 So, we continue here the discussion of topics under module 2 still on measurements and we briefly review the Willemey plate method and then move on to consider a couple of other methods including pendent drop and maximum bubble pressure methods. As you may recall from the discussion last time that this is a very widely used method for measurement of surface tensions over long intervals of time. Typically a very thin plate is attached to an arm of a balance or a light beam attached to a torsion wire as in the ring method and we measure the additional pull which is exerted on the plate when it becomes partially immersed in the liquid and that would be equal to the perimeter of the plate times the surface tension and for accurate results it is preferable not to detach the plate from the surface, but to keep it partly immersed and correct for buoyancy. That buoyancy correction could be minimized if we use a thin mica plate of dimensions such as 10 centimeter width 5 centimeters height and 200 super centimeter thickness and the method is valid only if the contact angle is 0 the liquid should completely weight the plate. In order to promote this weighting we might have to roughen the mica plate by using a very fine grade emery paper and the roughening is done in small circles making the roughness as uniform in all directions as possible. On the left hand side we have the action of surfactant if the contact angle is 0 more often the contact angle is not 0 and the situation like in part b would be common. So, one will have to attempt to make the contact angle as small as possible and that could be done by a suitable choice of the plate material and appropriate roughness. So, if the contact angle is 0 the vertical pull which would be normally equated to gamma cos theta would be simply equal to gamma. Now this was one situation which I had mentioned while talking about the work of addition calculation of work of addition from the measured contact angle and the surface tension. It is with reference to the Wilhame plate method that you might be able to measure the components of that equation on the right hand side directly by making use of suitable plate materials. One could in principle use this method also for measuring interfacial tensions one will require the plate to be completely weighted by one of the liquids at least. So, if you have a clean glass cover slide clean with hot chromic acid or roughen mica you would get water weighted surface, but if you require a oleophilic surface or what is preferentially oil weighted you may take the same mica plate and coat it with lamb black from a smoky Bunsen burner flame. In that case the contact angle for water would become close to 180 degrees. So, we wrap up the Wilhame plate method there and briefly look at a pendant drop method. Here the idea is that gravity if it is able to distort the shape of a drop then it is possible to estimate the surface tension from the shape of the drop. As the name suggests we have a drop hanging from a tip of a fine capillary the action of gravity distorts it from sphere and therefore, you would have the shape of the drop coming into the picture. You would be able to find out what are the principle radii then use the Laplace Young equation to estimate the surface tension from measured hydrostatic pressure. We can measure the surface and interfacial tensions by this technique even at high temperatures and large pressures. Geometry of the drop is to be analyzed either with the help of a photograph taken of the drop or by projecting the drop onto a squared paper and it is possible to make the force balance such that this surface tension or interfacial tension then could be extracted from the measurements. The next method that we discuss in detail is the capillary rise method. Now it is here that some of your common observations might come in handy. If you have seen what happens to the level of a liquid if a thin capillary is immersed in it in a vertical position. You might have seen that if the capillary is a glass capillary transparent one you dip it in if you dip it in water then the level of water inside it rises. But I do not know whether you observed what happens if you were to immerse such a capillary fine capillary in mercury. The behavior is just the opposite the level of the liquid inside the capillary drops down may show the figure here. At an air water interface a fine capillary would see level of water rising but for mercury the level drops. Second while this is not a finely drawn figure roughly we can see the meniscus is concave upwards for water and it is convex upwards for mercury. The shape of the meniscus has something to do with the contact angle obviously. So, we will have to take those concentrations into account. For glass dipped in water contact angle is 0 the surface tension force tends to pull the water upwards. Please remember that the rise of liquid in the capillary could be basis for some intelligent looking perpetual motion machines but nothing is possible which is thermodynamically justified as a perpetual motion machine. In literature you will find many ingenious devices claiming to produce energy without spending any that does not happen. Same glass dipped in mercury would see a contact angle of about 140 degrees that explains the shape of the meniscus. So, whenever a liquid makes a contact angle which is acute that is less than 90 degrees then the level