 We now come to this lecture number 6, in which we will try to address the concepts of interfacial tension, interfacial entropy and possibly cohesion and adhesion. You recall that a lower alcohol like butanol has a surface tension in the low 20s. For butanol it is 24 dimes per centimeter and when you take it together with water then the interfacial tension could be measured to be as low as 1.8 dimes per centimeter. Now, such low surface phenomena such low interfacial tensions are not uncommon especially with liquids containing polar groups. We will try to understand this as we go along and over next few lectures this should become amply clear theoretically as well as quantitatively. One first understands that at the interface a considerable orientation of dipolar molecules can occur. One could take another example of let us say nitrobenzene which has a surface tension of 43.9 dimes per centimeter and when placed in contact with water the interfacial tension could be measured to be about 25.1 dimes per centimeter. These lower than expected magnitudes of interfacial tensions are ascribable to the reorientation of molecules of one liquid in presence of another. And as we will see later this is not just restricted to only interfaces between liquids. Even for gases such phenomena could be witnessed. In contrast hydrocarbon oils display typically 50 dimes per centimeter for interfacial tension. Now, these are constably larger than what we just observed for the polar molecules. Before we go further let us look at some standard interfacial tensions between pure liquids and water. It is important to make note of the fact here that we are talking of pure liquid against water. So, for normal hexane at 20 degree centigrade we have 51.0 dimes per centimeter for interfacial tension. For normal octane it is about 50.8 for carbon tetrachloride 45.1 dimes per centimeter. We make a note of interfacial tension between benzene and water. For benzene in contact with water the interfacial tension is 35 dimes per centimeter. We might also observe one more trend here. For benzene at the two temperatures mentioned 20 and 25 degrees centigrade the interfacial tension drops from 35 to 34.71. When we go down to polar compounds like octanol or hexanol we have again expected low magnitudes for interfacial tension 8.5 and 6.8 dimes per centimeter respectively. Even for aniline the magnitude is low enough 5.85 pentanol 4.4. We just looked at butanol. Normal butanol at 25 degree centigrade has 1.6 dimes per centimeter. Mercury has interfacial tension against water of 375 dimes per centimeter. You recollect that the surface tension for mercury was extraordinarily high about 475 dimes per centimeter. So, there is a drop of about 100 dimes per centimeter here. Incidentally mercury will be used as a case study in deriving a certain important deduction which was first arrived at by Gibbs. Toluene comparable to benzene little higher 36.1 dimes per centimeter. Olig acid at 20 degree centigrade has interfacial tension of 15.59. You might wonder why Olig acid has relatively low interfacial tension. There are two reasons here. First is a presence of a double bond in a molecule of Olig acid. And second this is an unusual acid occurring naturally naturally in oil as triglyceride component. There is a hydroxyl group associated with Olig acid molecule. So, combined action of the hydroxyl group and a double bond perhaps is the reason for relatively low interfacial tension for Olig acid. In general like surface tension as we increase temperature interfacial tension will decrease. There are some interesting generic principles here which you need to understand. Once you understand that then all individual observations fall in place. So, first thing to note as a matter of principle in interfacial tension that here we are talking of a contractile tendency associated with an interface between two liquids. Having said that generically you could say that interfacial tension is a kind of a broader concept. If one liquid were to be replaced by vapor it would become surface tension right, but generally interfacial tension is reserved for liquid liquid systems. Conceptually there is no problem with that. So, one has to understand that general principles are similar ok. Then we talk about two liquids in contact which are immiscible or at most partially miscible. This is important. Why there is a constraint on miscibility will be the question that I will be answering a little well down this lecture sometime. Now, first recapitulate that surface tension was related to asymmetry in the environment for molecules in the surface. There are more neighbors on the liquid side and practically none on the vapor side, vapor being so much rarer than the liquid. So, as a result of this asymmetry the surface phase will correspond to higher chemical potential. When a surface is created afresh and the surface then responds by sending some of the surface molecules into the bulk. In the process intermolecular spacing in the surface will increase and therefore, a certain attractive tension will arise. That will tend to lower the chemical potential until the chemical potential for molecules in surface become becomes equal to that in the bulk at which point the net adsorption and desorption rates would be same right. In a sense you could regard surface tension as a virtually simple balance between contractile tendency that can be legitimately associated with a liquid. If one goes further and says that I would like to think of whatever is the attractive contractile tendency for a vapor phase, nobody stops us from taking that as a quantity which has to be taken 0. So, in a sense you have a surface which is contracting and vapor which has practically no contractile tendency. So, for a surface in contact with the vapor the contractile tendency is completely governed by the contractile tendency of the liquid right. In interfacial tension we replace