Introduction

Climate change and energy security are the two most important issues facing the world. The first requires a strong acceleration of innovation in energy technologies and non-carbon processes [1], and the second caused by the depletion of fossil resources leads massively to the introduction of intermittent renewable energy [2, 3]. Among the different energy sources, hydrogen has received a lot of attention because it has many fascinating benefits, including non-toxicity, abundance, and easy preparation [4,5,6,7]. It would thus constitute an opportunity to develop innovative systems integrating an ecological dimension that weighs more and more in individual and societal choices [8].

Although globally recognized as a high-potential energy carrier, its large-scale use has faced numerous production [9] and storage challenges [10, 11]. However, in recent years, its production has posed no problem because several environmentally friendly methods have emerged, like electrolysis associated with solar, wind, hydroelectric, or biomass energy, which are renewable sources allowing a large production of hydrogen without pollution [1]. It can also be produced by biological processes [4]. Yet, its safe and efficient storage remains very expensive for a wide application.

Several techniques exist for the storage of hydrogen [12]. But the two conceptually simple methods are compression under a pressure of 700 bars and liquefaction at a temperature of 20 K [13]. However, the pressurized gas tank presents key problems in the design and sealing of materials; moreover, reaching the desired pressure requires more than 10% of the stored energy [14, 15]. Also, in the cryogenic method, large amounts of energy are lost during the liquefaction and evaporation processes. Consequently, these two methods consume a lot of energy and are not economically the most indicated [15, 16]. To overcome these various difficulties, the use of adsorbent materials is a method which fascinates researchers in this field.

Among all porous materials, metal–organic frameworks (MOFs) are the best candidates for adsorption of H2 because they are made up of light atoms and are very porous. In addition, they hold the best hydrogen storage records these days [2, 3, 6, 17,18,19].

Some MOFs show the satisfactory results when they operate at cryogenic temperatures [19]. However, for operation at 77 K, additional energy and equipment are required to keep the tanks at a temperature below that of the environment [6]. In addition, there is also the problem of heat transfer [20]; this is why the adsorption of hydrogen at ambient temperature and pressure would be ideal [8]. But at room temperature, their storage capacity becomes low, due to the weak MOF-H2 interactions [8, 19]. It is, therefore, necessary to find materials which can function under these conditions, that is to say, which can respond to practical application requirements set by the United States Department of Energy (DOE) in 2020. (5.5wt.% of gravimetric density and 40 g. L − 1 of volumetric density at an operating temperature between 233 and 333 K and at a pressure below 12 atm) [20, 21].

Some work has already been done on the storage of hydrogen at moderate temperatures and pressures. Hirscher et al. [22] demonstrated that the properties of materials such as the surface, composition, and size of the pores can influence the storage capacity and that it would, therefore, be necessary to understand the correlation between the adsorption properties and the structure of MOFs to improve hydrogen storage. Njikamp et al. [23] found that carbon and low pore volume zeolites are not good candidates for storing hydrogen under its recommended conditions. Frost and Snurr [24] suggested that a hydrogen storage capacity of 9 wt.% and 30 g. L − 1could be reached with MOFs which can provide isosteric heat of 15 kJ. Mol − 1 while maintaining a free volume of 2.5 cm3. g − 1 and a vacuum fraction of 0.85. Bhatia and Myers [25] have determined operating conditions of 131 K and 1.5 to 100 bar for a microporous material having an enthalpy of adsorption equal to 6 kJ. Mol − 1. Thornton et al. [26] found that characteristics that maximize optimal storage capacities at room temperature include pores of about 6 Å in diameter and vacuum fractions of 0.1. The results have been corroborated with the work of Hao Li et al. [6], who find that the MOFs–H2 interaction force can be refined by the size and shape of the pores.

In this work, we study the influences of several characteristics of the MOF for optimal adsorption of the gravimetric and volumetric capacities coupled, because few hydrogen adsorbents balance high usable volumetric and gravimetric capacities. These characteristics are the gravimetric and volumetric surface of the MOF, the volume of the pores, the void fraction, the diameter of the pores, the heat of isosteric adsorption, the types of construction networks and the influence of the introduction of metal ions into the SBUs of MOFs. However, the large number of existing MOFs pushes researchers to turn to computer simulations to limit the expenses linked to the experiments. This will also allow a custom design of these hydrogen adsorbent materials.

