Webinar: Understanding Isotherm Shape & Isotherm Modelling from DVS Experiments Dr. Daniel J Burnett

Good morning, good afternoon, good evening to those of you who took the time out of their busy days to join us on this webinar. As Brad mentioned, we'll be focusing on isotherm shape isotherm modeling what we can learn once we obtain the isotherm on our materials. So the this is a little bit busy slide, but it's just shows I'm not going to get into how to measure an isotherm or what a DVS is or anything like that. I'm going to start and jump right into getting the isotherm and going from there. Just for those not familiar, a DBS is a gravimetric system. So we measure the weight change on this graph. This red line, this solid red line is showing the weight change and the dotted red or orange line is showing the relative humidity as a function of time on the x axis. So typically what happens is the sample was dried then exposed to increasing relative humidity. Steps, let's say from 0 to 95% relative humidity in this particular example. And ideally the sample mass reaches equilibrium, which means it levels off if I give it long enough time or measure the slope and give it a slope criteria that the sample will reach equilibrium with the surrounding vapor, in this case it's water vapor and then it will move on to the next programmed step. So from these equilibrium points we can construct what's called the isotherm. So the isotherm is plotted on the top x axis. So here we have target relative humidity and percentage weight change. So the solid line is the sorption or increasing relative partial pressure and the dotted line is the desorption or decreasing relative partial pressure. If this isotherm and the sorption isotherm, the desorption isotherm, the shape, the size and also what's called the hysteresis which if you look right here is the difference between the sorption isotherm and the desorption isotherm at a particular relative humidity. So the location, the size and the shape and the changing of this hysteresis and shape of the isotherm can give us a lot of information about how the particular vapor interacts with the material. In this case we're just looking at a polymer film. It's a nafion proton exchange membrane looking at moisture on moisture off onto this particular sample. So for those of you familiar with isotherm shapes and types, there is a classic BDDT classification. There is a revised one that shows more than this. I don't want to spend too much time going into the nitty gritty of these different isotherm shapes only because most of them were developed on rigid materials using nitrogen absorption under vacuum and at cryogenic temperatures. In a dbs you may not see all of these isotherms, but very briefly this is what's called a type 1 or a langmuir isotherm. Basically water comes on the surface or whatever vapor or gas comes on the surface, and that's it. What I will highlight is what's called a type 2 or type 4 isotherm. These have a traditional sigmoidal shape and the knee, which is right here, what's called the knee of the isothermic. It is possible to obtain a surface area from a monolayer capacity. So these two isotherms indicate that whatever gas or vapor forms a monolayer and then grows subsequent layers from there. So I'll get into some models and what they mean and how they can be used. But please keep in mind that it is highly unlikely for real world composite materials or food materials or amorphous or polymer materials to show a pure isotherm like you see here. Sometimes I'm going to get a mixture of different isotherms because I have different components or different surface groups that behave differently. I did mention most of these things are developed and based on gas or surface sorption onto rigid or highly crystalline materials. So here's an example of a quartz. So just think of silica, a quartz sample. And this is an octane isotherm which shows a very classic type 2 behavior. So you get a knee here in this sigmoidal shape. This is where the monolayer or the first layer of vapor forms on the surface and then additional layers pile on as we go to further higher relative vapor pressures. Here is a, what's called a type 5 isotherm where I get this capillary condensation effect due to mesoporosity. Mesoporosity is defined by the IUPAC as 20 to 500 angstroms or 2 to 50 nanometers. So this hysteresis gap is due to capillary condensation and I will get into some examples of that later on. But I just wanted to highlight this is on a amorphous carbon sample. So not only these two slides will show you that not only is the sample a function of the isotherm, but also the chemistry of the molecule is a function of the isotherm. In traditional volumetric nitrogen absorption, the nitrogen doesn't have any chemistry, so it really is not indicating any surface chemistry or Anything like that. But the isotherm that's measured is a function of both the surface it's measured on and the adsorbate that's being used. So this is an example on a crystalline lactose sample where we have water, which is in this blue, which is highly polar, and it is more of a type 3 behavior. And as we go from water to methanol to ethanol to propanol to butanol, we make the molecule less polar by making the alkane part longer. And we can see the isotherm shape changes as we go from a highly polar molecule to a less polar molecule like 1 butanol. So this is just to highlight and remind people that the isotherm