Transcript Slide 1

The Electrochemical Double Layer
Lecture 8.1
Heyrovsky looked at the Dropping Mercury Electrode (DME)
for measurement of surface tension:
System at hand
 G S
SurfaceTension    
 A
How did he measure


fixed
environmen
t
 ??
By applying various
Potentials to WE, he
noted differences in
drop rate of the Hg.
He also found:
td 
“Drop
time”
lifetime of drop
mass flow rate
of Hg in mg/s
2 rcap
mg
gravitational
acceleration
http://chem.ch.huji.ac.il/instruments/electrochemical/polarographs_heyrovsky.htm
The Electrochemical Double Layer
Lecture 8.2
So ,  Expt
td  m  g

2rcap
Why is this so?
At
t  td, the wt. of the drop is td  m .
At this point, the force of the drop
F  mA
td  m  g
is just balanced by the surface tension
 G 

 A  fixed
 
acting around the circumference of
environment
F  td  m  g
the capillary. Once
and the drop falls!
ECM or PZC
**Figure (12.2.1)**
t  td , then   td  m  g
What affects this?
-solvent properties
-ionic strength
-charge on metal drop
(all electrostatic
properties)
So, he (and others)
found:
How do we relate
 to E ???
The Electrochemical Double Layer
Lecture 8.3
Well, let us think about this!
What electrostatic forces are there in this situation?
And what changes with Eapp?
-
C+
C+ C+ X- C+
C+ C+C+ XC+
X- C+
C+ C+ X- XC+
C+C+C+C+ X-
C+
XC+
XC+
X-
Neutral Redox M? M
pure
metal
Phase
Make
cation
XC+
XC+
XC+
anion
pure electrolyte phase
(not ordered)
What about excess of H2O??? H 2O
We have excess of C+ near (or at) the
metal/solution interface.
- of PZC
This means that
or written as
  metal   soln
(near surface)
 M   S
  M  F e (surfaceconc. of e )
   
   
 How is  S relatedto C  and X  in thiscase, K  and Cl  ??
 S  zi F ( surf conc C   surf conc X  )
z=1
 S  F  (K  Cl )


But, how are , M , E, i all related?
The Electrochemical Double Layer
Lecture 8.4
Related through the
Electrocapillary Equation:
 d   M dE  K  (H O) d KCl  M (H O) d M
2
2
Must Ref H2O as solvent
Wherei is theelectrochemicalpotential(see Ch. 2) for
speciesi.
 

i
 G 

 

 n i T , P
in given phase,
must be specified.
0

i  i  RT ln ai
all variables
held cst
∂n is 
in # moles of i.
std. chem. potential
of species i.

activity of species i
in phase of choice
(must specify)
Across interface
So, as we change E , we change M and K 
(if E is  of PZC, Cl - )
and thus .
Also, we can see thateach electrolyte type
and concentration will affect differently with Eapp .
The Electrochemical Double Layer
Lecture 8.5
By using :  
td  m  g
and doing lots
2rcap
of measurements of td , one can obtain:
Chem. Rev. 1947 41, 441
**Figure 12.2.2**
E – Ez (V, vs. NaF)
dKCl  0
If we hold electrolyte type constant and neutral redox species
M constant, we obtain:
d M  0
So we can get
 M vs.
  

 E   KCl ,  M
 M  
(E vs PZC) plots.
The Electrochemical Double Layer
Lecture 8.6
Chem. Rev. 1947 41, 441
We can do this with
each type of electrolyte
at a fixed concentration.
M
**Figure 12.2.3**
But how is plot to
left related to CDL???
E – Ez
Take derivative
wrt E.
Can do two different ways:
Differential
Capacitance
**Figure 12.2.4**
  M
Cd  
 E



Integral
Capacitance
Ci 
 M at E 
E  E pzc
The Electrochemical Double Layer
Lecture 8.7
What does the Double Layer look like?
Well, that is a very interesting question, particularly from
our previous discussions.
We need a good model that predicts
• ion populations (surface xs concs, i ) and
• the field strength or electrostatic potential  (x)
as a function of distance.
This is because of the fact that the ions do the majority
of the screening of the applied potential.
Our original model was:
Helmholtz (Parallel Plate) Model
Neg.
of PZC
e-
-
+
+
+
+
+
+
+
metal conductor,
cannot support electric
fields within, so xs - or +
at surface only
C+
Voltage drop over distance, d, is V

o
is dielectric cst. of the medium
is permitivity of free space.

x
distance between plates
is d or x; The plane is at
x (OHP, IHP)
  o 
 
V
 d 
The Electrochemical Double Layer
Lecture 8.8
Recall that
So,
  M 

  Cd
 E 
, the differential
capacitance
     o
 Cd
 
 V  d
This states that Cd is constant. We know this not to be true!
Na I
NaF
 M
E – Epzc (NaF)
 M
( NaF)
E
+
Helmholtz Model
0.1 M
Cd
0.001 M NaF
0
E – Epzc (NaF)
The Electrochemical Double Layer
Lecture 8.9
The Helmholtz Model says:
• Charge in solution is fixed at the metal/solution
interface;
• Conc. of electrolyte is ~ inconsequential.
The electric field is ‘felt’ out in solution,
thus leading to a diffuse layer of ions.
M
-
C+
XC+ X- C+
C+ C+
C+
C+
X- XC+ XXC+ C+ C+ C+
s
At high T, we will
get randomized
structure.
What is distance?
What affects distance?
Thus, thermal excitation fights the electrostatic situation.
As you move away from electrode, thermal processes win.
Thus, we have two layers:
1. compact layer
2. diffuse layer
of ions near the surface.
 (x)
x
The Electrochemical Double Layer
Lecture 8.10
Gouy – Chapman Model
 (0)
M  -
+ electrostatics
k T (Boltzman) Thermal
Randomization
The number of carriers in a given energy plane (distance away
from electrode) is found to be:
electrostatic
thermal
ni  n  e
0
i
 zi e / kT
charge on e-
Bulk carrier # concentration
The potential profile is:
2kT
 d 

 
 o
 dx 
2
  zkieT

i n  e  1


0
i
For a 1:1 electrolyte (~e.g. NaF, CaSO4)
 8kTn
d
 
dx
  o
 0 is potential
at electrode
1/ 2



 z e 

sinh

2
k
T


 dx
tanh z e x  / 4kT 
tanh z e (0) / 4kT 
cm K  3.3x10 z C 
1
0
7
 1/ 2
mol/L
inverse thickness of diffuse layer
 e x
For aqueous at 25C