Porous carbon modeling

In order to see how the electrode thickness might be optimized in order to provide the lowest electrode resistivity, we have developed a theoretical model to describe the charge/discharge processes in porous carbon electrodes. As a first approximation, let us consider an electrode having two sets of cylindrical pores, namely, nanopores (NP) of less than 3 nm in diameter and transport channels (TC) of more than 20 nm in diameter, with each nanopore having an exit to only one TC. ... 

The electrodes in the direct methanol fuel cell (DMFC) (i.e. the anode for oxidising the fuel and the cathode for the reduction of oxygen) are based on finely divided Pt dispersed onto a porous carbon support, and the electro-oxidation of methanol at a polycrystalline Pt electrode as a model for the DMFC has been the subject of numerous electrochemical studies dating back to the early years ot the 20th century. In this particular section, the discussion is restricted to the identity of the species that result from the chemisorption of methanol at Pt in acid electrolyte. This is principally because (i) the identity of the catalytic poison formed during the chemisorption of methanol has been a source of controversy for many years, and (ii) the advent of in situ IR culminated in this controversy being resolved. 

Beshty B.S., A Mathematical Model for the Combustion of a Porous Carbon Particle , Combustion and Flame 32, 295-311(1978). 

There are many methods to manufacture a CMC. Only a small selection is discussed in this section. Let us first have a look at the production process of a SiC matrix reinforced with SiC fibres. First a model is made of fibres, the so-called preform, then CVI (Chemical Vapour Infiltration) is applied to produce a coating on the fibres in order to ensure a better attachment to the matrix. The next step is resin infiltration. After pyrolysis (heating to a high temperature without oxygen) a network matrix of the porous carbon arises. Silicon which has first been melted in an oven is then introduced into this network it reacts with the carbon to form the following matrix ... 

P. McAllister and E.E. Wolf, Modeling of Chemical Vapor Infiltration of Carbon in Porous Carbon Substrates, Carbon, Vol.29, 1991, p.387. 

We implement a modified version of the reconstruction method developed in a previous work to model two porous carbons produced by the pyrolysis of saccharose and subsequent heat treatment at two different temperatures. We use the Monte Carlo g(r) method to obtain the pair correlation functions of the two materials. We then use the resulting pair correlation functions as target functions in our reconstruction method. Our models present structural features that are missing in the slit-pore model. Structural analyses of our resulting configurations are useful to characterize the materials that we model. 

More realistic models have been proposed in the last few years and they have been recently reviewed [1]. Most of these models are based on very simple and qualitative reconstruction of experimental structure data. Our aim is to develop a method to generate atomic configurations of carbon atoms that quantitatively match the structural properties of real porous carbons. 

According to eq. 2 a constant current appears in the cyclic voltammogram (CV) when Q is plotted versus U. In real systems such as porous carbon electrodes, both load resistances due to the spatial distributed capacitance in the pores (circuit model in fig.l) and surface functional groups cause a deviation from the rectangular CV-shape. While the first induces a finite time constant in the charging process, the latter are identified by current peaks in the CV [14,6]. The voltage range used for cyclic voltammetry was -0.2 to 0.8 Volt vs.. g/, gCl at a scanrate of 5 mV/s, respectively. 

The introduction of a range of user-friendly equipment and software has accompanied the present widespread use of low-temperature nitrogen adsorption. Advances have been made in the development of both routine experimental procedures and on-line processing of the adsorption isotherm data. However, there is now a risk that an unskilled operator may gain the impression that with the aid of a manufacturer s user-friendly software it is relatively easy to evaluate the specific surface area and the pore size distribution of the material under examination. Furthermore, the ready access to sophisticated computational procedures may tend to obscure the limitations of the theoretical models on which they are based. The aims of this paper are to draw attention to these problems and to indicate how further progress can be made in the analysis of nitrogen isotherms on porous carbons. 

Figure 8.51 CMK-5 (a) TEM image viewed along the direction of the ordered nano porous carbon and the corresponding Fourier diffractogram. (b) Schematic model for the carbon structure, (c) XRD pattern indicating the hexagonal order between carbon cylinders. Reproduced with permission from [35]. Copyright (2001) Nature Publishing...

Wilemski, G. Simple porous electrode models for molten carbonate fuel cells. J. Electrochem. Soc. 1983, 130 (1), 117-120. 

Oberlin and coworkers [42, 90] (Fig. 2.7c) used a crumpled sheets of paper model to describe the nanotexture of porous carbons. Figure 2.19 depicts this model and includes an enlarged sketch of pores in sucrose-based carbons [91]. In Fig. 2.19a, each zone of molecular orientation is represented by a shaded area inside of which each individual stack is shown either as a rectangular unit or as two parallel segments depending on whether they are observed in perspective... 

We will not discuss here models for pores in carbons, as this topic is treated in Chapter 5, and elsewhere in specialist [15] or general reviews [106, 107]. For similar reasons, we will not discuss porosity control [44, 108] in detail. However, porous carbons prepared by the template technique, especially the ordered ones, deserve special attention. Ordered mesoporous carbons have been known to scientists since 1989 when two Korean groups independendy reported their synthesis using mesoporous silicas as templates [109, 110]. Further achievements have been described in more recent reports [111, 112]. One might have expected that the nanotexture of these materials would merely reflect the nature of the precursor used, namely phenol-formaldehyde [109] or sucrose [110] in the two first ordered mesoporous carbon syntheses (as is well known, these two precursors would have yielded randomly oriented, isotropic carbon had they been pyrolyzed/activated under more conventional conditions). However, the mesopore walls in some ordered mesoporous carbons exhibited a graphite-like, polyaromatic character [113, 114], as described in Chapter 18. This information was obtained by nitrogen adsorption at low relative pressures, as in classical... 

Except for the fullerenes, carbon nanotubes, nanohoms, and schwarzites, porous carbons are usually disordered materials, and cannot at present be completely characterized experimentally. Methods such as X-ray and neutron scattering and high-resolution transmission electron microscopy (HRTEM) give partial structural information, but are not yet able to provide a complete description of the atomic structure. Nevertheless, atomistic models of carbons are needed in order to interpret experimental characterization data (adsorption isotherms, heats of adsorption, etc.). They are also a necessary ingredient of any theory or molecular simulation for the prediction of the behavior of adsorbed phases within carbons - including diffusion, adsorption, heat effects, phase transitions, and chemical reactivity. 

Because the chemical and physical processes involved in the synthesis of disordered porous carbons are not well understood, attempts to develop mimetic modeling procedures, in which theory or simulation methods are used to mimic... 

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