is a function of both the solid that you're measuring and the vapor and or gas that you're using. So over the years there have been developed a wide range of isotherm models. So once I get an isotherm, I can fit it to either an empirical or semi empirical or a fundamental model. This is only a small selection of them. This is not all of them. Most of these, what I will call classic isotherm models, are typically assuming surface sorption only. So when we think of nitrogen, nitrogen only typically will lie on the surface of a material. When we think of a DVS experiment, I can use water or ethanol or acetone or some other solvent where the material might be partially soluble in. So I have surface and bulk sorption. So a lot of these classic equations, like the Langmuir equation, in particular the BET equation, only assume surface absorption, and that's important. So in a DBS environment, these models are typically applied when I'm looking at what I will call a rigid material like an oxide, alumina, silica, activated carbon, things like that, or a highly crystalline material where the molecule of choice, let's say water, is only laying on the surface of the material and is not partially soluble in the material of interest. When we're dealing with natural materials or amorphous materials or foodstuffs, these are very often, in particular with water, these materials will often get a significant amount of bulk absorption in addition to surface adsorption. And that's pretty, pretty well understood. The bad news is that very often when I'm using water on an amorphous polymer or a protein or a food material, I can very often get this isotherm shape that'll have a very similar isotherm shape. If I go back to this type 2 or sigmoidal isotherm, keep in mind this Isotherm assumes surface absorption only. However, with a lot of natural or organic materials, in particular, where water is partially soluble in, I can get this sigmoidal shape, but it is not due to surface sorption. I get this knee, this plateau in this upswing. And the reason for that, in particular, with amorphous materials, water can act as a very strong plasticizer. So when I'm below a critical relative humidity, the material is in the glassy state and I get a relatively slow uptake. Then it can increase and go into this glass transition region where it's shifting from the glassy to the rubbery state. Then eventually I get this large upswing. When it fully goes through and relaxes, water increases molecular mobility. And then I can see that this large upswing here is due to it going from the glassy to the rubbery state. And for good or bad I get this isotherm shape that may look like a surface sorption isotherm, but it's actually not. And that's due to the fact that the system itself, the material itself is maybe not even in equilibrium. So the material is changing. So the starting material is much different than the ending material. And I can, you know, there are some ways to model these are more based off of kind of polymer solvent isotherm models. And here are a few of them that you see on the, on the screen here. I'm not going to go into detail into all of these, but I just want to highlight the fact that many what I'll call real or real world or in particular organic or natural materials, or food based or starch based or cellulose based materials can behave in a very complex and in fact dynamic mode with water in particular or another solvent where it is highly soluble in. So for these type of materials it's very difficult to use one model or one type of mechanism. Water or the vapor of choice may be behaving in a very complex way and it may be changing throughout the experiment. So the SMS does have a isotherm suite to help analyze. Once I've collected an isotherm, we do have a range of a wide range of the kind of what I'll call classic isotherm models that are in the literature. So once I generate an isotherm, doesn't matter what instrument it is, doesn't matter what vapor or gas I'm using, then I can apply these models to try to elucidate mechanistic or structural information about the sample. So I'm going to very briefly go through some of These models and tell you when and when they cannot be applied. So the most common one or the most commonly things that people are interested in typically is the BET surface area. As I mentioned previously, this assumes surface sorption only. So I must choose a solvent that will lay on the surface. So water on a starch material would be a horrible choice. Or on a cellulose material I may have to use something like octane. Or for a very hydrophilic surface I want to choose a hydrophobic molecule, vice versa, something like polypropylene or polyethylene, which will dissolve octane or hexane. Maybe I want to use water or ethanol or something like that. So just remember that I have to have the right shape of isotherm and I have to have the right absorption mechanism. If I have those things, then what I can get is a BET surface area, a monolayer capacity and absorption constant which is related to the heat absorption. So what's typically done is I collect an isotherm. This is the similar to what I showed previously. This is on a calcite, this is on a mineral material and there is no bulk absorption. For this I can apply use the BET macro and I will get a BET surface area. It should be linear over the range of 5 to 35% P over P0 or percent RH. If you can use water, assuming that you have the right isotherm. So