 In this lecture 9th, we continue to discuss spreading its interrelation with interfacial and surface tensions and we also try to obtain a certain theoretical insight into what happens at the surface especially from the view point of works of adhesion and cohesion. We will also try to obtain certain insight into design of products which may be motivated by some of the basic concepts that we will try to outline here. We begin with a quick recap of what we have done in the last lecture. We had looked at this particular measure of spreading. The spreading coefficient as it implies an incomplete balance that would remain as a residual of the balance of horizontal components of surface and interfacial tensions when you attempt to spread one liquid on another. So, if we were to think of spreading of an oil on water, the spreading coefficient would be given by this surface tension of water in contact with air which is trying to spread the drop minus the maximum action that the surface tension of oil or the spreading liquid and the interfacial tension between the spreading oil and the substrate which is water that tries to oppose the surface tension. The magnitude by which these spreading and restraining factors come out as a balance that is the net spreading coefficient. We realize here that when the contact angle that the oil makes and the angle that the interface makes with respect to the horizontal, even if they were to reduce to 0, they would not be able to exceed the sum total of this gamma OA and gamma OW as the restraining action. So, if this coefficient is positive, we would expect spreading. Now, depending on the magnitude of the spreading coefficient, we may have spreading which just occurs or it might be a situation where there is a strong tendency for the spreading liquid to spread out on the lower substrate liquid and then we got into the nitty gritties which rise for the changes which occur when time is given for the phases to get perhaps mutually saturated and it turns out that in many cases the spreading coefficient may be marginally positive in the beginning, but turns out to be negative at the end. So, this was one example benzene being attempted to spread on water where we find initially the spreading coefficient is positive 8.9 not very high, Ergs per centimeter square, but when benzene gets saturated with water and water gets saturated with benzene, the final spreading coefficient turns out to be negative minus 1.4 Ergs per centimeter square and this has predominantly occurred because of the reduction in the surface tension of water by about 10.4 dyns per centimeter. What physically it means is that there is a monolayer of benzene which occupies the surface of water and there is a certain orientation the benzene molecules exhibit on the surface making benzene unfavorable for further spreading. Then should there be some extent of spreading right over the surface in the beginning then because the final spreading coefficient is negative the system responds by retracting benzene into a very flat lens which is clear indication that under the final conditions the spreading is not favorable. And then we looked at a number of values of spreading coefficients and especially we make note of here spreading question for methylene iodide which is a very large negative value minus 26.5 dyns per centimeter. We will return to this value a little while later in the light of what we are going to discuss today. Amyl alcohol on water exhibits a similar situation what it implies is that amyl alcohol would also retract into a lens under the final conditions situation might be somewhat like this. Physically it means that the oriented hydrocarbon layer is not favorable for spreading of amyl alcohol beyond a point and the amyl alcohol prefers to be in a random mixture of hydrophobic and hydrophilic parts rather than spread on the oriented less favorable monolayer which occupies the rest of the surface. So, spreading question in the beginning is about 44.3 dyns per centimeter, but in the final analysis it turns out to be minus 2.0 dyns per centimeter. And then we have other cases like carbon disulfide water where the initial spreading question itself is negative and would become further more negative going from minus 7.6 dyns per centimeter to minus 9.9 dyns per centimeter because the surface tension drops by this magnitude 2.3 dyns per centimeter which corresponds to an invisible monolayer of CS2 with this surface pressure pi equal to 2.3 dyns per centimeter. We may conclude for the last lecture that the saturation of liquids in general makes the final spreading question less favorable than what is implied by the initial spreading question. Then we briefly looked into the kinetics of spreading and benchmark the speed of spreading in context of the average speeds that we are familiar with our own movement on this planet. And these velocities of spreading or spreading kinetics are of importance in certain phenomena like kicking droplets or in the applications of anti foam agents. This was the apparatus that we had used where Tulk is used for visualizing what happens at the surface. And when you release a liquid spreading liquid from this glass plate into a surface or interface then it pushes the Tulk layer in this direction and we record the movement of that front with respect to time. And what we get is an initially changing distance versus time plot which changes slope then kind of stabilizes at a constant slope. And finally, we have the diminishing slope of distance versus time or the position of the interface versus time when the depletion arising out of either desorption into bulk of water of the spreading acetone like material or evaporation causes a fall in the rate of spreading. And typical Sine camera that was used in the past would have about 16 frames per second as the frame grabbing speed. Constrable precautions have to be taken in preparation of materials and that will reserve for later lectures. An important point here was that we tried to correlate the initial spreading rate for different liquids at surfaces of water or at interface between water and different liquids in presence or absence of surfactants. This was the case of a surfactant being used at an interface. And the last column reflected the measure of what the viscosity of adjacent liquids would do to the rate of spreading. So, trying to take that factor out we have here S by sigma eta where sigma eta would be at least the sum of viscosity of the underlying