Lecture 31

Added: 2026-05-09

[00:00:08][music] Hello students, my name is uh Shahab Alias Garnami and I'm serving as associate professor of chemistry at department of industrial chemistry.

[00:00:30]Aliger Muslim University Aligar. So in continuation of our previous lecture where we have talked about the illusion chromography and the various concepts which comes under the illusion chography most notably the distribution constant the retention factor retention times different retention times selectivity factors etc etc. So we have discussed them and they are we will be you know using them uh in our coming slides. So today we are going to start uh a brand new topic that is the zone broadening and column efficiency.

[00:01:10]So the efficiency of any column with regard to chromatographic separation actually depends upon zone broadening with regard to illusion of a particular solute from a column.

[00:01:25]Now in this series of lecture we are going to discuss the zone broadening and the efficiency in terms of certain parameters and we are going to study this zone broadening in terms of two closely related theories which we are going to discuss in the coming slides.

[00:01:45]So let us briefly sketch the outline of the topics which are to be covered in the lectures to become. So first of all we will study the concept of separation and of course the efficiency of a column with regard to zone broadening. Then we will uh go through the column efficiency with regard to a theoretical concept that that involves certain plates certain imaginary plates in the chromographic column. Then we are going to quantify that concept that theoretical concept into an equation that is called as the van demeter equation. And the van demeter equation actually involves three terms A, B and C. So we are going to study these three terms in detail and we will study the impact of this a b and c in terms of van demetric equation. Then we will move towards the optimum flow rate that how we are going to optimize different conditions so that we can have a better efficiency in terms of separation of an analyte and that efficiency can also be seen in terms of can also be defined in terms of a curve. Similarly, after going all this, then we are going to study certain applications of uh this vanerter equation in terms of the separation by using the gas chromography, by using the high performance liquid chromography and of course after that we will study one by one certain factors which affect the column efficiency. then some real life applications and of course at the end we are going to study the advantages the disadvantages and some of the key points which are very important and very interesting. So let us begin our journey of the zone broadening. So initially we have to understand that about the nature of the curve that how this curve actually you know gives you information about the illusion of certain analytes through a given column.

[00:03:59]Now we know that [clears throat] initially what happens is first of all we should understand that this illusion of certain substances which are to be separated are to be they actually come out of the column in a range of time.

[00:04:18]That is the separation occurs in a range of time that is maybe if you can say that is starting from t is equal to0 to t is equal to 10 minutes. So that is in a range of time that is the illusion occurs in a range of time not at a single point of time.

[00:04:40]For example, if you think that your solute is eluting at a single point of time, then you will obtain a graph like this that time is written here and the detector response detector response is here.

[00:04:57]Then if the illusion is occurring at a single point of time, then you will get a peak like this. A straight line perpendicular to the time axis.

[00:05:08]This actually if this is the case then it tells you that the solute are having no interaction with the stationary phase because the moment they start interacting they have to spend some time and the moment they spend time they will give you a curve.

[00:05:33]They will give you a curve. Now this curve the shape of the curve actually tells you about the rate of migration about the you know about the different velocities which the different solute particles at which the solute particles are traveling.

[00:05:53]Now ideally speaking a curve should be like this.

[00:06:00]Ideally speaking your curve should be like this.

[00:06:06]Now this curve actually is this curve is generally called as a gshian curve.

[00:06:15]Gossian curve or normal error curve.

[00:06:18]This can also be called as the normal curve. This curve actually is important in the sense that this part this part of the curve this part of the curve is called as the fronting. This is called as fronting part or front part of the curve. And this actually tells you about the solutes which are moving at a very fast rate as compared to their other you know as compared to the other neighboring molecules and because of their faster rate of migration they are eluting initially. So this forms the first part of the curve and this is called the fronting part. Similarly, the solute molecules which lag behind which are eluting after a certain time or after retaining more after having a more interaction with the stationary phase they are going to elute at a later time.

[00:07:15]This part of the curve is called tailing part tail. Okay, tailing part. This is the tailing curve or tailing part.

[00:07:25]While the mid part, this mid part actually this tells you about the average velocities of the solute particles forming the central part of the gshian curve or the central part of the curve or the peaks you can say.

[00:07:48]So in the first figure you can see that a broad curve is obtained enveloping two peaks and an ideal separation should give you the best possible resolution. Okay. So an peak becomes an ideal if it is resolved. Number one number one condition that you get a resolved peak.

