Chemically Functionalized Penta-Graphene for Electronic Device Applications: Journey from Theoretical Prediction to Practical Implementation

Ghosh, Kasturi; Rahaman, Hafizur; Bhattacharyya, Partha

doi:10.1007/978-981-32-9057-0_14

Kasturi Ghosh¹⁰,
Hafizur Rahaman¹⁰ &
Partha Bhattacharyya¹¹

Part of the book series: Carbon Nanostructures ((CARBON))

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Abstract

Penta-Graphene (PG), proposed in 2014 on the basis of theoretical simulations, is a two dimensional (2D) metastable carbon allotrope composed of carbon pentagons. PG is proposed to be synthesized by exfoliation from T12-carbon by hydrogen intercalation. Theoretical calculations confirm that PG is appreciably stable and can sustain the temperature as high as 1000 K. Unlike graphene which needs to be functionalized for opening a band gap, PG is itself a quasi-direct band gap semiconductor having a band gap of ~3.25 eV. PG offers an unusual negative Poisson’s ratio and very high mechanical strength exceeding than that of graphene. According to prediction, successful synthesis of penta-graphene may bring forth considerable makeover in future nano-electronics arena. However, synthesis of PG is still a challenge. It is not only difficult to isolate PG from the plethora of alternative isomers; it may rapidly restructure itself towards graphene in the presence of even a trace amount of specific catalytic impurities. Though unstable in its pure form, theoretical simulation shows suitable chemical functionalization stabilizes the penta-graphene structure by partially releasing the strain, which paves the path towards successful synthesis of penta-graphene considering its functionalized state as the precursor. In this book chapter, the strikingly interesting features/properties, procedure for predicting the characteristics through theoretical simulations, synthesis process, potential applications and critical bottlenecks of functionalized penta-graphene have been comprehensively discussed with special emphasis on its future prospects for next generation electronic device applications. Mainly three types of chemical functionalizations have been considered employing (i) hydrogen, (ii) fluorine and (iii) oxygen. Improvement of stability of functionalized PG, in terms of energy, lattice dynamics, mechanical and thermal in comparison to that of pristine PG have been discussed. Underlying mechanism for the corresponding dramatic improvement in electronic, mechanical and thermal properties of PG for the above mentioned functionalization(s) have also been discussed. Hydrogenation and fluorination of PG changes the Poisson’s ratio from negative to positive and turns the PG from a semiconductor to an insulator. Thermal conductivity of PG enhances dramatically on full hydrogenation. The three types of functionalizations mentioned above, improve mechanical strength of PG by enhancing the value of failure stress and failure strain. Chemical functionalizations widen the application potentiality of PG. Improvement in thermal conductivity of PG by partial functionalization facilitates its application in thermoelectric devices. Band gap tailoring by judicious chemical functionalization lays the foundation stone for future application of PG in the field of optoelectronic and photovoltaic devices. Hydrogen adsorption remarkably enhances the magnetic moment of PG which is useful for potential application in magnetic storage technology and next generation spintronic nano-devices. However, the practical implementation (synthesis and subsequent technology development to couple it successfully with device fabrication) is still in nascent stage and the future research endeavor of the researchers is inclined towards mitigating that bottleneck.

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Keywords

1 Introduction

Carbon, the most important and major constituent of the cycles on the Earth, is also an interesting and versatile element in the periodic table due to its enormous flexibility in bonding characteristics. The vast and ever expanding family of carbon allotropes, constructed with sp³, sp² and sp hybridized orbitals, offer a wide range of hierarchical nano-structures ranging from three dimensional (3D) to zero dimensional (0D) variety (such as, diamond (3D), graphene (2D), nanotubes (1D) and bucky balls (0D)) [1]. Such carbon allotropes are also be characterized with diversified material properties (viz., the electronic property of Carbon allotropes can vary drastically over the range; from metal to insulator). Graphene, constructed with sp² hybridized carbon atoms arranged in a hexagonal honeycomb lattice (2D), has initiated a new era in nano-electronics due to its unprecedentedly advantageous electronic properties. The great success of graphene has triggered the interest of the researchers across the globe in exploring other 2D nanomaterials specially based on carbon [2]. Since then, a number of low-dimensional carbon allotropes have been proposed from theoretical consideration [3,4,5], among which Penta-Graphene (PG) is one of the most remarkable one. Zhang et al. first identified penta-graphene by simulation in 2014 [5]. It is a two dimensional metastable carbon allotrope and is constructed from a mixture of sp²- and sp³ hybridized carbon atoms arranged in pentagonal lattice which closely resembles to the well-known Cairo pentagonal tiling. The key difference between PG and graphene is that graphene is zero band gap material whereas penta-graphene is a semiconductor with a finite band gap of ~3.25 eV [5]. Although experimental synthesis of PG is still a crucial challenge, some of its unique electronic, thermal, mechanical, magnetic and optical features and their tunability through suitable functionalization (as predicted from theoretical studies) projected this material as a potential candidate for applications in nano-electronics and nano-mechanics for the coming era. Like graphene, PG can also form nanoribbon and nanotube structure which are beyond the scope of this chapter [6,7,8,9].

