Carbon cylindrical pores, potential energy

Figure 5.10 Potential energy difference (W) for a single oxygen molecule at the entrance of a carbon cylindrical pore of diameter d. The pore regions where the diffusion mechanisms (activated diffusion, surface, and Knudsen flow) dominate are separated by the critical pore sizes dm, (where W = 0) and d,f (where W = 0.04eV), indicated by...

Immersion calorimetry provides a very useful means of assessing the total surface area of a microporous carbon (Denoyel et al., 1993). The basic principle of this method is that there is a direct relation between the energy of immersion and the total area of the microporous material. Indeed, for the two model cases of slit-shaped and cylindrical micropores, the predicted maximum enhancement of the adsorption potential (as compared with that of the flat surface of same nature) is 2.0 and 3.68, respectively (Everett and Powl, 1976). These values are remarkably similar to the increased surface area occupied by a molecule in the narrowest possible slit-shaped and cylindrical pores (i.e. 2.0 in a slit and 3.63 in a cylinder). To apply the method we... 

Second, similar simulations in cylindrical pores are reported, in which non-planar wall would hinder the liquid s freezing even with favorable "excess" potential energy. Non-monotonous variation of freezing point against the pore size, which was observed for U-methane in carbon pores, can be interpreted as the result of competition between the geometrical difficulty and the compression by the excess potential energy. 

Figure 5.7 Scaled potential energy minima e /e within cylindrical and slit-shaped pores with varying radius R and slit size 2d, respectively, where eS is the minimum potential within the pore and e is the minimum potential with a single flat surface. Curves that go below the horizontal axis are the scaled potentials within the centre of the pore e(0)/e where the potential in the centre e(0) becomes less than the minimum potential with a single flat surface e, i.e. e(0)/e < 1, within larger pores. Reprinted with permission from Journal of the Chemical Society Faraday Transactions I, Adsorption in slit-like and cylindrical micropores in the Henry s law region. A model for the microporosity of carbons by D. H. Everett and J. C. Fowl, 72, 619-636, Copyright (1976) Royal Society of Chemistry...

GCMC simulations, in which the temperature, the volume of the simulation cell and the chemical potential of the adsorbate are kept constant, were carried out for the adsorption isotherms of methane and ethane in slit-sh ed pores (representing pores in BPL carbon) and of ethane in cylindrical pores (representing pores in MCM-41). The absolute configurational energy of the adsorbates was obtained by a Canonical Monte Carlo (CMC) simulation, in which the number of molecules in the pore, the temperature and the volume of the simulation cell are kept constant. Details of the GCMC and CMC simulations can be found in refe. [8,9]. 

The GCMC simulation method of the same maimer as the previous section was employed. The pore-wall potential employed was that for a structureless U solid derived by Peterson et al. [10] with cylindrical coordinate integration. A carbon-like wall was set using the same energy and size parameter as stated in section 2.1, and again a methane wall was also employed here. 

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