of the liquid inside the capillary is expected to rise whereas, for obtuse contact angles greater than 90 degrees the level will be depressed as for mercury. We look into the pertinent force balance now and we will do that at two levels of sophistication or accuracies. Given small diameter capillaries one may argue that the meniscus at the top of the liquid inside the capillary could be regarded as a section of a sphere. And one may say that at a fine level of detail one may really want to account for all the liquid which is raised about the mean level of liquid in the container. If one does that then two questions arise how do we how do you estimate the contribution corresponding to liquid contained largely in the meniscus itself and how do you measure the height of the rise of liquid. So, we may respond this way that one may measure the height of the liquid from the mean level of liquid in the container up to the bottom of the meniscus if it is concave like in the case of water. And disregard whatever is the water present in meniscus above the mean level above the bottom of that meniscus, but maybe as a higher approximation one may want to even account for the amount of liquid which is present above the horizontal plane passing through the bottom of the concave meniscus. If one has to do that then one could see here that the volume of liquid there could be calculated from the volume of the cylinders circumscribing the meniscus minus the volume which is occupied by the vapor or air above this meniscus. So, you see here the volume of the cylinders circumscribing the meniscus minus the volume of the corresponding hemisphere approximation for the vapor space will give you the volume of liquid that times the density of liquid times acceleration due to gravity would give you weight of the liquid which is present above the horizontal plane passing through the bottom. So, we might want to take that into account in the first approximation we will exclude this and this excluded weight we represent here by this later W e that should be the density of liquid rule times acceleration due to gravity G into the terms in bracket. The first one is the volume of the cylinder circumscribing this meniscus. So, that should have area pi a square and height a because this is supposed to be now approximated by a hemisphere. So, that is the volume of the cylinder minus the hemisphere itself will have the volume half of the volume of the sphere which is 4 pi a cube by 3. So, when you simplify this you get this 1 minus 2 by 3 common into pi a cube. So, that gives you W e is equal to pi a cube by 3 rho L times G. I would like you to also start working things out as we go along and not just restrict yourself to mental calculations as I am trying to present to you. So, try to use pencil and paper to work out the things that come first over here it is quite a straight forward. Now, supposing we exclude this weight then how do we make the force balance? We need to worry about what is the vertical component of the surface tension force acting on the perimeter of the meniscus and that will be balanced by the raised level of liquid in the capillary and that will be basically the hydrostatic pressure of the column of liquid within the capillary times the area of the capillary right. So, this could be written in general as gamma cos theta the vertical component of surface tension times the perimeter 2 pi a. The rise of liquid is h measured up to the bottom of the concave meniscus times this density difference between liquid and vapor rho L minus rho V times acceleration due to gravity G there is a pressure for you and multiplied by pi a square the area. So, when you simplify this you get gamma equal to h times this delta rho G times a by 2 cos cos theta pi a gets cancelled. This is if we were to ignore the liquid present in the meniscus, but what if we need to account for that give it a thought what will change in the meniscus. So, what would that be that is W e we already calculated that right. So, over here we should have W e added. So, that is pi a cube by 3 rho L G. So, that means, if we were to take a square common and if we were to neglect the density of the vapor in relation to density of liquid, then we will get the corrected h in place of h. When we exclude that weight and ignore the density of the vapor in relation to the density of liquid gamma is given by this h rho L G a by 2 cos theta and that is pretty reasonable vapor density could be easily neglected in comparison to density of liquid. But if you include the weight of the liquid then this h will stand corrected and it will be modified as h plus a by 3. So, your final equation for the surface tension is h plus a by 3 rho L G a by 2 cos theta. This is equation that one should be using for estimating the surface tension from the capillary rise method. One could work out the analogous situation where the mercury like liquid with obtuse contact angle shows the depression in the level of liquid. This quotation is just a brief reminder that essence of everything is very little actually. So, there is no reason we should be forgetting that. We can forget most of the things that we study, but the important thing should not be. In context of methods and experiments the precautions form core part of the essence we should not be forgetting that otherwise we would make gross errors. With this we come to the next method that is maximum