[00:08:17]Resolved peak.

[00:08:20]Number one condition is that you get a resolved peak. Okay, that is it should be separated from the other peak in a very well manner which you can see here.

[00:08:29]And the number two condition is that peak should not be broad.

[00:08:42]That is ideally speaking you have slim peaks. The peak width should not be too much. That is ideally speaking you have a sharp peak like you have a sharp peak like this.

[00:08:56]Ideally that is what you have to do. You have to cover actually you have to take in mind two things. Number one is that they should be separated as much as possible that is there must be no overlapping like in this case and the peak width that is the peak width should be kept as small as possible.

[00:09:16]So if you get overlapping peaks then it implies that it is you get actually poor resolution. It implies poor resolution.

[00:09:25]So in the second case you can see the peaks are well separated. They are well separated. If you draw perpendicular like this perpendicular like this that is actually they are well separated and sometime we are going to study this is called as delta zed and that is very important to describe the efficiency or to describe the effectiveness of any chromographic column.

[00:09:53]Okay. So you have to keep two things in mind. Number one is that the peaks must be resolved and the peak width should be as small as possible. That is you should get ideally you should get sharp peaks.

[00:10:08]Sharp peaks. Okay.

[00:10:10]So you have minimum band broadening and you have maximum resolution. These are the two important factors which we have you know summarized here that is maximum resolution and this is donate denoted by RS. Similarly we have minimum band broad.

[00:10:28]Now the efficiency of of any column with regard to band broadening can be best explained by considering two theories of band broadening. These two related theories are called as number one theory is called as the plate theory plate theory and number two is called as the rate theory we are going to discuss the rate theory in very detail but just give you a I'm trying to give you a concept of at this point of time plate theory plot theory was actually given this this concept was given by the genius of their time that is the Martin and Cinch in 1941 and in fact because of their you know breakthrough theory and this theory is purely you know is purely a theoretical concept it has nothing to do with experimental approach and the beauty of this theory is that although it is a theoretical concept but the terms which this theory defined was later used in rate theory which is actually an experimental concept regarding which explains the band broadening. So this plate theory actually talks about the number of theoretical plates. Now what is number of theoretical plates? Let us briefly you know let us briefly just summarize it. According to the player theory, concept of player theory extended by Martin and Cinch what they considered?

[00:12:04]They considered that a column is actually made up of continuous plates.

[00:12:12]They are made up of continuous plates.

[00:12:15]Okay, they are made up of continuous plates.

[00:12:20]Your chromographic column. So it is made up of continuous plate and each plate is further divided into a stationary plate, half of a stationary plate, a stationary plate and half is the moving plate.

[00:12:40]That is half of the stationary phase and half of the mobile phase. And we know that the stationary phase this phase is remains fixed and the mobile phase is keeps on moving. So what they actually proposed that for example if you introduced if you introduce your sample which contains for say 200 molecules 200 solid molecules the moment you inject them.

[00:13:08]So this 200 molecules goes to this plates and these plates are actually continuous in nature that is one after the other one after the other and they are discrete. They are continuous and they are discrete. That is they are arranged in a one by one manner and a continuous manner that your column actually contains these plates and each plate is divided into a stationary plate and a mobile plate that is a stationary phase and mobile phase and on each plate equilibriation has to be done. That is equilibriation has to be done. For example, if you introduce 200 solute molecules, then 100 will be distributed here and 100 will go to stationary. Then these 100 will travel to the next plate and there 50 will be remaining here and 50 will get distributed in the stationary. Then 50 will go backward and 25 will remain here and 25 will get here. So it's actually continuous movement of your solute molecule across the across these theoretical plates and these theoretical plates are actually purely imaginary plates.

[00:14:15]You know what you have to keep in mind that that ideal columns or the practical columns does not contain any plate. They are actually hollow. They have the packed column. They these plates are purely imaginary in nature. And this concept is to actually equate this plate in terms of the resolution in terms of the band broadening of the column. Okay. Band broadening is actually the response of the detector. Okay. So we have seen it.

[00:14:47]This band is actually originated from the detector response with regard to time. And this is actually the illusion pattern. This is actually the illusion pattern of your solute molecules. So this concept of theoretical plates actually originated and in each plate you can see that there is an equilibriation and half of the molecule goes to stationary phase and half goes to mobile phase. So the solute keeps on moving downwards and after a certain period of time it gets eluted.

