nanoHUB-U Physics of Electronic Polymers/Lecture 4.2: Crystalline Domain Sizes in P3AT OFETs
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[Slide 1 L4.2] Hello and welcome back to The Physics of Electronic Polymers. I'm Bryan Boudouris and in this lecture we're going to talk about how we can go ahead and think about crystalline domain sizes and OFETs. Now, last time what we discussed was the idea that the degree of regio-regularity could impact the charge transport mobility of our semiconducting polymers. This time we're going to take it a step further and we're going to say that, okay, let's fix our regio-regularity at a relatively high value, because we saw that was good for charge transport mobility. This time we're going to go ahead and look at how the molecular weight impacts our crystalline domains, and in turn we'll argue that that also affects our charge mobility as well. So, really our two learning objectives for this lecture are to describe how the size of crystalline domains, and again we're going to look at poly (3-hexylthiophene) again, is tied to the charge carrier mobility in our system. And then hopefully, we'll be able to predict, based on what we know about the size of these crystalline domains, what we know about the mobility of these domains, what we can get in terms of mobility if we know what these domain sizes are in our P3HT materials. And you'll see a word here, nanofibril, and that word will come up a lot if you start to look through the semiconducting polymer literature. And really this is one type of crystalline domain that is seen quite often in this electronically active polymers kind of world. So, let's go ahead and see what these look like actually in an atomic force microscopy kind of image, okay. 

[Slide 2] And here's a whole lot of different AFM data, okay. And what you'll see is basically they're the same exact materials, same regio-regularity, they're all P3HT, but they have different degrees of polymerization and, because the repeat unit is the same, different molecular weights. And we're going to range anywhere from 2400 grams per mole, or 2.4 kilograms per mole, all the way to 18.4 kilograms per mole. And you'll note the size of all these are the same. This is a 500 nanometer scale bar, and that's consistent across all the images. And what that tells us then is that for our lower molecular weight samples, it's actually somewhat hard on this slide to see how big the domains are. But if I move up to something like 7K we can actually see these little fibrils start to play. And these little long crystals that are kind of orientated relative to one another, look parallel to one another. Those are what we are talking about are nanofibrils, okay? And what you can see is that you go from something that's very small and very thin to something you can start to see, to about 5K, you can really start to see it with your eyes underneath the AFM. And then all the way here, the 18.4 k, you can really see these nanofibril sizes pop. So we're able to go from very, very small things to very, very big things relatively speaking, right? This is all on the atomic force microscope. So, we're all on the order of about 20 to 30 nanometers. What does this do in terms of our charge transport? Well, what we were able to do, or what these researchers were able to do, 

[Slide 3] was to go ahead and connect this nanofibril width that they were able to see both to the contour length of our polythiophene, and to the weight average molecular weight. So, if we look at the red circles here, what we'll see is that as we increase the molecular weight of our system, we'll see that the width of the nanofibril increases, increases, increases up to about 25 nanometers, and then it starts to level off. In a very similar manner, the mobility of our system will increase with our nanofibril width, okay, and it too will start to level off. It'll go all the way from 10 to the negative fifth centimeter squared per volt second, up to 10 to the minus 2 centimeters squared per volt second. So, this nanofibril width is again controlling how our material behaves. And you'll notice that all these nanofibers are connected in such a way that they have the same orientation that we talked about in the previous lecture, where the perpendicular direction is the one that's favored. So we're able to transport charge in a relatively efficient manner. And really getting across the length scale from one fiber to the other is our rate limiting step. 

[Slide 4] So what this tells us is that you can actually find an empirical formula for the log of mobility, or the natural log of mobility, in centimeters squared per volt second versus this nanofibril width. And you can actually compare it very well, and you'll see that all these experimental data points actually fall on this line. So, you can actually predict, assuming that you can back out some parameter W0, which is basically a finite value that's some constant that you can get from the fitting experiment. And some prefactor found the exact same way, is that if you continue to increase what that fiber width is, you'll continue to increase the mobility in an exponential manner. And really, for a long time folks were trying to figure out how to increase that fiber width in a reasonable way, and try to control that fiber width, so that you could get there. Now, there obviously are practical limits to our systems, and how we can do things, but making sure that these are appropriate values, and making sure that we can try to tune these materials is very important to try to figure out exactly what the ultimate limit of our materials are. So, moving forward we're going to be able to talk about in our next lecture the idea of being able to align these P3HT domains. So if we know what our crystal is, and we know what these fibers are, how can we go ahead and try to align these materials so that we can continue to get longer fibers, bigger fibers, and try to have those fibers stretch from one contact to another in our organic electronic devices. So, with that, I thank you for your attention, and