New Frontiers in Carbon Research. A Discussion of Recent Discoveries

LARSON: Good afternoon. Again, from the MIT campus, Cambridge, Massachusetts, we welcome you to the third in our sequence of MIT CAES ILP Distinguished Lectures. The ILP is the Industrial Liason Program here at MIT. CAES is the Center for Advanced Educational Services.

For those of you not here presently in the audience on the MIT campus, I'm delighted to report that it's early March and, truthfully speaking, crocuses and daffodils have shown their sprouts. We won't discuss the weather any further than that.

We are delighted to have with us today a true icon of MIT, somebody we're very proud is a member of our faculty-- Institute Professor Millie Dresselhaus. She took time out of her busy schedule to join us today. She's an award-winning solid state physicist. And she's done lots of service in the scientific area as well as being a world-distinguished academician, researcher, and teacher.

Most recently, she adds to her long list of accomplishments, she's been named President-elect of the AAAS, the American Association for the Advancement of Science. And I guess she joins this pretty soon. Within the next several months, she becomes officially President-elect. Rumor has it that if she's good at this job, she then becomes president, in about a year. And then after that, chairman of the board of directors, 1998. Millie Dresselhaus is the ninth woman ever to be elected to be president of the AAAs-- a real distinction. Her leadership within that association reflects a desire to foster a more encouraging atmosphere for scientists and engineers in a time of shrinking and constrained public resources.

Professor Dresselhaus is a National Medal of Science winner whose research has helped unlock many mysteries, particularly mysteries of carbon, one of the most fundamental of organic elements. And she's studied various aspects of graphite and is author of a newly-published, comprehensive source book on fullerenes, known affectionately as buckyballs or buckytubes. In fact, I hadn't heard of buckytubes. I look forward to learning about them today. But she's going to show buckyballs today. And this is one of the symbols. This is, I guess, a smaller buckyball. She also has a larger one she's going to show us later today. That's supposed to be a joke, folks.

Her current research concerns various carbon-based systems, including these buckyballs and nanotubes, low-dimensional thermoelectricity, magnetism, high temperature superconductivity. She's been at MIT even longer than I have, since 1960. We won't say when I entered, but it was shortly thereafter. And she's been a member of the electrical engineering department, physics department.

And, perhaps most importantly, she likes to cite that with her husband, Dr. Gene F. Dresselhaus, who is a theoretical physicist, they have four children and three grandchildren at last count. Has the count changed since we heard about this?

DRESSELHAUS: No.

LARSON: OK. Millie Dresselhaus. Thank you very much for joining us today.

[APPLAUSE]

DRESSELHAUS: Well, I'm delighted to be here and participate in this series. It's really important for the professors to get out and talk to the public, including the industrial liaison members, and tell you what we're doing that's so exciting.

Today, I'm going to talk about these little objects. This is an object that's probably quite familiar to most of you. Many people play soccer. So this is just a soccer ball. But it is also a regular truncated icosahedron. And if you imagine that at every six-- if each of the 60 vertices of this object is a carbon atom, then we have the C60, the fullerene-- the smallest fullerene that we have, the most common of the fullerenes. And it's 7/10 of a nanometer in size, which is very, very small.

So that's what we're going to talk about. And I've entitled the talk here-- let's see if we can get the-- it even works-- New Frontiers of Carbon Research.

Well, I have been involved in carbon research, now, as I figure it, since 1962, which is a long time. But the kind of thing I've been involved with is very, very different from what I'm going to talk about today, which is something new. And I'd like to cite my collaborators, these people from around the world who are recent collaborators on the buckyballs and buckytubes. And I have a list-- well, Gene Dresselhaus wrestle is at the-- who was introduced by Professor Larson, plus a lot of graduate students who are currently and very recently involved with the buckyballs and related carbon objects that we've been studying in our lab.

Let's take a moment and think about more traditional carbon. In the field of material science, we always start out with a phase diagram, because that tells you-- it gives you some kind of scale of what's going on. This particular phase diagram for carbon is an especially interesting one, because it was the one that was used to first synthesize diamond-- 1960. So this is a very long-standing phase diagram.

And you notice that the temperature scale here goes to a very high temperature-- 5,000 degrees Kelvin. So the scale for carbon is the highest, the largest scale in temperature for any of the elements out there. And the scale and pressure is also quite large. The center of the Earth in these units of kilobars of pressure-- thousands of kilobars of pressure, so three megabars-- would be the center of the Earth. So we're talking about high pressures. And here, we have diamond somewhere in here-- with the help of a catalyst, was first synthesized in 1960 in the laboratory. It was a great discovery.

Now, I've spent my career working with this object here, which is the structure and properties of graphite, which is the ground state and the equilibrium situation for carbon. And it's the basis of an industry out there and all of that. What I mentioned on this phase diagram was this object, here. And maybe I'll try pointing down to the board, as well, for the people in the live audience.

That the three-dimensional object is a wide gap semiconductor-- that's become more and more important as time goes on because of the very unusual properties that all of these carbon-based materials have. They have the highest thermal conductivity for graphite, the highest anisotropy for any material. So they're interesting both from a scientific standpoint as a base material, a reference material, something that we like to talk about in the classroom to teach students about-- and then we go on from there to generate other materials relating to these, often having some stimulus. And we get ideas from these kinds of systems.

