ON SOME THEORETICAL AND EXPERIMENTAL (STM, STS, HREELS/LEED, PES, ARPS & RAMAN SPECTROSCOPY) DATA ON HYDROGEN SORPTION WITH GRAPHENE-LAYERS NANOMATERIALS, RELEVANCE TO THE CLEAN ENERGY APPLICATIONS Текст научной статьи по специальности «Физика»

ВОДОРОДНАЯ ЭКОНОМИКА

HYDROGEN ECONOMY

ВОДОРОДНАЯ ЭКОНОМИКА

HYDROGEN ECONOMY

Статья поступила в редакцию 29.08.14. Ред. рег. № 2085

УДК 541.67:541.142

The article has entered in publishing office 29.08.14. Ed. reg. No. 2085

О НЕКОТОРЫХ ТЕОРЕТИЧЕСКИХ И ЭКСПЕРИМЕНТАЛЬНЫХ (STM, STS, HREELS/LEED, PES, ARPS, RAMAN SPECTROSCOPY) ДАННЫХ ПО СОРБЦИИ ВОДОРОДА ГРАФЕНОВЫМИ НАНОМАТЕРИАЛАМИ В СВЯЗИ С ПРОБЛЕМАМИ ЧИСТОЙ ЭНЕРГЕТИКИ

Ю.С. Нечаев

ЦНИИчермет им. И.П. Бардина, Институт металловедения и физики металлов им. Г. В. Курдюмова 105005 Москва, 2-я Бауманская ул., д. 9/23 E-mail: Yuri1939@inbox.ru

Заключение совета рецензентов: 05.09.14 Заключение совета экспертов: 10.09.14 Принято к публикации: 15.09.14

Представлены результаты термодинамического анализа ряда теоретических и экспериментальных (TDS, STM, STS, HREELS/LEED, PES, ARPS, Raman spectroscopy и др.) данных по «обратимому» гидрированию и дегидрированию некоторых графеновых (моно- и полислойных) наноструктур.

В рамках приближения формальной кинетики для реакций первого порядка определены термодинамические характеристики процессов сорбции водорода этими наноструктурами (константы скорости, энергии активации, предэкспоненци-альные факторы констант скорости).

При интерпретации полученных термодинамических характеристик использованы некоторые модели и характеристики химической сорбции водорода на базальной и краевых поверхностях графита с целью раскрытия атомных механизмов гидрирования и дегидрированию различных графеновых (моно- и полислойных) наноструктур. Рассмотрена кинетика как сорбционных процессов, в которых не лимитирует диффузионный массоперенос водорода в сорбенте, так и процессов с лимитирующей диффузионной стадией.

Рассматриваются также некоторые «открытые вопросы» и перспективы решения актуальной проблемы эффективного хранения водорода «на борту» экоавтомобиля и ряда других проблем чистой энергетики на основе использования графитовых нановолокон.

Ключевые слова: эпитаксиальные и мембранные графены; слоистые графеновые системы; гидрирование-дегидрирование; термодинамические характеристики; атомные механизмы; проблема эффективного хранения водорода «на борту» экоавтомобиля.

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ON SOME THEORETICAL AND EXPERIMENTAL (STM, STS, HREELS/LEED, PES, ARPS & RAMAN SPECTROSCOPY) DATA ON HYDROGEN SORPTION WITH GRAPHENE-LAYERS NANOMATERIALS, RELEVANCE TO THE CLEAN ENERGY APPLICATIONS

Yu.S. Nechaev

Bardin Institute for Ferrous Metallurgy, Kurdumov Institute of Metals Science and Physics 9/23 Vtoraya Baumanskaya str., Moscow, 105005, Russia E-mail: Yuri1939@inbox.ru

Referred: 05.09.14 Expertise: 10.09.14 Accepted: 15.09.14

Herein, results of thermodynamic analysis of some theoretical and experimental (TDS, STM, STS, HREELS/LEED, PES, ARPS, Raman spectroscopy and others) data on "reversible" hydrogenation and dehydrogenation of some graphene-layer-nanostructures are presented.

In the framework of the formal kinetics 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-layer-systems. The cases of both a non-diffusion rate limiting kinetics, and a diffusion rate limiting kinetics are considered.

Some open questions and perspectives of solving of the actual problem of the effective hydrogen on-board storage and other clean energy applications, with using the graphite nanofibers, are also considered.

Keywords: epitaxial and membrane graphenes; other graphene-layer-systems; hydrogenation-dehydrogenation; thermodynamic characteristics; atomic mechanisms, the hydrogen on-board efficient storage problem.

1. Introduction

As is 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 ([1-44] and others).

It is relevant to the current problems of thermodynamic stability and thermodynamic characteristics of the hydrogenated graphene-layers-systems ([1-18] and others), and also to the current problem of hydrogen on-board storage ([19-21] and others).

In the case of epitaxial graphene on substrates such as SiO2 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 SiO2, 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 freestanding 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 SiO2 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-SiO2 interface is negligible, and perfect graphene is impermeable to any atom and molecule [32]. But, firstly, these two aspects are of the kinetic character, and therefore they can not influence the thermodynamic predictions [3, 24, 31]. Secondly, as is shown in the present analytical study, the above noted two aspects have not been studied in an enough degree.

As was shown in [5], 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

№ 17 (157) Международный научный журнал

graphene ([16] and others), and indeed it has been observed that some of their membranes rupture during hydrogenation. It was believed [5] that the stretched regions were 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 |im, and that the annealing of such membranes led to complete recovery of the periodicity in both stretched and compressed domains [5].

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 [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 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 [3]. The formation of graphane was attributed to the efficient strain relaxation for sp3 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 Eg ~ 5.4 eV [4, 23].

Only if hydrogen atoms adsorbed on one side of graphene (in graphane) are retained, we obtain graphone of C2H composition, which is a magnetic semiconductor with Eg ~ 0.5 eV and a Curie temperature of Tc ~ 300400 K [24].

As was noted in [6], neither graphone nor graphane are suitable for real practical applications, since the former has a low value of Eg, 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].

It is also expedient to refer to a theoretical single-side hydrogenated graphene (SSHG) of CH composition (that is an alternative to graphane [3]), in which hydrogen atoms are adsorbed only one side [7, 25]. In contrast to graphone, they are adsorbed on all carbon atoms rather than on every second carbon atom. The value of Eg 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 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 was noted in [7], it may be inappropriate to call the covalently bonded SSHG system sp3 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 sp3 bonded system. However, in SSHGraphene all the carbon atoms remain in one plane, making it difficult to call it sp3 hybridized. Obviously, this is some specific sp3-like hybridization.

The results ([14] and others), see also Tables 1A and 1B in the present paper, of thermodynamic analysis of a number of experimental data point that some specific local sp3-like hybridization, without the diamond-like strong distortion of the graphene network, may be manifested itself in the cases of hydrogen atoms dissolved between graphene layers in isotropic graphite, graphite nanofibers and nanostructured graphite, where obviously there is a situation similar (in a definite degree) to one of the rigidly fixed graphene membranes. As far as we know, it has not been taken into account in many recent theoretical studies.

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 [3, 5]. This can even induce magnetic moments [29-31].

Previous theoretical studies suggest that single-side hydrogenation of ideal graphene would be thermodynamically unstable [31, 24]. 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 [5, 44]. This puzzling situation is also considered in the present analytical study.

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 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, i.e., grain boundaries, their triple junctions (nodes) and/or vacancies [33-43]. As is shown in the present study, this is related to revealing the atomic mechanisms of reversible hydrogenation of epitaxial graphenes, comparing with membrane graphenes.

In the next Items 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 [16, 20, 21], particularly published in the open access journals. Therefore, the related figures (Figs.) from [16, 21] are referred in the present paper.

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Таблица1A

Теоретические, экспериментальные и аналитические величины характеристик,

рассматриваемых в разделах 1-4

Table 1A

Theoretical, experimental and analytical quantities related to Items 1-4

Material Value/Quantity

AH(c-h), eV AH(bmd), eV AH(c-c), eV AH(des.), eV (AH(ads.), eV) K0(des.), s 1 (L ~ (D0app./K0(des.)) )

Graphane (CH) [3] (theory) 2.5±0.1 (analysis) 6.56 (theory) 2.7 (analysis)

Graphane (CH) [25] (theory) 1.50 (theory) 5.03 (theory) 2.35 (analysis)

Graphane (CH) [4] (theory) 2.46+0.17 (analysis) 2.46 + 0.17 (theory) 2.01015 (analysis)

Free-standing graphane-like membrane [5]. (experiment) There are no experimental values in [5] if 2.5 ± 0.1 if 2.6 ± 0.1 (1.0 ± 0.2) (analysis ) then 71012 then 51013 (K0(ads.)~K0(des.))

Hydrogenated epitaxial graphene [5] (experiment) There are no experimental values in [5] then 1.84 then 1.94 if 0.3 if 0.6 if 0.9 (0.3 ± 0.2) (analysis) if 7-1012 if 51013 then 0.2 then 80 then 3.5104 (K0(ads.)~K0(des.)) (L — ^sample)

Hydrogenated epitaxial* grapheme [5], TDS-peak #1 (experiment) 0.6 ± 0.3 (as processes —I-II [14], -model "G") (analysis) 2-107 (or 2-103-2-10n) (L — ^sample) (analysis)

Hydrogenated epitaxial* grapheme [5], TDS-peak #2 (experiment) 0.6 ± 0.3 (as for processes —I-II [14], —model "G") (analysis) 1106 (or 4 102-2 109) (L — ^sample) (analysis)

Hydrogenated epitaxial* grapheme [5], TDS-peak #3 (experiment) 0.23 + 0.05 (as process — I [14], —models "F", "G") (analysis) 2.4 (or 0.8-7) (L — ^sample) (analysis)

Rigidly fixed hydrogenated graphene membrane [5] (experiment) There are no experimental values in [5] There are no experimental values in [5] There are no experimental values in [5]

Graphene [25] (theory) 7.40 (theory) 4.93 (analysis)

Graphite [45, 16] (empirical) 7.41+0.05 (analysis) 4.94+0.03 (analysis)

Diamond [45,16] (empirical) 7.38+0.04 (analysis) 3.69+0.02 (analysis)

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Таблица iB

Теоретические, экспериментальные и аналитические величины характеристик, рассматриваемых в разделах 1-11

Theoretical, experimental and analytical quantities related to Items 1-11

Table 1B

Material Value/Quantity

AH(c.h), eV AH(C-C), eV AH(des.), eV (His.), eV) K0(des.), s 1 (L ~ (D0app./K0(des.)) )

Hydrofullerene C60H36 [13] 2.64 ± 0.01 (experiment)

Hydrogenated carbon nanotubes (C2H) [12] 2.5 ± 0.2 (theory)

Hydrogenated isotropic graphite, graphite nanofibers and nanostructured graphite [14] (experiment) 2.50 ± 0.03 (analysis, process III [14], model "F*") 4.94+0.03 (analysis) 2.6 ± 0.03 (analysis, process III [14]) There are empirical values in [14] (analysis of experiment)

Hydrogenated isotropic graphite, graphite nanofibers, nanostructured graphite, defected carbon nanotubes [14] 2.90 ± 0.05 (analysis, process II [14], models "H", "G" (Fig. 4 in [16])) 1.24 ± 0.03 (analysis, process II [14]) There are empirical values in [14] (analysis of experiment)

Hydrogenated isotropic graphite, carbon nanotubes [14] (experiment) 2.40 ± 0.05 (analysis, process I [14], models "F", "G" (Fig. 4) in [16]) 0.21 ± 0.02 (analysis, process I [14]) There are empirical values in [14] (analysis of experiment)

Hydrogenated isotropic and pyrolytic and nanostructured graphite [14] (experiment) 3.77 ± 0.05 (analysis, process IV [14], models "C", "D" (Fig. 4) in [16]) 3.8 ± 0.5 (analysis, process IV [14]) There are empirical values in [14] (analysis of experiment)

2. Consideration of some energetic characteristics of theoretical graphanes [3, 25]

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 sp3 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, Fig. 1 in [16]) conformer and a boat-like (zigzag-like) conformer [3].

