On the Problem of “Super” Storage of Hydrogen in Graphite Nanofibers

This article is devoted to some fundamental aspects of “super” storage in graphite nanofibers (GNF) of “reversible” (~20–30 wt.%) and “irreversible” hydrogen (~7–10 wt.%). Extraordinary results for hydrogen “super” storage were previously published by the group of Rodriguez and Baker at the turn of the century, which been unable to be reproduced or explained in terms of physics by other researchers. For the first time, using an efficient method of processing and analysis of hydrogen thermal desorption spectra, the characteristics of the main desorption peak of “irreversible” hydrogen in GNF were determined: the temperature of the highest desorption rate (Tmax = 914–923 K), the activation energy of the desorption process (Q ≈ 40 kJ mol−1), the pre-exponential rate constant factor (K0 ≈ 2 × 10−1 s−1), and the amount of hydrogen released (~8 wt.%). The physics of hydrogen “super” sorption includes hydrogen diffusion, accompanied by the “reversible” capture of the diffusant by certain sorption “centers”; the hydrogen spillover effect, which provides local atomization of gaseous H2 during GNF hydrogenation; and the Kurdjumov phenomenon on thermoelastic phase equilibrium. It is shown that the above-mentioned extraordinary data on the hydrogen “super” storage in GNFs are neither a mistake nor a mystification, as most researchers believe.

The purpose of this work was to return the attention of researchers to the solution of this topical problem by showing that the corrected results [4][5][6][7][8][9][10][11][12] are not a mistake or a mystification, by determining the necessary conditions for their reproduction by other researchers, and also by considering the physics of processes.
One can expect that the conclusions arising from the results of the work will help to reproduce the effect of hydrogen "super" storage in GNF, and modern thermal desorption techniques, such as molecular beam thermal desorption spectrometry (MB-TDS) [33,34], will lead to more accurate experimental results for further theoretical work.
The developed methodology [17][18][19][20][21][22][23] makes it possible to reveal the physics of desorption processes by thermodynamic analysis of the obtained characteristics of thermal desorption peaks and comparison with the corresponding independent experimental and theoretical data. The technique [20] contains several stages of implementation, including the use of some non-standard reliability criteria and the confirmation and/or the final refinement of the results using numerical simulation methods [23].
The first stage consists of approximating the investigated spectrum by the smallest number of symmetric Gaussians. The second stage consists of determining, in the firstorder reaction approximation, for each of the Gaussians noted above (from the temperature dependence of the desorption rate (−dθ/dt) divided by β), the rate constant (K(T)) of hydrogen desorption at various temperatures around T max ; hence, the values of Q and K 0 are determined (using the Arrhenius equation). In this case, the kinetic equation for the first-order reaction is used in the form: where t is time; T is the absolute temperature; R is the universal gas constant; θ = (C/C 0 ) is the relative average hydrogen concentration in the sample corresponding to the considered Gaussian (for given values of T and t); θ = 1 at t = 0. The corresponding criterion of reliability (Q * ), showing the correspondence of the obtained value of Q to the Kissinger theory [36], can be obtained from the condition of the maximum desorption rate (d 2 θ/dT 2 = 0) in the form: The next stage consists of determining Q and K 0 in the second-order reaction approximation for each of the above-mentioned Gaussians. In this case, the kinetic equation for the second-order reaction is used in the form: The reliability criterion (Q * ) can be obtained from the condition (d 2 θ/dT 2 = 0) in the form: where the value of θ(T max ) can be taken to be equal to 0.5 (with an error of about 15%). The final stage is the refinement (and/or confirmation) of the above results using numerical simulation [23] of desorption spectra, taking into account (in the sense of a certain fixation) the values of Q * and K(T max ). It should be noted that, in this case, the spectra under consideration are approximated not by Gaussians, but by peaks corresponding to first-or second-order processes; the error (scatter of values) in determining Q and n K 0 in most cases is about 15%.
The effectiveness of this methodology is confirmed by the results obtained with its help and the recently published results of studies of the thermal desorption of hydrogen in a number of carbon nanostructures and graphite materials [19][20][21][22]25].

