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On the computer simulations of carbon nanoparticles porosity: statistical mechanics model for CO2 and N2 adsorption isotherms

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Abstract

A new approach model was developed for the pore size characterization of carbon porous materials, using adsorption gases. The experimental adsorption isotherms of CO2 and N2 onto carbon nanoparticles were used to test the validity of such model. The Trimodal-Gauss-Monolayer model has been found to adjust well the experimental data of CO2 sorption at 273 K and has allowed detect the ultra-micropores till 0.7 nm. For the mesopores and macropores, it has been concluded that the N2 sorption isotherms at 77 K are suitable to characterize this kind of porosity. These isotherms have been well fitted with the Gauss-Monolayer/Gauss-Finite Multilayer model derived from the same approach. Thereby, the novel method can be used as a generalized technique for the simulation of type IVa isotherms. Indeed, this novel method agreed with other methods, NLDFT, QSDFT, and VBS available for pore size distribution.

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References

  • Barrera, D., Villarroel-Rocha, J., Marenco, L., Oliva, M., Sapag, K.: Non-hydrothermal synthesis of cylindrical mesoporous materials: influence of the surfactant/silica molar ratio. Adsorpt. Sci. Technol. 29, 975–988 (2011)

    Article  CAS  Google Scholar 

  • Barrett, E.P., Joyner, L.G., Halenda, P.P.: The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms. J. Am. Chem. Soc. 73, 373–380 (1951)

    Article  CAS  Google Scholar 

  • Barroso-Bujans, F., Palomino, P., Fernandez-Alonso, F., Rudić, S., Alegría, A., Colmenero, J., Enciso, E.: Intercalation and confinement of poly (ethylene oxide) in porous carbon nanoparticles with controlled morphologies. Macromolecules 47, 8729–8737 (2014)

    Article  CAS  Google Scholar 

  • Bergaoui, M., Khalfaoui, M., Villarroel-Rocha, J., Barrera, D., Al-Muhtaseb, S., Enciso, E., Sapag, K., Ben Lamine, A.: New insights on estimating pore size distribution of latex particles: statistical mechanics approach and modeling. Microporous Mesoporous Mater. 224, 360–371 (2016)

    Article  CAS  Google Scholar 

  • Chan, L., Cheung, W., Allen, S., McKay, G.: Error analysis of adsorption isotherm models for acid dyes onto bamboo derived activated carbon. Chin. J. Chem. Eng. 20, 535–542 (2012)

    Article  CAS  Google Scholar 

  • Chu, W.C., Chiang, S.F., Li, J.G., Kuo, S.W.: Mesoporous silicas templated by symmetrical multiblock copolymers through evaporation-induced self-assembly. RSC Adv. 4, 784–793 (2014)

    Article  CAS  Google Scholar 

  • Dollimore, D., Heal, G.: Pore-size distribution in typical adsorbent systems. J. Colloid Interface Sci. 33, 508–519 (1970)

    Article  CAS  Google Scholar 

  • Garrido, J., Linares-Solano, A., Martin-Martinez, J., Molina-Sabio, M., Rodriguez-Reinoso, F., Torregrosa, R., Use of nitrogen vs. carbon dioxide in the characterization of activated carbons. Langmuir 3, 76–81 (1987)

    Article  CAS  Google Scholar 

  • Gelb, L.D., Gubbins, K.: Pore size distributions in porous glasses: a computer simulation study. Langmuir 15, 305–308 (1999)

    Article  CAS  Google Scholar 

  • Gregg, S., Sing, K.: Adsorption, Surface Area and Porosity. Academic Press, New York (1982)

    Google Scholar 

  • Grehov, V., Kalnacs, J., Mishnev, A., Kundzins, K.: Nitrogen adsorption on graphene sponges synthesized by annealing a mixture of nickel and carbon powders. Latv. J. Phys. Tech. Sci. 54, 36–48 (2017)

