Thermodynamic Aspects of the Graphene / Graphane / Hydrogen Systems : Relevance to the Hydrogen On-Board Storage Problem

The present analytical review is devoted to the current problem of thermodynamic stability and related thermodynamic characteristics of the following graphene layers systems: 1) double-side hydrogenated graphene of composition CH (theoretical graphane) (Sofo et al. 2007) and experimental graphane (Elias et al. 2009); 2) theoretical single-side hydrogenated graphene of composition CH; 3) theoretical single-side hydrogenated graphene of composition C2H (graphone); 4) experimental hydrogenated epitaxial graphene, bilayer graphene and a few layers of graphene on SiO2 or other substrates; 5) experimental and theoretical single-external side hydrogenated single-walled carbon nanotubes, and experimental hydrofullerene C60H36; 6) experimental single-internal side hydrogenated (up to C2H or CH composition) graphene nanoblisters with intercalated high pressure H2 gas inside them, formed on a surface of highly oriented pyrolytic graphite or epitaxial graphene under the atomic hydrogen treatment; and 7) experimental hydrogenated graphite nanofibers-multigraphene with intercalated solid H2 nano-regions of high density inside them, relevant to solving the problem of hydrogen on-board storage (Nechaev 2011-2012).


Introduction
As noted in a number of articles from 2007 through 2013, hydrogenation of grapheme-a single layer of carbon atoms arranged in a honeycomb lattice-as a prototype of covalent chemical functionality, and an effective tool to open the band gap of graphene is of fundamental importance [1,2].
In this analytical review, results of thermodynamic analysis and comparison of some theoretical and experimental data are presented, including those from the most cited works [3,5] and from the least non-cited works [18][19][20][21].
In [8], the double-side hydrogenation of graphene is now well understood, at least from a theoretical point of view.For example, Sofo et al. predicted theoretically a new insulating material of CH composition called graphane (double-side hydrogenated graphene), in which each hydrogen atom is adsorbed 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 [3].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 [3,22].In contrast to graphene (a zero-gap semiconductor), graphane is an insulator with an energy gap of E g  5.4 eV [4,23].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 -400 K [24].
As was noted in [6], neither graphone nor graphane is 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 [9].
Single-side hydrogenated graphene (SSHG) of CH composition is an alternative to graphane, in which hydrogen atoms are adsorbed only on one side [7,25].In contrast to graphone, they are also 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 in a solid substrate in principle.However, this quasi-two-dimensional carbon-hydrogen theoretical system is shown to have a relatively low thermal stability, which makes it difficult to use SSGG in practice [6,7].
As seen in [7], 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, i.e., 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 SSH Graphene 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.Such model is taken into further consideration in this analytical study [10][11][12][13][14][15][16][17][18][19][20][21].
It is worth repeating the prediction for the double-side hydrogenated graphene (a free-standing membrane) that was partially confirmed by Elias et al. [5].They demonstrated that graphene can react with atomic hydrogen, which transforms this highly conductive zero-overlap semimetal into an insulator of high thermal stability, and the double-side hydrogenation of graphene is reversible.The authors themselves expressed some doubts, relevant to the complete adequacy of the experimental graphane to the theoretical one [3].Alternatively, they supposed that the experimental graphane (a free-standing membrane) produced by them may have a more complex hydrogen bonding than the one suggested by the theory, and that the latter may be as an "until now theoretical material".
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. [5].The authors mentioned a possible contradiction with the theoretical results of Sofo et al. [3], 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 graphenebased crystal-the experimental graphane produced by them.
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 [5].
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 [32].But these two aspects are of the kinetic character, and therefore they can not influence the thermodynamic predictions [3,24,31].
Authors of [8] noted that their test calculations show that the barrier for the penetration of a hydrogen atom through the six-membered 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-membered ring of graphene at room temperature (from a private communication with H. G. Xiang and M.-H.Whangbo).
In the present analytical review, a real possibility 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, i.e., in grain boundaries and/or vacancies [33][34][35][36][37][38][39][40][41][42].This is related to further consideration of data in this analytical study as mentioned above.
Previous theoretical studies suggest that single-side hydrogenation of ideal graphene would be thermodynamically unstable [24,31].Thus, it remains a puzzle why the single-side hydrogenation of epitaxial graphene is possible and even reversible, and why the hydrogenated species are stable at room temperatures [5,43].This puzzling situation is also considered in the present analytical review.The main aim of this study is to show a real possibility, at least, from the thermodynamic point of view, of the existence of hydrogenated graphene-based nanostructures [18][19][20][21] possessing very high Young's modulus, and also showing a real possibility of intercalation in nanostructures of solid molecular hydrogen under definite hydrogenation conditions relevant to the current problem of hydrogen on-board storage.