bubble pressure method. Very quickly before I go into the maximum bubble pressure method I would like to recall that we looked at now several methods. We started with the ring method, then we reviewed the drop rate method. Next we looked at the willy me plate method, then we seen a pendant drop method and the capillary rise method. Now what is this maximum bubble pressure method? Maybe I should show you a figure first so that the discussion here is clearer. This is an exaggerated figure of the apparatus. What you do is you take a small tube like capillary, immerse it in a liquid and then have a provision to measure the pressure that is present inside this tube or inside the bubble which forms at the tip of this tube. And what you do is you introduce gas or air whatever you have through the capillary and form a bubble inside this liquid. I have deliberately shown here the liquid drop as an arbitrary shape, but I would like you to think in terms of how the drop, how the bubble would form at the tip of this capillary. Remember this cross section is exaggerated. So, you could think in terms of extremes whether the liquid weights a solid or not. Would that have influence on how the bubble will grow at the tip of this tube before eventually detaching? That is something I would like you to think about. So, if you take an inert gas and blow it through the liquid with the help of this small vertical tube and measure the pressure continuously, we may argue that the initial sequence of shapes that the bubble would assume during its growth would always again correspond to sections of spheres. However, what happens to the radius of bubble? As it grows the radius of bubble would become minimum when it has grown into a perfect hemisphere. And at this stage, this bubble radius would be equal to radius of the tube. That is outer radius of the tube. If the liquid were to weight the tube then the minimum radius of the bubble would be equal to inner radius of the tube. Correspondingly the pressure inside the bubble you remember from our early analysis will be equal to twice the surface tension by the radius of this bubble at the point where the radius is minimum and the pressure is maximum. So, during a typical extent one would measure the maximum pressure inside the tube when the bubbles are not able to grow any further and break away. In general, the tip of the tube is immersed in the liquid to a certain depth. If that is D then the hydrostatic pressure equivalent to D G delta rho should be subtracted from the measured maximum pressure for accurate results. So, delta P max will be P max minus this D G delta rho or delta P max is 2 gamma by R and that is equal to delta rho G H. That H is from the minimum pressure of the geometric arrangement for measuring the pressure. And if you look at the right hand side of equation 12 then express in equivalent terms of a column of liquid this equation would be identical in form to the one that we had in the capital rise method. So, one could proceed for estimation of surface tension from the major pressure, maximum pressure using this method, but there are certain limitations. This is a limiting treatment only valid for very small tubes. And there is a quantitative consideration here. We need to know what a capillary constant is. Capillary constant A is given by this equation A square equal to 2 gamma by delta rho G and equal to R times H. The tube radius divided by the capillary constant which is equal to square root R by H should be much less than 0.05 for this method to give you a dependable value for the surface tension. So, that is a constraint that you have to keep in mind R should be small enough such that square root of R by H is much less than 0.05. How good is this method? It is accurate to within a few tenths of a percent and does not depend on the contact angle, but one has to only ensure that either the inner or outer radius has to be used. And it requires only an approximate knowledge of the density of the liquid if twin tubes are used and the rate at which the bubbles are created should be about one bubble per second. You could interpret this as a cosy dynamic method involving freshly formed liquid air interfaces. As I have explained earlier to you, the impurities presence at the surface or interface could alter the surface tension or interfacial tension and one might get from slow migration of impurities to the interfaces variation of the surface or interfacial tensions over time. So, those dynamic surface tensions could be measured using a method like this and it could be therefore, use at short surface edges. You cannot study aging of surfaces or interfaces where you will require the static surface tension with this method. If pure liquids are used of course, then we have minimized the impurities, the surface active impurities and we should be able to use this method in those situations. One particular advantage offered by this method is that you could perform a remote operation. At times you have to measure surface tensions for example, systems like molten metals. Now these will be very high temperature systems, you cannot approach the system, but you could remotely operate a capillary through which an inert gas is blown into a molten metal and one could use this maximum mobile pressure method to measure the surface tension in the dynamic sense. There are other methods also for measurement of surface tension. Some