Research Article

Diffusion and adsorption of precursor gas in foam nickel rod substrate during CVD process for deposition of graphene

^{1}School of Petroleum Engineering, Changzhou University, No. 88 Xingyuan Road, Changzhou city 213016, the People′s
Republic of China

^{2}School of Mechanical and Power Engineering, Shanghai Jiaotong University, No.800 Dongchuan Road, Shanghai 200240, China

^{3}Wuxi entry-exit inspection and quarantine bureau, No. 10 Huangxia road, Wuxi, China

***Corresponding author: Bo Tang**, School of Petroleum Engineering, Changzhou University
No. 88 Xingyuan Road, Changzhou city 213016, the People′s Republic of China, Tel/Fax: +86 519 83295530 Email:
tangbo@cczu.edu.cn

**Received:** November 30, 2016 **Accepted:** December 27, 2016 **Published:** December 29, 2016

**Citation: ** Tang B, Hu G, Huang D. Diffusion
and adsorption of precursor gas in foam
nickel rod substrate during CVD process for
deposition of graphene. *Madridge J Anal Sci Instrum.* 2016; 1(1): 16-20.
doi: 10.18689/mjai-1000104

**Copyright: ** © 2016 The Author(s). This work
is licensed under a Creative Commons
Attribution 4.0 International License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the
original work is properly cited.

Abstract

Preparation of graphene by chemical vapor deposition (CVD) mehtod has attracted
increasing attention due to the high quality of the resulting samples. However, the
relative research on diffusion and adsorption of precursor gas (the first two steps of
graphene growth) on the transition metal surface is still insufficiently. In this study,
three-dimensional graphene networks (3DGNs) is prepared by CVD approach with a
foam nickel rod (FNR) as the template. The diffusion of CH_{4} in the FNR is discussed.
Then, the adsorption of CH_{4} on the FNR surface is studied by the expended Langmuir
equation, and the influences from H_{2} on the coverage ratio of CH_{4} and thickness of the
resutling 3DGNs is analyzed. In order to describe the dissolution-segregation process of
carbon atoms in the FNR , a parameter named “quasi-diffusivity” is proposed to avoid
the tedious calculation. Based on this parameter, the relationship between the scale of
3DGNs and growth time can be simulated, and the relationship b etween the thickness
of samples and their growth position can be predicted.

**Keywords:** Chemical Vapor Deposition; Graphene; Expanded Langmuir Equation;
Quasidiffusivity.

Introduction

Since its first isolation in 2004, graphene is regarded as a star material for the dyesensitized
solar cells (DSSCs) and supercapacitors fields because of its outstanding
electrical and mechanical properties [1]. Recently, graphene with various morphologies
including large-scale plane graphene, spherical graphene and three-dimensional
graphene networks (3DGNs) have been fabricated on Cu and Ni substrates by chemical
vapor deposition (CVD) method [2]. Ruoff′s group found that the deposition mechanisms
of graphene on Cu and Ni surfaces are similar [3]. Besides experimental results, some
theoretical mechanisms have been revealed. Zhang *et al*. and Meng *et al*. calculated the
thermodynamics of graphene growth on Cu and Ni surface by first-principle calculations
[4,5]. In previous reports, the attention was focused on the behavior of carbon atoms on
the substrate surface. However, the diffusion and adsorption of precursor gas on the
substrate surface did not arouse enough attention. In fact, these two processes are
closely related to the thickness and quality of the resulting graphene. Studying on these
processes is important to optimize the growth parameters and understand the growth
mechanism of graphene. Recently, our group prepared high-quality 3DGNs by
CVD approach with the foam nickel rod (FNR) as a template
[6,7], and the 3DGNs based DSSCs and supercapacitors show
high photovoltaic performance. Here, we further study the
growth mechanism and kinetics of 3DGNs during the CVD
process. In this study, the diffusion and adsorption properties
of CH_{4} in the porous FNR is discussed. The influence from H_{2}
on the adsorption of CH_{4} and thickness of the resulting
graphene is studied, as well. In order to simplify the calculation
on the kinetics of graphene growth, a parameter named
“quasi-diffusivity” is proposed. Based on this parameter, the
relationship between scale (thickness) of the 3DGNs and
growth time (growth position) can be predicted.