Consideration of Data on Theoretical Graphanes
In work [3], the stability of graphane, a fully saturated extended two-dimentional hydrocarbon derived from a single graphene 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 chair-like (diamond-like, Figure 1) conformer and a boat-like (zigzag- like) conformer [3].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 (

 
bind.graphane H  ) (i.e., the difference between the total energy of the isolated atoms and the total energy of the compounds), and the standard energy of formation (   ) of the compounds (   graphane ) from crystalline graphite (   graphite ) and gaseous molecular hydrogen (   2 gas ) at the standard pressure and temperature conditions [3].
For the diamond-like graphane, the former quantity is and the latter one is The latter quantity corresponds to the following reaction: where 1 H  is the standard energy (enthalpy) change for this reaction.
By using the theoretical quantity of   , one can evaluate, using the framework of the thermodynamic method of cyclic processes [44], a value of the energy of formation ( ) [3].For this, it is necessary to take into consideration the following three additional reactions: Reaction (2) can be presented as a sum of reactions ( 1), ( 3) and (4) using the framework of the thermodynamic method of cyclic processes [44]: Substituting in Equation ( 5) the known experimental values of


characterizes the break-down energy of C-H sp 3 bond in graphane (Figure 1), relevant to the breaking away of one hydrogen atom from the material, which is In evaluating the above mentioned value of ∆H This theoretical quantity coincides with the similar empirical quantities obtained in [18][19][20][21] from for C-C sp 2 bonds in graphene and graphite, which are The similar empirical quantity for C-C sp 3 bonds in diamond obtained from the diamond sublimation energy is It is important to note that chemisorption of hydrogen on graphene was studied using atomistic simulations, with a second generation reactive empirical bond order of Brenner inter-atomic potential.As it has been shown, the cohesive energy of graphane (CH) in the ground state is   cohes.graphane (C).This results in the binding of hydrogen energy, which is [25].
The theoretical quantity characterizes the break-down 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 bind.graphane

and
, one can evaluate the break-down energy of C-C sp 3 bonds in the theoretical graphane, which is .Also, by using the above noted theoretical values of and , one can evaluate similarly the break-down energy of C-C sp 3 bonds in the theoretical graphane, which is C-C gra .
Comparing the obtained values of , , , and show that the elastic and intrinsic strength properties, and particularly, the Young's modulus of the theoretical graphanes is much less than those for perfect

Thermal Desorption from Theoretical Experimental Graphanes
], the process of hydrogen therm graphane has been studied using the method of molecular dynamics.The temperature dependence for T = 1300 -3000 K at the time ( 0.01  ) of hydrogen desorption onset (i.e., the time of removal 1% ( C  ) of the initial hydrogen concentration C 0  0.
where k B is the Boltzmann constant.The authors predicted that their results would not contradict the experimental data [5], according to which the nearly complete desorption of hydrogen   0 0.9 C C   from a graphane membrane (Figure 2 d by annealing it in argon at T = 723 K for 24 hours (i.e.,   4 0.9 membr.723K 8. 64  (b an t y five orders) th  value [4].In the framework of the for approximatio mal kinetics n of the first order rate reaction [46], a characteristic quantity for the reaction of hydrogen desorption is 0.63-the time of the removal of ~ 63% ( C  ) of the initial hydrogen concentration C0 (i.e., 0 0.63   ) from the hydrogenated graphene.Such a fir e reaction (desorption) can be described by the following equations [14,46]: the reaction (desorption) activation energy, an the per-exponential (or frequency) factor of the reaction rate constant.In the case of a non-diffusion rate limiting kinetics, the quantity of K 0 may be the corresponding vibrational frequency (K 0 = ), and Equation ( 9) may be related to the Polanyi-Wigner value [14].By substituting in Equation (8)  mbranes [5].The  is less by one and a half orders of the vibraequency  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).tional fr The activation of which in the hydrogenated samples authors attribute to breaking of the translation symmetry of C-C sp 2 bonds after formation of C-H sp 3 bonds.Also,  is less by one order of the vibrational frequency  HREELS = 8.7•10 13 s −1 corresponding to an additional S peak arising from C-H sp 3 , and a stretching appears at 369 meV after a partial hydrogenation of the epitaxial graphene.The authors suppose that this peak can be assigned to the vertical C-H bonding, giving direct evidence for hydrogen attachment on the epitaxial graphene surface [47].
Taking into account  RD and  HREELS quantities, and substituting in Equation ( 9 ).
The abov analysis of the related data s s that for the e e how xperimental graphene membranes (hydrogenated up to the near-saturation) can be used for the following thermodesorption characteristics, relevant to Equation (9), of the empirical character:  The analysis also shows that this is a cas a nondiff e for usion rate limiting kinetics, when Equation (9) corresponds to the Polanyi-Wigner [14].Certainly, these tentative results could be directly confirmed and/or modified by receiving and treating within Equations ( 8) and ( 9) of the experimental data on  0.63 at several annealing temperatures.
The above noted fact that the empirical quantity ), is consistent with in [5].The alternative possibility that the experimental graphane membrane (a free-standing membrane) may have a more complex hydrogen bonding, than the suggested by the theory, may point out for further theoretical developments.

