Fundamentals of Electrochemistry

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Fundamentals of Electrochemistry
INSTRUMENTATION
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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.

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V I R or V / I R

• Where
• V Voltage
• I Current
• R Resistance

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Example
I ? V I R I V / R I 9 V /
18 O I 0.5 A
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Series connection
I I1 I2 I3 Vtotal V1 V1 V3 Since V
I R, then Vtotal I1R1 I2R2 I3R3
and 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
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Parallel connection

• Kirchhoffs Current Law states that
• Itotal I1 I2 I3
• from Ohms Law
• Itotal V1/R1 V2/R2 V3/R3
• but V1 V2 V3 V
• and Itotal V/Rtotal
• gives us

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Capacitors
where Vc voltage across the capacitor qc
charge stored C capacitance
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• 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

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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 Ohms Law V I Z
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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
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Low Pass Filter
Vin ZRC I and Vout XC I
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• f ? small
• XC ? large
• Z ? XC
• Vout ? Vin

f ? large XC ? small XC/Z ? small Vout
? 0
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For LPF with R 10 k? and C 0.1 µF
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High Pass Filter
Vin ZRC I and Vout R I
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f ? small XC ? large Z ? XC Vout ? 0
f ? large XC ? small Z ? R Vout ? Vin
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For HPF with R 10 k? and C 0.1 µF
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• Band Pass Filter
• Cascade an LPF and a HPF and you get BPF

In practice use Operational Amplifiers to
construct a BPF
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Why RC circuits?

• RC series creates filters
• electrochemical cell may be simplified with RC
  circuit (recall from lecture 2)

or, if faradaic process present
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Operational Amplifiers (Op-amps)

• - 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 !!

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• 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

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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 !
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• Ideal Op-Amp Behaviour
• 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.

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Open - loop Configuration

• Even if ? - ?- ? 0 then Vo is very large because
  ? is so large (ca. 106)
• Therefore an open-loop configuration is NOT VERY
  USEFUL.

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• 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.

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• Frequency Response of Op-Amps
• The op-amp doesnt respond to all frequencies
  equally.

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• Voltage Follower

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.
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• Current Amplifiers

Vo - Iin Rf
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• Summing Amplifiers

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• Integrating Amplifier

And if you wanted to integrate currents ?
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• A Simple Galvanostat

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• A Simple Potentiostat

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• A Real Potentiostat

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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.

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The design of electrochemical cell

• Electrodes
• working electrode(s),
• counter electrode and
• reference electrode
• Electrolyte
• Cell container

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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 lt 0.25 cm2
• smooth with well defined geometry for even
  current and potential distribution

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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

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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.

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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.

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Micropolarisation tests
(a) response of a good and (b) bad reference
electrode.
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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

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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

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Troubleshooting

• is there any response?
• is the response incorrect or erratic?
• is the response basically correct but noisy?

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For resistor as a dummy cell
W.E. C.E. R.E.
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For RC as a dummy cell (with some filtering in
pot.)
C.E. R.E.
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For RC as a dummy cell (without any filtering in
pot.)