So in this class first I want to describe electrode-electrolyte interface, okay. It

forms what is called double layer; I want to describe that and then we also want to

see why often times we use three electrode system and what is the role of what is called

supporting electrolyte. And if time permits, we would see how the rate constant in an electrochemical

system will vary with potential part, okay.

If you imagine, you have metal electrode on one side and water based electrolyte on the

other side. The moment we put a metal into the liquid, ions in the liquid will come and

adsorb on the metal, okay. So this can be visualized as follows: you have one layer

of ions adsorbed on this electrode and that forms what is called inner Helmholtz plane

or IHP, that is given by the green colour line here.

Once you have many ions adsorbed on the surface, ions of the other polarity, positive ions

here for example, would come close to this. So this forms what is called double layer.

Normally ions in the liquid or water will be solvated, that means water dipoles will

be surrounding these ions. I am not showing them here for simplicity, okay. If you have

a positive ion, like sodium, Na+, that is a cation and chloride, Cl-, is an anion.

Normally you have sodium that loses an electron and becomes Na+, that has a small volume.

It has unity charge, so it is having a large charge density. Chloride on the other hand

will have a small charge density compared to the Na+, okay. By and large anions have

small charge density, cations have large charge density. There are exceptions to this, but

by and large this is true. So this is one description where within 1 nanometer you have

one polarity for the metal, adsorbed ions right next to that, and then in the outer

Helmholtz plane, another set of ions.

This can be visualized like a capacitor and this is often called double layer capacitor.

And a typical value is between 10 to 30 microfarads per unit area. Unit area here means per unit

square centimeter. If you visualize, you might be supplying 1 volt across this interface.

1 volt in 1 nanometer is about 1 gigavolts per meter. So it is a very large electric

field occurring in a very small or very short range.

There is an another model called Gouy-Chapman model which says that from the electrode for

about 10 nanometer or so, the charge distribution occurs. So it is not occurring in 1 nanometer

but it actually occurs over a 10 nanometer distance. And there is a model called Stern

model which combines the inner Helmholtz plane, outer Helmholtz plane and Gouy-Chapman model

which says lot of discharges are lined up right next to the electrode but some charges

are distributed further away from the electrode.

So it is a combination of the Helmholtz plane as well as the Gouy-Chapman model, okay. If

you have electrolyte concentration in the range of 1 molar, then pretty much all the

charge separation or charge distribution occurs right next to the electrode and you do not

have to use the Gouy-Chapman model. If the concentration of the electrolyte and water

is about 1 millimolar, then probably it is better choice to use Gouy-Chapman model.

Now if I have 1 electrode right next to that is the electrolyte. I have shown that, you

can describe that by a capacitor and we call that as a double layer capacitor and we represent

that by Cdl. So on the left hand side picture in the blue colour diagram, you have got Cdl

but this assumes that there is no moment of electron or any material across the interface.

But at sufficient potential, you may have a reaction happening.

That means you have metal here, you have electrolyte here. Electrolyte may take an electron or

give an electron. The material can come out and dissolve or some material in the electrolyte

can go and deposit. If any of this happens, this type of reaction is called electrochemical

reaction. There is a chemical reaction but in addition to that, there is an electron

transfer. This reaction, electrochemical reaction would also give rise to current.

And this gives rise to, you can think of a resistance or a generalized resistance. We

call that as impedance. I will give you a better description of impedance later. But

right now, we can take impedance can be represented by the letter Z and we give a subscript F

to indicate it is a faradaic impedance that means it is associated with the electrochemical

reaction. So I have a capacitor; if current passes because of the capacitor, we call that

as a capacitor based impedance.

If the current passes because of a reaction, we call that as a faradaic impedance. In one

electrode you may have a reaction or you may not have a reaction. If you do not have a

reaction, we just represent by the double layer capacitor. If we have a reaction, we

say there is a capacitor, in parallel we have an impedance given by the Faraday process.

At the minimum in an electrochemical cell, you will need two electrodes.

So you have 1 electrode described or modeled by the circuit on the top left called Cdl1

and ZF1. You have another electrode which is given by the subscript 2, and in between,

you have the electrolyte, we call it as solution and the resistance offered by the solution

is called solution resistance or Rsol here. So this is a model for a simple two electrode

system with electrode on 1 side, electrode on the other side and electrolyte in between

these two , okay.