    Google Scholar 

  • Guillet-Nicolas, R., Ahmad, R., Cychosz, K.A., Kleitz, F., Thommes, M.: Insights into the pore structure of KIT-6 and SBA-15 ordered mesoporous silica—recent advances by combining physical adsorption with mercury porosimetry. New J. Chem. 40, 4351–4360 (2016)

    Article  CAS  Google Scholar 

  • Huang, B., Bartholomew, C.H., Woodfield, B.F.: Improved calculations of pore size distribution for relatively large, irregular slit-shaped mesopore structure. Microporous Mesoporous Mater. 184, 112–121 (2014)

    Article  CAS  Google Scholar 

  • Jagiello, J., Olivier, J.P.: 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation. Carbon 55, 70–80 (2013)

    Article  CAS  Google Scholar 

  • Jagiello, J., Thommes, M.: Comparison of DFT characterization methods based on N2, Ar, CO2, and H2 adsorption applied to carbons with various pore size distributions. Carbon 42, 1227–1232 (2004)

    Article  CAS  Google Scholar 

  • Jahandar Lashaki, M., Atkinson, J.D., Hashisho, Z., Phillips, J.H., Anderson, J.E., Nichols, M.: The role of beaded activated carbon’s pore size distribution on heel formation during cyclic adsorption/desorption of organic vapors. J. Hazard. Mater. 315, 42–51 (2016)

    Article  CAS  PubMed  Google Scholar 

  • Joshi, H.C., Kumar, R., Singh, R.K., Lal, D.: Preparation and characterization of molecular sieving carbon by methane and benzene cracking over activated carbon spheres. Carbon Lett. 8, 12–16 (2007)

    Article  Google Scholar 

  • Kakei, K., Ozeki, S., Suzuki, T., Kaneko, K.: Multi-stage micropore filling mechanism of nitrogen on microporous and micrographitic carbons. J. Chem. Soc. Faraday Trans. 86, 371–376 (1990)

    Article  CAS  Google Scholar 

  • Kaneko, K., Suzuki, T., Kakei, K.: Phase transition of nitrogen molecules filled in micropores of micrographitic carbons. Langmuir 5, 879–881 (1989)

    Article  CAS  Google Scholar 

  • Kapoor, A., Yang, R.: Correlation of equilibrium adsorption data of condensible vapours on porous adsorbents. Gas Sep. Purif. 3, 187–192 (1989)

    Article  CAS  Google Scholar 

  • Khalfaoui, M., Knani, S., Hachicha, M., Ben Lamine, A.: New theoretical expressions for the five adsorption type isotherms classified by BET based on statistical physics treatment. J. Colloid Interface Sci. 263, 350–356 (2003)

    Article  CAS  PubMed  Google Scholar 

  • Kruk, M., Jaroniec, M., Sayari, A.: Application of large pore MCM-41 molecular sieves to improve pore size analysis using nitrogen adsorption measurements. Langmuir 13, 6267–6273 (1997)

    Article  CAS  Google Scholar 

  • Landers, J., Gor, G.Y., Neimark, A.V.: Density functional theory methods for characterization of porous materials. Colloids Surf. A 437, 3–32 (2013)

    Article  CAS  Google Scholar 

  • Leo, W.R.: Statistics and the Treatment of Experimental Data, Techniques for Nuclear and Particle Physics Experiments, pp. 81–113. Springer, New York (1994)

    Google Scholar 

  • Li, Z., Jin, Z., Firoozabadi, A.: Phase behavior and adsorption of pure substances and mixtures and characterization in nanopore structures by density functional theory. SPE J. 19, 1096–1109 (2014)

    Article  Google Scholar 

  • Nagaraju, K., Reddy, R., Reddy, N.: A review on protein functionalized carbon nanotubes. J. Appl. Biomater. Funct. Mater. 13, e301–e312 (2015)

    CAS  PubMed  Google Scholar 

  • Nakai, K., Yoshida, M., Sonoda, J., Nakada, Y., Hakuman, M., Naono, H.: High resolution N2 adsorption isotherms by graphitized carbon black and nongraphitized carbon black—αs-curves, adsorption enthalpies and entropies. J. Colloid Interface Sci. 351, 507–514 (2010)

