Microporous carbon model

The aim of this work is to answer the follow questions (i) What is the maximum adsorption capacity of carbonaceous microporous solids and, (ii) Why CMS can not be prepared with a micropore volume higher than 0.3 cc/g . In doing that, micropore volume has been calculated in a series of very simple microporous carbon models, described as assemblages of slit-shaped pores, and using the parameters of graphitic structure (interlayer spacing and density) and the pore structure (pore width and micropore walls thickness). 

In order to develop a microporous carbon model, we will accept the following characteristics of adsorption process on active carbon described by different authors ... 

The formalism of nonlocal functional density theory provides an attractive way to describe the physical adsorption process at the fluid - solid interface.65 In particular, the ability to model adsorption in a pore of slit - like or cylindrical geometry has led to useful methods for extracting pore size distribution information from experimental adsorption isotherms. At the moment the model has only been tested for microporous carbons and slit - shaped materials.66,67 It is expected that the model will soon be implemented for silica surfaces. 

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... 

A good correlation between the reported experimental pore volume and the values obtained by applying the models proposed in this work has been found. From this simple approach, it has been shown that it is possible to obtain microporous carbons with a micropore volume higher than 2 cc/g, and that a volume higher than 2.5 cc/g can be achieved. On the other hand, it has been explained why CMS with micropore size around (5-6 A) can not present a micropore volume higher than 0.35 cc/g, as a consequence of their pore wall structure. 

Lastoskie, C.M., Gubbins, K.E. and Quiike, N.J., Pore size distribution analysis of microporous carbons a density functional theory approach. J. Phys. Chem. 97 (1993) 4786. Olivier, J.P., Modeling physical adsorption on porous and nonporous solids using density functional theoiy. J. Porous Materials 2 (1995) 9. 

Figure 16.22 Breakthrough curve normalized to the inlet concentration of CH4 and C)2 carried by helium through a 1 x 30 cm column packed with a microporous carbon (Kureha MAC). Dimensionless time, t = tug/L. Symbols show experimental results, the lines the calculated profiles with the models indicated. The variation of the gas velocity along the column was accounted for. Reproduced with permission from L.. P. van den Broeke, R. Krishna, Chem. Eng. Sci., 50 (1995) 2507 (Fig 12).

A morphological model for microporous carbons has recently been reported [32] in which rigid aromatic sheets of sp- bonded carbon are randomly placed in a three-dimensional cubic simulation cell with periodic boundaries. A typical carbon plate has the structure shown in Fig, 3a, The plates are roughly aligned in the simulation cell, as illustrated in Fig, 3b, but with random variations in their angles of tilt. RMC simulation is carried out by sampling three types of changes to the carbon structure (i) translation and... 

Structure correlation data from scattering experiments could be used in conjunction with the adsorption isotherm to construct model disordered structures for specific silica gel adsorbents, using the methodologies described in Section ll.B for activated microporous carbons. 

The simplest stmctural model for a microporous carbon is the sUt-pore model, in which each pore is in the form of a parallel-sided and rigid graphitic slit. It is also assumed that the filling and emptying processes are not dependent on the spatial arrangement of the pores. It therefore follows that for a given gas/carbon system and temperature, the notional thermodynamic state of the adsorbate (e.g., its chemical potential and enthalpy) is solely dependent on the distribution of... 

The adsorption of gas mixtures has been extensively studied. For example, Wendland et al. [64] applied the Bom—Green—Yvon approach using a coarse grained density to study the adsorption of subcritical Lennard-Jones fluids. In a subsequent paper, they tested their equations with simulated adsorption isotherms of several model mixtures [65]. They compared the adsorption of model gases with an equal molecular size but different adsorption potentials. They discussed the stmcture of the adsorbed phase, adsorption isotherms, and selectivity curves. Based on the vacancy solution theory [66], Nguyen and Do [67] developed a new technique for predicting the multicomponent adsorption equihbria of supercritical fluids in microporous carbons. They concluded that the degree of adsorption enhancement, due to the proximity of the pore... 

Thompson, K.T. and Gubbins, K.E. (2000). Modeling structural morphology of microporous carbons by reverse Monte Carlo. Langmuir, 16, 5761—73. 

Davies, G.M. and Seaton, N.A. (1998). The effect of the choice of pore model on the characterization of the internal structure of microporous carbons using pore size distributions. Carbon, 36, 1473—90. 

Segarra, E.l. and Glandt, E.D. (1994). Model microporous carbons -microstructure, surface polarity and gas-adsorption. Chem. Eng. Sci., 49, 2953-65. 

As an example of the above statement. Fig. 17.3 contains the Nj adsorption isotherms for powder AC vidth different adsorption capacities [3]. These isotherms, compared with those in Figs. 17.1 and 17.2, clearly demonstrate that the adsorption isotherms do not permit neither to distinguish the ACF from the AC nor to deduce differences in the pore size distribution. However, the unique fiber shape and porous structure of the ACF are advantages that permit to deepen into the fundamentals of adsorption in microporous solids [31]. ACFs are essentially microporous materials [13, 31], with sht-shaped pores and a quite uniform pore size distribution [42, 43]. Thus, they have simpler structures than ordinary granulated ACs [31] and can be considered as model microporous carbon materials. For this reason, important contributions to the understanding of adsorption in microporous solids for the assessment of pore size distribution have been made using ACF [31, 33, 34, 39, 42-46], which merit to be reviewed. 

As discussed above, the models presently available for the analysis of porous carbons may yield misleading results for the pore size distribution of OMCs. This also applies to other materials. For example, for purely mesoporous zeolites, some models wrongly indicate the presence of micropores [36]. Thus, it is preferable to verify the presence of micropores by model-less methods, such as a-plots. In a-plots, the amount of nitrogen adsorbed on the sample of interest (i ads.) is compared for all data points to the amount adsorbed on a nonporous standard (ttg. Fig. 18.11). The quantity is the amount of nitrogen adsorbed on... 

Figure 23>6 (a) 002 lattice fringes image on a cross section of a carbonized viscose fiber coated with pyrolytic carbon by CVD from propylene at 900°C. The continuous line shows the separation between a microporous carbon at the bottom (fiber) and the lamellar pyro-carbon at the top. The two insets represent a magnification of selected areas in these two parts, (b) Model showing the disordered nanotexture of the fiber and the lamellar and dense nanotexture of the coating. The coating acts as a barrier which hinders an easy diffusion of species to the core of the fiber. (Adapted from [22]). 

Both the BET and the Duhinin models are widely thought to adequately describe the physical adsorption of gases on solid carbons. BET surface areas from many microporous carbons range from 500 to 1500 m g . However, values of up to 4000 m g" are found for some super-activated carbons and these are unrealistically high. 

According to Eq. (75) the pore volume distribution J(x) can be obtained by multiplication of the adsoiption potential distribution by the negative derivative dA/pore geometry. For instance, for slit-like micropores (which are commonly used to model microporous carbons) the relationship betwren A and x can be expressed as follows [158] ... 

Figure 5.5 Schematic models for (a) parallel transport and (b) resistance in series transport [27], Reprinted from Journal of Membrane Science, 209, j. Gilron and /4. Soffer, Knudsen diffusion in microporous carbon membranes with molecular sieving character, 339-352, Copyright (2002), with permission from Elsevier...

Wickens, D.A. 1990. A generalization of the slit-model of pores in microporous carbons. Carbon 28 97-101. 

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