Well, what I'm going to talk about today is based on carbon, based on the phase diagram, but has a little different twist. And this is what we've been concerned with for the last 10 years. And it has to do with a cluster. So if, instead of having an infinite array-- very large, 10 to the 20th or so atoms-- we have a very small number, then the equilibrium state is no longer the three-dimensional-- or the two-dimensional graphite that I mentioned in these layered sheets, that are weakly hooked together, nor the diamond structure. But instead, we have some other structures.

And why is that? Well, the science behind it is that in this structure, you see we have all these edge sites. These edge sites have dangling bonds. Those give rise to additional energy. And that's very unfavorable. So if we have just a few carbon atoms, the equilibrium state is not the state of the solid but is something different. And if we have a very small number of atoms, then they form into these kinds of structures, as I'm going to show in a little while-- the buckyballs. And another possibility, the buckytubes. And I'm going to show those in the next viewgraph.

So the low dimensional structures which have been recently discovered-- so carbon's around, been studied by people-- chemists, material scientists, and many folks-- for hundreds of years. But it's only in the last 10 years that anybody has gained any insight into these small dimensional forms of carbon. So here we have the buckyball-- that's C60, which is the soccer ball that you know-- and the one-dimensional form, which I'm going to explain later, which has-- also has remarkable properties shown below, which is the tube. And that's a one-dimensional tube.

And you see that at the edges, the ends of the-- one end and the other end, we have half of one of these buckyballs. And in between, we have a cylinder of carbon atoms. And believe it or not, these things occur in nature. So we'll find out about them. And those are the remarkable new structures. And I'm going to tell you some of the remarkable properties that these structures have. And at the end of the lecture-- I'll try to rush through different things to give some time to show you that people in industry are probably also-- will have some interest in these kinds of materials, because they have promise for all kinds of applications.

So here is carbon. And just to review what I've said, we have the ground state, which is graphite. That's the lowest-energy state. That's the equilibrium phase. And very close in energy is diamond, 20 millivolts above. And we know that it's almost stable, it's metastable, because if you have a diamond ring, it will last, certainly, a lifetime. And then for your grandchildren, you can be quite comfortable in your heirloom properties.

The buckyballs, buckytubes, are next in energy. And they're at about 30 millivolts. So now why is that? They're almost like graphite that's rolled up in a tube. So the energy is almost the same. But when you make the buckyballs, you see that they have much higher energy. And that's because of the curvature of the balls. So that's the general picture. And so with the very small number of atoms, we gain energy by not having the edge unpaired carbon atoms, but we have high curvature.

So let's now-- I have-- my secretary, in putting together the poster for me in my absence, because she thought it should be more accessible to the general public, promised that I would tell you some other fields of interest. So I said, well, let's have some art. And here is a Renaissance-- pre-Renaissance painter. And in his spare time, he figured out how to assemble, out of the planar objects, one of these icosahedrons. So this was in the 15th century.

And Leonardo da Vinci-- so Leonardo was a great talent in many fields. And one of the things that he did was, he made a buckyball. And this mirror writing-- that tells you about the buckyball.

And in more recent times, we've had Buckminster Fuller. Here's Buckminster Fuller and his buckyball. That's a geodesic dome. And in fact, that's the reason that the buckyball got its name. It was named after Buckminster Fuller and then, for short, called buckyball. So that's the origin.

And you can see that-- how does the curvature comes-- come about? Well, the curvature on a buckyball comes about by putting in these black pentagons. You probably never looked at the soccer ball in this way, but the soccer ball consists of 20 hexagon faces-- those are the white faces-- and 12 pentagon faces. And the pentagons-- you could see every one of these units here with the five hexagons and the one pentagon in the middle-- that's corannulene, which is a common chemical molecule that has curvature. And the same curvature as in corannulene is also present on this cluster, this motif, in C60. So if you put these together, then you get the buckyball.

So this object is of interest to all kinds of people. And I had a viewgraph here to tell you it's interdisciplinary. I'll just say something, but I won't have much time to go through all of these. But the architects are interested-- Buckminster Fuller. And the astrophysicists are interested in this because a long time ago, when-- before the fullerenes were discovered, it was the astrophysicists that led to the buckyballs, because of anomalies in the spectra out there, coming from the cosmos.

And the chemists are interested-- sure, the chemists are interested. Why? Because here are the buckyballs, that we can append all kinds of molecules and appendages to them with all different properties. And many people believe that there's a whole science out there, and technology, that's derived from fullerene-derived molecules and solids. So you could see all kinds of phenyl groups and oxygen and whatever here. And I'll say more about that later.

Another thing that you can do with these fullerenes-- you can shine light on them. And when you do that, they find each other and they bond in this way. So we still have the same C60 atom here and 60 carbon atoms there. But if they're properly aligned, then they come together in such a way-- let me borrow Professor Larson's ball, here. I don't have two the same size, but they bind together and they come together in the right orientation, and they come closer together than, actually, the carbon-carbon distance on the ball. And so they form this polymerized state. And I'll tell you some applications based on this.

So this is very interesting, that you can do this. And it's a headache, on one hand, because sometimes you want to do optical experiments, and you put on too much light, and you fry the samples. But on the other hand, you can use this to make some devices in the laboratory.

Well, if you wanted to have-- find out a little bit more about buckyballs and buckytubes, we have a new book that's just come out from Academic Press. And it expands greatly on what I'm going to tell you here.