Prediction of either the existence of a material or the properties of a material (theoretically proposed or already existing) can be decided from “Density functional theory” (DFT) and “Molecular Dynamics” (MD) based calculations. DFT is the most successful ab initio/ first principle calculation which is based on the quantum mechanical description of the material and governed by the laws of condensed matter physics [10,11,12]. The underlying principle is that “the total energy of the system is a unique function of the electron density”. DFT calculations are based on ‘Kohn–Sham (KS)’ method which is an independent particle method for many-body electron problem. The framework of DFT is based on computing the ground state energy and charge density of many body system of electron by solving a set of Schrödinger like equations representing a fictitious but simplified system of non-interacting electrons moving in an effective potential [11, 12]. “Effective potential consists of external potential, Coulomb potential and Exchange-correlation (XC) potential. The XC potential is a measure of the quantum mechanical exchange and correlation of the particles” [13]. XC potential plays critical role in DFT calculation. The ground state energy of the material is identified from DFT calculation. “Ab initio Molecular Dynamics” (AIMD) simulation calculate the dynamics for systems for which the interatomic forces are derived from DFT based calculations.

The possibility of existence of penta-graphene and its properties were first predicted by Zhang et al. with the help of DFT based AIMD simulations performed using Vienna Ab initio Simulation Package (VASP) [14]. Interactions between ion cores and valance electrons were treated with “Projector augmented wave” (PAW) basis set [15]. Proper choice of “exchange-correlation” (XC) potential function is important for predicting material properties using DFT based calculations. Zhang et al. [5] used “generalized gradient approximation” (GGA) with ‘Perdew–Burke–Ernzerhof’ XC potential for most of the calculations. Since, electronic band structure calculations demand high precision, Zhang et al. [5] used ‘hybrid Heyd–Scuseria–Ernzerhof’ (HSE06) XC potential [17] only for calculation of electronic band structure of penta-graphene. ‘Phonopy package’ was used to determine phonon properties of PG using finite displacement method.

It is well established that electronic, magnetic, optical and mechanical properties of graphene can be tuned effectively by chemical functionalization [18, 19]. This triggered the curiosity among the researchers to find a way of tuning of various properties of PG through chemical functionalization. Although, penta-graphene is proposed very recently and its research is in very nascent stage, it is found that chemical functionalization will significantly widen the application of PG in electronic devices. Bonding characteristics (transformation from sp² to sp³, change of bond length, angle etc.), electronic and phonon band structure of PG change upon chemical functionalization which is reflected in electronic, thermal, mechanical, optical and magnetic properties of the same. Thus, the properties of PG can be tuned for suitable electronic device application employing judicious chemical functionalizations. The property of PG can also be changed by doping which is out of scope of this book chapter [20,21,22].

2 Structure and Properties of PG

Penta-graphene was first theoretically proposed by Zhang et al. in 2014 by exfoliation of single layer from T12-carbon, whose existence is also recently predicted from DFT based calculations [5]. PG shows tetragonal lattice structure with six carbon atoms per unit cell having optimized lattice parameters; a = b = 3.64 Å. The carbon atoms in PG shows two types of hybridization viz. sp³ and sp² which are customarily distinguished as C1 and C2, respectively [5].