Material and methods

Detailed growth process of the 3DGNs has described in previous reports [6,7]. The heat preservation time are 0s, 150s, 300s, 500s, 800s and 2400s for varied samples at 1273K . An added unit was put into the reaction chamber, and the FNR were placed in the unit during the CVD process (Fig. 1, in the real case, the FNR is put into the unit).

**Fig. 1.** (a)The schematic of the CVD system. (b) Schematic of the
CH_{4} and hydrogen molecules diffuse into the foam nickel rod
during the heat preservation process.

Results and discussion

The scale of 3DGNs on the FNR surface increases with the
extended heat preservation time (see inset of Fig. 4). No
3DGNs can be found for the sample without heat preservation
step, indicating that the growth of the 3DGNs depends on the
diffusion of CH_{4} during the heat preservation process.

**Fig. 4.** (a)The schematic of the CVD system. (b) Schematic of the
CH_{4} and hydrogen molecules diffuse into the foam nickel rod
during the heat preservation process.

**Diffusion of methane molecules in the FNR**

The FNR possesses a three-dimensional porous morphology
with 100-150 µm in porous diameter [6,7]. The diffusion law
of gas molecules in porous medium is closely related to the
relationship between the mean free path of gas molecules and bore diameter of medium. According to the followed
formula [8], the values of mean free path of CH_{4}, H_{2} and Ar at
1273K are ~380, ~660 and ~470 nm, respectively.

The *R, T, N _{A}, p* and

*d*are perfect gas constant, temperature, Avogadro′s constant, pressure and gas collision diameter. Due to the mean free paths of these gas molecules (atoms) are far smaller than the pore of the FNR (the ratio less than 0.01), the diffusion of them in the FNR obeys Fick′s law. For the sake of simplicity, a uniform pore structure of the FNR is assumed (~120µm in porous diameter) and the influence from its peripheral boundary is neglected. Therefore, the diffusion of CH

_{0}_{4}molecules in the FNR takes place along the axial direction only and the following one-dimensional partial differential equation can be employed to describe the diffuse process.

Where *C, u* and *k* are concentration, convection velocity
and consumption rate of CH_{4}, respectively. The D^{eff} is the
effective diffusivity of CH_{4} in the FNR, which contains the pore
characteristics (poriness (ε) and tortuosity (τ)) of the FNR
(*D ^{eff} = Dε/τ, D* represents diffusion coefficient of CH

_{4}in the free space). In the heat preservation process, the diffusion is an unsteady-state process and the convection velocity equals to zero. According to the results of tail gas analysis, the

*∂C/∂t*approximately equals a constant (

*a*~13.6mgm

^{-3}s

^{-1}), thereby, the diffusion equation can be simplified into the following form in the heat preservation process:

Selecting the right part of the FNR as a sample, the
calculation can be performed. L is the length of free space in
the right side of the unit, and l is the diffusion distance of CH_{4}
in the FNR. Q is the total amount of CH_{4} in the free space.
According to the results of tail analysis, the proportion of CH_{4}
in the reaction chamber is 4. 5% (the calculated value is 4.76%)
before introducing the unit. After adopting the unit, the
proportion of CH_{4} in the free space (right part) reduces to
4.1% (the unit separates the chamber into two parts), and the
proportion of CH_{4} in the free space (left part) is 4.7% by
calculation. A visible distinction of the CH_{4} concentration
appears in the right part and left part of the chamber,
indicating differences in the scale of the resulting 3DGNs from
the right and left parts. If the diffusion of CH_{4} in these two
directions is independent, the diffusivity of CH_{4} in the right
part of the NFR is ~10cm^{2}s^{-1} at 1273K.

