 Alright, in this lecture 5 which is still devoted to measurements, we will quickly review the indirect method for measurement of positive s values and then look at a direct method for measuring positive s values. We will briefly consider addition energies and then move on to the considerations of electrostatic phenomena. Among those, we need to look at some key concepts related to interfacial potentials. I will also try to give you a perspective for why interfacial potentials were studied at all in the manner that they were. To keep this discussion complete, we go back a few slides very quickly and the last topic that we had looked into was measurement of positive s values in a direct fashion. If a liquid like a lubricating oil is supposed to spread on a metal surface, there is no way of having the equilibrium situation, we cannot get the contact angle measurement to give us a measure of the spreading tendency. So, the way to do that would be to restrain it from spreading by using the surface pressure or counter surface pressure of a monolayer present in water. So, typically what one does is takes water, creates a monolayer on top of it, this monolayer could be like a steric acid or some long chain alcohol and keeps a solid on which the spreading cohesion has to be measured just beneath the surface a short distance below this surface and then allows a drop, small drop of liquid to fall on top of this water layer or the monolayer covered water layer. The impact would push the water layer away from the point of contact or impact and the oil drop would then directly come in contact with the solid surface. In an effort to spread on the solid surface, it will tend to push the surrounding monolayer which would presumably occupy a shape of this exaggerated kind. So, we do see the monolayer here with certain amount of compression occurring for the monolayer here that in turn as we will see later will create a surface pressure gradient which will oppose the further spread of this oil on the solid surface. It is interesting that for a variety of liquids and for different monolayers the entities you measure here turn out to be relatively constant values. We will shortly see what I mean by this, but what I want to indicate here is the situation would be similar for different oils and different monolayers, different kinds of monolayers. So much so that this angle theta 1 that you see here which is made by this restraining aqueous surface that will be pretty much constant and that simplifies our use of the theory considerably. Second thing is that irrespective of which kind of monolayer you have steric acid or satil alcohol any of the long chain alcohols, the spreading cohesion values you measure from here positive s values turn out to be same which means there is no risk of actually the contamination of the solid surface with the material which is forming the monolayer otherwise it should have given you different values if the contamination were to play a part. The method consistent measuring this theta 1 for now an equilibrium situation attainable in absence of this monolayer in the absence of this counter surface pressure this would have simply flattened into a very thick film and we would not be in a position to measure this equivalent of theta 1 there. However, the same surface which is spread over by this oil will not be amenable for spreading of water we understand that from the concentration of inverse spreading systems. So, it means that we can actually take a situation where the same solid surface now is used to keep a drop of water which unable to spread on this would form a contact angle theta 2 which you can measure and since it is a pure water drop the surface tension will be gamma 0 acting at this angle theta 2 measured through the liquid with this horizontal solid surface. The theory of this method is then very simple you just look at the definition of the spreading cohesion which will be fsis minus gamma l a plus fs l s and the energy balance for the monolayer restraining the oil drop. So, this is the hydrostatic pressure exerted by the aqueous phase this is the free energy per area for the solid liquid interface and gamma l a is the contribution coming from the surface tension of the liquid and yeah. This contact angle that you are measuring it is not actually the true contact angle because whenever that could be placed on a solid it will spread. Yeah. What is the application of this? Yeah, I think the point is the following. You have to remember that the whole effort is now for measuring the positive spreading cohesion and for positive spreading cohesion since that very basic equation s equal to gamma l a cos theta minus 1 is not applicable. We do not hope that the contact angle will give you any information as such because that contact angle will be 0 the solid the solid will be spread over by the liquid right. However, we want to measure this. So, how do we measure it? We have to overcome this problem of spreading in order to do that we achieve an equilibrium situation through this expedient of having a monolayer around this oil drop. If the oil drops tends to spread further it will be opposed by the surface pressure exerted by this monolayer any hydrostatic pressure that may be applicable per unit perimeter from this layer of water and the restraining forces which are corresponding to the surface tension free energy and the hydrostatic pressure arising from here. On the other hand FSWS is trying to operate in the tension force kind of situation in opposite direction. So, is the component of gamma trying to help the drop spread. So, is the balance of these energies visualize