of them will be handling in course of time. Suffice it to say here that the few methods in addition to what we have seen include the ripple method. We will talk about waves and ripples in detail in later lectures. A sissile drop method, once again we will talk about this sissile drop in some of the later lectures. A spinning drop method which is ideal for measuring low interfacial tensions and what one does here is diameter of a drop within a heavy phase is measured when both are rotated. Drop volume method is a dynamic technique for measuring the interfacial tension as a function of interfacial age. Liquid of one density is pumped into second liquid of a different density and time between drops produced is measured. In that sense we could be able to characterize the effect of varying impurities concentration on surface tension. We then go into what will be classified as differential measurements. Let us think of monolayers. If you have a monolayer present on a liquid, we will have a certain repulsive pressure within the monolayer. We have identified that as a positive repulsive repulsive pressure pi which would lower the surface tension to a value below that for pure liquid. So, this lowering of surface tension because of monolayer is studied using a surface balance and with suitable instrumentation it is possible to measure changes to within a few milli dynes per centimeter. Drop volume method or willy me plate method are often used for studying adsorbed films especially at oil water interfaces. What happens at solid interfaces? We need to measure the contact angles for the solid liquid systems. One could use the plate method for obtaining theta and especially if the solid is available in the form for relatively flat plate at least a few centimeters across the angle at which this plate dips into the liquid could be altered till the liquid becomes planar at the interface right up to the solid surface. I think while discussing the method of virtual displacement of three phase contact line, I had tried to pose this question before you. How does one ensure that you have actually taken care of contact angle by tilting an immerse solid plate to an angle exactly equal to contact angle such that on the on one side the liquid surface is planar right up to the three phase contact line. I am raising that again now. How does one assure that the surface is planar right up to the surface up to the three phase contact line or the surface of the solid? One ways just observe it very closely. Possibly you would not have keen enough side to be able to make out curvature very slightly different from planarity. The next thing is obviously use a microscope. One could use a microscope to look at the meniscus close to the three phase contact line. It might be possible to see if there is any left over curvature or they might be something simpler. I will give you a hint here. I am sure you are seeing light being reflected from patches of water on floor. You know how the reflection looks. Could we possibly use reflection of light to determine if the liquid surface is actually planar right up to the three phase contact line. There will be no interference pattern. We do not need interference pattern here. We just are considering possible use of reflection as a means of distinguishing between curvature and planarity. There is a related thing very distantly related. Maybe you might not think about that here, but in a very different course on chemical reaction engineering probably you would have been exposed to a method called method of elimination, where in principle when you think of a certain mechanism, whether it is actually corresponding to the rate equation that you have proposed, whether experiments are actually revealing the mechanism corresponding to the rate equation proposed. You could check by making a plot of a suitably chosen y versus suitably chosen x, where y is a function of concentration and x may be concentration. If your data reveal a curve, then you know that that is not the expectation. Expectation is a straight line. If the data show a curvilinear pattern, then you know that mechanism is not right. So, all those mechanisms which give you departure from a straight line could be straightaway rejected. Only the one which gives you gives you that fca versus ca as a straight line is likely to be. So, there we are using the method of elimination. In a sense, what I am expecting you to do is a qualitative analog of that method of elimination. The principle I am using is the planarity will show a difference from all curvilinear situations. Does any idea strike you? If you have begun thinking, maybe consider this. We just need to distinguish between the planarity and the curved surface. Suppose you take a slit through which light shines and this slit is rectangular. So, a rectangular beam of light is now shining at the three-phase contact line or liquid surface. It would get reflected. You could look at the reflection of that beam and looking at the shape of that reflection, you would be able to tell easily whether the surface is planar or not. If the surface is planar right up to the three-phase contact line, the reflection will also be linear. If there is a curvature, then this will get distorted from linear. So, you know very sensitively and you can use the optical lever by choosing the length of the path of incidence and the path up to the point of observation after