liquid and the liquid on top. In a rigorous analysis that should also take into account the viscosity of the spreading liquid. And we find that there is a good correlation between the initial spreading rate and this S by sigma eta. And when you compare the spreading at a surface against a situation corresponding to spreading at an interface likes between petroleum ether and water we find that there is a factor of 2 involved. The viscosities of the adjacent liquids tend to add up to an equivalent of diminishing the velocity of spreading by a factor of 2. So, that was our general conclusion that at oil water surfaces or interfaces the spreading is about half as fast as at air water surface. And since this cohesion S by sigma eta is a rough measure of factors controlling the rate of spreading we naturally come to a conclusion that a rate of spreading is equal to a constant times S by sigma eta. And the action of viscosity comes through the no slippage between the spreading layer and the liquid above and below it. In context of spreading from solids we noted that there is a very marked dependence on temperature and there is a critical temperature below which the spreading rate is extremely slow. The energetic is not favorable, but if you have temperature which is equal to or greater than critical temperature then the spreading is relatively rapid. Generally as you increase the number of carbon atoms in a homologous series the critical temperature increases. Another important point was what happens to the spreading when you contact a solid with liquid and where is the spreading occurring from? Where do the spreading molecules from the solid leave the surface of solid? It turns out it is not into the bulk of water but rather only at the periphery or at the three phase contact line where the solid has whole formation the molecules leave and then they occupy the position in the surface. And this can be demonstrated quite easily by placing a drop of water on a flat surface of solid steric acid. It just leaves an observable ring at the periphery with the inside of steric acid not dissolving at all practically. We just looked at the rates of spreading and the constants which characterize the spreading. In general the number of molecules spreading per second will be equal to constant times this perimeter into the driving force which is here the equilibrium spreading pressure minus the existing spreading pressure that gives the constant involved here of the order 2.4 to 3 into 10 raise to 12 molecules per dime per second. We concluded that lecture by noting that you can actually measure the molecular weight of protein by first having a monolayer of protein by touching a clean water surface by a protein crystal and withdrawing a hydrophobic fiber slowly through this surface there by depositing a monolayer of protein on the fiber by weighing the fiber before and after we know how much is deposition and from there we can actually figure out what is the molecular weight. We will go into the details of this kind of calculation measurement and calculation a few lectures later. Then we came to the relation between the surface and interfacial tensions and that will occupy most of our today's lecture and we began here looking at the thought experiment that Gibbs advocated. May be a little bit of information in way of digression I can pass on to you about this celebrated scientist Joshua Willard Gibbs. Most of you who have had exposure to thermodynamics at some level or other inescapably would have come across Gibbs's adsorption isotherm and various contributions. He was in a sense precision personified. So meticulous was he in his work as well as his day to day habits and so much was his punctuality that the, that was the point. The folklore has that people used to adjust their watches depending on when Gibbs would take his lunch break. You see that commitment and precision of work in his theories too. This is one simple example of how mind of a genius like of Gibbs really worked. This treatment of Gibbs in context of interfacial and surface tensions is something that I briefly introduced but will go into the details today. Gibbs started with the consideration of interfacial tension between mercury and water and like most of his subjects of interest he focused on equilibrium and he wanted to have a general deduction about interfacial tension in terms of surface tensions of the two components when they are in equilibrium. He deduced that the interfacial tension between mercury and water would be equal to the surface tension of mercury saturated with water minus the surface tension of water saturated with mercury. Obviously, the surface tensions are with reference to air being the phase in contact with the liquids that we are considering. We had in passing noted Gibbs's thought experiment. What he had presumed was you would have two chambers connected through the vapour space. On one side we have mercury, on other side we have water and his argument was the following. This space would have predominantly water vapour. Obviously, there will be a few mercury atoms or molecules here too but predominantly is water and then he argues by saying that we need to focus what happens here. What happens at the surface of mercury when it becomes accessible to the vapour of water which is present in the other chamber and when you look at the unit area here at the surface of mercury, this is where he expects to find an answer which would be justification for this. Now, let us look into this thought experiment closely. On a clean mercury surface, we would have a very high surface energy. The surface tension of mercury is very high close to about 485 dyns per centimeter compared to otherwise exceptionally high surface tension of water which is about 72 dyns per centimeter. He argues this way that that high surface energy of mercury will tend to lower itself and it would do so by adsorbing whatever vapour is present in its vicinity which means from the saturated water vapour some water molecules would be adsorbed on the surface of clean mercury surface with its high surface tension. It is impressive that he could visualize what might happen and he could ascribe some of the not so obvious attributes to the thin film of water that would be deposited on the mercury surface in the process. He argued that the thin film of water which therefore would result on the surface of water might be thin enough on one hand to be considered as a part of the surface of mercury