Analysis and Interpretation of TDS and TG Spectra of the Rodriguez and Becker Group for "Irreversible" Hydrogen in GNF
The results of processing and analysis (using the technique [20]) of the thermal desorption (TDS) spectrum for "irreversible" hydrogen from [5] are shown in Figure 1a and Table 1. It should be noted that the total (refined) content of "irreversible" hydrogen in GNF samples (C H2Σ ≈ 11 ± 3 wt.%) was determined from the data of [5,8].
the second-order reaction is used in the form: The reliability criterion (Q * ) can be obtained from the condition (d 2 θ/dT 2 = 0) in the form: where the value of θ(Tmax) can be taken to be equal to 0.5 (with an error of about 15%). The final stage is the refinement (and/or confirmation) of the above results using numerical simulation [23] of desorption spectra, taking into account (in the sense of a certain fixation) the values of Q * and K(Tmax). It should be noted that, in this case, the spectra under consideration are approximated not by Gaussians, but by peaks corresponding to first-or second-order processes; the error (scatter of values) in determining Q and ℓn K0 in most cases is about 15%.
The effectiveness of this methodology is confirmed by the results obtained with its help and the recently published results of studies of the thermal desorption of hydrogen in a number of carbon nanostructures and graphite materials [19][20][21][22]25].

Analysis and Interpretation of TDS and TG Spectra of the Rodriguez and Becker Group for "Irreversible" Hydrogen in GNF
The results of processing and analysis (using the technique [20]) of the thermal desorption (TDS) spectrum for "irreversible" hydrogen from [5] are shown in Figure 1a and Table 1. It should be noted that the total (refined) content of "irreversible" hydrogen in GNF samples (CH2Σ ≈ 11 ± 3 wt.%) was determined from the data of [5,8].
The results of processing and analysis [20] of the thermogravimetric (TG) spectrum from [5] are shown in Figure 1b and Table 2. There are reasons (in particular, from the consideration of curves (a), (b), and (c) in Figure 7 in [5]) to believe that peak #3 in Figure  1b is mainly associated with the gasification of carbon atoms and/or oxygen-containing functional complexes (groups). In this case, it should be taken into account that, in [5], when the material was heated in an inert atmosphere at temperatures up to 1300 K, no hydrocarbon products were found. Therefore, the value of the atomic ratio (H/C) for peak #3 (in Figure 1b) can be negligibly small, and there is no need to more accurately approximate this peak.    [20]) of thermal desorption (TDS) and thermogravimetric (TG) data from [5] for "super" desorption of "irreversible" hydrogen from GNF samples with a herringbone structure (see Figure 2 in [5] [20] of three peaks (Figure 1a) in the approximation of reactions of the first and second orders. Here γ is the proportion of the peak in the spectrum; (H/C) is the atomic ratio (hydrogen/carbon) corresponding to the hydrogen content (C H2 = γ·C H2Σ ) for the given peak; C H2Σ ≈ 11 ± 3 wt.% (from [5,8] The results of processing and analysis [20] of the thermogravimetric (TG) spectrum from [5] are shown in Figure 1b and Table 2. There are reasons (in particular, from the consideration of curves (a), (b), and (c) in Figure 7 in [5]) to believe that peak #3 in Figure 1b is mainly associated with the gasification of carbon atoms and/or oxygen-containing functional complexes (groups). In this case, it should be taken into account that, in [5], when the material was heated in an inert atmosphere at temperatures up to 1300 K, no hydrocarbon products were found. Therefore, the value of the atomic ratio (H/C) for peak #3 (in Figure 1b) can be negligibly small, and there is no need to more accurately approximate this peak. Table 2. The results of processing [20] of three peaks (Figure 1b) in the approximation of reactions of the first and second orders. Here γ is the proportion of the peak in the spectrum; (H/C) is the atomic ratio (hydrogen/carbon) corresponding to the hydrogen content (wt.%) for a given hydrogen peak, obtained by appropriate integration of this peak.

Peak #
T max , K By comparison, a significant noise level for the spectrum in Figure 1b does not interfere with determining the characteristics of the main hydrogen peak #1 (Figure 1b) with the required (to solve the set goal) accuracy.

