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

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

_{max}= 914–923 K), the activation energy of the desorption process (Q ≈ 40 kJ mol

^{−1}), the pre-exponential rate constant factor (K

_{0}≈ 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 H

_{2}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.

## 1. Introduction

## 2. Methods

_{0}) of rate constants (K) of desorption processes corresponding to desorption peaks with different temperatures (T

_{max}) of the maximum desorption rate. It should be noted that when developing this methodology, a number of other works were taken into account, including [35,36,37,38,39].

_{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:

_{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.

^{*}), 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:

_{max}and K(T

_{max}) can be taken (in a satisfactory approximation) from the results obtained above for the considered Gaussian.

_{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:

^{*}) can be obtained from the condition (d

^{2}θ/dT

^{2}= 0) in the form:

_{max}) can be taken to be equal to 0.5 (with an error of about 15%).

^{*}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 ℓn K

_{0}in most cases is about 15%.

## 3. Results of the Study of a Number of Experimental Data

#### 3.1. Analysis and Interpretation of TDS and TG Spectra of the Rodriguez and Becker Group for “Irreversible” Hydrogen in GNF

_{H2}

_{Σ}≈ 11 ± 3 wt.%) was determined from the data of [5,8].

_{max}= 914–923 K, Q ≈ 40 kJ mol

^{−1}, K

_{0}≈ 2 × 10

^{−1}s

^{−1}, C

_{H2}

_{Σ}≈ 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}, Table 1 and Table 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]).

_{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}.

#### 3.2. Analysis and Interpretation of the Kinetic Data of the Rodriguez and Becker Group on the “Super” Sorption of “Reversible” Hydrogen (~30 wt.%) in GNF

_{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.

_{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.

_{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).

#### 3.3. Consideration of the Kinetic Data of the Rodriguez and Becker Group on X-ray Diffraction

_{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}.

_{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 t

_{2}= 48 h leads to a

_{48}= 0.342 nm and a hydrogen content of C

_{48}. Within the framework of such a model, it can be shown that [(a

_{hyd.}− a

_{24})/((a

_{hyd.}− a

_{48})] = [(1 − exp (−24K))/(1 − exp (−48K))], where K (h

^{−1}) is the rate constant of the desorption process at 300 K, which is considered in the first-order reaction approximation.

_{hyd.}− a

_{24})/((a

_{hyd.}− a

_{48})] = 0.4, which differs significantly from the limiting (at K → 0) value of lim [(1 − exp (−24K))/(1 − exp (−48K))] = 0.5. It should be noted that the value [(a

_{hyd.}− a

_{24})/((a

_{hyd.}− a*

_{48})] = 0.5 if we use the possible (within the measurement error) value of the interplanar distance a*

_{48}= 0.343 nm (instead of a

_{48}= 0.342 nm).

_{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.

_{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]).

_{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).

_{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].

#### 3.4. Consideration of the Results of the Gupta’s Group on the “Super” Sorption of “Reversible” Hydrogen (~17 wt.%) in GNF

_{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.

#### 3.5. Physics of “Super” Storage of “Reversible” Hydrogen in GNF

## 4. Analysis of TDS Data for “Irreversible” Hydrogen in GNF

_{max}, Q, K

_{0}, C

_{H2}; 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].

_{0}) of this peak.

## 5. Conclusions

- The study carried out in this work (using the methodology and results of [17,18,19,20,21,22,23,24,25]) of a number of kinetic and thermodynamic aspects (fundamentals) related to solving the problem of “super” storage of hydrogen in graphite nanofibers (GNF) [1,2,3] shows that the results obtained in works [5,6,7,8,9,10,11,12], i.e., the extraordinary experimental results (accumulation of about 20–30 wt.% of “reversible” hydrogen and about 7–10 wt.% of “irreversible” hydrogen), are neither a mistake nor a mystification.
- It is shown that the physics of accumulation of ~20–30 wt.% of “reversible” high-density 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.
- 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.
- In this regard, further experimental and theoretical studies are needed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Cavity Model

_{0}= 3.35 Å) and $\epsilon $ is the value of the interplanar bond energy. The force constant corresponding to the Lennard-Jones potential is ${k}_{LJ}\approx 75\epsilon /{d}_{0}^{2}\approx 60\epsilon /{\sigma}^{2}$.