Figure 1 shows the top and side view of the optimized structure of penta-graphene along with its the first Brillouin zone in reciprocal lattice space identifying the high symmetry path Γ–M–X–Γ where Γ = (0, 0, 0)2π/a, M = (1/2, 1/2, 0)2π/a and X = (0, 1/2, 0)2π/a. From the top view, PG looks like Cairo pentagonal tiling. Carbon-carbon bond lengths in PG are 1.55 Å (C1–C2) and 1.34 Å (C2–C2) which show pronounced character of single and double bonds, respectively. However, these bond lengths differ from the carbon-carbon bond length in diamond and graphite/graphene which are 1.54 and 1.42 Å, respectively. Thus, the bonding characteristics in PG are somewhat different than well-known diamond and graphite/graphene structure. The bond angle (θ_C2–C1–C2) in PG is 134.2^° which also indicate the distorted sp³ character of C1 atoms. Since, sp³ carbon bonds are tetrahedral in nature; penta-graphene is not truly a planner structure [23]. A buckling of 0.6 Å is observed from the side view of PG. Thus, PG is a two dimensional sheet having a thickness of 1.2 Å. The structure of PG can be viewed as a “multidecker sandwich”, where the sp³ hybridized C atoms (C1) are sandwiched between the sp² hybridized C atoms (C2). It is interesting to note that the structure of PG is similar to experimentally identified layered silver azide (AgN₃) [5].

2.1 Stability Issues

Whenever a material is proposed theoretically, the first question arise regarding the stability of the material which can also be viewed as the feasibility of practical existence/synthesis of the material. Study of stability includes identifying ground state energy from the calculation of total energy by DFT as well as the behavior of the system in other perturbation like thermal, mechanical etc. Ab initio MD simulation within the framework of DFT is essential in studying the behavior of the system in perturbation.

Energetic Stability

Thermodynamic stability of penta-graphene has been examined by means of total energy calculation. PG is identified as metastable in comparison to graphene and other two dimensional carbon allotropes due to its violation of the IPR (isolated pentagon rule) [24]. However, it is more stable than some other nanostructures of carbon, like, 2D α-graphyne, 3D T-carbon and (3, 12)-carbon sheet [5].

Figure 2a shows the area dependence of total energy of penta-graphene along with graphene, graphyne, C₂₀, (3, 12)-carbon sheet, a-graphyne [5]. It can be envisaged that penta-graphene is energetically stable than some experimentally synthesized carbon nanostructures such as, the smallest carbon nanotube and C₂₀ (smallest fullerene). This study, therefore, affirmatively, indicates towards possibility of synthesis of the 2D penta-graphene sheet. The structural unit of both of the carbon allotropes, C₂₀ and penta-graphene is fused pentagons. Since C₂₀ is a highly curved structure, all carbon atoms in it are in strained condition with distorted sp² hybridization. On the contrary, in penta-graphene, the curvature is reduced due to the presence of sp³ hybridized carbon atoms along with sp² hybridized carbon atoms and thus the strain is released partially [5].

Dynamic Stability

Calculation of lattice vibration gives the phonon dispersion curve which determines whether a crystalline structure is dynamically stable or not. For a dynamically stable crystal structure, there should not have any imaginary frequency in entire Brillouin zone [25]. Phonon band structure and phonon DOS of PG are shown in Fig. 2b. The dynamic stability of penta-graphene is confirmed from the absence of imaginary frequencies in entire Brillouin zone i.e. in all high symmetry directions. Like graphene, three distinct acoustic modes are observed in phonon band structure of PG [5].

Thermal Stability

To ensure the thermal stability, Zhang et al. performed “Ab initio molecular dynamics” (AIMD) simulation (using canonical ensemble) of 2D supercell of penta-graphene [5]. No structural reconstruction is observed for 6 ps with a time step of 1 fs, at room temperature (300 K). It is revealed, penta-graphene can sustain temperatures as high as 1000 K. PG is found to be dynamically stable even in presence of different types of defects like Stone–Wales-like defect, mono and di-vacancies, edge atoms and adatoms [5].

Mechanical Stability

To ensure the feasibility of practical existence of a theoretically proposed material, it is necessary to know the effect of lattice distortion on structural stability. The linear elastic constants of a mechanically stable crystal should follow the “Born–Huang criteria” to guarantee the positive-definiteness of strain energy caused by lattice distortion. Accordingly, the four nonzero 2D elastic constants viz., C₁₁, C₂₂, C₁₂ and C₆₆ should satisfy the criteria $ C_{11} C_{22} - C_{12}^{2} $ and C₆₆ > 0 in a mechanically stable 2D sheet [26]. From the calculation of the change of energy due to the in-plane strain (uniaxial and biaxial), PG was found to satisfy the above criteria [5].