as forces that is simpler for visualization, but it is actually to be written in terms of energies right. Because the actual contact angle is not measurable, but this contact angle this particular effective contact angle for this new system is measurable. We hope that the spreading question that we define here would be measurable. It is our objective to find out what is this value right. So, in order to obtain this we can use the definition this is valid for any magnitude of spreading question positive or negative. If we can substitute for FSAS and FSLS in terms of the balance of energies for the two liquid system and just the water drop placed on the solid surface. We hope to get an expression for S which will give you from measurable quantities. The two contact angles theta 1 which is effective contact angle of this spreading oil when restrained by the aqueous monolayer and the second contact angle is what water drop would make on the same solid surface because water is unable to spread. So, we get around the problem of our inability to measure S directly this way right. So, how is this S is only that particular switching? Oh ok because we are substituting for these energies corresponding to the solid. This is for solid in contact with air, this is for the solid in contact with liquid. We are just obviating the difficulty of having the contact angle directly brought into the picture and we bring it in indirectly by having the apparent contact angle for the monolayer restrained drop surface. So, yeah. It does not matter because if you take a monolayer let us say of steric acid or C 16 alcohol or any other long chain alcohol the values that you finally, get for S they are the same. And the initial equation is also the same it has to be the equation this equation would not change in any way this equation would not change any way this is the basic definition. What may change is FSLS, FSLS could change if there is a contamination right. Same way FSAS may change if there is a contamination on the bare surface of solid ok. The fact and if that were the case then it could not have possibly lead you to the same value of S. So, the fact that measurements reveal a value of S independent of the type of monolayer it means that this method is robust we can rely on it. Any other question ok. So, our next equation was the balance of energies visualize through the tension. So, we could obtain FSLS from here and from the water drop placed on the steel surface with contact angle theta 2. Now, this is a true contact angle there is nothing to restrain it. For this case we take G plus FSAS there is the restraining there is the spreading part G is now exerted by this water drop itself in terms of what can contribute to spreading plus FSAS equal to gamma 0 cos theta 2 is equilibrium contact angle theta 2 plus FSWS right. You might have I think couple of clarifications here once again I had explained that last time, but I will repeat. We do not have a cos theta over here that is because this is a an oil which has a strong spreading tendency on the solid surface. So, even when you try to restrain it with the monolayer the monolayer is pushed apart far enough to make that contact angle very close to 0 right. It just short of enabling it to spread. So, we take that as 1 here. The second question which may arise in your mind and I think I deliberately left out last time was about this G. Look at this figure the G the symbol G is supposed to give you the extent of hydrostatic pressure contribution coming from the water head here right. And if you compare this against the equation we have written for a water drop placed on the solid surface over here once again we have G, but this is now acting in opposite direction. It is G is both for water in case of the two liquid system it is the restraining force because it is the aqueous phase trying to restrain the oil drop. Here this is contributing to spreading but it is again corresponding to water layer. Question which might arise in your mind is are we cheating here is G different in the two cases ok. So, if you look at it critically you have to understand that G is going to be quite small because the extent of elevation that monolayer covered water surface will have as a result of spreading of a single drop is going to be minuscule. Same way the hydrostatic force exerted by this water drop is probably incomparably small in relation to the interfacial and surface tension forces ok. So, these are going to be small quantities one could have neglected it, but the idea here is to give you an idea that hydrostatic pressure could also come into picture. And then in any case even if you were to choose different values for G and as let us say G 1 and G 2 they would be small values and difference of two small values would be even smaller that would then tell you that this is the kind of approximation you are making and there is no error in conceptualizing the analysis ok. So, the G values are small one could have neglected them straight away or one could have chosen different symbols, but they intrinsic values are small. So, the differences are going to be small. So, when you plug in in plug in the equation for S the magnitude magnitude for F s is from here over here and for F s ls from the previous equation from here we find now that these G's which are quite small will differ by even smaller magnitude. So, we could treat them to be nearly equal and cancel this off without any loss of clarity in the concept. What remains then is F s w also cancels we are left out with gamma 0 cos theta 2 and gamma cos theta 1 gamma l is also gone. So, we are left with this equation