# Trapping molecules in a covalent graphene-nanotube hybrid

Zhao Wang<EMAIL_ADDRESS>Laboratory for Relativistic Astrophysics, Department
of Physics, Guangxi University, Nanning 530004, China

###### Abstract

This study employs molecular dynamics simulations to examine the physisorption
behavior of hydrocarbon molecules on a covalent graphene-nanotube hybrid
nanostructure. The results indicate that the adsorbed molecules undergo self-
diffusion into the nanotubes without the need for external driving forces,
primarily driven by significant variations in binding energy throughout
different regions. Notably, these molecules remain securely trapped within the
tubes even at room temperature, thanks to a “gate” effect observed at the neck
region, despite the presence of a concentration gradient that would typically
hinder such trapping. This mechanism of passive mass transport and retention
holds implications for the storage and separation of gas molecules.

##  I Introduction

Reversible gas physisorption plays a crucial role in various applications like
hydrogen storage, sensing, carbon capture, pollutant removal, and the
separation and purification of chemical substances.Li et al. (2009) For these
purposes, an ideal adsorbent should possess high adsorption capacity,
selectivity, and favorable adsorption kinetics and regenerability. Carbon
nanotubes (CNTs) and graphene have emerged as promising gas adsorption
materials due to their large specific surface area, high chemical inertness,
light mass density, outstanding mechanical strength, and thermal
conductivity.Wang et al. (2013) However, each of these materials have their
own advantages and disadvantages. Graphene, for example, is an atomic layer
with an extreme theoretical specific surface area, yet its gas adsorption
capacity is highly anisotropic due to its default inter-layer spacing of only
$0.34$ nm. Conversely, CNT arrays are capable of adsorbing and storing
molecules in three dimensions (3D), yet their narrow entrances can result in
low adsorption efficiency.

Graphene-nanotube hybrids (GNHs) have been synthesized to offer the advantages
of both graphene and CNTs,Dasgupta et al. (2016); Lv et al. (2014) with the
potential of adsorbing gas molecules onto a graphene surface and transporting
them into CNTs for 3D storage. A variety of GNH structures have been designed
and characterized for molecular adsorption-related applications.Dimitrakakis
et al. (2008); Wesolowski and Terzyk (2011); Wu et al. (2012); Lei et al.
(2014); Wesolowski and Terzyk (2016); Zhou et al. (2016) However, while
previous studies have considered external pressure or pre-positioning of
molecules on the GNH surface, a solution for driving the motion of molecules
within the GNH has not been proposed.

The literature describes several active methods for transporting molecules or
particles on the surface of nanomaterials, including the application of a
thermal gradient,Schoen et al. (2006); Barreiro et al. (2008); Wang (2019,
2020) electric,Ohara et al. (2008); Dong et al. (2009) and mechanical
means.Russell et al. (2012); Wang and Kral (2007); Meng et al. (2020); Wang
(2019) However, implementing these active techniques on nanostructures is very
challenging. Heuristically, theoretical calculations have revealed that the
binding energy of molecules inside CNTs is higher than that on a graphene
layer, implying that molecules in CNTs could be more stable than those on
graphene.Henwood and Carey (2007); Fan et al. (2009); Denis and Iribarne
(2010); Kondratyuk et al. (2005) Inspired by this observation, we conducted
molecular dynamics (MD) to simulate the physisorption of hydrocarbon molecules
on a GNH nanostructure. The results indicated that, in a GNH, the molecules
could be efficiently transported into CNTs at room temperature, and then
firmly trapped inside the CNTs until released by heating. These findings
provide a solution for the passive transportation and retention of molecules
within GNHs, eliminating the need for an external driving force.

##  II Methods

The GNH nanostructure was composed of six (10,10) CNTs connected to a layer of
graphene via cylindrical holes. As illustrated in Figure 1(a), the tubes were
$11$ nm in length and $1.38$ nm in diameter, with their opposing ends capped
by the hemispheres of C240. The tubes were axially rotated to fit the graphene
holes, resulting in the formation of heptagon and hexagon rings at their
junctions, thus creating a stable configuration.Xu et al. (2012) The
simulation cell was periodic in the graphene plane, with an area of $x\times
y=6.42\times 6.30$ nm2. The 3rd dimension was $20$ and $13$ nm along $+z$ and
$-z$ from the graphene plane, respectively, resulting in a free space of
approximately $905$ nm3, including the volume of the tubes.

Figure 1:  Snapshots of the simulation cell at different time $t$ and
temperature $T$: (a) $t=0.01$ ns and $T=300$ K, (b) $t=7$ ns and $T=300$ K,
(c) $t=15$ ns and $T=700$ K.

