On the hydrogenation-dehydrogenation of graphene-layer-nanostructures : Relevance to the hydrogen on-board storage problem

Herein, results of thermodynamic analysis of some theoretical and experimental [thermal desorption (TDS), scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), high-resolution electron energy loss spectroscopy/low-energy electron diffraction (HREELS/LEED), photoelectron spectroscopy (PES), angle-resolved photoemission spectroscopy (ARPES), Raman spectroscopy and others] data on “reversible” hydrogenation and dehydrogenation of some graphene-layernanostructures are presented. In the framework of the formal kinetics and the approximation of the first order rate reaction, some thermodynamic quantities for the reaction of hydrogen sorption (the reaction rate constant, the reaction activation energy, the per-exponential factor of the reaction rate constant) have been determined. Some models and characteristics of hydrogen chemisorption on graphite (on the basal and edge planes) have been used for interpretation of the obtained quantities, with the aim of revealing the atomic mechanisms of hydrogenation and dehydrogenation of different graphene-layersystems. The cases of both non-diffusion rate limiting kinetics and diffusion rate limiting kinetics are considered. Some open questions and perspectives remain in solving the actual problem in effective hydrogen on-board storage; using the graphite nanofibers (GNFs) is also considered.


INTRODUCTION
As noted in a number of articles 2007 through 2014, hydrogenation of graphene-layers-systems, as a prototype of covalent chemical functionality and an effective tool to open the band gap of graphene, is of both fundamental and applied importance (Geim and Novoselov, 2007;Palerno, 2013).
It is relevant to the current problems of thermodynamic stability and thermodynamic characteristics of the hydrogenated graphene-layers-systems (Sofo et al., 2007;Openov and Podlivaev, 2010;Han et al., 2012), and also to the current problem of hydrogen on-board storage (Akiba, 2011;Zuettel, 2011;DOE targets, 2012).
In the case of epitaxial graphene on substrates, such as SiO 2 and others, hydrogenation occurs only on the top basal plane of graphene, and it is not accompanied with a strong (diamond-like) distortion of the graphene network, but only with some ripples.The first experimental indication of such a specific single-side hydrogenation came from Elias et al. (2009).The authors mentioned a possible contradiction with the theoretical results of Sofo et al. (2007), which had down-played the possibility of a single side hydrogenation.They proposed an important facilitating role of the material ripples for hydrogenation of graphene on SiO 2 , and believed that such a single-side hydrogenated epitaxial graphene can be a disordered material, similar to graphene oxide, rather than a new graphene-based crystal -the experimental graphane produced by them (on the free-standing graphene membrane).
On the other hand, it is expedient to note that changes in Raman spectra of graphene caused by hydrogenation were rather similar (with respect to locations of D, G, D′, 2D and (D+D′) peaks) both for the epitaxial graphene on SiO 2 and for the free-standing graphene membrane (Elias et al., 2009).
As it is supposed by many scientists, such a single side hydrogenation of epitaxial graphene occurs, because the diffusion of hydrogen along the graphene-SiO 2 interface is negligible, and perfect graphene is impermeable to any atom and molecule (Jiang et al., 2009).But, firstly, these two aspects are of the kinetic character, and therefore they cannot influence the thermodynamic predictions (Sofo et al., 2007;Boukhvalov et al., 2008;Zhou et al., 2009).Secondly, as shown in the present analytical study, the above noted two aspects have not been studied in an enough degree.
As shown in Elias et al. (2009), when a hydrogenated graphene membrane had no free boundaries (a rigidly fixed membrane) in the expanded regions of it, the lattice was stretched isotropically by nearly 10%, with respect to the pristine graphene.This amount of stretching (10%) is close to the limit of possible elastic deformations in graphene (Nechaev and Veziroglu, 2013), and indeed it has been observed that some of their membranes rupture during hydrogenation.It was believed (Elias et al., 2009) that the stretched regions were likely to remain nonhydrogenated.They also found that instead of exhibiting random stretching, hydrogenated graphene membranes normally split into domain-like regions of the size of the order of 1 µm, and that the annealing of such membranes led to complete recovery of the periodicity in both stretched and compressed domains (Elias et al., 2009).
It can be supposed that the rigidly fixed graphene membranes are related, in some degree, to the epitaxial graphenes.Those may be rigidly fixed by the cohesive interaction with the substrates.
As was noted in Xiang et al. (2010), the double-side hydrogenation of graphene is now well understood, at least from a theoretical point of view.For example, Sofo Nechaev and Veziroglu 55 et al. (2007) predicted theoretically a new insulating material of CH composition called graphane (double-side hydrogenated graphene), in which each hydrogen atom adsorbs on top of a carbon atom from both sides, so that the hydrogen atoms adsorbed in different carbon sublattices are on different sides of the monolayer plane (Sofo et al., 2007).The formation of graphane was attributed to the efficient strain relaxation for sp 3 hybridization, accompanied by a strong (diamond-like) distortion of the graphene network (Sofo et al., 2007;Xiang et al., 2009).In contrast to graphene (a zero-gap semiconductor), graphane is an insulator with an energy gap of E g  5.4 eV (Openov and Podlivaev, 2010;Lebegue et al., 2009).
Only if hydrogen atoms adsorbed on one side of graphene (in graphane) are retained, we obtain graphone of C 2 H composition, which is a magnetic semiconductor with E g  0.5 eV, and a Curie temperature of T c  300 to 400K (Zhou et al., 2009).
As was noted in Openov and Podlivaev (2012), neither graphone nor graphane are suitable for real practical applications, since the former has a low value of E g , and undergoes a rapid disordering because of hydrogen migration to neighboring vacant sites even at a low temperature, and the latter cannot be prepared on a solid substrate (Podlivaev and Openov, 2011).
It is also expedient to refer to a theoretical single-side hydrogenated graphene (SSHG) of CH composition (that is, an alternative to graphane (Sofo et al. (2007)), in which hydrogen atoms are adsorbed only on one side (Pujari et al., 2011;Dzhurakhalov and Peeters, 2011).In contrast to graphone, they are adsorbed on all carbon atoms rather than on every second carbon atom.The value of E g in SSHG is sufficiently high (1.6 eV lower than in graphane), and it can be prepared on a solid substrate in principle.But, this quasi-two-dimensional carbonhydrogen theoretical system is shown to have a relatively low thermal stability, which makes it difficult to use SSGG in practice (Openov and Podlivaev, 2012;Pujari et al., 2011).
As was noted in Pujari et al. (2011), it may be inappropriate to call the covalently bonded SSHG system sp 3 hybridized, since the characteristic bond angle of 109.5° is not present anywhere that is, there is no diamond-like strong distortion of the graphene network, rather than in graphane.Generally in the case of a few hydrogen atoms interacting with graphene or even for graphane, the underlining carbon atoms are displaced from their locations.For instance, there may be the diamond-like local distortion of the graphene network, showing the signature of sp 3 bonded system.However, in SSHGraphene all the carbon atoms remain in one plane, making it difficult to call it sp 3 hybridized.Obviously, this is some specific sp 3 -like hybridization.
The results of Nechaev (2010), and also Table 1A and B in the present paper, of thermodynamic analysis of a number of experimental data point that some specific Table 1A.Theoretical, experimental and analytical values of some related quantities.
In this connection, it is expedient to note that there are a number of theoretical works showing that hydrogen chemisorption corrugates the graphene sheet in fullerene, carbon nanotubes, graphite and graphene, and transforms them from a semimetal into a semiconductor (Sofo et al., 2007;Elias et al., 2009).This can even induce magnetic moments (Yazyev and Helm, 2007;Lehtinen et al., 2004;Boukhvalov et al., 2008).
Previous theoretical studies suggest that singleside hydrogenation of ideal graphene would be thermodynamically unstable (Boukhvalov et al., 2008;Zhou et al., 2009).Thus, it remains a puzzle why the single-side hydrogenation of epitaxial graphenes is possible and even reversible, and why the hydrogenated species are stable at room temperatures (Elias et al., 2009;Sessi et al., 2009).This puzzling situation is also considered in the present analytical study.Xiang et al. (2010) noted that their test calculations show that the barrier for the penetration of a hydrogen atom through the sixmember ring of graphene is larger than 2.0 eV.Thus, they believe that it is almost impossible for a hydrogen atom to pass through the six-member ring of graphene at room temperature (from a  (Sofo et al., 2007).
In the present analytical study, a real possibility of the penetration is considered when a hydrogen atom can pass through the graphene network at room temperature.This is the case of existing relevant defects in graphene, that is, grain boundaries, their triple junctions (nodes) and/or vacancies (Brito et al., 2011;Zhang et al., 2014;Banhart et al., 2011;Yazyev and Louie, 2010;Kim et al., 2011;Koepke et al., 2013;Zhang and Zhao, 2013;Yakobson and Ding, 2011;Cockayne et al., 2011;Zhang et al., 2012;Eckmann et al., 2012).The present study is related to revealing the atomic mechanisms of reversible hydrogenation of epitaxial graphenes, compared with membrane graphenes.
In the next parts of this paper, results of thermodynamic analysis, comparison and interpretation of some theoretical and experimental data are presented, which are related to better understanding and/or solving of the open questions mentioned above.It is related to a further development and modification of our previous analytical results (2010)(2011)(2012)(2013)(2014), particularly published in the openaccess journals.Therefore, in the present paper, the related figures 1-25 from our "open" publication (Nechaev and Veziroglu, 2013) are referred.