that is what we had seen last time. S is now gamma 0 cos theta 2 minus gamma cos theta 1 very quickly remember gamma 0 is the surface tension for pure water. Gamma is the surface tension for monolayer covered aqueous phase. Theta 1 is the contact angle in the two liquid system and theta 2 is the contact angle for water drop placed on the solid directly. Now, we just add a term gamma 0 cos theta 1 and subtract it. In the process we could then combine the second and third terms to get gamma 0 minus gamma cos theta 1 and we can combine the first and last term to get gamma 0 cos theta 2 minus cos theta 1, but gamma 0 minus gamma is nothing, but the surface pressure of the monolayer pi. So, that gives us this equation S is now pi cos theta 1 plus gamma 0 cos theta 2 minus cos theta 1 all right. We proceed from here, the argument is that experimentally one finds that this contact angle theta 1 in the two liquid system is about 58.33 degrees or cos theta 1 cos theta 1 is nearly constant at about 0.525 0.525 for different oils on chrome plated steel. Remember that many practical systems will have metallic surfaces spreading will be of interest with respect to lubricating oils and so on. And for different oils on chrome plated steel cos theta 1 is nearly constant at 0.525. Secondly, for clean water on steel the contact angle is about 45 degrees. So, cos theta 2 is about 0.707 and if you take approximately the surface tension for water at 73 dimes per centimeter, this gives you S equal to 0.525 the surface pressure pi plus 13.3. This equation is helpful in getting the spreading equations in a simple fashion just knowing the spreading pressure. I will like to connect this with one of the questions you had some time back. How does the nature of the solid influence the spreading right? Here it turns out that for a wide variety of oils on solids that effectively is not so much important in a simple fashion. So, as we can see here, but if it has to come into picture, it would come into picture where we have non-spreading conditions and that will appropriately be taken care of by the height of the drop like in sessile drop method. Next thing is we get some idea about the numbers what kind of condition should we have. Experimentally the guideline is that you take about a millimeter thick water layer above the solid surface or even lesser about half a millimeter thick water layer or the monolayer covered water surface should be just about half to 1 millimeter above the solid surface. The drop that you actually place on this solid surface should be released from about 3 centimeters height and the drop volume should be about 200th of a centimeter cube and you could use any of the long chain monolayers long chain alcohols or steric acid could be used. And the values you get would range for the spreading equations from about 10 to 20 dynes per centimeter for oxidized lubricating oils. For hydrocarbons on chrome plated steel the s value would range from about plus 17 to plus 25 dynes per centimeter. These are significant spreading equations and the analysis is relatively simple. We next look into indirect method for measurement of positive s values. Parts of this method we have seen earlier while we talked earlier about adsorption of vapor on a metal surface. We know generically that clean metal surfaces will have very high energy, surface energy and therefore, they will tend to adsorb vapors from even ambient air. If there are no impurities to adsorb air could be adsorbed. If water is available water could be adsorbed. Anything which is possible to be adsorbed on these high energy surfaces would be adsorbed and therefore, you may find that you can measure the contact angle directly. Supposing that there is a metal surface which is having a water monolayer adsorbed on it, the oil which will then normally to spread over it spread over the surface would not be able to spread because now the hydrophilic monolayer is there and you should be able to have an equilibrium shape of the drop. You can measure the contact angle and if you can measure the contact angle then you can measure the spreading question through this gamma l e cos theta minus 1. But we know that this is not the true situation. This is only an apparent situation because of adsorption. So, one has to make correction for the adsorption. Adding this energy change for the surface because of adsorbed vapor and this could be done through separate measurements. One can then obtain the spreading question for the clean surface through the similar approach that we had earlier and here we will require concentration of adhesion energies. The adhesion energies could be obtained either from the weighting balance method. Remember the willy me plate being pulled out of a liquid surface will let you have measurements for the vertical pull. If the liquid does not weight the solid then we will get F 1 equal to gamma l e cos theta 1. If you render a clean surface roughened to make contact angle 0, then the vertical pull in the second situation will be F 2 equal to gamma l e because cos theta 2 will be equal to 1. So, from that weighting balance method we can actually measure the work of adhesion or as in this case if the surface is contaminated then from the measurement of theta we can get W s l equal to gamma l e cos theta plus 1 or lastly any method which allows you to make measurement of spreading question could be used for deriving the work of adhesion because the spreading question is nothing but difference of work of adhesion and work of cohesion. So, spreading question plus twice gamma l e will give you the work of adhesion W s l. The steps involved the