A Potential Model for Cylindrical Pores

Abstract

Abstract: An analytical potential for cylindrical pores has been derived by introducing a variational
method into the integration for the calculation of the interaction energy between the wall
molecules and a test molecule, all of which are represented by Lennard-Jones potential. The
model proposed gives good fito the results from the cylindrical surface model and the
pseudoatom model. To test the potential proposed rigorously, we have carried out grand
canonical ensemble Monte Carlo(GCMC) simulation of nitrogen in the MCM-41 pore at 77 K, and
compared the simulated adsorption isotherm with the experimental data reported in the
literature. The simulated isotherm from our model is in almost qualitative agreement with
experiment. Consequently, the model proposed provides an explicit and accurate description
of cylindrical pores represented by the Lennard-Jones potential. Moreover, the model can be
easily applied to a variety of cylindrical pores, ranging from cylindrical surface to
finite thickness walls, in both theoretical studies and computer simulations.

Key words: potential model, cylindrical pores, GCMC, MCM-41

摘要： An analytical potential for cylindrical pores has been derived by introducing a variational
method into the integration for the calculation of the interaction energy between the wall
molecules and a test molecule, all of which are represented by Lennard-Jones potential. The
model proposed gives good fito the results from the cylindrical surface model and the
pseudoatom model. To test the potential proposed rigorously, we have carried out grand
canonical ensemble Monte Carlo(GCMC) simulation of nitrogen in the MCM-41 pore at 77 K, and
compared the simulated adsorption isotherm with the experimental data reported in the
literature. The simulated isotherm from our model is in almost qualitative agreement with
experiment. Consequently, the model proposed provides an explicit and accurate description
of cylindrical pores represented by the Lennard-Jones potential. Moreover, the model can be
easily applied to a variety of cylindrical pores, ranging from cylindrical surface to
finite thickness walls, in both theoretical studies and computer simulations.

关键词: 圆柱孔;势能模型;MCM-41;GCMC;模拟;等温线;圆柱面;多孔介质;中孔介质;氮;活性碳;吸附

ZHANG Xianren, WANG Wenchuan. A Potential Model for Cylindrical Pores[J]. .

张现仁, 汪文川. 圆柱孔的势能模型[J]. CIESC Journal.

