**The ***on-line* simulator based on the paper entitled

### "Quasi-reversible Voltammetric Response of Electrodes Coated with Electroactive Monolayer Films"

Masayuki Ohtani

*Kanazawa College of Art*

*Electrochemistry Communications*, 1999, **1**,
488-492

.

**--- ERRATUM in above paper ---**

f_{PET} in Eq.(3) --> s_{PET}

f_{M} in Eq.(25) --> s_{M}

I am very sorry.

**
**

This theory is based on (i) the Gouy-Chapman model, (ii) the Gauss' law of electromagnetics, and (iii) the Butler-Volmer kinetics.
The computational calculation for the cyclic voltammetry is carried out by (i) the finite difference method and (ii) the Newton-Raphson method.
The mathematical treatment is described in *Electrochem.Commun.*
, 1999, **1**, 488-492

.

Model:

We consider redox couple of O^{+}/R^{0} that is immobilized on an electrode substrate.

**O**^{+} + e^{-} = R^{0} (Quasi-reversible electrode reaction)

The Butler-Volmer kinetics with correction for potential distribution and ion pairing is used.

**O**^{+} + X^{-} = OX^{0} (Ion-pair formation)

Concentration of X^{-} is also influenced by the potential distribution. Ion pairing is assumed to be a reversible process.

**Parameters:**
The parameter **"e1"** is a relative dielectric constant at 0 <* x *< *d*_{1}.
The parameter **"d1"** is a chain length.
The parameter **"e2"** is a relative dielectric constant at *d*_{1} <* x *< *d*_{1}+*d*_{2}.
The parameter **"d2"** is a thickness of oriented solvent molecule layer or a distance from redox center to solution phase.
If you don't need the assumption, you should set d2 to zero.
The parameter **"e3"** is a relative dielectric constant at *d*_{1}+*d*_{2}< *x* , i.e., solution bulk.
The parameter **"Eo"** is a formal potential of a redox couple O^{+}/R^{0}.
The parameter **"ko"** is a rate constant. (For **reversible** case, set ko to be a large value.)
The parameter **"alpha"** is an electron transfer coefficient.
The **"Sur.Cov."** is total surface concentration of surface-confined redox species.
The parameter **"C"** is a concentration of 1:1-type electrolyte solution.
The parameter **"K1"** is a formation constant of ion pair OX^{0}. (For the case that ion pairing is not significant, set K1 to zero.)
The parameter **"Initial E"**, **"Switching E"**, and **"Scan Rate"** have their usual significance.

Temperature is fixed at 25 ^{o}C.

**OUTPUT:**

**Blue wave is not corrected** for the potential distribution. The change in chemical potential due to ion-pairing is considered.
**Red wave is corrected** for the potential distribution.
**Pink curve is capacitive component** of Red wave .
**Ipc** and **Ipa** mean cathodic and anodic peak currents, respectively.

**Only you have to do is putting parameter values and pushing the "Calc." button!
**

**Suggestion to Enjoy Simulator as Diagnostic Criteria:**
To investigate the effect of **chain length**, change the **d1** value.
To investigate the effect of **solvent**, change the **e3** value.
To investigate the effect of **rate constant**, change the **ko** value.
To investigate the effect of **surface concentration**, change the **Sur.Cov.** value.
To investigate the effect of **electrolyte concentration**, change the **C** value.
To investigate the effect of **energy due to ion pair formation**, change the **K1** value and check the peak potential.

**Previous Work**

The reversible case is treated. Although the ion pairing and triple ion formation are not corrected for the potential distribution,
the spike current of adsorbed redox species can be explained.

**ANALOGY APPEARED AMONG NATURAL PHENOMENON**

As described in *The Feynman Lectures on Physics*, natural events often shows their analogous feature as mathematical model.
Interestingly, above current-voltage curve is similar form to oil production curve
i.e., the Hubbert's curve. At present, oil depeletion is much more important problem than interfacial phenomana. My thinking (partly Japanese) about oil depletion problem is linked here.