OF SOME ENERGETIC CHARACTERISTICS OF THEORETICAL GRAPHANES
In the work of Sofo et al. (2007), the stability of graphane, a fully saturated extended two-dimensional hydrocarbon derived from a single grapheme sheet with formula CH, has been predicted on the basis of the first principles and total-energy calculations.All of the carbon atoms are in sp 3 hybridization forming a hexagonal network (a strongly diamond-like distorted graphene network) and the hydrogen atoms are bonded to carbon on both sides of the plane in an alternative manner.It has been found that graphane can have two favorable conformations: a chairlike (diamond-like, Figure 1) conformer and a boat-like (zigzag-like) conformer (Sofo et al., 2007).
The diamond-like conformer (Figure 1) is more stable than the zigzag-like one.This was concluded from the results of the calculations of binding energy (∆H bind.(graphane) ) (that is, the difference between the total energy of the isolated atoms and the total energy of the compounds), and the standard energy of formation (∆H 0 f298(graphane) ) of the compounds (CH (graphane) ) from crystalline graphite (C (graphite) ) and gaseous molecular hydrogen (H 2(gas) ) at the standard pressure and temperature conditions (Sofo et al., 2007;Dzhurakhalov and Peeters, 2011).
For the diamond-like graphane, the former quantity is ∆H bind.(graphane)= 6.56 eV/atom, and the latter one is ∆H 1 = ∆H 0 f298(graphane) = -0.15eV/atom.The latter quantity corresponds to the following reaction: Where ∆H 1 is the standard energy (enthalpy) change for this reaction.By using the theoretical quantity of ∆H 0 f298(graphane) , one can evaluate, using the framework of the thermodynamic method of cyclic processes (Karapet'yants and Karapet'yants, 1968;Bazarov, 1976), a value of the energy of formation (∆H 2 ) of graphane (CH (graphane) ) from graphene (C (graphene) ) and gaseous atomic hydrogen (H (gas) ).For this, it is necessary to take into consideration the following three additional reactions: where ∆H 2 , ∆H 3 and ∆H 4 are the standard energy (enthalpy) changes.
∆H cohes.(graphene)quantity characterizes the breakdown energy of1.5 C-C sp 2 bond in graphene, relevant to the breaking away of one carbon atom from the material.Consequently, one can evaluate the breakdown energy ofC-C sp 2 bonds in graphene, which is ∆H (C-C)grapheme = 4.93 eV.This theoretical quantity coincides with the similar empirical quantities obtained in (Nechaev and Veziroglu, 2013) from ∆H subl.(graphite)forC-C sp 2 bonds in graphene and graphite, which are ∆H (C-C)graphene  ∆H (C- C)graphite = 4.94 ± 0.03 eV.The similar empirical quantity for C-C sp 3 bonds in diamond obtained from the diamond sublimation energy ∆H subl.(diamond)(Karapet'yants and Karapet'yants, 1968) is ∆H (C-C)diamond = 3.69 ± 0.02 eV (Nechaev and Veziroglu, 2013).
It is important to note that chemisorption of hydrogen on graphene was studied (Dzhurakhalov and Peeters, 2011) using atomistic simulations, with a second Nechaev and Veziroglu 59 generation reactive empirical bond order of Brenner interatomic potential.As shown, the cohesive energy of graphane (CH) in the ground state is ∆H cohes.(graphane)= 5.03 eV/atom (C).This results in the binding energy of hydrogen, which is ∆H (C-H)graphane = 1.50 eV/atom (Dzhurakhalov and Peeters, 2011) (Table 1A).
The theoretical ∆H bind.(graphane)quantity characterizes the breakdown energy of one C-H sp 3 bond and 1.5 C-C sp 3 bonds (Figure 1).Hence, by using the above mentioned values of ∆H bind.(graphane) and ∆H (C-H)graphane , one can evaluate the breakdown energy ofC-C sp 3 bonds in the theoretical graphane (Sofo et al., 2007), which is ∆H (C- C)graphane = 2.7 eV (Table 1).Also, by using the above noted theoretical values of ∆H cohes.(graphane)and ∆H (C- H)graphane , one can evaluate similarly the breakdown energy ofC-C sp 3 bonds in the theoretical graphane (Dzhurakhalov and Peeters, 2011), which is ∆H (C-C)graphane = 2.35 eV (Table 1A).

CONSIDERATION AND INTERPRETATION OF THE DATA ON DEHYDROGENATION OF THEORETICAL GRAPHANE, COMPARING WITH THE RELATED EXPERIMENTAL DATA
In Openov and Podlivaev (2010) and Elias et al. (2009) the process of hydrogen thermal desorption (TDS) from graphane has been studied using the method of molecular dynamics.The temperature dependence (for T = 1300 -3000K) of the time (t 0.01 ) of hydrogen desorption onset (that is, the time t 0.01 of removal 1% of the initial hydrogen concentration C 0  0.5 (in atomic fractions), -∆C/C 0  0.01, C/C 0  0.99) from the C 54 H 7(54+18) clustered with 18 hydrogen passivating atoms at the edges to saturate the dangling bonds of sp 3 -hybridized carbon atoms have been calculated.The corresponding activation energy of ∆H (des.)= E a = 2.46 ± 0.17 eV and the corresponding (temperature independent) frequency factor A = (2.1 ± 0.5) × 10 17 s -1 have also been calculated.The process of hydrogen desorption at T = 1300 -3000K has been described in terms of the Arrhenius-type relationship: where k B is the Boltzmann constant.Openov and Podlivaev (2010) predicted that their results would not contradict the experimental data (Elias et al., 2009), according to which the nearly complete desorption of hydrogen (-∆C/C 0 0.9, C/C 0  0.1) from a free-standing graphane membrane (Figure 2B) was achieved by annealing it in argon at T = 723K for 24 h (that is, t 0.9(membr.[5]) 723K = 8.6 × 10 4 s).However, as the analysis presented below shows, this declaration (Openov and Podlivaev, 2010) is not enough adequate.
In the framework of the formal kinetics approximation in the first order rate reaction (Bazarov, 1976) a characteristic quantity for the reaction of hydrogen desorption is  0.63 -the time of the removal of ~ 63% of the initial hydrogen concentration C 0 (that is, -∆C/C 0  0.63, C/C 0  0.37) from the hydrogenated graphene.Such a first order rate reaction (desorption) can be described by the following equations (Nechaev, 2010;Nechaev and Veziroglu, 2013;Bazarov, 1976): Where C is the averaged concentration at the annealing time t, K = (1/ 0.63 ) is the reaction (desorption) rate constant, ∆H des. is the reaction (desorption) activation energy, and K 0 , the per-exponential (or frequency) factor of the reaction rate constant.
In the case of a diffusion rate limiting kinetics, the quantity of K 0 is related to a solution of the corresponding diffusion problem (K 0 ≈ D 0 /L 2 , where D 0 is the perexponential factor of the diffusion coefficient, L is the characteristic diffusion length) (Nechaev, 2010;Nechaev and Veziroglu, 2013).
The obtained quantity of  (membr.[5]) is less by one and a half orders of the vibrational frequency  RD = 2.5 × 10 14 s - 1 , corresponding to the D Raman peak (1342 cm -1 ) for hydrogenated graphene membrane and epitaxial graphene on SiO 2 (Figure 2).The activation of the D Raman peak in the hydrogenated samples authors (Elias et al., 2009) attribute to breaking of the translation symmetry of C-C sp 2 bonds after formation of C-H sp 3 bonds.
The quantity  (membr.[5]) is less by one order of the value (Xie et al., 2011) of the vibration frequency  HREELS = 8.7 × 10 13 s -1 corresponding to an additional HREELS peak arising from C-H sp 3 hybridization; a stretching appears at 369 meV after a partial hydrogenation of the epitaxial graphene.Xie et al. (2011) suppose that this peak can be assigned to the vertical C-H bonding, giving direct evidence for hydrogen attachment on the epitaxial graphene surface.
The above noted fact that the empirical (Elias et al., 2009;Nechaev and Veziroglu, 2013) quantity  0.63(membr.[5])723Kis much larger (by about 3 orders), than the theoretical (Openov and Podlivaev, 2010;Nechaev and Veziroglu, 2013) one ( 0.63(graphane[4])723K ), is consistent with that mentioned in (Elias et al., 2009).The alternative possibility has been supposed in Elias et al., (2009) that (i) the experimental graphane membrane (a free-standing one) may have "a more complex hydrogen bonding, than the suggested by the theory", and that (ii) graphane (CH) (Sofo et al., 2007) may be until now the theoretical material.(Elias et al., 2009).The spectra are normalized to have a similar integrated intensity of the G peak. (A) Graphene on SiO 2 .(B) Free-standing graphene.Red, blue, and green curves (top to bottom) correspond to pristine, hydrogenated, and annealed samples, respectively.Graphene was hydrogenated for 2 hours, and the spectra were measured with a Renishaw spectrometer at wavelength 514 nm and low power to avoid damage to the graphene during measurements.(Left inset) Comparison between the evoluation of D and D′ peaks for single-and double-sided exposure to atomic hydrogen.Shown is a partially hydrogenated state achieved after 1 hour of simultaneous exposure of graphene on SiO 2 (blue curve) and of a membrane (black curve).(Right inset) TEM image of one of the membranes that partially covers the aperture 50 μm in diameter.

