Transcript Methods involving forced convection—hydrodynamic methods

Methods involving forced convection—
hydrodynamic methods
• Methods involving convective mass transport of
reactants and products are sometimes called
hydrodynamic methods.
• The advantage of hydrodynamic methods is that
a steady state is attained rather quickly and
measurements can be made with high precision,
often without the need for recorders or
oscilloscopes. In addition, at steady state,
double-layer charging does not enter the
measurement.
Rotating disk electrode
• Construction of hydrodynamic electrodes that
provide known and reproducible mass transfer
conditions is more difficult than for stationary
electrodes.
• The most convenient and widely used system
involves the rotating disk electrode.
• This electrode is amenable to rigorous
theoretical treatment and is easy to construct
with a variety of electrode materials.
Rotating disk electrode
Brush contact
Shaft
Insulator
Disk
Schematic resultant streamlines
r=0
y=0
Rotating disk electrode
• RDE is rather simple to construct and
consists of a disk of the electrode material
imbedded in a rod of an insulating material.
• RDE is rotated at a certain frequency,
f(revolutions per second), but the
parameter of interest is the angular
velocity, ω(sec-1), where ω=2πf.
Theoretical treatment of convective
systems
• Within the layer, 0≤x≤δ, no solution movement
occurs and mass transfer takes place by
diffusion. Thus the convection problem is
converted to a diffusional one in which the
adjustable parameter δis introduced.
• In this model, it is assumed that convection
maintains the concentrations of all species
uniform and equal to the bulk values up to a
certain distance from the electrode, δ
The convective-diffusion equation
• Drive of fluid flow: diffusion, migration and
convection. For solutions containing an
excess of supporting electrolyte, the ionic
migration term can be neglected.
• When fluid flow is smooth and steady and
occurs at the separate layers, the flow
velocity is small right at the walls because
of friction between the fluid and the wall.
Levich equation
• This equation applies to the totally mass-trasferlimited condition at RDE and predicts that the
limiting current is proportional to C* and ω1/2.
• ν is called the kinematic viscosity and has units
of cm2/s, for water and dilute aqueous solutions
near 20℃, νis about 0.01 cm2/s.
il  0.620nFAD  
2/3
1/ 2 1/ 6
*
C
The concentration profile
C*
0
¦Ä
  1.61D 
1/ 3

1/ 2 1/ 6
General current-potential curves at
the RDE
1 1
1
 
* 2/ 3 1/ 6 1/ 2
i ik 0.62nFAC D  
ik  nFAk f (E)C
*
Rotating ring-disk electrode
Radius of disk: r1, Radius of insulator: r2, Radius of ring:r3
The collection efficiency
• The collection efficiency can be calculated
from the electrode geometry, since it
depends only on r1,r2,and r3, and is
independent of ω,C*,D, etc.
 r3 r2 
 3  3 
 r1 r1 
3
N cal
3
2/3
iR
N 
iD
RRDE apparatus: Biopotetiostat
N
N
N
N
N
N
N
N
bpy
phen
TATP
Fig. 1. Structure of ligands 2,2 -bipyridine (bpy), 1,10phenanthroline (phen) and 1,4,8,9-tetra-aza-trisphenylene (TATP).
120
100
a
B
il/A cm
-2
80
60
40
b
20
0
0
3
6
1/2
9
12
-1 1/2
¦Ø /(rad s )
15
0.05
2
0.04
0.11V
0.09V
0.07V
0.05V
0.03V
0.01V
0.03
-1
i /A cm
0.13V
B
-1
0.02
0.01
0.00
0.08
0.12
-1/2
0.16
-1 -1/2
 /(rad s )
0.20