Grand canonical Monte Carlo simulations of the hydrogen and methane storage capacities of novel but MOFs at room temperature

Grand canonical Monte Carlo simulations of the hydrogen and methane storage capacities of novel but MOFs at room temperature I. Cabria Departamento de Fı´sica Te orica, At omica y  Optica, Universidad de Valladolid, 47011 Valladolid, Spain highlights Hydrogen Storage Capacities of Novel BUT MOFs. Methane Storage Capacities of Novel BUT MOFs. Volumetric capacities highly correlated with product porosity and isosteric heat. Three BUTs have high hydrogen gravimetric storage capacities. One BUT MOF, BUT-107, reaches the methane DOE targets. article info Article history: Received 17 April 2023 Received in revised form 21 June 2023 Accepted 26 June 2023 Available online 14 July 2023 Keywords: Hydrogen storage Methane storage Metal-organic frameworks Grand canonical Monte Carlo simulations abstract Hydrogen Fuel Cell Electric Vehicles (HFCEVs) and Natural Gas Vehicles (NGVs) are cleaner alternatives to present oil-based vehicles. The main problem of these technologies is the on-board storage. Metal-organic frameworks (MOFs) is one of the main groups of solid porous materials that can be used to store hydrogen or methane on-board these vehicles at room temperature and low or moderate pressures. The synthesis of these materials is usually expensive. Recently a group of eleven new BUT MOFs (BUT: Beijing University of Technology) has been synthesized using cheap organic precursors. Grand Canonical Monte Carlo simulations (GCMC) of the hydrogen and methane storage capacities and isosteric heats of these BUTs have been carried out and analyzed at 298.15 K and at pressures in the range 0.5e50 MPa. The correlations between the storage capacities and the porosity, the density, the pore size and the isosteric heat of the MOFs are analyzed. According to the simulations, three of the newly developed BUTs demonstrated high storage capacities for both hydrogen and methane. BUT-104 and 105 exhibited useable hydrogen volumetric and gravimetric capacities of approximately 0.023e0.027 kg/L and 4 wt % at 50 MPa. Additionally, they showcased useable methane volumetric and gravimetric capacities of 0.16 e0.21 kg/L and 25 wt % at 25e35 MPa. Moreover, BUT-107 achieved the U.S. Department of Energy (DOE) hydrogen target for 2025, with a useable hydrogen gravimetric capacity of 5.5 wt % at 27 MPa. Furthermore, BUT-107 met the corresponding DOE methane targets, with useable methane volumetric and gravimetric capacities of 0.25 kg/L and 33.33 wt % at 50 MPa. ©2023 The Author(s). Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/). E-mail address: [email protected]. Available online at www.sciencedirect.com ScienceDirect journal homepage: www.elsevier.com/locate/he international journal of hydrogen energy 50 (2024) 160e177 https://doi.org/10.1016/j.ijhydene.2023.06.298 0360-3199/©2023 The Author(s). Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. This is an open access article under the CC BY-NC- ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Introduction The emission of greenhouse gases is one of the main reasons of the climate change. Fossil fuel based road transport is the main responsible for the CO 2 emissions and pollution. The goal of the European Union for 2050 is to reduce the pollution from transport by 60%, compared to the year 1990 [1]. Hydrogen is a long-term and non-polluting alternative to the oil fuels. Road transport based on HFCEVs would reduce dependence on oil, pollution, and greenhouse gas emissions. Hydrogen has a very high specific energy, but a low energy density under normal conditions. This makes difficult the storage of hydrogen on-board of vehicles. Hence, it is relevant to investigate and find methods that store enough hydrogen. The technological goal is a hydrogen vehicle that has a range autonomy similar to that of fossil fuel based vehicles, about 600 km. To reach that goal, the DOE established specific onboard hydrogen storage targets: For 2020, 0.030 kg H 2 /L and 4.5 wt % for the volumetric and gravimetric storage capacities, respectively, and for 2025, 0.040 kg/L and 5.5 