Global searching of interface configurations of (8,4) tube on flat solid surface

Chapter 3. Growth of Single-Walled Carbon Nanotube on Metal Catalyst Particles

3.5 Stability of various SWCNT-catalyst interfaces

3.5.1 Global searching of interface configurations of (8,4) tube on flat solid surface

The above two sets of simulations roughly show that interface with conventional flat (or say, minimal-length) edge is still more stable than the tilted one. It interested us to dig deeper into the CNT interface world, and figured out which kind of tube edges leads to better contact with the catalyst, and therefore a more favorable CNT growth model.

We started with one single tube—(8,4), as tube of only one chirality already has a variety of edge configurations. We subsequently defined 8 edges from edge 1 to 8 (Fig. 3.23), as the edges we would discuss. To note that, it does not mean that there are only 8 edge configurations for (8,4) tube. It is that these 8 edges are the most regular and relatively flat ones with minimal- length. One could always find more edge configurations if he/she cuts the tube with a larger tilted angle. But a larger tilted angle would lead to a longer circular length of the tube end and

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the contact between the CNT and the catalyst would be more difficult. Therefore, we chose only these 8 edge configurations, with both conventional flat edge—edge 8 with alternative A- Z and edge 1 with segregated A-Z, which already takes into consider most of the stable configurations.

Figure 3.23 (8,4) tube edges with different ways of cutting. (a) Edge 1 with only two armchair (A)- zigzag (Z) contacts. (b-g) Edge 2, 3, 4, and 7 with 4 A-Z contacts, respectively. (e-g) Edge 5 and 6 with 6 A-Z contacts, respectively. (h) Edge 8 with 8 A-Z contacts.

Figure 3.24 (a) Interface formation energies of the 8 edges of the (8,4) tube on solid Ni(111) surface with (red dots and red line) and without dangling C (grey dots and black line) using simple models with

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short tube segments. (b-e) Optimized atomic structures of the most stable interface between Edge 1, 2, 8, and 8 with dangling C and Ni(111) surface, respectively.

We firstly calculated the interface formation energies of the 8 edges on the solid Ni(111) surface using a simple model with a short (8,4) tube segment fitted onto the Ni surface (Fig. 3.24b-e).

The interface formation energy was calculated by

𝐸_𝑓= 𝐸_{𝑒𝑑𝑔𝑒} − 𝐸_{𝑏𝑖𝑛𝑑𝑖𝑛𝑔}

, (3.2) where

𝐸_{𝑒𝑑𝑔𝑒} = (𝐸(8,4)𝑐𝑢𝑡−𝑖𝑛𝑡𝑜−2− 𝐸_(8,4))/2, (3.3)

𝐸_{𝑏𝑖𝑛𝑑𝑖𝑛𝑔} = 𝐸𝐶𝑁𝑇−𝑐𝑎𝑡𝑎𝑙𝑠𝑦𝑡− 𝐸_𝐶𝑁𝑇− 𝐸_{𝑐𝑎𝑡𝑎𝑙𝑠𝑦𝑡}− 𝑁 × 𝐸_𝐶@(8,4)

. (3.4)

In equation (3.3), we first calculated the energy of a (8,4) tube, and then cut it into two pieces

with two same edges (edge 1 to 8) and calculated their energy. The energy difference dividing by two is the energy of the edge configuration. In equation (3.4), 𝐸𝐶𝑁𝑇−𝑐𝑎𝑡𝑎𝑙𝑠𝑦𝑡 is the energy of the entire system consisting of the CNT and the catalyst, 𝐸_𝐶𝑁𝑇

is the energy of the CNT in the system,

𝐸_{𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡}

is the energy of the catalyst in the system. If there is dangling C added to the interface, its energy should be subtracted as

𝑁 × 𝐸_𝐶@(8,4)

, where

𝑁 is

the number of C added, and

𝐸_𝐶@(8,4)

is the energy of each C atom in the (8,4) tube.

