 In this lecture 7, we take up discussion on cohesion, adhesion and spreading. We had seen couple of slides on cohesion and adhesion, we will take them up again for review. We define the work of adhesion between oil and water in terms of this expression. Sum of surface tensions of oil and water minus the interfacial tension between oil and water is a work of adhesion and that equation, Dupre's equation follows from this thought experiment in which you separate an oil layer from water and let air occupy the space in between. So, the final interfacial energy is the sum of the surface tensions and the initial one is the interfacial energy or interfacial tension. So, that gives us this work of adhesion. We looked at some magnitudes for the work of adhesion for water and paraffin oil. It comes out to be at 43 irks per centimeter square. Then we ask a question about cohesion. We just have to simplify this situation for two liquids. The liquid surfaces now will be both identical and therefore, the work of cohesion follows from the Dupre's equation as seen here because the interfacial energy between two identical surfaces will be 0 and the two surfaces will have the surface energy each of gamma OA. So, the work of adhesion of oil will be just simply twice the surface tension of the oil and that holds for any liquid. So, for water the work of cohesion is 72 into 2 that is 144 irks per centimeter square and for paraffinic oils it is about 44 irks per centimeter square. The last thing that should be noted here is that in terms of attraction the molecules of one kind if they have a greater attraction for the molecules of other kind then we expect these phases to be completely missable and this should happen spontaneously because it would be associated with a decrease in the free energy. So, missibility of two liquid phases could be argued as an overall effect related to adhesion. If the two different kinds of molecules have greater affinity for each other than for themselves then we expect the phases to become missable. We will try to this take this argument little more analytically forward. So, this is what we will try doing today. In terms of adhesion and cohesion what we are saying is let us take a scenario where WOW or work of adhesion between oil and water exceeds the work of cohesion of oil that is W oil. So, WOW is greater than or equal to W oil and likewise it is also greater than the work of cohesion for water. So, WOW is greater than or equal to W water. Now we can write WOW to be greater than W oil by 2 plus W water by 2. We just add up these divide by 2 and that amounts to WOW exceeding the sum of W oil plus W water divided by 2 or the average cohesion. If the work of adhesion exceeds average cohesion we expect these two phases oil and water to become missable, but just now we have seen the work of cohesion as it is related to the surface tension. So, half of W oil is nothing but gamma OA and half of W water is gamma WA. So that means WOW if it exceeds the sum of these surface tension gamma OA and gamma WA then we expect missibility to actually result. So we could take this forward interpret this way that the work of adhesion if it exceeds the average of work of cohesion of the two liquids we will get a missable system. Now imagine that we had two components and they are in molecularly, molecularly dispersed form. These could be visualized as a pseudo homogeneous phase and if this pseudo homogeneous phase has a high cohesion that is average of the two components cohesive energies such that this average cohesion is higher than the work of adhesion. If that is the case then of course the conditions are not favorable for missibility and this can happen for two reasons one both the works of cohesion are high or at least one of the phases has a very high work of cohesion such that the average cohesion exceeds the work of adhesion. Now if this is a situation we recognize that missibility is not favored. In such a case this pseudo homogeneous phase would not be stable because the high cohesions would imply there would be aggregation or merging together of individual molecules or molecular clusters and this aggregation will result into a separate phase ok. So if the adhesion were stronger the molecules would have favored molecules of other kind to themselves that would have form a missable system. But even if one component has a very strong cohesion enough to make the average cohesion exceed the work of adhesion then it would lead to aggregation, coalescence and eventually formation of a separate phase. That will leave the second component to itself stranded as a separate phase. So we now see missibility in the light of work of adhesion and cohesion. This is more insightful than thinking of missibility as a concept by itself. We can take an example mercury and water both have high cohesive energies, cohesions are high or you could take another example mercury against organic liquids in which case mercury alone has high cohesion and molecular dispersion even if we create it by applying temporarily some external energy source that molecular dispersion would be unstable and will break down into mercury and the organic liquid as separate phase. Now what can we say in terms of Dupre's equation? This would actually lead to result which is equivalent to saying that interfacial tension gamma O w is less than 0 for a two component system is that is less than or equal to 0 for a two component system. Look at this equation 44 if we substitute for w O w the expression which is statement of Dupre's equation w O w is