Consideration of a The
Substituting in Equation ( 12) above the consi show that the elastic and intrinsic strength properties (and particul f nostr be se for nec o note arly Young's modulus (E)) o graphane * -like na uctures can closer to tho graphene.In con tion with this, it is relevant t that a unique ed isotropically by nearly 10% (i.e., the elastic de experimental value from work [48] of a Young's modulus of graphene is E graphene = 1.0 terapascal. As was noted in [5], when a hydrogenated graphene membrane has no free boundaries (a rigidly fixed membrane) in the expanded regions of it, the lattice is stretch formation degree  fix.membr. 0.1) with respect to the pristine graphene.This amount of stretching (  0.1) is close to the limit of possible elastic deformations in graphene, and indeed it has been observed that some of their membranes rupture during hydrogenation.It is believed that the stretched regions are likely to remain non-hydrogenated.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 m, and that the annealing of such membranes led to complete recovery of the periodicy in both stretched and compressed domains [5].
By using the experimental value of the degree of elastic deformation ( in the expanded regions (domains or grains) of the material [5,48].This analytic ne al result in this study is consistent wit the analytical results of the related data considered from [15][16][17][18][19][20][21], relevant to the possibility of t e exis-h h tence of hydrogenated graphane * -like nanostructures possessing of a Young's modulus value close to that of grapheme ( * graphene graphane ).

Consideration of Data on Hydrogen
Desorption in the Hydrogenated Mono-and Bi-Layer Epitaxial Graphene Samples sidered ples dc p in the In [5], both the graphene membrane samples con above, and the epitaxial graphene and bi-graphene samon substrate SiO 2 were exposed to a cold hydrogen lasma for 2 hours to reach the saturation measured characteristics.They used a low-pressure (0.1 mbar) hydrogen-argon mixture of 10% H 2 ).Raman spectra for hydrogenated and subsequently annealed graphene membranes (Figure 2(b)) are rather similar to those for epitaxial graphene samples (Figure 2(a)), but with some notable differences.If hydrogenated simultaneously for 1 hour, and before reaching the saturation (a partial hydrogenation), the D peak area for a membrane was two factors greater than the area for graphene on a substrate (Figure 2, the left inset), which 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 hours, a near-complete hydrogenation) of membranes to atomic hydrogen.The integrated intensity area of the D peak in Figure 2(b) corresponding to the adsorbed hydrogen saturation concentration in the graphene membranes is larger by a factor of about 3 for the area of the D peak in Figure 2(a), corresponding to the hydrogen concentration in the epitaxial graphene samples.This may be related to some partial hydrogenation localized in some defected nano-regions of the epitaxial graphene samples even after the prolonged (3 hour) exposures, i.e. after reaching their near-saturation [33][34][35][36][37][38][39][40][41][42]49].It is expedient to note that in [5], the absolute values of the adsorbed hydrogen concentration (C 0 ) were neither considered for the hydrogenated graphene membranes, nor for the hydrogenated epitaxial graphene samples.
According to a private communication from D.C. Elias, a near-complete desorption of hydrogen .aman spectra of graphene [5] caused by hydrogenation were rather o locations of D, G, D', 2D and (D + D') peaks, both for SiO aphene membrane (Figure 2).Hence, one can suppose that Then, by substituting in Equation ( 9) the values of

and , one can evaluate
Here, the case is supposed of a non-diffusion-rateing kinetics, w rresponds to the Polanyi-Wigner one [14].Certainly, these tentative thermodynamic characteristics of the hydrogenated epitaxial gr limit hen Equation ( 9) co aphene on a substrate SiO 2 could be directly confirmed and/or modified by further experimental data on  at various annealing temperatures.It is now easy to state that: 1) these analytical results are not consistent with the mass spectrometry data (Figure 3) on thermal desorption of hydrogen from a spepared single-side graphane; and 2) the cially pre y cannot be graphane (under heating fr described in the framework of the theoretical models and characteristics of thermal stability of single-side hydrogenated graphene [6] or graphone [9].According to the further considerations in this study, it may be a hydrogen desorption case of a diffusion rate limiting kinetics, when K 0  , and Equation ( 9) does not correspond to the Polanyi-Wigner one [14].
By using the method of treatment for thermal desorption (TDS) spectra, relevant to the mass spectrometry data (Figure 3) on thermal desorption of hydrogen from a specially prepared single-side om room temperature to 573 K for 6 minutes), one can obtain the following results: 1) the total integrated area of the thermal desorption spectra corresponds to 2•10 −8 g of desorbed hydrogen; 2) the TDS spectra can be approximated by three thermodesorption (TDS) peaks (# 1, # 2 and # 3); 3) TDS peak # 1 (30% of the total area, T max#1  370 K) can be characterized by the activation energy of E TDS-peak # 1 = 0.6  0.3 eV and by the per-exponential factor of the reaction rate constant   ; and 5) TDS peak # 3 (55% of the total area, T max # 3  540 K) can be characterized by the activation energy E TDS-peak # 3 = 0.23  0.05 eV and by the per-exponential factor of the reaction rate constant miting kinetics, whe [14].These analytical results show that all three of the above noted thermal desorption (TDS) processes (# 1 TDS , # 2 TDS and # 3 TDS ) may be related to a hydrogen desorption case of a diffusion-rateli n in Equation 9 the value of 2 0 0 a p p .
and the value of des.app.
, where D 0app is the per-exponent factor of the apparent diffusion coefficient , L is the characteristic diffusional size (length), and Q app. is the appare n activation energy.s # 3 TDS may be related to TDS process (or peak) I in [14,[18][19][20][21] which may be related to the linear size of the graphene y be related to chemisorption models "H" and/or "G" (Figure 4) corresponding to TDS process (or peak) I in [14,[18][19][20][21].
It is important to note that in Items 2.1 -2.3 chemisorption of atomic hydrogen on graphene membranes may be related to model "F * " [14,16,[18][19][20][21], which is relevant to chemisorption of a single hydrogen atom on one of the carbon atoms possessing of 3 unoccupied (by hydrogen) nearest carbons, but not two hydrogen atoms on two carbons, as seen in model "F".Model "F * " is characterized [14,16,[18][19][20][21] by the quantity of e V which coincides with the similar quantities of graphanes as ier mobility an bi-layer and three-layer epitaxial grap e systems play an important role in some defects found in graphene nettion and the permeability of graphene networks for at of single and bi the optically extracted defect concentration, which is related to the defect distance (L def.).
In work [5], the same hydrogenation procedures of the 2 hour long expositions have been applied, as well bilayer epitaxial graphene on SiO 2 /Si wafer.Bilayer samples showed little change in their charge carr d a small D Raman peak, compared to the single-layer epitaxial graphene on SiO 2 /Si wafer exposed to the same hydrogenation procedures.The authors believe that higher rigidity of bilayers suppressed their rippling, thus reducing the probability of hydrogen adsorption.