Characteristics of hydrogenation-dehydrogenation of mono-layer epitaxial graphenes
In Elias et al. (2009), both the graphene membrane samples considered above, and the epitaxial graphene and bi-graphene samples on substrate SiO 2 were exposed to cold hydrogen DC plasma for 2 h to reach the saturation in the measured characteristics.They used a low-pressure (0.1 mbar) hydrogen-argon mixture of 10% H 2 .Raman spectra for hydrogenated and subsequently annealed free-standing graphene membranes (Figure 2B) are rather similar to those for epitaxial graphene samples (Figure 2A), but with some notable differences.If hydrogenated simultaneously for 1 h, and before reaching the saturation (a partial hydrogenation), the D peak area for a free-standing membrane is two factors greater than the area for graphene on a substrate (Figure 2, the left inset).This indicates the formation of twice as many C-H sp 3 bonds in the membrane.This result also agrees with the general expectation that atomic hydrogen attaches to both sides of the membranes.Moreover, the D peak area became up to about three times greater than the G peak area after prolonged exposures (for 2 h, a near-complete hydrogenation) of the membranes to atomic hydrogen.
The integrated intensity area of the D peak in Figure 2B corresponding to the adsorbed hydrogen saturation concentration in the graphene membranesis larger by a factor of about 3 for the area of the D peak in Figure 2A, corresponding to the hydrogen concentration in the epitaxial graphene samples.
The changes in Raman spectra of graphene (Elias et al., 2009) caused by hydrogenation were rather similar in respect to locations of D, G, D′, 2D and (D+D′) peaks, both for the epitaxial graphene on SiO 2 and for the freestanding graphene membrane (Figure 2).Hence, one can H(membr.[5]) (0.7 or 5) × 10 13 s -1 (Table 1A).Then, by substituting in Equation 9the values of 1A).Here, the case is supposed of a nondiffusion-rate-limiting kinetics, when Equation 9corresponds to thePolanyi-Wigner one (Nechaev, 2010).Certainly, these tentative thermodynamic characteristics of the hydrogenated epitaxial graphene on a substrate SiO 2 could be directly confirmed and/or modified by further experimental data on  0.63(epitax.) at various annealing temperatures.
It is easy to show that: 1) these analytical results (for the epitaxial graphene (Elias et al., 2009) are not consistent with the presented below analytical results for the mass spectrometry data (Figure 3, TDS peaks ## 1-3, Table 1A) on TDS of hydrogen from a specially prepared single-side (obviously, epitaxial*) graphane (Elias et al., 2009); and 2) they cannot be described in the framework of the theoretical models and characteristics of thermal  (Elias et al., 2009).The measurments were done by using a leak detector tuned to sense molecular hydrogen.The sample was heated to 573 K (the heater was switched on at t = 10 s).Control samples (exposed to pure argon plasma) exhibited much weaker and featureless response (< 5•10 -8 mbar L/s), which is attributed to desorption of water at heated surfaces and subtracted from the shown data (water molecules are ionized in the massspectrometer, which also gives rise to a small hydrogen signal).
According to further consideration presented below (both here and subsequently), the epitaxial graphene case (Elias et al., 2009) may be related to a hydrogen desorption case of a diffusion rate limiting kinetics, when K 0 , and Equation ( 9) does not correspond to the Polanyi-Wigner one (Nechaev, 2010).
These analytical results (on quantities of ∆H (des.) and K 0 ) show that all three of the above noted TDS processes (#1 TDS , #2 TDS and #3 TDS ) can not been described in the framework of the Polanyi-Wigner equation (Nechaev, 2010;Nechaev and Veziroglu, 2013) (due to the obtained low values of the K 0(des.) and ∆H (des.)quantities, in comparison with the  (C-H) and ∆H (C-H) ones).
As shown below, these results may be related to a hydrogen desorption case of a diffusion-rate-limiting kinetics (Nechaev, 2010;Nechaev and Veziroglu, 2013), when in Equation ( 9) the value of K 0 D 0app./ L 2 and the value of ∆H des.= Q app., where D 0app is the per-exponent factor of the apparent diffusion coefficient D app.= D 0app.exp (-Q app./k B T), Q app. is the apparent diffusion activation energy, and L is the characteristic diffusion size (length), which (as shown below) may correlate with the sample diameter (Elias et al., 2009) TDS process (or peak) #3 TDS (Figure 3, Table 1A) may be related to the diffusion-rate-limiting TDS process (or peak) I in (Nechaev, 2010), for which the apparent diffusion activation energy is Q app.I  0.2 eV E TDS-peak#3 and D 0app.I  3 × 10 -3 cm 2 /s, and which is related to chemisorption models "F" and/or "G" (Figure 4).
By supposing of L ~ d sample , that is, of the order of diameter of the epitaxial graphene specimens (Elias et al., 2009), one can evaluate the quantity of D 0app.(TDS- peak#3) L 2 • K 0(TDS-peak#3)  4 × 10 -5 cm (or within the errors limit, it is of (1.3 -11) × 10 -5 cm, for E TDS-peak #3 values 0.18 -0.28 eV, Table 1A).The obtained values of D 0app.(TDS-peak#3) satisfactory (within one-two orders, that may be within the errors limit) correlate with the D 0app.I quantity.Thus, the above analysis shows that for TDS process (or peak) # 3 TDS (Elias et al., 2009), the quantity of L may be of the order of diameter (d sample ) of the epitaxial* graphene samples.
Process II is characterized by the apparent diffusion activation energy Q app.II  1.2 eV (that is considerably higher of quantities of E TDS-peak#1 and E TDS-peak#2 ) andD 0app.II  1.810 3 cm 2 /s.It is related to chemisorption model "H" (Figure 4).Within approach (Nechaev, 2010), model "H" is related (as and model "G") to a "dissociative -associative" chemisorption of molecular hydrogen on definite defects in graphene layers of the epitaxial samples (Elias et al., 2009), for instance, vacancies, grain boundaries (domains) and/or triple junctions (nodes) of the grain-boundary network noted above, where the dangling carbon bonds can occur.
By supposing the possible values of E TDS-peaks##1,2 = 0.3, 0.6 or 0.9 eV, one can evaluate the quantities of K 0(TDS- peak#1) and K 0(TDS-peak#2) (Table 1A).Hence, by supposing of L ~ d sample , one can evaluate the quantities of D 0app.(TDS- peak#1) and D 0app.(TDS-peak#2) , some of them correlatewith the D 0app.I quantity or with D 0app.II quantity.It shows that for TDS processes (or peaks) #1 TDS and #2 TDS (Elias et al., 2009), the quantity of L may be of the order of diameter of the epitaxial* graphene samples.
For the epitaxial graphene (Elias et al., 2009) case, supposing the values of ∆H des.(epitax.[5]) 0.3, 0.6 or 0.9 eV results in relevant values of K 0(epitax.[5])(Table 1A).Hence, by supposing of L ~ d sample , one can evaluate the quantities of D 0app.(epitax.[5]) , some of them correlate with the D 0app.I quantity or with D 0app.II quantity.It shows that for these two processes, the quantity of L also may be of the order of diameter of the epitaxial graphene samples (Elias et al., 2009).
It is important to note that chemisorption of atomic hydrogen with free-standing graphane-like membranes (Elias et al., 2009) and with the theoretical graphanes may be related to model "F*" considered in (Nechaev, 2010).Unlike model "F" (Figure 4), where two hydrogen atoms are adsorbed by two alternated carbon atoms in a graphene-like network, in model "F*" a single hydrogen atom is adsorbed by one of the carbon atoms (in the graphene-like network) possessing of 3 unoccupied (by hydrogen) nearest carbons.Model "F*" is characterized (Nechaev, 2010) by the quantity of ∆H (C-H)"F*"  2.5 eV, which coincides (within the errors) with the similar quantities (∆H (C-H) ) for graphanes (Table 1A).As also shown in the previous paper parts, the dehydrogenation processes in graphanes (Elias et al., 2009;Openov and Podlivaev, 2010) may be the case of a non-diffusion rate limiting kinetics, for which the quantity of K 0 is the corresponding vibration frequency (K 0 = ), and Equation ( 9) is correspond to the Polanyi-Wigner one.
On the other hand, model "F*" is manifested in the diffusion-rate-limiting TDS process (or peak) III in (Nechaev, 2010) (Table 1B), for which the apparent diffusion activation energy is Q app.III  2.6 eV  ∆H (C-H)"F*" and D 0app.III  3 × 10 -3 cm 2 /s.Process III is relevant to a dissociative chemisorption of molecular hydrogen between graphene-like layers in graphite materials (isotropic graphite and nanostructured one) and nanomaterials -GNFs (Nechaev, 2010) (Table 1B).
It is expedient also to note about models "C" and "D", those manifested in the diffusion-rate-limiting TDS process (or peak) IV in (Nechaev, 2010) (Table 1B), for which the apparent diffusion activation energy is Q app.IV  3.8 eV  ∆H (C-H)"C","D" and D 0app.IV  6 × 10 2 cm 2 /s.Process IV is relevant to a dissociative chemisorption of molecular hydrogen in defected regions in graphite materials (isotropic graphite, pyrolytic graphane and nanostructured one) (Nechaev, 2010) (Table 1B).
But such processes (III and IV) have not manifested, when the TDS annealing of the hydrogenated epitaxial graphene samples (Elias et al., 2009) (Figure 3), unlike some hydrogen sorption processes in epitaxial graphenes and graphite samples considered in some next parts of this paper.

An interpretation of characteristics of hydrogenationdehydrogenation of mono-layer epitaxial graphenes
The above obtained values (Table 1A and B) of characteristics of dehydrogenation of mono-layer epitaxial graphene samples (Elias et al., 2009) can be presented as follows: ∆H des.~ Q app.I or ~ Q app.II (Nechaev, 2010), K 0(des.)~ (D 0app.I / L 2 ) or ~ (D 0app.II / L 2 ) (Nechaev, 2010), L ~ d sample , that is, being of the order of diameter of the epitaxial graphene samples.And it is related to the chemisorption models "F", "G" and/or "H" (Figure 4).These characteristics unambiguously point that in the epitaxial graphene samples (Elias et al., 2009), there are the rate-limiting processes (types of I and/or II (Nechaev, 2010) of diffusion of hydrogen, mainly, from chemisorption "centers" [of "F", "G" and/or "H" types (Figure 4)] localized on the internal graphene surfaces (and/or in the graphene/substrate interfaces) to the frontier edges of the samples.It corresponds to the characteristic diffusion length (L~ d sample ) of the order of diameter of the epitaxial graphene samples, which, obviously, cannot be manifested for a case of hydrogen desorption processes from the external graphene surfaces.Such interpretation is direct opposite, relevance to the interpretation of Elias et al. (2009) and a number of others, those probably believe in occurrence of hydrogen desorption processes, mainly, from the external epitaxial graphene surfaces.Such different (in some sense, extraordinary) interpretation is consisted with the above Nechaev and Veziroglu 65 analytical data (Table 1A) on activation energies of hydrogen adsorption for the epitaxial graphene samples (∆H (ads.)epitax.
On the basis of the above analytical results, one can suppose that a negligible hydrogen adsorption by the external graphene surfaces (in the epitaxial samples of Elias et al., 2009) is exhibited.Such situation may be due to a much higher rigidity of the epitaxial graphenes (in comparison with the free standing graphene membranes), that may suppress the diamond-like strong distortion of the graphene network attributed for graphene of Sofo et al. (2007).It may result (for the epitaxial graphenes of Elias et al. (2009) in disappearance of the hydrogen chemisorption with characteristics of ∆H (ads.)membr.[5] and ∆H (des.)membr.[5] (Table 1A) manifested in the case of the free standing graphene membranes of Elias et al. (2009).And the hydrogen chemisorption with characteristics of ∆H (ads.)epitax.[5] and (∆H (des.)epitax.[5](Table 1A) by the external graphene surfaces, in the epitaxial samples of Elias et al. (2009), is not observed, may be, due to a very fast desorption kinetics, unlike the kinetics in the case of the internal graphene surfaces.
Certainly, such an extraordinary interpretation also needs in a reasonable explanation of results (Figure 2) the fact that the changes in Raman spectra of graphene of Elias et al. (2009) caused by hydrogenation were rather similar with respect to locations of D, G, D′, 2D and (D+D′) peaks, both for the epitaxial graphene on SiO 2 and for the free-standing graphene membrane.