concepts other concepts involved will include Gibbs's equation and measured adsorption isotherm. One has to know how many molecules are adsorbed per area before you can make correction for the energy to obtain the addition energy for clean surface. So, you may remember the Gibbs equation where we have the variation of the surface tension with vapor pressure related to number of molecules adsorbed n. So, P times dou gamma by dou P at constant temperature was equal to minus k t n that equation could be used and once you know the change in the surface energy you can get W s l for clean surface. It is here that we change gears and begin a new topic which has considerable significance in all interfacial systems electro static phenomena. We are going to look into some of the fundamental concepts and the best way to go about would be to look into the historical account of how some of the concepts related to electro static phenomena were investigated in the first place and what were the debates or controversies and what conclusions prevailed. Last thing we would like to do is how do we take a current view of the old struggle of opposing concepts. First let me tell you that these experiments will appear very simple today. They actually were feasible experiments and the motivation was to understand what happens at the interfaces in living systems like membranes one comes across in living systems might have interfacial potentials. The curiosity was to understand what happens in living systems. I will make some generic comments there a little later, but we begin here by observing that the origin of interfacial potential was debated for surprisingly long period and there were two major research groups in this conflicting schools of thought. What was the conflict? It would appear very simple today and if you were to only look at it intuitively it is not difficult to comprehend it today as to why buteners school prevailed finally and while there are elements which support the thoughts of the other group laid by bar why those actually do not contribute significantly in the real life equilibrium systems. So, let us see what the debate was. The controversy actually spread over 1913 to 1946 buteners papers earliest papers appeared in 1913 and probably the last ones in 1946. Bors group had this opposing view which was for supported for a shorter time 1913 to 1926. The idea was if there is an interfacial potential what is the cause for it? What is the origin for the interfacial potential butener believed that they would be unequal distribution of cations and anions in the two phases across which we have an interface for which we are looking at the interfacial potential measurements. On the other hand, Bauer had this intuitive idea that some of these ions may actually be adsorbing at the interface and thereby give it a potential which would be measurable. When you look at this level each explanation appears plausible. It is conceivable that cations and anions may have different solubilities so they may distribute to different extents between the two phases. If you have long chain cations, let us say an organic chain is attached to a cation, it is also equally conceivable that in view of what we understand for amphipelic systems for surfactants these long chain cations might anchor at the interface forming a monolayer. So, at the first glance it appears that even the adsorption could be equally valid argument but it had to be settled and many things we cannot settle purely by thought has to be resolved by experiments. So, what are the experiments? The experiments were rather simple. Some kind of polar oil like salicyl aldehyde or ortho toluidine could be used as oil and placed in a tube between two aqueous phases. You could look at aqueous phase A, a salt bridge, aqueous phase B, a layer of oil and once again an aqueous layer here. All in a tube and with AG-AGCl electrodes coupled to an outer potential measuring device, you would be able to see if there is any change in the potential across the system. So, to start with we have certain aqueous solution A, B and G and an oil layer here. This is a rather thick oil layer. If one were to know what happens in the membranes or biological systems, one would feel that this is too thick a layer anyway, but then measurements would be possible only for such systems and then those elements of understanding could be carried forth to the other advanced situations. We focus on this interface C, interface between this aqueous phase B and the oil layer over here and what you could do is you could introduce a certain salt here, organic salt over here which would then dissociate from the cations and anions and after dissociation the cations and anions will have an option either to stay in the aqueous phase or to migrate to the oil phase or as bar conceived there might be a possibility of adsorption at this interface. Now anything is possible. At this point we are not making any commitment, but should there be any change in the potential here that should be recorded by this device. Remember the salt is neutral. We are adding it to aqueous phase. Upon addition and desolation in aqueous phase it will dissociate and then you find that the potential is changed. It could change for any reason and here the contention was that according to Butener the salt would unequally distribute its cations and anions between these two phases and according to Bohr cations would tend to long chain cations would tend to adsorb here and therefore would cause a change in potential. Whether the potential is because of unequal distribution of ions or because of adsorption it would be possible to