When we put an electrode or a metal in solution, it develops a potential. Can we measure the

potential? There is a difficulty associated with that, so I want to describe that here.

We cannot measure the potential of a single electrode. The moment we immerse the electrode;

it forms a double layer, there is a potential. We want to know the potential difference across

the double layer, across the electrode-electrolyte interface. In order to do that, we will connect

it to a multimeter.

The other side of that wire which we call as ground, normally call as ground, we want

to connect to the liquid. The moment we connect to that liquid, that probe will also form

a double layer. It is not going to have zero potential difference between the metal probe

that is a ground probe and the liquid. Liquid or solid whatever the electrolyte, that is

there. So that potential, let us say it is y and let us call the actual potential between

the metal and the liquid across this double layer as x.

All that we can measure is x-y. We cannot measure the exact value of x, because the

y value is comparable to x, it is not negligible compared to x value. So we will always be

able to measure only the potential drop across one electrode, potential drop, any potential

drop that can occur in the solution. It may be negligible, it may not be negligible; that

is a separate issue. But we will have to take into account, that there is 1 more electrode;

we do not mean it as an electrode, but the moment you insert a probe into this, that

becomes an electrode. So we cannot measure the potential across a single electrode. Not

just that, there is an additional problem.

Let us say we apply a voltage. We apply 1 volt, we have two electrodes; we apply 1 volt

and on the left side, let us say it is 0.8 volts above, meaning positive compared to

the liquid. On the right side electrode, it may be 0.2 volts below. That means, I have

total of 1 volt between these 2 terminals but 0.8 volts potential drop occurs in the

first electrode-liquid interface and in addition, compared to the liquid, this is 0.2 volts

below, the metal is 0.2 volts below.

So if you take the algebraic sum, you will get 1 volt. We do not know whether it is 0.8

or -0.2 but let us just imagine that this is the case. If I increase, the potential

from 1 volt to 1.5 volt, can I guarantee that increase will occur evenly? Can I guarantee

that the increase will occur only near one electrode? Can I get anything about the distribution

of the increase? So I cannot measure the potential across one interface. Fine.

I do not know the potential but if I increase a little, if I increase the applied potential

a little, can I at least say that increase will go into this or it will be going 50:50

or in some given ratio, can I guarantee that? It may go like the example given here. If

it changes from 1 volt to 1.5, the electrode on the left side can increase with 0.3 voltage,

the potential on the electrode on the left side may go from 0.8 to 1.1, and the potential

across the interface for the electrode on the right side may go from -0.2 to -0.4.

That is a possibility. It can also happen that for the same applied voltage, on the

left side the electrode might have changed slightly but the potential across the electrode

might have gone from 0.8 to 0.9 and on the right side, it might have dropped from -0.2

to -0.6. This is just 2 examples. There are many possibilities. So basically when I apply

a potential, I cannot tell how much is the potential drop from the electrode to this

liquid.

When I change it, I cannot tell how much increase has gone here. So basically that means, if

I have an electrochemical system, I can apply voltage, I can measure the current. I can

increase the voltage, I can measure the current. I can say this much is the increase or change

in the current but I cannot tell, this is the potential change here, this is the potential

change here. So you can imagine in this scenario, it is very difficult to come up with any interpretation

of the results.

So to overcome this difficulty, we introduced something called reference electrode. Reference

electrode is a particular type of electrode, where the potential drop across the interface

from the metal to the liquid, is a constant. We still cannot measure what that potential

drop is. But we know it is a constant. So in that scenario, it is beneficial to use

the reference electrode.

Let us say that C1 is the potential drop across the metal liquid interface. It usually consists

of multiple interfaces. From the metal to the electrolyte liquid, let us say the potential

drop is C1. It is fixed number, okay. That means if I apply 1 volt with the reference

electrode here and with the other electrode that is of interest to us, we call it as a

working electrode, okay.

If the potential is applied and if it is 1 volt, I do not know what C1 is but I know

the other electrode has 1-C1 as the potential drop. Now this is not very useful. However,

if I apply a slightly different voltage, if I change the voltage and make it 1.5 voltage

across these two electrodes, I can guarantee that the additional 0.5 voltage, that drop

will occur only at the working electrode.