I get a monolayer capacity, the C constant, which is related to heat absorption and a specific surface area. If you want to be 100% technical in a DVS experiment, I would call these specific surface areas because they're specific to the molecule that we're using to measure the surface area. The GAB equation is an extension of the BET equation. The BET equation assumes a monolayer and then every other layer is the same. The GAB equation adds an extra term to allow for subsequent layers to have a different heat absorption than the first monolayer. So again you generate an isotherm. Typically it should be a type 2 or type 4 isotherm and I can apply the macros appropriately and I will get a GAB plot. And the output that I will get in the GAB gives you the monolayer capacity, a C absorption constant, which is different from the bet. So it's not going to be exactly the same, but it's related to monolayer coverage and a K constant which is related to the multi layer heat absorption. Again, this assumes surface absorption only. The double Freundlich isotherm is typically mostly just an empirical model. It does not require monolayer formation. It could be used for water absorption. It doesn't have any physical or theoretical basis to give you information about the absorption process. It's basically just an empirical model. And it has four fit parameters because that's. There's a for fit model that is applied to this particular application. It is in the literature, so we have it in there. It's not as widely used for a direct application, but some people use it, so it's available. And again, you can get the plot with the fit and it gives you the fit parameters. The doctor stands for Dubin Radskiewicz. And this is to give you micropore volume. So according to IUPAC, micropores are those less than 20 angstroms. So by a DBS experiment or a gasorption experiment, it doesn't matter if it's volumetric or gravimetric. I showed you a mesopore isotherm. It is possible to also measure micropores. So the micropores are anything less than 20 angstroms. Mesopores, which I'll get to later, are between 20 and 500 angstroms. Above 500 angstroms, the pores are too large to give you any artifacts or effects in the isotherm. And they can't be measured by gas absorption techniques. They have to be measured by liquid sorption techniques like mercury, pore symmetry or other methods. So what this micropore volume does, it gives you the volume of the pores. So this should be on a microporous material. So examples could be a channel hydrate, a zeolite, a mof, an activated carbon, or anything else where you expect the pores to be below 20 angstroms. A typical artifact of something that is microporous is you'll get a very high uptake at low partial pressures. Basically, as soon as I introduce any vapor, it immediately fills those micropores and then above that I just have surface absorption. So here is the micropore range. Typically that's going to be below 5, maybe 10% P over P. Not. The pores fill very quickly and then on the desorption side, they may not always remove. Some of those pores might hold onto the water or other vapor or gas and may not be removed. So the behavior or what you'll get is something along these lines where I have a very fast uptake at low partial pressures and then almost nothing above that. Again, you can use the Dabin Rastkiewicz and it'll give you a plot and the output will be the total micropore volume. Essentially the volume of the micropores based on the absorption of the gas and or vapor that's in those micropores. So it gives you a volume, it does not give you an indication of the size of the pores. And that leads us on to this micropore size distribution. This is essentially based off a T plot. It's very commonly used and applied in a wide range of absorption equipment. And the output will be a micropore basically distribution and also a micropore volume. And again, this should be used on microporous materials. So in this case we have a 13x zeolite. And again we get this similar behavior where very fast uptakes where those pores are being filled and then surface absorption from there. And this I can get, basically this is the average radius of the pores. So I get a distribution of different pores and I can also get a total pore volume as well. Moving on to a mesopore distribution. This is typically between 20 and 500 angstroms. What this will show, and I'll show you an example, is typically some isotherm hysteresis in the intermediate to upper partial pressure range. And that is due to capillary condensation. This is based off the classic VJH equation. It also uses a T plot approach. And the output will give you the micro, the mesopor total volume and the mesopore distribution of sizes. And in general, this is again on mesoporous materials which can be metal oxides, minerals, agglomerates and some other engineered materials like silica or templated silicas and things like that. So what you will often get is this hysteresis gap at intermediate to high partial pressures. And this is due to the fact that in. Let me just. In these pores. So if I have a pore here. Sorry for my poor drawing. The first layer of vapor and or gas can form. Then a second layer forms until about the third or fourth layer. Typically these will cross and I get a meniscus. And this is due to capillary condensation. It's harder for the vapor to be removed than it is when it comes on. And that's what I get, this hysteresis gap.