gamma O a plus gamma w a minus gamma O w right. So gamma O a plus gamma w a cancels from both sides and leaves minus gamma O w on the left hand side greater than or equal to 0 or that leads you to gamma O w less than or equal to 0 clear. Gamma O w less than or equal to 0 means in physical terms that now there is no stable interface possible here because the molecules of the two liquids tend to mix as completely as possible. This result is true only for a binary system it is important to interpret our result our direction to the premises where we to consider effect of a third component which could be spread as a film at an interface between two coexisting immiscible liquids. Then the third component can momentarily indeed make the interfacial tension negative but it will lead to spontaneous emulsification. Because now the interface has instead of contractile tendency to expand and therefore limited by the constraints of the geometry the interface will keep expanding and will get buckled splitting one phase into another leading to spontaneous emulsification ok. So, interpretation of the same result gamma O w less than or equal to 0 has to be done in the ambit of what system we have, miscibility would follow in two component system. In three component system we may have completely different scenario we may have spontaneous emulsification. Now this brings us to spreading we all seen different liquids spreading on various substrate surfaces we know from a common experience certain liquid spread on surfaces others do not. What we going to say here is generically true for all spreading but for the sake of argument we will focus on liquid liquid surfaces. So, we going to talk about spreading of one liquid over another liquid and we begin with this thought experiment you can actually follow it up with actual experiment. Imagine that we have a small drop of a higher paraffin a high boiling paraffin placed on surface of water it would keep floating as a drop the high boiling paraffin oil will keep floating on water surface as a drop resembling a lens as shown in this figure. We have to begin with air water surface and we place this oil drop of a higher paraffin high boiling paraffin and we get this equilibrium shape of a drop. We have certain notations here let us familiarize ourselves with those the tangent along the oil surface in air that is the direction in which the surface tension of oil acts gamma o a gamma o slash a the tangent to the oil surface in water that arrow is showing gamma o w the direction in which interfacial tension between oil and water act. Along water surface we have the surface tension of water trying to pull the oil drop that is gamma w a this would be the equilibrium lens of a higher boiling paraffin oil floating on water this is the first scenario let us say we equate the horizontal components of the tensions here and we presume that the surface tension of water acts exactly horizontally with that we will have gamma w a equal to gamma o a cos theta 1 where theta 1 is the angle that gamma o a is making with the horizontal plus gamma o w cos theta 2. So the balance of horizontal components of forces acting along the surfaces will give you this gamma w a equal to gamma o a cos theta 1 plus gamma o w cos theta 2. Equilibrium will be attained and we have the equilibrium shape of lens here in our second phase of this hot experiment we replace we replace the high boiling paraffin oil drop with a lower boiling paraffin oil like octane if we do that we will have decrease the surface tension of oil and that to such an extent that the surface and interfacial tensions on the right hand side of our force balance must exert their full influence in order to balance the surface tension of water. If the two terms on the right hand side have to exert their full influence to balance gamma w a on the left hand side it means theta 1 and theta 2 must become 0 only then cos theta 1 and cos theta 2 will take up the highest values 1. If theta 1 and theta 2 both become 0 then there will be just enough opportunity for the water surface tension to be balanced by the sum of surface tension of oil and interfacial tension between oil and water. So, one may say that a near equilibrium situation would still be attainable. In the third phase we replace this lower boiling octane by a polar compound a polar liquid like normal octane. Now we have a situation that our equation corresponding to the horizontal component balance for tensions can never be satisfied because surface tension of water is greater than the sum of the surface tension of oil and the interfacial tension between oil and water. So, what would happen? Here the drop of octanol rests on the surface of water momentarily and then keeps on spreading out until the entire surface of water is covered with a thin film of octanol ok. Now this is something which will lead us to some useful index for characterizing spreading. Here we see a positive tendency of octanol to spread on water, but what quantitative index can it generate for us? Here theta 1 and theta 2 must again approach 0 the drop thins out during spreading and one may say that whatever equation is suggesting is that since that balance is not possible gamma w a will always exceed the sum of gamma o a and gamma o w. The difference between the surface tension of water and the sum of the surface tension of oil and interfacial tension between oil and water is a measure of the ability of the oil to spread on water and that we crescent as the initial spreading cohesion. We simply call it capital S initial