The simulation was performed in three stages. Initially, benzene molecules
were randomly placed in the upper space, as shown in Figure 1(a). The system
was run at $T_{1}=300$ K for $7.5$ ns in a canonical ensemble with a Nosé-
Hoover thermostat applied to the GNH, resulting in configurations e.g. that in
Figure 1(b). Subsequently, the temperature was linearly increased to a higher
temperature $T_{2}$ over $3$ ns, and was kept constant at $T_{2}$ for $9.5$ ns
in order to release the adsorbates, as shown in Figure 1(c). The MD was run
for $20$ ns in $4\times 10^{7}$ steps at a time step of $0.5\times 10^{-6}$
ns, using the Verlet algorithm for time integration as implemented in the
Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).Plimpton
(1995)

The Adaptive Interatomic Reactive Empirical Bond Order (AIREBO) force field
was used to describe interatomic interactions, which incorporate both covalent
and non-covalent contributions. The covalent component is described by the
Reactive Empirical Bond Order (REBO) model,Brenner et al. (2002) which
considers the influence of bond length, bond angle, dihedral angle, bond
order, and torsion of single bond. Meanwhile, the non-covalent component is
described by a $6-12$ Lennard-Jones term to account for long-range van der
Waals (vdW) interactions. Spline regression is applied to provide a smooth
transition between covalent and non-covalent interactions, with cutoff radii
of $0.2$ and $1.1\;\mathrm{nm}$, respectively. AIREBO is widely used for
hydrocarbon systems due to its high accuracy, despite of the expense of
computation time. Its ability to describe bond rotation and torsion in terms
of bond order is particularly important in the modeling of the adsorption
process,Gao et al. (2021); Li et al. (2014) as the deformation of the
adsorbate molecule induced by the substrate, or vice versa, can be accurately
represented.Petucci et al. (2013); Hantal et al. (2010); Kostov et al. (2002);
Ni et al. (2002); Hanine et al. (2020); Qi et al. (2018); Zhou et al. (2021);
Raghavan and Gupta (2017)

##  III Results and Discussion

A set of simulations were conducted for $100$ benzene molecules on the GNH. At
$T_{1}=300$ K, the molecules were adsorbed, and then released at different
temperatures ranging from $400$ to $900$ K. Figure 2 illustrates the evolution
of the number of adsorbed molecules inside the CNTs. It is seen that the
molecules were exhaustively captured and stored within the first $6$ ns at
$300$ K. Subsequently, with increasing temperature, the adsorbates start to
dissociate from the GNH. The number of released molecules depends on the
target temperature $T_{2}$. For instance, more than $80$ molecules dissociated
at $900$ K, while only less than $5$ did so at $400$ K. The dynamic process of
molecules being adsorbed on the graphene surface and spontaneously moving into
the tubes via self-diffusion is demonstrated in a video provided in Supporting
Information, which shows the GNH working as a vacuum cleaner at nanoscale.

Figure 2:  Time evolution of the number of molecules (among 100) inside the
CNTs (upper panel), and the corresponding system temperature (lower panel).

Interestingly, the molecules firmly stayed inside the CNTs once they moved in
during adsorption. This contradicts chemical intuition as the presence of a
concentration gradient would typically hinder retention. To understand this,
we conducted a set of simulations to calculate the vdW binding energy
($E_{vdw}$) of the adsorbate on different sites of the GNH. The simulations
were performed at $300$ K with $25$ benzene molecules on a GNH composed of a
single CNT with varying sizes. The average $E_{vdw}$ of the molecules in the
CNTs was found to be almost twice higher than that of the ones on the neck
regions, and illustrated in Figure3 (a). These results indicate that the
molecules may be more strongly bound to the CNTs than the neck regions, which
explains their persistent presence inside the CNTs.

Figure 3:  (a) Mean binding energy (per molecule) between the GNH and the
adsorbed benzene molecules on different sites vs the tube diameter, at a
constant temperature of $300$ K. (b) Number of the molecules inside the CNT vs
time for different tube diameters $D$.

The variation in binding energy across the GNH can be attributed to the
alterations in its crystalline structure. Specifically, the presence of
5-7-7-5 defects in the neck regions and the curvature of the tube surface
contribute to the observed differences in binding energy. As depicted in
Figure 3 (a), the binding energy disparity between graphene and the neck
region falls within the range of $0.025-0.06$ kcal/mol. The variation in
binding energy between the tube and graphene is in the range of $0.03-0.09$
kcal/mol, dependent upon the tube size. The molecules exhibit a preference for
staying within the tubes because the binding energy is lower, rendering them
more stable compared to the neck region. However, it is unlikely that we would
observe the same effect if the outer surface is utilized for the same purpose,
as the binding energies for molecules inside the CNTs are greater than those
for adsorption outside the tubes, as suggested by Henwood and Carey.Henwood
and Carey (2007)

The binding energy for benzene molecules inside and on the surface of a CNT
was found to be significantly lower than that of the molecules on the
graphene. This is in agreement with previous calculations.Henwood and Carey
(2007); Fan et al. (2009); Denis and Iribarne (2010) Interestingly, $E_{vdw}$
on the neck region was observed to be higher than on the other two regions.
This induces a “gate” effect of the neck that locks molecules inside the CNT.
Using the GNH with the CNT diameter of $3.74$ nm as an example, a molecule
would need a kinetic energy of $\approx 0.4$ kcal/mol to overcome the barrier
and move from the graphene to the CNT. However, it would require more than
$0.8$ kcal/mol to move back to the graphene. This barrier difference could be
a reason why molecules remain steady once they have moved into the CNTs.

