Mechanism and Energetics of the Unique Spillover Effect Manifestation , Relevance to the Efficient Hydrogen Storage in Graphite Nanofibers

The “thermodynamic forces” and energetics of intercalation of H2 nanophase of a high density into carbon-based nanostructures are considered. The hydrogen self-compression effect, at the expense of the free energy of association of the penetrating hydrogen atoms to the “captured” hydrogen molecules, is shown. The mechanisms of the extraordinary manifestation of both the hydrogen spillover effect, and the Kurdjumov-like effect are discussed.


Introduction
Over the past 20 years, many scientists have reported that hydrogen spillover is a viable technique to achieve more hydrogen storage on different carbon-based materials and nanomaterials, even at ambient conditions.However, as noted, for instance, in (Juarez-Mosqueda, Mavrandonakis, Kuc, Pettersson & Heine, 2015), the veracity of these results and the efficiency of such graphitic structures to store hydrogen are still questionable.In addition, the spillover mechanism and energetics of molecular hydrogen on different carbon-based materials and nanomaterials, in the presence of metallic catalysts, has not been satisfactorily understood up to nowadays (Juarez-Mosqueda et al., 2015).
These open questions are considered in the present study, which is a further development of results (Nechaev & Veziroglu, 2015) of an open access.The present study is related to the extraordinary data on molecular gaseous hydrogen interactions with graphite nanofibers (with metallic catalysts), when, as is shown in this study, a unique manifestation of both the spillover effect (Juarez-Mosqueda et al., 2015) and the Kurdjumov-like extraordinary effect (Koval, 2005) occur.The mechanism and energetics of such two effects are revealed, particularly, by comparing with data on atomic gaseous hydrogen interactions with highly oriented pyrolytic graphites (without any catalysts) and epitaxial graphenes (also without any catalysts).

Experimental Methodology
In this study, thermodynamic analysis approach of the related experimental data (including Figures 1-7 from (Nechaev & Veziroglu, 2015)) has been used.

