Characterization and Application of Nanomaterials 2025, 8(2), 10326.
https://doi.org/10.24294/can10326

Article

Functionalization of graphene by intercalation: A theoretical insight

Vittoria Urso

Department of Physics, Sapienza Università di Roma, 00185 Rome, Italy; vittoria.urso@uniroma1.it

CITATION

Urso V. Functionalization of graphene
by intercalation: A theoretical insight.
Characterization and Application of
Nanomaterials. 2025; 8(2): 10326.
https://doi.org/10.24294/can10326

ARTICLE INFO

Received: 14 November 2024
Accepted: 18 March 2025
Available online: 6 May 2025

COPYRIGHT

Copyright © 2025 Author(s).
Characterization and Application of
Nanomaterials is published by
EnPress Publisher, LLC. This work is
licensed under the Creative Commons
Attribution (CC BY) license.
https://creativecommons.org/
licenses/by/4.0/

Abstract: The intercalation of alkali metals in graphene monolayers and bilayers has been
studied using first-principles calculations in particular density functional theory. Alkali metals
intercalate into graphite, leading to the formation ofM-graphene layered materials (withM = Li,
Na, K, Rb, and Cs). Intercalated species can modify the very electronic structure of graphene
and consequently its electron mobility. Thanks to various experimental studies, it has been
possible to demonstrate that alkali metal intercalation can be used to modify the electronic
structure close to the Fermi level of the M-graphene materials and manipulate the carrier
mobility and therefore we want to do this also with computational studies. These materials
have a wide variety of applications, especially for the development of new batteries and other
devices. The first principles are discussed on the effects of the intercalation of a heavy-alkali
metal (K) on the electronic structure of graphene monolayers and bilayers.

Keywords: graphene; alkali metals; intercalation; Dirac cone shift
PACS numbers: 71.10.−w; 78.20.Bh; 81.05.ue

1. Introduction

Graphene is the most studied of two-dimensional (2D) materials [1–6], pristine
free-standing graphene has a high electron mobility, which is reduced when deposited
on a substrate due to graphene-substrate interactions [7–12]. Graphene and carbon
nanotube CNTs are among the most prominent nanoscale materials currently studied
[13]. Two-dimensional (2D) graphene [14] has a rather unique sublattice symmetry and
is a zero-gap semiconductor with a point-like Fermi surface and a linear dispersion at the
Fermi level; these properties are responsible for observed ballistic transport, Dirac-type
quasiparticles, and anomalous quantum Hall effects [15]. Graphene is a flat monolayer
of carbon atoms tightly packed in a two-dimensional (2-D) honeycomb lattice and is
a basic building block for graphitic materials of all other dimensions [16] as shown in
Figure 1.

Its interesting electrical and transport properties have attracted much attention
since its discovery in 2004. Graphene is one atom thick and its very high mobility
allows the quantum Hall effects to be observed even at room temperature [17]. Alkali
metals adsorbed onmetallic substrates have been studied for a long time [18,19], but the
nature of the alkali-substrate bond is not yet fully understood. A subset of these studies
concerns the adsorption of alkali in graphite [19]. The electronic properties of graphite
can change dramatically due to intercalators; for example, electrical conductivity along
the planes increases dramatically [19]. Potassium (K) has been the most studied of all
alkali metals intercalated on graphite [20–24]. The first step in studying the surface
structure of K in graphite is the intercalation process [25]. In Figure 2 there are some

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

methods of intercalation of K on graphite, in particular methods for investigating the
coverage of K/graphite, in the last column you can find a reference for each experiment:

Figure 1. Carbon allotropes. Top left: Graphene 2-D; top right: Graphite 3-D; bottom
left: nanotube 1-D; bottom right: fullerene 0-D [17].

Figure 2. Critical coverage for K/graphite condensation taken from reference [25].