References

[1] Steele, W. A., The Interaction of Gases with Solid Surface, Pergamon, Oxford (1974).
[2] Steele, W. A., "The interaction of rare gas atoms with graphitized carbon black", J.
Phys. Chem., 83, 817 (1978).
[3] Sokolowski, S., "Adsorption of oxygen in slit-like pores: Grand canonical ensemble
Monte Carlo studies", Mol.Phys., 75, 999 (1992).
[4] Jiang. S., Gubbins, K. E., Zollweg, J. A., "Adsorption, isosteric heat and
commensurate-incommensurate transition of methane on graphite", Mol. Phys., 80, 103 (1993).
[5] Jiang, S., Gubbins, K. E., Balbuena, P. B., "Theory of adsorption of trace components",
J. Phys. Chem., 98, 2403(1994).
[6] Tan, Z., Gubbins, K. E., "Selective adsorption of simple mixtures in slit pores: A
model of methane-ethane mixtures in carbon", J. Phys. Chem., 96, 845 (1992).
[7] Jiang, S., Rhykerd, C. L., Gubbins, K. E., "Layering, freezing transitions, capillary
condensation and diffusion of methane in slit carbon pores", Mol. Phys., 79, 373 (1993).
[8] Vishnyakov, A., Piotrovskaya, E. M., Brodskaya, E. N, "Monte Carlo computer simulation
of adsorption of diatomic fluids in slitlike pores", Langmuir, 12, 3643 (1996).
[9] Yin, Y. F., McEnaney, B., Mays, T. J., "Dependence of GCMC simulations of nitrogen
adsorption on activated carbons on input parameters", Carbon, 36, 1425 (1998).
[10] Cracknell, R. F., Nicholson, D., Gubbins, K. E., "Molecular dynamics study of the
self-diffusion of supercritical methane in slit-shaped graphitic micropores", J. Chem.Soc.
Faraday Trans., 91, 1377 (1995).
[11] Beck, J. S., Vartuli, J. C., Roth, W. J., Leonowicz, M. E., Kresge, C. T., Schmitt, K.
D., Chu, C. T. W., Olson, D. H.,Sheppard, E. W., McCullen, S. B., Higgins, J. B.,
Schlenker,J. L., "A new family of mesoporous molecular sieves prepared with liquid crystal
templates", J. Am. Chem. Soc.,114, 10834 (1992).
[12] Kresge, C. T., Leonowicz, M. E., Roth, W. J., Vartuli, J. C., Beck, J. S., "Ordered
mesoporous molecular sieves synthesized by a liquid-crystal template mechanism",
Nature,359, 710 (1992).
[13] Iijima, S., "Helical microtubules of graphitic carbon", Nature, 354, 56 (1991).
[14] Iijima, S., Icihashi, T., "Single-shelled carbon nanotubes of 1 nm diameter", Nature,
363, 603 (1993).
[15] Bethune, D. S., Hiang, C. H., deVries, M. S., Gormen, G.,Savoy, R., Beyers, R.,
"Cobalt-catalyzed growth of carbon nanotubes with single-atomic-layer walls", Nature,
363,605 (1993).
[16] Maddox, M. W., Gubbins, K. E., "Molecular simulation of fluid adsorption in Buckytubes
and MCM-41", Int. J.ThermPhys., 15, 1115 (1994).
[17] Maddox, M. W., Ulberg, D., Gubbins, K. E., "Molecular simulation of simple fluids and
water in porous carbons",Fluid Phase Equili., 104, 145 (1995).
[18] Maddox, M. W., Gubbins, K. E., "Molecular simulation of fluid adsorption in
Buckytubes", Langmuir, 11, 3988(1995).
[19] Maddox, M. W., Olivier, J. P., Gubbins, K. E., "Characterization of MGM-41 using
molecular simulation: Heterogeneity effects", Langmuir, 13, 1737 (1997).
[20] Ayappa, K. G., "Simulations of binary mixture adsorption in carbon nanotubes:
Transitions in adsorbed fluid composition’’, Langmuir, 14, 880 (1998).
[21] Darkrim, F., Levesque, D., "Monte Carlo simulations of hydrogen adsorption in single-
walled nanotubes", J. Chem.Phys., 109, 4981 (1998).
[22] Wang, Q., Johnson, J. K., "Molecular simulation of hydrogen adsorption in single-
walled carbon nanotubes and idealized carbon slit pores", J. Chem. Phys., 110, 577 (1999).
[23] Tjatjopoulos, G. J., Feke, D. L., Mann, J. A., "Moleculemicropore interaction
potentials", J. Phys. Chem., 92, 4006(1988).
[24] Nicholson, D., Gubbins, K. E., "Selectivity inversion in the adsorption of methane-
carbon dioxide mixtures", J. Chem.Phys., 104, 8126 (1996).
[25] Peterson, B. K., Walton, J. P. R. B., Gubbins, K. E., "Fluid behavior in narrow
pores", J. Chem. Soc. Faraday Trans.2, 82, 1789 (1986).
[26] Gelb, L. D., Gubbins, K. E., "Liquid-liquid phase separation in cylindrical pores:
Quench molecular dynamics and Monte Carlo simulations", Phys. Rev. E, 56, 3185 (1997).
[27] Johnson, J. K., Zollweg, J. A., Gubbins, K. E., "The Lennard-Jones equation of state
revisited", Mol. Phys., 78,591 (1993).
[28] Cao, D., Gao, G., Wang, W., "Grand canonical ensemble Monte Carlo simulation of
adsorption storage of methane in slit micropores", J. Chem. Ind. Eng. (China), 51, 23
(2000). (in Chinese)