The diamond-like conformer (Fig. 1 in [16]) is more stable than the zigzag-like one. This was concluded from the results of the calculations of binding energy (AHbmd(graphane)) (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

(AHf 298(graphane) ) of the compounds (CH(graphane)) from

crystalline graphite (C(graphite)) and gaseous molecular hydrogen (H2(gas)) at the standard pressure and temperature conditions [3].

For the diamond-like graphane, the former quantity is AHbind.(graphane) = 6.56 eV/atom, and the latter one is AH = AHf298(graphane) = -0.15 eV/atom. The latter quantity corresponds to the following reaction:

C(graphite) + /H2(gas) ^ CH(graphane), (AH1) (1)

where AH is the standard energy (enthalpy) change for this reaction.

By using the theoretical quantity °f AHf298(graphane),

one can evaluate, using the framework of the thermodynamic method of cyclic processes [45, 46], a value of the energy of formation (AH2) 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:

C(graphene)+ H(gas)^ CH(graphane), (AH2) (2)

C(graphene) * C(graphite> (AH3) (3)

H(gas) * '/2 H2(gas), (AH4) (4)

where AH2, AH3 and AH4 are the standard energy (enthalpy) changes.

Reaction (2) can be presented as a sum of reactions (1), (3) and (4) using the framework of the thermodynamic method of cyclic processes [46]:

AH = (AH3 + AH4 + AH1).

(5)

Substituting in Eq. (5) the known experimental values [45, 25] of AH = -2.26 eV/atom and AH3 « -0.05 eV/atom, and also the theoretical value [3] of AH = -0.15 eV/atom, one can obtain a desired value of AH2 = -2.5 ± 0.1 eV/atom. The quantity of -AH2 characterizes the break-down

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energy of C-H sp bond in graphane (Fig. 1 in [16]), relevant to the breaking away of one hydrogen atom from the material, which is AH(C-H)graphane = -AH2 = = 2.5 ± 0.1 eV (Table 1A).

In evaluating the above mentioned value of AH3, one can use the experimental data [45] on the graphite sublimation energy at 298 K (AHsubl(graphite) = 7.41 ± 0.05 eV/atom), and the theoretical data [25] on the binding cohesive energy at about 0 K for graphene (AHcohes(graphene)= = 7.40 eV/atom). Therefore, neglecting the temperature dependence of these quantities in the interval of 0-298 K, one obtains the value of AH3 « -0.05 eV/atom.

AHcohes.(graphene) quantity characterizes the break-down energy of 1.5 C-C sp2 bond in graphene, relevant to the breaking away of one carbon atom from the material. Consequently, one can evaluate the break-down energy of C-C sp2 bonds in graphene, which is AH(C-C)grapheme = = 4.93 eV. This theoretical quantity coincides with the similar empirical quantities obtained in [16] from

AHs

subl.(graphite)

for C-C sp bonds in graphene and

graphite, which are AH(C -

C)graphene

AH(

(C-C)graphite

= 4.94 ±

± 0.03 eV. The similar empirical quantity for C-C sp bonds in diamond obtained from the diamond sublimation energy AHsubl.(diamond) [45] is AH(C-C)diamond = = 3.69 ± 0.02 eV [16].

It is important to note that chemisorption of hydrogen on graphene was studied (in [25]) 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 AHcohes.(graphane) = 5.03 eV/atom(C). This results in the binding energy of hydrogen, which is AH(C-H)graphane = 1.50 eV/atom(H) [25] (Table 1A).

The theoretical AHbind.(graphane) quantity characterizes the break-down energy of one C-H sp3 bond and 1.5 C-C sp3 bonds (Fig. 1 in [16]). Hence, by using the above mentioned values of AHbmd.(graphane) and AH(C-H)graphane, one can evaluate the break-down energy of C-C sp3 bonds in the theoretical graphane [3], which is

AH(

(C-C)graphane

= 2.7 eV (Table 1). Also, by using the

above noted theoretical values of AHc

cohes.(graphane)

and

hybridized carbon atoms have been calculated. The corresponding activation energy of AH(des.) = Ea = 2.46 ± ± 0.17 eV and the corresponding (temperature independent) frequency factor A = (2.1 ± 0.5)-1017 s-1 have also been calculated. The process of hydrogen desorption at T = 1300-3000 K has been described in terms of the Arrhenius-type relationship:

1/t0.01 = A exp (-EjkBT),

(6)

AH(C-H)graphane, one can evaluate similarly the break-down energy of C-C sp3 bonds in the theoretical graphane [25], which is AH(C-C)graphane = 2.35 eV (Table 1A).

3. Consideration and interpretation of the data [4] on dehydrogenation of theoretical graphane [3], comparing with the related experimental data [5]

In [4], the process of hydrogen thermal desorption from graphane has been studied using the method of molecular dynamics. The temperature dependence (for T = 1300-3000 K) of the time (t0.01) of hydrogen desorption onset (i.e., the time t0.01 of removal —1% of the initial hydrogen concentration C0 ~ 0.5 (in atomic fractions), -AC/Co = 0.01, C/C0 = 0.99) from the

C54H

where kB is the Boltzmann constant.

The authors [4] predicted that their results would not contradict the experimental data [5], according to which the nearly complete desorption of hydrogen (-AC/C0 « 0.9, C/C0 « 0.1) from a free-standing graphane membrane (Fig. 2B in [16]) was achieved by annealing it in argon at T = 723 K for 24 hours (i.e., t0.9(membr.[5])723K = 8.6-104 s). But, as the below presented analysis shows, this declaration [4] is not enough adequate.

By using Eq. (6), the authors [4] evaluated the quantity of t0.01(graphane[4]) for T = 300 K (—1-1024 s) and for T = 600 K (—2-103 s). However, they noted that the above two values of t001(graphane) should be considered as rough estimates. Indeed, using Eq. (6), one can evaluate the value of t0.01(graphane[4])723K « 0.7 s for T = 723 K, which is much less (by five orders) than the

t0.9(membr.[5])723K value in [5].

In the framework of the formal kinetics approximation of the first order rate reaction [46], a characteristic quantity for the reaction of hydrogen desorption is r0.63 - the time of the removal of ~ 63 % of the initial hydrogen concentration C0 (i.e., -AC/C0 « 0.63, C/C0 « 0.37) from the hydrogenated graphene. Such a first order rate reaction (desorption) can be described by the following equations [14, 16, 46]:

dC/dt = -KC, (7)

(C/C0) = exp(-Kt) = exp(-t/T0.63), (8)

K = (1/T0.63) = K0exp(-AHdes./kBT), (9)

where C is the averaged concentration at the annealing time t, K = (1/t063) is the reaction (desorption) rate constant, AHdes. is the reaction (desorption) activation energy, and K0 is the per-exponential (or frequency) factor of the reaction rate constant.

In the case of a diffusion rate limiting kinetics, the quantity of K0 is related to a solution of the corresponding diffusion problem (K0 ~ D0/L2, where D0 is the per-exponential factor of the diffusion coefficient, L being the characteristic diffusion length) [14, 16].

In the case of a non-diffusion rate limiting kinetics, which is obviously related to the situation of [4, 5], the quantity of K0 may be the corresponding vibration (for (C-H) bonds) frequency (K0 = V(C-H)), the quantity AH(des.) = AH(C-H) (Table 1), and Eq. (9) is correspond to

54^-7(54+18)

clustered with 18 hydrogen passivating the Polanyi-Wigner one [14, 16].

atoms at the edges to saturate the dangling bonds of sp

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By substituting in Eq. (8) the quantities of t =

= t0.01(graphane[4])723K and (C/C0) = 0.99, one can evaluate the desired quantity T0.63(graphane[4])723K « 70 s. Analogically, the quantity of t0.9(graphane[4])723K « 160 s can be evaluated, which is less (by about three orders) than the experimental value [5] of t0.9(membr.[5])723K. In the same manner, one can evaluate the desired quantity T0.63(membr.[5])723K « 3.8-104 s, which is higher (by about

three orders) than T0.63(graphane[4])723K.

By using Eq. (9) and supposing that AHdes. = Ea and K = 1/x063(graphane[4])723K, one can evaluate the analytical quantity of K0(graphane[4]) = 2-1015 s-1 for graphane [4] (Table 1A).

By substituting in Eq. (9) the quantity of K =

= K(membr.[5])723K = 1/T0.63(membr.[5])723K and supposing that AHdes.(membr.[5]) ~ AHC-H(graphane[3,4]) ~ 2.5 eV [3, 16, 4]

(Table 1A), one can evaluate the quantity of K0(membr.[5]) = = V(membr.[5]) « 7-1012 s-1 for the experimental graphane membranes [5]. The obtained quantity of V(membr.[5]) is less by one and a half orders of the vibrational frequency vRD = 2.5-1014 s-1 corresponding to the D Raman peak (1342 cm-1) for hydrogenated graphene membrane and epitaxial graphene on SiO2 (Fig. 2 in [16]). The activation of the D Raman peak in the hydrogenated samples authors [5] attribute to breaking of the translation symmetry of C-C sp2 bonds after formation of C-H sp3 bonds.

The quantity V(membr.[5]) is less by one order of the value [47] of the vibration frequency vHREELS = 8.7-1013 s-1 corresponding to an additional HREELS peak arising from C-H sp3 hybridization; a stretching appears at 369 meV after a partial hydrogenation of the epitaxial graphene. The authors [47] suppose that this peak can be assigned to the vertical C-H bonding, giving direct evidence for hydrogen attachment on the epitaxial graphene surface.

Taking into account vRD and vHREELS quantities, and

substituting in Eq. (9) quantities of K = 1/T0.63(membr.[5])723K and K0 « K0(membr.[5]) ~ Vhreels, one can evaluate AHdes.(membr.[5]) = AHc-H(membr.[5]) » 2.66 eV (Table 1A). In such approximation, the obtained value of AHC-H(membr.[5]) coincides (within the errors) with the experimental value [13] of the break-down energy of C-H bonds in hydrofullerene C60H36 (AHc-h(c60H36) = 2.64 ± 0.01 eV, Table 1B).

