Structure and Dynamics of Boron Nitride Nanoscrolls Eric Perim and Douglas S. Galvao*

Applied Physics Department, Institute of Physics

University of Campinas – UNICAMP, 13083-970, Campinas-SP, Brazil

Abstract

Carbon nanoscrolls (CNSs) are structures formed by rolling up graphene layers into

a papyruslike shape. CNNs have been experimentally produced by different groups. Boron

nitride nanoscrolls (BNNSs) are similar structures using boron nitride instead of graphene

layers. In this work we report molecular mechanics and molecular dynamics results for the

structural and dynamical aspects of BNNS formation. Similarly to CNS, BNNS formation

is dominated by two major energy contributions, the increase in the elastic energy and the

energetic gain due to van der Waals interactions of the overlapping surface of the rolled

layers. The armchair scrolls are the most stable configuration while zigzag scrolls are

metastable structures which can be thermally converted to armchair. Chiral scrolls are

unstable and tend to evolve to zigzag or armchair configurations depending on their initial

geometries. The possible experimental routes to produce BNNSs are also addressed.

*corresponding author: galvao@ifi.unicamp.br,

Tel. +55-1935215369, FAX: +55-1935215376

1. Introduction

Nanometric structures have been intensively studied during the last years, due to

new physical phenomena and potential technological applications. Carbon-based materials

are among the most investigated in literature. In particular, carbon nanotubes (CNTs)1 are

one of most important subjects in materials science. In spite of more than two decades of

intense investigations, the detailed mechanisms of the CNT formation are still an open and

polemical question2. It has been proposed that CNTs could be a subsequent state of

papyruslike carbon structures, generically named carbon nanoscrolls (CNSs) (Fig. 1)3,4.

Although known since 1960s3 there are very few works on CNSs. This can be

explained in part by the intrinsic experimental difficulties in synthesis and characterization.

With the recent advances in low-temperature synthesis4,5,6 there is a renewed interest in

these materials7,8,9,10,11,12,13. Like CNTs, CNSs can be made of single or multiple graphene

sheets. However, in contrast to CNTs, their diameter can be easily varied (contraction or

expansion), making them extremely radially flexible, a very useful property to be exploited

to their potential use for Hydrogen storage14,15,16.

Figure 1 – (a) Graphene/BN sheet; (b) Nanoscroll; (c) Nanotube. See text for discussions.

Another important class of nanostructures is boron nitride nanotubes (BNNTs)

which were theoretically predicted17,18 and synthesized with different techniques19,20. For a

recent review see Goldberg et al 21. Although BNNTs share some of the remarkable

properties exhibited by CNTs, they have some peculiar features such as band gap chirality

independence, while CNTs can exhibit semiconducting or metallic characters depending on

their helicity21.

By analogy, CNTs and BNNTs can be formed by rolling up graphite and boron

nitride layers, respectively (Fig. 1). For CNSs and boron nitride nanoscrolls (BNSs) a

similar analogy may be considered (Fig. 1b).

In principle, the recently reported experimental techniques used to produce CNSs4,5

can be used to produce BNSs using cubic boron nitride crystals as starting materials.

Although a large number of theoretical and experimental works has been reported to

BNNTs, BNSs have not been explored so far. In this work we present the first theoretical

study of the dynamical and structural properties of BNSs.

Previous molecular mechanics and molecular dynamics studies8 of different CNSs

have shown that their formation results from two competing factors, elastic deformations

and van der Waals interactions among overlapping layers. Depending on the geometry and

chirality CNSs can be even structurally more stable than their equivalent planar

configurations (graphene).

In this work we used the same methodology reported in ref 8 to investigate the

dynamical and structural properties of different (size and chirality) BNSs. In particular a

critical analysis of similarities and differences among CNSs and BNSs is presented.

2. Methodology

In order to address the structural and dynamical aspects of BNSs we have carried

out molecular mechanics and molecular dynamics simulations using the well-known

molecular universal force field (UFF)22,23 as implemented in Cerius and Materials Studio24

software.