The Physics of Intercalation of H 2 Gaseous Nanophase of High Density into Graphene Nanoblisters in HOPG and Epitaxial Graphenes (Under Atomic Hydrogen Treatment)
Figures 1-3 shows the two steps ((a) and (b)) of hydrogenation (at 300 K and the atomic hydrogen flux, formally corresponding to pressure P (Hgas) ≈ 1×10 -4 Pa, without any catalyst) of surface graphene layers of a highly oriented pyrolytic graphite (HOPG) resulted in intercalation of H 2 gaseous nanophase of a high density into surface graphene nanoblisters.
Approximating the nanoblister to be of a semi-ellipse form, results in the blister area of S b ≈ 2.0 ×10 -11 cm 2 and its volume V b ≈ 8.4×10 -19 cm 3 .The amount of retained hydrogen in this sample becomes Q ≈ 2.8×10 14 H 2 /cm 2 , and the number of hydrogen molecules captured inside the blister becomes n ≈ (Q S b ) ≈ 5.5×10 3 .Thus, within the ideal gas approximation and accuracy of one order of the magnitude, the internal pressure of molecular hydrogen in a single nanoblister at near-room temperature (T ≈ 300 K) becomes Pa.The hydrogen molecular gas density in the blisters (at T ≈ 300 K and P H2 ≈ 1×10 8 Pa) can be estimated as ρ H2 ≈ {(QM H2 S b )/V b } ≈ 0.045 g/cm 3 , where M H2 is the hydrogen molecule mass.
Figure 1.Model (from STM and AFM data (Figures 2, 3)) showing the hydrogen accumulation (intercalation) in HOPG, with forming blister-like surface nanostructures; hydrogenation was done at 300 K and the atomic hydrogen flux, formally corresponding to pressure P (Hgas) ≈ 1×10 -4 Pa, without any catalyst.(a) Pre-atomic hydrogen penetration (intercalation) step.(b) Molecular gaseous hydrogen, "captured" inside the surface graphene nanoblisters (at P (H2gas) ≈ 1×10 8 Pa), after the intercalation step.Sizes are not drawn exactly in scale.The hydrogen self-compression effect is of 12 orders (from P (Hgas) ≈ 1×10 -4 Pa to P (H2gas) ≈ 1×10 8 Pa).According to analysis (Nechaev & Veziroglu, 2015), it occurs at the expense of the free energy of association of the penetrating hydrogen atoms to the "captured" hydrogen molecules (Equations 1 and 2, the Kurdjumov-like effect extraordinary manifestation).These data (Figures 1-3) can be quantitatively described, with an accuracy of one order of magnitude, and interpreted within the thermodynamic approach (Nechaev & Veziroglu, 2015), by using the condition of the thermal-elastic equilibrium of two phases (the Kurdjumov-like effect) for the process of (2H (gas) → H 2(gas_in_blisters) ), as follows: where P* H2 is related to the blister "wall" back pressure (caused by P H2 ) the so called surface pressure (P* H2 ≈ P H2 ≈ 1×10 8 Pa), P H is the atomic hydrogen pressure corresponding (formally) to the atomic hydrogen flux (P H ≈ 1×10 -4 Pa), P 0 H2 = P 0 H = 1 Pa is the standard pressure, ∆H dis = 4.6 eV is the dissociation energy (enthalpy) of one molecule of gaseous hydrogen (at room temperatures), ∆S dis = 11.8 k B is the dissociation entropy, ∆V ≈ (S b r b / n) is the apparent volume change, r b is the radius of curvature of nanoblisters at the nanoblister edge (r b ≈ 30 nm, Figure 1), N A is the Avogadro number, and T is the temperature (T ≈ 300K).The quantity of (P* H2 ∆V) is related to the work of the nanoblister surface increasing with an intercalation of 1 molecule of hydrogen.
It is necessary to emphasize that the process (2H (gas) → H 2(gas_in_blisters) ) is one directional, and the process ends when the thermo-elastic equilibrium of the two gas phases (H (gas) and H 2(gas_in_blisters) ) is reached (Figure 3(a), Equation ( 1)).This is a typical situation of the Kurdjumov effect.But in the case under the consideration, there is an unusually high energetics (at the expense of the free energy of association of penetrating (in the graphene nanoblisters) hydrogen atoms to the "captured" hydrogen molecules).
The value of the tensile stresses σ b (caused by P* H2 ) in the graphene nanoblister "walls" with a thickness of d b and a radius of curvature r b can be evaluated from another condition (equation) of the thermal-elastic equilibrium of the system in question, as follows: where ε b is a degree of elastic deformation of the graphene nanoblister walls, and E b is the Young's modulus of the graphene nanoblister walls.
Substituting in the first part of Equation ( 2 The degree of the elastic deformation of the graphene nanoblister walls, apparently reaches ε b ≈ 0.1 (Figures 1,  2).Hence, with Hooke's law of approximation, using the second part of Equation ( 2), one can estimate, with the accuracy of one order of the magnitude, the value of the Young's modulus of the graphene nanoblister walls: E b ≈ (σ b / ε b ) ≈ 0.1 TPa.The calculated quantity of E b is of one order lower than that considered in (Nechaev & Veziroglu, 2015) experimental value of the Young's modulus of graphene (E graphene ≈ 1.0 TPa).This difference may be related to a possible higher defect level of the graphene nanoblister walls, and/or to a possible internal side hydrogenation of the walls.
Similar STM, AFM and other data of different researchers for the epitaxial graphenes (for instance, Figures 4, 5) can be analyzed and interpreted in a similar manner, within the same physical concept (Equations 1 and 2, the Kurdjumov-like extraordinary effect).As is noted in (Nechaev & Veziroglu, 2015), a number of researchers have not sufficiently considered the "thermodynamic forces" and/or energetics of forming (under the atomic hydrogen treatment) graphene nanoblisters in the surface HOPG layers and epitaxial graphenes.Particularly, they have not taken into account a possibility of the Kurdjumov-like effect manifestation.It is also expedient to note that the recent experimental data (Hu et al., 2014) show that a hydrogen atom can not pass through a perfect graphene network.On the other hand, the analysis (Nechaev & Veziroglu, 2015) of a number of experimental data (including Figures 1 -7) shows that a hydrogen atom can pass through permeable defects in graphene, for instance, through triple junctions of grain boundaries.In Figures 3(b), 4(a) and 4(b), one can imagine some grain boundary network decorated (obviously, in some nanoregions at grain boundaries) by some nanoprotrusions.