Analysis of the Raman Spectroscopy Data on Thermal Desorption of Hydrogen from Hydrogenated Graphene Flakes
In [51], it is reported that the hydrogenation layer 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 This showed that under the chosen plasma condit process does not introduce considerable damage to the graphene sheet, and that a rather partial hydrogenation 0.05% ( H C  ) occurs primarily due to the hydrogen io the plasma, and not due to fragmentat ns ion of water from 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%.
In [51], they also performed the heating of the hydrogenated single graphene flakes (on the SiO 2 substrate) in a nitrogen environment, on a hot-plate, and with temperatures ranging from 348 K to 548 K, each time ( t  ) of 1 min.As seen in Figure 5, heating results decrease the integrated intensity ratio (I D /I G ) of Raman bands.Within a formal kinetics approach, the averaged kinetic data for samples of 10, 20 and 40 minute exposure can be treated by using Equation ( 7) transformed to a more su ta (7'): where t = 60 s, C  and C are determined from Figure 5.This resulted in finding 5 values of the reaction (desorption) rate constant (K) for 5 temperatures (T = 348, 398, 448, 498 and 548 K).Their temperature dependence is described by Equation ( 9).Hence, the desired quantities have been determined (Table 2) for the reaction (desorption) activation energy Graphane [3] (2.5 ± 0.1) an.6.56 (2.7) an.

I I 
), 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 to nanodefects (i.e., vacancies and/or triple junctions es) of the grain-boundary network) of diameter d def. su (nod const.In ch 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 I I L  .It was also found that after the Ar/H 2 plasma exposure, the (I D /I G ) ratio for bilayer graphene device is larger than that of the single graphene device.As noted in [51], this observation is in contradiction to the Raman ratios after exposure of graphene to atomic hydrogen and when o introduced.

Analysis of the STM and STS Data on n of Epitaxial nd Graphite Surfaces
In [5 ect of hydrogenation on topography and electro c properties of aphene grown by CVD on top of a nickel surface and h oriented pyrolytical graphite (HOPG) surfaces were studied by scanning nneling ield a simi avior after ws that the ther defects are

Reversible Hydrogenatio Graphene a
2], the eff ni gr igh tu microscopy (STM) and spectroscopy (STS).The surfaces were chemically modified using 40 min Ar/H 2 plasma (with 3 W power) treatment (Figure 6).This determined that the hydrogen chemisorption on the surface of graphite/graphene opens on average an energy bandgap 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 553 K), and the samples can be hydrogenated again to y lar, but slightly reduced, semiconducting beh the second hydrogenation.The data sho time of desorption from both the epitaxial graphene/Ni samples and HOPG samples of about 99% of hydrogen under 553 K annealing is  hemisorption of hydrogen atoms will change the sp 2 hy for the HOPG samples (Figures 6(a)-(c)).

icating the opening of a band gap in gr
As noted in [53], before the plasma treatment, the CVD graphene exhibits a Moiré pattern superimposed to the honeycomb lattice of graphene (Figure 6(d)).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 for the hydrogenated CVD graphene, the expected structural changes are twofold [53].First, the 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 Section 1 (Introduction).A similar model may be valid and relevant c bridization 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 [33][34][35][36][37][38][39][40][41][42]49]). Figure 6(e) shows the topography image of the surface CVD graphene after the extended (40 min) plasma treatment.The nano-ordercorrugation 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 that these bright nano-regions present a semiconducting behavior, while the rest of the surface remains conducting (Figures 6(g)-(h)) [52,53].
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, ind apheme [53,54].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 [53,54].A similar quantity (L def. 11 -17 nm, [51])) for the hydrogen adsorption centers in the single graphene flakes on the SiO 2 substrate has been considered in Section 3.1.