[00:15:19]It gets eluted and here the detector is connected and you actually get the detector response here. detector response.

[00:15:29]Okay.

[00:15:30]So you get a detector response.

[00:15:33]Now how actually these theoretical plates are connected. Now let us see. So let us suppose that the height that let us suppose this this height is called as h is called as height equivalent equivalent to theoretical plates.

[00:16:10]Sometime it is also written as H E T.

[00:16:14]Okay.

[00:16:16]So this packed column actually this packed column contains n number of theoretical plates. It contains n number of theoretical plates.

[00:16:28]Selectivity we know selectivity we have already discussed selectivity is K of for example if you have a two component system then it is called as KB upon Ka the distribution constant of B upon A where B is actually that solute which is eluted last. Okay, we have already discussed the selectivity in our previous slide and we have also discussed retention factor also that retention factor we have already discussed. So now we are actually trying to quantify this number of theoretical plate concept with this one.

[00:17:06]So one thing which we have to keep in mind that the next theory which we are going to discuss that is called as the rate theory which gives you a quantified idea of the band broadening uses the concept of HTTP.

[00:17:22]It uses the concept of number of plates.

[00:17:26]Although these two concept originated or proposed by the plate theory given by Martin and Sing but your rate theory is going to use it.

[00:17:37]So this is how this band broadening is defined by the continuous equilibriation of your solute molecules over the passing of them through a column and this you actually recorded it. So this band broadening is good goodly explained betterly explained by this plate theory.

[00:18:03]But the one important aspect of rejecting this plate theory was that plate theory does not give mechanistic explanation.

[00:18:21]Mechanistic explanation about band broadening that is about the resolution because band broadening is actually related with the resolution of peaks.

[00:18:42]So what happens is this now you can resol now you can relate the two things that is greater the number of theoretical plates greater will be equilibriation and greater will be its resolution.

[00:18:57]Okay so you can see that what you can write at this point of time that n is equal to l upon h. We are going to study this equation you know in coming slides also. So that is actually N is equal to L upon H. L is the length of the packed column. This is length of the packed column to this one. Okay, length of the packed column and H is the height equivalent to theoretical plate that is HTP simply sometimes can be written as H.

[00:19:28]Similarly you can ex in terms of quantification you can also think of resolution as 1 upon 4 of under root n is the number of theoretical plates alpha selectivity upon k dash that is the retention factor. So if you want to quantify it you can write like this in terms of equation 1 upon 4 under root n alpha - 1 upon alpha into k dash upon 1 + k dash. Now experimentally it has been observed that for all those separation where retention where resolution is greater than 1.5 is good that is there you get there you get actually non-over overlapping peaks you get nonover overlapping peaks.

[00:20:19]So you have to keep two things in mind that for attaining the best the best uh you can say efficiency what you have to have you have the maximum resolution and you have the minimum band that is this distance must be kept low and this distance must be kept high. So this must be kept as high as possible and this distance must be kept as low as possible.

[00:20:46]Okay. Now one important aspect which we want to emphasize at this point of time that this plate theory because all these explanation which we have given here is with regard to plate theory we have not come up to a rate theory. So up to this point of time you should note that plate theory does not account about the velocity of the mobile phase. there is no factor nothing is you know dependent here with regard to plate theory. So let us move forward and let us have a very specific idea about the band broadening.

[00:21:24]So you can see three different color uh three different colors giving you three types of band broadening. So you can see blue color is telling you about the initial zone.

[00:21:38]The yellow color is telling you about the intermediate zone and the broad zone is depicted by the red color. Now this broad this red zone is you can say it is column is not efficiently working is not efficient and this blue is actually an ideal curve. it's ideal.

[00:22:03]So our in most of the our experimental studies we find this because you cannot you cannot ignore the non idealities in flow the non idealities in terms of diffusion and the equilibrium although we are saying that at each imaginary plate there's an equilibriation but it is not so okay so at this point of time what is important to emphasize is this that even in ideal column diffusion comes comes into play and we can see that this diffusion gets maximum when we are dealing with the gas dealing with the gas where the gas are actually acting as the mobile phase which we are going to see when we are going to discuss the gas chromography.

[00:22:51]So mind that we cannot you know we cannot sometimes we have to take all the factors into account and we have to actually modulate it. So what we have to do we have to restrict the widening of solute zone because it leads to broadening and we cannot you know we cannot minus the nonidility factors in flow and of course in diffusion.