spreading cohesion make note of the fact that we not just calling this spreading cohesion but referring to as to it as initial spreading cohesion. Why we do this will become clear as we go further. So, now let us reaffirm that the spreading cohesion is gamma w a minus gamma o a plus gamma o w. The quantities here gamma w a, gamma o a and gamma o w are all measured before the two liquids have become mutually saturated. So, if you are dealing with pure oil pure water and you take their surface and interfacial tensions when plugged in here will give you the spreading cohesion but that is the initial spreading cohesion applies for only the scenario when we place the spreading oil on top of water just then not after waiting for long. Let us see some numbers here. If our higher boiling paraffinic oil is normal hexadecane the spreading cohesion is minus 9.3 dyns per centimeter. So, this normal hexadecane will not spread on water. We return to normal octane the spreading cohesion works out to be plus 0.2 dyns per centimeter. So, normal octane will just about spread and in case of octanol we get a very high positive value for the spreading cohesion as of plus 36.8 dyns per centimeter. Octanol has such high tendency to spread that what it means is it would spread on water surface even if we were to have impurities already adsorbed on water surface octanol will be able to push the impurities and that opposition in the surface can be overcome by the very strong spreading tendency of octanol. So, that quantifies the thought experiment that we started out with and then Ampli clarifies the concept of spreading cohesion initial spreading cohesion. Now we could go back to some interesting experiments in the history, but before we do that let us note that if impurities are present on water surface or contamination is present on water surface it would tend to lower the surface tension sometimes considerably below that for pure water and yet spreading often occurs on such surfaces. So, the liquids which can spread against such contaminated water surfaces clearly have very strong tendency to spread. Why do we need to go to history in context of spreading here because you might not have been aware of the fact that the first real conclusive evidence for the atomic theory or the ultimate indivisibility of matter came from this interfacial experiment conducted by Benjamin Franklin in 1765. He merely spread olive oil on water surface and measured the thickness of the layer that he got. It worked out to be 25 angstroms no smaller thickness was possible. It was clear that we cannot get a thinner layer than about 25 angstroms thick for olive oil because the hydrocarbon chain length itself is 25 angstroms. You cannot get anything lower than that. Naturally equation arises was as to how the system would respond if we were to try to make this layer thinner. Obviously at that time it was not known that it is not possible to get olive oil to a thinner layer for any other reason. However, the experiments were still conducted and while I encourage you to visualize what might happen I will provide you evidence that followed in later work by Lord Rayleigh that was in 1899. He took a different oil he took a different oil castor oil here he found something similar. Once again you could not get anything thinner than about 14 angstroms. An attempt to make a layer of castor oil thinner than 14 angstroms resulted in breaking up that layer in many islands. These islands seem to have very little interaction amongst themselves and the surface tension quickly rises to a value corresponding to pure water. Clearly implying that while the layer of castor oil or olive oil is present on water the surface tensions are lowered. But if you break the monolayer and form these islands then the surface tension climbs back to the surface tension for pure water. Physically what it means is that since you have got already a monomolecular like monomolecular layer if you provide larger area for that layer and make this expand you cannot split the hydrocarbon tails. But this layer breaks up into islands so looking from top you will see little floating islands in which there is this oil. But surrounding that is water so water becomes now interconnecting and then these islands have not much effect on the surface tension. Surface tension value then rises back to that for pure water. Is that clear? This diagram should show you what I am arguing the surface the surface tension here measured in dyes per centimeter on a scale from 0 to 80 dyes per centimeter is plotted against the thickness of oil in angstroms. And for convenience of representation we are showing the highest thickness here 100 angstrom 0 over here close to 0. You see for the olive oil case up to about 25 dyes per centimeter we have the surface tension covered by of water covered by oil changing very little. We just making the contamination layer thinner and thinner. But when you get down to about 25 angstroms and try to expand that film further it breaks into islands. The surface tension now climbs very quickly to the value for pure water 72 dyes per centimeter. Any attempt to get the average thickness lower than about 25 angstroms necessarily results in breaking up of this layer into islands and the rise in surface tension back to that for pure water. Similar plot could be obtained for castor oil from a release measurements. We next take up the task of inter relating the coefficient of spreading of one liquid on another that is capital S to the work of addition we start with a basic equations. The work