**Adsorption of methane molecules on the FNR surface**

During the CVD process, CH_{4} molecules adsorb on the
surface of the FNR, which is the previous step of catalytic
dehydrogenation reaction. Only the chemisorbed CH_{4} can
make contribution to the growth of 3DGNs, and the
dehydrogenation reactions will take place for the chemisorbed
CH_{4} due to the catalytic effect of the substrate. According to
Langmuir adsorption model, the covered fraction of adsorbent
surface by adsorbate at a given temperature can be expressed
as following [9]:

*θ , V _{∞}* , b and P are coverage, maximum capacity of the
adsorbent, adsorption coefficient and pressure of the
adsorbate, respectively. Subscript i represents varied
component, and n is the amount of components.

First of all, the adsorption amount of CH

_{4}molecules on the FNR surface at room temperature (300K) was detected. Six different pressures (101.325, 121.59, 141.855, 162.12, 182.385 and 202.65 KPa) were adopted, and the corresponding adsorption amounts of CH

_{4}are listed in the Table 1. The equation (5) can be rewritten as the following form:

**Table 1** Adsorption amount of CH_{4} on the FNR surface under varied
pressures at 300 K.

The slope and intercept are 1/*V _{∞}*
and 1/

*b*when the

_{∞}*P/V*is plotted against the

*P*, and the parameters

*b*and

*V*can be calculated according to the curve (Fig. 2). By using identical method, the parameters

_{∞}*b*and

*V*of CH

_{∞}_{4}under varied temperatures are calculated (Table 2).

**Fig. 2.** PV^{-1 vs P curves of CH4 adsorption on the FNR.}

**Table 2** Adsorption parameters of CH_{4} on the FNR surface under
varied temperatures.

Both the *b* and *V _{∞}* decrease with the increased
temperature, indicating that high temperature leads to lower
coverage of CH

_{4}on the FNR surface. The coverage values of CH

_{4}under varied temperatures are listed in the Table 3. In fact, the calculated values of the

*V*and θ under high temperature exceed the actual values, and two reasons may lead to this phenomenon. Firstly, the chemical adsorbed CH

_{∞}_{4}molecules start to decompose on the FNR surface under high temperature, then the resulted carbon atoms diffuse into the FNR and leave surface active sites to adsorb next CH

_{4}molecule. Moreover, nucleation reaction of CH

_{4}would take place in the gas phase under high temperature condition. Therefore, the

*V*value in the Table 2 includes adsorbed and consumed CH

_{∞}_{4}from above-mentioned two ways. However, the corresponding influence on the

*V*is not significant because the adsorption time is faster than that of nucleation and diffusion process based on composition analysis of the tail gas.

_{∞}**Table 3** Coverage values of CH_{4} on surface of the substrate under
varied temperature.

In the absence of H_{2} (the partial pressure of CH_{4} and Ar
are 5.7 and 95.6 KPa, respectively), the calculated coverage of
CH_{4} is 0.36% at 1273K. The corresponding coverage of CH_{4}
decreases ~10% when H_{2} is added in the atmosphere (the
partial pressure of argon, hydrogen and CH_{4} gases are 57.4,
38.2 and 5.7 KPa, respectively), demonstrating that H_{2} rather
than Ar would depress the adsorption of CH_{4} on the FNR
surface. The adsorption of Ar atoms on the FNR is physical
adsorption because Ar gas is an inert gas. Inversely, both CH_{4}
and H_{2} molecules can be decomposed on the FNR due to the
catalysis of transition metals, indicating that both the effective
adsorptions of CH_{4} and H_{2} are chemical adsorption [10]. Xu *et al*. and Watwe et al. studied the adsorption heat of CH_{4} and
H_{2} on Ni surface and calculated the needed dehydrogenation
energy of them [10,11]. The similar adsorption heat and
barrier height for dehydrogenation lead a competition for the
surface active sites of the FNR between CH_{4} and H_{2}. In previous
reports, the influence of H_{2} on graphene growth was proposed
[5]: H_{2} molecules reduce the roughness of Ni substrates,
eliminate impurities (such as S and P) in the Ni substrates,
avoid local variations in the carbon dissolvability and remove
defects of graphene at high temperature. Meanwhile, thinner
graphene can be prepared on Ni surface when H_{2} was
introduced in the atmosphere. Koskinen *et al*. suggested that
the dangling bond of carbon atom in the graphene islands
would be terminated by hydrogen atom, which limited the
thickness of the resulting graphene [12].