the vapor by another liquid. Now, this liquid must not be completely miscible with the first liquid that is the only constraint we are imposing. It could be immiscible it could be partial immiscible. Now, if you look at the same asymmetry point of view for this 2 liquid system at most partially miscible we still will have certain asymmetry of environment because on one side we have bulk of liquid 1 on the other side we have bulk of liquid 2 right. So, we have a liquid let us say 1 and a vapor it is here that the molecules in the surface are getting incompletely attracted because of the rare of the vapor here. Whereas, on the other side if we have liquid 1 in contact with liquid 2 and liquid 1 and liquid 2 are not completely miscible then we still have difference in the environment because the properties for these 2 liquids are different. However, if you come compare the asymmetry in the first case against the second case the asymmetry is reduced here because we have gone from a gas or vapor state to a condensed phase here alright. We will be talking about an interface which is stable interfacial tension we could not possibly be talking of meaningfully if the interface is not stable that will be possible only if these 2 liquids are in the worst case partially miscible ok. So, we expect here the interfacial properties or contractile tendency to be a reflection of the contractile tendencies of these individual liquids L 1 and L 2. If you have to get a mechanical equivalent of this in terms of understanding this liquid let us say has a higher surface tension compared to the liquid here then the lower liquid will have a greater contractile tendency than the lower liquid, but the 2 interfaces are in contact. So, the interface will behave somewhere in terms of these extremes as an intermediate. We have a greater contractile tendency for the lower liquid lesser for the upper one. So, when they are in contact and together the interface will have a contractile tendency which will be in between these 2 right. You could carry on this argument little further in our thought extent and we are jumping the slides we are going very far now from here. We come to the extreme of the partial miscibility which is complete miscibility. So, in this extreme let us say we have liquid L 1 in contact with L 1. Now, the interface between these 2 regions is only in manner of conjecture because we have the same environment on each side of some chosen interface. Now, what was the surface molecule here or interfacial molecule here has become a molecule in the bulk. Now, we have exactly same kind of environment on each side. What will be the tension that would measure here? It should be 0 right. So, you could look at look at interfacial tension as a left over contractile tendency when we place 2 condensed phases in contact with each other. If one condensed phase the second were replaced by vapor it becomes equivalent to surface tension. If we replace the upper liquid by the same liquid which is below then the residual is 0. So, in this sense you can completely understand what I mean by this choice of words here unlike the surface tension interfacial tension is the residual entity right. In case of surface tension that residue is identical with the contractile tendency of the liquid all right yeah go ahead. Suppose, there is a molecule on a surface right. So, there will be some force from the above molecule and there will be some right right. Sir, now the force of attraction on that particular interface molecule will be different. Yes, that will be different. Sir, why is it not folded in one of the. No, it depends on what molecules we have at the interface. Please remember if you go back to the first lecture I think you missed that. The interface is not planar it is not a geometrical plane it is a zone and now in context of 2 liquids in contact it will be a zone containing the components coming from both the phases. So, there will be a tendency for molecules of liquid 1 to go into liquid 1 itself and of 2 into 2, but it is not ruled out some of l 1 molecules land up into l 2 and l 2 molecules into l 1 that is possible right. Does that become clear now ok. So, I need this example to be able to go further. We are talking of butanol placed on water C 4 H 9 OH on top of water. How would butanol molecules respond when pure butanol is brought in contact with water at the first instance? Those molecules in the proximity of water they will tend to respond in the following fashion. Butanol molecules with C 4 H 9 OH as structure will get oriented near the interface and energetically it will be favorable to place hydroxyl groups in water. So, hydroxyl groups will be anchored in water. The C 4 H 9 tail hydrocarbon tail will be more comfortably located in the bulk of butanol because if that C 4 H 9 has to be accommodated in the structure of water it would be necessarily disrupting disrupting certain number of hydrogen bonds and water is very highly associated. Everything is like a gel giant water molecule. So, C 4 H 9 OH will respond by first layer orienting itself with the hydrocarbon tails facing butanol hydroxyl groups submerged in water. Now, next what happens is these hydroxyl groups are in proximity. They are almost in a very narrow region only theoretically in a plane and OH group with its associate dipole moment will tend to repel a like group. So, what we have is now water will tend to contract. The oriented monolayer of butanol near the surface will tend to have certain repulsion among OH groups. So, we have these two opposite tendencies if this where butanol and this is water there is a repulsion here among the OH groups. OH groups will tend to repel each other, but the water molecules in the surface will have cohesion. So, there is a contractile tendency. What we will see then is a net result of the cohesion against repulsion right. The orientation of butanol molecules leading to a state of low