We present a thermodynamic model of adsorption-induced deformation of microporous carbons. The model represents the carbon structure as a macroscopically isotropic disordered three-dimensional medium composed of stacks of slit-shaped pores of different sizes embedded in an incompressible amorphous matrix. Adsorption stress in pores is calculated by means of Monte Carlo simulations. The proposed model reproduces qualitatively the experimental nonmonotonic dilatometric deformation curve for argon adsorption on carbide-derived activated carbon at 243 K and pressure up to 1.2 MPa. The elastic deformation (contraction at low pressures and swelling at higher pressures) results from the adsorption stress that depends strongly on the pore size. The pore size distribution determines the shape of the deformation curve, whereas the bulk modulus controls the extent of the sample deformation.

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Grand canonical Monte Carlo (GCMC) simulations were used for the modeling of the hydrogen adsorption in idealized graphite slitlike pores. In all simulations, quantum effects were included through the Feynman and Hibbs second-order effective potential. The simulated surface excess isotherms of hydrogen were used for the determination of the total hydrogen storage, density of hydrogen in graphite slitlike pores, distribution of pore sizes and volumes, enthalpy of adsorption per mole, total surface area, total pore volume, and average pore size of pitch-based activated carbon fibers. Combining experimental results with simulations reveals that the density of hydrogen in graphite slitlike pores at 303 K does not exceed 0.014 g/cm(3), that is, 21% of the liquid-hydrogen density at the triple point. The optimal pore size for the storage of hydrogen at 303 K in the considered pore geometry depends on the pressure of storage. For lower storage pressures, p < 30MPa, the optimal pore width is equal to a 2.2 collision diameter of hydrogen (i.e., 0.65 nm), whereas, for p congruent with 50MPa, the pore width is equal to an approximately 7.2 collision diameter of hydrogen (i.e., 2.13 nm). For the wider pores, that is, the pore width exceeds a 7.2 collision diameter of hydrogen, the surface excess of hydrogen adsorption is constant. The importance of quantum effects is recognized in narrow graphite slitlike pores in the whole range of the hydrogen pressure as well as in wider ones at high pressures of bulk hydrogen. The enthalpies of adsorption per mole for the considered carbonaceous materials are practically constant with hydrogen loading and vary within the narrow range q(st) congruent with 7.28-7.85 kJ/mol. Our systematic study of hydrogen adsorption at 303 K in graphite slitlike pores gives deep insight into the timely problem of hydrogen storage as the most promising source of clean energy. The calculated maximum storage of hydrogen is equal to approximately 1.4 wt %, which is far from the United States Department of Energy (DOE) target (i.e., 6.5 wt %), thus concluding that the total storage amount of hydrogen obtained at 303 K in graphite slitlike pores of carbon fibers is not sufficient yet.

We investigate possible usage of single-walled carbon nanotubes (SWNTs) as an efficient storage and separation device of hydrogen−methane mixtures at room temperature. The study has been done using Grand Canonical Monte Carlo simulations for modeling storage and separation of hydrogen−methane mixtures in idealized SWNTs bundles. These mixtures have been studied at several pressures, up to 12 MPa. We have found that the values of the stored volumetric energy and equilibrium selectivity greatly depend on the chiral vector (i.e., pore diameter) of the nanotubes. The bundle formed by [5,4] SWNTs (nanotube diameter of 6.2 Å) can be regarded as a threshold value. Below that value the densification of hydrogen or methane is negligible. Bundles with wider nanotube diameter (i.e., 12.2, 13.6, 24.4 Å) seem to be promising nanomaterials for hydrogen−methane storage and separation at 293 K. SWNTs with pore diameters greater than 24.4 Å (i.e., [18,18]) are less efficient for both on-board vehicle energy storage and separation of hydrogen−methane mixture at 293 K with pressures up to 12 MPa. SWNTs comprised of cylindrical pores of 8.2 and 6.8 Å in diameter (equivalent chiral vector [6,6] and [5,5], respectively) are the most promising for separation of the hydrogen−methane mixture at room temperature, with the former selectively adsorbing methane and the latter selectively adsorbing hydrogen. We observed that inside the pores of [6,6] nanotubes absorbed methane forms a quasi-one-dimensional crystal when the system has thermalized. The average intermolecular distance of such a crystal is smaller than the one of liquid methane in bulk at 111.5 K, therefore exhibiting the quasi-one-dimensional system clear compression characteristics. On the other hand, for a smaller nanotube diameter of 6.8 Å the hydrogen can enter into the tubes and methane remaining in bulk. We found that in the interior of [5,5] nanotubes adsorbed/compressed hydrogen forms a quasi-one-dimensional crystal.

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Applying the thermodynamic model of adsorption-induced deformation of microporous carbons developed recently (Kowalczyk, P.; Ciach, A.; Neimark, A. Langmuir 2008, 24, 6603), we study the deformation of carbonaceous amorphous porous materials due to adsorption of carbon dioxide at 333 K and pressures up to 27 MPa. The internal adsorption stress induced by adsorbed/compressed carbon dioxide is very high in the smallest ultramicropores (for instance, solvation pressure in 0.23 nm ultramicropore reaches 3.2 GPa at 27 MPa). Model calculations show that any sample of carbonaceous porous solid containing a fraction of the smallest ultramicropores with pore size below 0.31 nm will expand at studied operating conditions. This is because the high internal adsorption stress in ultramicropores dominates sample deformation upon adsorption of carbon dioxide at studied operation conditions. Interestingly, the nonmonotonic deformation (i.e., initial contraction and further expansion) of the above mentioned porous materials upon adsorption of carbon dioxide at 333 K is also theoretically predicted. Our calculations reproduce quantitatively the strain isotherm of carbon dioxide on carbide-derived activated carbon at 333 K and experimental pressures up to 2.9 MPa. Moreover, we extrapolate adsorption and strain isotherms measured by the gravimetric/dilatometric method up to 27 MPa to mimic geosequestration operating conditions. And so, we predict that expansion of the studied carbon sample reaches 0.75% at 27 MPa and 333 K. Presented simulation results can be useful for the interpretation of the coal deformation upon sequestration of carbon dioxide at high pressures and temperatures.

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than approximately 4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

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