wt %, respectively [2,3]. The ultimate storage targets are 0.050 kg H 2 /L and 6.5 % wt. These values or targets correspond to the useable, also called delivery or working, capacities and also correspond to a reversible storage. One method to storage hydrogen is by compression on high pressure tanks. Hydrogen compressed storage systems at 70 MPa and room temperature have useable volumetric and gravimetric storage capacities of 0.0244 kg H 2 /L and 4.2 wt %, respectively [4], below the DOE 2025 targets. Hydrogen storage on solid porous materials is a promising method to reach the mentioned target. The hydrogen gas is stored by physisorption on the pores of these materials. One advantage of this storage method is that the storage of hydrogen gas on solid porous materials achieves higher densities at low and moderate pressures than the compression storage method at the same pressures. The storage at low and moderate pressure is cheaper than at high pressures. Another way to reduce CO 2 emissions is through road transport based on NGVs, which are less polluting than oilbased vehicles. They emit much less CO 2 and they could be a key element to reach the emission goals of the European Union, 95 g of CO 2 /km. Most of Natural Gas Vehicles are Compressed Natural Gas (CNG) vehicles. They store natural gas (most of natural gas is composed by methane) by compression up to 25, 35 or 70 MPa and have an autonomy of about 600 km. Adsorbed Natural Gas (ANG) vehicles, store methane (natural gas) on deposits that contain an adsorbent material, a solid porous material. This storage method has the same advantage that the storage of hydrogen on porous solid materials. The technological goal is an ANG vehicle that works at low or moderate pressures, with the same autonomy range than a CNG vehicle that works at high pressures. The U.S. DOE established the following on-board useable methane storage targets at room temperature and moderate pressures (6e25 MPa) to reach that technological goal: 0.250 kg CH 4 /L and 33.33 wt % for the useable volumetric and gravimetric storage capacities, respectively [5]. The research on the field of gas storage on solid porous materials is focused on the search of materials that can be used at room temperature and that store enough gas to be used in the deposits of a hydrogen vehicle [6,7] or an ANG vehicle. There are several classes of solid porous materials used for gas storage. Among them, nanoporous activated carbons (ACs) have been extensively studied for their exceptional gas storage capacities [8e13]. These materials exhibit a well-developed porosity, providing ample space for gas molecules to be stored, and they are relatively non-expensive to synthesize. Polymer composites, which consist of a polymer matrix reinforced with porous fillers, offer a unique combination of mechanical strength and gas storage capabilities [14,15]. Composites made with inexpensive polymers like polypropylene or polyester and low-cost fillers such as glass fibers can be relatively affordable. Polymers of Intrinsic Microporosity (PIMs) are an intriguing class of porous materials that have garnered significant attention in gas storage applications. PIMs possess a molecular structure that inherently incorporates microporosity, resulting in materials with exceptionally high internal surface areas. This characteristic allows PIMs to exhibit enhanced gas sorption capacities [6,16]. Covalent organic frameworks (COFs) are a class of porous materials constructed through covalent bonding of organic building blocks. COFs exhibit permanent porosity and tunable structures, making them attractive for gas storage applications [17,18]. Metal-Organic Frameworks (MOFs) are a significant and large class of porous materials that have gained considerable attention in gas storage applications. MOFs consist of metal nodes or clusters connected by organic ligands, forming highly ordered crystalline structures with well-defined pores. The tunable nature of MOFs allows for precise control over their porosity and gas adsorption properties. As a result, MOFs have shown great potential for various gas storage applications. There is very intense