[00:23:19]So what we have to do, we have to have as resolved peaks as possible keeping in mind that this peak width is to be controlled or this peak width is to be seized as as seized as possible. Okay, but we cannot you know we cannot overcome them. Ideally speaking, practically speaking, they exist. Okay.

[00:23:46]So what are the consequences of this zone broadening? Now the first and the foremost con consequence or the effect is that the moment you get a broad band you never know how many different you know uh different solute it has engulfed in it. For example, in this case, we have seen that this is actually solute one and this is solute two and that's this broadband has actually enveloped these two. So you cannot have a good resolution. So resolution is not good.

[00:24:20]You cannot quantify it because this if you are going to extrapolate it and extrapolate it like interpolate it like this and like this then this area is becomes common. So you so you cannot quantify quantification is not possible is not possible in overlapping peaks in overlapping peaks.

[00:24:52]Similarly if the resolution is not good then the quality is also affected. So loss of quantitative accuracy because of the overlap of the adjacent peaks and of course the resolution is poor because you already get a broadband. Now the common examples is that you cannot if if for example if some impurities is there you cannot separate it. Let us suppose that TR of uh let us suppose TR of your paracetamol paracetamol is 5 minute and unfortunately that of your impurity is 6 minute then it becomes difficult for you to you know then it becomes difficult for you to separate unless and until you have a very efficient column but at the same time if your column is efficient then you can purely get 5 minutes. Okay? Because now if you have an efficient column, it will actually make a distinction between the paracetamol and that of impurity.

[00:26:05]Okay. So this will happen provided your column is efficient. It is long enough because we have seen that n is equal to n is equal to l upon h.

[00:26:22]So if you want to have if you want to improve the resolution then you have n as far as you know as long as possible and h as small as possible that is the theoretical plate must be as small as possible and the length of column must be as long as possible so that you can have a an ideal column where you can separate the different peaks with regard to their illusion pattern. So what are the major causes?

[00:26:52]So the major causes of zone broadening are edifusion. What is edifusion? We are going to study in the coming slides.

[00:27:01]Then the longitudinal diffusion and the resistance to mass transfer or mass transfer resistance. So where it comes into play and why edit diffusion occurs, it occurs because of the multiple paths taken by the solute molecules within the column. And why this longitudinal diffusion occurs?

[00:27:22]Because of the spreading of the solute molecules in all directions. That is from high concentration region to from high concentration region to low concentration region.

[00:27:46]Okay.

[00:27:49]Now edit diffusion it is because of the multiple paths. So let us first you know discuss these in one by one. So let us first start with the longitudinal diffusion. What is actually longitudinal diffusion and why it happens and how it actually affects it. So these are actually if you just coming back to the previous slide these these are the parameters that is a b and c.

[00:28:20]These are actually the parameters of van demeter equation which we are going to discuss in very much detail that van demeter equation is http is equal to a + b upon u + c u. So it composed of three terms. A is the diffusion edifusion. B is the longitudinal diffusion and C is the resistance to mass transfer. So what we have to do this HTP or H to have a better resolution it must be kept as small as possible. That is H must be as small as possible to have the best resolution.

[00:29:16]To have the best resolution that is RS.

[00:29:23]You know what actually we are what we are doing is that we are trying to have a very efficient column and in doing so in order to have an efficient column the height equivalent to theoretical plate should be as small as possible and at the same time it can also be said in another way that greater the number of theoretical plates better will be its resolution because that n is equal to L upon H where L is the length of the packed column.

[00:29:59]We have already discussed it. So now let us take these three one by one and we are going to discuss them in detail and what this smaller particles and uniform packing mean to us. We will discuss this also. So at this point of time what we have to do we have to minimize this HTTP as much as can. So this can be minimized by minimizing A. This can be minimized by minimizing B upon U. And this can be minimized by minimizing C U. So what we have to do in order to have HTTP as small as possible, we have to have all these three factors that is A, B upon U and CU as small as possible. Okay. So now we have to look in terms of minimizing these you know these three factors that is the added diffusion longitudinal diffusion and the resistance to mass transfer. So let us take these one by one. Let us first take the longitudinal diffusion. This longitudinal diffusion is represented by the term B upon U where B upon U actually in B upon U u is the mobile phase velocity. It is the mobile phase velocity.

[00:31:14]And now actually we are discussing the this comes under the rate theory.

[00:31:21]This comes under the rate theory that is under the rate theory is defined by van demeter equation.