The Physics of Intercalation of the Solid H 2 Nanophase into Hydrogenated Graphite Nanofibers (With Metallic Catalysts)
The physics of intercalation of solid molecular hydrogen of high density (ρ H2 ≈ 0.5 g/cm 3 , Figure 6) into closed (in the definite sense) nanoregions in hydrogenated GNFs (Figure 7) is related to the same concept (Equations of type 1 and 2, the Kurdjumov-like effect).
Figure 6.Literary data on isentropes (S/R) and isotherms of deuterium and protium.The density (ρ) of protium (H 2 , H) is increased by a factor of two (for the scale reasons).The experimental and theoretical isotherms show that at T = 300 K and the external compression pressure of P = 50 GPa hydrogen exists in the solid molecular state of a high density ρ H2 ≈ 0.5 g/cm 3 .
Figure 7. Micrograph of hydrogenated graphite nanofibers (GNFs), with Pd-catalyst (hydrogenated at 300 K and initial pressure of P (H2gas) ≈ 8 MPa), after release from them, at 300 K, for 10 min, of the intercalated solid H 2 nanophase (17 mass.%) of a high density of ρ H2 ≈ 0.5 g/cm 3 (analysis (Nechaev & Veziroglu, 2015)).The arrows in the picture indicate some of the slit-like closed nanopores of the lens shape, where the solid H 2 intercalated nanophase (under pressure of ~50 GPa, according to data on Fig. 6) was localized.Such a pressure level can be also evaluated by the consideration of the material deformation and the necessary stresses for forming the lens shape closed nanopores (at the expense of the energy of association of penetrating (into the nanopores) hydrogen atoms to molecules "captured" inside the nanopores (Equations of type 1 and 2).(It may be an extraordinary manifestation of both the Kurdjumov-like effect, and the spillover effect).
The comparison with the previous results (presented in Item 3.1) shows that there is a unique manifestation of the spillover effect (particularly, in Figure 7), as related to providing of the necessary one direction flux of atomic hydrogen from Pd-catalyst to the nanopores (when the material hydrogenation at initial molecular hydrogen pressure P H2 = 8 MPa).
The atomic hydrogen, obviously, forms at the expense of the energy of the surroundings, by heat conducting from it to the Pd-catalyst system, which provides the dissociative dissolving of H 2 in Pd and some other related processes.It seems that this is not a violation of the Second Law of thermodynamics, since there should be a small difference in temperatures of the surroundings and the Pd-catalyst system (due to the hydrogen spillover effect).Also, the thermal-elastic self-compression (the Kurdjumov-like effect) of the "captured" H 2 in the nanopores occurs at the expense of the association energy of the penetrating hydrogen atoms (as considered in Item 3.1).
The recent related data ( (Naumov & Hemley, 2014), (Ting et al., in press)) can be taken into account in further studies.

Conclusions
1.The "thermodynamic forces" and energetics of forming of graphene nanoblisters (under atomic hydrogen treatment, without catalysts) in the surface HOPG layers (Figures 1-3) and epitaxial graphenes (Figures 4, 5) are quantitatively described, particularly, two conditions of the thermal-elastic thermodynamic equilibrium of the two gaseous phases (Equations 1 and 2, the Kurdjumov-like effect) are considered.
3. The physics of intercalation of the solid H 2 nanophase of a high density (ρ H2 ≈0.5 g/cm 3 ) into hydrogenated graphite nanofibers with Pd-catalyst (Figures 6, 7) is considered.Both the spillover effect and the Kurjumov-like effect are obviously manifested in the extraordinary data considered in (Nechaev & Veziroglu, 2015).
4. These results can be used for solving of the current problem of the efficient and safe hydrogen on-board storage (Nechaev et al., 2014).

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

Figure 3 .
Figure 3. (a) Hydrogen storage efficiency of HOPG samples, desorbed molecular hydrogen (Q) versus dose (D) of atomic hydrogen exposure.(b) STM image for 600x600 nm area of the HOPG sample subjected to atomic hydrogen dose of 1.8•10 16 H O /cm 2 , followed by hydrogen thermal desorption.(It may be the Kurdjumov-like effect extraordinary manifestation).