research related to these materials: There were over 90,000 MOFs synthesized and 900,000 MOF structures predicted by August 2020 [19]. The hydrogen and methane storage capacities of MOFs have been extensively studied in experiments and GCMC simulations [20e36]. The high porosity of MOFs and their high surface area to volume ratio make them promising candidates for on-board hydrogen and methane storage. However, the synthesis of most MOFs is very expensive [28]. Recently, a group of the Beijing University of Technology has published the synthesis of a new group of BUT MOFs using materials and a method that reduces the cost [37]. GCMC simulations were conducted to predict and understand the hydrogen and methane storage capacities of these new BUTs at room temperature and pressures ranging from 0.5 to 50 MPa. The paper is organized as follows. Section II is devoted to the details of the GCMC simulations and of the BUT cells. The results of the simulations are presented and analyzed in section III. Finally, section IV is devoted to the conclusions. Methodology and materials simulated Parameters and details of the GCMC simulations GCMC simulations of hydrogen and methane molecules inside the eleven BUTs recently synthesized [37] have been carried international journal of hydrogen energy 50 (2024) 160e177 161 out at room temperature, 298.15 K, and at pressures between 0.5 and 35 MPa. A few simulations have been also carried out at 50 MPa for some selected BUTs. Each GCMC simulation consisted of ten million iterations. The storage capacities were calculated using the last five million iterations of each simulation. The Metropolis algorithm was used in each iteration [38]. On each iteration there are three possible trials: Move, add or remove one molecule. 40% of the trials consisted on the deletion of one molecule, another 40% on the insertion of one molecule and the remaining 20% consisted on the movement of one molecule. These percentages of the trials were obtained after several test simulations. The simulations have been performed using an in-house code. The chemical potential used in the GCMC simulations was derived from the Soave-Redlich-Kwong (SRK) [39] equation of state (EOS), using for the dimensionless acentric factor u, the critical pressure P c and the critical temperature T c of hydrogen and methane, the values published by Zhou and Zhou [40] and Xu et al. [41], respectively (See Table 1). The Lennard-Jones (LJ) interaction potential energy [42] has been used to simulate the interactions between the gas (hydrogen or methane) molecules and between the gas molecules and the atoms of the BUTs. The LJ interaction potential energy has the form: V¼4εs r12 s r6;(1) where -εis the minimum value of the LJ interaction potential energy (ε>0), sis the distance at which the interaction between the two particles is zero and ris the distance between the two particles. The values of the parameters sand εdepend on the particles of the interaction. The sand εparameters of the interaction between atom iand gas jwere obtained through the Good-Hope [43] and Berthelot combining rules [44], respectively: sij ¼ffiffiffiffiffiffiffiffi sisj p εij ¼ffiffiffiffiffiffiffi εiεj p: (2) Table 2 shows the values of the LJ parameters εand sof the atoms and molecules used in the present GCMC simulations of the BUTs. The LJ parameters of the CeH 2 interaction used in the simulations were obtained from Rzepka et al. [45]. The LJ parameters of the rest of the interactions were obtained by means of the above-mentioned Good-Hope-Berthelot combining rule. The quantum effects have been included in the interaction potential by using the Feynman-Hibbs correction [46]. All the present GCMC simulations have been performed using that quantum correction. The LJ interaction potential was cut off at 20  A for the interactions with H 2 and at 7.5  A for the interactions with methane. These values of the cutoff radii were obtained after carrying out two sets of GCMC simulation tests of pure hydrogen and methane in a simulation box of 50 50 50  A 3 at 298.15 K and at several values of the ‘experimental’ or input pressure, between 0.1 and 25 MPa for