Frost and Snurr studied the effects of specific surface area, free volume and heat of adsorption on the absorption of H2 by GCMC simulations over a wide pressure range at 298 K, but this study was not carried out than on a series of MOFs belonging to a single family (IRMOF). However, in our work, we used ten MOFs from several families. These adsorbent materials have several topologies and are built according to two main objectives. The first is to increase the area and volume of the pores using ligand elongation or mixed ligand systems. And second, in order to increase the isosteric heat of hydrogen adsorption, MOFs are designed with: open metal sites, the introduction of cations generating a large electrostatic field in the cavities, doping with metal ions, the manufacture of metal nanoparticles, and the functionalization of ligands.

The first materials are the MOF which best balances the volumetric and gravimetric adsorption capacity of hydrogen at 77 K, like IRMOF-1 which is presented as the reference MOF by the Center of Excellence for Engineering hydrogen storage (HSECoE) [27, 28]. According to the work of Ahmed et al. [29, 30], IRMOF-20, PCN-610 / NU-100 [31], and SNU-70 [32] had higher capacities than those of IRMOF-1. Cu-BTC [33] is the type of open metallic MOF, designed to increase the attraction between MOF and the hydrogen molecule. The elongation of the ligands in the structure of MOF-177 and MOF-200 increases their specific surface [34]. Finally, MOF-74, ZnMOF-74, and MgMOF-74 [35] were chosen to evaluate the influence of the introduction of metal ions into MOF. For each MOF, the different characteristics such as the pore volume, the largest cavity diameters, the specific surface, the helium vacuum fractions, and the isosteric heats of adsorption are determined and are shown in Table 1.

Table 1 Properties of the MOF materials studies
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Simulation methods

In the simulations, linkage interactions are neglected because we have assumed rigid molecules. In this case, there are only intermolecular interactions between unbound atoms, which are modeled via a Lennard–Jones potential (LJ) + Coulomb potential [36] represented by Eq. (1).

$$U_{T} = \sum\nolimits_{i\langle j} {4\varepsilon_{ij} } .[(\frac{{\sigma_{ij} }}{{r_{ij} }})^{12} - (\frac{{\sigma_{ij} }}{{r_{ij} }})^{6} ] + \sum\nolimits_{i\rangle j} {\frac{{q_{i} q_{j} }}{{4\pi \varepsilon_{0} r_{ij} }}}$$
(1)

where \(\varepsilon\) is the depth of the potential well, \(\sigma\) is the finite distance at which the inter particle potential is zero, r is the distance between the particles, andq1 and q2 are the positive or negative magnitudes of the charges.

The hydrogen molecules have been modeled according to the Darkrim–Levesque model [37]. The LJ parameters for the MOF atoms were assigned according to the Universal Force Field (UFF) [38] and Dreiding [39]. A limit value of 12 Å was used for all LJ interactions, and Ewald summations were used to calculate Coulomb interactions. Equations (2) and (3) present the Lorentz–Berthelot [40] mixing rules used to determine the LJ parameters for the interactions between atoms.

$$\varepsilon_{ij} = \sqrt {\varepsilon_{ii} .\varepsilon_{jj} }$$
(2)
$$\sigma_{ij} = \frac{{\sigma_{ii} + \sigma_{jj} }}{2}$$
(3)

Adsorption simulations were performed in a single cell using Grand Canonical Monte Carlo simulations (GCMC) using the RASPA code [41]. To calculate the ensemble averages, in each cycle, an average of N displacements was made, where N is the number of H2 molecules in the system. Translation, rotation, insertion, deletion, and reintegration movements were used with equal probability.

The geometric area was calculated by the Monte Carlo method using a probe of 2.958 Å equal to the diameter of the hydrogen atom. The void fraction, which is the void of a structure divided by the total volume, is measured using helium, since the helium almost does not adsorb at room temperature. The isosteric heats of H2 adsorption shown are low coverage data, calculated at a temperature of 298 K and at a pressure of 0.5 Bar.

For the description of the MOFs, characteristics such as pore volume, largest cavity diameter, and specific surface area were calculated using Zoe +  + [42], while helium vacuum fractions and adsorption heats were determined using RASPA.