Reaction Order
Analysis (using the methodology of [20]) of the results obtained (Tables 1 and 2) for the main process of desorption of "irreversible" hydrogen (peak #1 in Figure 1a,b) from GNF samples [5] shows the process (reaction) of the first order (expression (1)), which corresponds to the following characteristics: T max = 914-923 K, Q ≈ 40 kJ mol −1 , K 0 ≈ 2 × 10 −1 s −1 , C H2Σ ≈ 8 wt.% (i.e., atomic ratio (H/C) ≈ 1). The analysis shows that the desorption process is limited by hydrogen diffusion, which is accompanied by "reversible" capture [17,18,[34][35][36] of the diffusant by certain "centers" of hydrogen chemisorption in GNF. This is comparable to diffusion processes of types I and II (with activation energies Q I ≈ 20 kJ mol −1 and Q II ≈ 120 kJ mol −1 , respectively) considered in [17,18], having open access on the Internet. The resulting desorption activation energy (Q ≈ 40 kJ mol −1 , Tables 1 and 2) is (in addition to the Q I and Q II values noted above) the effective activation energy of such diffusion and is close (in absolute value) to the binding energy of the diffusant with the corresponding chemisorption "centers" in carbon material [17,18]. Obviously, the "centers" are localized, as it were, between the basic carbon planes in the GNF [5]; at the same time, they are almost completely filled with hydrogen; these basic carbon planes are, as it were, "separated" by layers of chemisorbed hydrogen (as in multilayer graphane [18]).
The characteristic diffusion size for the process under consideration can be estimated (up to an order of magnitude) using the well-known expression [17,36] L ≈ (D 0 /K 0 ) 1/2 . In this expression, the value of the pre-exponential factor of the effective diffusion coefficient of hydrogen (D 0 ) in GNF [5] can be in the range of the corresponding values for processes of types I and II in [17,18] (i.e., in the range from D 0I ≈ 3 × 10 −3 cm 2 s −1 to D 0II ≈ 2 × 10 3 cm 2 s −1 ), which corresponds to the value L ≈ (1 × 10 −1 − 1 × 10 2 ) cm ≈ 1 cm, which corresponds to a certain size of the sample [4,5] (a bundle of graphite nanofibers), leading to the quite acceptable desired value D 0 ≈ 5 cm 2 s −1 .

Analysis and Interpretation of the Kinetic Data of the Rodriguez and Becker
Group on the "Super" Sorption of "Reversible" Hydrogen (~30 wt.%) in GNF As follows from the results of processing the kinetic data from [4] on the change in hydrogen pressure in the working chamber during the "super" adsorption of "reversible" hydrogen (at a temperature of about 300 K) for three samples (nos. 1, 2, and 3) of graphite nanofibers with a herringbone-type structure shown in Figure 2, the process proceeds as a first-order reaction with rate constants: K 1ads.rev. = 2.7 × 10 −5 s −1 , K 2ads.rev. = 3.8 × 10 −5 s −1 and K 3ads.rev. = 2.8 × 10 −5 s −1 , respectively. The characteristic time of "super" adsorption of "reversible" hydrogen (t ads.rev. = K ads.rev. −1 ) here was about 9 h, and the hydrogenation time of the samples was 24 h. they are almost completely filled with hydrogen; these basic carbon planes are, as it were, "separated" by layers of chemisorbed hydrogen (as in multilayer graphane [18]). The characteristic diffusion size for the process under consideration can be estimated (up to an order of magnitude) using the well-known expression [17,36] L ≈ (D0/K0) 1/2 . In this expression, the value of the pre-exponential factor of the effective diffusion coefficient of hydrogen (D0) in GNF [5] can be in the range of the corresponding values for processes of types I and II in [17,18] (i.e., in the range from D0I ≈ 3 × 10 −3 cm 2 s −1 to D0II ≈ 2 × 10 3 cm 2 s −1 ), which corresponds to the value L ≈ (1 × 10 −1 − 1 × 10 2 ) cm ≈ 1 cm, which corresponds to a certain size of the sample [4,5] (a bundle of graphite nanofibers), leading to the quite acceptable desired value D0 ≈ 5 cm 2 s −1 .