So.

And again I apply the BET equation. I'm sorry, the, the misopore equation. And then I can get the differential plot which will show you the distribution of pore sizes. And the total pore volume as well is listed here. Typically for both the micropore plot and the mesopore plot, you do need a reference material, something that's Non porous that has a similar chemistry and that's used as a reference in the T plot. I won't go into details. If you have questions, we can give you some information on that. The Langmuir plot is another commonly used one I showed you previously. It's Basically a type 1 isotherm and it shows surface absorption only. And you can see here I'm going to repeat this example of the zeolites with octane. And from this uptake it shows a typical Langmuir behavior, which is basically a monolayer forms and nothing else is what it assumes. And you can see here, here is the Langmuir plot. So moving on, there's two other models that I'm going to finish up with here. We do have, I showed you at the beginning, kind of a laundry list of commonly used models. And we have applied several of those into basically a fitting algorithm to try to find which model might have the best fit. So these are the models that are used. These are models that have been used over literature. A lot of them are from the food industry. But what this macro allows you to do is to rank the models based on which one gives you the best fit. So I take an isotherm, for instance, this is water on crystalline lactose. And I apply this and what you'll see is when I apply it, it will rank over here. So the Kuhn model had the best fit, that had the lowest least squares, the Oswin had the worst fit. So it'll rank them which one has the best fit, which one has the worst fit. And then what you can do is see here, the Kuhn has a very good fit, the Freundlich, which if we go back here, the Freundlich here was not very good. And you can see that here. And the reason for that is the Kuhn model is based on the assumption basically like something that has a type 3 behavior where it has a cluster formation and water on lactose behaves this way, where in contrast, the Freundlich isotherm is more similar to a languid isotherm where it has a monolayer and, and goes from there. So if I go back to the actual isotherm shape, we will see that this has more of a type three behavior, not a type two, where I'd have this sigmoidal shape. And this is why the Kuhn, which assumes a cluster formation, not a monolayer formation, fits the data better than a Freundlich, which will have a different type, more of a type two style assumptions to the model So I did mention that most of these assume surface absorption. One model that is used that does not assume surface sorption is the Young and Nelson model. Now when we measure a water isotherm, let's say on starch or microcrystal in cellulose, all we measure is a mass uptake. We don't know if that water is on the surface, on the multilayer or in the bulk. What this model does is it tries to deconvolute where the moisture is. Is it on the surface, is it in the multi layer, is it in the bulk of the sample? So if I apply the Young and Nelson model, here's on microcrystalline cellulose or avicel water absorption, and when I have a bulk absorption dominated mechanism, very often I will get a hysteresis gap across the entire humidity or partial pressure range. The reason for that is the moisture or vapor is harder to come out than it is to come in because as I increase the moisture, it partially dissolves and swells the polymer or the cellulose in this case. So on the desorption side, it's diffusion limited and it's harder for it to come out. And I apply the Young and Nelson equation and you can see here, it breaks the isotherm down into three components. A monolayer which is just the first layer. A multi layer which is in red, which is essentially layer upon layer upon layer, and then the green is the absorbed or how much is dissolved into the bulk of the sample. And this could be related to things like free water, which would be the water in the multilayer range, which is free to move around or bound water, which might be bound up or tightly bound either on the surface or in the bulk of the sample. So sometimes this can give you an indication, whereas the DBS just gives you total amount of water. This can give an indication of maybe how mobile or accessible that water might be to other components or other constituents or packaging material or things like that. So in conclusion, I've exceeded my 25 minutes, so sorry about that. The DBS instruments can readily obtain adsorption isotherms. We can do them on a wide range of gases or solvents. One thing to keep in mind is that a lot of isotherm models are based off of surface adsorption dominated mechanisms. If I have an isotherm, I can then use this to extract things like surface areas, porosities, heat absorption. These are typically for highly crystalline or inorganic materials that will not swell or dissolve into the solvent. When I'm Talking about natural or organic or food materials. These are often bulk absorption dominated mechanisms, particularly with water. And these have very complex and dynamic behavior and are difficult to define by a single absorption mechanism. The SMS does have an isotherm suite to help rapidly screen a wide range of isotherm models. It does not have them all. We are constantly developing. If you have ideas or suggestions for more models you'd like to see, our application science team is always open to expanding the functionality of this software. So I didn't get into other isotherm types, but hydrate, solvate, CO solvents, there's other things you can do. So in the interest of time, I'd like to thank you for your attention. I'd like to thank my colleagues at Surface Measurement Systems and the Particle Engineering Lab at London Imperial College who helped with some of the data and slides that I showed today.