UFF is a force field that includes bond stretch, bond-angle bending, inversion,

torsions, rotations and van der Waals terms. Electrostatic and solvent effects can be also

easily included. UFF has been proved to be very effective in the description of the

structural and dynamical aspects of CNTs and CNSs8,25,26,27.

Boron and nitrogen atoms were assumed as having partial double bonds and sp2

hybridization. No explicit charges were used and the systems are assumed to be neutral.

The calculations were carried out with high numerical precision (the used criterion

convergence was of 10-5 kcal/mol in energy and 5x10-3 kcal.Å/mol for maximum force

among atoms). We investigated structures containing up to ~ 20,000 atoms, which

precludes the use of full quantum methods. The evolution of the scroll structure was

simulated using molecular dynamics (MD) methods for different temperatures (up to 300

K) within the NVT ensemble making use of a Nosé thermostat28. In average, each

simulation was carried out for a period of 50 ps, with time steps of 1 fs.

The nanoscroll structures were generated by rolling a graphene or BN layer into a

truncated Archimedean-type spiral, by rotation around the y1 axis defined by the angle θ

shown in Fig. 2. This spiral is defined by the parametric equation

r = aφ + a0

where a and a0 are non-zero constants, and r and φ are the usual cylindrical coordinates.

The parameter a is related to the initial interlayer spacing d, as a = d / 2π, where d = 3.4 Å

for carbon interlayer distances. Archimedean-type spirals describe well the scroll structures

since they have a constant separation distance for successive turnings of the spirals. While

multi-layer BNSs are likely to exist, for simplicity we consider here only single layer

scrolls.

The angle θ defines the scroll configuration: zigzag for θ=0, armchair for θ=90º,

and chiral for 0 < θ < 90º. We restricted our analysis of the evolution of the structures

during scroll formation for two scroll types: α (Fig. 2b), where there are no uncurled

regions of the layer; and β (Fig. 2c), where flat and uncurled regions simultaneously

coexist. Although there are many other possible initial structures, the basic structural

features can be addressed using only these two structure types as demonstrated for the CNS

case8. We have considered α and β structures of different sizes (varying H and W values –

Fig. 2).

3. Results and Discussions

Similarly to CNSs, BNS formation is dominated by two major energetic

contributions, the elastic energy increase caused by bending the BN layer (decreasing

stability) and the free energy decrease generated by the van der Waals interaction energy of

overlapping regions of the layer (increasing stability).

We started analyzing the scroll stability as a function of its internal radius. In Fig. 3

we present the results for a structure of 30 Å x 121 Å that is rolled up with different radius.

The change in the configuration energy per atom relative to its equivalent undistorted layer,

considered as the reference energy value, ΔE, is also discussed.

Figure 2 - (a) The unwrapped honeycomb lattice of a single layer (width W and height H). Here x1 and y1 are the scroll axes, which are rotated by an angle θ with respect to the reference coordinate system xy. The scroll is generated by wrapping the sheet around the axis y1. Examples of (b) α and (c) β-type CNSs (with θ=45°) and their cross sections are shown. See text for discussions.

As the structure is rolled up and before layer overlap occurs, layer curvature

increases and so does the torsion and inversion contributions to the strain energy. Thus the

rolled structure becomes less stable in relation to the undistorted (planar) configuration.

This implies that the transition from planar to rolled structures must be energy assisted (e.

g., through sonication, as experimentally reported for the CNS case4,5). If no external

energy is provided, the curved structures will return to the more stable planar

configurations. When surfaces start to overlap, the van der Waals contributions increase the

structural stability.

100 80 60 40 20 0

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

110 100 90 80 70 60 50 40 30 20 10 0-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

ΔE (k

cal/m

ol)

Internal Diameter (Å)

Ebend

EvdW

ΔE (k

cal/m

ol)

Internal Diameter (Å)

(a)

(b)

Figure 3 – (a) Change in relative total energy (ΔE) during the wrapping of the plane BN sheet into BNNS. (b) contributions of bending and van der Waals terms to the total ΔE.