itself. On the other hand, he argues that it may be considered thick enough to behave as if bulk liquid water vapour would appear in contact with mercury. Now that is the part which is not so obvious whether this is true or not could only be checked in the face of experimental data. If that were true if those arguments were true the total surface tension or energy for mercury with adsorbed water should be equal to some of the surface tension of water which is present as a thin film and is part of the surface of mercury and the interfacial tension between mercury and water. That interfacial tension would have a value gamma Hgw where our thin film to behave like a bulk liquid water. But if you accept that then you at once see that gamma Hgw is nothing but gamma Hg saturated with water minus gamma w saturated with mercury and that is equation that we started out with. This is exactly identical with the equation that we have cited from Gibbs's deduction. In practice what happens to the surface tension of water? If water is also saturated with mercury that would happen given sufficient time for the two phases to achieve an equilibrium. It so happens that the surface tension of water is comparatively much lower and there is only a negligible effect on the surface tension of water because of presence of any mercury which might dissolve in it. And this relation advocated by Gibbs for especially mercury and water system has been tested at 25 degree centigrade and it gives you a value of 374 dynes per centimeter. Surface tension of mercury water system when we have these phases mutually saturated works out to be 447.6 minus 72 or about 375.6 dynes per centimeter. The measured value of interfacial tension between mercury and water of 374 against what is deduced from Gibbs's analysis is pretty much close to each other. In a sense that assumption which for most of us would not be very clear in the beginning that the thin film of water which is adsorbed on mercury would actually behave like bulk water is the same to be substantiated by experimental data. And when we question about the validity of such arguments for equilibrium between mercury and other organic liquids the same conclusion is reached. It is here that we run into a relationship I am certain all of you are exposed to some time in your chemistry courses and that is Antonov's relation. According to this the interfacial tension between two mutually saturated liquids is equal to the difference between their surface tensions when each of these liquids has been made saturated with each other. Antonov's relation in this manner is a generalization of Gibbs's statement. Gibbs's statement was deduced based on mercury water surface Antonov's relation is a general relationship. There are some caveats here one has to be aware. You may note in passing here that with respect to water and organic liquids the kinds of systems you often come across in practice the mutual saturation can occur extremely slowly sometimes as much as 10 days may be required to reach an equilibrium. This point is something most people are not aware of academicians are no exceptions. Let us say by B we indicate an oil phase then in terms of our chosen notations B W would be the phase B oil phase which is saturated with water. And by W B we would understand water saturated with the liquid given oil. To keep things simple let B be benzene. So, if you have benzene saturated with water according to Antonov's relationship gamma B W is the interfacial tension between benzene and water and that is equal to the surface tension of water saturated with benzene minus surface tension of benzene saturated with air. So, all tensions interfacial and surface tensions are when mutual saturation has been accomplished. This table gives you a set of values and sort of projects a certain result that we will try to establish in the next few slides. We see here for different oils benzene chloroform carbon tetrachloride toluene and methyl methylene iodide all at 25 degree centigrade. The surface tensions for water and the oil when they are saturated with each other and the interfacial tension between oil and water in these columns surface tension of water, surface tension of oil and interfacial tension. These are the major values for surface and interfacial tensions all at 25 degree centigrade. Last but one column gives you the difference between the surface tension of water and surface tension of oil when water is saturated with oil and oil is saturated with water. And the final column gives you the final spreading question for oil saturated with water and water saturated with oil using equilibrium values for surface and interfacial tensions that is the final spreading question. Now, we expect to see the validity of Antonov's relation or for that matter gives us deduction when we compare this experimental column against this theoretical prediction based on measured experimental surface tension values. So we see for benzene an exact agreement 27.2 dynes per centimeter. For chloroform it is 23.0 versus 24.3 some difference 1.3 is the final spreading question. For carbon tetrachloride again we have exact match for toluene again exact match for methylene iodide a stock difference very different values between these columns here. The interfacial tension is about 40.5 what is predicted by Antonov's relation is 19.6 the final spreading question is as we had seen earlier large negative value minus 24.2 dynes per centimeter. We will try to rationalize these data, experimental data in the phase of Antonov's relation. And in the process C whether we can get some more insight a very interesting result was obtained by Adam he combined Antonov's relationship with Dupri's equation. I am tempted to give you a mnemonic here if we represent Antonov's relation by A and Dupri's equation by D A plus D gives you A D A D for Adam. So you will never forget which relations go into which final result. We start with Dupri's equation. Dupri's equation gives you the work of addition between the oil and water W B W that is equal to gamma B W A plus gamma W gamma W B A. Minus gamma B W, gamma B W A that is the surface tension of oil saturated with water plus gamma W B A which is surface tension of water saturated with oil minus the interfacial tension between oil and water gamma B W. And then we plug in for gamma B W for gamma Antonov's relation. So we take the Dupri's equation and plug in for interfacial tension the expression given by Antonov's relation. So first