The above analysis of the related data shows that for the experimental graphene membranes (hydrogenated up to the near-saturation) can be used the following thermodesorption characteristics of the empirical character, relevant to Eq. (9): AHfaXmembr^]) = AHc-H(membr.[5]) = 2.6 ± ± 0.1 eV, K0(membr.[5]) = Vc-H(membr.[5]) « 5-1013 s-1(Table 1A). The analysis also shows that this is a case for a nondiffusion rate limiting kinetics, when Eq. (9) corresponds to the Polanyi-Wigner one [14, 16]. Certainly, these tentative results could be directly confirmed and/or modified by receiving and treating within Eqs. (8, 9) of the experimental data on t0.63 at several annealing temperatures.

The above noted fact that the empirical [5, 16] quantity T0.63(membr.[5])723K is much larger (by about 3 orders), than the theoretical [4, 16] one (T063(graphane[4])723K), is consistent with that mentioned in [5]. The alternative possibility has been supposed in [5] that (i) the experimental graphane membrane (a freestanding one) may have "a more complex hydrogen bonding, than the suggested by the theory", and that (ii) graphane (CH) [3] may be "the until-now-theoretical material".

4. Consideration of the experimental data [5] on hydrogenation-dehydrogenation of mono- and bi-layer epitaxial graphenes, comparing with the related data [5] for free-standing graphene membranes

4.1. Characteristics of hydrogenation-dehydrogenation of mono-layer epitaxial graphenes In [5], both the graphene membrane samples considered above, and the epitaxial graphene and bi-graphene samples on substrate SiO2 were exposed to a cold hydrogen dc plasma for 2 hours to reach the saturation in the measured characteristics. They used a low-pressure (0.1 mbar) hydrogen-argon mixture of 10% H2. Raman spectra for hydrogenated and subsequently annealed free-standing graphene membranes (Fig. 2B in [16]) are rather similar to those for epitaxial graphene samples (Fig. 2A in [16]), 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 free-standing membrane was two factors greater than the area for graphene on a substrate (Fig. 2 in [16], the left inset), which indicates the formation of twice as many C-H sp3 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 the membranes to atomic hydrogen.

The integrated intensity area of the D peak in Fig. 2B in [16] 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 Fig. 2A in [16], corresponding to the hydrogen concentration in the epitaxial graphene samples.

The above noted Raman spectroscopy data [5] on dependence of the concentration (C) of adsorbed hydrogen from the hydrogenation time (t) (obviously, at about 300 K) can be described with the equation [14, 46]:

(C0 - C)/C0 = exp(-Kt) = exp(-t/ib.63), (8*)

where C0 is the saturation value.

By using the above noted Raman spectroscopy data [5] (Fig. 2 in [16]), one can suppose that the near-saturation ((C/C0) = 0.95) time (t0.95) for the free standing

№ 17 (157) Международный научный журнал

graphene membranes (at ~300 K) is about 3 h, and a maximum possible (but not defined experimentally) value of C0(membr.) = 0.5 (atomic fraction, i.e. the atomic ratio (H/C) =1). Hence, using Eq. (8*) results in the

quantities of т

0.63(membr.[5])hydr.300K

1.0 h, C

3h(membr.[5])

- °.475, C2h(membr.[5]) ~ 0.43 and C1h(membr.[5]) ~ 0.32, where, C3h(membr.[5]> C2h(membr.[5]) and C1h(membr.[5]) being the

adsorbed hydrogen concentration at the hydrogenation time (t) equal to 3 h, 2 h and 1 h, respectively. It is expedient to note that the quantity of C0(membr.[5]) - 0.5 corresponds to the local concentration of C0(membr.[5]one_side) - 0.33 for each of the two sides of a membrane, i.e. the local atomic ratio (H/C) = 0.50.

The evaluated value of T0.63(membr.[5])hydr.300K (for process of hydrogenation of the free standing graphene membranes [5]) is much less (by about 26 orders) of the evaluated value of the similar quantity of

T0.63(membr.[5])dehydr.300K - (0.4-2.7)'1026 h (if AH(des.) =

= (2.49-2.61) eV, K0№s.) = (0.7-5)-1013 s-1, Item 3, Table 1A) for process of dehydrogenation of the same free standing graphene membranes [5]. It shows that the activation energy of the hydrogen adsorption (AH(ads.)) for the free standing graphene membranes [5] is considerably less, than the activation energy of the hydrogen desorption (AH(des.) = (2.5 or 2.6) eV). Hence, by using Eq. 9 and supposing that K0(ads.) - K0(des.), one can obtain a reasonable value of AH(ads.)membr.[5] = 1.0 ± ± 0.2 eV (Table 1). The heat of adsorption of atomic hydrogen by the free standing graphene membranes [5] may be evaluated as [14, 46]: (AH(ads.)membr.[5] -AH(des.)membr.[5]) = -1.5 ± 0.2 eV (an exothermic reaction).

One can also suppose that the near-saturation ((C/C0) -- 0.95) time (t0.95) for the epitaxial graphene samples (at —300 K) is about 2 h. Hence, by using Eq. (8*) and the above noted data [5] on the relative concentrations

((C1h(membr. [5])/C1h(epitax.[5])) - 2 and ((C3h(membr.[5])/

C3h(epitax.[5])) - 3), one can evaluate the quantities of

T0.63(epitax.[5])hydr.300K - 0.7 h and C^tax^]) ~ 0.16.

Obviously, C0(epitax.[5]) is related only for one of the two sides of an epitaxial graphene layer, and the local atomic ration is (H/C) - 0.19. It is considerably less (about 2.6 times) of the above considered local atomic ratio (H/C) = = 0.5 for each of two sides the free standing hydrogenated graphene membranes.

The obtained value of T0.63(epitax.[5])hydr.300K - 0.7 h (for process of hydrogenation of the epitaxial graphene samples [5]) is much less (by about two - seven orders) of the evaluated values of the similar quantity for the process of dehydrogenation of the same epitaxial graphene samples [5] (T0.63(epitax.[5])dehydr.300K ~ (1.5-1021.0-107) h, for AH(des) = (0.3-0.9) eV and K0(des) = (0.23.5-104) s-1, Item 4.2, Table 1A). Hence, by using Eq. 9 and supposing that K0(ads.) - K0(des.) (a rough approximation), one can obtain a reasonable value of AH(ads.)epitax.[5] ~ 0.3 ± 0.2 eV (Table 1A). The heat of adsorption of atomic hydrogen by the free standing

graphene membranes [5] may be evaluated as [14, 46]:

(AH(ads .)epitax.[5] - AH(des .)epitax. [5]) = -0.3 ± 0.2 eV (an exothermic reaction).

The smaller values of C0(epitax.[5]) - 0.16 and (H/C)(epitax.[5]) - 0.19 (in comparison with

C0(membr.[5]one_side) -0.33 and (H/C)(membr.[5]one_side) - 0.50)

may point to a partial hydrogenation localized in some defected nanoregions [33-43] for the epitaxial graphene samples (even after their prolonged (3 hour) exposures, i.e. after reaching their near-saturation. Similar analytical results, relevance to some other epitaxial graphenes are presented in some next Items.

4.2. Characteristics of dehydrogenation of mono-layer epitaxial graphenes [5] According to a private communication from D.C. Elias, a near-complete desorption of hydrogen (-AC/C0 « « 0.95) from a hydrogenated epitaxial graphene on a substrate SiO2 (Fig. 2A in [16]) has been achieved by annealing it in 90% Ar/10% H2 mixture at T = 573 K for 2 hours (i.e., t0.95(epitax.[5])573K = 7.2-103 s). Hence, by using Eq. (8), one can evaluate the value of T0.63(epitax.[5])573K = = 2.4-103 s for the epitaxial graphene [5], which is about six orders less than the evaluated (as in Item 3) value of T0.63(membr.[5])573K = 1.5-109 s for the free-standing membranes [5].

The changes in Raman spectra of graphene [5] 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 SiO2 and for the free-standing graphene membrane (Fig. 2 in [16]). Hence, one can

suppose that K0(epitax.[5]) = VC-H(epitax.[5]) ~ K0(membr.[5]) =

= Vc-H(membr.[5]) « (0.7 or 5)-1013 s-1 (Item 3, Table 1A). Then, by substituting in Eq. (9) the values of K =

= K(e

Hepitax.[5])573K = 1/T0 .63(epitax.[5])573K

~ K0(membr.[5]), one can evaluate AHdes .(epitax.[5]) = AHc-H(epitax.[5]) = (1.84 or 1.94) eV (Table 1A). Here, the case is supposed of a non-diffusion-rate-limiting kinetics, when Eq. (9) corresponds to the Polanyi-Wigner one [14]. Certainly, these tentative thermodynamic characteristics of the hydrogenated epitaxial graphene on a substrate SiO2 could be directly confirmed and/or modified by further experimental data on T0.63(epitax.) at various annealing temperatures.

It is easy to show that: 1) these analytical results (for the epitaxial graphene [5]) are not consistent with the presented below analytical results for the mass spectrometry data (Fig. 3 in [16], TDS peaks ## 1-3, Table 1A) on thermal desorption of hydrogen from a specially prepared single-side (obviously, epitaxial*) graphane [5]; and 2) they cannot be 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 consideration presented below (both in this Item, and in Items 5-11), the epitaxial graphene case ([5] and others) may be related to a

and K0 « K(

0(epitax.[5])

№ 17 (157) Международный научный журнал

hydrogen desorption case of a diffusion rate limiting kinetics, when K0 ^ v, and Eq. (9) does not correspond to the Polanyi-Wigner one [14].

By using the method [14] of treatment of thermal desorption (TDS) spectra, relevant to the mass spectrometry data [5] (Fig. 3 in [16]) on thermal desorption of hydrogen from the specially prepared single-side (epitaxial*) graphane (under heating from room temperature to 573 K for 6 minutes), one can obtain the following tentative results:

1) the total integrated area of the thermal desorption spectra corresponds to ~10-8 g of desorbed hydrogen, that may correlate with the graphene layer mass (unfortunately, it's not considered in [5], particularly, for evaluation of the C0 quantities);

2) the TDS spectra can be approximated by three thermodesorption (TDS) peaks (# # 1-3);

3) TDS peak # 1 (~30 % of the total area, « « 370 K) can be characterized by the activation energy of AH(des) = EiDs-peak # 1= 0.6 ± 0.3 eV and by the per-exponential factor of the reaction rate constant

K0(TDS-peak # 1) ~ 2-10 s ;

4) TDS peak # 2 (~15 % of the total area, Tmax#2 « «445 K) can be characterized by the activation energy AH(des ) = ETDS-peak #2 = 0.6 ± 0.3 eV, and by the per-exponential factor of the reaction rate constant K0(TDS-peak # 2) « 1-106 s-1;

5) TDS peak # 3 (~55 % of the total area, 7max#3 « « 540 K) can be characterized by the activation energy AH(des) = ETDS-peak # 3 = 0.23 ± 0.05 eV and by the per-exponential factor of the reaction rate constant K0(TDS-peak # 3) « 2.4 s-1.

These analytical results (on quantities of AH(des.) and K0) show that all three of the above noted thermal desorption (TDS) processes (# 1TDS, # 2TDS and # 3TDS) can not been described in the framework of the Polanyi-Wigner equation [14, 16] (due to the obtained low values of the K0(des.) and AH(des.) quantities, in comparison with the v(C-H) and AH(C-H) ones).