Well, first, I'll have some-- make a couple of comments that might engage the mathematics people in the audience. No, mathematicians already know this. But this is good for kids. I'd like to explain a fundamental aspect of these buckyballs that was essential and of great importance in their first identification. How do we know we have buckyballs? And it was through a specter, of course, of some sort that we found this out. So what should we look for? And the Euler theorem that goes back to the early 1700s tells us about this.

So what does the Euler theorem say? It says here that-- it's given up here. It says the number of faces, f, plus the number of vertices, v, is equal to the number of edges plus two. And that's true for all closed polyhedra.

Now, if the polyhedra-- the polygons or the polyhedra happen to be pentagons and hexagons, p and h, and that all the faces, f, is equal to p plus h, that gives us one equation. And then the number of edges. And that's shared up here. You can see that every time you have an edge, like here, it's shared by two polygons.

So 2e is equal to 5p plus 6h because a hexagon has six edges, of course. And for the vertices, likewise-- each vertex is shared by three polygons. And the number vertices for the pentagons is five. The hexagon is six. So we get, then, three equations and three unknowns. You solve them together, you get a remarkable result that, for the fullerenes-- any kind of fullerene composed of pentagons and hexagons, the number of pentagons is always 12. 12 pentagons are needed to take a flat sheet and convert it into some closed object. That's what this theorem is saying.

And if you have a bigger polygon-- polyhedron-- what happens in making the bigger size is just the addition of hexagons. But the number of pentagons remains the same. And every time you add a hexagon, you add two carbon atoms. So if you're looking for a signature of fullerenes, you look for objects that have an even number of carbon atoms. And, in fact, that was the main item, main issue, main point that was used in the initial identification.

So now I go back to some historical aspects about the identification of the fullerenes. So this is 1984, which is one year before the first paper on buckyballs. That comes in 1985. And we at MIT here had a PhD student who did an absolutely wonderful thesis on liquid carbon. And that was not of great interest to the practical world of industry, because it's very hard to make liquid carbon. The melting point is 4,500 degrees Kelvin. And we could keep the carbon liquid for only nanoseconds in time. So we had to make-- do quick work to find out about our liquid carbon.

Anyhow, one of the things that we were able to do was to figure out how much material left the surface when we applied a certain amount of energy with a laser to the surface. So we had some idea of the energy balance. And we knew that the carbon had to come off in large chunks. But at the time that we did the work, it was only known that carbon clusters existed in very small numbers like C2, C3, C5s. Even C10s were not very common.

Around that time, I visited Exxon and talked about our work. And they assured me that there were no higher fullerenes-- higher clusters of carbon. Well, they pursued this work, whether it was because of our work or because of other people's work-- because as you know, in science, many things come together all at once. And they had the courage to go and look for what happened at these higher mass units.

Here we see a plot of the number of species of a given type that are found. And on this axis, on the x-axis, how many carbon atoms are contained therein. And you can see that there's a new series that starts up somewhere close to 40 carbon atoms. And in this series, each peak is separated from each other peak by two carbon atoms. So that's a sign of what we were talking about. And there's a very large peak, much larger than its neighbors, around C60, and then a secondary peak over here around C70.

Now, the people that-- the Exxon group that published this paper, they were very excited about finding this series and also finding a series where the peaks, the objects, were all separated by two. But they had no idea that this was related to anything new, that it had anything to do with closed shell molecules or fullerenes or anything. So they did a wonderful piece of work, but they sort of missed the boat. And science is sometimes a little cruel that way.

But the group at Rice University-- they were doing a similar experiment. And they were doing it for totally different reasons. They were trying to understand why the spectrum from outer space that has to do with carbon is anomalous. They had all kinds of shifts of the spectra-- of the spectral species with respect to the spectra of carbon that we measure in the laboratory here on Earth. And what forms of carbon were out there in the cosmos? That was their big question.

So they were looking around for this, and they also found the C60. And they-- but they went at it a different way, because they were looking for special species that were responsible. And they postulated this creature. And because it had the n plus 2 sequence, they stuck their necks out and they said it had something to do with a closed shell molecule. They had very little evidence beyond that. It was very flimsy evidence.

Well, the vibrational spectra of the fullerenes are unique and somewhat wonderful. Why? We have 60 carbon atoms. So we have a huge number of degrees of freedom. 60 times 3 is 180. And even if you subtract the rotation and translation, it's still a huge number. So there are many, many modes.

But the high degeneracy, the high symmetry makes these modes rather special. And only a very small number of these modes are either infrared or Raman active. So if you're doing experiments in the laboratory, the spectra are really quite simple . And the upper trace here is the infrared mode. You see four lines, four big lines. And then below is the Raman spectra, with 10 lines. And there are 32 silent modes. That's very, very unusual in molecular spectroscopy. And here we have this situation.

There's another thing that's very nice about it, is that because the system is so highly molecular, it is possible to look at higher order spectrum and actually get-- do molecular spectroscopy to identify these higher order modes. Won't go into that today. Like to leave some time for applications.

The electronic structure is also very unusual and could be understood by just thinking of electrons shared throughout this surface. There are 60 carbon atoms, one pi electron for each carbon atom. So we have 60 electrons to account for, 60 filled states for the molecule.