reflection. And then you could distinguish between a curved surface, very little curved surface from planarity. So, this is a simple technique which you could use in place of a microscope. However, there are details here which I think I should also mention. You might have wondered as to how we are going to do this experiment, how are we going to hold this solid plate which could be lower to whatever depth you want and also could be adjusted to measure the angle required to achieve the planarity or an angle equal to the contact angle. So, you can actually use an adjustable holder which can be tilted to any angle and which allows this solid plate to be raised or lowered such that both the advancing as well as the receding contact angles can be measured. I mentioned the details of preparation of liquid surfaces, impurities removal is very essential. You do it by directing a jet of clean air at the surface. You might do a better job by sprinkling ignited talc powder on a surface or interface before cleaning up. All this is done in a Langmuir trough. Langmuir trough I had already mentioned while we are talking about the kinetic subspreading. Over here the Langmuir trough is also provided with barriers which can sweep the surface repeatedly and thereby you can push out impurities from the surface and ensure that the surface tension gamma LA is not less than that for pure liquid. Measurement of surface tension is a sensitive way of ensuring purity of the liquid surface. The Langmuir trough and barriers are made of polytetrafluoroethylene and for accurate work we need to study the liquid surface where it meets the solid by the optical technique which I just mentioned. After ensuring that we have inclined the solid plate to an angle exactly equal to contact angle we should be in a position to make measurements in the advancing or receding cycles. Here is another way the plate method can be used to find the contact angle between two liquids and a solid. In your mental picture the air on top is replaced by another liquid such as benzene above water. We could use the same technique for the measurement of contact angle for these two liquids in relation to a given solid. Now a few words about the preparation of solids are also in order. The solids should be clean and smooth because we understand that solids have incredibly large surface energies they are prone to adsorb vapors. So, generally the solid should be freshly cut and in order to ensure the smoothness of surface we need to do polishing in several steps. I just cited the example of preparation of a specimen for SEM it is an elaborate procedure if you do it carefully it would take a long time. Here we have to prepare a freshly cut solid and polish it with increasingly finer grates of emery cloth followed by leather hone and finally with a fine grade filter paper. Then you got to wash the solid with re-distilled ethanol and then with re-distilled water. Finally it is vacuum dried in a desiccator. There are other solids which may be easier to prepare paraffin wax for example can be prepared in a smooth surface form by repeatedly dipping a clean microscope slide quickly in and out of molten wax. Talk on the other hand is prepared by cleavage. Let us talk about the wetting balance method for finding the contact angle, the work of adhesion and negative spreading cohesion. Wetting balance method is proposed by Guia Stalla and uses the Wilemi plate method to measure the work of adhesion or the work of wetting without measuring the contact angle directly. However, the work of adhesion is likely to be relative to the adsorbed monolayer of water or surfactant. A thin slide with a perimeter about 1 centimeter is initially immersed in the liquid and then raised through the surface till this external pull F becomes constant. They might be a little source of confusion especially when we started talking about the Wilemi plate method in the beginning and when I talked about the additional pull required when the plate becomes partly immersed in water and then I talked about the buoyancy correction. If there was any confusion there, this should dispel it. Here what you are actually visualizing is that the plate is being withdrawn from the liquid until the external pull required F is constant. We are still talking of a situation where the plate is partly immersed and the buoyancy correction will have to be performed and the force which will be required then will be gamma LA cos theta. The work from this stage onwards of withdrawing this solid slide will be equal to work of dewetting the slide. If the slide is hydrophobic or contact angle is greater than 90 degrees then cos theta is negative. This would imply gamma cos theta and therefore, the work to be negative. While withdrawing such a plate through water, such a hydrophobic plate through water the work is actually done when the plate is immersed. You could visualize this through a mnemonic analogue. Think of a plastic ball being dipped in water with or without a hole in its wall. If there is a hole in it, water can enter it, fill it, make it sink. But without a hole the work will have to be done to immerse it against the buoyancy. The hysteresis that we talked of between the advancing and contacting cycles on raising or lowering the slide is often significant and one has to deal with this in practical systems. Question may arise as to what would the area of this hysteresis