Analysis of the HREELS/LEED Data on
Thermal Desorption of Hydrogen from 0 own a significant band gap pecthe quas its therm uterium cm −2 at a surface temperature of 950 K. Finally, hydrogenation up to saturation of quasi-free-standing monolayer graphene has been performed at room temperature with a 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.
According to a private communication from .Bisson, ture ramp (not linear) of 5 minutes.Within a formal kinetics approach for the first Hydrogenated Graphene on SiC n [55], hydrogenation of deuterium-intercalated quasi-the temperature indicated at each point in Figure 9 corresponds to successive tempera I free-standing monolayer graphene on SiC (00 1) was obtained and studied with low-energy electron diffraction (LEED) and high-resolution electron energy loss spectroscopy (HREELS).While the carbon honeycomb structure remained intact, it has sh opening in the hydrogenated material.Vibrational s troscopy evidences for hydrogen chemisorption on i-free-standing graphene has been provided and al stability has been studied (Figure 9).De intercalation, transforming the buffer layer in quasi-freestanding monolayer graphene (denoted as SiC-D/QFMLG), has been performed with a D atom exposure of 5•10 17 order reactions [14,46], one can treat the above noted points at T i = 543 K, 611 K and 686 K, by using Equation (8) transformed to a more suitable form (8'): where t = 300 s, and the corresponding quantities C 0i and C are determined from Figure 9.It resulted in finding values of the reaction (hydrogen desorption from SiC-D/ QFMLG-H samples) rate constant K i for 3 temperatures T i = 543 K, 611 K and 686 K.The temperature dependence is described by Equation ( 9).Hence, the desired quantities have been determined (Table 2) as the reaction (hydrogen desorption) activation energy H is close ilar ones (E TDS-peak # 1 [5] and E ocesses # 1 and # 2 (Item 2.4, Tabl ) , Table 1).Nevr "G" (Figure 4).Model "H" corresponds to TDS process II in [14,[18][19][20][21], for which the apparent diffusion activation energy is Q app.II  1.2 eV.
In the same way, one can treat the points from Figure 9 at T i = 1010 K, 1120 K a la D/QFMLG samples.This results in finding the desired quantities (Table 2): the reaction (d and th he reaction rate constan . Formally, this desorption process (of a diffusion-limiting character) may be described similarly to TDS process (peak) III in [14,[18][19][20][21] diffusion activation energy may be close to the brea y of the s concluded in [55], 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.
The obtained characteristics (Table 2) of desorption processes [51,52,55] show that these processes may be of a diffusion-rate-controlling character [14].

Analysis of the Raman Spectroscopy Data on Thermal Desorption of Hydrogen from Hydrogenated Graphene Layers on SiO 2 Substrate
In [56], graphene layers on SiO 2 /Si su emically decorated by radio frequency hydrogen plasma (the power of 5 -15 W, the pressure of 1 Tor) treatment for 1 min.As seen from the investigation of hydrogen coverage by Raman spectroscopy and micro-x-ray photoelectron spectroscopy characterization demonstrates that the hydrogenation of a single layer graphene on SiO 2 /Si substrate is much less feasible than that of bilayer and multilayer graphene.Both the hydrogenation and dehydrogenation processes of the graphene layers are controlled by the corresponding energy barriers, which show significant dependence o ese results [56] on bilayer graphene/SiO 2 /Si are in contradiction to the results [5] on a negligible hydrogenation of bilayer epitaxial graphene on SiO 2 /Si wa Within a formal kinetics approach [14,46], the kinetic from Figure 10(a) for single layer graphene sam -5W and 1LG-15W ones) can be treated.E s used to transform into a where t  = 1800 s, and C and C are determined from Figure 10(a).
The results have been obtained for 1LG-15W sample 3 values of the I reaction rate constant K for 3 temperatures (T = 523, 573 and 623 K).Hence, by using Equation (9), the following values for 1LG-15W samples have been determined (Table 3): the I reaction activation energy  K for 4 temperatures (T = 623, 673, 723 and 773 K).Hence, by using Equation ( 9), the following desired values are found (Table 3): the II reaction activation energy , the per-exponential factor of the II [56] reaction rate constant . A similar treatment of the kinetic data from Figure 6(c) in [56] for bilayer graphene 2LG-5W samples results in obtaining 4 values for the I reaction onstant for 3 temp nce is io

