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Fundamentals of
Electrochemistry
CHEM*7234 / CHEM 720
Lecture 4
INSTRUMENTATION
OHM'S LAW
Ohms law, or more correctly called Ohm's
Law, named after Mr. Georg Ohm, German
mathematician and physicist
(b. 1789 - d. 1854), defines the relationship
between voltage, current and resistance.
Where:
V = Voltage
I = Current
R = Resistance
or
V=I·R
V/I = R
Example:
I=?
V=I*R
I = 0.5 [A]
I=V/R
I = 9 [V] / 18 [Ω]
Series connection
I = I1 = I2 = I3
Vtotal = V1 + V1 + V3
Since V = I R, then
and
Vtotal = I1R1 + I2R2 + I3R3
Vtotal = I Rtotal
Setting both equations equal, we get:
I Rtotal = I1R1 + I2R2 + I3R3
We know that the current through each resistor (from the first
equation) is just I.
so
I Rtotal = I(R1 + R2 + R3)
Rtotal = R1 + R2 + R3
Parallel connection
Kirchhoff’s Current Law states that
Itotal = I1 + I2 + I3
from Ohm’s Law
Itotal = V1/R1 + V2/R2 + V3/R3
but V1 = V2 = V3 = V
and Itotal = V/Rtotal
gives us:
1
1
1
1



Rtotal
R 1 R 2 R3
Capacitors
Vc 
qc 1
  i dt
C C
where:
if
i  imax  sin( ωt)
where ω  2f
Vc – voltage across the
capacitor
qc – charge stored
then
1
Vc   imax  sin (ωt) dt
C
1
π

imax  sin( ωt - )
ωC
2

1
 Xc  imax  sin( t - ) where Xc 
2
C
C – capacitance
Vc = Xc · Imax (sint - /2)
Vc max = XC.Imax




there is 90º difference in phase between
current and voltage
Xc is called capacitive reactance
Xc = 1/(C) = 1/(2fC)
Xc – a frequency dependent resistor
Impedance, resistance and reactance



Impedance, Z, is the general name we give to the ratio
of voltage to current.
Resistance, R, is a special case of impedance where
voltage and current are NOT phase shifted relative to
each other.
Reactance, Xc, is an another special case in which the
voltage and current are out of phase by 90°
Generalized Ohm’s Law
V=I·Z
RC circuit
Because of the 90º phase shift between VC and VR the
resistance and capacitive reactance add according to
vector addition !!!
so
Z2RC = R2 + XC2
ZRC  R  XC
2
2
Low Pass Filter
Vin = ZRC· I
and
Vout = XC · I
XC
Vout  Vin
ZRC
ZRC  R  XC
2
2
1
XC 
2fC
Vout  Vin
f
XC
Z



small
large
XC
Vout  Vin
XC
R 2  XC 2
f

XC

XC/Z 
large
small
small
Vout  0
For LPF with
R = 10 k and C = 0.1 µF
Vout/ Vin 1.0
0.8
0.6
0.4
0.2
0.0
1
10
100
Frequency / Hz
1000
10000
High Pass Filter
Vin = ZRC· I
and
Vout = R · I
R
Vout  Vin
ZRC
ZRC  R  XC
2
2
1
XC 
2fC
Vout  Vin
f
XC
Z



small
large
XC
Vout  0
R
R 2  XC 2
f
XC
Z



large
small
R
Vout  Vin
For HPF with
R = 10 k and C = 0.1 µF
Vout/ Vin 1.0
0.8
0.6
0.4
0.2
0.0
1
10
100
Frequency / Hz
1000
10000
Band Pass Filter
Cascade an LPF and a HPF and you get BPF
In practice use Operational Amplifiers to construct a BPF
Why RC circuits?


RC series creates filters
electrochemical cell may be simplified with RC
circuit (recall from lecture 2)
or, if faradaic process present:
http://www.phy.ntnu.edu.tw/java/rc/rc.html
Operational Amplifiers (Op-amps)
What are they and why do
we need them ?
- very high DC (and to a lesser extent AC) gain amplifiers
- proper design of circuits containing Op-amps allows electronic algebraic
arithmetic to be performed as well as many more useful applications.
- they are essential components of modern-day equipment including your
POTENTIOSTAT / GALVANOSTAT !!
General Characteristics





very high input gain (104 to 106)
has high unity gain bandwidth
two inputs and one output
very high input impedance (109 to 1014 )
GOLDEN RULE #1 : an Op-amp draws no appreciable current into its
input terminals.
General Response
Electronically
speaking, the
output will do whatever is
necessary to make the voltage
difference between the inputs
zero !!
GOLDEN RULE #2
+ 15 V
I
N
P
U
T
S
-
OUTPUT
+
- 15 V
In op-amps (as in life) you never get anything for free. The
gain () is achieved by using power from a power supply
(usually  15V). Thus the output of your op-amp can never
exceed the power supply voltage !
Ideal Op-Amp Behaviour