2. Theory

Graphene is made out of carbon atoms with a structure shown in Figure 3 [26].
The lattice vectors can be written as

a1 =
a

2
(3,

√
3) a2 =

a

2
(3,−

√
3) (1)

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

where a ≈ 1.42Å. The reciprocal-lattice vectors are given by

b1 =
2π

3a
(1,

√
3) b2 =

2π

3a
(1,−

√
3). (2)

The two pointsK andK’ at the corners of the Brillouin zone (BZ) are of particular
importance, these are named Dirac points, their positions in momentum space are [26]:

K =

(
2π

3a
,

2π

3
√
3a

)
K′ =

(
2π

3a
,− 2π

3
√
3a

)
. (3)

Figure 3. Honeycomb lattice and its Brillouin zone. Left: lattice structure of graphene,
made out of two interpenetrating triangular lattices (a1 and a2 are the lattice unit vectors,
and δi, i = 1, 2, 3 are the nearest-neighbor vectors). Right: corresponding Brillouin
zone. The Dirac cones are located at theK andK ′ points [26].

The three nearest-neighbor vectors in real space are given by

δ1 =
a

2
(1,

√
3), δ2 =

a

2
(1,−

√
3), δ3 = −a(1, 0). (4)

Usually the Schrödinger equation is quite sufficient to describe the electronic
properties of materials. Charge carriers in semiconductors have a non-zero effective
mass and their behavior can be well described by Schrödinger’s equation. Graphene is
an exception [27–30]: its charge carriers behave like relativistic particles and therefore
it is more natural to describe them with the Dirac equation rather than the Schrödinger
equation [31] (see Figure 4).

The tight-binding Hamiltonian for electrons is:

H = −t
∑

<i,j>,σ

(a+σ,ibσ,j + H.c.) − t′
∑

<<i,j>>,σ

(a+σ,iaσ,j + b+σ,ibσ,j + H.c.) (5)

where t ≈ 2.8 eV is the nearest-neighbor hopping energy and t’ = 0.1 eV (obtained
from ab initio calculations) is the next nearest-neighbor hopping energy. The energy
bands have the form:

E±(k) = ±t
√
3 + f(k)− t′f(k) (6)

with

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

f(k) = 2 cos (
√
3kya) + 4 cos (

√
3

2
kya)cos (

3

2
kxa) (7)

where the plus sign applies to the upper (π∗) and the minus sign to the lower (π) band,
from Equation (7) can be seen that the spectrum is symmetric around zero energy if
t′ = 0. For a finite value of t′, the electron-hole symmetry is broken and the π and π∗

bands become asymmetric. In Figure 5 there is the full band structure with both t and
t′, there is also a zoom in of the band structure close to one of the Dirac points (at the
K or K ′ point in the BZ). This dispersion can be obtained by expanding the full band
structure, Equation (7), close to the K (or K′) vector, Equation (3), as k = K+ q, with
|q| ≪ |K|

E±(q) ≈ ±vF |q|+O[(q/K)2] (8)

where vF is the Fermi velocity, given by vF = 3ta/2, with a value of vF ≃ 1×106 m/s.
The most important difference between this result and the usual case ϵ(q) = q2/(2m),
wherem is the electron mass, is that the Fermi velocity does not depend on the energy
or momentum.

Figure 4. (A) Charge carriers are normally described by the Schrödinger equation
with an effective mass m∗ different from the free electron mass (p is the momentum
operator). (B) Relativistic particles in the limit of zero rest mass follow the Dirac
equation, where c is the speed of light and σ is the Pauli matrix. (C) Charge carriers
in graphene are called massless Dirac fermions, with the Fermi velocity vF = 1× 106

m/s playing the role of the speed of light. (D) Bilayer graphene provides us another
type of quasi-particles: they are massive Dirac fermions described by a rather bizarre
Hamiltonian that combines features of both Dirac and Schrödinger equations [31].

The coverage-dependent behavior of K/graphite is obtained by means of a
combination of one-dimensional low energy electron diffraction (LEED) and electron
energy loss spectroscopy (EELS): low covers can be prepared in which the K atoms
are partially ionized and evenly distributed over the surface due to dipole-dipole
interactions. As coverage increases, the upper layer compresses uniformly until it
reaches a critical coverage (Θ) of 0.1 monolayer (ML) [19]. Coverages below this limit
are defined as dispersed phase, while the critical coverage (0.1 ML) will be referred to
as saturated dispersed phase. At 0.1 ML, potassium forms approximately a covering
layer (7 × 7 ). Above 0.1 ML, islands (2 × 2) start to nucleate until the covering layer

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

(2 × 2) is fully developed and corresponds to Θ = 1 ML. The region between 0.1 and
1 ML will be defined as mixed phase.

