A hybrid cylindrical model for characterization of MCM-41 by density functional theory

Abstract

A hybrid cylindrical model for characterization of MCM-41 by density functional theory (DFT) is proposed in this work, where the surface heterogeneity of MCM-41 is taken into account by using a hybrid potential model to represent the interactions between a pore wall and molecules inside the pore. This model consists of two parts: (1) the potential energies from the oxygen atoms inside the wall, represented by the potential model proposed by our group; (2) the potential energies from the silanol coverage and/or other unknown factors in the surface of the channel of MCM-41, represented by the cylindrical surface potential function of Tjatjopoulos et al. (G. J. Tjatjopoulos, D. L. Feke and J. A. Mann, J. Phys. Chem., 1988, 92, 4006–4007). To test the new model, the DFT method was used to calculate the adsorption isotherm of nitrogen in MCM-41 at 77 K. The isotherm calculated is compared with the experimental data as well as the calculated results of Maddox et al., who divided the surface of MCM-41 into eight sectors and adopted different parameters for each sector to consider the heterogeneity of the surface. Compared with the work of Maddox et al. (M. W. Maddox, J. P. Olivier and K. E. Gubbins, Langmuir, 1997, 13, 1737–1745), our model gives a much better fit to the experimental isotherm of nitrogen at 77 K in the pressure range of P/P₀ = 0.2–0.5 with much less parameter and computation effort, where phase transition and capillary condensation occur. Furthermore, the relationship between the reduced pressure, at which capillary condensation takes place, and the pore diameter by the hybrid model is in good agreement with that obtained by Maddox et al. In addition, adsorption and phase behavior of methane and ethane are studied by the model, and the calculated results also coincide well with the experimental isotherms of methane and ethane at 264 K–373 K. Therefore, the hybrid potential model incorporating into the DFT method provides a useful tool for characterization of MCM-41.