So this is useful. Although I cannot tell exactly how much is the potential drop across

an electrode. When I change the potential, I can say this is the change in the potential

across this electrode. Therefore, any change in the current, I can assign it to that change

in potential. So now I can make some sense out of this system.

Lot of times, we use what is called Luggin capillary. Basically we want to minimize the

resistance, solution resistance between the working electrode and the reference electrode,

okay. So if you are able to place the reference electrode close to this working electrode

without affecting anything else in the system, it is well and good. If you have some difficulty,

we can fill this, fill this entire system with the normal electrolyte, and then place

the reference electrode within this Luggin capillary system and place the tip of the

capillary right next to the working electrode, okay. This way we always report the potential

of the working electrode with respect to a reference electrode. It is not correct to

say potential of this electrode is 1 volt. We have to say this is with respect to this

reference electrode. There are different types of reference electrodes available, okay.

One is called standard hydrogen electrode, SHE, another is called standard calomel electrode

or SCE, another is called silver-silver chloride or Ag-AgCl immersed in various concentrations

of KCl. As long as you report it correctly, you can translate from one reference electrode

to another reference electrode. So if you do experiment at 1 voltage with respect to

Ag-AgCl, to do the same experiment with another reference electrode, you have to apply a constant

offset. These are available in literature.

Now if you make the impedance of the reference electrode as very small, okay, so the re-

should have constant potential drop. It should ideally also have very little impedance. Then

I can describe the entire system, that is two cells with this circuit. On the other

side, the impedance of the reference electrode is very little, then I can just look at the

system and say only the working electrode has double layer capacitance and the faradaic

impedance, significant faradaic impedance, and you can possibly have solution resistance.

There is one more circuit to describe the reference electrode but that offers very little

impedance. So when I consider the total impedance, I can neglect that. But there is one difficulty

in using the reference electrode. If significant current passes through the reference electrode,

then it loses the property that it has a constant potential drop across this interface. So that

means if you apply voltage, if current comes or current is taken up by this system, then

I have to put another electrode and supply that current to the system or take away the

current from the system, so that any current that comes from the working electrode is taken

up by the other electrode and that is called auxiliary or counter electrode. Other than

taking up the current of giving this current, it should give minimum disturbance or minimum

changes to the system.

That is one requirement of a counter electrode. So we end up using three electrode system

so that we can have control over the potential drop across the working electrode, okay. So

the potential is measured between the reference electrode and the working electrode. If we

do the experiment correctly, the current will go from working electrode to the counter electrode,

and the potential of the counter electrode will be controlled by the instrument.

It will be adjusted so that any current that comes through the working electrode is taken

up by the counter electrode. Normally, we want to have a large counter electrode area,

large area counter electrode. There is a reason for that, okay. When we change the potential,

what is controlling the electrochemical system, is the current density. If you happen to have

a large working electrode, then for a given current density, the current will be large.

Now all the current generated here has to be taken up by the counter electrode, okay.

In case you have a small area counter electrode, the current density requirement is high. So

compared to the working electrode, if the counter electrode area is small, the current

density that is taken into the counter electrode or current density requirement for the counter

electrode is high. That means it has to be taken to a large potential and possibly you

can have problems.

So it is better to have a large area counter electrode, then the load on the equipment,

the potential on this counter electrode with respect to the reference electrode and the

load on the equipment will be less. So what we end up doing is to use platinum mesh. Platinum

because it is inert, mesh because it permits large area for a given geometric area, okay.

When you buy an instrument or when you look at the specification of an instrument, it

gives you what is called applied voltage range and the compliance voltage range.

Applied voltage tells the voltage between the reference and working. Compliance tells

the voltage between counter and the working electrode. Now you can imagine if current

comes through this, the counter electrode potential has to be adjusted very fast, that

means you need a fast response system, you need a close loop system. Based on this, the

potential has to be adjusted.

It cannot exceed a particular limit. If it becomes too high, then too much current will

come from this, if it is too little, then sufficient current will not be taken up by

this. Either case, you want a fast response system, you want a closed loop control and

it has to accurately measure the current. We want to measure current in microamps, nanoamps,

possibly picoamps, and the instrument which controls three electrodes, the three electrode

system is much more expensive than a simple DC current or DC potential power supply, okay.