loop imply? It would be major the area of hysteresis loop will be a measure of the work lost in removing adsorbed gas from the surface cracks and sometimes also in leaving a film, a thin film of water in these cracks after withdrawal of the slide. With very clean systems, expectedly we would not get the hysteresis and therefore, this area of hysteresis loop will become 0. Let us look at some numbers here. For a paraffin wax slide with a perimeter of about 1 centimeter, the measured pole is about minus 24 dynes. So, when you equate F to gamma e cos theta, you get theta equal to 110 degrees. This is close to the measured value. So, you see how we could use this method for estimating contact angle. We could do a little trick here. Suppose, we were to use a surfactant here m t m a b meristil trimethyl ammonium bromide in water. This will allow weighting of the wax surface because there would be adsorption of a monolayer possible and that will give you F now as 15 dynes. When we now equate gamma e cos theta to this measured value, we see that positive F value indicates that after adsorption of the surfactant monolayer, the wax slide will be immersed spontaneously unless you restrain it with an external pull of this amount. So, you can see that slight differences in compositions or presence of impurities can alter the measurements drastically. Weighting will be complete if F becomes close to gamma L a for the solution that is corresponding to theta equal to 0 or maybe less than 0. This would be attained at high concentrations of this surfactant m t m a b which is greater than a small looking value 1 milli normal. Very small concentration of this surfactant can actually produce a drastic change in the weightability. We could say that the same solution actually would devate glass. We had seen the devating phenomenon. What is weighting now? A paraffin wax would have been seen as devating otherwise hydrophilic glass surface. This would be done by adsorption of a monolayer of the long chain cations and it could leave the surface totally dry. In chemical engineering context, what this implies may have to be 30 dynes per second thought in a broader perspective. One might think of trickle bed reactors where liquid and gas streams have to be contacted and the expectation is that you will be able to provide very large area in this heterogeneous reactor. Everything may be designed as per the requirement. However, small changes in levels of concentrations of impurities could totally alter the performance of a trickle bed reactor or any heterogeneous reactor where weighting of the packings is critical. You might find that weightability of the solid for given composition to be a critical parameter governing the performance of the reactor which normal chemical engineering constructions would have ignored. So, if you were to imagine that the given liquid would weight the solid and unexpectedly you find there is hardly any useful contact. So, area between gas and liquid it could be attributed to the surface actually becoming dry on account of the role played by a monolayer which turns what is otherwise hydrophilic surface into practically hydrophobic surface with minuscule concentrations. Here I will wrap up the discussion by saying that we could actually measure gamma L A and F separately and then one could obtain the contact angle. This is one way, measure gamma L A separately, measure the vertical pull required to pull this plate out of the liquid and then from these measurements we can obtain cos theta. Alternatively, what you could do is for the same liquid you could take two plates one which is chosen to give you whatever contact angle there is to be measured, another one which is preferentially weighted by this liquid because when you repeat this experiment in the second case the vertical pull measured if you call that as F 2 that will be simply equal to gamma L A because you have chosen this solid such that the given liquid is ensuring weighting. That means the theta 2 is 0 and so F 2 is simply equal to gamma L A. The theta that you want to measure is then obtained from F 1 equated to gamma L A cos theta 1, theta 1 is something you want to measure. So, gamma L A itself can come from the plate method where you are ensuring the weighting of the solid by the liquid and then measuring the vertical pull again when the contact is not complete. Therefore, you get the desired contact angle value. So, from the measured F and gamma L A and Young's equation for the work of adsorption and the equation for spreading cohesion recall this S equal to gamma L A cos theta minus 1 which is valid for positive theta we could obtain W S L and S respectively. So, here we sum it up experimentally it is very simple you take a immersed plate vertically oriented out of a liquid measure the pull replace this given plate by one which is weighted by the liquid measure the pull from the second pull you get the surface tension from the first you get the contact angle. Once you know the surface tension and contact angle then using W S L equal to gamma L A cos theta plus 1 and S equal to gamma L A cos theta minus 1 we will be able to obtain the work of addition and the spreading cohesion. And admittedly these will be values corresponding to may be a layer of adsorb monolayer or impurities and if you need the true values then you need to do the corrections. We will take a logical break here stopping.