measure this. So, it is not a very simple extent in which from the end result you could conclude what is the level at which the cause is that is what we want to investigate in course of time. If they took 23 years to finally have one school prevailing or other we might require a few lectures here. But I expect to begin today with the concept. So, I made already a comment about the oil layer being very thick, but it was hope it was hope that what happens in such a system may help elucidate the behavior of more complex membranes in living cells. In order to make these measurements in potential differences, measurements in potential differences you cannot have an oil layer very thin. If you have this oil layer very thin comparable to the membranes constituting the membranes in living cells, we would not get observable observable potential differences ok. So, in order to mimic what happens in these small scale living systems we need in the inanimate analog a much thicker oil layer that is about the only difference ok. And it is necessary to take this thick layer because we need to have measurable reliable potential differences ok that is the reason. So, the aesthetic objection that the oil layer is too thick to mimic a thin membrane in a real cell that is only aesthetic objection there is no big issue about the scientific principle ok. Like tetra methyl ammonium salts or picrates could be chosen as the salt and added to the quiz phase we talked of here B. One expects that whatever the cause whether it is unequal distribution on account of different solubilities or adsorption it is only the potential across the interface C that would change the one over here ions can not cross the solvage and this oil layer is too thick for the ions to actually first selectively prefer oil phase and then or for the aqueous phase it can cannot happen right. So, it is clear that whatever happens is around this interface. So, we kind of narrow down the range of action to the vicinity of this interface C ok. And whatever potential we measure we call delta phi potential change delta phi potential change measured across the extreme aqueous phases present in this tube will be delta phi. Butener believed that it was unequal distribution of cations and anions and that would change the potential. Therefore, the interface will become electrically charged. There are some notations and jargon over here. One of the other significant contributors to this area of activity was Lange and he called such distribution potentials as psi potentials or outer potentials. I have tried to think about why these particular terms were used and I will share with you as we go along. So, psi potentials or outer potentials are the ones arising out of differences in solubilities. And therefore, unequal distribution of the anions and cations across the interface between the two adjacent phases. I have a question here for you. If I have tetramethyl ammonium chloride as the salt which I introduce in that aqueous compartment B. And if I get a picture like this with no clarification whether this schematic diagram is to correspond to that physical representation of the extendable setup. If you only look at the picture to be this, if for some reason you had to know that the distribution of the ions is this way, what would you think of the left hand compartment and the right hand compartment to contain? Do not read the description below. Just focus on this figure top portion and see whether you can infer simply put which one is oil and which one is water. Sometimes the question will make a greater impression. Do you see a difference between the two compartments? There is a difference. So, what is the difference? Left one is oil and right one is water. Does everyone agree? Exactly opposite. I am not doing it that frequently, but I am fond of asking questions where I get divided opinions. Now, you can think a little bit of which one is correct. So, we got a butener and we got a bore. It should not take 23 years though. Why oil on the left? Why water on the left? What is the difference first? I mean what are the ions can be hydrated and can be more stable and they can stay apart. Okay. Oil, since we can see in the right hand side the number of ions of equal signs opposite signs are equal and they are not so far apart. We can see that. The trouble with details is that details get you lost. You do not see the obvious first. Maybe forget about all that I have said so far. Think afresh, look at the diagram and see what is there. It is like I think that puzzle you have spot the differences between two pictures. So, why miss the obvious ones? The chloride ion is more in the left side and positive in the side. Anion is more in the side. Okay. So, we see that this was a tetramethyl ammonium chloride salt. Dissociated will give you chloride ions and this tetramethyl ammonium cations. Tetramethyl ammonium would have a large hydrophobic character. Relatively large hydrophobic character. Chloride will be hydrophilic. So, we see that chloride is much more concentrated on the left. So, that should be water. So, sometimes maybe you do the pattern recognition at a glance you can tell that this is water, but then you have to probe deeper as to why it is claimed to be water. That is the reason. This cannot be oil because there is an overabundance of chloride here and relatively few chloride ions over here. I hope I am not confuse you by the representative population of ions displayed here. Anyway, so this was the idea which Butner had unequal distribution of cations and anions in the two phases. So obviously, if there are more anions here and more cations here, this