Analysis and Interpretation of the Kinetic Data of the Rodriguez and Becker Group on the "Super" Sorption of "Reversible" Hydrogen (~30 wt.%) in GNF
As follows from the results of processing the kinetic data from [4] on the change in hydrogen pressure in the working chamber during the "super" adsorption of "reversible" hydrogen (at a temperature of about 300 K) for three samples (nos. 1, 2, and 3) of graphite nanofibers with a herringbone-type structure shown in Figure 2, the process proceeds as a first-order reaction with rate constants: K1ads.rev. = 2.7 × 10 −5 s −1 , K2ads.rev. = 3.8 × 10 −5 s −1 and K3ads.rev. = 2.8 × 10 −5 s −1 , respectively. The characteristic time of "super" adsorption of "reversible" hydrogen (tads.rev. = Kads.rev. −1 ) here was about 9 h, and the hydrogenation time of the samples was 24 h. Processing (in the first-order reaction approximation) of kinetic data from [4] on the change in hydrogen pressure in the working chamber during "super" adsorption of "reversible" hydrogen (at a temperature of about 300 K) for three samples of graphite nanofibers with a "herringbone" structure.
There are reasons to believe that the process is limited by the diffusion of hydrogen over the characteristic distance Lsamp. ≈ 1 cm, corresponding to the sample size [4,5] (a bundle of graphite nanofibers), and is accompanied by "reversible" capture [17,18,[36][37][38] of the diffusant by certain sorption "centers" in graphite nanofibers. This leads to an acceptable value of the effective diffusion coefficient of "reversible" hydrogen (Dads.rev. ≈ (Lsamp. 2 × Kads.rev.) ≈ 3 × 10 −5 cm 2 s −1 corresponding to the type I process noted above (in Section 3.1) [17], and/or "centers" of physical sorption [17,40] in a carbon nanomaterial.
As shown in [4], the time of "super" desorption (at 300 K) of the predominant part of "reversible" hydrogen from GNF samples was about 10 min; the characteristic desorption time of "reversible" hydrogen can be taken (up to an order of magnitude) as tdes.rev. = (1/Kdes.rev.) ≈ 6 × 10 2 s, where Kdes.rev. is the rate constant of the desorption process (in the approximation of a first-order reaction). Assuming that the process is limited by the dif- Processing (in the first-order reaction approximation) of kinetic data from [4] on the change in hydrogen pressure in the working chamber during "super" adsorption of "reversible" hydrogen (at a temperature of about 300 K) for three samples of graphite nanofibers with a "herringbone" structure.
There are reasons to believe that the process is limited by the diffusion of hydrogen over the characteristic distance L samp. ≈ 1 cm, corresponding to the sample size [4,5] (a bundle of graphite nanofibers), and is accompanied by "reversible" capture [17,18,[36][37][38] of the diffusant by certain sorption "centers" in graphite nanofibers. This leads to an acceptable value of the effective diffusion coefficient of "reversible" hydrogen (D ads.rev. ≈ (L samp. 2 × K ads.rev. ) ≈ 3 × 10 −5 cm 2 s −1 corresponding to the type I process noted above (in Section 3.1) [17], and/or "centers" of physical sorption [17,40] in a carbon nanomaterial.
As shown in [4], the time of "super" desorption (at 300 K) of the predominant part of "reversible" hydrogen from GNF samples was about 10 min; the characteristic desorption time of "reversible" hydrogen can be taken (up to an order of magnitude) as t des.rev. = (1/K des.rev. ) ≈ 6 × 10 2 s, where K des.rev. is the rate constant of the desorption process (in the approximation of a first-order reaction). Assuming that the process is limited by the diffusion of hydrogen over the characteristic distance L samp. ≈ 1 cm, corresponding to the sample size [4,5], and is accompanied by "reversible" capture of the diffusant by certain sorption "centers" in graphite nanofibers, we obtain an acceptable value of the effective diffusion coefficient of "reversible" hydrogen (D des.rev. ≈ (L samp. 2 × K des.rev. ) ≈ 1.7 × 10 −3 cm 2 s −1 ), which is possible with the "reversible" capture of the diffusant by the "centers" of physical sorption [17,40] in the carbon nanomaterial (see also Section 5 of the article). In this case, the "centers" of chemisorption in GNF [4,5] can apparently have a limiting filling with hydrogen, that is, a certain saturation, which leads to the cessation of their influence on hydrogen diffusion (see Equations (11) and (8 ) in [41], having open access on the Internet).