hydrogen and between 0.1 and 35 MPa for methane. The goal of those tests was the calculation of the density and the pressure of the gas. The first set of tests consisted on the comparison of the SRK EOS density and the density obtained in the GCMC simulations at 298.15 K. Fig. 1 contains this comparison for hydrogen and methane. There is a good agreement between these two densities for hydrogen and methane using the mentioned values of the cutoff radii. The present tests for H 2 were previously published and were performed using the same LJ parameters [59]. The second tests consisted on the comparison of the input pressure and the pressure calculated in the GCMC simulations at 298.15 K. The input pressures were in the range 0.5e25 MPa for hydrogen and in the range 0.5e35 MPa for methane. The calculated pressure, P calc , was computed by means of [60,61]: Pcalc ¼NkBT V2pN2 3V2Z ∞ 0 r3UðrÞgðrÞdr;(3) where N,Tand Vare the average number of H 2 or CH 4 molecules, the temperature and the volume of the simulation box, respectively. k B is the Boltzmann constant, U(r) is the LJ interaction potential between the molecules and g(r) is the pair distribution function. That function was calculated from the positions of the molecules obtained in 50,000 configurations on each simulation. The comparisons of the input and calculated pressures for hydrogen and methane are plotted in Fig. 2. There is a good agreement between these two pressures for both gases. Definitions of the storage capacities The total (hydrogen or methane) volumetric and gravimetric storage capacities have been calculated in the GCMC simulations, according to the following definitions. The total (hydrogen or methane) volumetric storage capacity, v c , also called the density of stored (hydrogen or methane), is defined by vc¼Mg V;(4) where Vis the volume of the simulation cell and M g is the mass of gas (hydrogen or methane) stored in the simulation cell. Throughout this paper, v c is calculated in kg of gas (H 2 or CH 4 )/L units. The other storage capacity obtained in the simulations is the total (hydrogen or methane) gravimetric storage capacity, g c , which is defined by gc¼100Mg MgþMads ;(5) where M ads is the mass of the adsorbent solid porous material of the simulation cell. According to this definition, the total gravimetric capacity is calculated in wt. % units. The definition of the useable (hydrogen or methane) storage capacities is related to the total storage capacities. The useable mass of gas (hydrogen or methane) stored at a given pressure Pand temperature Tis the difference between the Table 1 eParameters of the SRK equation of state of hydrogen and methane: u,P c in MPa and T c in K. Gas uP c T c Source H 2 0.216 1.28 33.2 [40] CH 4 0.01142 4.5992 190.56 [41] international journal of hydrogen energy 50 (2024) 160e177162 total mass of gas stored at that Pand Tand the total mass of gas stored at the depletion (also called minimum or back) pressure and T[3,62e64]. The useable (hydrogen or methane) volumetric and gravimetric capacities are calculated inserting in Eqs. (4) and (5) the useable mass of gas stored. Throughout this paper, the focus will solely be on total and useable storage capacities. Simulation cells of the BUTs The simulation cells of the new BUTs (See Fig. 3) were obtained from the data in Crystallographic Information File (CIF) format reported by Kong et al. [37]. These CIF files were retrieved from the Cambridge Crystallographic Data Centre, CCDC [65]. There are eleven new BUTs: BUT-101(Zn), BUT- Table 2 eLJ parameters of the atoms and molecules used in the GCMC simulations. sis in  A and εin eV. sεSource sεSource B 3.453 0.004116 [47]H 2 2.970 0.002870 [45] C 3.400 0.003744 [48] In 2.810 0.052290 [49] Cd 2.700 0.000259 [50] Mn 2.587 0.047219 [51] Cu 2.297 0.520310 [52] N 3.310 0.003214 [53] CH 4 3.730 0.012748 [54] O 3.033 0.004150 [55] Hf 2.798 0.003122 [56] Zn 0.998 0.008291 [57] H 2.846 0.000659 [55] Zr 2.910 0.735981 [58] CeH 2 3.190 0.002628 [45] Fig. 1 eSRK EOS density and GCMC density vs pressure obtained in the simulations of one and ten million of iterations of pure H 2 (left panel) and CH 4 (right panel) vs pressure