Detection of gas atoms with graphene sheets

Computational Materials Science 60 (2012) 245–249

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Detection of gas atoms with graphene sheets Behrouz Arash, Quan Wang ⇑ Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 5V6

a r t i c l e

i n f o

Article history: Received 5 March 2012 Received in revised form 24 March 2012 Accepted 27 March 2012 Available online 21 April 2012 Keywords: Graphene sheets Nano-sensor Wave propagation Noble gases Molecular dynamics simulations

a b s t r a c t The potential of single-layered graphene sheets as nano-sensors in detection of noble gases through a wave propagation analysis is investigated using molecular dynamics simulations. An index based on wave velocity shifts in a graphene subjected to an impact of noble gases from an exit aperture is defined and examined to measure the sensitivity of the graphene sensor. The wave velocity shifts are measured by applying a sinusoidal signal to one end of the sheet and acquiring the induced wave signals at two locations on the sheet, i.e. acquiring locations. The simulation results indicate that the nano-sensor is able to differentiate noble gas atoms with a recognizable sensitivity. The dependence of the mass flow rate of gases from the aperture, environmental temperature, and the relative location of the gas exit aperture with respect to the acquiring locations on the sensitivity is studied. The simulation results also show that the resolution of a sensor made of the graphene sheet with a size of 3.62 nm  15.03 nm can achieve an order of the impact rate of 107 femtograms per picoseconds. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction A single-layered graphene sheet (SLGS) is a monolayer of graphite consisting of a repetitive honeycomb lattice in which carbon atoms bond covalently with their neighbors. Since successful fabrications of isolated graphenes [1], graphenes have arisen intense research interests owing to their distinctive and outstanding properties [2], i.e. extremely high elasticity [3] and large thermal conductivity [4]. These properties have made graphene sheets (GSs) as one of the most promising materials in wide potential applications in nanotechnology [5–7], such as gas detection, graphene transistors, solar cells, and diagnosis devices. Recently, interests have been generated in the area of terahertz physics of nanoscale materials and devices [8–11] which opens a new topic on nano-materials wave characteristics. Wang [9] reported a transportation of helium atoms in a single-walled carbon nanotube (SWCNT) through a kink propagation initiated in the nanotube. Chen et al. [10] provided a potentially useful mechanism for using an SWCNT as a vehicle to deliver large drug molecules. Their simulations showed that the transport and ejection of molecules with an SWCNT can be achieved by wave propagation in SWCNTs. One of the main goals in the area of terahertz devices in nanotechnology is to design a nano-sensor that is able to fulfill a detection of atoms or molecules. In general, the detection using a nano-resonator from a vibration analysis is based on the fact that atoms attached on the nano-sensor would induce a recognizable ⇑ Corresponding author. Tel.: +1 204 4746443; fax: +1 204 2657507. E-mail address: [email protected] (Q. Wang). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.03.053

decrease in resonant frequencies. The key challenge in mass detection is thus to identify the decrease in the resonant frequencies with a sufficiently high resolution. The idea of using carbon nanotubes (CNTs) as nanobalances with a high sensitivity was proposed by Poncharal et al. [12]. Static and dynamic mechanical deflections were electrically induced in cantilevered multi-walled CNTs (MWCNTs) in a transmission electron microscope. The methods were developed to apply to a nanobalance for detection of nanoscopic particles and a Kelvin probe. Mateiu et al. [13] reported an approach for designing mass sensors based on MWCNTs. Cantilever SWCNTs as mass sensors were studied analytically and by finite element method (FEM) and the resonant frequency shift of SWCNTs caused by a nano-scale particle was explored [14]. Chiu et al. [15] studied atomic scale mass sensing using doubly clamped suspended CNT nanomechanical resonators. They employed the shifts in the resonant frequency of the nanotubes to sense and determine the inertial mass of atoms as well as the mass of the nanotube. Li et al. [16] used a molecular structure mechanics method to investigate potential of super CNTs constructed by SWCNTs and CNT Y-junctions as mass and strain sensors. The mechanical responses of SWCNT-based sensors modeled as thin shells were studied using FEM [17]. Results show that the mass sensitivity of carbon nanotube nanobalances can reach an order of 1021 g. Arash et al. [18] studied the potential of SWCNTs as nano-sensors in detection of noble gases by a vibration analysis. A GS is a potential candidate of an excellent atomic and molecular sensor owing to its two-dimensional structure [5]. Its entire volume is exposed to its surroundings and hence it becomes a potential candidate for detection of adsorbed molecules. High electrical conductivity and low noise are also superior properties of GSs

