recalling:Totally irreversible reaction of O Rkf >>> kb+necorrectionssoFrumkinCorrectionThis is the apparent rate constant.
7Of course, x2, and thus, , vary with electrolyte size/type. Examples:Mg(ClO4)20.025-63.0120.400.25-220.127.116.11meansdelocalizedand“An”The [ ] at x2 is being depleted dueto 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 inmost cases.