2.2 Properties of Pristine PG

Confirmation of stability of the material invokes the curiosity regarding the properties of penta-graphene. Researches are in progress in investigating the electronic, thermal, mechanical, magnetic, optical properties of penta-graphene [5, 20, 23, 27,28,29,30].

Electronic Properties

From the computation of band structure using—Scuseria–Ernzerhof (HSE06) potential functional, penta-graphene is found to be an indirect band-gap semiconductor with a band gap of ~3.25 eV (computed with HSE06 potential function) [5]. Figure 3 shows the electronic band structure of PG computed with hybrid HSE06 potential function (solid lines) and GW correction (dotted line). It is observed from the electronic band structure that the conduction band minimum lies on the M–Γ path whereas the valance band maximum (VBM) is located on the Γ–X path. However, there exists a sub-VBM on the M–Γ path whose energy value is very close to that of true VBM [5]. Thus, penta-graphene can also be considered as a “quasi-direct–band-gap” semiconductor. Analysis of partial DOS reveals that the major contribution of electronic states near the Fermi level is due to the sp² hybridized C2 atoms. In penta-graphene, the p_z orbitals of sp²-hybridized C2 atoms are spatially separated by the sp³-hybridized C1 atoms. Thus, full electron delocalization is hindered which gives rise to finite band gap. According to Zhang et al., there is possibility to achieve superconductivity in penta-graphene through hole doping since there are dispersion-less, partially degenerate valance bands which leads a high total DOS near the Fermi level [5, 31].

Mechanical Properties

The elastic strain per unit area in a 2D material can be expressed as [5];

$$ U = \frac{1}{2}C_{11} \varepsilon_{xx}^{2} + \frac{1}{2}C_{22} \varepsilon_{yy}^{2} + \frac{1}{2}C_{12} \varepsilon_{xx}^{2} \varepsilon_{yy}^{2} + 2C_{66} \varepsilon_{xy}^{2} $$

(1)

where the constants, C₁₁, C₂₂, C₁₂ and C₆₆ are the components of the elastic modulus tensor and can be obtained from second order partial derivative of strain energy as a function of strain. $ \varepsilon_{xx} $, $ \varepsilon_{yy} $ and $ \varepsilon_{xy} $ are the components of strain tensor. C₁₁, C₂₂, C₁₂ and C₆₆ can be obtained by fitting the energy curves as a function of with uniaxial ($ \varepsilon_{yy} = 0 $) and equi-biaxial strains ($ \varepsilon_{xx} = \varepsilon_{yy} $).

Young’s modulus of a material is defined as $ E = \left( {C_{11}^{2} - C_{12}^{2} } \right)/C_{11} $ [5]. The value of Young modulus in penta-graphene is found to be 263.8 GPa nm whereas the corresponding value is 345 GPa nm in case of graphene [32]. The value of Young modulus in penta-graphene is comparable to that of h-BN monolayer [33].

Another important parameter which articulates the mechanical property of a material is Poisson’s ratio. It is defined as the negative ratio of the transverse strain to the corresponding axial strain. In case of most of the solids, this ratio is positive since under a uniaxial compression, solids expand in the transverse direction. Although the continuum mechanics theory does not discard the possibility of existence of negative Poisson’s ratio (NPR) in a stable linear elastic material, it is rarely found in nature. Very few artificial materials are characterized with NPR. Materials with NPR, known as “auxetic materials”, are of great scientific and technological interest [34, 35]. The major area of application of “auxetic materials” are in biomedical field as a material for structure/muscle/alignment anchors, surgical implant, prosthetic materials, dilator to open up blood vessels during heart surgery etc. Other application field of “auxetic materials” is piezoelectric sensors and actuators. Auxetic foams and fibers find application in filters and woven structures. Interestingly, penta-graphene exhibit negative Poisson’s ratio viz., ν12 = ν21 = C12/C11 = − 0.068 since C12 is negative for PG [5].

The NPR characteristics of PG has been testified comprehensively for both of the cases i.e. the lateral response in the x direction when the tensile strain is applied in the y direction and vice versa. Penta-graphene as a nano-auxetic material may have multiple applications in micro-mechanical and micro-electromechanical systems (MEMS).