Figure 5. Electronic dispersion in the honeycomb lattice. Left: energy spectrum. Right:
zoom in of the energy bands close to one of the Dirac points.

3. Computational details

Calculations are performed within the first-principles density functional theory
(DFT) under the local density approximation (LDA). Our main goal is to observe the
effect of doping on graphene, and since we are not directly interested in describing
long-range interactions or structural distortions, we focus on the simplest approach:
LDA. LDA is sufficient to observe charge transfer from the alkali metal to graphene,
changes in the electronic bands of graphene, such as filling of conduction bands, and
changes in local electronic properties, such as the change of the density of states (DOS)
near the Fermi level. LDA is an approximation that works well when dispersion
effects (van der Waals forces) are not dominant or are not crucial for the interaction
between the alkali metal and graphene; there are no large structural distortions in the
graphene lattice that significantly affect the geometry or symmetry of the electronic
bands. LDA is preferred in all cases like these for computational simplicity because it
is less computationally expensive than GGA making it more suitable for preliminary
studies or large-scale simulations and for the description of local electronic changes;
and because LDA can provide an accurate idea of the change in electron density and
energy levels as a result of doping without the need to deal with the weak interactions
between the alkali metal and graphene. In practice we use the so-called “rigid band
model”, a simple model in which the interaction between graphite and an adsorbate
or intercalant is limited to the donation or removal of the charge by the atom, with no
other influences on the graphite bands [19]. The model thus allows us to understand
the observed binding energy shifts, estimate the amount of charge transferred, etc.
The QUANTUM ESPRESSO package is used to perform all calculations [32]. The
primitive unit cell and the experimental value of the lattice constant are shown inFigure
6, my calculated lattice constant is 2.44Å =

√
3×1.41Å, which is slightly smaller than

the experimental value.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

  

Figure 6. On the left: Model of (a) two-dimensional and (b) three-dimensional
graphite together with the structural parameters. In (a), the surface unit cell, containing
two C atoms, is highlighted. On the right: A schematic diagram of the (2 × 2) structure
formed by K on the graphite surface. Both the substrate and the overlayer unit cells are
represented [25].

Calculations for the isolated graphene layer (2 × 2) and (4 × 4), the isolated adatom
layer (2 × 2) and (4 × 4), and the adatom-graphene system (2 × 2) and (4 × 4) are
performed with the same hexagonal supercell. The Brillouin zone is sampled with
a grid of 8 × 8 × 1 k points centered on Γ, and Gaussian smearing with a width of
σ = 0.01 eV is used for the occupation of the electronic levels. A larger supercell
improves the description of the interactions between alkalines and graphene, reducing
periodic confinement effects and improving the convergence of physical properties.
Finer sampling of the Brillouin zone allows for a better description of electronic bands
and densities of states, especially in regions close to the Dirac points of graphene. With
alkaline intercalation, the effect on electronic bands (e.g., shifting of conduction bands
or formation of new states) can be more precisely predicted. The self-consistency
convergence threshold was set at 1.0d−9, the convergence threshold on total energy at
1.0d−5, and the convergence threshold on forces (a.u.) at 1.0d−4. We have performed
calculations of K on graphite at the H site; see Figure 7:

Figure 7. The three adsorption sites: Hollow H, bridge B, and top T [33].

4. Results

We have analyzed 11 different systems through self-consistent field calculations
with QUANTUM ESPRESSO under the local density approximation (LDA) and
Perdew-Zunger functionals and the Von Barth-Car method (pz-vbc), including spin
polarization, and we have obtained the results showed in Table 1:

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

Table 1. The results of all systems, the greater the shift of the Dirac cone the greater
the doping.

System
Total energy (eV)
/num. atoms

Schift Dirac
cone (eV)

dk−graphene

(Å)

1. KC8 −138.9405 −1.07 2.89
2. KC32 −150.6698 −0.90 2.73
2bis. KC32 (s = 2) −150.6703 −0.88 2.73
3. K4C32 −138.9397 −1.07 2.93
4. K4C32 (alt. side) −138.9153 −1.18 2.84
5. K4C32 (check.) −138.9153 −1.18 2.83
6. C8KC8 (st. AB) −146.5524 −1.07 2.84
7. C8KC8 (st. AA) −146.5547 −1.18 2.85
8. KC8C8 −146.54465 −1.07 2.91
9. KC8C8K −138.9507 −1.07 2.92
10. KC2 −105.6311 −2.30 2.66
11. K2C32 −146.5225 −0.98 2.83

The following subsections show the systems visualized with xcrysden and the
DOS visualized with xmgrace.