As is shown below, these results may be related to a hydrogen desorption case of a diffusion-rate-limiting kinetics [14, 16], when in Eq. 9 the value of K0 « D0app./L2 and the value of AHdes. = gapp., where D0app is the perexponent factor of the apparent diffusion coefficient Dapp. = = D0app.exp (-Qapp/kBT), Qapp. is the apparent diffusion activation energy, and L is the characteristic diffusion size (length), which (as is shown below) may correlate with the sample diameter [5] (L ~ dsample « 4-10-3 cm, Fig. 2 in [16], Right inset).

TDS process (or peak) # 3TDS (Fig. 3 in [16], Table 1A) may be related to the diffusion-rate-limiting TDS process (or peak) I in [14], for which the apparent diffusion activation energy is QappI « 0.2 eV « ETDS-peak#3

can

evaluate the quantity of Dcapp.(TDS-peak#3)

-5

and D,

Capp.I

3 10-3 cm2/s,

and which is related to

chemisorption models "F" and/or "G" (Fig. 4 in [16]).

By supposing of L ~ dsample, i.e. of the order of diameter of the epitaxial graphene specimens [5], one

« L2K0(TDS-peak#3) « 4 -10-5 cm (or within the errors limit, it is of (1.3 -11)-10-5 cm, for Etds -peak # 3 values 0.18-0.28 eV, Table 1A). The obtained values of D0app.(TDS-peak#3) satisfactory (within one-two orders, that may be within the errors limit) correlate with the D0appI quantity. Thus, the above analysis shows that for TDS process (or peak)

# 3TDS [5], the quantity of L may be of the order of diameter (dsample) of the epitaxial* graphene samples.

Within approach [14], model "F" (Fig. 4 in [16]) is related to a "dissociative-associative" chemisorption of molecular hydrogen on free surfaces of graphene layers of the epitaxial samples [5]. Model "G" (Fig. 4 in [16]) is related, within [14] approach, to a "dissociative-associative" chemisorption of molecular hydrogen on definite defects in graphene layers of the epitaxial samples [5], for instance, vacancies, grain boundaries (domains) and/or triple junctions (nodes) of the grain-boundary network [33-43], where the dangling carbon bonds can occur.

TDS processes (or peaks) # 1TDS and # 2TDS [5] (Table 1A) may be (in some extent) related to the diffusion-rate-limiting TDS processes (or peaks) I and II in [14].

Process II is characterized by the apparent diffusion activation energy QappII « 1.2 eV (that is considerably higher of quantities of ETDS-peak#1 and ETDS-peak#2) and D0appII « 1.8-103 cm2/s. It is related to chemisorption model "H" (Fig. 4 in [16]). Within approach [14], 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 [5], for instance, vacancies, grain boundaries (domains) and/or triple junctions (nodes) of the grain-boundary network [33-43], where the dangling carbon bonds can occur.

By supposing the possible values of ETDS -peaks##1,2 = = 0.3, 0.6 or 0.9 eV, one can evaluate the quantities of K0(TDS-peak#1) and K0(TDS-peak#2) (Table 1A). Hence, by supposing of L ~ dsample, one can evaluate the quantities

of D0app.(TDS-peak#1) and D0app.(TDS-peak#2> some of them

correlate with the D0appI quantity or with D0app ii quantity. It shows that for TDS processes (or peaks) # 1TDS and

# 2TDS [5], the quantity of L may be of the order of diameter of the epitaxial* graphene samples.

For the epitaxial graphene [5] case, supposing the values of AHdes.(epitax.[5]) « 0.3, 0.6 or 0.9 eV results in relevant values of K0(epitax.[5]) (Table 1A). Hence, by supposing of L ~ dsample, one can evaluate the quantities of D0app.(epitax.[5]), some of them correlate with the D0app.I quantity or with D0appII 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 [5].

It is important to note that considered in Items 2 and 3 chemisorption of atomic hydrogen with free-standing graphane-like membranes [5] and with theoretical graphanes [3, 4] may be related to model "F*" considered in [14]. Unlike model "F" (Fig. 4 in [16]),

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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 [14] by the quantity of AH(C-H)"F»" « 2.5 eV, which coincides (within the errors) with the similar quantities (AH(C-H)) for graphanes [3-5] (Table 1A). As is also shown in Items 2 and 3, the dehydrogenation processes in graphanes [5, 4] may be the case of a non-diffusion rate limiting kinetics, for which the quantity of K0 is the corresponding vibration frequency (K0 = v), and Eq. (9) is correspond to the Polanyi-Wigner one [14, 16].

On the other hand, model "F*" is manifested in the diffusion-rate-limiting TDS process (or peak) III in [14] (Table 1B), for which the apparent diffusion activation

energy is Q

app.III

2.6 eV = AH(

(C-H)"F*

" and D

Оарр.Ш

« 3-10-3 cm2/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 (graphite nanofibers) [14] (Table 1B).

It is expedient also to note about models "C" and "D", those are manifested in the diffusion-rate-limiting TDS process (or peak) IV in [14] (Table 1B), for which the apparent diffusion activation energy is Qapp.IV ~ 3.8 eV « AH(C-H)"C","D" and D0appIV « 6-102 cm2/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) [14] (Table 1B).

But such processes (III and IV) have not manifested, when the thermal desorption annealing of the hydrogenated epitaxial graphene samples [5] (Fig. 3 in [16]), unlike some hydrogen sorption processes in epitaxial graphenes and graphite samples considered in some next Items.

4.3. An interpretation of characteristics of hydrogenation-dehydrogenation of mono-layer epitaxial graphenes [5]

The above obtained values (Item 4.2, Tables 1A, 1B) of characteristics of dehydrogenation of mono-layer epitaxial graphene samples [5] can be presented, as follows: AHdes—

— Qapp.I or — Qapp.II [14], K0(des.) — (^ppl/i ) or — (D0app.II/L )

[14], L — dsample, i.e. being of the order of diameter of the epitaxial graphene samples [5]. And it is related to the chemisorption models "F", "G" and/or "H" (Fig. 4 in [16]).

These characteristics unambiguously point that in the epitaxial graphene samples [5], there are the rate-limiting processes (types of I and/or II [14]) of diffusion of hydrogen, mainly, from chemisorption "centers" (of "F", "G" and/or "H" types (Fig. 4 in [16])) 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 — dsample) of the order of diameter of the epitaxial graphene samples, which, obviously, can not be manifested for a case of hydrogen desorption processes from the external graphene surfaces. Such interpretation is direct opposite, relevance to the interpretation of authors [5] 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 analytical data (Item 4.1, Table 1A) on activation energies of hydrogen adsorption for the epitaxial graphene samples (AH(ads.)epitax.[5] « 0.3 ± 0.2 eV), which is much less than the similar one for the free standing graphene membranes [5] (AH(ads.)membr.[5] = 1.0 ± 0.2 eV). It may be understood for the case of chemisorotion (of "F", "G" and/or "H" types (Fig. 4 in [16])) on the internal graphene surfaces (neighboring to the substrate (SiO2) surfaces), which obviously proceeds without the diamond-like strong distortion of the graphene network, unlike graphane [3] (Item 1).

Such an extraordinary interpretation is also consisted with the above analytical results (Item 4.1) about the smaller values of ^^.[5]) « 0.16 and (H/C)(epitax.[5]) « « 0.19, in comparison with C0(membr.[5]one_side) « 0.33 and (H/C)(membr.[5]one_side) » 0 50. It may point to an "internal" (in the above considered sense) local hydrogenation in the epitaxial graphene layers. It may be, for instance, an "internal" hydrogenation localized, mainly, in some defected nano-regions [33-43] mentioned above (Items 1, 4.2), where their near-saturation may be reached after prolonged (3 hour) exposures.

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 [5]) 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 graphane [3] (Item 1). It may result (for the epitaxial graphenes [5]) in disappearance of the hydrogen chemisorption with

characteristics of AH(

(ads.)membr.[5]

and AH(

(des.)membr.[5]

(Table 1A) manifested in the case of the free standing graphene membranes [5]. And the hydrogen chemisorption with characteristics of AH(ads.)epitax.[5] and (AH(des.)epitax.[5] (Table 1A) by the external graphene surfaces, in the epitaxial samples [5], 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 (Fig. 2 in [16]) the fact that the changes in Raman spectra of graphene [5] 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 SiO2 and for the free-standing graphene membrane.

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4.4. An interpretation of the data on hydrogenation of bi-layer epitaxial graphenes [5] In work [5], the same hydrogenation procedures of the 2 hour long expositions have been applied also for bi-layer epitaxial graphene on SiO2/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 SiO2/Si wafer exposed to the same hydrogenation procedures. The authors [5] believe that higher rigidity of bi-layers suppressed their rippling, thus reducing the probability of hydrogen adsorption.

But such an interpretation [5] seems not enough adequate, if to take into account the above (Item 4.3) and below (next Items) presented consideration and interpretation of a number of data.

By using the above extraordinary interpretation (Item 4.3) and results on characteristics (Qapp.m ~ 2.6 eV, A)app.m = 3 10-3 cm2/s (Item 4.2, Table 1B) of a rather slow diffusion of atomic hydrogen between neighboring graphene-like layers in graphitic materials and nanostructures (process III, model "F*" [14]), one can suppose a negligible diffusion penetration of atomic hydrogen between the two graphene layers in the bi-layer epitaxial samples [5] (during the hydrogenation procedures of the 2 hour long expositions, obviously, at T ~ 300 K). Indeed, by using values of QappIII and

Д

Qapp.III;

one can estimate the characteristic diffusion size

(length) L ~ 7-10- cm, which points to absence of such diffusion penetration.

In the next Items 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 is there shown) an important role plays some defects found in graphene networks [3343], relevant to the probability of hydrogen adsorption and the permeability of graphene networks for atomic hydrogen (Item 1).

5. Consideration and interpretation of the Raman spectroscopy data [51] on hydrogenation-dehydrogenation of graphene flakes

In [51], 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 SiO2 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 (Ldef). 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 (CH < 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 (ZD//G) of Raman bands. The hydrogen coverage (CH) determined from the defect distance (Ldef.) did not exceed ~ 0.05%.

In [16], the data [51] (Fig. 5 in [16]) have been treated and analyzed. The obtained analytical results (Table 2) on characteristics of hydrogenation-dehydrogenation of graphene flakes [51] may be interpreted within the models used in Item 4 for interpretation of the similar characteristics for the epitaxial graphenes [5] (Table 1A), which are also presented (for comparing) in Table 2.