An interpretation of the data on hydrogenation of bilayer epitaxial graphenes
In Elias et al. (2009), the same hydrogenation procedures of the 2 h long expositions have been applied also for bilayer epitaxial graphene on SiO 2 /Si wafer.Bi-layer samples showed little change in their charge carrier mobility and a small D Raman peak, compared to the single-layer epitaxial graphene on SiO 2 /Si wafer exposed to the same hydrogenation procedures.Elias et al. (2009) believe that higher rigidity of bi-layers suppressed their rippling, thus reducing the probability of hydrogen adsorption.
But such an interpretation (Elias et al., 2009) does not seem adequate, in order to take into account the above, and below (next parts of this paper) the presented consideration and interpretation of a number of data.
By using the above extraordinary interpretation, and results on characteristics (Q app.III  2.6 eV, D 0app.III  3 × 10 - 3 cm 2 /s (Table 1B) of a rather slow diffusion of atomic hydrogen between neighboring graphene-like layers in graphitic materials and nanostructures (process III, model "F*" (Nechaev, 2010), one can suppose a negligible diffusion penetration of atomic hydrogen between the two graphene layers in the bi-layer epitaxial samples of Elias et al. (2009) (during the hydrogenation procedures of the 2 h long expositions, obviously, at T 300K).Indeed, by using values of Q app.III andD 0app.III , one can estimate the characteristic diffusion size (length) L ~ 7 × 10 -22 cm, which points to absence of such diffusion penetration.
In the next next parts of this study, a further consideration of some other known experimental data on hydrogenation and thermal stability characteristics of mono-layer, bi-layer and three-layer epitaxial graphene systems is given, where (as shown) an important role plays some defects found in graphene networks (Brito et al., 2011;Zhang et al., 2014;Banhart et al., 2011;Yazyev and Louie, 2010;Kim et al., 2011;Koepke et al., 2013;Zhang and Zhao, 2013;Yakobson and Ding, 2011;Cockayne et al., 2011;Zhang et al., 2012;Eckmann et al., 2012), relevant to the probability of hydrogen adsorption and the permeability of graphene networks for atomic hydrogen.In Wojtaszek et al. (2011), it is reported that the hydrogenation of single and bilayer graphene flakes by an argon-hydrogen plasma produced a reactive ion etching (RIE) system.They analyzed two cases: One where the graphene flakes were electrically insulated from the chamber electrodes by the SiO 2 substrate, and the other where the flakes were in electrical contact with the source electrode (a graphene device).Electronic transport measurements in combination with Raman spectroscopy were used to link the electric mean free path to the optically extracted defect concentration, which is related to the defect distance (L def.).This showed that under the chosen plasma conditions, the process does not introduce considerable damage to the graphene sheet, and that a rather partial hydrogenation (C H ≤ 0.05%) occurs primarily due to the hydrogen ions from the plasma, and not due to fragmentation of water adsorbates on the graphene surface by highly accelerated plasma electrons.To quantify the level of hydrogenation, they used the integrated intensity ratio (I D /I G ) of Raman bands.The hydrogen coverage (C H ) determined from the defect distance (L def. ) did not exceed ~ 0.05%.

Consideration and interpretation of the
In Nechaev and Veziroglu (2013), the data (Wojtaszek et al., 2011) (Figure 5) has been treated and analyzed.The obtained analytical results (Table 2) on characteristics of hydrogenation-dehydrogenation of graphene flakes (Wojtaszek et al., 2011) may be interpreted within the models used for interpretation of the similar characteristics for the epitaxial graphenes of Elias et al. (2009) (Table 1A), which are also presented (for comparing) in Table 2.
By taking into account the fact that the RIE exposure regime (Wojtaszek et al., 2011) is characterized by a form of (I D /I G ) ~ L def.
-2 (for (I D /I G ) < 2.5), L def.  11 -17 nm and the hydrogen concentration C H ≤ 5 × 10 4 , one can suppose that the hydrogen adsorption centers in the single graphene flakes (on the SiO 2 substrate) are related in some point, nanodefects (that is, vacancies and/or triple junctions (nodes) of the grain-boundary network) of diameter d def. const.In such a model, the quantity C H can be described satisfactory as: Where n H  const. is the number of hydrogen atoms adsorbed by a center; C H ~ (I D /I G ) ~ L def.
-2 .It was also found (Wojtaszek et al., 2011) that after the Ar/H 2 plasma exposure, the (I D /I G ) ratio for bi-layer graphene device is larger than that of the single graphene device.As noted in (Wojtaszek et al. (2011), this observation is in contradiction to the Raman ratios after exposure of graphene to atomic hydrogen and when other defects are introduced.Such a situation may have place in Elias et al. (2009) for bi-layer epitaxial graphene on SiO 2 /Si wafer.
In Castellanos-Gomez (2012) and Wojtaszek et al. (2012), the effect of hydrogenation on topography and electronic properties of graphene grown by CVD on top of a nickel surface and HOPG surfaces were studied by scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS).The surfaces were chemically modified using 40 min Ar/H 2 plasma (with 3 W power) treatment (Figure 6) average an energy band gap of 0.4 eV around the Fermi level.Although the plasma treatment modifies the surface topography in an irreversible way, the change in the electronic properties can be reversed by moderate thermal annealing (for 10 min at 553K), and the samples can be hydrogenated again to yield a similar, but slightly reduced, semiconducting behavior after the second hydrogenation.The data (Figure 6) show that the time of desorption from both the epitaxial graphene/Ni samples and HOPG samples of about 90 to 99% of hydrogen under 553K annealing is t 0.9(des.)553K(or t 0.99(des.)553K )  6 × 10 2 s.Hence, by using Equation ( 8), one can evaluate the quantity  0.63(des.)553K[52] 260 (or 130) s, which is close (within the errors) to the similar quantity of  0.63(des.)553K[51] 70 s for the epitaxial graphene flakes (Wojtaszek et al., 2011) (Table 2).
As noted in Castellanos-Gomes et al. ( 2012) and Arramel et al. (2012), before the plasma treatment, the CVD graphene exhibits a Moiré pattern superimposed to the honeycomb lattice of graphene (Figure 6d).This is due to the lattice parameter mismatch between the graphene and the nickel surfaces, and thus the characteristics of the most of the epitaxial graphene samples.On the other hand, as is also noted in Castellanos-Gomes et al. ( 2012) and Arramel et al., 2012), for the hydrogenated CVD graphene, the expected For the HOPG, the typical triangular lattice can be resolved all over the surface.For the CVD graphene, a Moiré pattern, due to the lattice mismatch between the graphene and the nickel lattices, superimposed onto the honeycomb lattice is observed.b,e) After 40 min of Ar/H 2 plasma treatment, the roughness of the surfaces increases.The surfaces are covered with bright spots where the atomic resolution is lost or strongly distorted.c,f) graphene surface after 10 min of moderate annealing; the topography of both the HOPG and CVD graphene surfaces does not fully recover its original crystallinity.g) Current-voltage traces measured for a CVD graphene sample in several regions with pristine atomic resolution, such as the one marked with the red square in (e).h) The same as (g) but measured in several bright regions, such as the one marked with the blue circle in (e), where the atomic resolution is distorted.
structural changes are twofold.First, the chemisorption of hydrogen atoms will change the sp 2 hybridization of carbon atoms to tetragonal sp 3 hybridization, modifying the surface geometry.Second, the impact of heavy Ar ions, present in the plasma, could also modify the surface by inducing geometrical displacement of carbon atoms (rippling graphene surface) or creating vacancies and other defects (for instance, grain or domain boundaries (Brito et al., 2011;Zhang et al., 2014;Banhart et al., 2011;Yazyev and Louie, 2010;Kim et al., 2011;Koepke et al., 2013;Zhang and Zhao, 2013;Yakobson and Ding, 2011;Cockayne et al., 2011;Zhang et al., 2012;Eckmann et al., 2012).Figure 6e shows the topography image of the surface CVD graphene after the extended (40 min) plasma treatment.The nano-order-corrugation increases after the treatment, and there are brighter nano-regions (of about 1 nm in height and several nm in diameter) in which the atomic resolution is lost or strongly distorted.It was also found (Castellanos-Gomez, Wojtaszek et al., 2012;Castellanos-Gomes, Arramel et al., 2012) that these bright nano-regions present a semiconducting behavior, while the rest of the surface remains conducting (Figure 6g to h).
It is reasonable to assume that most of the chemisorbed hydrogen is localized into these bright nano-regions, which have a blister-like form.Moreover, it is also reasonable to assume that the monolayer (single) graphene flakes on the Ni substrate are permeable to atomic hydrogen only in these defected nano-regions.This problem has been formulated in Introduction.A similar model may be valid and relevant for the HOPG samples (Figure 6a to c).
It has been found out that when graphene is deposited on a SiO 2 surface (Figures 7 and 8) the charged impurities presented in the graphene/substrate interface produce strong inhomogeneities of the electronic properties of graphene.On the other hand, it has also been shown how homogeneous graphene grown by CVD can be altered by chemical modification of its surface by the chemisoption of hydrogen.It strongly depresses the local conductance at low biases, indicating the opening of a band gap in graphene (Castellanos-Gomes, Arramel et al., 2012;Castellanos-Gomez, Smit et al., 2012).
The charge inhomogeneities (defects) of epitaxial hydrogenated graphene/SiO 2 samples do not show long range ordering, and the mean spacing between them is  L def.  20 nm (Figure 8).It is reasonable to assume that the charge inhomogeneities (defects) are located at the interface between the SiO 2 layer (300 nm thick) and the graphene flake (Castellanos-Gomes, 2012;Arramel et al., 2012;Smit et al., 2012).A similar quantity[L def. 11 -17 nm, (Wojtaszek et al., 2011) for the hydrogen adsorption centers in the monolayer graphene flakes on the SiO 2 substrate has been above considered.
In Bocquet et al. ( 2012), hydrogenation of deuteriumintercalated quasi-free-standing monolayer graphene on SiC(0001) was obtained and studied with LEED and HREELS.While the carbon honeycomb structure remained intact, it has shown a significant band gap opening in the hydrogenated material.Vibrational spectroscopy evidences for hydrogen chemisorption on the quasi-free-standing graphene has been provided and its thermal stability has been studied (Figure 9).Deuterium intercalation, transforming the buffer layer in quasi-free-standing monolayer graphene (denoted as SiC-D/QFMLG), has been performed with a D atom exposure of ~5 × 10 17 cm -2 at a surface temperature of 950K.Finally, hydrogenation up to saturation of quasi-free-standing monolayer graphene has been performed at room temperature with H atom exposure > 3 × 10 15 cm -2 .The latter sample has been denoted as SiC-D/QFMLG-H to stress the different isotopes used.
These analytical results on characteristics of hydrogen desorption (dehydrogenation) from (of) SiC-D/QFMLG-H samples (Bocquet et al., 2012) may be also (as the previous results) interpreted within the models used for interpretation of the similar characteristics for the epitaxial graphenes (Elias et al., 2009) (Tables 1A and 2).
In the same way, one can treat the points from Figure 9 (at T i = 1010, 1120 and 1200 K), which are related to the intercalated deuterium desorption from SiC-D/QFMLG samples.This results in finding the desired quantities (Table 2) points out that the process cannot be described within the Polanyi-Wigner model (Nechaev, 2010;Nechaev and Veziroglu, 2013), related to the case of a non-diffusion rate limiting kinetics.And as concluded in Bocquet et al. (2012), the exact intercalation mechanism of hydrogen diffusion through the anchored graphene lattice, at a defect or at a boundary of the anchored graphene layer, remains an open question.
Formally, this desorption process (obviously, of a diffusion-limiting character) may be described (as shown below) similarly to TDS process III (model "F*") (Table 1B), and the apparent diffusion activation energy may be close to the break-down energies of the C-H bonds.
Obviously such analytical results on characteristics of deuterium desorption from SiC-D/QFMLG samples (Bocquet et al., 2012) may not be interpreted within the models used for interpretation of the similar characteristics for the epitaxial graphenes (Elias et al., 2009) (Tables 1A and 2).
But these results (for SiC-D/QFMLG samples of Bocquet et al. ( 2012) may be quantitatively interpreted on the basis of using the characteristics of process III (Table 1B).Indeed, by using the quantities' values (from Table 1) of ∆H (des.)(SiC-D/QFMLG)[55]Q app.III  2.6 eV, K 0(des.)(SiC-D/QFMLG)[55]  6 × 10 8 s -1 and D 0app.III 3 × 10 -3 cm 2 /s, one can evaluate the quantity of L  (D 0app.III / K 0(des.) ) 1/2 = 22 nm.The obtained value of L coincides (within the errors) with values of the quantities of L def.  11 -17 nm [Equation (10)] and L def.  20 nm (Figure 8b).It shows that in the case under consideration, the intercalation mechanism of hydrogen (deuterium) diffusion through the anchored graphene lattice at the corresponding point type defects (Brito et al., 2011;Zhang et al., 2014;Banhart et al., 2011;Yazyev and Louie, 2010;Kim et al., 2011;Koepke et al., 2013;Zhang and Zhao, 2013;Yakobson and Ding, 2011;Cockayne et al., 2011;Zhang et al., 2012;Eckmann et al., 2012), of the anchored graphene layer may have place.And the desorption process of the intercalated deuterium may be rate-limited by diffusion of deuterium atoms to a nearest one of such point type defects of the anchored graphene layer.

