Modeling adsorption in microporous carbons: Bridging methods and crossing boundaries between applications
Microporous carbons are an important class of materials, present as natural or artificial compounds in many industrial and technological applications including hydrocarbon recovery, gas storage, water purification and energy storage. In all these applications knowing the structure of the carbon, both in the pristine state and under operation, usually involving adsorption/desorption of species, is key to understanding and predicting the performance of the process. The accurate characterisation of microporous carbons and their evolution upon adsorption/desorption presents a number of challenges associated with the disordered nature of these materials and the multiphysics, and often multi-scale, character of the processes at play. In this context, simulations can provide valuable insights. The modelling process involves i) the generation of carbon structure models, ii) the simulation of adsorption and iii) the determination of relevant properties; all of these steps raising specific challenges.
Common ways to characterise porous carbons include gas adsorption and X-ray diffraction. Adsorption isotherms measured using small molecules such as argon, nitrogen or carbon dioxide, are usually exploited to determine the pore size distributions of the porous materials. A common approach to do so is to decompose the experimentally measured isotherm into a set of partial isotherms which requires a number of assumptions related, for example, to the adsorption process (e.g. that the pore surface is completely wetted by the liquid) or to the shape of the pores (e.g. cylindrical in the case of the Barrett-Joyner-Halenda approach  or slit shaped in the case of the Non Local Density Functional Theory ). While these assumptions lead to relatively crude models, with in particular no consideration of the interconnectivity between pores, recent comparisons of the pore size distributions obtained with such methods to data derived from Small Angle X-ray Scattering  and average pore sizes determined by Nuclear Magnetic Resonance (NMR)  strengthens the confidence in this type of porosity characterisation.
The mesoscale picture provided by pore size distributions remains insufficient to model a number of phenomena as adsorbate-adsorbent interactions at the atomistic scale can affect macroscopic properties significantly. As a consequence, atomistic models of microporous carbons are invaluable to get insight into experimental results and molecular mechanisms. Early attempts to generate atomistic models commonly involved Reverse Monte Carlo (RMC) approaches. This approach aims to reconstruct the atomic coordinates of the porous carbon with input from experiments such as pair distribution functions (i.e. histograms of atom to atom distances showing the likelihood of finding an atom pair separated by a certain distance) . To improve the models, interaction potentials between carbon atoms were introduced in the so-called “hybrid RMC” approach [6-7].
In recent years, atomistic carbon models generated without any input from experimental data have become more common. These can be produced, for example, through quench molecular dynamics [8-10], zeolite templating using grand canonical Monte Carlo simulations (GCMC)  or annealing of disordered precursors [12-14]. Mimetic approaches aiming at simulating the formation of the material using accelerated MD techniques also emerged as a promising alternative [15-16]. Advances in interaction potentials , including machine learning based force fields , are crucial in making a range of atomistic structures available, corresponding to carbons synthesised using various conditions, and opening new avenues of research. Assessing the quality of these structures still remains a challenge as many experimental techniques do not provide sufficiently resolved information to discriminate between models. Combination of experimental techniques, sensitive to different characteristics of the porous carbon materials, and associated with adequate theoretical studies can be useful in that regard . Techniques such as electron energy-loss spectroscopy to determine relative sp2/sp3 content [20-21], Raman spectroscopy which provides a measure of disorder in the carbon bonding network  and 13C NMR and XPS, sensitive to different hybridization states and the presence of hydrogen  as well as other heteroelements and surface groups, are valuable tools to get insight into the carbon microstructure.
Once suitable atomistic models have been generated, additional challenges come with the simulation of adsorption processes. Reactive force fields used to generate atomistic carbon models usually represent Van der Waals and electrostatic interactions inaccurately and are thus inadequate to model adsorption. Beyond the necessity to develop suitable carbon-adsorbate interactions, including additional effects such as the flexibility of the porous material can be complex but crucial and requires to go beyond the traditional GCMC calculations under frozen matrix approximation. In the case of hydrocarbon recovery from shale organic matter, e.g. kerogen, the effect of poromechanics, which was neglected for a long time in simulations, has been shown to have a significant impact on the adsorption isotherms . In the case of gas adsorption, small micropores were shown to contribute significantly to the adsorption stress across a large range of pressures . In that study, the pore size distribution, derived from a simultaneous analysis of the adsorption and strain isotherms obtained with CO2, was used to predict strain isotherms for N2 and Ar showing good agreement with experimental data. This demonstrates once again the advantage of combining techniques to interpret experiments.