Таблица 2

Аналитические величины характеристик, рассматриваемых в разделах 5-7, и сопоставление с величинами характеристик, рассматриваемых в разделах 1-4

Analytical quantities related to Items 5-7, comparing with ones of Items 1-4

Table 2

Value/Quantity

Material AH(des.), eV {AH(ads.), eV} ^Q(des.), s 1 {L ~ (D0app.III/K0(des.)) } T0.63(des.)553K; s {T0.63(ads.)300Ki s}

Graphene flakes/SiO2 [51] 0.11 + 0.07 (as process ~ I [14], -models "F", "G", Fig.4 in [16]) Q.15 (for 0.11 eV) {L ~ ^sample} 0.7T02 {0.9T03}

Graphene/Ni [52] HOPG [52] 1.3102 - 2.6-102 {0.5-103 - 1.0 103} 1.3102 - 2.6-102 {0.5-103 - 1.0 103}

(SiC-D/QFMLG-H) [55] 0.7+0.2 (as processes -I-II [14], -model "G", Fig.4 in [16]) 9102 (for 0.7 eV) {L ~ ^sample} 2.7-103

(SiC-D/QFMLG) [55] 2.0 + 0.6 2.6 (as process ~ III [14], -model "F*") 1106 (for 2.0 eV) 6108 (for 2.6 eV) {L = 22 nm} 1.7-1012 8-1014

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Graphene/SiO2 [5] (Table 1A) If 0.3 if 0.6 if 0.9 (as processes —I-II [14], -model "G", Fig.4 in [16]) {0.3 + 0.2} then 0.2 then 0.S102 then 3.5104 {L — dsample} 0.3102 3.7-103 4.6-103 {2.5-103} Item 4.1

Graphene*/SiO2 (TDS-peak #3) [5] (Table 1A) 0.23+0.05 (as process — I [14], —models "F", "G", Fig.4 in [16]) 2.4 (for 0.23 eV) {L — dsample} 0.5-102

Graphene*/SiO2 (TDS-peak #2) [5] (Table 1A) 0.6+0.3 (as processes —I-II [14], —model "G", Fig.4 in [16]) 1-106 (for 0.6 eV) {L — dsample} 0.3

Graphene*/SiO2 (TDS-peak #1) [5] (Table 1A) 0.6+0.3 (as processes —I-II [14], —model "G", Fig.4 in [16]) 2-107 (for 0.6 eV) {L — dsample} 1.510-2

By taking into account the facts that the REI exposure regime [51] is characterized by a form of (Id/Ig) ~ Lf. (for (Id/Ig) < 2.5), Ldef. « 11-17 nm and the hydrogen concentration CH < 510-4, one can suppose that the hydrogen adsorption centers in the single graphene flakes (on the SiO2 substrate) are related to some point nanodefects (i.e., vacancies and/or triple junctions (nodes) of the grain-boundary network) of diameter ddf ~ const. In such a model, the quantity CH can be described satisfactory as:

Сн

! n^ádeíf/Lef.)2,

(10)

where nH « const is the number of hydrogen atoms adsorbed by a center; CH ~ (ID/IG) ~ Ld2f..

It was also found [51] that after the Ar/H2 plasma exposure, the (ID/IG) ratio for bi-layer 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 other defects are introduced. Such a situation may have place in [5] for bi-layer epitaxial graphene on SiO2/Si wafer (Item 4.4).

6. Consideration and interpretation of the STM/STS data [52] on hydrogenation-dehydrogenation of epitaxial graphene and graphite (HOPG) surfaces

In [52], the effect of hydrogenation on topography and electronic properties of graphene grown by CVD on top of a nickel surface and high oriented pyrolytical graphite (HOPG) surfaces were studied by scanning tunneling microscopy (STM) and spectroscopy (STS). The surfaces were chemically modified using 40 min Ar/H2 plasma (with 3 W power) treatment (Fig. 6 in [16]). 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 yield a similar, but slightly reduced, semiconducting behavior after the second hydrogenation.

The data (Fig. 6 in [16]) show that the time of desorption from both the epitaxial graphene/Ni samples and HOPG samples of about 90-99% of hydrogen under 553 K annealing is t0.9(des.)553K (or ¿0.99(des.)553K) « 6102 s. Hence, by using Eq. (8), one can evaluate the quantity T0 63(des.)553K[52] « 260 (or 130) s, which is close (within the errors) to the similar quantity of T0.63(des.)553K[51] « 70 s for the epitaxial graphene flakes [51] (Table 2).

The data (Fig. 6 in [16]) also show that the time of adsorption (for both the epitaxial graphene/Ni samples and HOPG samples) of about 90-99% of the saturation hydrogen amount (under charging at about 300 K) is ¿0.9(ads.)300K (or t0.99(ads.)300K) « 2.4-103 s. Hence, by using Eq. (8*), one can evaluate the quantity T0.63(ads.)300K[52] « « (1.1 or 0.5)-102 s, which coincides (within the errors) with the similar quantity of T0.63(ads.)300K[51] « 9-102 s for the epitaxial graphene flakes [51] (Table 2).

The data (Fig. 6 in [16]) also show that the time of adsorption (for both the epitaxial graphene/Ni samples and HOPG samples) of about 90-99% of the saturation hydrogen amount (under charging at about 300 K) is t0.9(ads.)300K (or t0.99(ads.)300K) « 2.4-103 s. Hence, by using Eq. (8*), one can evaluate the quantity T0.63(ads.)300K[52] « « (1.1 or 0.5)-102 s, which coincides (within the errors) with the similar quantity of T0 63(ads.)300K[51] « 9-102 s for the epitaxial graphene flakes [51] considered in the previous Item (Table 2).

These analytical results on characteristics of hydrogenation-dehydrogenation of epitaxial graphene and graphite surfaces [52] (also as the results for graphene flakes [51] presented in the previous Item) may be interpreted within the models used in Item 4 for interpretation of the similar characteristics for the epitaxial graphenes [5] (Tables 1, 2).

As is noted in [53], before the plasma treatment, the CVD graphene exhibits a Moiré pattern superimposed to the honeycomb lattice of graphene (Fig. 6(d) in [16]). 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 [53], for the hydrogenated CVD graphene, the expected structural changes are twofold. First, the chemisorption of

№ 17 (157) Международный научный журнал

hydrogen atoms will change the sp hybridization of carbon atoms to tetragonal sp3 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 [33-43]). Fig. 6(e) in [16] 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 [52, 53] that these bright nano-regions present a semiconducting behavior, while the rest of the surface remains conducting (Fig. 6(g)-(h) in [16]).

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 Item 1 (Introduction). A similar model may be valid and relevant for the HOPG samples (Fig. 6 (a)-(c) in [16]).

It has been found out that when graphene is deposited on a SiO2 surface (Figs. 7, 8 in [16]), 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 [53, 54].

The charge inhomogeneities (defects) of epitaxial hydrogenated graphene/ SiO2 samples do not show long range ordering, and the mean spacing between them is Ldef. « 20 nm (Fig. 8 in [16]). It is reasonable to assume that the charge inhomogeneities (defects) are located at the interface between the SiO2 layer (300 nm thick) and the graphene flake [53, 54]. A similar quantity (Ldef. « « 11-17 nm, [51])) for the hydrogen adsorption centers in the monolayer graphene flakes on the SiO2 substrate has been considered in Item 5.

7. Consideration and interpretation of the HREELS/LEED data [55] on dehydrogenation of epitaxial graphene on SiC substrate

In [55], hydrogenation of deuterium-intercalated quasi-free-standing monolayer graphene on SiC(0001) 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 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 (Fig. 9 in [16]). 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 ~51017 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 1015 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 R. Bisson, the temperature indicated at each point in Fig. 9 in [16] corresponds to successive temperature ramp (not linear) of 5 minutes. Within a formal kinetics approach for the first order reactions [14, 46], one can treat the above noted points at T = 543 K, 611 K and 686 K, by using Eq. (8) transformed to a more suitable form (8'): K, = -(ln(C/C0,)/i), where t = 300 s, and the corresponding quantities C0i and C are determined from Fig. 9 in [16]. It resulted in finding values of the reaction (hydrogen desorption from SiC-D/QFMLG-H samples) rate constant K,(des.) for 3 temperatures Ti = 543, 611 and 686 K. The temperature dependence is described by Eq. (9). Hence, the desired quantities have been determined (Table 2) as the reaction (hydrogen desorption) activation energy AHdes.xsiC-D/QFMLG-H)^] = 0.7 ± 0.2 eV, and the per-exponential factor of the reaction rate constant K0(des.)(SiC-D/QFMLG-H)[55] « 9102 s-1. The obtained value of Atf(des.)(SiC-D/QFMLG-H)[55] is close (within the errors) to the similar ones (£Wpeak # 1[5] and ¿Tos-peak # 2[5]) for TDS processes # 1 and # 2 (Item 4.2, Table 1A). But the obtained value K0des.(SiC-D/QFMLG-H)[55] differs by several orders from the similar ones (K0des.(TDS-peak # ^ and K0des.(TDs-peak # 2)[5]) for TDS processes # 1 and # 2 (Item 4.2, Table 1A). Nevertheless, these three desorption processes may be (in some extent) related to chemisorption models "H" and/or "G" (Fig. 4 in [16]).

These analytical results on characteristics of hydrogen desorption (dehydrogenation) from (of) SiC-D/QFMLG-H samples [55] may be also (as the results from Items 5 and 6) interpreted within the models used in Item 4 for interpretation of the similar characteristics for the epitaxial graphenes [5] (Tables 1A, 2).

In the same way, one can treat the points from Fig. 9 in [16] (at T, = 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): the reaction (deuterium desorption) activation energy A#(des.)(SiC-D/QFMLG)[55] = 2.0 ± 0.6 eV, and the per-exponential factor of the reaction rate constant K0(des.)(SiC-D/QFMLG)[55] » 1T06 s-1.

Such a relatively low (in comparison with the vibration C-H or C-D frequencies) value of K0(des.)(SiC-D/QFMLG)[55] points to that the process can not be described within the Polanyi-Wigner model [14, 16] related the case of a non-diffusion rate limiting kinetics.

№ 17 (157) Международный научный журнал

And as is 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.

Formally, this desorption process (obviously, of a diffusion-limiting character) may be described (as is shown below) similarly to TDS process III (model "F*") in [14] (Table 1B), and the apparent diffusion activation energy may be close to the break-down energies of the C-H bonds.

Obviously that such analytical results on characteristics of deuterium desorption from SiC-D/QFMLG samples [55] may not be interpreted within the models used in Item 4 for interpretation of the similar characteristics for the epitaxial graphenes [5] (Tables 1A, 2).

But these results (for SiC-D/QFMLG samples [55]) may be quantitatively interpreted on the basis of using the characteristics of process III in [14] noted in Item 4.2 (Table 1B). Indeed, by using the quantities' values (from

Table 1) of ДЯ(

(des.)(SiC-D/QFMLG)[55]

6108 s-1

Q

and D

app.III ~ 'Oapp.III

2.6 eV,

310

-3

K0(des.)(SiC-D/QFMLG)[55]

cm2/s, one can evaluate the quantity of L ~ (D0appIII / K0(des.))1/2 = 22 nm. The obtained value of L coincides (within the errors) with values of the quantities of Ldef. « = 11-17 nm (Item 5, Eq. (10)) and Ldef. = 20 nm (Item 6, Fig. 8(b) in [16]). 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 [33-43] 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.

It is reasonable to assume that the quasi-free-standing monolayer graphene on the SiC-D substrate is permeable to atomic hydrogen (at room temperature) in some defect nano-regions (probably, in vacancies and/or triple junctions (nodes) of the grain-boundary network [3343]).

It would be expedient to note that the HREELS data [55] on bending and stretching vibration C-H frequencies in SiC-D/QFMLG-H samples (153 meV (3.71013 s-1) and 331 meV (8.0-1013 s-1), respectively) are consistent with those [47] considered in Items 3, related to the HREELS data for the epitaxial graphene [5].