CONSIDERATION AND INTERPRETATION OF THE RAMAN SPECTROSCOPY DATA ON DEHYDROGENATION OF GRAPHENE LAYERS ON SIO 2 SUBSTRATE
In Luo et al. (2009), graphene layers on SiO 2 /Si substrate have been chemically decorated by radio frequency hydrogen plasma (the power of 5 -15 W, the pressure of 1 T or) treatment for 1 min.The investigation of hydrogen coverage by Raman spectroscopy and micro-x-ray photoelectron spectroscopy (PES) characterization demonstrates that the hydrogenation of a single layer graphene on SiO 2 /Si substrate is much less feasible than that of bi-layer and multilayer graphene.Both the hydrogenation and dehydrogenation processes of the graphene layers are controlled by the corresponding energy barriers, which show significant dependence on the number of layers.These results (Luo et al., 2009) on bilayer graphene/SiO 2 /Si are in contradiction to the results (Elias et al., 2009) on a negligible hydrogenation of bi-layer epitaxial graphene on SiO 2 /Si wafer, when obviously other defects are produced.
A similar treatment of the kinetic data from (Figure 6c) in Luo et al. (2009) for bi-layer graphene 2LG-5W samples results in obtaining 4 values for the #1 reaction rate constant K 1(2LG-5W) for 4 temperatures (T = 348, 373, 398 and 423K), and 3 values for the #2 reaction rate constant K 2(2LG-5W) for 3 temperatures (T = 573, 623 and 673K).Their temperature dependence is described by Equation ( 9).Hence, one can evaluate the following desired values (Table 3): the #1 reaction activation energy ∆H des.1[(2LG-5W) = 0.50 ± 0.15 eV, the perexponential factor of the #1 reaction rate constant K 0des.1(2LG-5W) 210 3 s -1 , the #2reaction activation energy ∆H des.2(2LG-5W) = 0.40 ± 0.15 eV, and the per-exponential factor of the #2 reaction rate constant K 0des.2(2LG-5W) 1 s - 1 .The obtained analytical results (Table 3) on characteristics of desorption (dehydrogenation) processes #1and #2 (Luo et al., 2009) may be interpreted within the models used for interpretation of the similar characteristics for the epitaxial graphenes (Elias et al.,2009) (Table 1A).It shows that the desorption processes #1and #2 in Luo et al. (2009) may be of a diffusion-rate-controlling character.et al. (2006) present results of a STM study of HOPG samples treated by atomic deuterium, which reveals the existence of two distinct hydrogen dimer nano-states on graphite basal planes (Figures 11 and  12b).The density functional theory calculations allow them to identify the atomic structure of these nano-states and to determine their recombination and desorption pathways.As predicted, the direct recombination is only possible from one of the two dimer nano-states.In conclusion (Hornekaer et al., 2006), this results in an increased stability of one dimer nanospecies, and explains the puzzling double peak structure observed in temperature programmed desorption spectra (TPD or TDS) for hydrogen on graphite (Figure 12a).
It shows that the desorption processes #1and #2 (in Hornekaer et al. (2006) and Luo et al. (2009) may be of a diffusion-rate-controlling character.Therefore, these processes cannot be described by using the Polanyi-Wigner equation (as it has been done in Hornekaer et al. (2006).

CONSIDERATION AND INTERPRETATION OF THE PES/ARPES DATA ON HYDROGENATION-DEHYDROGENATION OF GRAPHENE/SIC SAMPLES
In Watcharinyanon et al. (2011), atomic hydrogen exposures at a pressure of P H  1 × 10 -4 Pa and temperature T = 973K on a monolayer graphene grown on the SiC(0001) surface are shown, to result in hydrogen intercalation.The hydrogen intercalation induces a transformation of the monolayer graphene and the carbon buffer layer to bi-layer graphene without a buffer layer.The STM, LEED, and core-level PES measurements reveal that hydrogen atoms can go underneath the graphene and the carbon buffer layer.This transforms the buffer layer into a second graphene layer.Hydrogen exposure (15 min) results initially in the formation of bi-layer graphene (blister-like) islands with a height of ~ 0.17 nm and a linear size of ~ 20 -40 nm, covering about 40% of the sample (Figures 15b and e),   (Watcharinyanon et al., 2011) collected at V = -1 V and I = 500 pA of a) monolayer graphene, b) after a small hydrogen exposure, and c) after a large hydrogen exposure.d) Selected part of the LEED patern collected at E = 107 eV from monolayer graphene, e) after a small hydrogen exposure, and f) after a large hydrogen exposure.16a and b).With larger (additional 15 min) atomic hydrogen exposures, the islands grow in size and merge until the surface is fully covered with bi-layer grapheme (Figures 15c and 15f, 16c and d).A ( 3 ×  3) R30° periodicity is observed on the bi-layer areas.Angle resolved PES and energy filtered X-ray photoelectron emission microscopy (XPEEM) investigations of the electron band structure confirm that after hydrogenation the single -band characteristic of monolayer graphene is replaced by two bands that represent bi-layer graphene.
Annealing an intercalated sample, representing bi-layer graphene, to a temperature of1123K or higher, re-establishes the monolayer graphene with a buffer layer on SiC (0001).The dehydrogenation has been performed by subsequently annealing (for a few minutes) the hydrogenated samples at different temperatures, from 1023 to 1273K.After each annealing step, the depletion of hydrogen has been probed by PES and ARPES (Figures 17 and 18).From this data, using Equations ( 8) and ( 9), one can determine the following tentative quantities:  0.63(des.)(at 1023 and 1123K), ∆H (des.) 3.6 eV and K 0(des.)2 × 10 14 s -1 (Table 3).
The obtained value of the quantity of ∆H (des.)coincides (within the errors) with values of the quantities of Q app.IV  3.8 eV  ∆H (C-H)"C","D" (Table 1B), which are related to the diffusion-rate-limiting TDS process IV of a dissociative chemisorption of molecular hydrogen in defected regions in graphite materials (Table 1B), and to the chemisorption models "C" and "D"(Figure 4).
The obtained value of the quantity of K 0(des.) may be correlated with possible values of the (C-H) bonds' vibration frequency (ν (C-H)"C","D" ).Hence, by taking also into account that ∆H (des.) ∆H (C-H)"C","D" , one may suppose the case of a non-diffusion-rate-controlling process corresponding to the Polanyi-Wigner model (Nechaev, 2010).
On the other hand, by taking also into account that ∆H (des.) ∆H (C-H)"C","D" , one may suppose the case of a diffusion-rate-controlling process corresponding to the TDS process IV (Table 1B).Hence, by using the value (Nechaev, 2010) of D 0app.IV  6 × 10 2 cm 2 /s, one can evaluate the quantity of L ≈ (D 0app.IV / K 0(des.) ) 1/2 = 17 nm (Table 3).The obtained value of L (also, as and in the case of (SiC-D/QFMLG) (Bocquet et al., 2012), Table 2) coincides (within the errors) with values of the quantities of L def.  11 -17 nm [Equation (10)] and L def.  20 nm (Figure 8b).The obtained value of L is also correlated with the STM data (Figures 15 and 16).It shows that the desorption process of the intercalated hydrogen may be rate-limited by diffusion of hydrogen atoms to a nearest one of the permeable defects of the anchored graphene layer.
When interpretation of these results, one can also take into account the model (proposed in (Watcharinyanon et al., 2011) of the interaction of hydrogen and silicon atoms at the graphene-SiC interface resulted in Si-C bonds at the intercalated islands.

