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## 8. Fundamentals of Charged Surfaces Moving the reagents Quickly in addition to with Little

Barr, Alistair, Finance Reporter has reference to this Academic Journal, PHwiki organized this Journal 8. Fundamentals of Charged Surfaces Moving the reagents Quickly in addition to with Little energy Diffusion electric fields Yo Charged Surface X=0 1. Cations distributed thermally with respect to potential 2. Cations shield surface in addition to reduce the effective surface potential Yo

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Yo Charged Surface X=0 Yo dx dx Yo dx Yo Surface Potentials Poisson-Boltzman equation Charge near electrode depends upon potential in addition to is integrated over distance from surface – affects the effective surface potential Cation distribution has to account as long as all species, i Dielectric constant of solution Permitivity of free space Solution to the Poisson-Boltzman equation can be simple if the initial surface potential is small: Potential decays from the surface potential exponentially with distance

Largest term Let Then: General Solution of: Because Y goes to zero as x goes to infinity B must be zero Because Y goes to Y0 as x goes to zero (e0 =1) A must be Y0 thus Potential decays from the surface potential exponentially with distance When k=1/x or x=1/k then The DEBYE LENGTH x=1/k

Yo Charged Surface Y=0.36 Yo X=0 X=1/k What is k Debye Length Units are 1/cm Does not belong =1/cm Debye Length Units are 1/cm

In the event we can not use a series approximation to solve the Poisson-Boltzman equation we get the following: Check as Compared to tanh By Bard Set up excel sheet ot have them calc effect Of kappa on the decay Example Problem A 10 mV perturbation is applied to an electrode surface bathed in 0.01 M NaCl. What potential does the outer edge of a Ru(bpy)33+ molecule feel Debye length, x Since the potential applied (10 mV) is less than 50 can use the simplified equation. Units are 1/cm

The potential the Ru(bpy)33+ compound experiences is less than the 10 mV applied. This will affect the rate of the electron transfer event from the electrode to the molecule. Radius of Ru Surface Charge Density The surface charge distance is the integration over all the charge lined up at the surface of the electrode The full solution to this equation is: C is in mol/L Yo Charged Surface Y=0.36 Yo X=0 X=1/k Can be modeled as a capacitor: d d differential

For the full equation At 25oC, water d d Differential capacitance Ends with units of uF/cm2 Conc. Is in mol/L Can be simplified if Specific Capacitance is the differential space charge per unit area/potential Specific Capacitance Independent of potential For small potentials

Flat in this region Gouy-Chapman Model Real differential capacitance plots appear to roll off instead of Steadily increasing with increased potential Henrik Jensen , David J. Fermn in addition to Hubert H. Girault Received 16th February 2001 , Accepted 3rd April 2001 Published on the Web 17th May 2001 Yo Charged Surface X=0 Linear drop in potential first in the Helmholtz or Stern specifically adsorbed layer Exponential in the thermally equilibrated or diffuse layer Cdiffuse CHelmholtz or Stern x2

Capacitors in series Wrong should be x distance of stern layer For large applied potentials in addition to /or as long as large salt concentrations 1. ions become compressed near the electrode surface to create a Helmholtz layer. 2. Need to consider the diffuse layer as beginning at the Helmholtz edge Capacitance Due to Helmholtz layer Capacitance due to diffuse layer Deviation Is dependent upon The salt conc. The larger the dip For the lower The salt conc.

Create an excel problem And ask students to determine the smallest Amount of effect of an adsorbed layer Experimental data does not Correspond that well to the Diffuse double layer double capacitor model (Bard in addition to Faulkner 2nd Ed) Fig. 5 Capacitancepotential curve as long as the Au(111)/25 mM KI in DMSO interface with time. Siv K. Si in addition to Andrew A. Gewirth Received 8th February 2001 , Accepted 20th April 2001 Published on the Web 1st June 2001 Model needs to be altered to account For the drop with large potentials

How does this effect the rate of electron transfer Probability factor Collisional factor Where m is the reduced mass. Z is typically, at room temperature, 104 cm/s Activation energy Free energy change work required to change bonds And bring molecules together Formal potential Work of bringing ions together When one ion is very large with respect to other (like an electrode) Then the work term can be simplified to: The larger kappa the smaller the activation energy, the closer Ions can approach each other without work

## Barr, Alistair Finance Reporter

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