The obtained characteristics (Table 2) of desorption processes [51, 52, 55] show that all these processes may be of a diffusion-rate-controlling character [14].

8. Consideration and interpretation of the Raman spectroscopy data [56] on dehydrogenation of graphene layers on SiO2 substrate

In [56], graphene layers on SiO2/Si substrate have been chemically decorated by radio frequency hydrogen plasma (the power of 5-15 W, the pressure of 1 Tor)

treatment for 1 min. 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 SiO2/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 on the number of layers. These results [56] on bilayer graphene/SiO2/Si are in contradiction to the results [5] on a negligible hydrogenation of bi-layer epitaxial graphene on SiO2/Si wafer, when obviously other defects are produced.

Within a formal kinetics approach [14, 46], the kinetic data (from Fig. 10 (a) in [16]) for single layer graphene samples (1LG-5W and 1LG-15W ones) can be treated. Eq. (7) is used to transform into a more suitable form (7'): K = -((AC/At)/C), where At = 1800 s, and AC and C are determined from Fig. 10 (a) in [16].

The results have been obtained for 1LG-15W sample 3 values of the # 1 reaction rate constant Ki(iLG-i5W) for 3 temperatures (T = 373, 398 and 423 K), and 3 values of the # 2 reaction rate constant K2(1lg-15w) for 3 temperatures (T = 523, 573 and 623 K). Hence, by using Eq. (9), the following quantities for 1LG-15W samples have been determined (Table 3): the # 1 reaction activation energy A^des1(iLG-15W) = 0.6 ± 0.2 eV, the per-exponential factor of the # 1 reaction rate constant K0des.i(iLG-i5W) « 2-104 s-1, the # 2 reaction activation energy A^des.2[(1LG-15W) = 0.19 ± 0.07 eV, and the per-exponential factor of the # 2 reaction rate constant K

0des.2[(1LG-15W) :

: 310-2 s-1.

It also resulted in finding for 1LG-5W sample 4 values of the # 1 reaction rate constant KI(1LG-5W) for 4 temperatures (T = 348, 373, 398 and 423 K), and 2 values of the # 2 reaction rate constant K2(1LG-5W) for 2 temperatures (T = 523 and 573 K). Therefore by using Eq. (9), one can evaluate the desired quantities for 1LG-5W specimens (Table 3): the # 1 reaction activation energy A#des.1(1LG-5W) = 0.15 ± 0.04 eV, the per-exponential factor of the # 1 reaction rate constant

K

0des.1[(1LG-5W)

210-2 s-1,

the # 2 reaction activation

energy A^des2(1LG-5W) = 0.31 ± 0.07 eV, and the per-exponential factor of the # 2 reaction rate constant

K

0des.2(1LG-5W)

■■ 0.5 s-1.

A similar treatment of the kinetic data (from Fig. 10 (c) in [16]) for bilayer graphene 2LG-15W samples resulted in obtaining 4 values of the # 2 reaction rate constant K2(2LG-15W) for 4 temperatures (T = 623, 673, 723 and 773 K). Hence, by using Eq. (9), the following desired values are found (Table 3): the #2 reaction activation energy A^des2(2LG-15W) = 0.9 ± 0.3 eV, the per-exponential factor of the # 2 reaction rate constant

K

0des.2(2LG

15W) ~1'1° s .

A similar treatment of the kinetic data (from Fig. 6 (c) in [56]) for bilayer graphene 2LG-5W samples results in obtaining 4 values for the # 1 reaction rate constant

№ 17 (157) Международный научный журнал

Ki(2LG-5W) for 4 temperatures (T = 348, 373, 398 and 423 K), and 3 values for the # 2 reaction rate constant K2(2LG-5W) for 3 temperatures (T = 573, 623 and 673 K). Their temperature dependence is described by Eq. (9). Hence, one can evaluate the following desired values (Table 3): the # 1 reaction activation energy AHdes1[(2LG-5W) = 0.50 ± 0.15 eV, the per-exponential factor of the # 1 reaction rate constant K0des1(2LG-5W) « 2103 s-1, the # 2 reaction activation energy AHdes.2(2LG-5W) = 0.40 ± 0.15

eV, and the per-exponential factor of the # 2 reaction rate constant K0des.2(2LG-5W) « 1 s-1.

The obtained analytical results (Table 3) on characteristics of the desorption (dehydrogenation) processes # 1 and # 2 [56] may be interpreted within the models used in Item 4 for interpretation of the similar characteristics for the epitaxial graphenes [5] (Table 1A). It shows that the desorption processes # 1 and # 2 (in [56]) may be of a diffusion-rate-controlling character.

Аналитические величины характеристик, рассматриваемых в разделах 8-11 Some analytical results of Items 8-11

Таблица 3

Table 3

Samples Values/Quantities

AH(des.)1 (eV) K0(des.)1 (s 1) {L} AH(des.)2 (eV) K0(des.)2 (s 1) {L}

- с - ХАУ ЧТ 1LG-15W 0.6±0.2 (as processes -I-II [14], 2-104 0.19±0.07 (as process -I [14], 310-2

(graphene) [56] -model "G", Fig.4 in [16]) {L — ^sample} -models "F", "G", Fig.4 in [16]) {L — ^sample}

2LG-15W (bi-graphene) [56] 0.9±0.3 (as processes -I-II [14], -model"G", Fig.4 in [16]) 1103 {L — ^sample}

ф о 1LG-5W 0.15±0.04 (as process -I [14], 2-10"2 0.31±0.07 (as process-I [14], 510-1

а (graphene) [56] -models "F","G",Fig.4 in [16]) {L — ^sample} -models "F" ,"G",Fig.4 in [16]) {L — ^sample}

Í2 2LG-5W 0.50±0.15 (as processes -I-II 2103 0.40±0.15 (as processes -I-II [14], 1.0

íi о (bi-graphene) [56] [14], -model"G", Fig.4 in [16]) {L ~ ^sample} -model"G", Fig. 4 in [16]) {L — ^sample}

к-. 01 о. HOPG [57], 0.6±0.2 (as processes -I-II [14], 1.5104 1.0±0.3 (as processes -I-II [14], 2-106

о TDS-peaks 1, 2 -model"G", Fig.4 in [16]) {L ~ ^sample} -model "G", Fig.4 in [16]) {L — ^sample}

с .0) 3 tn 2. о Graphene/SiC [17] 3.6 (as process -IV [14], -models "C","D", Fig.4 in [16]) 2-1014 —V(C-H) {L — 17 nm}

о HOPG [59], 2.4 [59] (as process -III [14],

Ot> с TDS-peaks 1, 2 -model "F*") 2-1010 4.1 [59] (as process -IV [14],

-S2 Q. HOPG [59], TDS-peak 1 2.4±0.5 (as process - III [14], -model "F*") {L - 4 nm} -models "C", "D", Fig.4 in [16])

9. Consideration and interpretation of the TDS/STM data [57] for HOPG treated by atomic deuterium

In [57], the results are present of a scanning tunneling microscopy (STM) study of HOPG (high oriented pyrolytical graphite) samples treated by atomic deuterium, which reveals the existence of two distinct hydrogen dimer nano-states on graphite basal planes (Figs. 11 and 12 (b) in [16]). 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 [57], 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 (Fig. 12 (a) in [16]).

By using the method [14] of TDS peaks' treatment, for the case of TDS peak 1 (~65% of the total area, Tmax#1 ~ 473 K) in Fig. 12(a) in [16], one can obtain values of the reaction # 1 rate constant (K(des.)1 = 1/%.63(des.)1) for several temperatures (for instance, T = 458, 482 and 496 K). Their temperature dependence can be described by Eq. (9). Hence, the desired values are defined as follows (Table 3): the # 1 reaction (desorption) activation energy Aff(des.)1 = 0.6 ± 0.2 eV, and the per-exponential factor of the # 1 reaction rate constant K0(des.)1 « 1.5104 s-1.

In a similar way, for the case of TDS peak 2 (~35% of the total area, Tmax#2 = 588 K)) in Fig. 12(a) in [16], one can obtain values of the # 2 reaction rate constant (K(des.)2 = 1/T0.63(des.)2) for several temperatures (for instance, T = 561 and 607 K). Hence, the desired values are defined as follows (Table 3): the # 2 reaction

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(desorption) activation energy AH(des.)2 = 10 ± 0.3 eV, and the per-exponential factor of the # 2 reaction rate constant K0(des.)2 « 2-106 s-1.

The obtained analytical results (Table 3) on characteristics of the desorption (dehydrogenation) processes # 1 and # 2 in [57] (also as in [56], Item 8) may be interpreted within the models used in Item 4 for interpretation of the similar characteristics for the epitaxial graphenes [5] (Table 1A). It shows that the desorption processes # 1 and # 2 (in [57] and [56]) may be of a diffusion-rate-controlling character. Therefore, these processes can not be described by using the Polanyi-Wigner equation (as it has been done in [57]).

The observed "dimer nano-states" or "nano-protrusions" (Figs. 11 and 12(b) in [16] (from [57])) may be related to the defected nano-regions, probably, as grain (domain) boundaries [33-43] and/or triple and other junctions (nodes) of the grain-boundary network in the HOPG samples. Some defected nano-regions at the grain boundary network (hydrogen adsorption centres # 1, mainly, the "dimer B" nano-structures) can be related to TPD (TDS) peak 1, the others (hydrogen adsorption centres # 2, mainly, the "dimer A" nano-structures) to TPD (TDS) peak 2.

In Figs. 11(a) and 12(b) in [16] (from [57]), one can imagine some grain boundary network (with the grain size of about 2-5 nm) decorated (obviously, in some nano-regions at grain boundaries) by some bright nano-protrusions. Similar "nano-protrusions" are observed and in graphene/SiC systems [58, 17] (Figs. 13-16 in [16]).

In [58], hydrogenation was studied by a beam of atomic deuterium 1012-1013 cm-2s-1 (corresponding to PD ® « 10-4 Pa) at 1600 K, and the time of exposure of 5-90 s, for single graphene on SiC-substrate. The formation of graphene blisters were observed, and intercalated with hydrogen in them (Figs. 13 and 14 in [16]), similar to those observed on graphite [57] (Figs. 11 and 12 in [16]) and graphene/SiO2 [17] (Figs. 15 and 16 in [16]). The blisters [58] disappeared after keeping the samples in vacuum at 1073 K (~ 15 min). By using Eq. (8), one can evaluate the quantity of T0.63(des.)1073K[58] ~ 5 min, which coincides (within the errors) with the similar quantity of T0.63(des.)1073K[17] ~ 7 min evaluated for graphene/SiC samples [17] (Item 10, Table 3).

A nearly complete decoration of the grain boundary network [33-43] can be imagined in Fig. 15(b) in [16] (from [17]). Also, as is seen in Fig. 16 in [16] (from [17]), such decoration of the nano-regions (obviously, located at the grain boundaries [33-43]) has a blister-like cross-section of height of about 1.7 nm and width of 10 nm order.

According to the thermodynamic analysis presented in Item 11, Eq. (15), such blister-like decoration nano-regions (obviously, located at the grain boundaries [3343]) may contain the intercalated gaseous molecular hydrogen at a high pressure.