And if you just assign angular momentum quantum numbers to this series, you can account for-- those are indicated by the pluses here. And the minuses are the unfilled states so that the-- there's a band gap. Then the 60 electrons go up to here. And this is unfilled. So we get a band gap between those.

And the simplest models already are able to give the rough electronic structure of this molecule. This is really quite remarkable. And it's kind of nice for teaching, because we could give this as a homework assignment to students, and they get great gratification. With just a few weeks of introductory quantum mechanics, they're able to explain something as complicated as what happens on the-- to the electrons on a buckyball.

So here is the molecular picture. And I just repeat that all the levels are filled up to this HOMO level, H [INAUDIBLE]. Highest Occupied Molecular Orbital-- that's what HOMO stands for. And then the LUMO, which is just the level above it, is the Lowest Unoccupied Molecular Orbital. So a band gap forms between the two.

And we have, then, a semiconductor with a band gap. And then when we make a solid, we crystallize it. We get a lot of buckyballs near each other. Then there's some weak interaction between them, so you get some band states.

But the bandwidth is very, very small compared to the band gap. And that's totally different from what we're used to-- semiconductor physics like, for example, silicon or gallium arsenide or something like that. So this is kind of a different physics and has changed, in fact, my way of teaching and thinking about many things for student purposes.

Well, let me say something about the condensed phase and the-- take the electronic structure from a different standpoint. Here is our molecule. And it has 60 equivalent sites. Every site on the buckyball is just like every other site.

So let's look at one of these. And you see that two of the sites-- two of the bonds emanating from a carbon atom are in a pentagon. And they are single bonds-- so one electron. And this bond here is between two hexagon. So that's a double bond.

So 1 plus 1 plus 2 is 4. And that takes care of all the electrons for an element in column 4 of the periodic table. Of course, carbon is an element in column 4 of the periodic table. So all the bonds are satisfied. You expect this to be an insulator or semiconductor. And that's exactly what it is.

But we can dope the semiconductor, just like we can dope silicon-- except that we can dope this semiconductor in many ways. So here are the three common ways. The first one is, we can put something inside the icosahedron. Well, that's really fun. And that gives rise to something that we call an endohedral fullerene.

Right now, this is the year 1996, approximately 10 years, a decade, since the first discovery of the buckyball. We've known about buckyballs now for some time. And we know the existence of these endohedral fullerenes. But nobody has figured out how to produce these endohedral fullerenes in mass quantities, in gram quantities, all the same. So we have just very flimsy knowledge about this. And this is an emerging field. Maybe it'll be interesting. Maybe there'll be some interesting applications and properties.

So we have many things to look forward to. As I progress in my talk today, I will point out whole areas of lack of knowledge. And for young students, that's always the great thing, is sometimes they come to the university, they think everything has been solved. And we have to tell them it's not so, that just for all-- every time we find out something, there are 10 new things that we find out that are also interesting to pursue.

So this is a fundamental thing that we don't understand. This is an object. And you can imagine a whole series of fullerenes with additional hexagons, a little bit bigger in size. But in all of these, we could put something in the middle and make something that's endohedral, with unusual properties.

Well, could take one of these atoms off the-- one of the carbon atoms and substitute, say, a boron atom. So that's substitutional doping, as is done in silicon to make N and P-type junctions. We could do that. And that's another possibility.

But the most interesting possibility is is the third one here, which is called exohedral doping, where we put some guest species, like an alkali atom, between the buckyballs. And an alkali metal has one electron that's very weakly bound. That electron will come off and will find its way to the buckyball. Buckyballs love to have extra electrons on them. They just love that. They love to be anions. And if you have a whole bunch of these anions, the electrons can hop from one buckyball to the neighbor and do a hopping, and then to the next one. And like that, you can get induction.

So the possibility of doping these buckyballs and making anions makes the possibility of making conducting buckyballs. Well, if you have conducting buckyballs, maybe you can do even better than that. And that's what I'm trying to show on this viewgraph. So here, we have the introduction of dopants. And so we have different structures here with different numbers of dopants. This is one per unit cell, and here are two, and so forth.

And one of them I colored in green, here, so you could see that was special. And that is three of these electrons. So we have a buckyball with three extra electrons, three anions. And with that, we get the conduction band. The conduction band can hold six electrons. Three electrons fills it in half-- half fills it. And that gives the maximum conductivity.

So for that one, we, in fact, get metallic conductivity. So the conductance-- the resistivity goes up with temperature. That's a sign of metallic conduction. And when we go down to low temperatures, what happens is, voila, at some transition temperature, the resistivity goes to zero and we get a superconductor. So not only do the buckyballs support metallic conduction, but they also support superconductivity.

This phenomenon was discovered in 1991. Unfortunately, it wasn't discovered in 1986. 1986 was when high TC was discovered. And buckyballs were discovered in 1985. And there was really no reason that high TC superconductivity in these materials couldn't have been discovered at that time, because the transition temperature-- the highest transition temperature until the year 1986 was 23 degrees. And you can see, there are many buckyballs that-- buckyballs that are-- have transition temperatures well in excess of that. The highest transition temperature in buckyballs so far is 40 degrees Kelvin.

However, people that are in companies and want to make a living out of superconductors-- this isn't the way to go, because these are not stable superconductors. They're wonderful for a study for my students' thesis work, but they're never going to make it, or not for some time-- unless somebody has a good idea, and we can make a stable superconductor out of these.

