Fundamentals of Fundamentals of ElectrochemistryElectrochemistry

CHEM*7234 / CHEM 720CHEM*7234 / CHEM 720

Lecture 4Lecture 4

INSTRUMENTATIONINSTRUMENTATION

OHM'S LAWOHM'S LAW

Ohms law, or more correctly called Ohms law, or more correctly called Ohm's Law, named after Mr. Georg Ohm, Ohm's Law, named after Mr. Georg Ohm, German mathematician and physicist German mathematician and physicist

(b. 1789 - d. 1854), defines the (b. 1789 - d. 1854), defines the relationship between voltage, current relationship between voltage, current and resistance.and resistance.

V = I · RV = I · Roror

V / I = R V / I = R

Where: Where:

V = Voltage V = Voltage

I = Current I = Current

R = ResistanceR = Resistance

Example:Example:

I = ?I = ?V = I * R I = V / R I = 9 [V] / 18 V = I * R I = V / R I = 9 [V] / 18 [Ω] I = 0.5 [A][Ω] I = 0.5 [A]

Series connectionSeries connectionI = II = I11 = I = I2 2 = I= I33

VVtotaltotal = V = V11 + V + V11 + V + V33

Since V = I R, then VSince V = I R, then Vtotaltotal = I = I11RR11 + I + I22RR22 + + II33RR33

and Vand Vtotaltotal = I R = I RtotaltotalSetting both equations equal, we get: I RSetting both equations equal, we get: I Rtotaltotal = I = I11RR11 + I + I22RR22 + + II33RR33

We know that the current through each resistor (from the first We know that the current through each resistor (from the first equation) is just I. equation) is just I. soso

I RI Rtotaltotal = I(R = I(R11 + R + R22 + R + R33))

Rtotal = R1 + R2 + R3

Parallel connectionParallel connection

Kirchhoff’s Current Law states that Kirchhoff’s Current Law states that

IItotaltotal = I = I11 + I + I22 + I + I33

from Ohm’s Lawfrom Ohm’s Law

IItotaltotal = V = V11/R/R11 + V + V22/R/R22 + V + V33/R/R3 3

but Vbut V11 = V = V22 = V = V33 = V = V

and Iand Itotaltotal = V/R = V/Rtotaltotal

gives us:gives us:

321total R

1

R

1

R

1

R

1

CapacitorsCapacitorswhere:

Vc – voltage across the capacitor

qc – charge stored

C – capacitancedt t)(sin iC

1 V

f2 t)sin( i i

dt iC

1

C

qV

maxc

max

cc

ω

then

ω whereω

if

C

1 X )

2 -t sin( i X

)2

-t sin( i C

1

cmaxc

max

where

πω

ω

VVcc = X = Xc c · I· Imaxmax (sin (sint - t - /2)/2)

VVc maxc max = X = XCC.I.Imaxmax

there is 90º difference in phase there is 90º difference in phase between current and voltagebetween current and voltage

XXcc is called is called capacitive reactancecapacitive reactance XXcc = 1/( = 1/(C) = 1/(2C) = 1/(2fC)fC) XXcc – a frequency dependent resistor – a frequency dependent resistor

Impedance, resistance and Impedance, resistance and reactancereactance

Impedance, Z,Impedance, Z, is the general name we give to the is the general name we give to the ratio of voltage to current. ratio of voltage to current.

Resistance, R,Resistance, R, is a special case of impedance is a special case of impedance where voltage and current are NOT phase shifted where voltage and current are NOT phase shifted relative to each other.relative to each other.