10. Consideration and interpretation

of the PES/ARPES data [17] on hydrogenation-dehydrogenation of graphene/SiC samples

In [17], atomic hydrogen exposures at a pressure of Ph = 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. 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 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 (Figs. 15(b), 15(e), 16(a) and 16(b) in [16] (from [17])). With larger /¡j'-. (additional 15 min) atomic hydrogen exposures, the islands grow in size and merge until the surface is fully covered with bi-layer graphene (Figs. 15(c), 15(f), 16(c) and 16(d) in [16] (from [17])). A (V3 x V3) R30° periodicity is observed on the bi-layer areas. Angle resolved photoelectron spectroscopy (ARPES) and energy filtered X-ray photoelectron emission microscopy (XPEEM) investigations of the electron band structure confirm that after hydrogenation the single n-band characteristic of monolayer graphene is replaced by two n-bands 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 (Figs. 17 and 18 in [16] (from [17])). From this data, by using Eqs. (8, 9), one can determine the following tentative quantities: T0.63(des.) (at 1023 K and 1123 K), AH(des.) « 3.6 eV and K^.) = 2-1014 s-1 (Table 3).

The obtained value of the quantity of AH(des.) coincides (within the errors) with values of the quantities of &pp.IV « 3.8 eV « AH(c-h)"c","d" (Item 4.2, Table 1B), which are related to the diffusion-rate-limiting TDS process IV [14] of a dissociative chemisorption of molecular hydrogen in defected regions in graphite materials (Table 1B), and to the chemisorption models "C" and "D"(Fig. 4 in [16]).

The obtained value of the quantity of K0(des.) may be correlated with possible values of the (C-H) bonds' vibration frequency (v(C-H)"C","D-). Hence, by taking also into account that AH(des.) « AH(C-H)"C",-D", one may suppose the case of a non-diffusion-rate-controlling process corresponding to the Polanyi-Wigner model [14].

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On the other hand, by taking also into account that AH(des.) - AH(c-h)"c","d", one may suppose the case of a diffusion-rate-controlling process corresponding to the TDS process IV [14] (Table 1B). Hence, by using the value [14] of D0appIV - 6102 cm2/s, one can evaluate the quantity of L - D0app.1v Ko(des.))1/2 = 17 nm (Table 3). The obtained value of L (also, as and in the case of (SiC-D/QFMLG) [55], item 7, Table 2) coincides (within the errors) with values of the quantities of Ldef. - 11-17 nm (Item 5, Eq. (10)) and Ldef. - 20 nm (Item 6, Fig. 8(b) in [16] (from [53, 54])). The obtained value of L is also correlated with the STM data (Figs. 15 and 16 in [16] (from [17])). 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 [17]) of the interaction of hydrogen and silicon atoms at the graphene-SiC interface resulted in Si-C bonds at the intercalated islands.

11. Consideration and interpretation

of the TDS/STM data [15, 59] for HOPG treated by atomic hydrogen

In [15], atomic hydrogen accumulation in HOPG (high oriented pyrolytical graphite) samples and etching their surface under 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 atomically flat (Fig. 19 (a) in [16]), with a typical periodic structure of graphite (Fig. 19 (b) in [16]). Atomic hydrogen exposure (treatment) of the reference HOPG samples (30-125 min at atomic hydrogen pressure Ph - 10-4 Pa and a near-room temperature (~300 K)) 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 (Figs. 19 (c) and 19 (d) in [16]).

Thermal desorption (TD) of hydrogen has been found in heating of the HOPG samples under mass spectrometer control. As shown in Fig. 20 (a) in [16], 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 covered with some etch-pits of nearly circular shapes, one or two layers thick (Fig. 20 (b) in [16]). 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 [15], nanoblisters found on the HOPG surface after atomic hydrogen exposure are simply monolayer graphite (graphene) blisters, containing hydrogen gas in molecular form (Fig. 21 in [16]). As suggested in [15], 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 H2 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 Item 1 (Introduction) results [8, 32], that it is almost impossible for a hydrogen atom to pass through the six-membered ring of graphene at room temperature.

It is reasonable to assume (as it's been done in some previous Items) that in HOPG [15] 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 [33-43]) in the surface graphene layer. It is also expedient to note that in Fig. 20(b) in [16], 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 (Fig. 19 in [16]). Approximating the nanoblister to be a semi-ellipse form, results in the blister area Sb - 2.0-10-11 cm2 and its volume Vb - 8.4-10-19 cm3. The amount of retained hydrogen in this sample becomes Q - 2.8-1014 H2/cm2 and the number of hydrogen molecules captured inside the blister becomes n - (QSb)

- 5.5-103. 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 PH2 -

- {kB(QSb)T/Vb} - 108 Pa. The hydrogen molecular gas density in the blisters (at T - 300 K and Ph2 - 1108 Pa) can be estimated as p - {(QMH2Sb)/Vb} - 0.045 g/cm3, where MH2 is the hydrogen molecule mass. It agrees with data [60] considered in [16], 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 [46], by using the condition of the thermo-elastic equilibrium for the reaction of (2H(gas) ^ H2(gas_m_blisters)), as follows [16, 20]:

(PH2 / O -

- (Ph /Ph0 )2 exp{[AHdis - TASds - PH2 AV)]/kBT}, (11)

where PH* is related to the blister "wall" back pressure (caused by PH) - the so called surface pressure [46] (PH* -

- PH2 - 1108 Pa), PH is the atomic hydrogen pressure corresponding to the atomic flux [15] (Ph - 110-4 Pa),

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= PH0 = 1 Pa is the standard pressure [46], AH^ =

= 4.6 eV is the experimental value [45] of the dissociation energy (enthalpy) of one molecule of gaseous hydrogen (at room temperatures), A^dis = 11.8 kB is the dissociation entropy [45], AV ~ (Sbrb/n) is the apparent volume change, rb is the radius of curvature of nanoblisters at the nanoblister edge (rb « 30 nm, Figs. 19, 21(b) in [16]), NA is the Avogadro number, and T is the temperature (T « 300 K). The quantity of (PH* AV) is

related to the work of the nanoblister surface increasing with an intercalation of 1 molecule of H2.

The value of the tensile stresses cb (caused by PH* )

in the graphene nanoblister "walls" with a thickness of db and a radius of curvature rb can be evaluated from another condition (equation) of the thermo-elastic equilibrium of the system in question, which is related to Eq. (11), as follows [16, 20]:

Cb « (PH2 rb/2db) « (£b£b), (12)

where eb is a degree of elastic deformation of the graphene nanoblister walls, and Eb is the Young's modulus of the graphene nanoblister walls. Substituting in the first part of Eq. (12), the quantities of PH* ~ 1108

Pa, rb « 30 nm and db « 0.15 nm results in the value of Cb[15] « 11010 Pa.

The degree of elastic deformation of the graphene nanoblister walls, apparently reaches eb[i5] « 0.1 (Fig. 21(b) in [16]). Hence, with Hooke's law of approximation, using the second part of Eq. (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: Eb « (ob/eb) « 0.1 TPa. It is close (within the errors) to the experimental value [48, 49] of the Young's modulus of a perfect (i.e. without defects) graphene (Egraphene « 1.0 TPa).

The experimental data [15, 59] on the thermal desorption (the flux Jdes) of hydrogen from graphene nanoblisters in pyrolytic graphite can be approximated by three thermodesorption (TDS) peaks, i.e., # 1 with Tmax#1 = 1123 K, # 2 with Tmax#2 = 1523 K, and # 3 with Tmax#3 ~ 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 Jdes quantity.

Nevertheless, TDS peak # 1 [59] can be characterized by the activation desorption energy AH(des.)1[59] = 2.4 ± ± 0.5 eV, and by the per-exponential factor of the reaction rate constant of ^0(des.)1[59] ~ 21010 s-1 (Table 3). It points that TDS peak 1 [59] may be related to TDS peak (process) III in [14], for which the apparent diffusion activation energy is Qapp.m = (2.6 ± 0.3) eV and D

Oapp.III

3 10-3 cm2/s (Table 1B). Hence, one can obtain

obviously related to the separating distance between the graphene nanoblisters (Fig. 21(b) in [16]) or (within the errors) to the separation distance between etch-pits (Fig. 20(b) in [16]) in the HOPG specimens [15, 59].

As is noted in Items 4.2 and 4.4, process III [14] is related to model "F*" (with AH(c-h)"f*" = (2.5 ± 0.3) eV), and it is a rate-limiting by diffusion of atomic hydrogen between graphene-like layers (in graphite materials and nanomaterials), where molecular hydrogen can not penetrate (according to analysis [14] of a number of the related experimental data).

Thus, TDS peak (process) 1 [15, 59] 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.

(with accuracy of one-two orders of the magnitude) a reasonable value of the diffusion characteristic size of

LTDS-peak1[59] ~ (Doapp.III/^0(des.)1[59])

4 nm, which is

As is considered in the next Item, a similar (relevance to results [15, 59]) 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 graphite nanfibers (GNFs).

12. A possibility of intercalation of solid H2 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 H2) into closed (in the definite sense) nanoregions in hydrogenated graphite nanofibers is based both on the analytical results presented in Items 2-11 (Tables 1-3), and on the following facts [16, 20].

1. According to the experimental and theoretical data [60] (Figs. 22 and 23 in [16]), a solid molecular hydrogen (or deuterium) of density of pH2 = 0.3-0.5 g/cm3(H2) can exist at 300 K and an external pressure of P = 30-50 Gpa.

2. As seen from data in Figs. 19-21 (in [16]) and Eqs. (11) and (12), the external (surface) pressure of P = = PH*2 = 30-50 GPa at T = 300 K may be provided at the

expense of the association energy of atomic hydrogen (TASdis -AHdis), into some closed (in the definite sense) nanoregions in hydrogenated (in gaseous atomic hydrogen with the corresponding pressure PH) graphene-layer-nanostructures possessing of a high Young's modulus (Egraphene » 1 TPa).

3. As shown in [16, 20], the treatment of the extraordinary experimental data [61] (Fig. 24 in [16]) on hydrogenation of graphite nanofibers (GNFs) results in the empirical value of the hydrogen density pH2 = (0.5 ±

±0.2) g(H2)/cm3(H2) (or P(H2-C-system) « 0.2 g(H2)/cm3(H2-C-system)) of the intercalated (at T ~ 300 K) high-purity reversible hydrogen (about 17 mass.% H2); it corresponds to the state of solid molecular hydrogen at

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the pressure of P = PH* - 50 GPa, according to data from Figs. (22) and (23) in [16].

4. Substituting in Eq. (12) the quantities of PH* -

- 5-1010 Pa, £b - 0.1 (Fig. 24 in [16]), the largest possible value of Eb - 1012 Pa [48, 49], the largest possible value of the tensile stresses (ob - 1011 Pa [48, 49]) in the edge graphene "walls" (of a thickness of db and a radius of curvature of rb) of the slit-like closed nanopores of the lens shape (Fig. 24 in [16]), one can obtain the quantity of (rb/db) - 4. It is reasonable to assume rb - 20 nm; hence, a reasonable value follows of db - 5 nm.

5. As noted in [16, 20], a definite residual plastic deformation of the hydrogenated graphite (graphene) nano-regions is observed in Fig. 24 (in [16]). Such plastic deformation of the nanoregins during hydrogenation of GNFs, may be accompanied with some mass transfer resulting in such thickness (db) of the walls.

