Unveiling pore size contributions and host-guest interactions in methane adsorption under varying pressure conditions: a semi-empirical adsorption model

Abstract Natural gas, primarily composed of methane (CH 4 ), offers a greener alternative to conventional fuels. Efficient storage through adsorbed natural gas technology necessitates an understanding of CH 4 –adsorbent interactions. This study explored CH 4 adsorption on activated carbons at 1–35 bar and 298 K, determining an efficiency factor ( φ ) as an indicator of optimal pore size. In the given system, φ ranged from 2.0 at 1 bar to 2.5 at 35 bar, indicating an increasing trend with pressure. To gain further insights, quantitative contributions ( $${k}_{x}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) were established based on different micropore sizes ( $${d}_{{\rm{i}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:math> &lt; 0.76 nm, 0.76 nm &lt; $${d}_{{\rm{ii}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ii</mml:mi> </mml:mrow> </mml:msub> </mml:math> &lt; 1.14 nm, and 1.14 nm &lt; $${d}_{{\rm{iii}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>iii</mml:mi> </mml:mrow> </mml:msub> </mml:math> &lt; 2 nm). At 1 bar, $${k}_{{\rm{i}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $${k}_{{\rm{ii}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ii</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and $${k}_{{\rm{iii}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>iii</mml:mi> </mml:mrow> </mml:msub> </mml:math> contributed 91, 9, and 1%, respectively. These contribution values shifted to 35, 54, and 11% at 35 bar, suggesting that effective pore sizes increase with increasing pressure. Notably, CH 4 capacity directly correlated with $${d}_{{\rm{ii}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ii</mml:mi> </mml:mrow> </mml:msub> </mml:math> in the high-pressure adsorption. Atomistic computations were used to elucidate the role of pore sizes in facilitating CH 4 accessibility at different pressures. This comprehensive model provides valuable insights for designing optimal adsorbents, specifically targeting pore size-dependent applications such as gas adsorption and separation, as well as catalyst supports.