Molecular models for porous carbons

Pikunic J, Pellenq RJ-M, Thomson KT, Rouzaud J-N, Levitz P, Gubbins KE. Improved molecular models for porous carbons. Stud Surf Sci Catal 2001 132 647-652. 

The evolution of molecular models for disordered porous carbons is strongly connected with the advance of experimental techniques such as diffraction methods and electron microscopy. First, X-ray studies on carbon blacks revealed that these materials consist of a wealth of small graphitic crystallites. 

In previous works Pikunic et al. [1,2] developed molecular models of CS400 and CSIOOO based on RMC and using three body constraints for porous carbons (see Fig. 1). 

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. 

The issue of multicomponent adsorption still poses a fundamental problem to researchers working in the adsorption area. Many mathematical models have been proposed to address this problem, and there have been reviews such as those cited in this chapter. The choice of an appropriate model rests on the balance of simplicity and capability of the model as weU as the intended application of the model. For example, for quick calculation of the multicomponent equilibria of similar adsorbates (such as low-order paraffin gases), simple models such as the FastlAS and the extended Sips model are adequate. However, to study the influence of the porous structure of activated carbon on the adsorption equilibrium properties of nonpolar adsorbents, the MPSD model is complex enough, while still retaining some simplicity, to explain the effects of factors such as micropore size distribution and adsorbate molecular properties on the adsorption equilibria. 

As described in this chapter, the physieal theory and molecular modeling of catalyst layers provide various tools for relating the global performance metrics to local distributions of physical parameters and to structural details of the complex composite media at the hierarchy of scales from nanoscale to macroscale. The subsisting challenges and recent advances in the major areas of theoretical catalyst layer research include (i) structure and reactivity of catalyst nanoparticles, (ii) selforganization phenomena in catalyst layers at the mesoscopic scale, (iii) effectiveness of current conversion in agglomerates of carbon/Pt, and (iv) interplay of porous structure, liquid water formation, and performance at the macroscopic scale. 

In this work we show that the pore size distributions of porous carbons, obtained from lignin pyrolysis and KOH activation, determined from molecular simulation and DFT are equivcdent. We suggest that the spurious minimum observed in the PSD of carbons obtained form inversion of the integral adsorption isotherms is due to artifacts of the model, such as the fact that, uniform size, infinite non-connected pores are considered. In such cases, for the pore width where transition Ifom two to three layers occurs, the difference in shape of the calculated adsorption isotherms results in an exclusion of some pore widths at the time of the inversion of the integral. Taking into account smooth changes between pore sizes, or pore connectivity may solve this problem. 

Porous carbons are disordered materials with heterogeneous pore structures. These materials are usually modeled using the slit pore model, in which the material is assumed to be made up of independent and unconnected pores. However this model fails to account for the comphcated pore geometry and also the pore connectivity present in the real porous carbons. In recent times, reconstruction methods have been popular to develop realistic molecular models of these materials. In this approach a 3D stmctural model is built that is... 

The DS method has been successfully employed for the PSD determination of micro-porous carbons [14,22,23,50,62,63]. An example is shown in Fig. 1, which shows the PSD of an activated carbon fiber (KF-1500) calculated using the DS model with CO2 adsorption data (253-323 K) and using molecular simulations of CH4 isotherms calculated at 308 K. 

N. A. Seaton, J.P.R.B. Walton and N. Qulrke, A new analysis method for the determination of the pore size distribution of porous carbons from nitrogen adsorption measurements, Carbon, 27, 853 (1989) C.A. Jessop, S.M. Riddlford, N.A. Seaton, J.P.R.B. Walton and N. Qulrke, The determination of the pore size distribution of porous solids using a molecular model to Interpret nitrogen adsorption measurement, paper presented at lUPAC Symposium on Characterization of Porous Solids, Alicante, Spain, May 6-9, 1990. 

The pore size distributions of several types of porous solid have been determined from their nitrogen adsorption isotherms using a new analysis method (ref. 1). In contrast to earlier thermodynamic methods (which break down at small pore sizes), the new approach is based on a molecular model of nitrogen adsorption in a pore. The development of this technique means that, for the first time, the distribution of pore sizes may be calculated over both the mesopore and micropore size ranges using a single analysis method. The use of the new method is illustrated with a series of results obtained from carbon, silica and alumina samples. Its predictions are compared with those obtained using established analysis methods. 

The calculations in ref. 25 for model micropores only consider interactions between a single adsorptive molecule and the walls of the model micropore. They do not account for interactions between adsorptive molecules and so cannot model the process of micropore filling. Recently (ref. 43) results from molecular modelling studies were reported for the adsorption of nitrogen on porous carbons in which both adsorptive-adsorbent and inter-adsorptive interactions were considered. Using an approximate theory of inhomogeneous fluids known as mean-field theory, a function p(p, w) was derived (ref. 43) which relates the... 

Chapters I to III introduce the reader to the general problems of fuel cells. The nature and role of the electrode material which acts as a solid electrocatalyst for a specific reaction is considered in chapters IV to VI. Mechanisms of the anodic oxidation of different fuels and of the reduction of molecular oxygen are discussed in chapters VII to XII for the low-temperature fuel cells and the strong influence of chemisorhed species or oxide layers on the electrode reaction is outlined. Processes in molten carbonate fuel cells and solid electrolyte fuel cells are covered in chapters XIII and XIV. The important properties of porous electrodes and structures and models used in the mathematical analysis of the operation of these electrodes are discussed in chapters XV and XVI. 

Nguyen and Bhatia476,477 have developed new (molecular) non-local density functional theories that account for the finite thickness of pore walls in porous systems. It has been demonstrated using experimental data that nanoporous carbons such as activated carbons and coal chars have pore walls that typically only consist of one or two layers. The extension of the DFT methods to treat such systems was therefore essential if accurate modelling is to be carried out. These models have been used to determine the capacity of C02 in carbon slit pores, and the results are compared with simulation.478... 

Riccardo and coworkers [50, 51] reported the results of a statistical thermodynamic approach to study linear adsorbates on heterogeneous surfaces based on Eqns (3.33)—(3.35). In the first paper, they dealt with low dimensional systems (e.g., carbon nanotubes, pores of molecular dimensions, comers in steps found on flat surfaces). In the second paper, they presented an improved solution for multilayer adsorption they compared their results with the standard BET formalism and found that monolayer capacities could be up to 1.5 times larger than the one from the BET model. They argued that their model is simple and easy to apply in practice and leads to new values of surface area and adsorption heats. These advantages are a consequence of correctly assessing the configurational entropy of the adsorbed phase. Rzysko et al. [52] presented a theoretical description of adsorption in a templated porous material. Their method of solution uses expansions of size-dependent correlation functions into Fourier series. They tested... 

The existing structural models are overwhelmingly of the reconstructive type, in which the model is constructed based on experimental structural data. This is a result of the complex and poorly understood synthesis of the carbons. Mimetic simulation methods, in which the synthesis is modeled using molecular or ab initio simulations, have been successfully used for some other porous materials. 

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