PORE ACCESSIBILITY IN NANOPOROUS CARBONS: EXPERIMENT, THEORY AND SIMULATION

S. K. Bhatia and T. X. Nguyen

Department of Chemical Engineering, The University of Queensland, QLD 4072, Australia

1 INTRODUCTION

The understanding of pore accessibility in adsorbents is important to adsorbent design for gas mixture separation and storage. It is also a long-standing issue related to experimentally-observed complex adsorption behaviour, such as enhancement of adsorbed quantity with increasing temperature as well as the phenomenon of open loop hysteresis. The accessibility is not simply a result of the difference between the size of the adsorbate molecule and that of pores in the adsorbent, i.e. the result of a size exclusion mechanism, but more intricately influenced by the kinetic energy of the adsorbate molecule. The dependence of accessibility on the kinetic energy also leads to its strong temperature dependence.

Despite the considerable effort directed at tackling the issue of accessibility in porous carbons using percolation theory, with the underlying assumption of a size exclusion mechanism, little effort has been made at comprehensive investigation of this phenomenon based on atomistic modelling. The latter enables one to capture the dynamic nature of the pore accessibility, as well as to explain several complex adsorption behaviours in porous carbons, which may provide understanding crucial to optimal adsorbent design for gas mixture separation and storage. Accordingly, in this article we present an overview of our recent atomistic level studies on determination of the temperature dependent accessibility of simple gases (Ar, N2, CH4, CO2) in a Hybrid Reverse Monte Carlo (HRMC) model of saccharose char CS1000a constructed using our proposed approach. Subsequently, we also present the validation of our calculated pore connectivity results against experimental adsorption data.

2 METHOD AND RESULTS

2.1 Determination of Pore Accessibility

In this section, we review two recent methods for determination of pore accessibility in porous carbonaceous materials.

2.1.1 Percolation model. The first method is based on percolation theory modelling. In this model, the accessibility is assumed to be temperature independent, and pore network connectivity is simply characterized by a mean coordination number, Z, which represents the mean number of pores connected at an intersection. For any adsorbate of molecular size dc the accessible pore volume is then obtained as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where Vtot is the actual total pore volume, f(H) is the pore volume distribution, Ω is the number fraction of available pores, given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

and Ωa(Z, Ω) is the fraction of accessible pores. This fraction is given by percolation theory, based on an assumed network model. For a random network of uniform coordination number an expression for the function Ωa(Z, Ω) has been provided by Lopez-Ramon et. al., and utilised by Ismadji and Bhatia to study accessibility of ester molecules in carbons. Although the percolation model with the assumption of temperature-independent accessibility does not reflect the experimentally observed kinetic nature of accessibility and its temperature dependence, it may approximate well the behaviour for large molecules such as esters. This is seen in Figure 1 depicting Ideal Adsorbed Solution Theory based as well as experimental ester mixture isotherms at 313 K on Filtrasorb F-400 activated carbon. The predictions are based on the fit of pure component isotherms with the coordination number, Z, used as a fitting parameter. The subsequent mixture predictions are parameter free, and consider the different zones that are inaccessible to both components or accessible only to the smaller molecule, and the zone accessible to both species. The excellent correspondence with the experimental data provides good support for the approach. On the other hand when the accessibility was assumed to be unity in the pure component isotherm fits, the mixture predictions were less satisfactory

The above success of the percolation theory is due to the fact that in practice observation of the kinetic nature of the accessibility is very much dependent upon the difference between the experimental time scale and that of activated diffusion of adsorbate molecules in the porous solid. The latter is dictated by the ratio of activation energy to kinetic energy, i.e. Ea/kBT. For large adsorbate molecules, having strong interaction with the adsorbent, the activation energy could be significantly enhanced compared to the maximum kinetic energy in the experimental temperature range. This leads to temperature-independent accessibility, as pores with constricted entries remain inaccessible over a wide temperature range. In contrast, for small adsorbate molecules with weak interactions the time scale of activated diffusion through the pore mouth is very sensitive to temperature, leading to strongly temperature dependent accessibility. Accordingly, atomistic structural modelling of porous carbon is essential for capturing the kinetic feature of the accessibility.

2.1.2 Atomistic model. In this subsection, we briefly present our recently proposed method to determine pore accessibility using an atomistic structural model. In general, our approach is based on the analysis of continuity of a close packed adsorbed phase in the adsorbent, comprising three main steps: (1) Filling all pore spaces of the solid structure with close packed adsorbate using grand canonical Monte Carlo (GCMC) simulation; (2) identification of all adsorbate clusters; (3) determination of pore accessibility based on continuity of each cluster throughout the structure. The approach has been successfully applied to the determination of accessibility of Ar, N2, CH4 and CO2 over a wide range of temperature, with further analysis of its kinetic features using transition state theory (TST). According to TST, the mean crossing time between cages A and B is given as

τA [right arrow] B = 1/kA [right arrow] B (3)

where kA [right arrow] B is a rate constant, given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where the integral in the numerator is taken over the dividing surface of maximum potential energy, between cages A and B. Here κ is a transmission coefficient shown to be nearly unity, kB is the Boltzmann constant, T is temperature and m is the mass of the particle. φsf is the interaction potential between the adsorbate particle i at position r and all solid atoms of the adsorbent phase, given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where u is the solid-fluid pair potential, taken to be the 12-6 Lennard-Jones potential. As an example Figure 2a depicts the temperature dependence of the crossing time of Ar and N2 between cages A and B in the atomistic model of saccharose char, shown in Figure 2b.

2.2 Impact of Pore Accessibility

2.2.1 Adsorption Equilibrium. Pore...