DC potential power supply, you can get it for less than 50,000 rupees, that is less

than 1000 dollars, very easily. If you look at potentiostats, even a small potentiostat

will probably cost about few lakhs, that is few 1000 dollars, okay. One that can supply

large current will cost you lot more money, okay. The main difference is that this can

handle the three electrode system, it has to have a fast response with the closed loop

without any stability problem.

If you have a two electrode system, it is very easy to get an instrumentation for that.

But then two electrode system is probably useful only in electrical and in some special

cases. Electrical circuit analysis and special cases, two electrode system is fine, electrochemical

system, it is better to employ a three electrode system.

So this is just a pictorial description to tell you what is the applied voltage, where

it is measured and what is the compliance voltage, it is measured across the working

electrode and the counter electrode.

Next in a simple electrical circuit, when you have a resistor, you change the potential,

you will see a change in current and usually that relationship is linear, that is V/I = R

and that is a constant. The R can vary with temperature. Sometimes you would see a slight

difference but by and large, it is a constant. There is a huge difference between electrical

system response and the electrochemical system response.

This is one curve; I have just drawn it in the PPT here. If you take water and let us

say you put some salt to make it better conductor, and then you control the potential and measure

the current over a range, you would find that for a wide range, there is no current or there

is very little current. So you can go to one potential, measure the current. Go to another

potential, measure the current.

So let us say you have a two electrode system, two platinum meshes are there immersed into

salt water. If you measure the current and potential, you would find that for a large

range, large range here meaning about 1.8 volts, you would see no current at all, and

after that, if you go to very positive potential for one electrode, obviously it means negative

potential for the other electrode; current will be higher and it is going to be positive

because oxygen will come from this electrode and hydrogen will come from the other electrode.

If you go to very negative potential for a given electrode, you will find hydrogen is

evolving in that electrode and oxygen is evolving in the other electrode. Basically water splitting

happens, and if you want to study any reaction other than water splitting, other than hydrogen

evolution or oxygen evolution reaction, then you have to work within this window. If you

put water base system and then want to study a reaction, then I have a limited window available

for experiments.

It is possible to extend this window by using certain electrodes. So for hydrogen evolution,

certain electrodes are good catalysts, certain electrodes are poor catalysts. So if you use

zinc, if I use mercury, hydrogen evolution does not occur that easily. So thermodynamics

tells beyond this potential, hydrogen evolution has to occur. But kinetics tells, at what

rate this occurs. So in certain electrodes like platinum electrode, it occurs at a good

rate, it is a good catalyst.

Some electrodes like zinc, lead, or mercury, hydrogen evolution does not occur that well.

So the rate of production of hydrogen is very low, so I can extend the window and still

study some other reaction, this is one trick. Another possibility is to use different electrolyte

so I can use non-water based or non-aqueous solvents and extend the window. But every

solvent will have a breakdown voltage and beyond that window, we cannot use it.

Now, I can increase the conductivity of this electrolyte by using what is called supporting

electrolyte. Supporting electrolyte is basically a salt or acid which you can use without causing

any change to the system except for change in conductivity. That is it should not undergo

any reaction, it should just increase the conductivity, okay.

If you have good conductivity, if you have lot of supporting electrolyte, then you can

take this model, this is for a good reference electrode, the model on the orange colour

is given for a good reference electrode. Working electrode is given as Cdl and ZF. Solution

resistance is present, If it is negligible when you have lot of supporting electrolyte;

supporting electrolyte for ex ample can be sodium perchlorate, okay.

Then all the potential drop in the working electrode will occur just across the interface.

If you look at the potential, I have drawn here; It is going to go from a large voltage

to a lower voltage in a very small space. This is to indicate about 1 nanometer or so

across the Helmholtz plane. If the conductivity is low, if it is just water with little bit

of salt, little bit meaning like millimolar, micromolar of salt, then when you have a reaction

that you study, current passes through this interface, current also passes through the

electrolyte and significant potential drop will occur across the electrolyte.

and whatever we imagine that we are applying this potential, and we are changing the potential,

the additional potential is applied across this electrode. We imagine that it is occurring

across the electrode but a significant change may occur across the, or between the two electrodes

in the system. So this is a description of how the potential will look like if you have

high solution resistance.

So in order to avoid this, many times we add pretty much inert material, inert material

as far as the reaction is concerned but as far as the conductivity is concerned, it increases

the conductivity, and basically, it make sure that the electric field is such that all the

potential drop occurs only across the interface.