In addition to in-plane stiffness, ideal strength (i.e. the maximum stress that a material can sustain) is also an important mechanical property of a nanomaterial. Figure 4a shows the stress–strain relationship of penta-graphene under equi-biaxial tensile strain [5]. It is observed from the curve that the strain at maximum stress is 21% (denoted by red arrow) beyond which the mechanical failure starts. However, the critical strain is less than 21% for penta-graphene since phonon instability i.e. phonon softening induced by Kohn anomaly occurs before the stress reaches its maximum [5, 36]. Figure 4b and c represent Phonon bands at the extreme of equi-biaxial strain of penta-graphene and graphene, respectively. It is found that in case of penta-graphene, phonon softening arise when the equi-biaxial strain reaches 17.2% whereas the corresponding value is 14.8% for graphene. Thus, the ideal strength of PG is higher than that of graphene. At the critical strained condition, the single bond lengths between C1 and C2 atoms are found to be ~1.77 Å, which is comparable with the experimentally and theoretically reported longest C–C bond length. Beyond critical strength, the structure fracture starts through breaking of the bonds between C1 and C2 atoms.

Thermal Property

Thermal conductivity is an important physical parameter which asses heat dissipation ability of a material and high temperature application possibility. Joule heating is a major problem in electronic devices which affect performance, reliability and life time of the device. Moreover, lower heat capacity of nano-electronic devices is a critical issue. Hence, the device material should be thermally highly conductive so that the generated heat during device operation can dissipate fast. On the other hand, thermoelectric devices demands lower thermal conductivity. Although graphene is characterized with ultrahigh lattice thermal conductivity (3000–5800 W/mK), the absence of bandgap limits its application in most of the electronic devices including transistor. From the solution of linearized phonon “Boltzman transport equation” (BTE) with first principle calculation, lattice thermal conductivity of PG is found to be 645 W/mK at room temperature which is significantly lower in comparison to that of graphene. The presence of more scattering channels in buckled penta-graphene structure may be the possible reason behind significantly lower thermal conductivity of PG in comparison to that of graphene [27]. It is found that lattice thermal conductivity of stacked PG does not depend on the number of layers present. This characteristic of PG is also in sharp contrast to that of graphene. In metals, the thermal conductivity is mainly due to electrons while in semiconductors and insulators, phonons play a significant role in determining the resultant thermal conductivity.

From “classical equilibrium molecular dynamics simulations” using the original “Tersoff interatomic potential”, the intrinsic thermal conductivity of PG is found to be 167 W/mK [28]. In PG, the acoustic phonon lifetimes are 20 ps and 1–10 ps for lower (1–5 THz) and higher (5–15 THz) frequency range, respectively which are comparable to that of the graphene. However, the remarkably lower thermal conductivity of PG, in comparison to graphene, arises from the lower phonon group velocities and fewer collective phonon excitations in PG.

In penta-graphene, the phonon scattering rate is proportional to temperature and consequently, the thermal conductivity is inversely proportional to the temperature [28]. The variation of thermal conductivity of PG as a function of size of the simulating sample for constant temperature (300 K) is shown in Fig. 5a. Figure 5b shows the variation of thermal conductivity of PG as a function of temperature for a fixed size of the simulating sample (60 × 60 unit cell). From non-equilibrium molecular dynamics (NEMD) simulations using ReaxFF force field, thermal conductivity of infinitely long penta-graphene is found to be 112.35 W/mK [37]. The cause behind the difference in results is due to the method of simulation and the type of interatomic force field employed. Researchers are still in search of appropriate potential for penta-graphene [3].

Optical Property

Although Kohn-Sham DFT estimate ground state energy most successfully, it cannot assess optical absorption accurately since “Kohn-Sham DFT eigenvalues” do not consider the electron addition and removal energies. It is necessary to include the calculation of electron-hole interaction to get information regarding the optical spectra. GW (G₀W₀) approximation/correction is a “many-body perturbation theory” which can successfully predict the optical properties of the materials. In this method, ground state energy and electronic density are computed by DFT Kohn-Sham framework and then, G₀W₀ i.e. the green function G and dynamically screened interaction W is computed from the obtained Kohn-Sham electronic structure. Applying G₀W₀ correction, the “quasi-direct band gap” of PG is found to lie in the range of 4.1–4.5 eV which corresponds to ultra-violet region (wavelength for optical absorption). Since visible light is not absorbed in PG, it is transparent in nature and photoelectron can’t be produced easily in PG [23].