Consideration of the Kinetic Data of the Rodriguez and Becker Group on X-ray Diffraction
X-ray diffraction experiments carried out by the Rodriguez and Becker group showed (see Figure 12 in [5]) that hydrogenation causes an increase in the interplanar spacing in graphite nanofibers from the initial value a 0 = 0.340 nm (before hydrogenation) to a hyd. = 0.347 nm (after hydrogenation for 24 h and removal of "reversible" hydrogen). Such an expansion of the lattice is obviously due to the "super" adsorption of "irreversible" hydrogen up to a certain content of C hyd ≈ 8 wt.%, corresponding to desorption peak #1 in Figure 1a (see Section 3.1 and also Appendix A: Cavity model). In this case, it can be assumed that (a hyd. − a 0 ) = χ × C hyd. , where the coefficient of proportionality χ ≈ 9 × 10 −4 nm wt.% −1 .
It was shown (see Figure 12 in [5]) that desorption aging (of hydrogenated samples) for t 1 = 24 h in air at a temperature of 300 K leads to the value of the interplanar spacing of a 24 = 0.345 nm and the corresponding content of "irreversible" hydrogen C 24 , and desorption aging for To estimate the rate constant (at 300 K) of the process under consideration, one can use the expression K = −(1/t) ln (C t /C hyd. ), where the desorption time t is 24 and 48 h, and the corresponding hydrogen content C t is C 24 = 5.6 wt.% and C 48 = 2.2 wt.% (or C* 48 = 3.3 wt.%). From here we obtain (up to an order of magnitude) the value K = K des.irrev.300K ≈ 1.7 × 10 −2 h −1 , corresponding to the characteristic desorption time of~60 h. This value of the rate constant for the desorption of "irreversible" hydrogen (K des.irrev.300K ) is in satisfactory agreement with the kinetic data of the group of Rodriguez and Becker on the change in the pore size distribution in GNF samples, where the desorption period at 300 K was 92 h (see Figure 11 in [5]).
In addition, it should be emphasized that such a value of the rate constant (K des.irrev.300K ≈ 4.6 × 10 −6 s −1 ) is two orders of magnitude higher than the rate constant at 300 K obtained using the characteristics (Q and K 0 ) for the desorption peak #1 (See Figure 1a and Table 1).
The analysis shows that the desorption process is limited by the diffusion of hydrogen along the characteristic distance L samp. ≈ 1 cm, corresponding to the size of the sample [5] (a bundle of graphite nanofibers), and is accompanied by "reversible" capture of the diffusant by certain sorption "centers" in graphite nanofibers. This leads to an acceptable value of the effective diffusion coefficient of "irreversible" hydrogen at 300 K (D des.irrev. 300K ≈ (L samp. 2 × K des.irrev.300K ) ≈ 5 × 10 −6 cm 2 s −1 ), which is expected in the case of "reversible" capture of the diffusant with chemisorption "centers" in GNF corresponding to the type I process in [17] and/or "centers" of physical sorption [17,40].

Consideration of the Results of the Gupta's Group on the "Super" Sorption of "Reversible" Hydrogen (~17 wt.%) in GNF
The data obtained by Gupta's group [10,11] on multiple "super" sorption of "reversible" hydrogen in graphite nanofibers and presented (to a certain extent) in Figures 3  and 4 can be regarded as a satisfactory reproduction of the data [5,8] of the Rodriguez and Becker group (see Section 3.2). There is a correspondence (within the same order of magnitude) both in the amount of "reversible" hydrogen (~15 wt.% and~17 wt.% (see Figures 3a and 4)), and in the value of the characteristic time of its desorption at 300 K (t des.rev. = K des.rev. −1 ≈ 1 × 10 3 s, where K des.rev. is the rate constant of the desorption process obtained from the kinetic data in Figure 3b.