Adsorption-induced deformations, coupled with changes in electronic structure, are also observed in carbon-based supercapacitors using electrochemical dilatometry experiments [26-27]. Such deformations are believed to affect the quantity of energy which can be stored in such electrochemical energy storage systems but, to-date, computational tools which include both carbon flexibility and response to an applied potential difference (to study charging/discharging mechanisms) are not available. The emergence of applications involving multiple species and processes, such as electrochemical CO2 capture [28-29], are an additional incentive to develop such approaches.
Once adsorption properties are known, elucidation of transport properties is the key step to assess the efficiency of the processes in time. In the continuity of the studies of adsorption, both equilibrium and out-of-equilibrium Molecular Dynamics (MD) studies have been performed highlighting the purely diffusive nature of transport in kerogen due to the ultraconfining nature of their amorphous microporosities [30-32]. Also, MD simulations of carbide-derived microporous carbons have shown that the disordered topology of such systems has a crucial impact on the diffusion of adsorbed species . However, these studies consider the carbon structures to be rigid, thus neglecting the poromechanics. Couplings between the dynamics of the carbon microstructure and the fluid diffusion have been investigated by MD for an immature kerogen showing that those couplings are increasingly important as the amount of adsorbed fluid decreases for a viscoelastic carbon exhibiting significant adsorption-induced swelling . The effects and the importance of the viscoelasticity of microporous carbons on the transport properties yet remain to be investigated.
In addition to the improvement of atomistic models for porous carbons and their evolution during adsorption processes, a number of methods have been proposed recently to bridge the gap between molecular and macroscopic scales. These new approaches can allow one to move away from a representation of pore using simple geometries to understand diffusion in disordered systems  or to predict NMR spectra of carbon particles with realistic pore size distributions .
 E.P. Barrett, L.G. Joyner, P.P. Halenda, J. Am. Chem. Soc. 73, 373-380 (1951)
 R.J. Dombrowski, D.R. Hyduke, C.M. Lastoskie, Langmuir 16, 5041-5050 (2000)
 C. Prehal, S. Grätz, B. Krüner, M. Thommes, L. Borchardt, V. Presser and O. Paris, Carbon, 152, 416-423 (2019)
 L. Cervini, O.D. Lynes, G.R. Akien, A. Kerridge, N.S. Barrow, J. M. Griffin, Energy Storage Mater., 21, 335-346 (2019)
 T. Petersen, I. Yarovsky, I. Snook, D.G. McCulloch and G. Opletal, Carbon, 42, 2457-2469 (2004)
 A.H. Farmahini and S.K. Bhatia, Carbon, 83, 53–70 (2015)
 S.K. Bhatia, Langmuir, 33, 831-847 (2017)
 J.C. Palmer, A. Llobet, S.-H. Yeon, J.E. Fischer, Y. Shi, Y. Gogotsi, K.E. Gubbins, Carbon, 2010, 48, 1116-1123.
 S. Schweizer, R. Meissner, M. Amkreutz, K. Thiel, P. Schiffels, J. Landwehr, B.J.M. Etzold and J.-R. Hill, J. Phys. Chem. C, 121, 7221-7231 (2017)
 L.M. Mejía-Mendoza, M. Valdez-Gonzalez, J. Muñiz, U. Santiago, A.K. Cuentas-Gallegos and M. Robles, Carbon, 120, 233-243 (2017)
 T. Roussel, A. Didion, R.J.M. Pellenq, R. Gadiou, C. Bichara, C. Vix-Guterl, J. Phys. Chem. C 2007, 111, 15863-15876 (2007)
 R.C. Powles, N.A. Marks and D.W.M. Lau, Phys. Rev. B: Condens. Matter Mater. Phys., 79, 75430 (2009)
 R. Ranganathan, S. Rokkam, T. Desai, P. Keblinski, Carbon, 113, 87-99 (2007)
 C. de Tomas, I. Suarez-Martinez, F. Vallejos-Burgos, M. J. López,
K. Kaneko, N. A. Marks, Carbon, 119, 1-9 (2017)
 L. Atmani, C. Bichara, R. J.-M. Pellenq, H. Van Damme, A. C. T. van Duin, Z. Raza, L. A. Truflandier, A. Obliger, P. G. Kralert, F. J. Ulm, J.-M. Leyssale, Chem. Sci. 8, 8325-8335 (2017)
 L. Atmani, P.-L. Valdenaire, R. J.-M. Pellenq, C. Bichara, H. Van Damme, A. C. T. van Duin, F. J. Ulm, J.-M. Leyssale, Energy Fuels 34, 1537-1547 (2020).