Analysis of TDS and STM Data o OPG Treated by Deuterium
In [57], the results are present of a scanni tunneling microscopy (ST udy of graphite (HOP ) treated by atomic deuteriu hich reveals the exis nce of two distinct hydrogen dimer states on graphite basal planes e 11 and eratures (T = 573, 623 and 673 K).Their temperature depende described by Equation (9).Hence, one can evaluate the following desired values (Table 3): the I reaction activation energy an d the per-exponential factor of the II reaction rate constant . The obtained characteristics (Table 3) of the desorpt n processes I and II show that these processes may be of a diffusion-rate-controlling character.
) eory calculations allow them to identify the atomic structure of these states and to determine their recombination and desorption pathways.As pred recombination is only possible from one of the two dim states.In conclusion, this results in an increased stabil of one dimer species, and explains the puzzling double peak structure observed in temperature programmed desorption (TPD or TDS) spectra for hydrogen on graphite (Figure 12(a)) [57].
By using the described method of TPD (TDS) peak treatment (for the first order reactions), relevant to TPD (TDS) peak I (65% of the total area, T max # I  473 K) in Figure 12(a), one can obtain values of the reaction I rate constant ( ) for several temperatures (for instance, T = 458, 482 and 496 K) [14].Their temperature dependence can be described by Equation (9).Hence, the desired values are defined as follows (Table 3): the reaction (desorption) I activation energy .In a similar way, relevant to TPD (TDS) peak II (35% of the total area, T max#II  588 K)) in Figure 12( ) for several temperatures (for instance, T = 561 and 607 K).Hence, the desired values are defined as follows (Table 3): the reac tion (desorption) II activation energy Table 3.Some analytical (an.) res ults of Items 3.4, 3.5, 3.6, 3.7 and 4.
(2•10 10 ) an.  iffusion-ratelling case, processes ot be described g the gner equatio (as it has been d [57]).d in " er states" or "nan 11 and Fi ) ay be related to the defe egions, p ly, as grain (dom oundaries r triple a d other unctions (nodes) of the dary netwo in the OPG sam ome defe ons at the grain boundary network (hydrogen adsorption centers #I, mainly, the "dimer B" structu ) can be related to TPD S) pe others ( n adsorption centers #II, mainly, the "dimer A" structures) to TPD (TDS) eak II.

Analysis of PES and ARPES Data on
Dehydrogenation of Graphene/SiC Samples is fully covered with bi-layer graphene (F stigations of the electron band structure confirm that after hydrogenation the single -band chartwo band Atomic hydrogen exposures at a pressure of P H  1•10 −4 Pa and temperature T = 973 K on a monolayer graphene grown on the SiC (0001) surface are shown, to result in hydrogen intercalation [17].This shows that 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 photoelectron spectroscopy (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 bilayer 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 15(b), 15(e), 16(a) and 16(b)).With larger (additional 15 min) atomic hydrogen exposures, the islands grow in size and merge until the surface igures 15(c), 15(f), 16(c) and 16(d)).A (√3 ×√3) R30˚ periodicity is observed on the bi-layer areas.Angle resolved photoelectron spectroscopy (ARPES) and energy filtred X-ray photoelectron emission microscopy (XPEEM) inve acteristic of monolayer graphene is replaced by s that represent bi-layer graphene.Annealing an intercalated sample, representing bi-layer graphene, to a temperature of 1123 K 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 1273 K.After each annealing step, the depletion of hydrogen has been probed by PES and ARPES (Figures 17 and 18).From this data, by using Equations (8) and 9), one can determine the following tentative quantities:  (Table 3).These results can be interpreted so that the model of the interaction of hydrogen and silicon atoms at the graphene-SiC interface result in Si-C bonds at the intercalated islands.Obviously, the quantities of   0 des.

K and  
des.
H  correspond to those of the Polanyi-Wigner equation [14] relevant for the Si-C bonds [17].

Analysis of TDS and STM Data on HOPG Treated by Hydrogen
Atomic hydrogen accumulation in HOPG samples and etching their surface on hydrogen thermal desorption (TD) have been studied by using a scanning tunneling microscope (STM) and atomic force microscope (AFM).STM investigations revealed that the surface morphology of untreated reference HOPG samples was found to be d with ge radius of 25 nm and an average height of 4 nm (Figure 9(c) and 19(d)) [15].ermal desorption ( the dr atomically flat (Figure 19(a)), with a typical periodic structure of graphite (Figure 19(b)).Atomic hydrogen exposure (treatment) of the reference HOPG samples (30 -125 min at atomic hydrogen pressure Th TD) of hydrogen has been found in heating of the HOPG samples under mass spectrometer control.As shown in Figure 20(a), with the increase of the total hydrogen doses (D) to which HOPG samples have been exposed, desorbed hy ogen amounts (Q) increase and the percentage of D retained in samples (Q) approaches towards a saturation stage.After TD, no  nanoblisters were visible on the HOPG surface, the graphite surface was atomically flat, and covered with some etch-pits of nearly circular shapes, one or two layers thick (Figure 20(b)).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.
gas in molecular form (Figure 21).As suggested, 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 Section 1 (Introduction) results [8,32], that it is almost impossible for a hydrogen atom to pass through the sixface closed nano-regions network) in the surface graphene layer.It also expedient to note that in Figure 20(b), one can u de th According to [15], nanoblisters found on the HOPG surface after atomic hydrogen exposure are simply monolayer graphite (graphene) blisters, containing hydrogen (the graphene nanoblisters) through defects (perhaps, mainly through triple junctions of the grain and/or subgrain boundary membered ring of graphene at room temperature.It is reasonable to assume (as it's been done in the previous Sections) that in HOPG [15] samples atomic hydrogen passes into the graphite near-sur is imagine some grain boundary network decorated by the etch-pits.
The average blister has a radius of 25 nm and a height 4 nm.Approximating the nanoblister to be a semi-ellipse form, results in the blister area   data [60] considered in [18][19][20][21], on the hydrogen (protium) isotherm of 300 K.These results can be quantitatively described, with an accuracy of one order of magnitude, with the thermodynamic approach [44,46], by using the condition of the thermo-elastic equilibrium for the reaction of ( ), as follows [18]: where is related to the blister "wall" back d by )-the so called surface press 1•10 -4 he atomic hydrogen g to t e atomic flux [15], a essure [44,46],   graphite can be approximated by three thermodesorption (TDS) peaks, i.e., # I with T max # I  1123 K, # II with T max # II  1523 K, and # III with T max # III  1273 K.But their treatment, with using the above mentioned methods [14], is difficult due to some uncertainty relating to the zero level of the J des quantity.Nevertheless, TDS peak # I can be characterized by the activation desorption energy and by the per-exponential factor nstant of  3).Analyses have shown that TDS peak I is related to TDS peak (process) III in [14,[18][19][20][21], for which the apparent diffusion activation energy is  [15,59].Thus, TDS peak (process) I is related to TDS peak (process) III in [14,[18][19][20][21], which is related to model "F * " (Figure 4) considered in Item 2.4.Model "F * " is characterized by the quantity that coincides with th Table 1) [14,[18][19][20][21].
Finally, it is reasonable to assume that the inner surfaces "walls" in the graphene nanoblisters in HOPG are hydrogenated, and that the graphene "walls" situation is related to some hydrogenated graphenes (Table 1).Obviously, such hydrogenation of the inner graphene surfaces in the nanoblisters occurs under action of the gaseous molecular hydrogen of a high pressure intercalated into the stressed (expanded) hydr graphene nanoblister "walls" possessing of a high Young's modulus [15,59].
As considered in the next Section, a similar (to some ) situation may occur in hydrogenated aphite na- The possibility of intercalation of solid H 2 into hydrogenated graphite nanofibers (considered in [18][19][20][21]) is based on the following facts: 1) According to the data from