4.1. KC8

In Figure 8 theKC8 system is shown and in Figure 9 its DOS.

  

Figure 8. In the upper there is theKC8 system in top view (on the left) and in side view
(on the right) in (2 × 2) unit cell and in the lower there is the replicated KC8 system
in the top view (on the left) and in the side view (on the right) in (6× 6) unit cell. The
carbon-carbon distance is dc−c = 1.4106Å.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

Figure 9. The DOS (density of states) of the KC8 system, on the left the full DOS and on the right a range of energy
around the Fermi level.

In Figure 10 are shown the PDOS (projected DOS).

Figure 10. The full and its partial DOS s and p.

4.2. KC32

In Figure 11 theKC32 system is shown and in Figure 12 its DOS.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

  

Figure 11. In the upper there is the KC32 system in top view (on the left) and in side
view (on the right) in (4 × 4) unit cell and in the lower there is the replicated KC32

system in the top view (on the left) and in the side view (on the right) in (12× 12) unit
cell. The carbon-carbon distance is dc−c = 1.4106.

Figure 12. The DOS of the KC32 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

Only in this case do we have a magnetic case as shown in Figures 13 and 14.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

Figure 13. The DOS of theKC32 system with spin = 2, on the left the DOS of my calculation and on the right the DOS
of Figure 3 of the reference [34].

Figure 14. The DOS of theKC32 system with spin = 2, on the left a range of energy around the Fermi level of my DOS
and on the right Figure 4 of the reference [34].

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

4.3. K4C32

In Figure 15 theK4C32 system is shown and in Figure 16 its DOS.

  

Figure 15. In the upper there is the K4C32 with (4 × 4) cell and in the lower there is
the replicatedK4C32 system. The carbon-carbon distance is dc−c = 1.4102.

Figure 16. The DOS of theK4C32 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

4.4. K4C32 with K on alternate side
In Figure 17 the K4C32 with K on alternate side system is shown and in Figure

18 its DOS.

  

Figure 17. In the upper there is the K4C32 system with (4 × 4) cell and in the lower
there is the replicatedK4C32 system. The carbon-carbon distance is dc−c = 1.4119.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

  

Figure 18. The DOS of theK4C32 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

4.5. K4C32 with K at checkerboard
In Figure 19 the K4C32 with K at checkerboard system is shown and in Figure

20 its DOS.

  

Figure 19. In the upper there is the K4C32 system with (4 × 4) cell and in the lower
there is the replicatedK4C32 system. The carbon-carbon distance is dc−c = 1.4111.

  

Figure 20. The DOS of theK4C32 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

4.6. C8KC8 with stacking AB
In Figure 21 the C8KC8 with stacking AB system is shown and in Figure 22 its

DOS.

  

Figure 21. In the upper there is the C8KC8 system with (2× 2) cell and in the lower
there is the replicated C8KC8 system. The carbon-carbon distance is dc−c = 1.4131.

  

Figure 22. The DOS of the C8KC8 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

4.7. C8KC8 with stacking AA
In Figure 23 the C8KC8 with stacking AA system is shown and in Figure 24 its

DOS.

  

Figure 23. In the upper there is the C8KC8 system with (2× 2) cell and in the lower
there is the replicated C8KC8 system. The carbon-carbon distance is dc−c = 1.4121.

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Figure 24. The DOS of the C8KC8 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

4.8. KC8C8

In Figure 25 theKC8C8 system is shown and in Figure 26 its DOS.

  

Figure 25. In the upper there is the KC8C8 system with (2× 2) cell and in the lower
there is the replicatedKC8C8 system. The carbon-carbon distance is dc−c = 1.4083.

  

Figure 26. The DOS of theKC8C8 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

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4.9. KC8C8K
In Figure 27 theKC8C8K system is shown and in Figure 28 its DOS.