would become positive related to this. So, that interface C with unequal distribution of cations and anions will eventually lead to measure delta phi across the electrodes, a g, a g cell electrodes in the terminal aqueous phases. Now, there is a little detail which I will just mention that you can see how much is the mean distance of these charges on either side of interface. You could think of that there is a certain plane here which will represent the mean distance of the anions over here and of cations over here. So, those are those distances, mean distances where the ions could be equivalently located that is called d by Herkel function, this one by Kappa. And that magnitude is quite small for water about a few tens of an angstrom to about a few hundreds of angstroms. That is the kind of distance of the anions in water away from interface. So, on the average tens or hundreds of angstroms are the length scales for separation of these ions and ions from the interface. In oil on the other hand, it can become about 100th of a centimeter, 10th of a millimeter which means if you take the ratios, you will find that the d by Herkel length in oil can be anywhere between 10000 to 100000 times that in water. So, the mean distance the charges or the ions are away in oil can be much larger in this region compared to over here. This is a matter of detail which may have to make which may have to be taken into account in later discussion. So, I am just glossing over this. Barr however maintained that this is not the picture, rather he thought that NMe4 plus will be anchored in the form of a monolayer here and that is what would contribute to the positive charge. Conceptually at first glance nothing looks awry with this. The name given for this potential is contact potential. So, ascribe able to an adsorb monolayer is Bauer's concept of contact potential delta v and then naturally what is measured one could say and in more precise work especially in transient systems one could think of some contributions coming from both. So, the total potential phi will be sum of these two. I will clarify this point a little bit because little bit later because this can be a source of confusion at times and we later theoretically prove that actually the contact potential cannot make stable contribution. So, at equilibrium always saying is we are still working with the notations and jargon. The total potential is this inner or Galvani potential phi is equal to the outer or distribution potential psi plus the contact potential v. So, phi is psi plus v. We are playing safe we are saying that if at all there is a contribution from adsorption that will be given by this. It is another matter that we admit this and then it contributes nothing in equilibrium system then it becomes phi equal to psi. This is what we will prove later. For the time being we admit that the outer plus contact potentials will give you the total or inner or Galvani potential. Since I have included quite a few mnemonics here and I know that students tend to get confused between notations and some of these equations I have a lighter representation here. One may look at phi as Galvani's insight inner potential that would be the outer potential plus contact potential. You might want to look at this as Galvani's eye with a contact lens. The total potential phi, yeah. I am discussing on the basics of life suppose we have oil and water. Now we are putting some iron like tetra methyl that is right. And we are now discussing on whether that particular ion will be distributed in oil and water as in suppose that has a hydrophobic part. Now we are discussing that that particular hydrophobic part will be distributed in water or with all the hydrophobic part in water. Now on the hydrophilic part in oil we come to the interface. We will all come to the interface. I will be discussing this issue that all the hydrophilic part will be distributed in itself because of their unlikeness. Yeah. What you are bringing us back to the point where we started this discussion. The question was what happens to the cations and anions? Looking at a transient picture. See the equilibrium situation is something which is ultimate. What happens finally? The transient one will have traces of many things. So when you begin at time 0 when you added this salt and supposing that immediately that gets dissociated then we have cations and anions in the first place. Now these will move about they will come to the interface. At the interface the cations realize that because of their hydrophobic character they have greater solubility in oil. So they will migrate there right. So it is possible that in the transient sense they might be accumulation near the interface of these adsorbed cations. But they may be adsorbed may be in only a certain time scale. So you might have a situation some of the anions are also there. So you could in principle have somewhat more general situation like Bauer imagined that there is an adsorption and he imagined that the adsorption will be predominantly of the cations that would contribute to this. But you could always think of adsorption of two monolayers. One on the oil side another on the water side. But conceptually it is not different from Bauer's because it is attributing arising a potential to adsorb monolayer or monolayers. And what the other school says butener school says that it is not this adsorption which is contributing in the long run to the equilibrium difference in potential. He says that the anions are going to distribute unequally because of their solubilities. So given sufficient time the distribution will be capable of making sure