Pa).
2) As shown in [18], the treatment of the data ure 24 from [61]) on hydrogenation of graphite na bers
4) As noted in [18][19][20][21], a definite residual plastic deformation of the hydrogenated graphite (graphene) nanoas, ma ng in regions is observed in  is the relevance to hydrogenation of GNFs [18][19][20][21]6 ity of a number of hydrogenated grapheme layers systems (Tables 1-3) has shown expediency of further related (mainly experimental) studies for the determination of a complete and compatible set of thermodynamic characteristics of such systems.
2) It confirms that the alternative viewpoint of the experimental graphane (a free-standing membrane) may have a more complex hydrogen bonding than the one suggested by theory [3], and that the epitaxial graphene may be a different material, rather than the theoretical graphane (Table 1) [3,5].

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 diamondlike distorted hexagonal network with carbon in sp 3 hybridization [3].

1 
−0.05 eV/atom, and also the theoretical value of H  = −0.15эВ/atom, one can obtain a desired value of 2 H  = −2.5 ± 0.1 eV/atom.The quantity of 2 H

Figure 2 .
Figure 2. Changes in Raman spectra of graphene caused by hydrogenation [5].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.
In connection with the above consideration, it seems ex-Probability of Existence of Hydrogenated Graphenes-Graphanes * Possessing of a Ve High 90% Ar/10% H m T = 57 or 2 hours (i.e., ).Hence, b using Equation (8), similar in respect t the epitaxial graphene on 2 and for the free-standing gr om a hydrogenated epitaxial graphene on a substrate SiO 2 (Figure 2(a)) has been achieved by a about six orders less than the evaluated value of TDS peak # 2 (15% of the total area, T max # 2  445 K) can be characterized by the activation energy E TDS-peak # 2 = 0.6  0.3 eV, and by the per-exponential factor of the reaction rate constant

Figure 3 .
Figure 3. Desorption of hydrogen from single-side graphane [5].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 mass-spectrometer, which also gives rise to a small hydrogen signal).

Figure 4 .
Figure 4. Schematics of some theoretical models (ab initio molecular orbital calculations [50]) 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) [51].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 I D G 0.2  ) s not significantly , which confirms the hydrogen-type origin of defects.In longer exposed samples (80 min and 2 h), annealing doe reduce I D /I which suggests a different nature of defects, e.g., vacancies.G , by using Equation (8), one can evaluate the quantity   0.63 des.553K 130 s   , which is close (within the errors) to the similar quantity of   0.63 des.553K 70 s   for the epitaxial graphene flakes considered in the previous Section 3.1.

Figure 6 .
Figure 6.(a)-(f) Topography images acquired in the constant-current STM mode [52]: (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 distored.

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 L, 6 L, 4 L 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 (1 L) graphene region, and (d) STM topography image of the regions marked by the dashed rectangle in (b) [53,54].

Figure 8 .
Figure 8.(a) and (b) show the local tunneling decay constant maps measured on a multilayer and a single-layer (1 L) region, respectively.(c) Radial autocorrelation function of the local tunneling decay image in (b) [53,54].