at 298.15 K. Fig. 2 eGCMC calculated pressure vs the ‘experimental’ or input pressure, obtained in the simulations of one and ten million of iterations of H 2 (left panel) and CH 4 (right panel) at 298.15 K. international journal of hydrogen energy 50 (2024) 160e177 163 101(Cu), BUT-102, BUT-103, BUT-104, BUT-105, BUT-106, BUT- 107, BUT-108(Hf), BUT-108(Zr) and BUT-109(Zr). The CCDC numbers of this group of BUTs are 1888829e1888839. The volume of the simulation cells of these eleven BUTs is in the range 9300e28000  A 3 , except the volume of the BUT-105 cell, which is much larger, about 108,000  A 3 . Calculation of the porosity The porosity is calculated as the ratio of the available volume and the volume of the simulation cell of a MOF. It is a dimensionless magnitude. The available volume to a gas molecule is the difference between the volume of the simulation cell, V, and the volume occupied by the atoms of the MOF, V occ . The volume V occ is calculated approximately as follows: A grid of npoints contained in the simulation cell is created. ni is the number of grid points that are inside the sphere of some atom of the simulation cell. The volume V occ is given by the Vni/n. The volume of the sphere of an atom is given by 4pr 3 /3, where ris the radius of the atom and is equal to s(atom, molecule). The LJ interaction potential energy is zero at an atom-molecule distance equal to s(atom, molecule). Due to this definition of the radius of an atom interacting with a molecule, the volume occupied by the atoms, the available volume and the porosity depend on the type of gas molecule. The porosity measured in the experiments also depends on the type of gas. Calculation of the pore size The BUTs were analyzed using an algorithm to determine the presence of pores with a radius equal to or greater than 3  A. Pores with a smaller radius cannot accommodate hydrogen and methane molecules. The algorithm begins by generating a three-dimensional grid of points within the BUT cell. The grid points are spaced at a distance of 1.0  A. In the next step, for each grid point i, the algorithm calculates the distance d ij from point ito each atom jin the cell. The minimum distance, denoted as dmin(i), is then determined for each grid point. This process is repeated for all grid points i. In the third step, the algorithm calculates the pore radius as follows: the largest value among all dmin(i) is considered the radius of a pore, with the corresponding grid point iserving as the center of the pore. The set of dmin(i) values is then recalculated. The grid points contained within this new pore are treated as ‘atoms’ within the BUT structure, and the second step is repeated to obtain a new set of dmin(i) values. This process continues until the largest value among all dmin(i) values is smaller than 3  A. The algorithm yields a collection of pore radii, along with the average pore radius. The initial pore radius obtained using this algorithm corresponds to the largest pore radius found. It is important to note that the spherical pores obtained using this algorithm do not overlap. Results and discussion GCMC hydrogen storage capacities of BUTs Hydrogen storage capacities vs porosity, density and pore size The useable capacities of the eleven novel BUTs obtained in the GCMC simulations at 298.15 K and 25 MPa are tabulated in Table 3 and plotted in Fig. 4, as functions of the porosity, density and largest pore radius of the BUTs. Eight of the new BUTs have volumetric capacities in the range of 0.011e0.016 kg/L and gravimetric capacities above 1 wt % at 298.15 K and 25 MPa (See Table 3). The remaining three BUTs (102, 103 and 106) have volumetric capacities below 0.008 kg/L and gravimetric capacities below 0.5 wt %. BUT- 104, 105 and 107 have the largest storage capacities. These three BUTs have been selected to make more simulations and further analysis in another subsection. The analysis of the dependence on those variables shows that there are approximate correlations between the storage capacities and the porosity and density: a) The smaller the density, the larger the storage capacities, b) The larger the porosity, the larger the