-
1.0
0.5
0.0
-0.5
-1.0
0
100
200
300
400
time
+
1.0
0.5
Signal

0.0
-0.5
-1.0
-50
0
50
100
150
200
250
300
350
400
time
-
1.0
0.5
1.0
0.5
Signal

Signal

infinite gain ( = )
Rin = 
Rout = 0
Bandwidth = 
The + and – terminals have nothing to do with polarity they simply
indicate the phase relationship between the input and output
signals.
Signal

0.0
+
-0.5
-1.0
0.0
-0.5
-1.0
0
0
100
200
time
300
400
100
200
time
300
400
Open - loop Configuration
-
-
+
+
V0
Even if + - -  0 then Vo is very large because  is so
large (ca. 106)
Therefore an open-loop configuration is NOT VERY
USEFUL.
Close-loop Configuration
Often it is desirable to return a fraction of the output
signal from an operational amplifier back to the input
terminal. This fractional signal is termed feedback.
Rf
Vin
Rin
S
- + +
V0
Frequency Response of Op-Amps
The op-amp doesn’t respond to all frequencies equally.
Voltage Follower
Vin
V0
+
Vo = V
in
Why would this be of any use ?
Allows you to measure a voltage without drawing any
current – almost completely eliminates loading errors.
Current Amplifiers
Rf
Iin
+
Vo = - Iin Rf
V0
Summing Amplifiers
Rf
V1
R1
V2
R2
-
V3
R3
+
 V1 V2 V3 
Vo  - Rf  
 
 R1 R2 R3 
V0
Integrating Amplifier
C
R
Vi
+
V0
1
Vo  Vi dt

RC
And if you wanted to integrate currents ?
A Simple Galvanostat
A Simple Potentiostat
A Real Potentiostat
The design of electrochemical
experiments

Equilibrium techniques
potentiometry, amperometry differential capacitance

Steady state techniques
voltammetry, polarography, coulometry and rotating
electrodes

Transient techniques
chronoamperometry, chronocoulometry,
chronopotentiometry
In all experiments, precise control or measurements of
potential, charge and/or current is an essential requirement
of the experiment.
The design of electrochemical cell

Electrodes
working electrode(s),
counter electrode and
reference electrode


Electrolyte
Cell container
Working electrode




most common is a small sphere, small disc
or a short wire, but it could also be metal
foil, a single crystal of metal or
semiconductor or evaporated thin film
has to have useful working potential range
can be large or small – usually < 0.25 cm2
smooth with well defined geometry for
even current and potential distribution
Working electrode - examples

mercury and amalgam electrodes
reproducible homogeneous surface,
large hydrogen overvoltage.

wide range of solid materials – most
common are “inert” solid electrodes like
gold, platinum, glassy carbon.
reproducible pretreatment procedure,
proper mounting
Counter electrodes




to supply the current required by the W.E. without
limiting the measured response.
current should flow readily without the need for a
large overpotential.
products of the C.E. reaction should not interfere
with the reaction being studied.
it should have a large area compared to the W.E.
and should ensure equipotentiality of the W.E.
Reference electrode
The role of the R.E. is to provide a fixed
potential which does not vary during the
experiment.
A good R.E. should be able to maintain a
constant potential even if a few microamps
are passed through its surface.
Micropolarisation tests
(a) response of a good and (b) bad reference electrode.
Reference electrodes - examples

mercury – mercurous chloride (calomel)
the most popular R.E. in aq. solutions; usually
made up in saturated KCl solution (SCE);
may require separate compartment if chloride
ions must be kept out of W.E.

silver – silver halide
gives very stable potential; easy to prepare;
may be used in non aqueous solutions
The electrolyte solution


it consists of solvent and a high concentration of an
ionised salt and electroactive species
to increase the conductivity of the solution, to reduce
the resistance between


W.E. and C.E. (to help maintain a uniform current and
potential distribution)
and between W.E. and R.E. to minimize the potential error
due to the uncompensated solution resistance iRu
Troubleshooting



is there any response?
is the response incorrect or erratic?
is the response basically correct but noisy?
For resistor as a dummy cell:
W.E.
C.E. + R.E.
For RC as a dummy cell (with some filtering in pot.):
W.E.
C.E. + R.E.
For RC as a dummy cell (without any filtering in pot.):