    Article  CAS  PubMed  Google Scholar 

  • Nakhli, A., Khalfaoui, M., Aguir, C., Bergaoui, M., M’henni, M.F., Ben Lamine A.: Statistical physics studies of multilayer adsorption on solid surface: adsorption of basic blue 41 dye onto functionalized Posidonia biomass. Sep. Sci. Technol. 49, 2525–2533 (2014)

    Article  CAS  Google Scholar 

  • Neimark, A.V., Lin, Y., Ravikovitch, P.I., Thommes, M.: Quenched solid density functional theory and pore size analysis of micro-mesoporous carbons. Carbon 47, 1617–1628 (2009)

    Article  CAS  Google Scholar 

  • Nicholson, D.: Simulation of adsorption in model microporous graphite, In: Rodriguez-Reinoso, F., Rouquerol, J., Sing, K.S.W., Unger, K.K. (eds.) Studies in Surface Science and Catalysis, pp. 11–20. Elsevier, Amsterdam (1991)

    Google Scholar 

  • Pekala, R.: Organic aerogels from the polycondensation of resorcinol with formaldehyde. J. Mater. Sci. 24, 3221–3227 (1989)

    Article  CAS  Google Scholar 

  • Pierce, C.: Computation of pore sizes from physical adsorption data. J. Phys. Chem. 57, 149–152 (1953)

    Article  CAS  Google Scholar 

  • Prehal, C., Koczwara, C., Jäckel, N., Amenitsch, H., Presser, V., Paris, O.: A carbon nanopore model to quantify structure and kinetics of ion electrosorption with in situ small angle X-ray scattering. Phys. Chem. Chem. Phys. 19, 15549–15561 (2017)

    Article  CAS  PubMed  Google Scholar 

  • Przepiórski, J., Czyżewski, A., Pietrzak, R., Toyoda, M., Morawski, A.W.: Porous carbon material containing CaO for acidic gas capture: preparation and properties. J. Hazard. Mater. 263, 353–360 (2013)

    Article  PubMed  Google Scholar 

  • Ravikovitch, P.I., Vishnyakov, A., Russo, R., Neimark, A.V.: Unified approach to pore size characterization of microporous carbonaceous materials from N2, Ar, and CO2 adsorption isotherms. Langmuir 16, 2311–2320 (2000)

    Article  CAS  Google Scholar 

  • Reichhardt, N.V., Guillet-Nicolas, R., Thommes, M., Klösgen, B., Nylander, T., Kleitz, F., Alfredsson, V.: Mapping the location of grafted PNIPAAM in mesoporous SBA-15 silica using gas adsorption analysis. Phys. Chem. Chem. Phys. 14, 5651–5661 (2012)

    Article  CAS  PubMed  Google Scholar 

  • Rodriguez-Reinoso, F., Linares-Solano, A.: Chemistry and Physics of Carbon. Marcel Dekker, New York (1988)

    Google Scholar 

  • Rouquerol, F., Rouquerol, J., Sing, K.: Adsorption by Powders and Porous Solids: Principles, Methodology and Applications. Academic Press, London (1999)

    Google Scholar 

  • Rouquerol, J., Rouquerol, F., Llewellyn, P., Maurin, G., Sing, K.S.: Adsorption by Powders and Porous Solids: Principles, Methodology and Applications. Academic Press, San Diego (2013)

    Google Scholar 

  • Seaton, N., Walton, J.: A new analysis method for the determination of the pore size distribution of porous carbons from nitrogen adsorption measurements. Carbon 27, 853–861 (1989)

    Article  CAS  Google Scholar 

  • Seo, M., Kim, S., Oh, J., Kim, S.-J., Hillmyer, M.A.: Hierarchically porous polymers from hyper-cross-linked block polymer precursors. J. Am. Chem. Soc. 137, 600–603 (2015)