  

Figure 27. In the upper there is theKC8C8K system with (2×2) cell and in the lower
there is the replicatedKC8C8K system. The carbon-carbon distance is dc−c = 1.4100.

  

Figure 28. The DOS of the KC8C8K system, on the left the full DOS and on the right a range of energy around the
Fermi level.

4.10. KC2

In Figure 29 the C8KC8 system is shown and in Figure 30 its DOS.

  

Figure 29. In the upper there is theKC2 system with (1×1) cell and in the lower there
is the replicatedKC2 system. The carbon-carbon distance is dc−c = 1.50.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

  

Figure 30. The DOS of the KC2 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

4.11. K2C32

In Figure 31 the C8KC8 system is shown and in Figure 32 its DOS.

  

Figure 31. In the upper there is the KC16 system with (2 × 2) cell and in the lower
there is the replicatedKC16 system. The carbon-carbon distance is dc−c = 1.4106.

  

Figure 32. The DOS of the KC16 system, on the left the full DOS and on the right a range of energy around the Fermi
level.

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

5. Conclusions

Chemical doping is a natural way to increase the performance or personalize the
properties of graphene or any other 2D material. The band gap can be produced in
graphene by chemical doping with a significant reduction in its carrier mobility [35].
However, there are several methods for modifying the band gap of graphene without
the use of traditional chemical doping. These approaches exploit geometry, physical
interactions (such as quantum confinement [36] or strain engineering [37]), and
structural modifications such as oxidation [38] or the use of multilayer structures [39]
to achieve semiconductor-like electronic behavior, opening the band gap of graphene,
or simply the application of electric fields [40]. After doping graphene, several
mechanisms contribute to the reduction of charge carrier mobility. The main ones
are the following: impurity scattering [41], phonon scattering (lattice vibrations) [42],
defect [43] and dislocation scattering, local structure distortions. The computational
results obtained are well compared to the experimental data of reference [44] shown in
Figure 33 and with some literature dealing with this topic [45–52] and could be useful
for predicting material properties [53,54].

Figure 33. (a) UV photoemission spectral density of the K-NPG system as a function
of K exposure (spectra vertically stacked for the sake of clarity). (b) Perspective 3D
view of the spectral density evolution of the VB close to the Fermi level (black line) as
a function of K dose; the Dirac point energy shift ΔE due to charge injection is reported
as a red line in the top projection of the 3D perspective view. (c) Experimental spectral
density of K-NPG at saturation coverage (red line) compared with clean NPG, shifted
by −0.6 eV in spectral density (gray filled area) [44].

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

The experimental results of Figure 33 are obtained with UPS, ultraviolet
photoelectron spectroscopy, (h̄ν = 21.2 eV and h̄ν = 40.8 eV whose sources
are HeI and HeII, respectively) used to probe the surfaces of materials (see Figure
34). The most significant observation is an intensity peak at the Fermi energy EF

in the intercalation compounds. This peak is mainly due to alkali-like s states [55].
Photoelectron spectroscopy is the most powerful and versatile technique to study the
electronic structure of the valence bands in atoms, solids, and molecules (ionization
energy of molecules, HOMO).

Multiplying the DOS of the computational calculations with the Fermi-Dirac
distribution f(E), we get the density of conduction electrons at any particular energy
N(E) = DOS · f(E). For the Koopmans Theorem we have Ii = −ϵi, where Ii is
the binding energy of an electron in the state i and ϵi is the orbital energy of the state
i-th. Identification of calculated orbital energies with ionization potentials is possible
as shown in Figure 35.

Figure 34. With XPS (with hν > 1000 eV) the electron emission is a good reflection
of the density of states (weighted by the transition rate across the VB). At low photon
energies (hν < 50 eV) as in UPS the situation is more complex but richer in
information.

Figure 35. Left: Computational results for pristine graphene (QUANTUM ESPRESSO (qe) C8) and K-doped graphene
(qe K4C32 instead of KC8 and KC32) compared with experimental results from reference [44]. Right: A zoom of the
same data.

UPS results involving a coverage of 0.3–0.4 ML are very similar to those obtained
computationally with QUANTUM ESPRESSO for theKC32 system (1 ML→ KC8).
Finally, it is possible to observe from the total energy values of systems 6,7 and 11 that
the bilayer is more favored than the monolayer (it is also possible to verify this for the
KC8 systems) and this compares well with other works [56–58].