Figure 9 .
Figure 9. Evaluation of the HREELS elastic peak FWHM of SiC-D/QFMLG-H upon annealing.The uncertain annealing

Figure 10 . 1
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 [56]; (b) the evoluation of   Δ D G I I evoluation of 5 and 15 with annealing temperatures of 1 LG hydrogenated by 5 and 15 W, 1 Torr hydrogen plasma for 1 min; (c) the the D and G band intensity ratio (I D /I G ) with annealing temperatures of 2 LG (bi-layer graphene) hydrogenated by W, 1 Torr hydrogen plasma for 1 min; (d) the evoluation of   Δ D G I I sk ( *

K
for 4 temperatures (T = 348, 373, 398 and 423 K), and 3 values for the II reaction rate constant  II 56 a), one can obtain values of the reaction II rate constant (

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 [57].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) [57].The arrow indicates the aximum 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 [17] 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.
of retained hydrogen in this sample becomes Q  2.8•10 14 H 2 /cm 2 and the n mber of hydrogen molecules captured insi e , 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 molecular gas density in the blisters (at T  300 K and P H2  1•10 8 Pa) can be estimated as M H2 is the hydrogen molecule mass.It agrees with

Figure 17 .
Figure 17.Normalized C 1 s core level spectra of monolayer graphene [17] 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 grapheme [17] 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 apparent volume change, r b  vature of nanoblisters (at 21(b)), N A is the Avogadro number, and T ≈ 300 K.The quantity of ( * H2 P 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 b  (caused by in the graphene nanoblister "walls" hickness 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 (15), as follows [44,18]: The degree o is a degree of elastic deformation of the graphene nanoblister walls, and E b is the Young's modulus of the g hene nanoblister walls.By substituting the first part of Equation (16), the quantities of r b  30 and d b  0.15 e of .elastic deform nanoblister walls, apparently reaches

Figure 19 .
Figure 19.STM images of the untreated HOPG sample [15] nm and (b) 10.9 × 10.9 nm (high resolution image of the squar sample subjected se (D) of 1.8•10 16 H 0 (unde e in image (a)) to atomic hydrogen do /cm 2 .reported in (c).The STM tunnel V bias and current are 50 -100 m .(c) AFM image (area of 1 × 1 nm) of the HOPG (d) Surface height profile obtained from the AFM image V and 1 -1.5 mA, respectively.

Figure 20 .
Figure 20.(a) Hydrogen storage efficiency of HOPG samples [15], desorbed molecular hydrogen (Q) versus dose (D) of atomic hydrogen exposure.(b) STM image for 600 × 600 n a of the HOPG sample subjected to atomic hy rogen dose of 1.8•10 16 H 0 /cm 2 , followed by hydrogen using the second part of Equation (16), 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: m are d thermal desorption.

Q = ( 2 . 6
 0.3) eV can obtain (with accur app.III and D 0app.III  3•10 −3 cm 2 /s.Hence, one acy of one-two orders of the magnitude) a reasonable value of the diffusion characteristic size of to the separating distance between the grapheme nanoblisters (Figure 21(b)) or (within the errors) to the separation distance between etch-pits (Figure 20(b)) in the HOPG specimens

Figures 22 and 23 (
from[60]), a solid molecular hydrogen (or deuterium) of density of 3 -0.5 g/cm 3 (H 2 ) can exist at 300 K, and an exte pressure of P = 30 -50 GPa. 2) As seen from data in Figures 19-21 and Equations (15) and (16), the external surface pressure of P = = 30 -50 GPa at T  300 K may be provided at pense of the association energy of atomic hydrogen * H2 P the ex

Figure 22 .
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 [60].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 a value of the twinned density ρ  1 g/cm 3 of solid H (at T to 

Figure 23 .
Figure 23.Phase diagram [60], 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 cu perimental data.ad rres rve-the exponds to a value of temperat -megabar value xternal compression pressure P  50 GPa [18].

3 ) 1 ( b 61 E 61 
The ditional red circle co ure T  300 K and a near of the e ( T S H   dis dis ), into some closed hydrogenated (in gaseous atomic hydrogen with the corresponding pressure P H ) graphene nanostructures possessing of a high Young's modulus (E graphene  1 T (Fig nofi (GNFs) results in the experimental value of the hydrogen density C-system)) of the intercalated high-purity reversible hydrogen (17 mass.% H 2 ) corresponding to the state of solid molecular hydrogen at * Pa and T  300 K, according to data from Figures 22 and 23 [61, 62]. a surface pressure of P = H2 P Substituting in Equation (16) the quantities of Figure 24), the largest possi-ble value of   10 12 Pa, the largest possible value of the tensile stresses (   b 10 11 Pa) in the edge gra-phene "walls" (of a thickness of d b and a radius of cur-vature of r b ) of the slit-like closed nanopores of the lens shape, one can obtain the quantity of  a reasonable value follows of d b  5 nm.A similar result can be obtained, supposing the quantity of   b 61

Figure 24 .
Such plastic deform tion of the nanoregins during hydrogenation of GNF y be accompanied with some mass transfer resulti such thickness (   b 61 d ) of the walls.A very important role

Figure 25 .
Figure 25.It is shown [71] (in the face of known achievements) hydrogen on-board storage densities for 2010 (6.0 mass.%kg(H )/m 3 (systems)).The ad U H 2 e so ur