Reactance, XReactance, Xcc,, is an another special case in which is an another special case in which the voltage and current are out of phase by 90° the voltage and current are out of phase by 90°

Generalized Ohm’s LawGeneralized Ohm’s Law

V = I · ZV = I · Z

RC circuitRC circuit

Because of the 90º phase shift between VBecause of the 90º phase shift between VCC and V and VRR the resistance and capacitive reactance add the resistance and capacitive reactance add according to vector addition !!!according to vector addition !!!

so so ZZ22RCRC = R = R22 + X + XCC

22

2C

2RC X R Z

Low Pass FilterLow Pass Filter

Vin = ZRC· I

and

Vout = XC · I

RC

Cinout

Z

X V V 2

C2

RC X R Z fC2

1 XC

ff smallsmall

XXCC largelarge

ZZ XXCC

VVoutout V Vinin

ff largelarge

XXCC smallsmall

XXCC/Z /Z smallsmall

VVoutout 0 0

2C

2

Cinout

X R

X V V

1 10 100 1000 10000

0.0

0.2

0.4

0.6

0.8

1.0Vout

/ Vin

Frequency / Hz

For LPF with R = 10 kFor LPF with R = 10 k and C = 0.1 µF and C = 0.1 µF

High Pass FilterHigh Pass Filter

RCinout

Z

R V V 2

C2

RC X R Z fC2

1 XC

Vin = ZRC· I

and

Vout = R · I

ff smallsmall

XXCC largelarge

ZZ XXCC

VVoutout 0 0

ff largelarge

XXCC smallsmall

Z Z RR

VVoutout V Vinin

2C

2inout

X R

R V V

For HPF with R = 10 kFor HPF with R = 10 k and C = 0.1 µF and C = 0.1 µF

1 10 100 1000 10000

0.0

0.2

0.4

0.6

0.8

1.0

V

out/ V

in

Frequency / Hz

Band Pass FilterBand Pass FilterCascade an LPF and a HPF and you get BPFCascade an LPF and a HPF and you get BPF

In practice use Operational Amplifiers to construct In practice use Operational Amplifiers to construct a BPFa BPF

Why RC circuits?Why RC circuits? RC series creates filters RC series creates filters electrochemical cell may be simplified with electrochemical cell may be simplified with

RC circuit (recall from lecture 2)RC circuit (recall from lecture 2)

or, if faradaic process or, if faradaic process present:present:

http://www.phy.ntnu.edu.tw/java/rc/rc.html

Operational Amplifiers (Op-amps)Operational Amplifiers (Op-amps)

- very high DC (and to a lesser extent AC) gain amplifiersvery high DC (and to a lesser extent AC) gain amplifiers- proper design of circuits containing Op-amps allows electronic algebraic proper design of circuits containing Op-amps allows electronic algebraic

arithmetic to be performed as well as many more useful applications.arithmetic to be performed as well as many more useful applications.- they are essential components of modern-day equipment including your they are essential components of modern-day equipment including your

POTENTIOSTAT / GALVANOSTAT !!POTENTIOSTAT / GALVANOSTAT !!

What are they and why do we need them ?

General CharacteristicsGeneral Characteristics very high input gain (10very high input gain (1044 to 10 to 1066)) has high unity gain bandwidthhas high unity gain bandwidth two inputs and one outputtwo inputs and one output very high input impedance (10very high input impedance (1099 to 10 to 101414 )) GOLDEN RULE #1 : an Op-amp draws no appreciable GOLDEN RULE #1 : an Op-amp draws no appreciable

current into its input terminals.current into its input terminals.

General ResponseGeneral ResponseElectronically speaking, the Electronically speaking, the output will do whatever is output will do whatever is necessary to make the necessary to make the voltage difference between voltage difference between the inputs zero !!the inputs zero !!GOLDEN RULE #2GOLDEN RULE #2

+ 15 V

+

-INP U TS

OUTPUT

- 15 V

In op-amps (as in life) you never get anything for free. In op-amps (as in life) you never get anything for free. The gain (The gain () is achieved by using power from a power ) is achieved by using power from a power supply (usually supply (usually 15V). Thus the output of your op- 15V). Thus the output of your op-amp can never exceed the power supply voltage !amp can never exceed the power supply voltage !

Ideal Op-Amp BehaviourIdeal Op-Amp Behaviour infinite gain (infinite gain ( = = )) RRinin = = RRoutout = 0 = 0 Bandwidth = Bandwidth = The + and – terminals have nothing to do with polarity they The + and – terminals have nothing to do with polarity they

simply indicate the phase relationship between the input simply indicate the phase relationship between the input and output signals.and output signals.