6. The related data (presented in Fig. 25 in [16] and Fig. 9 in [21]) allow us reasonably to assume a breakthrough character of results [16, 20] on the possibility (and particularly, physics) of intercalation of a high density molecular hydrogen (up to solid H2) into closed (in the definite sense) nanoregions in hydrogenated graphite nanofibers ([61, 62] and others), relevant for solving of the current problem ([19, 20] and others) of the hydrogen on-board effective storage.

7. Some fundamental aspects - open questions on engineering of "super" hydrogen storage carbonaceous nanomaterials (on the basis of results [16, 20]), relevance for clean energy applications, are considered in [21].

13. Discussion

13.1. On the "thermodynamic forces" and/or energetics of forming (under atomic hydrogen treatment) of graphene nanoblisters in the surface HOPG layers and epitaxial graphenes A number of researchers (for instance, [15, 17, 5259]) has not considered (in a sufficient extent) the "thermodynamic forces" and/or energetics of forming (under atomic hydrogen treatment) of graphene nanoblisters in the surface HOPG layers and epitaxial graphenes.

Therefore, in this study, the results of the thermodynamic analysis of the related data (Item 11, Eds. (11, 12)) are presented those may be used for interpretation of other related data (for instance, Figs. 68, 11-16, 19-21 in [16]).

13.2. 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 (for instance, [15, 17, 52-59]) has not taken into account (in a sufficient extent) the calculation results ([8] and others) showing that the barrier for the penetration of a hydrogen atom through the six-

membered 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-membered ring of a perfect (i.e., without defects) graphene layer at room temperature.

Therefore, in this study, a real possibility of the atomic hydrogen penetration through some nanodefects in the graphene-layer-structures, i.e., grain boundaries, their triple junctions (nodes) and/or vacancies [33-43], is considered. These analytical results may be used for interpretation of the related data (for instance, Figs. 6-8, 11-16, 19-21 in [16]).

13.3. On finding and interpretation of the thermodynamic characteristics of "reversible" hydrogenation-dehydrogenation of epitaxial graphenes and membrane ones A number of researchers (for instance, [3-5, 15, 17, 51-57, 59]) has not treated and compared (in a sufficient extent) 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, Eqs. 1-12), such treatment results of reated theoretical and experimental data (Tables 1-3) and their interpretation (Items 2-11) are presented. As is shown (in Items 12.4 and 12.5), 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 (out of the declared errors, and without any explanation) in theoretical values of the energetic graphane (CH) quantities (AH(C-H), AH(bind), AH(C-C)) obtained in different theoretical studies, for instance, in [3] and [25] (Table 1A).

Unfortunately, the theoretical values of the graphane quantity of AH(C-C) is not usually evaluated by the researchers and not compared by them with the much higher values of the graphene (both theoretical, and experimental) quantity of AH(C-C) (Table 1A). It could be useful, for instance, when consideration of the fundamental strength properties of graphane and graphene structues.

As far as we know, the most of researchers have not taken into account the alternative possibility supposed in [5] that (i) the experimental graphane membrane (a freestanding one) may have "a more complex hydrogen bonding, than the suggested by the theory", and that (ii) graphane (CH) [3] may be "the until-now-theoretical material".

In this connection, it seems expedient to take into account also some other approaches and results, for instance [63-67].

13.4. On the thermodynamic characteristics and atomic mechanisms of "reversible" hydrogenation-dehydrogenation of free-standing graphene membranes The thermodynamic analysis (Item 3) of experimental data [5] on "reversible" hydrogenation-

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dehydrogenation of free-standing graphene membranes has resulted in the following conclusive suppositions and/or statements.

1. These chemisorption processes are related to a non-diffusion-rate-limiting case. They can be described and interpreted within the physical model of the Polanyi-Wigner equation for the first order rate reactions [14, 16, 20, 21], but not for the second order rate ones [68].

2. The desorption activation energy is of

AHdes.(membr.[5]) = A^C-H(membr.[5]) = 2.6 ± 0.1 eV (Table

IA). The value of the quantity of A^C-H(membr.[5]) coincides (within the errors), in accordance with the Polanyi-Wigner model [14, 16, 20, 21], with the values of the similar quantities for theoretical graphanes [3, 4] (Table 1A) possessing of a diamond-like distortion of the graphene network. The value of the quantity of A^C-H(membr.[5]) coincides (within the errors) with the value of the similar quantity for model "F*" (Item 4.2, Table

IB) manifested in graphitic structures and nanostructures not possessing of a diamond-like distortion of the graphene network (an open theoretical question).

3. The desorption frequency factor is of ^0des.(membr.[5]) = vc-H(membr.[5]) ~ 51013 s-1 (Table 1A); it is related to the corresponding vibration frequency for the C-H bonds (in accordance with the Polanyi-Wigner model for the first order rate reactions [14, 16, 20, 21]).

4. The adsorption activation energy (in the approximation of K^ds. « K)des.) is of AHads.(membr.[5]) = 1.0 ± 0.2 eV (Table 1A). The heat of adsorption of atomic hydrogen by the free standing graphene membranes [5] can be evaluated as [14, 46]: (AHads.(membr.[5]) -AHdes. (membr. [5])) = -1.5 ± 0.2 eV (an exothermic reaction).

5. Certainly, these tentative analytical results could be directly confirmed and/or modified by receiving and treating (within Eqs. (8, 9) approach) of the experimental data on t0.63 at several annealing temperatures.

13.5. On the thermodynamic characteristics and atomic mechanisms of "reversible" hydrogenation-dehydrogenation of epitaxial graphenes

The thermodynamic analysis (Items 3-8, 10) of experimental data [5, 17, 51-56] on "reversible" hydrogenation-dehydrogenation of epitaxial graphenes has resulted in the following conclusive suppositions and/or statements.

1. These chemisorption processes for all 16 considered epitaxial graphenes [5, 51, 52, 55, 56, 17] (Tables 1A, 2, 3), unlike ones for the free-standing graphene membranes (Item 12.4, 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 [14, 16, 20, 21], but not within the physical models of the Polanyi-Wigner equations for the first [14, 16, 20] or for the second [68] order rate reactions.

2. The averaged desorption activation energy for 14 of 16 considered epitaxial graphenes (Tables 1A, 2, 3) is of AHdes.(epitax.) = 0.5 ± 0.4 eV, and the averaged quantity

of ln K0des.(epitax.) = 5 ± 8 ^^ K0des.(epitax.) ~ 15102 s 1 (or

5 10-2 - 5 105 s-1); the adsorption activation energy (in a

rough approximation of K^ds. ~ ^0des.) is of AHads.(epitax.) =

= 0.3 ± 0.2 eV.

3. The above obtained values of characteristics of dehydrogenation of the epitaxial graphenes can be presented, as follows: AHdes~ Qapp.I, K0des. ~ (D0app.i / L2), where gappI and D0appI are the characteristics of process I (Item 4.2, Table 1B), L ~ dsample, i.e. being of the order of diameter (dsample) of the epitaxial graphene samples. The diffusion-rate-limiting process I is related to the chemisorption models "F" and "G" (Fig. 4 in [16]). These results unambiguously point that in the epitaxial graphenes the dehydrogenation processes are rate-limiting by diffusion of hydrogen, mainly, from chemisorption "centers" (of "F" and/or "G" types (Fig. 4 in [16])) 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 [14], 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 (noted in Item 1) of many scientists that the diffusion of hydrogen along the graphene-substrate interface is negligible.

5. In this connection, it is expedient to take into account also some other related experimental results, for instance [69-74], on the peculiarities of the hydrogenation-dehydrogenation processes in epitaxial graphenes, particularly, in the graphene-substrare interfaces.

14. Conclusion remarks

1. The chemisorption processes in the free-standing graphene membranes are related to a non-diffusion-rate-limiting 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 ones.

The desorption activation energy is of AHdes.(membr.) = = AHC-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 K0des.(membr.) = = Vc -H(membr.) = 51013 s-1 (Table 1A). It is related to the corresponding vibration frequency for the C-H bonds (in accordance with the Polanyi-Wigner model).

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The adsorption activation energy (in the approximation of K0ads. « K0des.) is of AHads.^embr.) = 1.0 ± 0.2 eV (Table 1A). The heat of adsorption of atomic hydrogen by the free standing graphene membranes [5] may be as (AHad^membr.) - AHdes.(membr.)) = "1.5 ± 0.2 eV (an exothermic reaction).

2. The hydrogen chemisorption processes in epitaxial graphenes (Tables 1A, 2, 3), unlike ones for the freestanding 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, but not within the physical models of the Polanyi-Wigner equations for the first or for the second order rate reactions.

The desorption activation energy is of AHdes.(epitax.) = 0.5 ± 0.4 eV. The quantity of In K0des.(epitax.) is of 5 ± 8, and the per-exponential factor of the desorption rate constant is of K0des.(epitax.) « 1.5102 s"1 (or 510-2 - 5105 s-1). The adsorption activation energy (in a rough approximation of K0ads. ~ K0des.) is of AHadi.(epitax.) = 0.3 ± 0.2 eV.

The above obtained values of characteristics of dehydrogenation of the epitaxial graphenes can be presented as AHdes ~ Qapp.I and K)des. ~ (D0app.I/L2), where Qapp.i and D0appI are the characteristics of process I (Table 1B), L ~ dsample, i.e. being of the order of diameter (dsample) of the epitaxial graphene samples. The diffusion-rate-limiting process I is related to the chemisorption models "F" and "G" (Fig. 4 in [16]). These results unambiguously point that in the epitaxial graphenes the dehydrogenation processes are rate-limiting by diffusion of hydrogen, mainly, from chemisorption "centers" (of "F" and/or "G" types (Fig. 4 in [16])) 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 occurs in the interfaces between the graphene layers and the substrates. It differs from the case of the graphene neighbor layers in graphitic structures and nanostructures, where only atomic hydrogen solution and diffusion can occur (process III, model "F*" [14], Table 1B). Such an interpretation (model) is direct opposite, relevance to the supposition (model) of a number of researchers, those believe in occurrence of hydrogen desorption 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 graphene-substrate interface is negligible.

3. The possibility (and particularly, the physics) of intercalation of a high density molecular hydrogen (up to solid H2) into closed (in the definite sense) nanoregions in hydrogenated graphite nanofibers has been discussed, in the light of the analytical results presented in Items 211 (Tables 1-3) and the empirical facts [16, 20, 21, 61, 62] presented in Item 12.

It is relevant for developing of a key breakthrough nanotechnology of the hydrogen on-board efficient and compact storage (Fig. 25 in [16] and Fig. 9 in [21]) - the very current problem.

Such a nanotechnology may be developed within a reasonable (for the current hydrogen energy demands and predictions considered, for instance, in [19, 20]) time frame of several years. The International cooperation is necessary.

Acknowledgements

The authors are grateful to H.G. Xiang, M.-H. Whangbo, D.C. Elias, C. Casiraghi, A. Eckmann, N. Tombros, B.J. Van Wees, A. Castellanos-Gomez, R. Bisson, T. Yu, L. Hornekaer and Z. Waqar for helpful discussions, and valuable completing and/or reading of the related parts of the paper.

This work has been supported by the RFBR (Project #14-08-91376 CT).

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