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that make the electrical resistance detectable [5]. Molecular structural mechanics was implemented by Sakhaee-Pour et al. [19] to model the vibrational behavior of mass sensors and atomistic dust detectors made of defect-free SLGSs. The potential of a GS sensor for detection of gas atoms by a vibration analysis was proposed and an index based on frequency shift of the GS attached by gas atoms on its surface was presented [11]. In most previous research works, atoms or molecules, that are intended to be detected by CNT- and GS-based sensors, are assumed to be initially attached on surface of the sensors. In addition, the density of atoms or molecules on sensors should be much higher than their density in standard conditions to ensure a detectable sensitivity [11,18]. Therefore, the current research is to build up a more practical study on potential of graphene sensors by studying the following problem: gases flowing from an aperture with a mass flow rate to a GS are to be detected instead of gas atoms initially attached on the GS. In solving the problem, a wave propagation analysis on the nano-system is used. Since the wave velocity can be altered by a locally induced impact of gases on the sheet, the resolution of the potential sensor is expected to be enhanced by detecting foreign gases even with lower density. This paper aims to explore the potential of GSs in design of nano-sensors with a wave propagation analysis in SLGSs with molecular dynamics (MD) simulations. An index representing the sensitivity based on the wave velocity shifts of the graphene sensors subjected to impacts of noble gases, i.e. Neon (Ne), Argon (Ar), Krypton (Kr), Xeon (Xe), from an aperture is defined and examined. The effects of the mass flow rate of gases, environmental temperature, and the relative location of the gas exit aperture with respect to the acquiring locations on the sensitivity of graphene sensors are studied.

Table 1 Atomic mass, well-depth energy (e), and the equilibrium distance (r) of C, Ne, Ar, Kr and Xe atoms taken from Ref. [22].

a

Type of atom

Atomic mass (amu)

e/Kb (K)a

r (nm)

Carbon (C) Neon (Ne) Argon (Ar) Krypton (Kr) Xenon (Xe)

12.011 20.179 39.948 83. 798 131.293

51.2 47 119 164 224.5

0.335 0.272 0.341 0.383 0.407

Kb is the Boltzmann’s constant.

(a)

(b)

Aperture

0.6 nm A harmonic motion

2. Molecular dynamics simulations MD is a powerful method to analyze a nanoscale system by solving Newtonian equations of motion governed by interatomic interactions to numerically determine the trajectories of a large number of atoms in the system. For the interaction potential, the second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons developed by Brenner et al. [20] is adopted to simulate wave propagations in GSs. In the second-generation REBO potential, the total potential energy of a system is given by

EREBO ¼

PP

 EA ðr Þ; ½ER ðr ij Þ  b ij ij

ð1Þ

i j¼iþ1

where rij is the distance between a pair of adjacent atoms i and j, and  is a many-bond empirical bond-order term. The vdW interactions b ij between a GS and gas atoms are modeled by the Lennard–Jones potential [21],

"  12

V ij ðrij Þ ¼ 4e

r

rij



 6 # r ; r ij

ð2Þ

where e and r are the coefficients of the well-depth energy and the equilibrium distance. For carbon atoms in a GS and the attached noble gas atoms, the coefficients can be approximated using the venerable Lorentz–Berthelot mixing rules [22] and are listed below

rAB ¼ 12 ðrAA þ rBB Þ : pffiffiffiffiffiffiffiffiffiffiffiffiffi eAB ¼ eAA eBB

ð3Þ

The noble gases investigated in the research, i.e. Neon (Ne), Argon (Ar), Krypton (Kr) and Xeon (Xe), are to be detected by a process of supplying them from an aperture with different mass flow rates (the mass of gases which passes through the aperture per unit time). The coefficients of the well-depth energy, e, and the