If you have a 100 milligram pile up of powder, which models are reliable? Considering the gap form between the particles.

It really should be anything. What's critical and is a balance between time and experiment is if you're at equilibrium, it shouldn't matter. So if I give this mass long enough to reach equilibrium, it really shouldn't matter. I will say there's one caveat. So you know, if I give it, it doesn't matter If I have 1mg or 100mg. If I give it enough time, the vapor should find all of that material and it will reach equilibrium. Now I will say that for things like proteins and other things that can go through a glassy to rubbery transition, these are kinetically controlled. So the longer I leave it there, it is possible that I could cause this transformation to occur at different times or at different humidity. There is basically two things happening. A thermodynamic absorption. We also have a kinetically controlled or limited phase transition that could be occurring. So I will say it can be complex. If I'm dealing with an amorphous material that's partially soluble in your, in your. In your gas or vapor that you're using.

In the microcellulose is the hysteresis kinetic example. If you wait long enough for the Rh to step the hysteresis, will it go away?

In my experience, it will not go away completely. I've done very long experiments where I've left it there for a day at each humidity and there is some real hysteresis. And that's due to the fact that the starting material is not the same as the ending material. If you think about it, the material is swelled and so it's physically changing and the void volumes are different and everything. So although this hysteresis gap can narrow, it typically does not go away. Now, if I did a second absorption cycle, the hysteresis gap will be narrowed, but it doesn't go away because what happens is that the void volumes and things rearrange and restructure. It does get slightly smaller. So the second absorption cycle is typically up here a little bit, but does not go away completely. It's because the material is physically different. So a dry material is going to be different than a wet material. So it's not only kinetically limited, but it can be minimized if I give it there long enough.

What isotherm models would you recommend for pronounced type 3 data where the J shape is really exaggerated?

Type 3. Here's kind of what a type 3. If we're talking about this here, off the top of my head, like I said, I believe that the Kuhn model is one that will fit a Type 3, and that's what we see here. And I think I have to go back and look at all of them to remember off the top of my head which other ones. But it might be this hasly, because this does have a good fit to this as well. But those are models that can be applied. Clearly, the GAB or the BET or the Langinger models would not apply because they all assume monolayer formation.

Are the models exact to the pore size distribution of especially small micropores? Example.7 nm.

The limiting factor on the micropore size would be the size of the adsorbate. So the critical thing is on a microporous material, and I'll be quite frank, a microporous material. Let me go to here. The more data points you have at low partial pressures, the better your data will be. Now, the DVS vacuum is more suited for very low partial pressure steps. And if I was only interested in microporous materials, the DVS vacuum allows us to do, you know, very low 0.01% RH depths. And I can get more resolution here at the lower end on a traditional volumetric gravimetric atmospheric DBS, maybe 0.1% RH as opposed to 0.01% partial pressure. So the quality of the data is going to be limited by the number of isotherm points I can get in the micropore range. And for a lot of materials that may be required to use something like the DVS vacuum as opposed to the atmospheric DBS Systems.

How do we get the DVS Data Analysis suite?

Well, I would contact us. I mean, you should check. You can check. If you contact us, we can check with your original order to see if you purchased it. And then we can. There's usually CDs sent with the instrument, but they all get lost. IT departments steal them. So I would contact your local salesperson and we can look up your record to see if you purchased this. And then if you did purchase and don't have it, we can supply you with a license with it and you can download it and install it. So if you didn't purchase it, then you'd have to purchase it. I would suggest talk to your local salesperson. If you're interested in the Isotherm Analysis.