_{B}is the Boltzmann constant. The interplanar repulsion of region 2, caused by pressure ${P}_{\mathrm{H}2}^{2b}$, is counteracted by specific (per unit area) van der Waals forces of attraction equal to: ${f}_{22}=-{k}_{LJ}\mathsf{\Delta}{d}_{b}/S$, ${f}_{12}={f}_{32}=-{k}_{LJ}\mathsf{\Delta}{d}_{b}/2S$, where $\mathsf{\Delta}{d}_{b}={d}_{b}-{d}_{0}$ and $S=3\sqrt{3}{a}_{0}^{2}/4$ ≈ 2.62 Å

^{2}is the area per carbon atom in graphene, a

_{0}≈ 1.42 Å is the distance between adjacent carbons in graphene. Then, the total specific compression force is equal to ${f}^{2b}=-2{k}_{LJ}\mathsf{\Delta}{d}_{b}/S$.

_{0}, we obtain the specific electrostatic repulsion force ${f}_{el}^{2b}={q}^{2}/{\epsilon}_{\mathrm{H}2}{d}_{b}^{2}S$, where ${\epsilon}_{{\mathrm{H}}_{2}}$ is the dielectric permittivity caused by the polarization of hydrogen molecules. Then, the equilibrium condition in the case b has the form:

^{3}. Further, ${P}_{\mathrm{H}2}^{2b}S{d}_{0}={N}_{\mathrm{H}2}^{2}{k}_{B}T$, where ${N}_{\mathrm{H}2}^{2}$ is the number of H

_{2}molecules in a parallelepiped with a base area S and height d

_{0}. Assuming the volume of a hydrogen molecule ~1 Å

^{3}, we obtain ${N}_{{\mathrm{H}}_{2}}^{2}\approx 7$ and ${P}_{\mathrm{H}2}^{2\mathrm{qb}}S{d}_{0}\approx 50{k}_{B}T$. For $T=500\text{}\mathrm{K}$, we obtain ${P}_{\mathrm{H}2}^{2b}S{d}_{0}\approx 2.16\text{}\mathrm{eV}$, so that ${P}_{{\mathrm{H}}_{2}}^{2\mathrm{qb}}S{d}_{0}\approx {e}^{2}/2{d}_{0}$ (this estimate corresponds to $Z=1$ and ${\epsilon}_{\mathrm{H}2}>>1$). Thus, the value of $\delta $ (both magnitude and sign) depends on the parameters $\left|Z\right|<1$, ${\epsilon}_{\mathrm{H}2}>1$ and $T$. Model estimates for the adsorption of a single hydrogen atom on single sheet graphene [44] give $Z~0.2\u20130.4$. Numerical calculations performed within the framework of various variants of DFT (density functional theory) lead to noticeably different results. Further, the value of ${\epsilon}_{\mathrm{H}2}$ for such a specific hydrogen medium (more similar, at least, to a viscous liquid, if not to an amorphous solid formation, than to a gas [25]) is absolutely unknown. Taking into account these two circumstances, we can only assume that the value of A lies in the interval A ~0.01–2 eV. Both theoretical estimates [45] and experimental data [46] show that $\epsilon \approx 0.52\text{}\mathrm{meV}/\mathrm{atom}$. Hence for ${\epsilon}_{\mathrm{H}2}>>1$ we get $\delta ~0\text{}(Z=1)-0.25\text{}(Z=0)$.

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**Figure 1.**Processing (using the technique [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]). (

**a**) Fitting by three Gaussians (peaks ##1–3) of the TDS spectrum (β = 0.17 K s

^{−1}) for samples subjected to hydrogenation in gaseous H

_{2}(at 300 K, 11–4 MPa, 24 h); the red curve corresponds to the sum of three peaks. (

**b**) Fitting by three Gaussians (peaks ##1–3) of the temperature derivative of the TG spectrum for samples subjected to hydrogenation in gaseous H

_{2}(at 300 K, 11–4 MPa, 24 h) and subsequent heating (β = 0.17 K/s) in He; the red curve corresponds to the sum of three peaks.

**Figure 2.**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.

**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.

**Figure 4.**A micrograph of graphite nanofibers [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.

**Figure 5.**Approximation by two Gaussians of the thermal desorption spectrum (kinetic curves 0.08 wt.% and 0.02 wt.% from 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 1.**The results of processing [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

_{H2}

_{Σ}≈ 11 ± 3 wt.% (from [5,8]).