0 100 200 300 400

-1.0

-0.5

0.0

0.5

1.0

Sig

na

l

time -50 0 50 100 150 200 250 300 350 400

-1.0

-0.5

0.0

0.5

1.0

Sig

na

l

time

+

-

0 100 200 300 400

-1.0

-0.5

0.0

0.5

1.0

Sig

na

l

time

0 100 200 300 400

-1.0

-0.5

0.0

0.5

1.0

Sig

na

l

time

+

-

Even if Even if ++ - - -- 0 then V 0 then Voo is very large because is very large because is so large (ca. 10is so large (ca. 1066))

Therefore an open-loop configuration is NOT VERY Therefore an open-loop configuration is NOT VERY USEFUL.USEFUL.

+

- V0-

+

Open - loop ConfigurationOpen - loop Configuration

Close-loop ConfigurationClose-loop Configuration

Often it is desirable to return a fraction of the Often it is desirable to return a fraction of the output signal from an operational amplifier back to output signal from an operational amplifier back to the input terminal. This fractional signal is termed the input terminal. This fractional signal is termed feedback.feedback.

+

- V0S

Rin

Rf

-

+

Vin

Frequency Response of Op-AmpsFrequency Response of Op-AmpsThe op-amp doesn’t respond to all frequencies equally.The op-amp doesn’t respond to all frequencies equally.

Voltage FollowerVoltage Follower

+

- V0

Vin

VVoo = V = V inin

Why would this be of any use ?Why would this be of any use ?Allows you to measure a voltage without Allows you to measure a voltage without drawing any current – almost completely drawing any current – almost completely eliminates loading errorseliminates loading errors..

Current AmplifiersCurrent Amplifiers

+

- V0

Iin

Rf

VVoo = - I = - Iinin R Rff

Summing AmplifiersSumming Amplifiers

+

- V0

RfR1V1

R2V2

R3V3

3

3

2

2

1

1fo

R

V

R

V

R

VR - V

Integrating AmplifierIntegrating Amplifier

V0

+

-R

Vi

C

dt V RC

1 - V io

And if you wanted to integrate And if you wanted to integrate currentscurrents ?

A Simple GalvanostatA Simple Galvanostat

A Simple PotentiostatA Simple Potentiostat

A Real PotentiostatA Real Potentiostat

The design of electrochemical The design of electrochemical experimentsexperiments

Equilibrium techniquesEquilibrium techniquespotentiometry, amperometry differential potentiometry, amperometry differential capacitancecapacitance

Steady state techniquesSteady state techniquesvoltammetry, polarography, coulometry and voltammetry, polarography, coulometry and rotating electrodesrotating electrodes

Transient techniquesTransient techniqueschronoamperometry, chronocoulometry, chronoamperometry, chronocoulometry, chronopotentiometrychronopotentiometry

In all experiments, precise control or measurements In all experiments, precise control or measurements of potential, charge and/or current is an essential of potential, charge and/or current is an essential requirement of the experiment.requirement of the experiment.

The design of electrochemical The design of electrochemical cellcell

ElectrodesElectrodesworking electrode(s), working electrode(s),

counter electrode and counter electrode and

reference electrodereference electrode ElectrolyteElectrolyte Cell containerCell container

Working electrodeWorking electrode most common is a small sphere, small most common is a small sphere, small

disc or a short wire, but it could also be disc or a short wire, but it could also be metal foil, a single crystal of metal or metal foil, a single crystal of metal or semiconductor or evaporated thin filmsemiconductor or evaporated thin film

has to have useful working potential has to have useful working potential rangerange

can be large or small – usually < 0.25 can be large or small – usually < 0.25 cmcm22

smooth with well defined geometry for smooth with well defined geometry for even current and potential distributioneven current and potential distribution

Working electrode - Working electrode - examplesexamples

mercury and amalgam electrodesmercury and amalgam electrodesreproducible homogeneous surface,reproducible homogeneous surface,large hydrogen overvoltage.large hydrogen overvoltage.

wide range of solid materials – most wide range of solid materials – most common are “inert” solid electrodes common are “inert” solid electrodes like gold, platinum, glassy carbon.like gold, platinum, glassy carbon.reproducible pretreatment procedure, reproducible pretreatment procedure, proper mountingproper mounting

Counter electrodesCounter electrodes

to supply the current required by the W.E. to supply the current required by the W.E. without limiting the measured response.without limiting the measured response.

current should flow readily without the need current should flow readily without the need for a large overpotential.for a large overpotential.

products of the C.E. reaction should not products of the C.E. reaction should not interfere with the reaction being studied.interfere with the reaction being studied.

it should have a large area compared to the it should have a large area compared to the W.E. and should ensure equipotentiality of W.E. and should ensure equipotentiality of the W.E.the W.E.