storage capacities, and c) The BUTs with the highest capacities have porosities above 0.4 and densities smaller than 0.6 kg/L. These are approximate correlations, because not all the capacities of the BUTs follow exactly these correlations. Fig. 3 eSimulation cell of BUT-104 (left panel) and BUT-107 (right panel). Oxygen, nitrogen, carbon, hydrogen, zirconium and indium atoms are represented by blue, red, gray, yellow, green and orange balls, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) international journal of hydrogen energy 50 (2024) 160e177164 Another important structural factor of the BUTs is the pore size. The largest and average pore radius of the BUTs have been calculated. The dependence of the useable v c and g c on the largest and average pore radius can be noticed in Fig. 5. The volumetric capacity increases rapidly as the (largest or average) radius Rincreases and then reaches a constant value. Wide pores can not contain or store more gas molecules and this explains the trend towards a constant value. In contrast, the gravimetric capacity increases linearly with the (largest or average) radius R,iftheg c corresponding to BUT-107, which is an outlier, is not considered. The gravimetric capacity of BUT-107 is very high due to its low density, 0.286 kg/L (See Table 3). That linear increase can be explained as follows: As the pore radius increases, the BUTs are, in general, lighter and hence, the gravimetric capacity increases. Table 3 eUseable hydrogen storage capacities and isosteric heat at room temperature and 25 MPa of the new BUTs. The porosity is dimensionless. The density, the largest pore radius, the average pore radius, the isosteric heat, v c and g c are in kg/L,  A,  A, eV, kg of H 2 /L and wt. %, respectively. Rstands for pore radius. BUT porosity density largest R average R Q st v c g c 101(Cu) 0.214 0.967 6.95 6.82 0.072 0.0138 1.41 101(Zn) 0.207 0.995 6.74 6.55 0.066 0.0114 1.13 102 0.106 1.592 4.73 3.92 0.067 0.0078 0.49 103 0.025 1.299 4.15 3.46 0.076 0.0035 0.27 104 0.416 0.596 7.57 7.44 0.051 0.0159 2.60 105 0.539 0.496 12.66 7.35 0.039 0.0139 2.73 106 0.061 1.323 4.39 3.71 0.066 0.0066 0.49 107 0.680 0.286 8.80 6.89 0.038 0.0161 5.32 108(Hf) 0.308 1.250 6.84 4.40 0.055 0.0129 1.02 108(Zr) 0.310 0.966 6.88 4.81 0.063 0.0155 1.58 109(Zr) 0.328 0.859 8.43 7.74 0.059 0.0135 1.55 Fig. 4 eUseable hydrogen volumetric and gravimetric capacities of BUTs at room temperature and 25 MPa vs their porosities (upper panels) and densities (lower panels). international journal of hydrogen energy 50 (2024) 160e177 165 Isosteric heat of hydrogen adsorption The isosteric heat, Q st , of hydrogen adsorption of MOFs at room temperature is usually in the range 0.04e0.07 eV [33] (See Table 4). Recently, a research group measured the isosteric heat of hydrogen adsorption of a Vanadium-based MOF and obtained a value of 0.217 ±0.002 eV [66]. The highest isosteric heat among the MOFs corresponds to Cu I -MFU-4L (Multi-Functionalized): 0.33 eV [67]. These isosteric heats can be compared with those of activated carbons, which have hydrogen isosteric heats at room temperature in the range of 0.06e0.11 eV (See Table 4). Different theoretical approaches [68e70] showed that the isosteric heat of adsorption should be about 0.1e0.3 eV in order to reach the DOE hydrogen storage targets and a reversible storage at room temperature and moderate pressures. Bae and Snurr [71] studied eight MOFs at 298 K and pressures between 0.15 and 12 MPa and found that the optimal isosteric heat was between 0.19 and 0.23 eV. The isosteric heat of hydrogen adsorption of the novel BUTs obtained in the present GCMC simulations at 298.15 K and 25 MPa lies in the range 0.038e0.076 eV (See Tables 3 and 4), within the usual range of values for MOFs, and smaller than the isosteric heats of zeolites. According to the mentioned theoretical approaches, these values seem to be low and below the estimated isosteric heat necessary to reach the DOE hydrogen targets. However, according to the GCMC simulations, the storage capacities of some BUTs are relatively high, even close to some DOE 2025 target. The mentioned theoretical approaches