Now, let me make a few comments about the buckytubes. The buckytubes are really interesting and kind of remarkable. And I'll just say-- make a few comments about them to leave some time for the applications part of my talk.

So we start out with a buckyball. Here's our buckyball. And let's imagine that we take the-- we cut the buckyball normal to the axis that joins these two pentagons. So we just cut like that. And then we're going to add a whole row of carbon atoms around the belly.

And the number of carbon atoms that you would need to go around the belly is exactly 10. If you look at the picture here, you'll see it's exactly 10. So that makes C70. And that's why C70 is stable, because it's just like C60 with 10-- extra ring of carbon atoms.

And now, if we put two rings around, we get C80. And we put many rings, eventually we get a tube. So that's what I'm going to show you. So here are the tubes-- examples of tubes.

Now, this is just gedanken. This is fantasy. Now a fantasy world. And I'll show you reality in a bit.

So we have-- we can make the tubes normal to a fivefold axis, or we could also cut the-- a buckyball normal to an axis that goes through these hexagons. And that's a threefold axis, another possibility. And then we have many more possibilities. But that's what I'm discussing.

So we have a half of a buckyball here. The other half is over there. And we join those two halves with a cylinder. And similarly for the bottom.

Now, let me show you a little bit better about that. So here is the honeycomb lattice for graphite. Single layer-- just one layer of carbon atoms. And you see over here, I have zigzag edge. And what I do to form the cylinder is, I fold this over to make them fit perfectly, one onto the other. And you can see that they would fit perfectly.

And what we have over at the edge is something with steps. And those steps is what we call the arm chair. That's shown over here. So that's our arm chair.

And if we instead take this sheet and we fold it this way-- so we make the arm chair edge superimpose like this-- then what's left at the-- to join up to the hemisphere of the buckyball is this zigzag edge. And that gives us this kind of a buckyball-- buckytube. So that's how we get these, in simplicity. I'm going to leave this out in case I want it again.

Why people might be interested in these buckytubes is the remarkable properties that the carbon fibers have, to which the buckytubes are related. As you know, carbon fiber is the strongest and stiffest material that we have out there. Here is steel, for comparison. And steel is usually considered as something quite strong, that if you pull on it, it won't break very easily. Or if you bend it like this-- this is what modulus means-- it won't-- it doesn't bend very well. So it has a high modulus.

But relative to steel, bucky-- carbon fibers are very much better. And the question is, if you have buckytube, how would that compare? And we thought that buckytubes might be the embellishment, the-- an example, a prototype of the theoretical carbon fiber. And in fact, that's true. But it has some remarkable properties, of course, now that we've been studying buckytubes, that we hadn't expected. Science is always that way. It has a few surprises.

Well, very shortly after people started thinking about these tubes, there was a report, literature-- Nature Magazine. And here are some tubes. 67 angstroms-- so a little bit less than 7 nanometers in diameter. And inner diameters for this tube, this last tube here-- that's the smallest inner diameter of a little over 2 nanometers. So very small tubes. And the length is a micron. So they have a very large aspect ratio. So very interesting.

Now, the theoretical work that was done in our lab here at MIT and around the world is almost all for single-wall tubes, because those are the easiest to discuss. So there was some impetus to the experimental community to come up with single-wall nanotubes. And sure enough, within a year, they came up with them.

So here are single-wall nanotubes. And they're made with catalysts, transition metals. And the bar chart that's on the bottom of this viewgraph is very interesting, because it shows, for the single-wall nanotubes, the largest diameters are very small. They're less than 2 nanometers. There are hardly any in this beyond 2 nanometers. The maximum is about 1 nanometer. That's the most probable size. And the smallest size is 7 angstroms, or 7/10 of a nanometer. What's 7/10 of a nanometer? This thing.

So what it tells you is that you have to cap these tubes with something. Otherwise, you have exposed carbon atoms-- unsatisfied boards. So that's not very favorable. And the smallest ball that you can make, fullerene you can make with pentagons that are not on top of one another, that is separated pentagons, is the buck-- is the C60. So this is a very special molecule. It has special properties-- and also defines the smallest nanotube that you can make. So that was a very interesting discovery.

In fact, science is very interesting. Years ago-- 20 years ago, because this new graph shows dates of publications that are 20 years old-- people were studying carbon fibers of very small diameter. They call them carbon fibers. They're really nanotubes, but they call them carbon fibers because the method of preparation is the same as what we use today. So they are carbon fibers.

And even the question was asked-- what is the smallest diameter that you could ever have for carbon fiber? And that was Professor [? Kubo. ?] Those people that are in physics will recognize the name-- very famous theoretical physicist of this century. And he wanted to know, what's the-- if you have these things, what's the smallest diameter you can have?

Of course, at that time, nobody understood the connection between the tubes and the fullerenes. So there was no answer to that question. So that's what we really waited for all this time, is to understand in a more microscopic way what these smallest tubes are.

Well, I'm going to tell you a little bit, in very short, about the remarkable electrical properties. This gets into a little bit of math. And maybe the most interesting part is what the end result is. We can, in fact, make a whole family of nanotubes, because all that's important is we have to have some way of rolling up the sheet so that the two sides can match.

There are many ways to do that. And this picture, on top, shows the different ways. So if I go from O to A here, in the viewgraph-- so point O and point A are exactly identical. They're the same point from a crystallographic standpoint. And if I-- then that's an arbitrary lattice point. There are many like point A. That's not unique. And if I now drop normals like OB or AB prime to the line OA, then I have the lines that I have to join.