Reference electrodeReference electrode

The role of the R.E. is to provide a The role of the R.E. is to provide a fixed potential which does not vary fixed potential which does not vary during the experiment. during the experiment.

A good R.E. should be able to maintain A good R.E. should be able to maintain a constant potential even if a few a constant potential even if a few microamps are passed through its microamps are passed through its surface.surface.

Micropolarisation testsMicropolarisation tests

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

Reference electrodes - Reference electrodes - examplesexamples

mercury – mercurous chloride (calomel)mercury – mercurous chloride (calomel)the most popular R.E. in aq. solutions; usually the most popular R.E. in aq. solutions; usually made up in saturated KCl solution (SCE);made up in saturated KCl solution (SCE);

may require separate compartment if chloride may require separate compartment if chloride ions must be kept out of W.E.ions must be kept out of W.E.

silver – silver halide silver – silver halide gives very stable potential; easy to prepare;gives very stable potential; easy to prepare;

may be used in non aqueous solutionsmay be used in non aqueous solutions

The electrolyte solutionThe electrolyte solution

it consists of solvent and a high concentration it consists of solvent and a high concentration of an ionised salt and electroactive speciesof an ionised salt and electroactive species

to increase the conductivity of the solution, to to increase the conductivity of the solution, to reduce the resistance between reduce the resistance between W.E. and C.E. (to help maintain a uniform current W.E. and C.E. (to help maintain a uniform current

and potential distribution) and potential distribution) and between W.E. and R.E. to minimize the and between W.E. and R.E. to minimize the

potential error due to the uncompensated solution potential error due to the uncompensated solution resistance iRresistance iRuu

TroubleshootingTroubleshooting

is there is there anyany response? response? is the response incorrect or erratic?is the response incorrect or erratic? is the response basically correct but is the response basically correct but

noisy?noisy?

2.200E +0

-2.000E +0

-1.800E +0

-1.600E +0

-1.400E +0

-1.200E +0

-1.000E +0

-8.000E -1

-6.000E -1

-4.000E -1

-2.000E -1

-2.776E -16

2.000E -1

4.000E -1

6.000E -1

8.000E -1

1.000E +0

1.200E +0

1.400E +0

1.600E +0

1.800E +0

2.000E +0

E/ V vs RE

0.300-0.300 -0.250 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200 0.250

Cyclic Voltammogram

For resistor as a dummy For resistor as a dummy cell:cell:

W.E. C.E. + R.E.

2.500E -1

-2.500E -1

-2.250E -1

-2.000E -1

-1.750E -1

-1.500E -1

-1.250E -1

-1.000E -1

-7.500E -2

-5.000E -2

-2.500E -2

-3.469E -17

2.500E -2

5.000E -2

7.500E -2

1.000E -1

1.250E -1

1.500E -1

1.750E -1

2.000E -1

2.250E -1

E/ V vs RE

0.300-0.300 -0.250 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200 0.250

Cyclic Voltammogram

For RC as a dummy cell (with some filtering in pot.):For RC as a dummy cell (with some filtering in pot.):W.E. C.E. + R.E.

3.000E +0

-3.000E +0

-2.500E +0

-2.000E +0

-1.500E +0

-1.000E +0

-5.000E -1

0.000E +0

5.000E -1

1.000E +0

1.500E +0

2.000E +0

2.500E +0

E/ V vs RE

0.225-0.225 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200

Cyclic Voltammogram

For RC as a dummy cell (without any filtering in pot.):For RC as a dummy cell (without any filtering in pot.):