two terms are identical gamma B W A plus gamma W B A minus for gamma B W we substitute gamma W B A plus sorry gamma gamma B gamma W B A minus gamma B W A. So when we substituted for gamma B W as gamma W B A minus gamma B W A we see that this gamma W B A cancels that turns into a plus sign. So we get two gamma B W A. Work of addition between oil and water is seen to be here equal to the work of cohesion of oil. This is something which I think we should analyze and understand. Gives a statement gives us the starting point to understand this. It would also help you understand why in this column there is some failure seen. Clearly this is approximate this is total failure right and we must understand why this is happening. We expect Adam's result to help us understand what is happening. I am sure some of you must be imagining the picture at the level of the interface. That is where the answer should lie. I will try to make it obvious to you. How is it that the work of addition between an oil and water comes out to be equal to work of cohesion of oil? Next diagram should make it clear. If we have benzene in contact with water our result is the work of addition between benzene saturated with water and water saturated with benzene is equal to work of cohesion of benzene. It implies that water must have retained a film very thin film of benzene. Something similar to the film of water which was postulated by Gibbs on mercury surface and that too would behave like the bulk of water and the Dupre's experiment which involves separation of benzene and water would lead to a separation of the two phases with benzene layer a thin benzene layer still sticking to water. If this is the case what is what has happened is the benzene has separated from itself. So, when you are looking at benzene being separated from water when you pull apart unit area of this interface you leave part of benzene on water. In effect you are separating benzene from itself and that will be the work of cohesion of benzene. That is what is written in words here the work of addition between two mutually saturated liquids is equal to the work of cohesion of the liquid of lower surface tension provided it has been saturated with the liquid of higher surface tension. There could be a certain projection which will serve the rule of another mnemonic here. You would never forget this if you look at the next observation and we will try to see if there is a projection for product development here. In my first lecture I listed out lots of common products which I stated would be influenced by interfacial phenomena surface phenomena at some stage either during their production or during their usage. I would like to bring from that that list this particular product adhesive. In general what attributes the adhesive should have and how does all that fit in into this mnemonic I am trying to explain to you. What has happened to separation of benzene and water when benzene is saturated with water and water is saturated with benzene is something similar to your observation when you try to pull apart an adhesive tape stuck onto a paper. You all seen that when you peel off this adhesive tape from paper it brings with it a thin layer of paper that is provided you have a proper adhesive. And what is that proper adhesive? The proper adhesive should have enough of its own strength that the bond is stronger than the bond it forms with the substrate. So, when you try to forcefully take away an adhesive tape it must be able to snap off a thin layer of paper and not snap off in the middle of itself. So, adhesive use on adhesive and adhesive tape must have enough of its work of cohesion to exceed the work of addition. So, to say in equivalent terms for liquids between the surface of the adhesive and paper. So, that work of cohesion must exceed the work of addition that is the only way that the adhesive will not fail. Talking about failures I am also tempted to tell you another aspect of this and we will try to confine it to the context of the adhesives. Sometimes the failures have as much to teach you as successes at times even more than successes. This is no greater a truth in the context of product development than in any other context. You could think of this for a moment what if our adhesive were not appropriate. We intended to make an adhesive which would serve the proper bonding with the substrate, but what if something goes wrong has that happened historically potentially creating a new product. In the light of what visualization I have asked you to make you can think of the post-it notes. Post-it notes probably were designed to have work of cohesion smaller than the work of addition. So, while we have temporary bond with the substrate paper when you take off a post-it note it would still be left with an adhesive layer. So, the adhesive layer must have snap form itself work of cohesion must have been lower than the work of addition and this would be possible a number of times. Unless this is possible a number of times the post-it notes would not be a successful product. There is a lot here than I intended to convey to you. I must tell you that such a simple thing as an adhesive tape a cello tape has been the instrument of experiments done by a couple of physicists each one all know that graphite is layers of carbon layer by layer structure. Nobody believed that you can take off individual sheets of carbon layers from graphite, but these physicists at Manchester actually managed to repeatedly peel off layers of carbon atoms from graphite and in roughly about 50 odd repetitions they could get down to a layer thin enough to be atomically thick. So, what was never theoretically expected was achieved experimentally and that is what has now created a great interest both in research and applications in the area of graphines. You can have attributes to graphene which are very different from you may otherwise realize in any other form of carbon. I will just complete this lecture by saying that in context of this benzene water interface there is a decrease in surface tension of water by about 15.5 units. So, the surface tension drops from 72 to 56.5 dynes per centimeter and this is not surprising because benzene is known to adsorb on water surface giving monolayers with this kind of surface pressure and it exactly analogous to the original suggestion by Gibbs that the adsorb film of water on mercury behaved as though a normal liquid water were in contact with mercury. We will stop here for today.