    Article  CAS  PubMed  Google Scholar 

  • Sevilla, M., Parra, J.B., Fuertes, A.B.: Assessment of the role of micropore size and N-doping in CO2 capture by porous carbons. ACS Appl. Mater. Interfaces 5, 6360–6368 (2013)

    Article  CAS  PubMed  Google Scholar 

  • Sing, K.S.: Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (recommendations 1984). Pure Appl. Chem. 57, 603–619 (1985)

    Article  CAS  Google Scholar 

  • Sun, J.: Pore size distribution model derived from a modified DR equation and simulated pore filling for nitrogen adsorption at 77 K. Carbon 40, 1051–1062 (2002)

    Article  CAS  Google Scholar 

  • Tan, Z., Gubbins, K.E.: Adsorption in carbon micropores at supercritical temperatures. J. Phys. Chem. 94, 6061–6069 (1990)

    Article  CAS  Google Scholar 

  • Tao, Y., Endo, M., Kaneko, K.: Hydrophilicity-controlled carbon aerogels with high mesoporosity. J. Am. Chem. Soc. 131, 904–905 (2009)

    Article  CAS  PubMed  Google Scholar 

  • Thommes, M., Kaneko, K., Neimark, A.V., Olivier, J.P., Rodriguez-Reinoso, F., Rouquerol, J., Sing, K.S.: Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report). Pure Appl. Chem. 87, 1051–1069 (2015)

    Article  CAS  Google Scholar 

  • Villarroel-Rocha, J., Barrera, D., Sapag, K.: Improvement in the pore size distribution for ordered mesoporous materials with cylindrical and spherical pores using the Kelvin equation. Top. Catal. 54, 121–134 (2011)

    Article  CAS  Google Scholar 

  • Villarroel-Rocha, J., Barrera, D., Sapag, K.: Introducing a self-consistent test and the corresponding modification in the Barrett, Joyner and Halenda method for pore-size determination. Microporous Mesoporous Mater. 200, 68–78 (2014)

    Article  CAS  Google Scholar 

  • Wongkoblap, A., Intomya, W., Somrup, W., Charoensuk, S., Junpirom, S., Tangsathitkulchai, C.: Pore size distribution of carbon with different probe molecules. Eng. J. 14, 45–56 (2010)

    Article  Google Scholar 

  • Zeller, M., Lorrmann, V., Reichenauer, G., Wiener, M., Pflaum, J.: Relationship between structural properties and electrochemical characteristics of monolithic carbon xerogel-based electrochemical double-layer electrodes in aqueous and organic electrolytes. Adv. Energy Mater. 2, 598–605 (2012)

    Article  CAS  Google Scholar 

  • Zhang, B., Xing, Y., Li, Z., Zhou, H., Mu, Q., Yan, B.: Functionalized carbon nanotubes specifically bind to α-chymotrypsin’s catalytic site and regulate its enzymatic function. Nano Lett. 9, 2280–2284 (2009)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Zhang, L., Yang, X., Zhang, F., Long, G., Zhang, T., Leng, K., Zhang, Y., Huang, Y., Ma, Y., Zhang, M.: Controlling the effective surface area and pore size distribution of sp2 carbon materials and their impact on the capacitance performance of these materials. J. Am. Chem. Soc. 135, 5921–5929 (2013)

    Article  CAS  PubMed  Google Scholar 

  • Zhang, X., Gao, B., Creamer, A.E., Cao, C., Li, Y.: Adsorption of VOCs onto engineered carbon materials: a review. J. Hazard. Mater. 338, 102–123 (2017)

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

This research has been partially supported by the research project N MAT2015-68394-R from MINECO (Spain).

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Correspondence to Mohamed Khalfaoui.

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Bergaoui, M., Aguir, C., Khalfaoui, M. et al. On the computer simulations of carbon nanoparticles porosity: statistical mechanics model for CO2 and N2 adsorption isotherms. Adsorption 24, 769–779 (2018). https://doi.org/10.1007/s10450-018-9983-9

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