So that shows you that there's a whole family of these tubes I can make. They have a different property in that they're chiral. That is, the atoms wind around in spirals as they go up the tube rather than just circles for the simple cases that I mentioned before. But there's a whole family of them. And what's most remarkable about these tubes is that 1/3 of them are metallic and 2/3 of them are semiconducting depending on geometry. So that's a very interesting thing.

And I'll give you a very brief summary about why that comes about, but I can't give a very simple display of that. The argument is based on the following concept-- that when we have the tube-- we make the tube like this. And we have a finite number of carbon atoms that go around the circumference. The number of wave vectors that we would have assigned to the system in reciprocal space, for those people that understand those things, is equal to the number of atoms

And if-- what we want to do is, as we go around the cylinder, we want our electronic wave function to be continuous as we go around. So going from this sheet to the next sheet, we should have continuity. So we max the boundary conditions. And that imposes certain restrictions on what the dispersion relations can be.

What it all boils down to in the end is-- and I guess that I need my next picture to show that-- is, here are dispersion relations with nine atoms across the belly of the tube. This is two. Now imagine, in the belly, nine atoms. And then the one on the right has 10 atoms. That seems almost very little difference.

But when you look at it, for the nine atom case, there's a bad degeneracy. That is the, conduction and valence states, the occupied states, and the empty states are degenerate. So with almost no additional energy, an electron can conduct. So we have metallic systems. And-- which is just like graphite, which is a good-- rather good conductor.

In this case here, a band gap forms. And so what's the difference? Well, the difference has to do with the number of wave vectors, which is totally a geometric effect. On this diagram, we go-- this is now reciprocal space. And that, we have vertical lines for all the wave vectors. And you'll see that there are nine such lines that are drawn here. The distance between M and the edge, which is also a gamma point, which I should have mentioned-- noted on the viewgraph, is 1/3. So if the number of atoms is divisible by 3, we get a metallic state, because then we'll always have a wave vector that goes through this M point, which is our degeneracy point.

But if we have 10, 10 is not divisible by 3. There's no wave vector going through that point. And therefore, we have a semiconductor. This is a quantum mechanical phenomenon, but it has remarkable properties and effects on these tubes.

Well, it's wonderful to talk about basic science in this way, but can we demonstrate this in the laboratory? And the answer is yes. And here is 1994-- so it took a little while to do this. Difficult experiment. And this is done with scanning tunneling microscopy and scanning tunneling spectroscopy.

And we see here the IV characteristic current versus voltage, and for a set of different nanotubes-- they had a whole bunch of nanotubes, and there were three of them that are shown in this picture for illustration. On nanotube number 1, the IV characteristic goes through the origin, here, straight. So this is an ohmic one. So that's metallic. And 2 and 3 have a step. They don't go through straight. They have a kink.

And the size-- from the size of this kink, you can figure out what the band gap is supposed to be. And with the scanning tunneling microscope, they can also, on the same tubule-- nanotube-- measure what the diameter is. So they measured the electrical properties and the geometrical properties all at once. That's really remarkable that you could do that with something that's as small as this-- 1 or 2 nanometers in diameter.

And what they come up with is this result, that the energy gap for the semiconducting tubules all collected together goes as the reciprocal of the diameter, which is in that-- that functional forum is what you come up with, also, theoretically. The experiment did it first, so they weren't influenced by the theory.

Well, I could tell you many more remarkable things about the nanotubes and the fullerenes, but I thought I would say a little bit about the practical applications in my remaining-- I think I have five or six minutes. Let me say a couple of things about the nanotubes.

If you could have nanotubes that are conducting and insulating-- so M is metallic and I is insulating-- you could imagine you have a cable here, a cable. Memory device-- put it in some kind of shell so they-- you could preserve what information you've put in. Also, here is a junction-- metal semiconductor junction, et cetera. So you could imagine different structures.

Now, this is all-- nobody's made these. This is just gedanken experiments. Right now, we're only at this stage of measuring with scanning tunneling spectroscopy. There is some measurement already of transport properties of these objects on a single nanotube, which is quite remarkable-- putting-- so here's a single nanotube. 20 nanometers in diameter-- that's the best they've done so far. Four leads, two on each side. And of course, they get metallic conduction. And it's about the right magnitude.

So we're making progress. It's an interesting thing, because usually in semiconductor physics, as some people in the audience work on, we deal with planar structures. And here, the metallic system is a cylinder. So-- a re-entrance cylinder. So it has some different physical properties.

I'd like to mention some other applications, because people-- industry is more interested in new materials if they have some promise of doing some new things. Let me talk about several applications. In our book, we have many applications. We have maybe 100 applications. But here are-- and we talk about maybe 20 of them in some detail. But I've selected a few for today.

Photo transformation-- what is that good for? Photo transformation is the foundation of photoresists. Here we have objects that are very small. They less than 1 nanometer. They're all the same. We can make a whole bottle of buckyballs pretty cheap, now, that are all the same.

And if you put light on, you hook them together. When you hook them together, they're no longer soluble. So there's a different solubility between the polymerized buckyballs and those that exist in the monomer form, that haven't been exposed to light. So you can make a pattern system. And for some applications, this could be quite interesting.