GS GS with a size of

3.62nm×15.03nm

Acquiring locations

z

y Fig. 1. Schematic graph of the GS subjected to an impact of gas atoms: (a) perspective view; and (b) side view.

equilibrium distance, r, used in Eqs. (2) and (3) taken from Ref. [22] are provided in Table 1 for each type of atoms. A VelocityVerlet algorithm is used to integrate the equations of motion and an incremental time step is set to be 1 fs. The Nose–Hoover feedback thermostat [23] is used for system temperature conversion. The detection of gas atoms is studied with a wave propagation analysis. In simulations, a GS with a size of 3.62 nm  15.03 nm excited by a harmonic deflection with a period of T = 800 fs on one shorter side is studied. The principle of using the sheet as a gas sensor is to identify a recognizable phase velocity shift in the GS when gas atoms with a certain mass flow rate from an aperture are supplied to the sheet. The GS is subjected to an impact of noble gases with a mass flow rate to the sheet from an aperture with a diameter of an order of nano-meter [24] at z = 0.6 nm on top of the GS as shown in Fig. 1a and b. The corresponding velocity of the mass flow rate is set to be 500 m/s. Gas atoms from the aperture arrive on the GS first. Then some of them leave the surface of the sheet, while other distributing on the surface. Such an impact process affects the velocity of the wave propagating in the graphene. An index representing the sensitivity of the possible c c graphene sensor is defined to be 100 0c0 g . In the definition, cg and c0 are phase velocities in a pristine GS and a GS subjected to an impact of noble gases respectively.

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c¼

y2  y1 2p xT x ¼ ; ;k ¼ ¼ k Dt k c

247

ð5Þ

where k is the wavelength; and y1 and y2 are acquiring locations at Sections 1 and 2, respectively. We follow the process to calculate the phase velocity of the sheet with impacts of noble gases in simulations. y

z

x

3. Results and discussions Fig. 2. A snapshot of wave propagation in a 3.62 nm  15.03 nm GS with two fixed and two free edges and an initial strain of 4% in y-direction subjected to a harmonic deflection of period T = 800 fs at y = 0 .

As GSs have been acknowledged to be a membrane structure among researches in nano-community with negligible bending rigidity [25], two layers of carbon atoms are fixed at the graphene edges at y = 0 and y = 15.03 nm and an initial tensile strain of 4% is applied in y-direction to make the GS stiffer and ensure a complete wave propagation in the sheet. In the simulations, a total number of wave peaks n = 10 is considered to reach a good convergence. Fig. 2 illustrates a snapshot of wave propagation in the pristine GS. To obtain the sensitivity, the histories of center atoms of two sections of the GS defined by acquiring locations in Fig. 1b are recorded for a period of 8 ps for deriving the phase velocity of the wave. The phase velocity can be determined from the signals of the transverse vibrations of atoms at the acquiring locations. Fig. 3 presents the calculation process of the phase velocity in the pristine GS illustrated in Fig. 1. One atomic layer located in Section 0 at y = 0 is subjected to a harmonic deflection of period T = 800 fs, as shown in Fig. 3a, and an environmental temperature of 300 K. Fig. 3b and c provide the transverse vibrations of the centric atoms in the acquiring locations in Section 1 at y = 6.22 nm and in Section 2 at y = 8.89 nm, respectively. The transient deflections of the first two periods are neglected to remove the effect of initial uncertainties on velocity measurements. The propagation duration Dt of the wave from Section 1 to Section 2 can be estimated [26] by

Dt 

ðt 23  t13 Þ þ ðt24  t 14 Þ þ    þ ðt 2n  t1n Þ ; n2

ð4Þ

where subscripts i and j in tij represent the number of the sections and the number of the wave peaks, respectively. To apply the tensile strain, two fixed ends of the graphene are strained along ydirection by an amount of 0.01 nm in each step and the whole structure is fully relaxed for 0.2 ps to reach the new equilibrium state at environment temperature. The phase velocity and wavenumber are thus respectively obtained to be,