Suite, what models would you recommend for hydrated materials such as MGNH4P046H20? Sorry.

That's okay. Well, I didn't show it here, but I do have an example and this can be somewhat tricky if I have an actual structural hydrate. So this is an actual stoichiometric hydrate. Where this is a. It starts out as a dihydrate. During the drying stage, it dehydrates, then it forms a hydrate and then dehydrates. And what I can. These will often hydrate and dehydrate at different relative humidities. And what I get is, I get this, what I'll call is like a rectangle or very sharp hysteresis where I can get this. So here I have the anhydrous form. It gets to a critical relative humidity and then hydrates. And then I just get surface absorption from there and then it dehydrates. So in reality, this material is different from this material. So I can't really use an isotherm model because the model assumes that the material isn't changing. But what I can use, I can use this to see how stable this hydrate is. The location and the width of this hysteresis will tell me how high, how stable or unstable or how reversible this hydrate is. You can see this one has two cycles. The second cycle is exactly the same as the first cycle. So this one, water comes in and out very easily. Hydrates, dehydrates. That's not always the case. Sometimes it'll hydrate and doesn't come out. Sometimes when it dehydrates, it collapses the structure of the material. But you very often get this hysteresis gap of where the hydration occurs and the dehydration occurs.

Second part to that question, given the dehydrated crystal already has six water molecules, is it possible to gain meaningful information using DBS of water?

If the. Yeah, I mean, you can adjust two things. If the material itself already has a certain number of water molecules in the structure, we can adjust this change in mass to correlate to those six added water molecules. And the software actually allows you to plot this. Instead of percent change in mass, you can plot it versus on number of water molecules or solvent to solid ratios. Second of all, if it's a very stable hydrate, then you can just look at the water on top. One example in the pharmaceutical is lactose monohydrate. It's very stable. It doesn't get removed during a DBS experiment. But I can still learn a lot about the water absorption on the hydrated form.

Can this tool make fitting for kinetics of absorption or only the isotherm?

What I showed you today was just the isotherm. Let me go to the DBS software we do have in. This was our isotherm suite. The isotherm is just looking at the isotherm. There are models and we do have things to look at. Diffusion, kinetics and other kinetically limited. So I want to measure the rate of absorption. We have a simple ficion 1D diffusion kinetics and also permeability. So we can look at both diffusion and permeability in films or powders or fibers or things like that. So what I showed today and talked today was focused on the isotherms. But certainly we can use the kinetic information. So for instance, looking here, we can fit these slopes to different models to try to deconvolute the diffusion or the kinetic or dynamic information.

Does water isotherm imply porosity of the sample.

Water isotherm? Not directly. I mean, the shape and the behavior of the isotherm could give us some indication if the material is porous or not. You can use water molecules for porosity measurements. Again, these would be typically on rigid materials. But there's nothing in the model, in terms of the mesopore or micropore model that says you have to use a certain gas and or vapor. I can use water certainly to obtain both mesopore and micropore size distributions and volumes. There's nothing in the models that requires it to be a particular vapor. It just has to be the right type of isotherm and the right system for it to be used.

Can I apply any of these models if my materials are omivorous and recrystallize during the watersorption process that's going to.

Be difficult because once it recrystallizes again, the material has changed. So your material at the beginning is different than your material at the end. So the isotherm model is assuming that the material isn't changing. So the only thing you could do is if, for instance, let's say not in this example, but let's say that the material recrystallized above 70% RH, you can in these isotherm models put in the limits. I can only fit the data. Let's say I don't want to use the entire isothermic, but I only want to use the data from 0 to 60% relative humidity, then I can certainly use all of these models. So in all of these, let's say all of these models you can put in specific upper and lower RH or partial pressure limits. So if it recrystallizes at a high humidity, I can still use the isotherm models at a lower humidity below that point.

What model would you recommend for porous polymers? Fully and not fully cross linked.