Consideration of the Results of the Gupta's Group on the "Super" Sorption of "Reversible" Hydrogen (~17 wt.%) in GNF
The data obtained by Gupta's group [10,11] on multiple "super" sorption of "reversible" hydrogen in graphite nanofibers and presented (to a certain extent) in Figures 3 and  4 can be regarded as a satisfactory reproduction of the data [5,8] of the Rodriguez and Becker group (see Section 3.2). There is a correspondence (within the same order of magnitude) both in the amount of "reversible" hydrogen (~15 wt.% and ~17 wt.% (see Figures  3a and 4)), and in the value of the characteristic time of its desorption at 300 K (tdes.rev. = Kdes.rev. −1 ≈ 1 × 10 3 s, where Kdes.rev. is the rate constant of the desorption process obtained from the kinetic data in Figure 3b.  Figure 3. Processing of thermodynamic and kinetic data from [10] on the "super" sorption of "reversible" hydrogen (~15 wt.%) for GNF samples with a "plate" structure (see Figure 4) subjected to hydrogenation (24 h) in gaseous molecular hydrogen (at a pressure of 12 MPa and a temperature of 300 K) and subsequent dehydrogenation with a decrease in hydrogen pressure to 0.1 MPa: (a) processing of adsorption data in the approximation of the sorption isotherm of the Henry-Langmuir type [17]; (b) processing of thermal desorption data in the first-order reaction approximation.
As shown in [2,17,18,24,25], the TEM results ( Figure 4) can be considered as direct experimental evidence (proof) of multiple "super" adsorptions of "reversible" hydrogen (~17 wt.%) in GNF [11]. The similar transmission electron micrographs of GNF were also obtained in the works [9,10]. Detailed consideration of how the micrograph shown in Figure 4 is related to a direct proof of "super" hydrogen adsorption is presented in work [24], and in work [18], which has open access on the Internet.  [11] subjected to hydrogenation (24 h) in gaseous molecular hydrogen at a pressure of 12 MPa and a temperature of 300 K to a content of "reversible" hydrogen of ~17 wt.%. The sizes of lenticular nanocavities in one of the nanofibers are shown, which are necessary for estimating (see works [2,17,18,24]) the volume of such nanocavities and the density of "reversible" hydrogen localized in them.   [10] on the "super" sorption of "reversible" hydrogen (~15 wt.%) for GNF samples with a "plate" structure (see Figure 4) subjected to hydrogenation (24 h) in gaseous molecular hydrogen (at a pressure of 12 MPa and a temperature of 300 K) and subsequent dehydrogenation with a decrease in hydrogen pressure to 0.1 MPa: (a) processing of adsorption data in the approximation of the sorption isotherm of the Henry-Langmuir type [17]; (b) processing of thermal desorption data in the first-order reaction approximation.
As shown in [2,17,18,24,25], the TEM results ( Figure 4) can be considered as direct experimental evidence (proof) of multiple "super" adsorptions of "reversible" hydrogen (~17 wt.%) in GNF [11]. The similar transmission electron micrographs of GNF were also obtained in the works [9,10]. Detailed consideration of how the micrograph shown in Figure 4 is related to a direct proof of "super" hydrogen adsorption is presented in work [24], and in work [18], which has open access on the Internet.

Consideration of the Results of the Gupta's Group on the "Super" Sorption of "Reversible" Hydrogen (~17 wt.%) in GNF
The data obtained by Gupta's group [10,11] on multiple "super" sorption of "reversible" hydrogen in graphite nanofibers and presented (to a certain extent) in Figures 3 and  4 can be regarded as a satisfactory reproduction of the data [5,8] of the Rodriguez and Becker group (see Section 3.2). There is a correspondence (within the same order of magnitude) both in the amount of "reversible" hydrogen (~15 wt.% and ~17 wt.% (see Figures  3a and 4)), and in the value of the characteristic time of its desorption at 300 K (tdes.rev. = Kdes.rev. −1 ≈ 1 × 10 3 s, where Kdes.rev. is the rate constant of the desorption process obtained from the kinetic data in Figure 3b.  Figure 3. Processing of thermodynamic and kinetic data from [10] on the "super" sorption of "reversible" hydrogen (~15 wt.%) for GNF samples with a "plate" structure (see Figure 4) subjected to hydrogenation (24 h) in gaseous molecular hydrogen (at a pressure of 12 MPa and a temperature of 300 K) and subsequent dehydrogenation with a decrease in hydrogen pressure to 0.1 MPa: (a) processing of adsorption data in the approximation of the sorption isotherm of the Henry-Langmuir type [17]; (b) processing of thermal desorption data in the first-order reaction approximation.
As shown in [2,17,18,24,25], the TEM results ( Figure 4) can be considered as direct experimental evidence (proof) of multiple "super" adsorptions of "reversible" hydrogen (~17 wt.%) in GNF [11]. The similar transmission electron micrographs of GNF were also obtained in the works [9,10]. Detailed consideration of how the micrograph shown in Figure 4 is related to a direct proof of "super" hydrogen adsorption is presented in work [24], and in work [18], which has open access on the Internet.  [11] subjected to hydrogenation (24 h) in gaseous molecular hydrogen at a pressure of 12 MPa and a temperature of 300 K to a content of "reversible" hydrogen of ~17 wt.%. The sizes of lenticular nanocavities in one of the nanofibers are shown, which are necessary for estimating (see works [2,17,18,24]) the volume of such nanocavities and the density of "reversible" hydrogen localized in them.   [11] subjected to hydrogenation (24 h) in gaseous molecular hydrogen at a pressure of 12 MPa and a temperature of 300 K to a content of "reversible" hydrogen of~17 wt.%. The sizes of lenticular nanocavities in one of the nanofibers are shown, which are necessary for estimating (see works [2,17,18,24]) the volume of such nanocavities and the density of "reversible" hydrogen localized in them.