Peak # | T_{max},K | Reaction Order | Q, kJ mol ^{−1} | K_{0},s ^{−1} | K(T_{max}),s ^{−1} | Q^{*},kJ mol ^{−1} | γ | C_{H2},wt.% | (H/C) |
---|---|---|---|---|---|---|---|---|---|

1 | 914 | 1 | 39.0 | 1.5 × 10^{−1} | 9 × 10^{−4} | 39 | 0.76 | 8.4 | 1.1 |

2 | 77.5 | 5.1 × 10^{1} | 2 × 10^{−3} | 77.5 | |||||

2 | 1036 | 1 | 199 | 4.2 × 10^{7} | 4 × 10^{−3} | 198 | 0.02 | 0.2 | 0.02 |

2 | 398 | 8.8 × 10^{17} | 7 × 10^{−3} | 396 | |||||

3 | 1161 | 1 | 126 | 8.5 × 10^{2} | 2 × 10^{−3} | 125 | 0.22 | 2.4 | 0.30 |

2 | 250 | 7.0 × 10^{8} | 4 × 10^{−3} | 250 |

**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 | Reaction Order | Q, kJ mol ^{−1} | K_{0},s ^{−1} | K(T_{max}),s ^{−1} | Q^{*},kJ mol ^{−1} | γ | wt. % | (H/C) |
---|---|---|---|---|---|---|---|---|---|

1 | 923 | 1 | 43 | 2.9 × 10^{−1} | 1 × 10^{−3} | 43 | 0.23 | 8.5 | 1.1 |

2 | 87 | 1.7 × 10^{2} | 2 × 10^{−3} | 87 | |||||

2 | 1165 | 1 | 152 | 1.5 × 10^{4} | 2 × 10^{−3} | 152 | 0.08 | 2.9 | 0.4 |

2 | 304 | 2.0 × 10^{11} | 4 × 10^{−3} | 303 | |||||

3 | 1345 | 1 | 149 | 1.0 × 10^{3} | 2 × 10^{−3} | 148 | 0.69 | 26 | |

2 | 298 | 1.2 × 10^{9} | 1 × 10^{−3} | 297 |

Peak # | T_{max},K | Reaction Order | Q, kJ mol ^{−1} | K_{0},s ^{−1} | K(T_{max}),s ^{−1} | Q^{*},kJ mol ^{−1} | γ | wt. % | (H/C) |
---|---|---|---|---|---|---|---|---|---|

1 | 1203 | 1 | 163 | 1.6 × 10^{4} | 1.3 × 10^{−3} | 162 | 0.96 | 0.08 | 0.010 |

2 | 325 | 3.6 × 10^{11} | 2.7 × 10^{−3} | 324 | |||||

2 | 397 | 1 | 68 | 4.5 × 10^{6} | 5.1 × 10^{−3} | 67 | 0.04 | 0.02 | 0.002 |

2 | 133 | 4.1 × 10^{15} | 1.0 × 10^{−3} | 134 |

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**MDPI and ACS Style**

Nechaev, Y.S.; Denisov, E.A.; Cheretaeva, A.O.; Shurygina, N.A.; Kostikova, E.K.; Öchsner, A.; Davydov, S.Y.
On the Problem of “Super” Storage of Hydrogen in Graphite Nanofibers. *C* **2022**, *8*, 23.
https://doi.org/10.3390/c8020023

**AMA Style**

Nechaev YS, Denisov EA, Cheretaeva AO, Shurygina NA, Kostikova EK, Öchsner A, Davydov SY.
On the Problem of “Super” Storage of Hydrogen in Graphite Nanofibers. *C*. 2022; 8(2):23.
https://doi.org/10.3390/c8020023

**Chicago/Turabian Style**

Nechaev, Yury S., Evgeny A. Denisov, Alisa O. Cheretaeva, Nadezhda A. Shurygina, Ekaterina K. Kostikova, Andreas Öchsner, and Sergei Yu. Davydov.
2022. "On the Problem of “Super” Storage of Hydrogen in Graphite Nanofibers" *C* 8, no. 2: 23.
https://doi.org/10.3390/c8020023