For porous polymers. I mean, in my experience polymers could be porous, but they're not going to be meso or microporous. They're typically macroporousand which is larger than 500 Angstroms, which unfortunately we can't measure those. We can't quantify the porosity. We certainly can measure an isotherm and it can give us some valid information, but it's not going to give you porosity. I could be wrong. I'm sure there's examples where polymer or amorphous materials are mesoporous. But most of the time meso and microporosity are for things like silicas, aluminas, activated carbons, zeolites and things like that.

Why? Hysteresis loop sometimes is closed at P over P 0 equals 0.6 or 7 or 0.7 and sometimes that P over P 0 equals 0.4.

Sure. I mean, this hysteresis, let me go down. It all depends on the mechanism and that's actually gives us a lot of information. So for instance, in this one the hysteresis closes at like 60% and that's because I have capillary condensation. Now I could have multiple things happening. So I could have a sample that's both mesoporousand I'd get a hysteresis gap here and mycoporous, where I might get a hysteresis gap here as well. If I look at something like, let me go down On a starch or a cellulose based material, very often the hysteresis gap is across the entire humidity range because the sample is diffusion limited across the entire humidity range. It really is a function of both the vapor and the sample and how that vapor is interacting with the sample. There's no reason why I couldn't have multiple things that happen, especially in a composite that might have more than one material. I could have something that's partially crystalline, or I could have, you know, Avicel along with, you know, an API that forms the stoichiometric hydrate. And I can get all sorts of complex things that happen.

All right, so we are going to be answering the last few questions and then we're going to wrap everything up. So one of the last questions, and then there's. There's one more after this one.

Okay.

Which models are ideal for a 13x and 4a zeolites characterization, surface area, etcetera?

Yeah, for the zeolite models, I mean, they're typically microporous. So things like the Langmuir Isotherm, the Ohmicopore or the Dvene Radzkiewicz gives you micropore volume. The micropore T plot can give you some information there. The Langmuir isotherm would apply to that as well. I mean, one thing to note, when you're dealing with microporous materials, very often, if you want to use the BET model for mycoporous materials, very often for microporous materials, you have to be very careful about the range in P over P0 that you use. If I want to not use this very sharp uptake for microporous materials like MOFs and zeolites, if I do it over the entire range, I'll get a negative C constant. What people typically do is they bump up this lower limit. Maybe not 0.05, maybe 0.1, maybe 0.15. They keep increasing this upper limit until the C constant is positive. It's not physically possible, based on the assumptions of the BET equation, to get a negative C constant. So if I apply the BET equation to a microporous material and I get a negative C constant, that's the C term here. Then what I would recommend is that you increase this lower limit and until it becomes positive. And that's typically what people in the nitrogen or gas areas do on microporous materials as well.

Okay, so we have two more questions and then we're going to have to end this session, but feel free to ask us questions after this webinar at Scienceurface measurement systems.

Right. I'm just going to say that you can email us at Science at Surface Measurement Systems with anything else after the fact, but go ahead. Brad.

What are the reasons for hysteresis at the microporous level when measured with the water as a probe molecule that is.

Purely a kinetic limitation, typically is because the water, as I mentioned, maybe I can get to it here. Let me just go down.

Sorry.

That's a kinetic limitation. So for instance, it just takes a really, really long time to get out of those micropores and very often I might have to use temperature to get it out fast enough. So in theory, if I left it there long enough, this should go down and the water should come out. But it is a very slow and kinetically limited process to get all of the vapor or water out of a microporous material.

And for the last and final question, can you please mention a couple of sample for natural porous material along with their application.

Naturally porous materials? Sorry, that's, that's a bit daunting for me to think of right off the top of my head. But I mean I can do a search and see what some of our customers are using this for. But I mean certainly, you know, there are some cellulose based, there's some spray dried and freeze dried materials that are porous. They form like little spheres that can be highly porous. So in particular spray drying on some polymeric or naturally based materials like, you know, there's some technosphere and there's some other technology that's out there that different companies have developed as carrier molecules in pharmaceutics to make them porous. So it really would typically depend on the process to make them either a controlled or not controlled porosity.

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