Physics of "Super" Storage of "Reversible" Hydrogen in GNF
According to [2,17,18,24,25], the physics of extraordinary results [5,8,10,11] on the "super" storage of "reversible" hydrogen (about 20-30 wt.%) in graphite nanofibers can be associated with the hydrogen spillover effect [26][27][28][29][30], which ensures the atomization of molecular hydrogen and manifests itself near the particles of a metal catalyst in GNF samples, and with the G.V. Kurdjumov phenomenon of thermoelastic phase equilibrium [31,32]. In this case, there is a thermoelastic "megabar" compression (up to a solid state) of molecular hydrogen localized in lenticular nanocavities (see Figure 4) between the base carbon layers of the material, which occurs due to the association energy of atoms hydrogen penetrating into closed nanocavities through certain defects in the graphene material (see [18,22,42]). In this regard, it should be noted that the hydrogen molecules formed in closed nanocavities cannot escape from them, since only atomic hydrogen passes through defects, while a certain purification of hydrogen used for hydrogenation of GNF samples takes place.
Detailed consideration of how the spillover effect and the Kurdjumov phenomenon in the thermal elastic phase equilibrium may be active in the nanocavities, to clarify the claimed high density of hydrogen storage, is presented in work [24], and also in work [18], which has open access on the Internet. It can be also considered as a direct comparison between the theoretical and experimental analyses of the results.

Analysis of TDS Data for "Irreversible" Hydrogen in GNF
The results of processing and analysis of TDS data [13,14], which were obtained by Rzepka et al. with the advisory participation of Becker [8], are shown in Figure 5 and in Table 3.

Physics of "Super" Storage of "Reversible" Hydrogen in GNF
According to [2,17,18,24,25], the physics of extraordinary results [5,8,10,11] on the "super" storage of "reversible" hydrogen (about 20-30 wt.%) in graphite nanofibers can be associated with the hydrogen spillover effect [26][27][28][29][30], which ensures the atomization of molecular hydrogen and manifests itself near the particles of a metal catalyst in GNF samples, and with the G.V. Kurdjumov phenomenon of thermoelastic phase equilibrium [31,32]. In this case, there is a thermoelastic "megabar" compression (up to a solid state) of molecular hydrogen localized in lenticular nanocavities (see Figure 4) between the base carbon layers of the material, which occurs due to the association energy of atoms hydrogen penetrating into closed nanocavities through certain defects in the graphene material (see [18,22,42]). In this regard, it should be noted that the hydrogen molecules formed in closed nanocavities cannot escape from them, since only atomic hydrogen passes through defects, while a certain purification of hydrogen used for hydrogenation of GNF samples takes place.
Detailed consideration of how the spillover effect and the Kurdjumov phenomenon in the thermal elastic phase equilibrium may be active in the nanocavities, to clarify the claimed high density of hydrogen storage, is presented in work [24], and also in work [18], which has open access on the Internet. It can be also considered as a direct comparison between the theoretical and experimental analyses of the results.