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

The electron donating ability of alkalis, which increases as we move down the
group, from Li to Cs [59–66], changes the electronic balance and therefore shifts the
Fermi level. Li being the lightest and having a low electronegativity has a tendency
to easily donate its valence electron to the graphene surface. Consequently, the
introduction of Li is expected to shift the Fermi level upwards, potentially increasing the
density of electronic states near the Fermi level. This could increase the conductivity
of the system and, in some cases, lead to metallic behavior. Na, although larger than Li
maintains a similar behavior, the Fermi level could shift even higher than pure graphene,
but to a lesser extent than Li. K being larger than Na tends to donate its valence electron
even more easily, but the bond strength between graphene and the adatom is generally
weaker. It could be observed that the interaction of potassium with graphene leads to a
marked upward shift of the Fermi level but due to the lower electron affinity the effect
may be more transient or less stable. Rb and Cs [67], the heavier of the family, the
adatomics become even more reactive and tend to donate electrons to graphene more
easily. However, the chemical stability of systems with Rb [68] and Cs may decrease,
since these alkali atoms tend to have a low adhesion energy to graphene, leading to
possible desorption phenomena at relatively low temperatures. In these cases, it could
be observed significant shifts of the Fermi level, but with a less stable behavior over
time, especially at high temperatures. The interaction between graphene and alkali
adatomics, as we have seen, also affects the band structure of the system, in particular
the Dirac cone, Li adsorption on graphene may cause minimal distortion of the Dirac
cone, but the symmetry of the cone should remain fairly intact. However, a shift in the
Fermi level upwards can make the systemmore conductive. At low concentrations, this
effect may not be sufficient to significantly alter the structure of the Dirac cone, but at
higher concentrations, changes in the symmetry of the band structure may emerge, with
stronger coupling between the graphene electrons and the Li p-orbitals [69]. When Na
and K are adsorbed on graphene they can influence the Dirac cone more pronouncedly.
The stronger coupling between the alkali s-orbitals and the graphene p-orbitals may
lead to more pronounced distortions in the Dirac cone, changing the shape and position
of the conduction and valence bands. In particular, the stronger interaction with Na
and K may also affect the characteristic symmetry of graphene, leading to asymmetric
effects in the cone [70]. For Rb [71] and Cs [72], the interaction with graphene is
weaker, but the change in band structure could be significant in terms of the shift and
deformation of the Dirac cone. We may see asymmetric deformations in the Dirac
cone and a reduction in band structure symmetry, as the heavier alkali adatomics can
more strongly influence the local electronic properties of graphene. Li and Na are more
stable than their heavier counterparts. Their reactivity may be more easily manageable
under experimental conditions, although their adhesion to graphene may not be very
strong. This means that the adatom can remain stably adsorbed on graphene, with little
problem of desorption at moderate temperatures. K, Rb, and Cs are more reactive and
less stable on the graphene surface. These adatomics tend to desorb easily at higher
temperatures, and thus the system may not be viable in long-term devices, especially
if thermal stability is critical. They could also change the structure of graphene more
dramatically, causing structural deformations. Li could be used to improve electronic

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Characterization and Application of Nanomaterials 2025, 8(2), 10326.

conductivity in batteries or other electronic devices. Its high reactivity with graphene
could also make it useful for improving energy storage. Na [73] and K are useful
for applications where increased conductivity is needed but long-term stability is less
critical (e.g., short-lifetime devices or fuel cells). Rb and Cs, due to their low stability
on graphene, are not ideal for electronic devices that require stable performance over
time. However, they could be explored in transient systems or in basic research.

Data availability statement: All data generated or analyzed during this study are
included in this published article.

Institutional review board statement: Not applicable.

Informed consent statement: Not applicable.

Conflict of interest: The author declares no conflict of interest.

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22


	Introduction
	Theory
	Computational details
	Results
	KC8
	KC32
	K4C32
	K4C32 with K on alternate side
	K4C32 with K at checkerboard
	C8KC8 with stacking AB
	C8KC8 with stacking AA
	KC8C8
	KC8C8K
	KC2
	K2C32

	Conclusions