indicate that the lower the isosteric heat, the lower the capacities. A plot of the useable hydrogen capacities of all the novel BUTs vs the isosteric heat at 298.15 and 25 MPa in Fig. 6 shows that there is not a clear correlation between the useable hydrogen v c and the isosteric heat. The useable g c seems to decrease as the isosteric heat increases. BUT-107 has the highest useable v c and g c , 0.016 kg/L and 5.32 wt %, respectively, and also has the lowest isosteric heat, 0.038 eV, among the novel BUTs at 298.15 and 25 MPa. These GCMC results do not coincide with the theoretical approaches. Some authors have argued that, besides of a large isosteric heat, a large porosity, especially at pressures larger than approximately 5e7 MPa, is also necessary to Fig. 5 eUseable hydrogen volumetric and gravimetric capacities of BUTs at room temperature and 25 MPa vs their largest pore radius (upper panels) and average pore radius (lower panels). Table 4 eHydrogen isosteric heat (in eV) of several solid porous materials. Temperature is in K. Material Q st Temperature Source Zeolites 0.21e0.83 279e323 [72,73] Activated carbons 0.06e0.11 298.15 [74,75] MOFs 0.04e0.33 298e300 [33,66,67] BUTs 0.038e0.076 298.15 Present work international journal of hydrogen energy 50 (2024) 160e177166 reach the DOE hydrogen targets [30]. Frost and Snurr showed that MOFs with larger porosities provide, in general, lower isosteric heats [76]. That general correlation also exists in BUTs: BUT-104, 105 and 107 have the highest storage capacities, the highest porosities and the lowest isosteric heats (See Table 3). In order to understand the storage capacities, the isosteric heat and the porosity must be considered. The storage capacities have been plotted as a function of the product of the isosteric heat and the porosity at 298.15 K and 25 MPa in Fig. 6. The v c is approximately correlated with that product: The volumetric capacity increases as the product increases, in general. The g c also increases, in general, with the product, although the correlation is less clear than in the case of the volumetric capacity. These results indicate that both, the isosteric heat and the porosity, play a role in the storage capacities. The useable hydrogen gravimetric capacity has a much better correlation with Q st if the density of the adsorbent material, r ads , is also considered as follows. The gravimetric capacity is given by Eq. (5). The mass of the adsorbent material is equal to r ads V, where Vis the volume of the cell containing the material. The mass of gas is given by v c V. Therefore, Eq. (5) can be also written as gc¼100vc vcþrads :(6) The useable hydrogen volumetric capacity is much smaller than r ads and hence, Eq. (6) can be approximated by gcz100vc rads :(7) According to Eq. (7) g c is inversely proportional to the density of the adsorbent material. Therefore, it makes sense to analyze g c as a function of Q st /r ads and Q st /r ads Porosity. Fig. 7 contains the plots of g c vs those two variables. The g c is approximately proportional to Q st /r ads , but there is not a clear correlation at low values of Q st /r ads . On the other hand, there is a very good correlation between g c and the product of porosity and Q st /r ads , much better than between g c and Q st /r ads (Compare Figs. 6 and 7). The dependence of the isosteric heat of the BUTs on the largest and average pore radius is plotted in Fig. 8. It can be noticed in that figure that the isosteric heat has not a clear dependence on the average pore radius: All the isosteric heat points are concentrated in a short region of the isosteric heataverage pore radius plot. On the other hand, there is a dependence on the largest pore radius: The isosteric heat, in Fig. 6 eUseable hydrogen volumetric and gravimetric capacities vs isosteric heat (upper panels) and vs isosteric heat multiplied by porosity (lower panels) at room temperature and 25 MPa of the novel BUTs. international journal of hydrogen energy 50 (2024) 160e177 167 general, decreases linearly as the largest pore radius increases. Hydrogen storage capacities vs pressure The total and useable storage capacities at 298.15 K of the