Modeling of adsorption on porous material plays a crucial role in providing a better understanding of adsorption phenomena, isotherms, and isosteric heats, and predicting the thermodynamics of adsorption-based storage systems. In this work, the multicomponent potential theory of adsorption (MPTA) coupled with the modified Dubinin potential (MDP), the modified Dubinin-Astakhov (DA) model, and the Unilan model are compared for their effectiveness in nonlinear least square fitting of experimental hydrogen adsorption data on three prototypical metal-organic frameworks (MOFs) in two temperature ranges: 30 K room temperature (RT) for MOF-5, and 77 K RT for MOF-5, Cu-BTC, and MIL-101. The ability of each model to accurately describe excess adsorption is found to depend on the pore size and the energetic pore heterogeneity of MOFs, and the latter's relation to the assumptions used within each model. The simpler Langmuir-like Unilan model complies best with the monolayer type adsorption mechanism in MOFs with large pores and homogenous pore distribution, such as in MOF-5, while the pore filling models like modified DA and MPTA-MDP better represent the adsorption phenomena in MOFs with smaller pores and heterogeneous pore distributions, such as Cu-BTC and MIL-101. In the vicinity of hydrogen's critical temperature, adsorbed hydrogen inside the pores of MOF-5 undergoes a phase-transition to solid-like phase with densities higher than that of bulk solid hydrogen, which is attributed to the increased force field in the confined pores of MOF-5. (C) 2013 Elsevier B.V. All rights reserved.