of addition between oil and water is like earlier sum of gamma O A and gamma W A minus the interfacial tension between oil and water gamma O W. The work of cohesion of oil on the other hand is simply 2 gamma O A and the spreading coefficient that we have is for oil being spread on water S equal to gamma W A minus gamma O A plus gamma O W. Here we could replace minus gamma O A by gamma O A minus 2 gamma O A. We have not done anything merely rewriting minus gamma O A as gamma O A minus 2 gamma O A. And then in view of the expressions for works of addition and cohesion we can rewrite equation 5 as gamma W A plus gamma O A minus gamma O W that is W O W minus 2 gamma O A which is W oil or our spreading coefficient is nothing but the difference between the work of addition between oil and water and the work of cohesion of oil. So, that is our final summary of spreading coefficient. It could be written as work of addition between the two liquids minus work of cohesion of the spreading liquid. Here oil was considered to spread on water and that looks physically completely clear. If the spreading coefficient is positive it means the work of addition is exceeding the work of cohesion. A drop of oil placed on water cannot cohere to itself but is rather pulled apart by the large addition with water. That is what positive spreading cohesion we will mean for us. The question next arises this could be a little exercise for you. If let us say we have one liquid spreading on another one oil is spreading on water. What can we say about water spreading on that oil? Think about it perhaps take a minute to answer this question quantitatively analytically. You have all the information with you here. Given oil spreads on water we are asking what if I place water on that oil? Maybe your answers can be in two parts. One simply the hunch. What do you feel intuitively? And second is actual analytical which will take a minute to work out. So, actually we cannot guess from this thing because it depends totally on the cohesion between water and between water. So, you are saying for the first part you cannot say off hand. You cannot guess. If it is not possible to guess maybe you should work out. Yeah. What is spread? In second case S will be just negative of the first. Which means water will not spread on oil. That is the inverse system for you. If a given drop of oil spreads on water then we can show that since S is greater than 0, S is 0 or positive and this would happen only if this oil drop adheres to water more strongly than it coheres to itself. We should be able to analyze the inverse system. S which is gamma w a minus gamma o a plus gamma o w is greater than 0. So, gamma o a minus gamma w a plus gamma o w should be less than 0. And because gamma o w is same as gamma w o as a positive quantity, we have gamma o a minus gamma w a plus gamma o w minus 2 times gamma o w less than 0 or that is simply gamma o a minus gamma w a minus gamma o w which is nothing but the spreading cohesion for the inverse system water being placed on top of oil. So, we call it S prime. S prime is less than 0. So, if one liquid spreads on another the other liquid will not spread on the first. If that is clear one could ask another question. Based on this could we venture to say something about let us say a next scenario. Will it be possible for us to find two liquids both of which will not spread on each other? What it means is is it possible that if S is less than 0? Is it possible that S prime for the inverse system is also less than 0? That may be not so straightforward to answer, but yes the answer is affirmative there is possible to find two liquids neither of which will spread on the other. We take example of hexadecane on water. S is minus 9.3 dynes per centimeter. If you calculate S prime it works out to be minus 94.9 dynes per centimeter. It is possible for us to find two liquids neither of which spreads on the other. If all this is very clear one could go further and ask about the spreading at an interface not on surface, surface we are considered. Spreading at an interface let us say between oil and water. Actually spreading here at an interface is subject to same conditions. Take for instance benzene in contact with water. If at this interface between benzene and water we try to place a drop of ethanol. For benzene water system interfacial tension is 35 dynes per centimeter. Ethanol is ultimately miscible both with water and with benzene which will mean that S is 35 minus 0 minus 0. Gamma benzene ethanol is 0, gamma water ethanol is 0. So, S is 35 dynes per centimeter here. Take another instance normal hexane in contact with water. If you place ethanol here the spreading cohesion is even larger 51 dynes per centimeter. Mind you these are very high spreading cohesions and there is an application for this. We could make use of such high spreading we can make use of such high spreading monolayers to have certain polymers or large molecular weight materials create a monolayer otherwise spreading them at the surface might be difficult. But spread from solution followed by evaporation of ethanol will leave a monolayer of polymer at an interface. The second consequence of high spreading cohesions is the interfacial turbulence because ethanol tends to spread so quickly at the surface it tends to drag water and the oil along with it leading to an interfacial turbulence which may be responsible for increase in certain transfer phenomena like mass transfer there. Impurities also greatly affect spreading of oil on water. We take one rather dramatic