 C. de Tomas, I. Suarez-Martinez, N.A. Marks, Carbon, 109, 681-693 (2016)
 V.L. Deringer, G. Csányi, Phys. Rev. B., 95, 094203 (2017)
 A.C. Forse, C. Merlet, P.K. Allan, E.K. Humphreys, J.M. Griffin, M. Aslan, M. Zeiger, V. Presser, Y. Gogotsi, C.P. Grey, Chem. Mater., 27, 6848-6857 (2015)
 S. Urbonaite, S. Wachtmeister, C. Mirguet, E. Coronel, W.Y. Zou, S. Csillag, G. Svensson, Carbon, 45, 2047–2053 (2007)
 J. Schwan, S. Ulrich, H. Roth, H. Ehrhardt, S.R.P. Silva, R. J., et al., J. App. Phys., 79, 1416-1422 (1996)
 A.C. Ferrari, J. Robertson, Phys. Rev. B: Condens. Matter Mater. Phys., 61, 14095-14107 (2000)
 A.R. Ambrozio, J.-M. Leyssale, R. J.-M. Pellenq, F.A.L. de Souza, G.L. Vignoles, W.L. Scopel, and J.C.C. Freitas, J. Phys. Chem. C, 124, 12784-12793 (2020)
 A. Obliger, P.-L. Valdenaire, N. Capit, F.-J. Ulm, R. J-M. Pellenq, J.-M. Leyssale, Langmuir, 34, 13766–13780 (2018)
 C. Balzer, R.T. Cimino, G.Y. Gor, A.V. Neimark, G. Reichenauer, Langmuir, 32, 8265-8274 (2016)
 M.M. Hantel, V. Presser, R. Kötz, Y. Gogotsi, Electrochem. Commun., 13, 1221-1224 (2011)
 M.M. Hantel, D. Weingarth, R. Kötz, Carbon, 69, 275 (2014)
 B. Kokoszka, N.K. Jarrah, C. Liu, D.T. Moore, K. Landskron, Angew. Chem. 126, 3772-3775 (2014)
 S. Zhu, J. Li, A. Toth, K. Landskron, ACS Appl. Mater. Interfaces, 11, 21489-21495 (2019)
 K. Falk, R. J-M. Pellenq, F.-J. Ulm, L. Bocquet, Nat. Comm., 6, 6949 (2015)
 A. Obliger, R. J-M. Pellenq, F.-J. Ulm, B. Coasne, J. Phys. Chem. Lett., 7, 3712–3717 (2016)
 M. Vasileiadis, L.D. Peristeras, K.D. Papavasileiou, I.G. Economou, J. Phys. Chem. C, 122, 11, 6166–6177, (2018)
 A. Shahtalebi, P. Shukla, A.H. Farmahini, S.K. Bhatia, Carbon, 88, 1–15 (2015)
 A. Obliger, P.-L. Valdenaire, F.-J. Ulm, R. J-M. Pellenq, J.-M. Leyssale, J. Phys. Chem. B, 123, 5635-5640 (2019)
 C. Bousige, P. Levitz, B. Coasne, Nature Commun., 12, 1043 (2021)
 C. Merlet, A.C. Forse, J.M. Griffin, D. Frenkel, and C.P. Grey, J. Chem. Phys. 142, 094701 (2015)
Jean-Marc Leyssale (CNRS, Université de Bordeaux) - Organiser
Celine Merlet (CNRS - Université Paul Sabatier) - Organiser
Amaël Obliger (CNRS, Université de Bordeaux) - Organiser
Alexander Forse (University of Cambridge) - Organiser
Carla de Tomas (Happy Electron Ltd.) - Organiser
Gennady Gor (New Jersey Institute of technology) - Organiser