CONSIDERATION AND INTERPRETATION OF THE TDS/STM DATA FOR HOPG TREATED BY ATOMIC HYDROGEN
In Waqar (2007), atomic hydrogen accumulation in HOPG samples and etching their surface under hydrogen TDS have been studied by using a STM and atomic force microscope (AFM).STM investigations revealed that the  surface morphology of untreated reference HOPG samples was found to be atomically flat (Figure 19a), with a typical periodic structure of graphite (Figure 19b).Atomic hydrogen exposure (treatment) of the reference HOPG samples (30 -125 min at atomic hydrogen pressure P H  10 -4 Pa and a near-room temperature (~300K)) with different atomic hydrogen doses (D), has drastically changed the initially flat HOPG surface into a rough surface, covered with nanoblisters with an average radius of ~25 nm and an average height of ~4 nm   (Waqar, 2007), desorbed molecular hydrogen (Q) versus dose (D) of atomic hydrogen exposure.(b) STM image for 600x600 nm area of the HOPG sample subjected to atomic hydrogen dose of 1.8•10 16 H 0 /cm 2 , followed by hydrogen thermal desorption.
TDS of hydrogen has been found in heating of the HOPG samples under mass spectrometer control.As shown in Figure 20a, with the increase of the total hydrogen doses (D) to which HOPG samples have been exposed, the desorbed hydrogen amounts (Q) increase and the percentage of D retained in samples approaches towards a saturation stage.
After TD, no nanoblisters were visible on the HOPG surface, the graphite surface was atomically flat, and  (Waqar, 2007).covered with some etch-pits of nearly circular shapes, one or two layers thick (Figure 20b).This implies that after release of the captured hydrogen gas, the blisters become empty of hydrogen, and the HOPG surface restores to a flat surface morphology under the action of corresponding forces.
According to the concept by Waqar (2007), nanoblisters found on the HOPG surface after atomic hydrogen exposure are simply monolayer graphite (graphene) blisters, containing hydrogen gas in molecular form (Figure 21).As suggested in Waqar (2007), atomic hydrogen intercalates between layers in the graphite net through holes in graphene hexagons, because of the small diameter of atomic hydrogen, compared to the hole's size, and is then converted to a H 2 gas form which is captured inside the graphene blisters, due to the relatively large kinetic diameter of hydrogen molecules.
However, such interpretation is in contradiction with that noted in Introduction results (Xiang et al., 2010;Jiang et al., 2009), that it is almost impossible for a hydrogen atom to pass through the six-member ring of graphene at room temperature.
It is reasonable to assume (as it has been done in some previous parts of this paper) that in HOPG (Waqar, 2007) samples atomic hydrogen passes into the graphite near-surface closed nano-regions (the graphene nanoblisters) through defects (perhaps, mainly through triple junctions of the grain and/or subgrain boundary network (Brito et al., 2011;Zhang et al., 2014;Banhart et al., 2011;Yazyev and Louie, 2010;Kim et al., 2011;Koepke et al., 2013;Zhang and Zhao, 2013;Yakobson and Ding, 2011;Cockayne et al., 2011;Zhang et al., 2012;Eckmann et al., 2012), in the surface graphene layer.It is also expedient to note that in Figure 20b, one can imagine some grain boundary network decorated by the etch-pits.
The average blister has a radius of ~25 nm and a height ~4 nm (Figure 19).Approximating the nanoblister to be a semi-ellipse form, results in the blister area of S b  2.0 × 10 -11 cm 2 and its volume V b  8.4 × 10 -19 cm 3 .The amount of retained hydrogen in this sample becomes Q  2.8 × 10 14 H 2 /cm 2 and the number of hydrogen molecules captured inside the blister becomes n (Q S b )  5.5 × 10 3 .Thus, within the ideal gas approximation, and accuracy of one order of the magnitude, the internal pressure of molecular hydrogen in a single nanoblister at near-room temperature (T  300 K) becomes 10 8 Pa.The hydrogen molecular gas density in the blisters (at T  300K and P H2  1 × 10 8 Pa) can be estimated as {(QM H2 S b )/V b }  0.045 g/cm 3 , where M H2 is the hydrogen molecule mass.It agrees with data (Trunin et al., 2010) considered in Nechaev and Veziroglu (2013), on the hydrogen (protium) isotherm of 300K.
These results can be quantitatively described, with an accuracy of one order of magnitude, with the thermodynamic approach (Bazarov, 1976), and by using the condition of the thermo-elastic equilibrium for the reaction of (2H (gas) → H 2(gas_in_blisters) ), as follows (Nechaev and Veziroglu, 2013): Where P* H2 is related to the blister "wall" back pressure (caused by P H2 ) -the so called (Bazarov, 1976) surface pressure (P* H2 P H2  1 × 10 8 Pa), P H is the atomic hydrogen pressure corresponding to the atomic flux (Waqar, 2007) (P H  110 -4 Pa), P 0 H2 = P 0 H = 1 Pa is the standard pressure, ∆H dis = 4.6 eV is the experimental value (Karapet'yants and Karapet'yants, 1968) of the dissociation energy (enthalpy) of one molecule of gaseous hydrogen (at room temperatures), ∆S dis = 11.8 k B is the dissociation entropy (Karapet'yants and Karapet'yants, 1968), ∆V (S b r b / n) is the apparent volume change, r b is the radius of curvature of nanoblisters at the nanoblister edge (r b  30 nm, Figures 19 and 21b), N A is the Avogadro number, and Tis the temperature (T  300K).The quantity of (P* H2 ∆V) is related to the work of the nanoblister surface increasing with an intercalation of 1 molecule of H 2 .
The value of the tensile stresses σ b (caused by P* H2 ) in the graphene nanoblister "walls" with a thickness of d b and a radius of curvature r b can be evaluated from another condition (equation) of the thermo-elastic equilibrium of the system in question, which is related to Equation 11 as follows (Nechaev and Veziroglu, 2013): Where  b is a degree of elastic deformation of the graphene nanoblister walls, and E b is the Young's modulus of the graphene nanoblister walls.Substituting in the first part of Equation ( 12 21b).Hence, with Hooke's law of approximation, using the second part of Equation ( 12), one can estimate, with the accuracy of one-two orders of the magnitude, the value of the Young's modulus of the graphene nanoblister walls: It is close (within the errors) to the experimental value (Lee et al., 2008;Pinto and Leszczynski, 2014) of the Young's modulus of a perfect (that is, without defects) graphene (E graphene  1.0 TPa).The experimental data (Waqar, 2007;Waqar et al., 2010) on the TDS (the flux J des ) of hydrogen from graphene nanoblisters in pyrolytic graphite can be approximated by three thermodesorption (TDS) peaks, that is, #1 with T max#1  1123K, #2 with T max#2  1523K, and #3 with T max#3  1273K.But their treatment, with using the above mentioned methods (Nechaev, 2010), is difficult due to some uncertainty relating to the zero level of the J des quantity.
As noted in the previous parts of this paper, process III is related to model "F*" (Yang and Yang, 2002) (with ∆H (C-H)"F*" = (2.5 ± 0.3) eV (Nechaev, 2010), and it is a rate-limiting by diffusion of atomic hydrogen between graphene-like layers (in graphite materials and nanomaterials), where molecular hydrogen cannot penetrate (according to analysis (Nechaev, 2010) of a number of the related experimental data).
Thus, TDS peak (process) 1 (Waqar, 2007;Waqar et al., 2010) may be related to a rate-limiting diffusion of atomic hydrogen, between the surface graphene-like layer and neighboring (near-surface) one, from the graphene nanoblisters to the nearest penetrable defects of the separation distance L TDS-peak1[59] ~ 4 nm.
As considered below, a similar (relevance to results (Waqar, 2007;Waqar et al., 2010) situation, with respect to intercalation of a high density molecular hydrogen into closed (in the definite sense) nanoblisters and/or nanoregions in graphene-layer-structures, may occur in hydrogenated GNFs.