interfacial free energy will exhibit contractile tendency. It will be reduced compared to the contractile tendency of water by an amount which will be a contribution in the surface of the repulsive pressure attributable to the OH groups and associated dipole moments. However, we have to understand that this orientation is not as often described in textbooks. It is not a palisade like structure, but rather it is a rough orientation. So, we have some idea now as to influence of miscibility of liquids possibly on interfacial tension because we required at most partial miscibility. So, it is conceivable that you could take pairs of liquids one of them always water with different degrees of miscibility. We could measure the mutual insolubilities in terms of relative miscibility. And by taking different water organic phase pairs, it may be possible to get different relative miscibility or the opposite of insolubilities. And then one could measure the interfacial tension and seek a correlation between the relative insolubility and interfacial tension. This was exactly what Bikerman had done in 1958 and he pointed out a general principle experimentally observed which runs as follows mutual insolubility of the oil phase and water runs parallel to interfacial tensions. So, greater the insolubilities degrees of insolubilities greater will be the interfacial tensions. So, he actually constructs a plot we can look at that plot first where on y axis we have the interfacial tension and on x axis we have relative miscibility of phases. And the relative miscibility is chosen to run from about 0 to 30. The interfacial tensions measured seem to vary from 50 to a very low value. What we note here is that when the relative miscibility goes from about 0 to 10 the interfacial tension drops from 50 to about 3 that is a pretty rapid decrease in this portion to the left of the cursor here. So, we have this drop of about 50 minus 3 47 dines per centimeter in the interfacial tension over range of miscibility is from 0 to 10. However, when you go beyond relative miscibility of 10 up to 30 there is hardly any further decrease. This fact has to be kept in mind and by 30 we still do not have complete miscibility recognize that. We will return to some of the quantitative considerations later, but if this is clear for pairs of liquids one of them always kept water for simplicity and because of its common occurrence to form interface with different liquids. One could then build up an argument for three component systems. Let us say butanol is dissolved first in benzene and then this butanol in benzene solution is placed on top of water. What would happen? Butanol was dissolved in benzene then placed in contact with water. Once again butanol molecules will migrate to the interface. Hydroxyl groups will get immersed in water. The C4H9 tails stay facing benzene side. Once again there will be mutual repulsion arising out of hydroxyl groups anchored at the interface and it would have a similar effect as one anticipated in just butanol water interface. Suppose butanol were absent we were to have benzene pure benzene against water. We would still have some interfacial tension, but if butanol is pre-dissolved in benzene its migration and accumulation at the interface will reduce whatever was the contractile tendency for benzene water interface because of this repulsion mutual repulsion among OH groups. So, the three components systems in principle are similar to two component systems. The third component which is accumulating at the interface is offsetting the residual interfacial tension between the two pure liquids benzene and water here. Is that clear? We could make it further clearer if we look at this diagram. The hatch portion below is water and the clear portion on top is benzene and the molecules shown here are the butanol molecules. Hydroxyl head group circular hydrocarbon tail C4H9 as this elongated portion. Given enough time butanol molecules would reach the interface actually crowd at interface. Most of these molecules will orient themselves such that OH groups are immersed in water, but it may not be a perfect structure. It is a roughly oriented accumulation of butanol at the interface between benzene and water. The head groups will repel and therefore reduce whatever is the contractile tendency of the pure benzene, pure water interface. We could write the interfacial tension in the form of this equation now where gamma is the interfacial tension for a three component system. That should be equal to interfacial tension for the pure benzene, pure water. There is two pure liquids in contact gamma i minus a repulsive pressure pi with the same dimensions or units 9s per centimeter as of gamma i or gamma. That repulsive pressure is pi here. It is coming out of whatever the repulsion is there among adsorbed hydroxyl groups. And if you go back to some of the earlier lectures you recognize that form of this equation is identical to what we had in context of surface tension. We merely replaced the surface tension for a pure liquid gamma 0 by the interfacial tension gamma i here right. So, conceptually there is no contradiction over here. Now what would happen if we were to play with the miscibility greater the miscibility of the two liquids lower will be the interfacial tension. That is what Bickerman plot had shown. We will take an example. The example is of water and isopentanol. Isopentanol a polar compound will have a low interfacial tension against water 4.4 dynes per centimeter. Now let us say for this isopentanol water system we add small quantities of ethanol. With the gradual addition of ethanol the interfacial tension would get reduced. When ethanol reaches about 25 percent weight by weight the interfacial tension becomes 0. And at this point we get a single phase. We have a completely miscible system here. By adding ethanol we are kind of reducing the differences between the so called oil phase