This process can be better visualized analyzing the van der Waals and bending

energy contributions separately (Fig. 3b). For small diameter values the bending

contributions outweigh the van der Waals energetic gains and the structure become unstable

and tend to evolve to the planar structures. There is a critical minimum inner diameter

necessary for the scroll to attain structural stability. Beyond this limit the rolling process

would evolve spontaneously and the final structure can be even more stable than its parent

planar configuration. For the case displayed in Fig. 3a this occurs for diameter values

between 13 and 30 Å. Although these critical values are size and chirality dependent, the

general behavior displayed in Fig. 3 is valid for all BNS structures.

We have carried out molecular dynamics simulations in order to address the relative

importance of size and chirality in the BNS formation. We considered structures with

internal radius above and below the stability line, built from a 100 Å X 100 Å planar

structure, in all three configurations (armchair, chiral and zigzag).

In Fig. 4 we present the time evolution energy profile for structures above the

stability line which shows that the dynamical behavior is mostly independent of scroll

chirality (Fig. 4a). Although oscillations in the scroll structure can exist for some time, they

all eventually unfold and converge to planar configurations (see video 4 in the

supplementary materials).

0 20 40 60 80 100 120 140 160

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 5 10 15 20

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

θ=0º θ=45º θ=90º

ΔE (k

cal/m

ol)

Time (ps)

(a)

(b)

θ=0º θ=45º θ=90º

ΔE (k

cal/m

ol)

Time (ps)

Figure 4 - ΔE time evolution profile for scrolls of different chiralities with radius above stability line. (a) Initial temporal stages. (b) Complete temporal process.

In Fig. 5 we present results for structures below the stability line. Although scroll

formation is possible for all the different chiralities, their dynamical evolution is

differentiated since the onset of the scrolling process (Fig. 5a).

The armchair scrolls are the most stable configurations, even more stable than the

planar structures. This aspect can be observed from the first temporal stages (Fig. 5a).

Chiral scrolls are the least stable configurations. The simulations show that chiral scrolls

can evolve to armchair or zigzag configurations depending on the initial geometries. For the

case presented in Fig. 5, the scroll oscillates between zigzag and armchair, but converged to

the armchair configuration. Zigzag scrolls, although less stable than the armchair ones, do

not easily undergo structural changes (at least for low temperatures) and remain in the

zigzag form.

These results indicate that BN armchair scrolls are more likely to be found,

especially at high temperatures, where the zigzag scrolls can be thermally converted to

armchair ones.

0 20 40 60 80 100 120 140 160

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 5 10 15 20 25 30

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

Time (ps)

θ=0º θ=45º θ=90º

ΔE (k

cal/m

ol)

θ=0º θ=45º θ=90º

ΔE (k

cal/m

ol)

Time (ps)(a)

(b)

Figure 5 - ΔE time evolution profile for scrolls of different chiralities with radius below stability line. (a) Initial temporal stages; (b) Complete temporal processes.

For scrolls formed from rectangular geometries (Fig. 2) BNSs and CNSs present

quite similar behavior (Fig. 6) with relation to the stability energies, although for the same

dimensions and internal radius BNSs are more stable. This suggests that the van der Waals

interactions are more relevant for the BNS than for the CNS case.

The stability energy increases rapidly with the scroll area. This is a direct result

from the van der Waals interactions, which are mainly responsible for the stability

structural gains and are also proportional to the surface area. For large H and W values the

ΔE curve tends towards a constant value.