A POSSIBILITY OF INTERCALATION OF SOLID H 2 INTO CLOSED NANOREGIONS IN HYDROGENATED GRAPHITE NANOFIBERS (GNFS) RELEVANT TO THE HYDROGEN ON-BOARD STORAGE PROBLEM
The possibility of intercalation of a high density molecular hydrogen (up to solid H 2 ) into closed (in the definite sense) nanoregions in hydrogenated GNFs is based both on the analytical results presented in the previous psrts of this study (Tables 1 to 3), and on the following facts (Nechaev and Veziroglu, 2013): (1) According to the experimental and theoretical data (Trunin et al., 2010) (Figures 22 and 23), a solid molecular hydrogen (or deuterium) of density of ρ H2 = 0.3 -0.5 g/cm 3 (H 2 )can exist at 300K and an external pressure of P = 30 -50 Gpa.
(2) As seen from data in Figures 19 to 21and Equations 11 and 12, the external (surface) pressure of P = P* H2 = 30 to 50 GPa at T 300K may be provided at the expense of the association energy of atomic hydrogen (T∆S dis -∆H dis ), into some closed (in the definite sense) nano-Figure 22. Isentropes (at entropies S/R = 10, 12 and 14, in units of the gas constant R) and isotherms (at T = 300 K) of molecular and atomic deuterium (Trunin et al., 2010).The symbols show the experimental data, and curves fit calculated dependences.The density (ρ) of protium was increased by a factor of two (for the scale reasons).Thickened portion of the curve is an experimental isotherm of solid form of molecular hydrogen (H 2 ).The additional red circle corresponds to a value of the twinned density ρ  1 g/cm 3 of solid H 2 (at T 300 K) and a near-megabar value of the external compression pressure P  50 GPa (Nechaev and Veziroglu, 2013).
regions in hydrogenated (in gaseous atomic hydrogen with the corresponding pressure P H ) graphene-layernanostructures possessing of a high Young's modulus (E graphene  1 TPa).
(4) Substituting in Equation ( 12) the quantities of P* H2  5 × 10 10 Pa,  b  0.1 (Figure 24), the largest possible value of E b  10 12 Pa (Lee et al., 2008;Pinto and Leszczynski (2014)), the largest possible value of the tensile stresses (σ b  10 11 Pa (Lee et al., 2008;Pinto and Leszczynski, 2014) in the edge graphene "walls" (of a thickness of d b and a radius of curvature of r b ) of the slit-like closed nanopores of the lens shape (Figure 24), one can obtain the quantity of (r b / d b )  4. It is reasonable to assume r b  20 nm; hence, a reasonable value follows of d b  5 nm.
(5) As noted in (Nechaev and Veziroglu, 2013), a definite residual plastic deformation of the hydrogenated graphite (graphene) nano-regions is observed in Figure 24.Such plastic deformation of the nanoregins during hydrogenation of GNFs may be accompanied with some mass transfer resulting in such thickness (d b ) of the walls.(6) The related data (Figure 25) allows us to reasonably assume a break-through in results (Nechaev and Veziroglu, 2013) on the possibility (and particularly, physics) of intercalation of a high density molecular hydrogen (up to solid H 2 ) into closed (in the definite sense) nanoregions in hydrogenated GNFs (Gupta et al., 2004;Park et al., 1999), relevant for solving of the current problem (Akiba, 2011;Zuettel, 2011;DOE targets, 2012) of the hydrogen on-board effective storage.(7) Some fundamental aspects -open questions on engineering of "super" hydrogen storage carbonaceous nanomaterials, relevance for clean energy applications, are also considered in (Nechaev and Veziroglu, 2013) and in this study, as well.
Therefore, in this study, the results of the thermodynamic analysis (Equations 11 and 12) are presented, which may be used for interpretation of related data (Figures 6 to 8,11 to 16,19 to 21).
On some nanodefects (grain boundaries, their triple junctions and others), penetrable for atomic hydrogen, in the surface HOPG graphene-layers and epitaxial graphenes A number of researchers noted above have not taken into account (in a sufficient extent) the calculation results (Xiang et al., 2010) showing that the barrier for the penetration of a hydrogen atom through the six-member ring of a perfect graphene is larger than 2.0 eV.Thus, it is almost impossible for a hydrogen atom to pass through the six-member ring of a perfect (that is, without defects) graphene layer at room temperature.

On finding and interpretation of the thermodynamic characteristics of "reversible" hydrogenationdehydrogenation of epitaxial graphenes and membrane ones
A number of researchers, for instance ones noted above have not treated and compared their data on "reversible" hydrogenation-dehydrogenation of membrane graphenes and epitaxial ones, with the aim of finding and interpretation of the thermodynamic characteristics.Therefore, in this analytical study, the thermodynamic approaches (particularly, Equations 1 to 12), such  (Gupta et al., 2004) of hydrogenated graphite nanofibers (GNFs) after release from them (at 300 K for 10 min (Park et al., 1999) of intercalated high-density hydrogen (17 mass.%-the gravimetrical reversible hydrogen capacity).The arrows in the picture indicate some of the slit-like closed nanopores of the lens shape, where the intercalated high-density solid hydrogen nanophase (Nechaev and Veziroglu, 2013) was localized.treatment results of related theoretical and experimental data (Tables 1 to 3) and their interpretation are presented.As shown, these analytical results may be used for a more detailed understanding and revealing of the atomic mechanisms of the processes.
There is a considerable difference (in the declared errors and without any explanation) in the theoretical values of the energetic graphene (CH) quantities (∆H (C-H) , ∆H (bind.), ∆H (C-C) ) obtained in different theoretical studies, for instance, in (Sofo et al., 2007;Dzhurakhalov and Peeters, 2011) (Table 1A).
Unfortunately, the theoretical values of the graphene quantity of ∆H (C-C) is usually not evaluated by the researchers, and not compared by them with the much higher values of the graphene (both theoretical, and experimental) quantity of ∆H (C-C) (Table 1A).It could be useful, for instance, when considering the fundamental strength properties of graphane and graphene structures.As far as we know, most researchers have not taken into account the alternative possibility supposed in (Elias et al., 2009) that (i) the experimental graphene membrane (a free-standing one) may have "a more complex hydrogen bonding, than the suggested by the theory", and that (ii) graphane (CH) (Sofo et al., 2007) may be the until now theoretical material.

On the thermodynamic characteristics and atomic mechanisms of "reversible" hydrogenationdehydrogenation of free-standing graphene membranes
The thermodynamic analysis of experimental data (Elias et al., 2009) on "reversible" hydrogenationdehydrogenation of free-standing graphene membranes have resulted in the following conclusive suppositions and/or statements: (1) These chemisorption processes are related to a nondiffusion-rate-limiting case.They can be described and interpreted within the physical model of the Polanyi-Wigner equation for the first order rate reactions (Nechaev, 2010;Nechaev and Veziroglu, 2013), but not for the second order rate ones (Zhao et al., 2006).
(2) The desorption activation energy is of ∆H des.(membr.[5])= ∆H C-H(membr.[5])= 2.6 ± 0.1 eV (Table 1A).The value of the quantity of ∆H C-H(membr.[5]) coincides (within the errors), in accordance with the Polanyi-Wigner model, with the values of the similar quantities for theoretical graphenes (Sofo et al., 2007;Openov and Podlivaev, 2010) (Table1A) possessing of a diamond-like distortion of the graphene network.The value of the quantity of ∆H C- H(membr.[5]) coincides (within the errors) with the value of the similar quantity for model "F*" (Table 1B) manifested in graphitic structures and nanostructures not possessing of a diamond-like distortion of the graphene network (an open theoretical question).
(5) Certainly, these tentative analytical results could be directly confirmed and/or modified by receiving and treating (within Equations ( 8) and ( 9) approach) of the experimental data on  0.63 at several annealing temperatures.

On the thermodynamic characteristics and atomic mechanisms of "reversible" hydrogenationdehydrogenation of epitaxial graphenes
The thermodynamic analyses of experimental data (Waqar, 2007;Watcharinyanon et al., 2011;Wojtaszek et al., 2011;Castellanos-Gomez et al., 2012;Bocquet et al., 2012;Luo et al., 2009) on "reversible" hydrogenationdehydrogenation of epitaxial graphenes have resulted in the following conclusive suppositions and/or statements: (1) These chemisorption processes for all 16 considered epitaxial graphenes (Tables 1A, 2 and 3), unlike ones for the free-standing graphene membranes (Table 1A), are related to a diffusion-rate-limiting case.They can be described and interpreted within the known diffusion approximation of the first order rate reactions (Nechaev, 2010;Nechaev and Veziroglu, 2013), but not within the physical models of the Polanyi-Wigner equations for the first (Hornekaer et al., 2006) or for the second (Zhao et al., 2006) order rate reactions.
(3) The above obtained values of characteristics of dehydrogenation of the epitaxial graphenes can be presented, as follows: ∆H des.~ Q app.I , K 0des.~ (D 0app.I / L 2 ), where Q app.I and D 0app.I are the characteristics of process I (Table 1B), L ~ d sample , that is, being of the order of diameter (d sample ) of the epitaxial graphene samples.The diffusion-rate-limiting process I is related to the chemisorption models "F" and "G" (Figure 4).These results unambiguously point that in the epitaxial graphenes the dehydrogenation processes are ratelimiting by diffusion of hydrogen, mainly, from chemisorption "centers" (of "F" and/or "G" types (Figure (4) localized on the internal graphene surfaces to the frontier edges of the samples.These results also point that the solution and the diffusion of molecular hydrogen may occur between the graphene layer and the substrate, unlike for a case of the graphene neighbor layers in graphitic structures and nanostructures, where the solution and the diffusion of only atomic hydrogen (but not molecular one) can occur (process III (Nechaev, 2010), Table 1B).(4) The above formulated interpretation (model) is direct opposite to the supposition (model) of a number of researchers, those believe in occurrence of hydrogen desorption (dehydrogenation) processes, mainly, from the external epitaxial graphene surfaces.And it is direct opposite to the supposition -model of many scientists that the diffusion of hydrogen along the graphenesubstrate interface is negligible.

Conclusion
(1) The chemisorption processes in the free-standing graphene membranes are related to a non-diffusion-ratelimiting case.They can be described and interpreted within the physical model of the Polanyi-Wigner equation for the first order rate reactions, but not for the second order rate reactions.
The desorption activation energy is of ∆H des.(membr.)= ∆H C-H(membr.)= 2.6 ± 0.1 eV.It coincides (within the errors), in accordance with the Polanyi-Wigner model, with the values of the similar quantities for theoretical graphanes (Table 1A) possessing of a diamond-like distortion of the graphene network.It also coincides (within the errors) with the value of the similar quantity [process III, model "F*" (Table 1B)] manifested in graphitic structures and nanostructures, not possessing of a diamond-like distortion of the graphene network (an open theoretical question).
The desorption frequency factor is of K 0des.(membr.)=  C- H(membr.)  5 × 10 13 s -1 (Table 1A).It is related to the corresponding vibration frequency for the C-H bonds (in accordance with the Polanyi-Wigner model).
The adsorption activation energy (in the approximation of K 0ads.≈ K 0des. ) is of ∆H ads.(membr.)= 1.0 ± 0.2 eV (Table and predictions) time frame of several years.International cooperation is necessary.

