Using vapor sorption isotherms to analyze shelf life and packaging performance
MG: People often ask me how to calculate shelf life.
To do the calculation, you’ll need to take into account the sorption properties of the product, so the isotherm in particular, and the storage conditions. We need to know what that product is going to experience. So: temperature, relative humidity, atmospheric pressure, and lastly, the packaging. So for this, we need surface area, mass of the product in the package and the very important water vapor transmission rate.
So packaging is what is going to protect your product from the outside conditions. So if you have good packaging, it's going to limit the vapor that's able to go through.
So let's get started on how I actually do this calculation. So I start by generating an isotherm. And this is an isotherm for granola. And in particular, I'm interested in the absorption only. So I've made this file of just the absorption. Now, I want to know for my product, for a granola bar, the shelf life is going to be limited on its texture change. This is a crunchy granola bar, and we don't want it to stale or get soft or whatever. So it's going to be texture that's going to be what is going to end our shelf life.
So when we look at this isotherm here, it might be difficult to be able to figure out any of the specific transitions that are happening. So what we use is this Savitzky–Golay second derivative. And basically, it's evaluating the slope change and highlighting those in peaks and valleys in this lower graph in the blue.
Now, I get this question quite a bit too, because you'll notice that there's two peaks. And peaks means that there's an uptake in water. We're increasing the moisture. And I get this question, which one do I choose? There is the smaller one that's around little past 0.4. And then there's a bigger one past 0.7.
The tendency might be to pick the higher one, but really we want to know when it transitions first. The water activity of this granola bar natively is about 0.2. So as we're moving up and increasing water activity, we want to know when it will first hit that transition.
So I want to use the first transition. And the first transition is right there at 0.42 water activity. So that's the one I'm going to be using in my calculations. I'm not going to use the bigger one, because by the time we get there, it's already had a change.
All right. So this is the calculator that we use here at METER. You can see some of the information. We're going to go through a little bit of what I talked about before.
So for my granola bar, it's going to be the humidity I picked, 65% relative humidity. We've got C level atmospheric pressure at a 100 kPa, and my temperature is going to be 25 degrees C. Now, for this is just a little granola bar, so we've got a very small sample, 35 grams. The surface area for that also is quite small, but we're in meter squared. So that all is good.
And then I chose one as my water vapor transmission rate, which is actually a pretty good packaging in grams meter squared per day. And then we're going to start with the initial water activity that I talked about. So where it natively starts is at 0.2. And then the critical shelf life. That's where the water activity once it hits that point, it would end shelf life. Now, I put 0.42 because I want it to be easily tracked. You could see where I was getting that data point. I would agree with Zachary that I probably wouldn't actually put 0.42, because by the time it hits this, it's already starting to transition a little bit. We don't want it to get that close.
So I would recommend dropping this critical water activity down a little bit, maybe to 0.4 or maybe 0.38, something like that, just to make sure that we're not getting close to that transition. But for this example, we're going to keep it at 0.42.
In this isotherm, I've trimmed it. You can see that it doesn't have the higher water activity. I'm going to focus on the area where I'm interested in. So the range of water activity I'm interested in, and I want to make sure I'm modeling really well between where it starts and the point for where it's critical. So I can get a good representation of that data.
So we'll look here. We like to use the DLP, which is a double log polynomial. And we have a really great R squared value here of 0.9996. So it's a really great fit. You can use other modeling equations like the GAB or the BET. There's some limitations to those. But in particular, what we really are caring about is getting a good fit to the data, because that's how it's going to predict it well. So it doesn't really matter what it is as long as it's going to model your data correctly.
Back to where we were. Now, when I put this isotherm in, I'm going to put in the trimmed one. I want to put in the one that's going to have the really good model fit. And then from here, I'm going to calculate the shelf life.
Now, when I do that for this granola bar under these conditions, the shelf life is 151 days. That's about five months. So that's not too bad, but let's say that's not quite where you're hoping for. Maybe you're hoping for this granola that would be a whole year. So how do we figure that out? What can we change? And in this case, it's really easy. What we would change is the water vapor transmission rate. So we can use this to determine what packaging will give us the shelf life we need.
So this is a similar calculation, but now with the same data that we put in before, but now instead of the water vapor transmission rate, we're actually going to put in the shelf life that we're looking to get. We're going to put that same trimmed down isotherm that has the good model fit, push calculate.
And now we know that if we have a water vapor transmission rate in our packaging of 0.42, that it's going to give us this whole year shelf life under these conditions. And that's very similar to what would be like a foil line packaging. So this tracks very nicely.
Next, Zachary is going to talk about the business value for isotherms.