Figure 4:  (a) Ratio of the molecules in the CNTs vs time. (b) Absolute
binding energy of molecules of different species on graphene (black bars) and
in CNTs (red bars).

In addition to the gate effect, the collision of molecules with the neck
region could also be inhibited within the CNT. e.g. the molecules are able to
move freely to the neck region from all directions on graphene, whereas only
those molecules that are close to the neck region have the potential to do so
when they are in the CNT. The combination of the increased energy barrier at
the neck region and the reduced collision probability due to the tube-
structure may explain why molecules are mostly trapped within the CNT during
the adsorption process. Furthermore, the simulation results show a correlation
between the tube size and the speed of adsorption, as illustrated in Figure3
(b). The largest tubes, with $D=4.66$ nm, are able to adsorb molecules the
quickest, whereas the smallest tube, with $D=1.38$ nm, is seemingly filled
with $15$ molecules.

We have simulated the adsorption and desorption processes of propane C3H8,
toluene C7H8, isobutane C4H10, cyclohexane C6H12 and H2, in comparison to
benzene on a GNH, to explore the potential of the “locking” mechanism. The GNH
was composed of six CNTs as in Figure 1. The simulations were conducted with a
roughly constant gas concentration of 1.326 atom/nm3, and the temperature was
maintained at $T_{1}=300$ K for $7.5$ ns, before being heated up to
$T_{2}=700$ K in $3$ ns, after which it remained constant at $T_{2}$ for
another $9.5$ ns. The ratio of the molecules inside the CNTs with respect to
their total numbers was calculated and is plotted in Figure4 (a). The results
demonstrate that the adsorption and desorption rates vary significantly among
the different species, with C4H10 and C3H8 having the highest speeds, and
C7H8, C6H6, and C6H12 adsorbing and dissociating more slowly. The observed
differences in adsorption and desorption rates have potential implications for
gas separation applications, leveraging the selectivity and binding energy
variations.

The adsorption and desorption rates are inversely related to the absolute
binding energy between the substrate and the adsorbates. Figure 4 (b)
demonstrates that, due to their small molecular mass and aliphatic structure,
the potential well depths of C4H10 and C3H8 are lower than those of other
hydrocarbons. This results in faster adsorption and desorption of these
molecules onto and from the GNH. Conversely, C7H8, C6H12 and C6H6, which
possess higher molecular mass and aromatic-type geometry, experience strong
vdW interactions that impede their removal from the GNH at high temperatures.

Simulations have demonstrated that H2 capture is sensitive to the temperature
of the substrate. At $300$ K, only about $7\%$ of the total H2 mass was
adsorbed into the CNTs. Further simulations have been performed for H2
capture, considering $T_{1}=100,115,130,150,200$, and $250$ K and $T_{2}=300$
K. Figure 5 shows that, when $T_{1}$ was set to $100$ K, approximately $80$%
of H2 was captured within the CNTs. This ratio decreased sensitively with
increasing $T_{1}$, with only $20$% captured at $200$ K and $10$% at $250$ K.
Thus, in order to achieve effective H2 capture, say 50%, $T_{1}$ should be set
to a temperature below $130$ K. We finally note that the temperature mentioned
is currently unsuitable for practical use and requires improvement through
chemical doping, as previously suggested by Dimitrakakis et al. Dimitrakakis
et al. (2008).

Figure 5:  Ratio of H2 molecules in the CNTs vs time at different
temperatures. Inset: A snapshot of captured H2 at $100$ K when $t=7.5$ ns.

##  IV Conclusions

In this study, MD simulations demonstrated that the covalent GNH nanostructure
has the ability to transport adsorbed molecules into CNTs without any external
force, which remained inside at room temperature despite the concentration
gradient. This intriguing gate effect arises from the distinct binding energy
variations across the GNH, attributed to the presence of topological defects
in the neck regions and the curvature of the tube surface. This discovery
could potentially have implications for gas molecule storage and separation in
covalent GNH nanostructures. The simulations conducted on different species
also highlighted the distinct adsorption and desorption speeds of aromatic and
aliphatic molecules, giving insight into the selective adsorption or
separation of organic species using GNHs. Additionally, the study observed the
gate effect in the adsorption of H2 despite low temperature.

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