The on-line simulator based on the paper entitled
"Quasi-reversible Voltammetric Response of Electrodes Coated with Electroactive Monolayer Films"
Kanazawa College of Art
Electrochemistry Communications, 1999, 1,
--- ERRATUM in above paper ---
fPET in Eq.(3) --> sPET
fM in Eq.(25) --> sM
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
We consider redox couple of O+/R0 that is immobilized on an electrode substrate.
O+ + e- = R0 (Quasi-reversible electrode reaction)
The Butler-Volmer kinetics with correction for potential distribution and ion pairing is used.
O+ + X- = OX0 (Ion-pair formation)
Concentration of X- is also influenced by the potential distribution. Ion pairing is assumed to be a reversible process.
The parameter "e1" is a relative dielectric constant at 0 < x < d1.
The parameter "d1" is a chain length.
The parameter "e2" is a relative dielectric constant at d1 < x < d1+d2.
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 d1+d2< x , i.e., solution bulk.
The parameter "Eo" is a formal potential of a redox couple O+/R0.
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 OX0. (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 oC.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.
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.