0 10 20 30 40 50 60 70 80 90 100110120-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

70 80 90 100 110 120 130 140 150 160 170 180-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.4

ΔE (k

cal/m

ol)

H(Å)

BN Carbon

BN Carbon

ΔE (k

cal/m

ol)

W (Å)

(a)

(b) Figure 6 - Relative stability for Boron Nitride and Carbon nanoscrolls formed from rectangular sheets with internal diameter ~20Å and (a) W=107Å; (b) H=30Å. Finally we analyzed the energetics of scroll formation for α- and β-type scrolls from

rectangular layers (Fig. 2). Fig. 7 shows the total energy and the van der Waals and bending

energy contributions. The α-type configuration is energetically more favorable and the

scrolling process occurs faster than for the β-type. This can be seen from the initial energy

values and from the slope of the curves (Fig. 7a).

As the α-type allows the simultaneous movement of both overlapped edges in

opposite directions, the scrolls are formed faster (see video 3, supplementary materials).

This feature can also be seen in Fig. 7b where the fast van der Waals gain for the α-type is

clearly observed. The β-type configuration presents a more complex behavior, especially

for the bending energy (Fig. 7c), because geometrical changes in the flat layer region occur

simultaneously with scroll formation (see video 1 and 5, supplementary materials). It costs

less energy to start the bending layer from both extremities (α-type) than to start rolling it

from one extremity to the other (β-type). Both types can generate the same BNS by self-

rolling processes, but it is more likely (as in the case of sonicated CNSs4,5) that the layers

can exhibit bending in many directions simultaneously.

0 5 10 15 20 25 30

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 5 10 15 20 25 30-1.2

-1.0

-0.8

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5 10 15 20 25 30-0.1

0.0

0.1

0.2

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0.4

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0.6

0.7

β−type α-type

ΔE (k

cal/m

ol)

Time (ps)

β-type α-type

ΔE(k

cal/m

ol)

Time (ps)

β-type α-type

ΔE (k

cal/m

ol)

Time (ps)

(a)

(b)

(c)

Figure 7 - Relative energy time evolution for α and β type scrolls. (a) Total energy; (b) van der Waals energy; (c) Bending energy.

In Figs. 8 and 9 we show conical and non-conical shape BNSs obtained from MD

simulations for structures containing ~ 20,000 atoms. We observed that the conical

structures are metastable states and their occurrence is size and chirality dependent, with

the probability of occurrence being proportional to scroll size. The conical CNSs were

experimentally observed4,5 and our results suggest that they should also occur to BNSs (see

video 5, supplementary materials).

Figure 8 – BNNS metastable conical shape.

Figure 9 – BNNS minimum energy configuration.

4. Summary and Conclusions

We have investigated the energetics and dynamical aspects of Boron Nitride

Nanoscrolls (BNNSs) using molecular mechanics and molecular dynamics methods. Our

results show that the BNNS formation mechanisms are quite similar to those from Carbon

Nanoscrolls (CNSs)8. Similarly to CNS, BNNS formation is dominated by two major

energy contributions, the increase in the elastic energy due to the bending of the initial

planar structure (decreasing structural stability) and the energetic gain due to the van der

Waals interactions of the overlapping surface of the rolled layers (increasing structural

stability). There is a critical diameter for scroll stability; beyond this limit the scrolled

structure can be even more stable than its parent planar structures.

The armchair scrolls are the most stable configuration; zigzag scrolls are metastable

structures that can be thermally converted to armchair. Chiral scrolls are unstable and tend

to evolve to zigzag or armchair scrolls depending on their initial geometries. Similarly to

the experimentally observed conical shape CNSs, our results show that BNNS are also

likely to be found in these configurations. In principle, the same experimental techniques

used to produce CNSs4,5 could be used to produce BNNSs using cubic boron nitride as

starting materials. We believe that our results may stimulate further works along these

lines.

Acknowledgements – The authors acknowledge financial support from the Brazilian

Agencies CNPq, CAPES and FAPESP. We also wish to thank Profs. R. H. Baughman, V.

Coluci, S. B. Legoas, F. Sato for helpful discussions, and Prof. M. A. Cotta for critical

reading of this manuscript.

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