Based on the results of this study, the reduced coverage
of CH_{4} shows that the influence from H_{2} on graphene growth
starts from the adsorption stage. The presence of H_{2} not only
terminates the dangling bond of graphene, but also depresses
the adsorption of CH_{4}, which reduce the thickness of the asprepared
sample.

**Kinetic control step of the 3DGNs**

According to the calculated diffusivity of CH_{4} in the FNR
(~10 cm^{2}s^{-1}), CH_{4} can fill the FNR in several seconds. Therefore,
the 3DGNs should cover the whole surface of the FNR, which
contradicts to the experimental results. There are two possible
reasons can lead to this phenomenon: the CH_{4} is exhausted or
the dehydrogenation reaction only takes place at the endpoint
of the FNR. The result demonstrates that ~0.3% CH_{4} (the CH_{4}
concentration is 4.1% before reaction) can be found in the tail
gas even the heat preservation time is as long as 2400s.
Therefore, the adsorption and dehydrogenation reactions of
CH_{4} only happen at the endpoint part of the FNR is the
fundamental reason. Diffusion velocity of CH_{4} is slower than
the velocity of adsorption and dehydrogenation reactions of
CH_{4} in the surface. The endpoint part of the FNR always
possesses enough active sites to chemisorb the CH_{4}, and the
resulting carbon atoms diffusion into the FNR both along the
axial and radial directions. Thereby, the kinetic control factor
of the 3DGNs growth is the diffusion of CH_{4}. The result
indicating that the thicknesses of 3DGNs should generally
reduce along the axial direction due to the concentration
gradient of carbon atoms in the substrate, which is proved by
our group [6,7].

**Kinetic of 3DGNs growth**

In the cooling process, the decreased solubility of carbon
atoms in the FNR leads to the formation of graphene on
substrate surface. According to the Langmuir-Mclean model
[13], the surface segregation process of carbon atoms
complies with the following equation:

where *C _{s}* and

*C*represent the carbon atoms concentration on the surface and inner of the substrate. The ΔG

_{b}_{seg}is the segregation free energy of carbon atom,

*k*and

*T*represent the Boltzmann constant and temperature, respectively. In fact, the segregation of carbon atoms is a onedimensional diffusion process and the time-dependent equation is:

where D_{b} is the diffusion constant. As for the initial and
boundary conditions, the C_{s} can be assumed as zero at the
beginning of the cooling process, and the initial C_{b} can be
considered as a constant at specified depth (
C_{b} (z > 0,t= o) C(x) , x represent the depth). The bulk
concentration of carbon atoms satisfies _{0}∫^{1}C(x)*dx = M* , and
the M is the total amount of carbon atoms in the FNR, which
equals the change in the weight of the FNR before and after
CVD process. However, the ΔG_{seg} is a function depending on
concentration of carbon atom and temperature, which is
difficult to calculate for the varied position of the FNR.
Moreover, the precise concentration of carbon atoms at
varied position of the FNR before and after cooling process
could not to be detected. Thereby, studying the growth
kinetic of the 3DGNs through precise calculation is difficult.

In order to simplify the related calculation and give a clear
physical picture, we suggest a parameter named “quasidiffusivity”
to describe the growth of 3DGNs. In this model,
the processes of adsorption and dehydrogenation of CH_{4} and
the processes of diffusion and segregation of carbon atoms
are deemed as an equivalent process: the 3DGNs growth in
the FNR surface directly. Therefore, the relationship between
the scale of 3DGNs and heat preservation time satisfies the
following equation:

*D'* is the "quasi-diffusivity", which is not corresponded to
any actual process.

