### Controlled current microelectrode techniques

```Controlled current microelectrode
techniques
• The experiment is carried out by applying
the controlled current between the working
and auxiliary electrodes with a current
source and determining the potential
between the working electrode and a
reference electrode.
• Chronopotentiometry: E is determined as
a function of time.
Simplified block diagram of apparatus for
chronopotentiometric measurements
Current Step
• When the RsCd circuit is charged by a constant
current i, for a current step, assuming a constant
Cd, the potential increases linearly with time.
E  i(Rs  t / Cd )
Different types of controlled current
techniques:
(a)
(b)
(c)
(d)
Constant current chronopotentiometry
Chronopotentiometry with linearly increasing current
Current reversal chronopotentiometry
Cyclic chronopotentiometry
Current step
E
I
0
t
Signal
0
t
Resulting E-t curve
Transition time, τ
• After the concentration of electroactive species
drops to zero at the electrode surface, the flux of
electroactive species to the surface is insufficient
to accept all of the electrons being forced across
the electro-solution interface. The potential of
the electrode will rapidly change toward more
negative values until a new, second reduction
process can start.
• The time after application of the constant current
for this potential transition to occur is called τ,
the transition time.
Sand equation
• The measured value of τat known i can be used
to determine C* or D. A lack of constancy of the
transition time constant, iτ1/2/C*, with i or C*
indicates complications to the electrode reaction
from coupled homogeneous chemical reactions,
adsorption, double-layer charging or the onset of
convection.
i 1/ 2 nFAD1/ 2 1/ 2

*
C
2
Reversible waves
• For rapid electron transfer, the Nernst applies.
The following equation is obtained.
RT  1/ 2  t1/ 2
E  E / 4 
ln
nF
t1/ 2
• Where Eτ/4, the quarter-wave potential, is
DO
RT
`
E / 4  E 
ln
2nF DR
• So that Eτ/4 is the chronopotentiometric
equivalent of the voltammetric E1/2 value.
Totally irreversible waves
• For a totally irreversible cathodic reaction, I is
related to E by the following equations:
0`



n
(
E

E
)
i
0

 k C (0, t ) exp 

nFA
RT


• The E-t relation is depicted by the following
equation:
0



  RT 
RT
2
k
0`
1/ 2
1/ 2
E  E 
ln

ln(


t
)
 


1/ 2 
  n F   ( D)    nF 
• The whole E-t wave shifts toward more negative
potentials with increasing current.
Quasi-reversible waves
• Usually the study of the kinetics of quansi –
reversible electrode reaction by constant current
techniques involves the use of such small
current perturbations that the potential change is
small.
RT  2t1/ 2  1
1  1
 
i
 * 1/ 2   
1/ 2 
*
1/ 2
nF  nFA  CO DO
CR DR  i0 
• Thus a plot of η vs. t1/2, for small values of η, will
be linear, and i0 can be obtained from the
intercept.
Muticomponent systems and
multistep reactions
• According the following equation and the
transition time ratio, the electrons per
reactive species:
 FA
(n1D C  n2 D C ) 
 2
1/ 2
1
*
1
1/ 2
2
*
2
 2 2n2  n2 

 
1
n1  n1 
2
1/ 2

1/ 2
  i(1   2 )

Charging profiles, voltage, current
and battery temperature
(a )Two-step charging with 0.5 + 0.05 C
(b) Two-step charging with 0.7 + 0.05 C
(c) Three-step charging with 0.5 + 0.2 + 0.05 C
(d) Three-step charging with 1.0 + 0.2 + 0.05 C
[1] T. Ikeya, N. Sawada, S. Takagi, J. Murakami, K.
Kobayashi, T. Sakabe, E. Kousaka, H. Yoshioka, S. Kato, M.
Yamashita, H. Narisoko, Y. Mita, K. Nishiyama, K. Adachil,
K. Ishihar. Multi-step constant-current charging method for
electric vehicle, valve-regulated, leadracid batteries during
night time for load-levelling. Journal of Power Sources 75
1998 101–107.
Constant-current discharge capacity of battery
system with two-step or three-step charging
Constant-current discharge capacity of
battery system with multistep charging
```