The use of NO in the process makes this quite efficient and makes it compatible and interesting in terms of efficiency compared to presently-used photoresists. So I imagine there could be some interest in the applications.

Well, how does this all work? This shows the temperature range in which the photo transformation works well. You have to be at a temperature that's high enough so that the buckyballs move around a bit, so that they find each other in the right orientation, but not so energetic that they have energy to break the bond. So that's the temperature range where this thing works.

And you can form bonds between these and others. You can have many bonds. Some of them have a polymer. And that's what's shown here-- number of bonds. And you can detect this remotely with some kind of spectroscopic tool, like Raman or infrared spectroscopy, where they-- because the carbon atoms that come together are-- the distance between the carbon-carbon bond is smaller for the phototransformed ones than it is otherwise, there's a different signature. There's different vibrational frequency. So you can detect them-- remotely. So you have an easy way to know when your system is working or if it's not working and you'd better fix it.

Let me give you another example of where buckyballs-- one of- I like this example. Silicon carbide-- what's silicon carbide good for? It's a wide band gap semiconductor. Three electron volts is the band gap. It has some excellent properties in terms of stability. It has good mobility, thermal conductivity, et cetera.

But it's almost never used, because it cannot be patterned and it cannot be controlled very well. So you can't etch it. You can't pattern it. And there aren't very good techniques for growing nice single-crystal films.

But with buckyballs, you can do that. Now, why? On this picture here, I show you a transistor-- a textbook transistor, in fact. So we have silicon. That's the dark area. And the hatched area-- silicon dioxide is the darkened area. And the hatched area is silicon. That's your transistor.

Silicon has the property of having many dangling bonds. And that's the nature of silicon-- the silicon surface. Those dangling bonds engage the buckyballs readily. So buckyballs will stick very nicely to silicon. Silicon dioxide doesn't have dangling bonds, so the buckyballs do not stick to the silicon.

So if you have that transistor, for example, and you have a rain of buckyballs coming on the surface, they'll stick only where the transistor place is. And where the silicon dioxide is, they won't stick it all. So like that, you can build up a surface. If you heat up the system, the silicon, and the carbon from the buckyball will react and make silicon carbide. And you get a film. And the film is crystalline, as I'll show you in the next viewgraph.

So this is a way. And it's been done, now, in quite a number of labs around the world. All right now is in universities. There's no practical device yet, but I think there could be. And this shows you that it's single crystal. And here are the reflections for cubic silicon carbide. It has very nice fricitonal properties, so people that are in MEMS, micro mechanical systems, they might find this a good system. And you can prepare films up to 2,000 angstroms, which is about as thick as you want to go for device applications. And there may be other things that you could do with the buckyballs. This is one example of-- that has already been done.

As I mentioned earlier, there are many chemistry applications. And at least in some of the chemistry labs around the world, people are working on these. There are patents out there-- new materials is-- about half the patents in the patent literature on buckyballs are for new materials based on buckyballs-- new materials derived because of interaction with buckyballs. So chemistry is a large part of this. And here, you see the polymers. You see halogens, oxygen, and different species that you can attach to these and make some interesting systems.

I thought I'd show, in my last viewgraph, something that's stylish nowadays. Biochemistry people are working hard to try to find some way of reducing the activity of the HIV virus. And so this picture here is the HIV virus. And then you see there's a cleft in there.

The cleft in the virus is exactly the right size of buckyball. So if you-- if you send buckyballs raining on the HIV virus, some will attach in this place. And then they will destabilize the virus and it won't multiply anymore. So this started out as a theory paper. And then people tried it in the laboratory, and they've had some laboratory tests with mice. And it even works. So there may be some possibilities in biochemistry for this remarkable molecule.

So I think my time is just about over. And this is a good time to stop and ask for questions.

[APPLAUSE]

Who wants the first one? Yes.

AUDIENCE: Sort of three questions. Two may be the same.

DRESSELHAUS: Well, let's try with one, and then we'll give somebody else a chance.

AUDIENCE: That's all right. [INAUDIBLE] you mentioned metal semiconductor transitions. You didn't mention the word insulator. Can any of the bucky structures be insulators?

DRESSELHAUS: Well, they could be insulators. But one of the problems with buckyballs that makes-- well, if you have a buckyball surface that's out, exposed to oxygen, it will have a very high resistivity. If the buckyballs are very clean and pure, then the resistivity goes down. So for the practical device, if you want to have a good insulator, I suppose you could say that a surface will be insulating. I wouldn't be out selling this for my best-- world's best insulator. But in principle, it has a band gap of 1.5 eV. Breakdown voltage-- I'm not sure that we know exactly what it is. It's not very high.

AUDIENCE: [INAUDIBLE] why the superconductors are unstable?

DRESSELHAUS: No, no. The reason why the superconductor-- no. That isn't related to that. The reason why the superconductors are unstable is that every single dopant that has been successfully used to make a superconducting fullerene is chemically unstable-- that is, if you leave it in the atmosphere, the reagent that you've added to-- like you have an alkali metal, you add that to a fullerene. You leave it out in the air, the alkaline metal leaves. It oxidizes immediately upon exposure to air. So that's not-- to keep the superconductor superconducting, you have to encapsulate them. And that makes the material not very practical for commercial applications. That's quite a different story from the dielectric properties.

Another question. Yes.