With the increased heat preservation time, the scale of
3DGNs increases. The length of the 3DGNs enhances to 2.46
cm from 0.94 cm when the heat preservation time increases to
2400s from 300s at 1273K condition (take right part of the
FNR as an example, see inset of Fig. 3a). The calculated D' is
0.0028cm^{2}s-1 for the sample with 300s heat preservation
progress, which is about one-three thousandth of CH_{4}
diffusivity, indicating that graphene can forms on the substrate
surface only if the density of carbon atom in the FNR exceeds
a certain value. By adopting the D' , the relationship between
heat preservation time and scale of the resulting 3DGNs can
be revealed. After comparing the calculated and practical
values, it can be found that the fitting values can be used to
predict the scale of the 3DGNs. However, the distinctions
between the fitting and practical values become obviously
when the heat preservation time is expended. Because the
total amount of CH_{4} is unvaried, the amount of carbon atom
diffusion into the substrate in unit time gradual reduces.
Therefore, the D' decreases with the increased heat
preservation time. By employing the identical method, the
corresponding curve of the samples in the left part is calculated
( D' ~0.0041cm^{2}s^{-1}, is calculated by the sample with 300s heat
preservation time, Fig. 3b). The digital image of the whole
FNR after 2400s heat preservation time is displayed in the
inset of Fig. 3b. The simulated and experimental results
demonstrate that the length of 3DGNs can be designed by
controlling heat preservation time, which is important to
achieve the controllable growth of the 3DGNs. Moreover,
based on the relationship between diffusivity and temperature
(D~T^{1.51}), the scale of the 3DGNs under varied temperatures is
calculated (Fig. 3).

**Fig. 3** Experimental and simulation results of the lengths of the
3DGNs from (a) right and (b) left sides of the FNR after varied heat
preservation times.

In the cooling processes, due to carbon atoms at varied
positions of the substrate possess identical segregation time, the different thicknesses of the 3DGNs results from varied
densities of carbon atoms at varied positions. Based on “quasidiffusivity”,
thickness of the 3DGNs at a specific position is
proportional to ~ (*t _{0} - d^{2}/D* where

*t*and

_{0}*d*represent heat preservation time and distance from the terminal of the FNR. Therefore, the relationship between thickness of 3DGNs and the growth position can be calculated. The simulated and real results of the 3DGNs in the two sides of the FNR with 2400s heat preservation time (1273K) are displayed in Fig. 4. The results show that the variation tendency of the thickness can be predicted by the curves, although the precision need improving. The “quasi-diffusivity” reduces with time, which results to the gradually increase deviation between the calculated and practical values. In order to obtain the better fitting results, the further optimization for the assumption and approximation is under study.

Conclusions

The diffusion and adsorption of CH_{4} on the FNR is studied.
The diffusion of CH_{4} in the FNR complies Fick′s law. The
coverage of CH_{4} decrease with increased temperature, and
the presence of H_{2} further reduces the coverage of CH_{4} due to
the competition for the surface active sites. Moreover, the
growth kinetic of 3DGNs is studied. The diffusion of CH_{4} is
found the kinetic control factor for the growth of 3DGNs. In
order to simplified calculation, “quasi-diffusivity” was
proposed to describe the growth process of 3DGNs. By
adopting this parameter, the relationship between the scale
of 3DGNs and heat preservation time can be obtained.
Moreover, a preliminary study on the thickness of the prepared
3DGNs at varied position is performed. All the results manifest
that the growth of 3DGNs can be predicted by “quasidiffusivity”,
which is important to achieve the controllable
growth of 3DGNs.

Acknowledge

This work was supported by National Natural Science Foundation of China under Grant (51506012), Jiangsu Science Foundation Fund under Grant (BK20150266); and the Basic Research Project of Changzhou City under Grant (CJ20159032).

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