Results and discussions

Figure 1 compares the results obtained in this work to those of Frost and Snurr [24]. Figure 1a shows the excess adsorption of H2 in IRMOF-1 at 298 K, and Fig. 1b shows the results of excess adsorption in Cu-BTC or HKUST-1 at 298 K. Simulations were performed over a pressure range from 1 to 100 bar. The results were compared to those of Frost and Snurr because they used a relatively simple model similar to that used in the current work and obtained the acceptable results. However, we can observe a slight difference (0.1–0.5) during the increased pressures. This could be explained by the fact that our model takes a limit value of 12 Å for all interactions of Lennard–Jones J compared to the 12,8 Å used in their work. Although these results are significantly lower than the experimental results which were high (up to 1wt.% at 20 bar) [43], it was shown that these experimental results were very likely to be contaminated by the presence of another gas.

Fig. 1
figure 1

a Simulated adsorption isotherms for IRMOF-1 at 298 K and b simulated adsorption isotherms for Cu-BTC at 298 K

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Figure 2 shows the gravimetric hydrogen adsorption capacities of the different MOFs studied. This capacity is given by the ratio between the mass of hydrogen stored and that of the MOF loaded with hydrogen. we note that the MOF-200 provides the greatest absolute gravimetric capacity at 298 K; it adsorbs up to 3.7 wt.% H2 at 100 bar, followed by the PCN-610 which has a capacity of 2.8 wt.% under the same conditions. The MOF-177 having the same topology as the MOF-200 has a capacity of 1.9 wt.% SNU-70 has a capacity of 1.77 wt.%; IRMOF-20 adsorbs 1.55 wt.%, and IRMOF-1 stores 1.3 wt.% H2. It is observed that the curves of the hydrogen adsorption isotherms at 298 K obtained for the different materials are linear pressure functions like that found in the literature [43]. This is justified by the fact that no saturation occurs in the pressure range studied and that the layer of hydrogen adsorbed on the surface of the MOF is very dilute. The difference between the performances of MOFs comes first from the specific surface. As the specific surface is the total surface, it comprises on the one hand the geometric or “exterior” area, and on the other hand, the “interior” surface formed by the walls of the capillaries, pores, or crevices of the solid. Then, the MOF having the largest surface will be able to adsorb a large quantity of hydrogen because adsorption is a surface phenomenon that occurs during contact between a gas or a liquid with a solid. This is why Fig. 2b shows that the correlation between the absolute gravimetric adsorption and the gravimetric surface of the different MOFs is 0.8507. From the characteristics of the MOFs calculated in Table 1, we observe that the surface mainly increases with the diameters of the pores. However, as the MOF-177 has pores with diameters equal to 11.17 A and shows a greater specific surface area than the ZnMOF-74 or MgMOF-74 which have pores with diameters 11.91 and 11.86 A, respectively, we can also affirm that the topology of MOFs is a factor which also influences their gravimetric capacity of hydrogen adsorption.

Fig. 2
figure 2

a Absolute gravimetric hydrogen adsorption in ten MOF materials at 298 K, b correlation of the absolute gravimetric H2 adsorption at 100 bar and 298 K gravimetric surface area and c correlation of the absolute gravimetric H2 adsorption at 100 bar and 298 K with free volume

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As we said above, the surface called here “interior” which is formed by the walls of capillaries, pores, or crevices can certainly contain small cavities inaccessible to the molecules to be adsorbed. To assess their influence, we calculated the pore volume with a probe size equal to that of hydrogen which is 2.958 A. The results of R2 in Fig. 2c for the absolute gravimetric adsorption show a correlation with the free volume greater than that obtained with the gravimetric surface in Fig. 2b. We can then say that the materials with the largest free volume available will contain the most hydrogen. This is why, for the design of a material capable of overcoming the challenges of gravimetric adsorption, it is necessary to increase the specific surface of the MOFs and to eliminate the cavities of size smaller than the diameter of the hydrogen because they will not allow its penetration.

The isosteric adsorption heat of the Materials can be increased by decreasing the pore size. This is what one can observe in Fig. 3. MOF-74 has pore sizes of 7 Å and provides an isosteric heat of 6.38 kJ. mol −1  which is the largest of all MOF studied. We have also noted that the introduction into this material of the metal ions Mg (II) and Zn (II) does not increase the isosteric heat of adsorption but earlier increases the pore diameters which are 11.86 and 11.91 Å for MgMOF-74 and ZnMOF-74, respectively, for an isosteric heat of 5.57 and 5.77 kJ. mol −1 , but comparing to materials with the same pore diameters, such as MOF-177, MgMOF-74, and ZnMOF-74 are much better. We can say that MOFs doped with metal ions provide more adsorption heat than MOFs with the same characteristics. The main reason why the MOF-74 has the smallest gravimetric capacity is that it has small pores that give it a small free volume. Pore size can affect the interaction between hydrogen molecules and porous solids. The materials containing small pores and high curvature walls interact more strongly with hydrogen molecules than large-pore materials. This provides solid evidence that the smaller the pores, the stronger the interactions between MOF and H2.