experiment here think of having a high boiling paraffinic oil floating as a lens on water left to itself it will form equilibrium lens shape would remain there. But if you add a little bit of oleic acid to this lens then you see that there is a violent burst of this lens into smaller drops. This happens because of very strong spreading action of oleic acid on the surface and interface. What might happen to oleic acid it could land up finally on the free surface of waterism monolayer or if enough oleic acid is present it would tend to cover the entire water surface with the solution of oleic acid in paraffinic oil. They might be lenses also floating but in between there will be this much thicker film of oleic acid plus paraffinic oil. Mathematically we could say here that addition between oil and water has been locally modified to make the spreading cohesion positive or if we keep the definition of spreading cohesion in mind it will correspond to decreasing the interfacial tension between oil and water. By virtue this oleic acid added that may be conceived as the effect of impurity in oil phase. What if impurities are present in water naturally they would lower the surface tension of water and surface tension of water would be reduced more than the interfacial tension between oil and water especially if the interfacial tension is already low. What happens under these circumstances could be seen in light of tabulated values for spreading cohesions referring to the initial state of the system that is at the moment the oil drop has been placed on clean water surface before much spreading has occurred and in that stage we may take the surface tension of water to be that initial value 72.8 dynes per centimeter. We can look at some of the values in this table these are all initial values of spreading cohesion. For ethanol itself about 50.4 dynes per centimeter comparable to the high values for methanol propanol etcetera. For benzene note interestingly it is plus 8.9 toluene again positive 6.8 carbon disulfide minus 7.6 hexadecane we have already seen liquid petrol atom minus 13.6 methylene iodide a very low value minus 26.5 dynes per centimeter. So high initial spreading cohesions will mean we have our liquid oil showing a definite positive spreading tendency. But the moderate spreading tendency might show some curious result. Initially the conditions may be favorable for spreading like for benzene that I mentioned and it would mean that after some spreading has occurred perhaps there are changes in tensions. Surface tension of water for example would be reduced and then s value will be decreased. So initial value is positive favor spreading but final value does not favor spreading how will the system respond is the question. If you were to look at this as a game the system would find that the rules of game have changed at the end conditions have been changed. Take this numerical example benzene placed on water initial spreading cohesion works out to be 8.9 Ergs per centimeter square. Benzene will definitely spread on water but wait long enough and let benzene be saturated with water and water gets saturated with benzene and you find that the surface tension of water saturated with benzene now drops from 70 to 0.8 by 10.4 units to 62.4. Interficial tension decreases somewhat but it will be limited practically 35. Surface tension of oil marginal decreases and we have the final spreading cohesion now working out to be instead of plus 8.9 minus 1.4 Ergs per centimeter square. Benzene having spread on water finally finds that conditions properties values have changed is no more favorable for spreading and it changes its mind. It retracts it retracts collecting some of the benzene in the form of some very flat lenses in contact with water surface which still retains a monolayer of benzene. So, what has happened is by virtue of the initial spreading velocity the benzene is taken all over but then as benzene got adsorbed on water the surface tension dropped by 10.49 per centimeter that reduces the spreading cohesion to a negative value. While benzene will still tend to spread on pure water it will not tend to spread on benzene covered water that is not now favorable. So, it retracts and collects in the form of lenses. We already looked at these values you could take another example amyl alcohol on water. Once again you will be able to verify that there is initial spread followed by retraction. The monolayer covered water surface is not energetically favorable for further spreading of amyl alcohol negative s is the final result. If one goes into the visualization of what might happen the hydrophobic chains of amyl alcohol are less preferred by it compared to the tails plus heads in its lens form. Amyl alcohol itself gets oriented on water surface and for it to spread on this hydrophobic layer the conditions are not energetically favorable. The oil this amyl alcohol will prefer to have its additional molecules remain in contact with the hydrophobic and hydrophilic parts of it in the lens. Even at the boundary between this lens and air the tails will tend to hide away from the bulk. So, there is one more degree of freedom the tails flip out in air preferring air instead of interior of amyl alcohol. So, area facing only tails is least in the lens compared especially to the flattened film form. So, the system is always working to minimize the surface energy. In that contracted lens form the tails are facing air and have minimize area. So, I think we probably can stop here for today and resume from here next time.