3 Hydrogen Functionalization of Penta-Graphene

Hydrogen functionalization is the most widely studied functionalization method for penta-graphene. It is found that hydrogen functionalization not only stabilize the structure of penta-graphene but also tune its property flexibly.

Among sp³ (i.e. C1 atom) and sp² (i.e. C2 atom) hybridized carbon atoms in penta-graphene, only sp² hybridized carbon atoms are capable of adsorbing hydrogen. Figure 6 depicts the top and side views of the optimized structures of the fully hydrogenated penta-graphene. In fully hydrogenated penta-graphene, the ratio of C:H is 3:2, whereas this ratio is 1:1 in case of fully hydrogenated graphene. Li et al. [38] studied hydrogen functionalization of penta-graphene with the help of DFT based AIMD simulations using PAW method. Most of the calculations were performed using GGA-PBE exchange correlation (XC) potential functional whereas the hybrid HSE06 was considered for high precision electronic structure calculations. It is found that crystallographic symmetry of penta-graphene does not change even with full hydrogenation.

In fully hydrogenated PG, both of the bond lenghts (C1–C2 and C2–C2) are 1.55Å which resembles the single bond character. The bond angles θ_C2–C1–C2 and θ_C1–C2–C1 are 116.9^° and 105.9^°, respectively, indicating the distorted sp³ hybridization of the carbon atoms [38]. Change of bond length of C2–C2 from 1.34 to 1.55 Å, indicates that the C2–C2 bond transforms from double bond to single bond due to hydrogenation. After hydrogenation of penta-graphene, the thickness buckling increases. Vertical distance between topmost and bottommost carbon atom in fully hydrogenated penta-graphene is 1.62 Å whereas the value is 1.20 Å for pristine penta-graphene.

3.1 Stability Issues

The binding energy of each hydrogen atom in penta-graphene is defined as [38];

$$ E_{b} = - \left( {E_{total} - E_{PG} - 4E_{adatom} } \right)/4 $$

(2)

where, $ E_{total} ,E_{PG} , and E_{adatom} $ are total energy of the ground state configuration of the unit cell of fully hydrogenated penta-graphene, pristine penta-graphene, and isolated hydrogen atom, respectively. There are four adsorbed hydrogen atoms per unit cell. The calculated binding energy is 3.65 eV whereas the corresponding value is 2.47 eV for graphene. Thus, adsorption of hydrogen in penta-graphene is energetically favorable over that of graphene. In fully hydrogenated PG, all sp² hybridized carbon atoms are transformed into sp³ hybridized atoms. C2–C2 bonds get elongated and bonding characteristic changes from double bond to single bond. The strain stored in pristine PG is released partially due to such hydrogenation leading towards more stability of functionalized PG than its pristine counterpart.

Figure 7 shows the variations of total potential energy of fully hydrogenated penta-graphene during the AIMD simulations for 300 K and 1000 K. It is found that the structures remain integrated and the average value of the total potential energies remains nearly constant throughout the simulation time for both the temperature 300 and 1000 K [38]. Thus, it can be inferred that hydrogenated PG sheets are not only thermally stable at room temperature, but it can also sustain at a temperatures as high as 1000 K.

Figure 8 represents phonon band structure of fully hydrogenated PG along the high symmetric paths (Γ–X–M–Γ) in the first Brillouin zone. The dynamic stability of the hydrogenated penta-graphene is confirmed by the absence of imaginary frequencies in the entire Brillouin zone. Like penta- graphene, there exist three distinct acoustic modes and the two-fold degeneracy on the X–M path in hydrogenated penta-graphene also [38]. A large phonon gap is observed in phonon band structure of penta-graphene. From the vibrational activity at the Γ point in the Brillouin zone, Raman and Infrared (IR) spectra of hydrogenated penta-graphene can be studied. In hydrogenated penta-graphene, Raman-activity was found at 2945.89, 2911.14, 1267.57, 1179.84, 1115.23, 990.23 and 780.64 cm⁻¹ and IR-activity was found at 2943.53 and 2911.14 cm⁻¹, respectively.