Fig. 3
figure 3

Correlation of Qst with pore diameter for the ten MOFs

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The study of excess adsorption is crucial to understanding the physical adsorption of materials. Absolute adsorption is the sum of excess adsorption (molecules that attach to the surface through Van der Waal interactions) and the capacity that resides in the pores. The reason why we have an almost linear correlation with the free volume, to observe in Fig. 2c, comes from the fact that the interactions are very weak at ambient temperature. The excess of adsorptions presents a complex correlation. We can notice that the excess is related to the accessible or available surface because, for a large area, there will also be many hydrogen molecules that can be adsorbed. In Fig. 4, the MOF-200 exhibits the largest PCN-610 over-capacity survivability that provides 0.42 wt.% capacitances and 0.41 wt.% at 100 bar and 298 K, because they have the biggest surfaces. However, we observe that they have curves that already reach their saturation at 100 bar, unlike MOFs that have higher isosteric heat. Although not having the highest performance over this range of pressures, the MgMOF-74 and ZnMOF-74 provide nearly linear curves that prove that for slightly greater pressures these materials will give the greatest excess capacity.

Fig. 4
figure 4

Excess hydrogen adsorption in ten MOF materials at 298 K

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Conceptually, the difference between absolute values and excessive values can be considered as a gas in its ambient state, that is to say a gas that would exist in the pores even if the material did not provide interaction energy. As the density of ambient H2 will be the same in all materials, it is the free volume that determines the amount of ambient H2 that exists per mass of material.

The MOF-filled tank required to store a certain amount of the hydrogen should be neither too heavy nor too large to meet certain requirements in the current fashion of vehicle design. However, these tanks must also have reasonable autonomy. To determine the size and mass of these tanks, the volumetric and gravimetric capacities are key factors. Yet, as we observe in Fig. 5, in which we have shown the volumetric capacity curves of the different materials over a pressure range from 1 to 100 bar at 298 K, the MOF-200 which has the highest gravimetric capacity provides a volumetric capacity of 8.89 gH2. L − 1 which is the lowest. We note then that the objectives of individual maximization of volumetric and gravimetric hydrogen adsorption charges MOF are incompatible, which is related to the ref. [44]. The poor performance of materials in general is due to the low density of hydrogen at room temperature. As can be seen in Fig. 6a, materials with large specific surface areas have low volumetric capacities. MgMOF-74, ZnMOF-74, and SNU-70 are the three materials that provide the largest volumetric capacities that are 13.02, 12.69, and 12.64 gH2. L − 1, respectively, at a temperature of 298 K and a pressure of 100 bar.

Fig. 5
figure 5

Absolute volumetric hydrogen adsorption in ten MOF materials at 298 K

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Fig. 6
figure 6

a Correlation of the absolute volumetric H2 adsorption at 100 bar and 298 K with absolute gravimetric H2 adsorption in ten MOF, b correlation of the absolute volumetric H2 adsorption at 100 bar and 298 K pores diameters of ten MOF, and c correlation of absolute volumetric H2 adsorption at 100 bar and 298 K with adsorption isosteric heat in ten MOF

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Some work has found that the density of H2 in the H2 pores depends on the size of the pores. We note in Fig. 6b that the SNU-70 has pores approximately 17.98 Å in diameter which are largely above the other MOFs studied but have a capacity close to MgMOF-74 and ZnMOF-74. We note that the study of the density of H2 in the pores or the free volume makes it possible to examine more clearly the effects of the characteristics on the adsorption of the H2 in the MOFs, because the quantity of hydrogen in a volume should be the same then the difference that we notice would be due to the excess of adsorption that is to say the quantity which is fixed on the surface. Intuitively, we can already see that at low pressure the excess is correlated with the accessible surface and that at high pressures, MOF–H2 interactions control this capacity.

Because a material with large pores can provide strong interaction energies near the walls but will have more space farther from the walls where the adsorbate molecules have little attraction on the surface of the material, in Fig. 6c, we can notice that there is a slight correlation with isosteric adsorption heat. But as the MOF-74 has a very small surface, despite its high isosteric heat it has a low capacity.