that there is no contribution coming from the adsorb monolayer. Although in shorter time scale they might be possibilities of something arising out of adsorption. To some see the point is there is here to remember this that and I think this is what you should reconcile. Some of these questions help me clarify what we discussed earlier. To a very different and unrelated looking system remember when we discussed the general Kelvin equation. General Kelvin equation to derive a relation between the radius of curvature and solubility right. Oil we say is immiscible in water right. So at a level of concentration that you can easily measure if you shake oil and water together there will be hardly any oil in water. But if you just choose let say a bit of petrol and water and shake it together even after separating water from petrol. I think what would have been originally portable water would not be portable anyway because you would be able to smell some petrol. Petrol is relatively immiscible with water but some of it traces actually managed to land up in water. So when we are talking of these hydrophobic parts and hydrophobic cations and hydrophilic anions we would not say that they are hydrophobic in the truest sense. As long as there is some positive charge there is always a finite probability of finding some of these cations in the water structure because water has so much of association charges also right the dipole moment. So if some of the cations get hydrated by water some of them could stay but not in overabundance because what it means is if you have to accommodate too many of these ME groups in otherwise structured water you are creating energetically unbearable situation. So at equilibrium will be certain number of cations locked up in water and most of them will be found in oil and same way some of the anions can actually be found in oil very few of them but most of them will concentrate in water right. So we are yet not saying that it is one way or other and the degree of freedom we get is from the point of view of what happens in the transient system. If it is equilibrium situation then it is a different thing and we will prove later that it is only the unequal distribution which contributes to the observed potential and it is not the adsorption. So delta v does not contribute at equilibrium but it will take a while before we come to that theoretical point. So let we have a few minutes left we will discuss a few things here. So it could be inferred from later measurements and discussion analysis that adsorption does not contribute to the stable interfacial potential in an equilibrium system. Now there is a different issue this is a slightly different point of view. Supposing the monolayer where to contribute something if it is monolayer which is contributing to measured interfacial potential delta phi one thing we will admit that monolayer will be necessarily very thin. So it is not going to be able to alter the potential of bulk phase for oil or water because it is a very thin layer at the interface far away from the interface how would it change the potential. Even if it were nonzero in the beginning the ions will always distribute themselves between the phases such that the electrochemical potential indicated by mu bar here this this bar has gone underneath this is mu super bar will be restored to the initial values but you need to know what the electrochemical potential is. The electrochemical potential is defined by this equation this is the chemical potential that is a Faraday unit this is the potential measured. So mu bar is mu plus phi times f because the thickness of monolayer is so small it would not be able to alter the chemical potential of each of the bulk phases. And also unaltered therefore is this potential phi between the phases because we have this equation here mu bar related to mu plus phi f ions somehow automatically redistribute. So that is the total potential drop across the interface is unaffected by the presence of a monolayer and origin of these various potentials could be illustrated experimentally by choosing different systems. We will look at many experimental measurements later to make these sentences meaningful in view of the measurements. We could for instance choose different non aqueous phases different oils could be chosen and you could alter the contributions of psi and V to phi. It may be possible for instance to have no possibility of distribution can you think the degree of freedom you have is you can choose non aqueous phase according to your will. Question is what kind of non aqueous phase will be ensuring that there is no contact potential no there is no distribution potential contributing at all what is generally believed to be the predominant contributor to phi. In view of what we discussed just now as long as you have a condensed second phase non aqueous phase is always a possibility of some an ions going there. Obviously very strong likelihood of most cations going there, but supposing we want all our ions to be only restricted to one phase what kind of non aqueous phase can we choose. The answer is very simple let go of condensed phase choose air. Now if you have air in contact with water the ions can cannot go into air. So, practically the every contribution that can come for phi will be only through the contact potential. So, this is only a dramatic example of how choice of a non aqueous phase can give you a contribution solely from V to phi and by choosing different condensed phases different degrees of polarities we may be able to vary the contribution of psi to phi. I think we can stop here and resume from here next time.