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3.4 THE BUTLER-VOLMER MODEL, Study Guides, Projects, Research of Chemistry

The electrode potential and the surface concentrations of О and R are described by an equation of the Nernst form, regardless of the current flow.

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3.4 THE BUTLER-VOLMER MODEL
A plot of log i vs. η
known as a Tafel plot
can obtain the values of α and i0η = 2.3
 log 2.3
 log
At large negative overpotentials
The plots deviate sharply from
linear behavior as η approaches
zero, because the back reactions
can no longer be regarded as
negligible
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3.4 THE BUTLER-VOLMER MODEL

▪^

A plot of log i vs. η 

known as a

Tafel plot

can obtain the values of α and i

0

log 

^

log 

At large negative overpotentials

The plots

deviate

sharply from

linear behavior as η approacheszero, because the back reactionscan no longer be regarded asnegligible

3.4 THE BUTLER-VOLMER MODEL

▪^

Real Tafel plots for the Mn(IV)/Mn(III) system in concentrated acid 

The deviations from linearity at very largeoverpotentials: by

mass transfer

The deviations at very low overpotentials: by nonnegligible amounts of a

reverse

reaction

3.4 THE BUTLER-VOLMER MODEL

Can be rewritten as 

Take the log of both sides





Make a plot of log [i/(1 - e

)] vs. η

: obtain an intercept of log i

0

and a slope of -αF/2.3RT

▪^

Let us reconsider the

Butler-Volmer equation for quasi-reversible cases

as follows

3.4 THE BUTLER-VOLMER MODEL

▪^

Let us reconsider the current-overpotential equation as follows

: the

Butler-Volmer equation

▪^

Let us consider its behavior when

i

0

becomes very large

compared to any current of

interest 

The ratio i/i

0

then approaches zero

, and we can rearrange the limiting form of

equation

3.4 THE BUTLER-VOLMER MODEL

▪^

Net current flows

because the surface concentrations are not at equilibrium with

the bulk 

mass transfer continuously moves material

to the surface, where it must be

reconciled to the potential by electrochemical change ▪^

Previously, a system that is always at equilibrium is termed a reversible System 

an electrochemical system in which the

charge transfer interface is always at

equilibrium

is also called a

reversible

(or, alternatively, a nernstian) system

3.4 THE BUTLER-VOLMER MODEL

▪^

At extreme η (blue box), 

the current approaches the limiting current 

the current is

limited by mass transfer

1.4.2 Steady-State Mass-Transfer vs. Current^ ▪

We assume here that

stirring is ineffective at the electrode surface

so the solution velocity term need not be considered at x = 0. ▪^

This simplified treatment is based on the idea that

a stagnant layer of thickness δ

O

exists at the electrode surface (Nernst diffusion layer), with stirring

maintaining the

concentration of О at

C

O

  • beyond x = δ

O

Electrode

Bulk solution

stagnant layer

1.4.2 Steady-State Mass-Transfer vs. Current

▪^

Since we also assume that there is an excess of

supporting electrolyte

migration is not important

the

rate of mass transfer

is proportional to the

concentration gradient at the

electrode surface

,^

as given by the first (diffusive) term in the equation:

1.4.2 Steady-State Mass-Transfer vs. Current

▪^

The proportionality constant,

m

, called theO

mass-transfer coefficient

, has units of

cm/s ▪^

Can also be thought of as

volume flow/s per unit area (cm

3

-1s

cm

)^

▪^

Thus, from the following equations and taking a

reduction current as positive

[i.e., i is

positive when

C

O

C

(x = 0)], we obtainO

1.4.2 Steady-State Mass-Transfer vs. Current

▪^

The

largest rate of mass transfer

of О occurs

when

C

(x = 0) = 0O

or more precisely, when Co (x = 0) <<

C

O

*, so that

C

* -O

C

(x = 0)O

C

*O

▪^

The

value of the current

under these conditions (maximum current)

is called

the limiting current, i

,^ l

where

▪^

When the limiting current flows, 

the electrode process is occurring

at the maximum rate

possible for a given set of

mass-transfer conditions, 

О is being reduced

as fast as it can be brought to the electrode surface

1.4.2 Steady-State Mass-Transfer vs. Current

▪^

Or for the particular case when

C

  • = 0 (no R in the bulk solution),R

▪^

The

values of

C

O

(x = 0) and

C

(x = 0) are functions of electrode potential, ER

. (Nernst

equation: ch. 2) ▪^

Under the conditions of a net cathodic reaction, 

R is produced at the electrode surface, 

so that

C

(x = 0) >R

C

  • (whereR

C

  • is the bulk concentration of R).R

Therefore,

1.4.2 Semiempirical Treatment of Steady-State Mass Transfer

▪^

If the kinetics of

electron transfer are rapid

the concentrations of О and R at the electrode surface can be assumed to be

at

equilibrium

with the electrode potential, as governed by the

Nernst equation

for the

half-reaction ▪^

Let us derive the steady-state

i-E curves for nernstian reactions

under several

different conditions.

  1. R Initially Absent2) Both О and R Initially Present3) R Insoluble

1.4.2 Semiempirical Treatment of Steady-State Mass Transfer

a plot of log[(i

  • i)/i] vs. El

a plot of i - E

a slope of nF/2.3RT 

an E-intercept of Е

1/

1.4.2 Semiempirical Treatment of Steady-State Mass Transfer

(b) Both О and R Initially Present

▪^

When

both members of the redox couple exist

in the bulk, we must distinguish between

a cathodic limiting current, i

l,c

, when C

(x = 0)O

and an anodic limiting current, i

l,a

, when C

(x = 0)R

▪^

The limiting anodic current naturally reflects the

maximum rate

at which R can be

brought to the electrode surface for conversion to O

Sign convention

: cathodic currents are taken as positive and anodic ones as negative