three selected BUTs (104, 105 and 107) are plotted in Fig. 9, respectively, as a function of the pressure between 0.5 and 50 MPa. These are the so-called isotherms and can be compared with experiments and theoretical results (See Table 5). The total hydrogen volumetric storage capacities of carbon slit pores and nanotubes of pore width or diameter of 7e15  A are between 0.016 and 0.022 kg/L at 25 MPa and 298.15 K, according to previous GCMC simulations [59]. The total hydrogen volumetric capacities of the three BUTs at 25 MPa and 298.15 K are between 0.0142 and 0.0166 kg/L, slightly lower than the total volumetric capacities of the above-mentioned carbon nanostructures. Rzepka et al. [45] obtained in GCMC simulations of carbon-based slit pores a volumetric capacity of 0.0235 kg/L at 30 MPa and 300 K for a pore width of 7  A. The total volumetric capacities of the three BUTs at 298.15 K and 30 MPa are between 0.0165 and 0.0192 kg/L. Hence, these BUTs have slightly lower volumetric capacities than carbon-based slit pores. Kunowsky et al. made hydrogen storage experiments of a large range of KOH activated carbon fibres (ACFs) and obtained that the maximum total volumetric capacity of the ACFs at 298 K and 20 MPa was 0.0171 kg/L [77]. At 298.15 K and 20 MPa, the total hydrogen volumetric capacities of the three BUTs are between 0.012 and 0.014 kg/L, about a 20e30% smaller than the total volumetric capacities of ACFs. The volumetric capacities of MOFs at room temperature and 5e10 MPa are between 0.0005 and 0.0150 kg/L [30]. The volumetric capacities of the three BUTs at 298.15 K and 10 MPa are between and 0.0066 and 0.0080 kg/L, within the above-mentioned range of values. The useable hydrogen volumetric storage capacities of these three BUTs at 298.15 K and 25e35 MPa are high and between 0.014 and 0.021 kg/L. At 50 MPa and 298.15 K, the useable hydrogen volumetric capacities of the three BUTs are between 0.023 and 0.027 kg/L, close to the DOE 2020 target, 0.030 kg/L, but they are about a 30e60% below the DOE 2025 target, 0.040 kg/L. As regards gravimetric capacities, the total gravimetric capacities of the BUTs 104, 105 and 107 are 2.70, 2.78 and Fig. 7 eUseable hydrogen gravimetric capacities vs Q st /r ads vs Q st /r ads multiplied by porosity at room temperature and 25 MPa of the novel BUTs. Fig. 8 eHydrogen isosteric heat (in eV) at 25 MPa and 298.15 K vs the average and largest pore radius (in  A) of the novel BUTs. international journal of hydrogen energy 50 (2024) 160e177168 result is that the useable hydrogen gravimetric capacity of BUT-107 reaches the DOE 2025 target at 27 MPa. As regards methane storage capacities, the useable methane gravimetric and volumetric capacities of BUT-104 and 105 at 25e35 MPa are about 25 wt % and 0.16e0.21 kg/L, close to the respective DOE methane targets, 33.33 wt % and 0.25 kg/L. The useable methane gravimetric and volumetric capacities of BUT-107 are 44 wt % and 0.23 kg/L at 35 MPa, respectively. According to the present simulations, BUT-107 reaches the two DOE methane targets at room temperature and 50 MPa and hence, this is a not expensive and suitable adsorbent material for adsorbed natural gas vehicles. To enhance the hydrogen and methane storage capacities of these materials, one promising approach is the doping of Li and/or other light metals. These dopants have the ability to interact stronger with hydrogen and methane molecules, leading to enhanced adsorption and storage. Through careful selection and optimization of the doping process, the storage capacities of these materials can be effectively enhanced, opening up new possibilities for advanced gas storage applications. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was founded by a research project from the Spain Ministry of Science, Innovation and Universities (MICINN) (Grant PGC2018-093745-B-I00), Junta de Castilla y Le on (Grant VA124G18) and the University of Valladolid, Spain. The use of the computer facilities of Centro de Proceso de Datos - Parque Cientı´fico of the University of Valladolid is acknowledged. references [1] News European Parliament. 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