Figure 1 .
Figure 1.Structure of the theoretical graphane in chair configuration.The carbon atoms are shown in gray and the hydrogen atoms in white.The figure shows the diamond-like distorted hexagonal network with carbon in sp 3 hybridization(Sofo et al., 2007).

Figure 2 .
Figure 2. Changes in Raman spectra of graphene caused by hydrogenation(Elias et al., 2009).The spectra are normalized to have a similar integrated intensity of the G peak. (A) Graphene on SiO 2 .(B) Free-standing graphene.Red, blue, and green curves (top to bottom) correspond to pristine, hydrogenated, and annealed samples, respectively.Graphene was hydrogenated for 2 hours, and the spectra were measured with a Renishaw spectrometer at wavelength 514 nm and low power to avoid damage to the graphene during measurements.(Left inset) Comparison between the evoluation of D and D′ peaks for single-and double-sided exposure to atomic hydrogen.Shown is a partially hydrogenated state achieved after 1 hour of simultaneous exposure of graphene on SiO 2 (blue curve) and of a membrane (black curve).(Right inset) TEM image of one of the membranes that partially covers the aperture 50 μm in diameter.

Figure 3 .
Figure3.Desorption of hydrogen from single-side graphane(Elias et al., 2009).The measurments were done by using a leak detector tuned to sense molecular hydrogen.The sample was heated to 573 K (the heater was switched on at t = 10 s).Control samples (exposed to pure argon plasma) exhibited much weaker and featureless response (< 5•10 -8 mbar L/s), which is attributed to desorption of water at heated surfaces and subtracted from the shown data (water molecules are ionized in the massspectrometer, which also gives rise to a small hydrogen signal).

Figure 4 .
Figure 4. Schematics of some theoretical models (ab initio molecular orbital calculations (Yang and Yang, 2002) of chemisorption of atomic hydrogen on graphite on the basal and edge planes.

Figure 5 .
Figure 5. (a) Raman spectrum of pristine single layer graphene -SLG (black) and after 20 min of exposure to the Ar/H 2 plasma (blue) (Wojtaszek et al., 2011).Exposure induces additional Raman bands: a D band around 1340 cm -1 and a weaker D′ band around 1620 cm -1 .The increase of FWHM of original graphene bands (G, 2D) is apparent.(b) Integrated intensity ratio between the D and G bands (I D /I G ) of SLG after different Ar/H 2 plasma exposure times.The scattering of the data for different samples is attributed to the floating potential of the graphene flake during exposure.(c) The change of the I D /I G ratio of exposed flakes under annealing on hot-plate for 1 min.The plasma exposure time for each flake is indicated next to the corresponding I D /I G values.In flakes exposed for less than 1 h the D band could be almost fully suppressed (I D /I G < 0.2), which confirms the hydrogen-type origin of defects.In longer exposed samples (80 min and 2 h), annealing does not significantly reduce I D /I G , which suggests a different nature of defects, e.g., vacancies.

Figure 6 .
Figure 6.(a-f) Topography images acquired in the constant-current STM mode (Castellanos-Gomez, Wojtaszek et al., 2012): (a-c) HOPG, d-f) graphene grown by CVD on top of a nickel surface at different steps of the hydrogenation/dehydrogenation process.a,d) Topography of the surface before the hydrogen plasma treatment.For the HOPG, the typical triangular lattice can be resolved all over the surface.For the CVD graphene, a Moiré pattern, due to the lattice mismatch between the graphene and the nickel lattices, superimposed onto the honeycomb lattice is observed.b,e) After 40 min of Ar/H 2 plasma treatment, the roughness of the surfaces increases.The surfaces are covered with bright spots where the atomic resolution is lost or strongly distorted.c,f) graphene surface after 10 min of moderate annealing; the topography of both the HOPG and CVD graphene surfaces does not fully recover its original crystallinity.g) Current-voltage traces measured for a CVD graphene sample in several regions with pristine atomic resolution, such as the one marked with the red square in (e).h) The same as (g) but measured in several bright regions, such as the one marked with the blue circle in (e), where the atomic resolution is distorted.

Figure 7 .
Figure 7. (a) Optical image of the coarse tip positioning on a few-layers graphene flake on the SiO 2 substrate, (b) AFM topography image of the interface between the few-layers graphene flake and the the SiO 2 substrate and areas with different number of layers (labeled as >10, 6, 4 and 1 L) are found, (c) Topographic line profile acquired along the dotted line in (b), showing the interface between the SiO 2 substrate and a monolayer (1L) graphene region, and (d) STM topography image of the regions marked by the dashed rectangle in (b) (Castellanos-Gomes, 2012; Arramelet al., 2012; Castellanos-Gomez, 2012; Smit et al., 2012).

Figure 9 .
Figure 9. Evaluation of the HREELS elastic peak FWHM of SiC-D/QFMLG-H upon annealing.The uncertain annealing temperature is estimated to be 5 %.Error bars represent the σ variation of FWHM measured across the entire surface of several samples (Bocquet et al., 2012).

Figure 10 .
Figure 10.(a) The evoluation of the D and G band intensity ratio (I D /I G ) with annealing temperatures of 1LG (single-layer graphene) hydrogenated by 5 and 15 W (the power), 1 Torr hydrogen plasma for 1 min (Luo et al. (2009)); (b) the evoluation of ∆(I D /I G ) with annealing temperatures of 1 LG hydrogenated by 5 and 15 W, 1 Torr hydrogen plasma for 1 min; (c) the evoluation of the D and G band intensity ratio (I D /I G ) with annealing temperatures of 2LG (bi-layer graphene) hydrogenated by 5 and 15 W, 1 Torr hydrogen plasma for 1 min; (d) the evoluation of ∆(I D /I G ) with annealing temperatures of 2LG hydrogenated by 5 and 15 W, 1 Torr hydrogen plasma for 1 min.The asterisk (*) denotes the astreated sample by H 2 plasma.

Figure 11 .
Figure 11.(a) STM image (103 × 114 Å 2 ) of dimer structures of hydrogen atoms on the graphite surface after a 1 min deposition at room temperature (Hornekaer et al., 2006).Imaging parameters: V t = 884 mV, I t = 160 pA.Examples of dimmer type A and B are marked.Black arrows indicate ‹21⎯1⎯0› directions and white arrows indicate the orientation of the dimers 30˚ off.(c) Close up of dimer B structure in lower white circle in image (a).

Figure 12 .
Figure 12.(a) A mass 4 amu, i.e., D 2 , TPD spectrum from the HOPG surface after a 2 min D atom dose (ramp rate: 2 K / s below 450 K, 1 K / s above) (Hornekaer et al., 2006).The arrow indicates the maximum temperatue of the thermal anneal performed before recording the STM image in (b).(b) STM image (103 × 114 Å 2 ) of dimer structures of hydrogen atoms on the graphite surface after a 1 min deposition at room temperature and subsequent anneal to 525 K (ramp rate: 1 K / S, 30 s dwell at maximum temperature).Imaging parameters: V t = 884 mV, I t = 190 pA.The inset shows a higher resolution STM image of dimer structures of hydrogen atoms on the graphite surface after a 6 min deposition at room temperature and subsequent anneal to 550 K. Imaging parameters: V t = -884 mV, I t = -210 pA.

Figure 15 .
Figure 15.STM images(Watcharinyanon et al., 2011) collected at V = -1 V and I = 500 pA of a) monolayer graphene, b) after a small hydrogen exposure, and c) after a large hydrogen exposure.d) Selected part of the LEED patern collected at E = 107 eV from monolayer graphene, e) after a small hydrogen exposure, and f) after a large hydrogen exposure.

Figure 17 .
Figure 17.Normalized C 1s core level spectra of monolayer graphene (Watcharinyanon et al., 2011) before and after hydrogenation and subsequent annealing at 1023, 1123, 1223, and 1273 K. b) Fully hydrogenated graphene along with monolayer graphene before hydrogenation.The spectra were acquired at a photon energy of 600 eV.

Figure 18 .
Figure 18.Normolized Si 2p core level spectra of monolayer graphene (Watcharinyanon et al., 2011) before and after hydrogenation and subsequent annealing at 1023, 1123, 1223, and 1273 K.The spectra were acquired at a photon energy of 140 eV.

Figure 19 .
Figure 19.STM images of the untreated HOPG sample (Waqar, 2007) (under ambient conditions) taken from areas of (a) 60.8 x60.8 nm and (b) 10.9x10.9nm (high resolution image of the square in image (a)).(c).AFM image (area of 1x1 nm) of the HOPG sample subjected to atomic hydrogen dose (D) of 1.8•10 16 H 0 /cm 2 .(d) Surface height profile obtained from the AFM image reported in (c).The STM tunnel V bias and current are 50-100 mV and 1-1.5 mA, respectively.

Figure 23 .
Figure 23.Phase diagram(Trunin et al., 2010), adiabats, and isentropes of deuterium calculated with the equation of state: 1 and 2 are a single and a doubled adiabat, • -the experimental data, 3 -melting curve, thickened portion of the curve -the experimental data.The additional red circle corresponds to a value of temperature T  300 K and a near-megabar value of the external compression pressure P  50 GPa (Nechaev and Veziroglu, 2013).

Figure 24 .
Figure 24.Micrographs(Gupta et al., 2004) of hydrogenated graphite nanofibers (GNFs) after release from them (at 300 K for 10 min(Park et al., 1999) of intercalated high-density hydrogen (17 mass.%-the gravimetrical reversible hydrogen capacity).The arrows in the picture indicate some of the slit-like closed nanopores of the lens shape, where the intercalated high-density solid hydrogen nanophase (Nechaev and Veziroglu, 2013) was localized.

Figure 25 .
Figure 25.It is shown (in the face of known achievements) U.S. DOE system targets for 2010 and 2015, relevant to gravimetric and volumetric hydrogen on-board storage densities.The additional red circle is related to the solid hydrogen nanophase (Nechaev and Veziroglu, 2013) intercalated into the hydrogenated GNFs (Figure 24).

Table 1B .
Theoretical, experimental and analytical values of some related quantities.

Table 2 .
Analytical values of some related quantities.

Table 3 .
Analytical values of some related quantities.