[00:31:34]Now the beauty of this theory is it gives you a it gives you a quantitative idea quantitative idea of band broadly.

[00:31:53]Okay. So this rate theory actually talks about two important things. Rate theory talks about number one is the random walk.

[00:32:07]Random walk. It talks about the random walk of solute molecules.

[00:32:16]And the number two point, second point, the most important with regard to rate theory is that it talks about or it accounts it accounts.

[00:32:28]It accounts the mobile phase velocity.

[00:32:35]mobile phase or mobile phase velocity or you can say the rate of migration.

[00:32:44]Now let us suppose let us suppose you have a column. Let us suppose you have a column.

[00:32:55]Let us suppose you have a column. Let me draw you know a a column which is a little bit wide. Let us draw like this.

[00:33:05]Now the moment now let us suppose that you introduce your mixture. You introduce a mixture which is to be separated. This is a column and you introduce mixture which is to be separated. The moment you add mobile phase, the moment you add mobile phase, what happens is the solute molecules, let me draw another one. The solute molecules will start will start moving along the mobile phase and they will move in all directions.

[00:33:49]They will move in this direction, this direction, this direction. They move in a random manner.

[00:33:55]they move they move in every you know every part of the column.

[00:33:59]Okay. So they diffuse your solute diffuse in almost all the direction and this diffusion actually give rise to the illusion of these particles at different points of time and it leads to zone broadening that is the broadening of your peak. It leads to broadening of peaks.

[00:34:25]Okay. Now if you consider your mobile phase as gas, if you consider your mobile phase as gas, then this this random movement becomes very high because now gas has a very high diffusion. Gas has a very high diffusion.

[00:34:46]Okay. So this this longitudinal diffusion becomes very important when we deal with the gas chromography because in gas chromography the mobile phase is always a gas an inert gas and the gas has the highest diffusion and the solid has the lowest diffusion. So here the diff because of diffusion they these particles take random paths and because of the taking of random paths they elute at random times and because of the random time illusion your band your band actually broadens and this gives you then that actually leaves your separation inefficient.

[00:35:32]Okay. So in order you have to what you have to do you have to restrict the band broadening you have to restrict the band widening you have to restrict it and this can be restricted by increasing the mobile phase velocity because the moment you increase it then these particle for example if you increase the mobile phase velocity then these particles will be directed more towards the towards the bottom of the column that is towards the towards the bottom which is connected to the detector you know. So you have to what you have to do you have to have you have to increase the velocity of the mobile so that they can move further fast and their dispersion can be minimized.

[00:36:28]Now this actually dispersion can can also be related from the Taylor's dis dispersion theory. Okay. So what you do at this point of time in order to avoid this band broading you have to increase the velocity. But mind that your van equation if you remember it was h is equal to a + b upon u plus cu. Now the moment you increase it, the moment you increase the velocity, if velocity is increased, let us suppose then B upon U will be decreased will be decreased. Good. Very good.

[00:37:14]But the problem is that CU will increase and overall these three will increase and the increase in three is the increase in H and the increase in H implies that you have a your resolution is compromised.

[00:37:32]So what is the answer now? The answer is itself there that you have to increase in an optimized manner that is your velocity your mobile phase velocity should be optimized and it must be towards the higher side keeping in mind.

[00:37:54]So you can see this is depicted here that is if your velocity is low then the diffusion is very very high and you can see that a this this is a very broadband.

[00:38:12]Okay. But at the same time if you increase the flow too much then of course you get a very slim peak but again if you increase it too much then this CU will increase. So you have to have a medium optimum velocity where the band broadening is not too much and you can also control CU. So this is actually the interplay the interplay of the mobile phase velocity. So you have to optimize it not very not you have to take a very high velocity because it will increase CU and at the same time you cannot have a low velocity because if you have a low velocity then this BU term will increase and more diffusion is there and the band will be broad like the that is shown by the red line. So you have to have an optimum velocity so that you can get this yellow curve.

[00:39:07]So an example is that in GC where you always have a mobile phase as the gas then what happens is the diffusion occurs because the gas has the highest diffusion and because of the high diffusion you get broad peaks and broad peaks means that your efficiency your column is actually is inefficient. It is not resolving the peaks.

[00:39:32]Okay. So you have to keep in mind about the velocity. So rate theory which was given by vanerter equation gives an idea about the velocity. So it gives an idea about the velocity. So with this thank you very much. Thank you all. [music]