the pentanol phase and water. So, we get an idea which is in line with the expectation from Bickerman's plot. If we go far away from the origin on x axis when the relative miscibility is corresponding to miscible phases the interfacial tension would drop down to 0. This is just to give you some idea about the solubilities of alcohol in water. Express in units of moles per 100 gram of water at 1 atmosphere and 25 degree centigrade. Methanol, ethanol, propanol as you know are all miscible with water. Starting with butanol we have a deviation. Butanol has about 0.11 gram mole per 100 gram of water as the solubility. When you increase the carbon chain length with pentanol you have little over factor of 3 of reduction in solubility. Hexanol is again 5 times less soluble compared to pentanol, heftanol about 7, 7 times. So, solubilities are decreasing rapidly as you increase the carbon chain length. We return to this question of what happens if we do not add enough ethanol so that we do not have complete miscibility. If the added ethanol concentration is less than what is required for complete miscibility we might have something interesting. Let me show that over here. We take the interface between isopentanol water and add ethanol here on account of difference in concentration ethanol will tend to go into water phase. This is simple result of the diffusional process. When large molecule large number of molecules of ethanol get into water they tend to drag some pentanol here. Ethanol upon reaching water phase finds itself completely miscible, but isopentanol has only a limited solubility. So, that would be stranded over here in the form of very tiny droplets. That is why we call this diffusion and stranding mechanism and because one phase is getting split in another to get emulsified and this is happening spontaneously we have spontaneous emulsification. This is the example I had mentioned in one of the earliest lectures that if you have some pesticide formulations when they are based in a solvent like kerosene with suitable composition addition of these solutions can lead to spontaneously emulsifiable systems. You will have water turning whitish upon dispersion of the oil phase in the form of tiny droplets through this diffusion and stranding mechanism. Now, we sum up what we have been saying. We may have spontaneous emulsification in case we are not reach the complete miscibility which means spontaneous emulsification can occur even when interfacial tension is still significant. If we have enough ethanol added then of course, everything becomes one phase ok. We will come to one more sharper contrast between spontaneous emulsification and achieving miscibility in an example to be covered later, but let me sum up what we can say here. Entune with our expectation we could say that complete miscibility necessarily implies that interfacial tension gamma i is 0. If you have two liquids which are or two liquid phases which are completely miscible the interfacial tension ought to be 0. That is a deduction deductive conclusion there is no exception. If you have two miscible phases interfacial tension will simply be 0. The converse however is not true. If you measure interfacial tension to be 0 sometime it is not necessary that we will have complete miscibility ok. We could take an example to make this clear. Think of water and mercury. We could apply an electric field and reduce the interfacial tension to 0 for interface between water and mercury. If interfacial tension is made 0 then the two phases become emulsified. We will have spontaneous emulsification induced by this applied electric field. But if you look at how much mercury is dissolved in water or how much water is dissolved in mercury you will find none. So, interfacial tension being 0 does not mean that we will have a miscibility. We can have spontaneous emulsification. So, we have two examples of spontaneous emulsification one through the diffusion and stranding induced by ethanol added to let us say isopentanol water system or through application of electric field to truly immiscible phases like water and mercury. We next return to the new concept of interfacial entropy as a generalization of surface entropy. We talked of surface entropy earlier. We tried to extend those arguments over here to an interface. At the interface between a hydrocarbon oil and water we expect some of the water molecules to get oriented under the influence of CH2 groups. What would this lead to? The water molecules are partly oriented by the hydrogen bonding in somewhat like a form of ice. We might want to question how much of ice like nature this orientation induced in water molecules by CH2 groups of a hydrocarbon oil could be. We do see rare gases and hydrocarbon gases to cause formation of such icebergs when they are present in water. Those of you who have read about gas hydrates would be able to relate to the phenomenon which I am trying to describe here. Under the influence of the CH2 groups water becomes somewhat like ice. This oriented set of layers of water molecules actually exhibit density greater than that of liquid water. Now, one could make measurements on how the interfacial temperature interfacial tension would vary with temperature for such model systems like like paraffin oil and water. And once we know the temperature coefficient of interfacial tension we should be able to get the entropy change corresponding to formation of let us say 8 square angstroms of water interface. From this approach from measured interfacial temperature dependence, major interfacial tension dependence on temperature we get the entropy change or the entropy of the interface as plus 0.6 entropy units. If we apply the theory the Boltzmann Planck equation will give you here entropy for the interface per unit molecular area as R ln w, w here will be 4. This is because on similar lines as what we had earlier since surface could be realized as 2 layers