Analysis of TDS Data for "Irreversible" Hydrogen in GNF
The results of processing and analysis of TDS data [13,14], which were obtained by Rzepka et al. with the advisory participation of Becker [8], are shown in Figure 5 and in Table 3.
The obtained characteristics of the main desorption peak #1.6 in Figure 5 (Tmax, Q, K0, CH2; see Table 3) are very different from the analogous characteristics of the main desorption peak #1.1a in Figure 1a (see Table 1), i.e., peak type #1.1a is absent in the TDS spectrum for GNF samples [13,14].   Figure 18 in [13]) for sample #3 GNF with a herringbone structure ( Table  3 in [13]), subjected to the action of gaseous molecular hydrogen at a pressure of 13 MPa and subsequent heating from 293 K (β = 0.10 K s −1 ) to a stop and isothermal holding at 1173 K. Table 3. The results of processing [20] of two peaks ( Figure 5) in the approximation of reactions of the first and second orders.   Figure 18 in [13]) for sample #3 GNF with a herringbone structure ( Table 3 in [13]), subjected to the action of gaseous molecular hydrogen at a pressure of 13 MPa and subsequent heating from 293 K (β = 0.10 K s −1 ) to a stop and isothermal holding at 1173 K. Table 3. The results of processing [20] of two peaks ( Figure 5) in the approximation of reactions of the first and second orders. The obtained characteristics of the main desorption peak #1.6 in Figure 5 (T max , Q, K 0 , C H2 ; see Table 3) are very different from the analogous characteristics of the main C 2022, 8, 23 9 of 13 desorption peak #1.1a in Figure 1a (see Table 1), i.e., peak type #1.1a is absent in the TDS spectrum for GNF samples [13,14].

Peak
In [13], in particular, the authors noted (on p. 8) that Rodriguez and Becker [5,7] considered the presence of a certain high-temperature desorption peak to be an indicator (attribute) of a material for "super" storage of "reversible" hydrogen, while they [5,7] associated this peak with a relatively small part of the stored hydrogen, which could be released only at high temperatures, i.e., with the presence of a relatively small amount of "irreversible" hydrogen. Obviously, Rodriguez and Becker [5,7] had in mind the desorption peak of type #1.1a (see Figure 1a and Table 1), but they did not determine the characteristics (Q and K 0 ) of this peak.
It should be emphasized that such desorption of a relatively small amount of "irreversible" hydrogen (corresponding to a peak of type #1.1a) from hydrogenated GNF was also noted in the works of the Gupta group [9][10][11][12].
The peak of type #1.1a was absent in the GNF TDS spectra in [13,14] (see Figure 3), so it was not possible to reproduce the results of [5,8,10,11] on the "super" storage of "reversible" hydrogen in GNF.
In works [13,14] (with the participation of Becker [8] as a consultant) the lowest (among the known values; see Figure 3 in the analytical review [17]) value of the amount of hydrogen adsorbed by graphite nanofibers (about 0.1 wt.%) was obtained by the Tibbetts group [16] (from the Research Center of the General Motors Corporation (see [2,3])).
In this regard, it should also be emphasized that typical results on hydrogen storage in GNF (see Figure 3 in [17]), obtained by other researchers, were reproduced by the group of Rodriguez and Becker (see Figure 5 in [5], where the quantity of hydrogen is~2 wt.%, and Figure 4 in [43], where the quantity of hydrogen is~3 wt.%. As noted in [17], in order to reproduce the extraordinary results [5,8,10,11] of the Rodriguez-Becker and Gupta groups on the "super" storage of "reversible" hydrogen (~20-30 wt.%), it is necessary to disclose the treatment they used to activate the GNF, which ensures the appearance of the #1.1a-type peak in the TDS spectra (see Figure 1a). It is also necessary to study, with the use of recent theoretical and experimental techniques, the data [5] about the effect of cycle experiments on the GNF hydrogen absorption/desorption characteristics ( Figures 5, 6, 9 and 10 in [5]), the pore size distribution measurements ( Figure  11 in [5]), the effect of surface properties on the hydrogen adsorption on GNF (Figures 13  and 14 in [5]), and some others.

2.
It is shown that the physics of accumulation of~20-30 wt.% of "reversible" highdensity hydrogen intercalated in nanocavities between the base carbon layers in GNF is connected with the Kurdjumov phenomenon and the spillover effect in terms of thermoelastic phase equilibrium.

3.
The conducted study shows that there is a real possibility of reproducing the earlier extraordinary experimental results [5][6][7][8][9][10][11][12], but only if the details of the technologies used in these works for activating GNF are revealed, which led to the appearance of a type #1 thermal desorption peak in the material (Figure 1a) corresponding to "irreversible" chemisorbed hydrogen (in an amount of~8 wt.%) with certain kinetic and thermodynamic characteristics.

4.
In this regard, further experimental and theoretical studies are needed.

5.
There are reasons ( [1][2][3] and others) to believe that, in the foreseeable future, these technologies will be used by one of the largest automotive companies to gain a great competitive advantage.