AUDIENCE: You mentioned there was a lot of patent activity with regard to designer molecules, I guess, with buckyballs combined with other things. Would you care to comment a little more about that? What kinds of processes are being patented, and does this interfere with academic research in any sense?

DRESSELHAUS: Maybe. It interferes somewhat with the literature, because some of the best ideas probably are under patent, so they're not published in the open literature immediately. So that's one thing-- especially in the area of chemistry and new materials. Some of the active areas are diamond synthesis.

There are quite a number of patents out-- that is-- here. This is a curved surface. The diamond differs from graphite. Graphite's planar. Diamond has S, P, Q bonding. So when you get a curved surface, you have some admixture of S, P, Q bonding. So by having this curvature built in here, it is thought that it would promote, in some way, formation of diamond. And in fact, it does.

And people have used this as a source for clusters-- carbon clusters that are used in the diamond film synthesis. And it works very well and produces a kind of diamond that has very small grains, which means that you have a nanocrystalline size so that the surface doesn't have so much friction as the usual diamond surface that is produced by present day techniques.

So for some applications-- you imagine a stylus going along a surface. To have non-bumpy surface is an advantage. So there's some people that are pushing that-- improving the technology, trying to make it competitive in cost and reproducibility. So that's-- I don't know how close to commercialization it is, but there's a lot of activity worldwide in that area.

But there are just many-- for sensors and just many different things-- nanotechnology. There's just a whole range of different applications. I have a listing of all the different patent areas in the book, if you're interested.

Yes.

AUDIENCE: Did you say something about whether any of these structures are-- can be fabricated, or whether it's known that-- whether they can be fabricated biologically, and maybe speculate as to-- as far as I'm aware, the answer to that is no-- and speculate, maybe, why that's true? Why haven't they arisen as structures that we see in the biological world?

DRESSELHAUS: Well, in the biological world, we see some structures related to buckyballs, but we don't see buckyballs themselves. In fact, in astrophysics, people have now been searching for-- now that they know the existence of buckyballs, they have been searching religiously to try to reconcile the various spectra that we find here on Earth from these whole menagerie of fullerenes.

And there is no correspondence yet. There's no verification that the anomalies in space are really associated with these objects. So in some sense, the unknown still remains with us. This has been an active research area since 1920-- some time like that. So it's many, many years. And when buckyballs were discovered, they thought, aha, well, we have the answer. But it's still not certain that there's much connection between the anomalies in astrophysics and the balls.

Now, getting back to the biological systems, which is what you asked about, there are many viruses that have this kind of shape. But they're not only fuller-- they're not only carbon. They have other things. Study of these is interesting for the biologists because of the similarities of the structure. And perhaps they can learn something. But this itself is not known to exist. But it is believed that this is benign in the body-- that is, if you swallow some buckyballs, it's not going to kill you. There has been research. And this is important for researchers-- that you work on some new chemical, that it's okay.

The tubes are another matter. You look in biological works, there is a lot of evidence for very narrow tubules. And what they have seems somehow to be related-- although nobody has yet made the connection. But there seems to be some correspondence to me, anyway, looking at the two kinds of pictures of what I know that we have in the inanimate world and what I see on biology friends. There are a lot of tubes that join different things and functions and so forth. If we understand these nanotubes, I think we could be quite helpful to the biology people that are trying to understand these structures that exist in living systems. But they're not only carbon.

AUDIENCE: Are very long tubes-- say, is it possible to make a 20-foot long nanotube? No one, of course, has done it. But I'm wondering, is there any theoretical reason why we couldn't have reels of the stuff, kilometers, use it for something interesting?

DRESSELHAUS: Well, with carbon fibers, which are a little bit larger in size, you could make meter-long lengths, I think, has been-- for something that's about 1 micron in diameter. That has been demonstrated.

With the nanotubes, it-- nobody has been working on that particular aspect. The main thing with the nanotubes is the lack of control-- is that one knows how to make nanotubes. You can always make nanotubes reliably. But you take what you get. And you don't have real control about what the diameter is going to be, what is the length, what is the chirality. And this is future research.

LARSON: Last question.

AUDIENCE: Oh, that's me. How about the optical properties?

DRESSELHAUS: The optical properties are quite remarkable and interesting and have real possibilities for applications. Why is that? It has to do with the fact that you have a molecular solid-- that's number one. The valence and conduction band have the same parity. And because of that, dipole transitions are forbidden so that at the absorption edge, you have to do things to make that transition take place. So that means that you can control it.

If you can, by some means, get electrons in the excited state, then they can more easily make transitions to higher states, because then you can have allowed transitions. Well, what that allows you to then achieve is a metastable state for the lowest state in the conduction band. So that becomes metastable. And it therefore becomes a way to get saturation and absorption. So that is the basis of an optical limiter, which works much better than any other material in terms of efficiency-- at the appropriate wavelength. So that's one application that probably will find some use in-- soon, just because it works so well.

But there are many other optical properties. Most of the optical properties are not so well understood, because the polymerization effect that I mentioned has been in the way of serious studies when people haven't realized that when they put light on the samples, they're making phototransform material-- which lowers the symmetry and therefore changes many things. So once you understand that, you can work around it-- work at a higher temperature or do something to break those polymerized bonds. And when that takes place, then we'll know much more about the optical properties in detail. That's the one area that's not well understood right now about the buckyballs.

LARSON: Millie, thank you very much.

[APPLAUSE]