To examine the potential of GSs as gas sensors, wave propagation in the GS shown in Fig. 1 subjected to an impact of Ar atoms is investigated in Fig. 4. In the following simulations, otherwise stated, the environmental temperature is set to be 300 K. First, from Eq. (5) the phase velocity of the pristine GS in Figs. 2 and 3 is obtained to be c0 = 3.06  103 m/s. Fig. 4 provides the time history of centric atoms at y = 0 and the acquiring locations at y = 6.22 nm and y = 8.89 nm of the GS subjected to an impact of Ar atoms with a mass flow rate of 2.7  107 fg/ps. The mass flow rate can be practically achieved by applying a pressure of 3.6 MPa in a gas container at a room temperature of 300 K. The aperture is located at y = 7.5 nm and z = 0.6 nm, as described in Fig. 1. From Fig. 4, the phase velocity in the GS is obtained to be cg = 2.77  103 m/s revealing the sensitivity of 9.48%. The observation shows that supplying gas atoms to the surface of the GS locally increases a resistance of wave propagation on the sheet and hence induces a decrease in the phase velocity. To study the effect of the mass flow rate of the gases on the sensitivity, Table 2 provides the results of the sensitivity of the GS subjected to an impact of Ar gases with different mass flow rates. The location of the aperture and the acquiring locations remain the same. The phase velocity in the GS subjected to an impact of Ar atoms with mass flow rates of 1.8  107 fg/ps and 4.5  107 fg/ ps are respectively to be 2.87  103 m/s and 2.63  103 m/s showing an increase in the sensitivity from 6.54% to 14.05%. It reveals that the sensitivity is increased by an increase in the mass flow rate of gases. Table 3 indicates the effect of relative location of the gas exit aperture with respect to the acquiring locations on the sensitivity of the GS subjected to an impact of Ar atoms with a mass flow rate of 2.7  107 fg/ps. The acquiring locations remain the same with the above simulations, i.e. y = 6.22 nm and y = 8.89 nm. The sensitivities decrease from 9.48% to 5.69% and 5.23% when the aperture is located from the position y = 7.5 nm, which is closer the acquiring locations, to other two locations y = 3.5 nm and y = 11.5 nm, which are 4 nm far from the center the acquiring locations, respectively. It can be concluded that the sensitivities are higher when

Fig. 3. Time histories of centric atoms of the GS in: (a) Section 0 at y = 0; (b) Section 1 at y = 6.22 nm; and (c) Section 2 at y = 8.89 nm. Environmental temperature is 300 K.

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Fig. 4. Time histories of centric atoms of the GS in; (a) Section 0; (b) Section 1 at y = 6.22 nm; and (c) Section 2 at y = 8.89 nm. The GS is subjected to an impact of Ar atoms with a mass flow rate of 2.7  107fg/ps and a velocity of 500 m/s, the aperture is located at y = 7.5 nm; and environmental temperature is 300 K.

Table 2 The sensitivity of a 3.62 nm  15.03 nm GS with two fixed and two free edges and an initial strain of 4% in y-direction subjected to a harmonic deflection of period T = 800 fs at y = 0 and an impact of Ar atoms with a velocity of 500 m/s. The aperture is located at y = 7.5 nm, and the acquiring locations are respectively at y = 6.22 nm and y = 8.89 nm. The environmental temperature is 300 K. Mass flow rate of Ar atoms (107 fg/ ps)

Phase velocity (103 m/s)

Sensitivity (%)

0 1.8 2.7 4.5

3.0587 2.8616 2.7739 2.6306

0 6.54 9.48 14.05

Table 3 Effect of relative location of the aperture with respect to acquiring locations on the sensitivity of the GS subjected to an impact of Ar atoms with a mass flow rate of 2.7  107 fg/ps and a velocity of 500 m/s. The acquiring locations are respectively at y = 6.22 nm and y = 8.89 nm and the environmental temperature is 300 K. Location of the aperture in y-direction (nm)

Phase velocity (103 m/s)

Sensitivity (%)