3.2 Properties of Hydrogenated Penta-Graphene

Electronic Property

Like penta-graphene, fully hydrogenated PG is also characterized with indirect band gap since its conduction band minimum (CBM) and valence band maximum (VBM) are located at different k points in the momentum space. Figure 9a shows the electronic band structure and atom-decomposed partial DOS of fully hydrogenated penta-graphene computed with PBE and HSE06 functional. The computed band gap of fully hydrogenated penta-graphene with PBE and hybrid HSE06 functional are 4.29 and 5.35 eV, respectively. It is well known that calculation with PBE functional underestimate the bandgap of a material.

Hydrogen functionalization changes penta-graphene from a semiconductor to an insulator [38]. Due to hydrogenation, the CBM/VBM of penta-graphene shifts from the M–Γ/Γ–X path to the M–Γ path. From the analysis of partial DOS of fully hydrogenated penta graphene, it is found that the electronic states near the Fermi level are mainly contributed from C1 and C2 atoms.

Mechanical Property

Molecular Dynamics simulation confirms that hydrogenation significantly enhance the mechanical strength of penta-graphene [39]. Figure 9b shows stress–strain curves of pristine and hydrogenated PG with four different hydrogenation coverage of 25, 50, 75, and 100% at 300 K [39]. Stress increases linearly with the increase of tensile strain and attain a maximum after which stress drops sharply indicating a material degradation. The strain for which the stress is the maximum is identified as the failure strain and the corresponding strain is the failure stress. The simulated failure stress and failure strain value for pristine penta-graphene are 50.2 GPa and 0.127, respectively which are significantly lower than that of graphene (130 GPa and 0.25, found experimentally and 125.2 GPa and 0.191, found by MD simulations) [39]. It is revealed from Fig. 9 that fully hydrogenated PG is characterized with the highest value of failure stress and strain. This phenomenon is strikingly in contrast with graphene where hydrogenation (up to 30%) significantly reduces the value of failure stress and failure strain. For a hydrogenation range of 30–100%, mechanical properties of graphene are almost insensitive to functionalization [40].

The failure stress and failure strain of pristine and hydrogenated PGs are represented in the form of a bar diagram summarized in Fig. 10a and b, respectively. When PG is hydrogenated to 25%, the failure stress and failure strain decrease by 16.9 and 22.8%, respectively than that of pristine PG. With further increase of hydrogenation, failure stress failure and strain increase monotonically. For 100% hydrogenated PG, failure stress and failure strain increase by 74.9 and 52.8% with respect to that of pristine PG.

Structural transformation from pentagon to polygon (6-, 7-, 8-, or more atom rings) is the cause behind the failure of pristine as well as partially hydrogenated PGs beyond failure strain [39]. For 100% hydrogenated PG, the failure mechanism is entirely different. Any structural transition induced failure is not observed in fully hydrogenated PG. In the 100% hydrogenated PG, all the sp²-hybridized carbon atoms transforms to sp³-hybridized. Thus, fully hydrogenated PG is more stable structure and is characterized with higher value of failure stress and failure strain (87.8 GPa and 0.194). In fully hydrogenated PG, the failure mechanism is initiated (for a strain 0.1944) with C–C bond breaking and a visible crack is formed in the structure [39]. With further increase of strain, the crack rapidly spreads in the direction perpendicular to the loading direction and causes fully hydrogenated PG to rupture finally [39].

These improvements in the mechanical properties of hydrogenated PG remain almost unaltered for the temperature range of 200–600 K. Figures 5a and b represent the failure stress and failure strain as a function of temperature for pristine and fully hydrogenated PG. It can be observed that with the increase in temperature from 200 to 600 K, the value of failure stress and failure strain decrease slightly for pristine as well as fully hydrogenated PGs (Fig. 11).

Decrease of failure stress and failure strain with temperature can be caused by the stronger thermal vibration of atoms at higher temperature which renders the atomic bonds more likely to reach the critical bond length and subsequently to break. In spite of the degradation of the mechanical properties with increasing temperature, the failure stress and failure strain of fully hydrogenated PG are still much higher (about 71–88% higher) than that of pristine PG [39].

In Edge Hydroxyl, OP: The “in-plane Young’s modulus” reduces to 205.50 GPa from 263.8 GPa upon full hydrogenation of PG [38]. In contrast to the pristine penta-graphene (−0.068), Poisson’s ratio of fully hydrogenated PG is found to be positive (0.243) [38].