of nearest neighbors. On one side we have l 1, on other side we have l 2. We have interface realization possible through 4 different ways in which the interface can be realized. You can have this molecule here or here and we achieve the surface in that state. Same way here we have 2 other different ways. So, total of 4 ways in which we can realize the interface now. So, our R ln w is equal to 2 R ln 2 and that is 2.8 entropy units. Let us try to put this in perspective. From temperature coefficient of interfacial tension you find the entropy of interface as 0.6 entropy units. From theoretical calculation you find 2.8 entropy units. We notice here that in experimentally measured manner we incur a deficit of 2.2 entropy units. Entropy change is 2.2 entropy units less than expected. This probably is a result of the order created. The oriented layer of water against hydrocarbon is possibly the reason why the measured entropy is less by this 2.2 entropy units. You could take another approach and contrast. This entropy change of minus 2.2 entropy units presumably due to the orientation and semi solidification of water molecules and compare it against the entropy change for formation of ordinary ice. If ordinary ice were to form we would have an entropy change of minus 5 entropy units. So, what it is indicating is that this is a kind of semi solidification. It is not complete ice formation, but is similar to ice in a greater sense compared to water. We are returning to water once again. This picture shows many interesting phenomena how a water droplet would form at the surface if we just get the force dynamics in appropriate manner. A drop seems to be pinching off from the water surface by snapping off a neck which is a neck which is connection connecting it with the bulk of water. This is where it will snap off. Spherical surface governed by surface tension. The waves are ripples forming at the water surface. Drop formation in this simple picture actually bears out a very important model for formation of drops as well as bubbles. A two stage model for formation of drops or bubbles. So, a lot can be read from here. We hope to touch upon some of the aspects which are visible in this picture in lectures to come perhaps much later. The waves are ripples on much larger water bodies. Relevance of concentration of what happens at the surface of large water bodies. Practical applications specifically in context of our country where we have lots of hot and arid areas and conservation of water is of utmost significance. We hope to touch on these in later parts. For the time being we proceed with what I promised. We revisit the concepts of cohesion and adhesion. As you would all recall, cohesion refers to what is experienced by molecules of same kind whereas adhesion will reflect on what is experienced by molecules of different kinds. First we define the work of adhesion. Perhaps I return to this, I will return to this slide after showing you a picture. This diagram is supposed to give you an idealization of the following thought experiment. Let us say we have oil placed on top of water. We have this oil on water in a column. And for the sake of argument, let us say the cross sectional area is 1 centimeter square. And what we do next is we separate oil and water and allow air to fill the gap. And we look at the energy for each state of this system. So, to begin with we have the left hand part of this diagram oil in contact with water. The interfacial energy will be simply equal to the interfacial tension gamma OW. Since this is the first time we are diagrammatically representing oil water case. Let us understand that these are only simplifying conventions. Because water occurs in vast number of cases, we just call one phase water another generically oil. It need not be, it could be anything which is very different from water. So, when oil and water are in contact, the interfacial energy or arcs per centimeter square will be same as interfacial tension in dines per centimeter. The two quantities are identical. Now, if you separate oil from water and allow air to get in between the total energy of the system in this right hand part of the diagram would be the sum of two surface energies, one for oil in contact with air and associated vapor, another for water in contact with air and associated vapor. But those surface energies are nothing but surface tension. So, total interfacial energy will be sum of the two surface tensions gamma OA plus gamma WA, surface tension of oil against air and of water against air. So, when we go from oil water in contact to oil air water system, the amount of work that you need to do is the work of addition in order to separate these. And the amount of work done will be difference of these energies or gamma OA plus gamma WA that sum minus gamma OW. This simple result is Dupre's equation, work of addition between oil and water. So, if this is clear, we could look at some magnitudes. For water paraffin oil system, the work of addition is 43 oaks per centimeter square. Question arises, what will be the work of cohesion? It is clear that the work of cohesion will follow as a special case. When a single phase is separated by two identical interfaces with water with air, the initial energy is 0, final is 2 times the surface tension. So, work of cohesion will be simply 2 times gamma OA, if oil is separated with air in between. So, work of cohesion of any pure liquid is simply twice its surface tension. For water therefore, it is 144 oaks per centimeter square and for paraffinic oil it is 44 oaks per centimeter square. It is here that we may choose to stop, but not before mentioning that we should next be thinking in terms of work of addition and work of cohesion together and see whether this consideration will lead us to any better understanding of miscibility or otherwise. So, we will conclude the lecture here. In case you have any questions, we can discuss.