3.5 7.5 11.5

2.5791 2.7739 2.9032

5.69 9.48 5.23

Table 4 Thermal effect on the sensitivity of the GS subjected to an impact of Ar atoms with a mass flow rate of 2.7  107 fg/ps and a velocity of 500 m/s. The aperture is located at y = 7.5 nm, and the acquiring locations are respectively at y = 6.22 nm and y = 8.89 nm. Temperature (K)

Phase velocity (103 m/s)

Sensitivity (%)

300 2000 3000

2.7739 2.7380 2.6847

9.48 10.75 12.42

the aperture is located closer to the acquiring locations. These findings are owing to the fact that gas atoms have considerable local influence on wave propagation in the graphene. To show temperature effect on the sensitivity, we calculate the sensitivity at temperatures of 300 K, 2000 K and 3000 K in Table 4. In the calculations, the location of the aperture and the acquiring locations remain the same with those considered in Table 2 or Fig. 4. The sensitivity of the GS subjected to an impact Ar with a

Table 5 The sensitivities of the GS subjected to impacts of respective four noble atoms with a mass flow rate of 2.7  107 fg/ps and a velocity of 500 m/s. The aperture is located at y = 7.5 nm, and the acquiring locations are respectively at y = 6.22 nm and y = 8.89 nm. The environmental temperature is 300 K. Type of gas atoms

Phase velocity (103 m/s)

Sensitivity (%)

– Ne Ar Kr Xe

3.0587 2.8569 2.7739 2.6566 2.6051

0 6.59 9.48 13.15 14.83

mass flow rate of 2.7  107 fg/ps is increased from 9.48% to 10.75% and 12.42% with increases in the environmental temperature from 300 K to 2000 K and 3000 K, respectively. It demonstrates that environmental temperature has relatively less effect on the sensitivity of the GS. To explore the applicability of the graphene sensor to differentiate distinct gases, the sensitivities of the GS subjected to an impact of individual Ne, Ar, Kr and Xe gases with a mass flow rate of 2.7  107 fg/ps are presented in Table 5. In the calculations, the location of aperture, the acquiring locations, and environmental temperature remain the same with those considered in Table 2. The phase velocities in the GS subjected to an impact of Ne and Xe gas atoms are 2.86  103 m/s and 2.61  103 m/s respectively showing a finding of a decrease in the phase velocity with an increase in atomic mass of gas atoms. The sensitivity indexes are respectively found to be 6.59, 9.48, 13.15 and 14.83% for Ne, Ar, Kr and Xe atoms in simulations which justify the potential of the graphene sensor in detection of different gases with the same mass flow rate. These findings can be interpreted below. The impact process of gas atoms and the graphene has considerable influence on the sensitivity. In simulations, it is found that most of lighter atoms leave the surface of the GS after the impact, because of higher restitution coefficient, while most of heavier atoms staying on the surface of the GS after the impact. Thus, heavier atoms have more significant effect on wave propagation in the graphene and lead to higher sensitivities during their impact with the GS.

4. Conclusions The potential of GSs as nano-sensors is explored. The wave propagation of a GS subjected to an impact of different noble gas

B. Arash, Q. Wang / Computational Materials Science 60 (2012) 245–249

atoms with different mass flow rates from an aperture on top of the GS is simulated by MD simulations. In simulations of the GS with a width of 3.62 nm and a length of 15.03 nm, an initial strain is applied to ensure a complete wave propagation in the sheet. It is found that the resolution of the mass flow rate can reach an order of 107 fg/ps. Distinct noble gas atoms with the same mass flow rate are successfully differentiated by identifying detectable sensitivities. The sensitivity is increased with an increase in the mass flow rate of gas atoms. In addition, it is found that a higher sensitivity is obtained when the aperture and the acquiring locations are located closer. It is found that temperature has less effect on the sensitivity. The study provides a comprehensive investigation on GS-based nano-sensors which may open a new way for detection of noble gases with graphenes. Acknowledgments This research was undertaken, in part, thanks to funding from the Canada Research Chairs Program (CRC) and the National Science and Engineering Research Council (NSERC). References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306 (2004) 666–669. [2] T. Ohta, A. Bostwick, T. Seyller, K. Horn, E. Rotenberg, Science 313 (2006) 951–954.

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