Figure 4 provides a useful relationship between the gravimetric hydrogen capacity in the MOFs to study and the free volume at 100 bar and 298 K. A line fitted to their data gives us the empirical equation:

$$N_{\rm abs} = 0.86 \times V_{l} + 0.24$$
(4)

where Nabs is the absolute capacity in wt. % and \(V_{l}\) the free volume by mass.

From this relationship, we vary the free volume by mass for the ten MOF to find a correlation between gravimetric and volumetric capacity. We find in Fig. 7 that it is difficult for a material to balance high volumetric and gravimetric capacity with low isosteric adsorption scale.

Fig. 7
figure 7

Equilibrium between the gravimetric and volumetric adsorption capacities in the MOF at 298 K and 100

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Using the empirical Frost–Snurr equation [24] linking the absolute density of hydrogen in the pores and the low charge isosteric heat is given by:

$$\rho_{\rm abs} = 2,38 \times q_{\rm st} + 1,79$$
(5)

where \(\rho_{\rm abs}\) is the absolute density of hydrogen in the pores and qst isosteric low-load adsorption heat.

As this empirical equation has been adjusted to give the IRMOF-1 and Cu-BTC, we have chosen to use these two materials. We have calculated the adsorption capacity of these MOFs for two isosteric adsorption heat. As shown in Fig. 8, the first points showing weak capabilities were calculated with their natural isosteric heat. The higher points were calculated for an adsorption isosteric heat of 15 kJ. mol −1 . As already predicted Frost, we notice that they give the results very close to the goal. We also want to emphasize that the balance between gravimetric and volumetric capacity seems to be perfect for this value of Qst.

Fig. 8
figure 8

Influence of isosteric adsorption heat on the balance between gravimetric and volumetric adsorption capacities in IRMOF-1 and Cu-BTC

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Figure 9a and b shows the usable capacities of the different materials studied in this work. The useful capacity is defined as the difference in total absorption at 100 bar (filled tank) and 5 bar (empty tank) [29]. As shown in Fig. 9a, we note that the usable volumetric capacity varies from 8.5 to 12.3 gH2.L − 1 and MgMOF-74 is the material which obtains the highest performances. Figure 9b also shows that the usable gravimetric capacities vary from 0.25 to 3.59% by weight. The MOF-200 has the highest usable gravimetric capacity. We note that the balance of usable adsorption capacities of MOFs at room temperature is different from that obtained at 77 k [29]. The usable gravimetric capacities of four materials calculated here always follow the order of the capacities measured at 77 k, PCN-610 (2.66 wt%), SNU-70 (1.67 wt%), IRMOF-20(1.45 wt%), and IRMOF-1(1.22 wt%). However, for the usable volumetric capacity, the order differs from that measured at low temperature. The PCN-610 which has the largest capacity at 77 k obtains at 298 k a capacity (9.17 gH2. L − 1) lower than IRMOF-20 (9.42 gH2. L − 1). At low temperature, the materials which have the greatest usable volumetric capacities also exhibit the greatest gravimetric capacities. we can, therefore, conclude here that the properties that some MOFs have for balancing the usable gravimetric and volumetric capacities can change with temperature.

Fig. 9
figure 9

Usable capacities of hydrogen stored by MOFs. a Volumetric basis and b gravimetric basis. Capacities are calculated at a temperature of 298 k and with a pressure variation of 100 and 5 bars

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MOFs that can store hydrogen at room temperature must have large pores to increase free volume. To increase the excess capacity, we have found that it takes a large area and increase the isosteric heat of adsorption. The functionalization of the surface of the host material with a transition metal attracting hydrogen by Kubas interactions will improve the physisorption energy of hydrogen by MOF.

Conclusion

We evaluated the influence of accessible surface area, pore size, and isosteric heat for a series of ten MOFs for adsorption at room temperature over a pressure range of 1 to 100 bar. Our results showed that the absolute gravimetric adsorption capacity of all materials is well correlated with the free volume of the pores. The excess has a somewhat more complex correlation; it is correlated with the accessible surface, but for pressures above 100 bar the materials providing isosteric heat of higher adsorption will adsorb more hydrogen. MOFs with a large gravimetric capacity give a low volumetric capacity. So, to achieve the objectives set for the storage of hydrogen must be designed MOF with high isosteric heat. Small pores increase the adsorbent–adsorbate interaction but give a low absolute capacity. To increase the isosteric heat of MOF, the functionalization of the surface of the host material with a transition metal seems to be the best option.