The resulting interface formation energy is shown in Fig. 3.24 labeled with grey dots. For each edge configuration, there are 5 different energy values (grey dots) according to the different positions of the Ni(111) surface that the tube has been fitted onto. The lowest energies of each edge configuration have been connected by a black line (we consider here the lowest energy should be the one approaching to the global minimum energy of interface between this edge configuration and the solid Ni(111) surface). So the figure shows a similar result as in the previously introduced ACS nano paper²¹³ that edge with segregated A-Z is with lowest interface formation energy with the solid metal surface. And the conventionally recognized stable edge—

edge 8 has a much higher interface formation energy, ~1.66 eV higher than edge 1. This is a quite high energy difference that definitely can’t be overlooked.

With such an energy difference, the A-Z segregated edge is of course more preferred and should be considered as the real growth model. This means most of the previous theories, considering the CNT-catalyst interface using the conventional model--edge 8 should be wrong, including the dislocation theory that derives the growth rate by the density of the kinks at the edge which depends on the chiral angle. Now if the A-Z segregated edge is preferred, then the dependence

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of the kink density on the chiral angle no longer exists, and therefore the failure of the theory.

This result can be understood in a way that the conventional flat edge contains more A-Z contacts, resulting in more kinks which could not contact with the metal surface properly. While for A-Z segregated edge, it contains least kinks and could contact better with the Ni(111) surface.

While the result really surprised us, we thought about the complexity of the materials’ interface.

There are reports showing that for the interface between CNT and catalyst, klein edge, which is normal edge with dangling C, has advantage in energy compared to other edges¹³⁹. We therefore, added dangling C atoms onto the pristine edge 1 to 8, and calculated the corresponding interface formation energies. As shown in Fig. 3.24 with red dots and red line, edges with dangling C show higher stability than those without. The interface formation energy of edge 8 drops ~1.44 eV with dangling C, and is only 0.22 eV higher than that of edge 1 now.

And edge 2 now instead of edge 1 is the most stable one.

But there are still things unreasonable in this result. Firstly, the formation energies are all around -4 eV to -6 eV, far too low that the tube might prefer to open wider and grow larger. Then according to the optimized atomic structures (Fig. 3.24b-e), the small segments of the tube are all highly distorted to better fit to the substrate surface, while in reality, it should not be allowed.

Therefore, we changed our model slightly to employ a longer segment of the tube, and did the same calculations as before.

Figure 3.25 (a) Interface formation energies of the 8 edges of the (8,4) tube on solid Ni(111) surface with (red dots and red line) and without dangling C (grey dots and grey line) using simple models with long tube segments. (b-d) Optimized atomic structures of the most stable interface between Edge 1, 7, and 8 with dangling C and Ni(111) surface, respectively.

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The results are shown in Fig. 3.25 where the interfaces of pristine edges are labeled with grey dots and grey line, the interfaces of edges with dangling C are labeled with red dots and red line. It can be seen that the tendency of the interface formation energy with different edge configurations is the same as the previous result with short-tube-segment model, while the energy of the A-Z segregated edge (edge 1) is lifted relatively to be higher than that of the conventional A-Z separated edge (edge 8). The energies of the two special edge configurations are now of the same order of magnitude, both more stable than the other configurations. The raise of the A-Z segregated edge energy is reasonable that, as the new model forbids the dramatic distortion of the tube, the highly tilted tube edge could not better fit on the surface. In addition, now the interface formation energies are in the range from -0.5 eV to -1.8 eV, not too low and much more reasonable than before.

Now the result of the interface formation energy between different edge configurations and the solid catalyst is more reasonable and convincible. It shows that there are no special configurations with extraordinarily high stability. The conventional A-Z separated edge and the A-Z segregated edge are with the similar stability. But the interface formation energy difference among the configurations we considered is still about 1.3 eV, too large to be neglected.