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 accessibility has a major impact on adsorption equilibrium. In particular, from Figure 2a, it can be predicted that Ar and N2 may have a pore accessibility problem at low temperatures (<100 K) due to extremely long crossing times (τ > 100 seconds), but not at higher temperatures (>150 K) where the crossing time is much shorter (< 10-2 second). The former prevents the attainment of equilibrium, while the latter enables the adsorption system to instantly reach equilibrium at experimental time scales. This is consistent with our recent experimental observation of an increase in adsorbed amount of argon with increase in temperature in coals, depicted in Figure 3. The increase in adsorption capacity with temperature, evident in Figure 3, is due to the increase in kinetic energy, and the resulting higher accessibility, with increase in temperature.

Figure 2a shows that the estimated crossing time, or adsorption time, of N2 at 77 K from cage A to B is extremely large (about 5 hrs to ~3.7 million years), for both choices of LJ parameters for N2, while that of argon at 87 K is of the order of minutes. This suggests an accessibility problem for N2 at 77 K, but not for Ar 87 K. This is supported by the results shown in Figure 4, where experimental adsorption data for CO2 in BPL carbon at temperatures of 273 K and 323 K8 (triangles and squares respectively) are correctly predicted by the use of structural parameters derived from experimental Ar adsorption data at 87 K (solid and dashed lines) using our finite wall thickness based density functional theory model, but significantly underpredicted by the use of parameters derived from experimental N2 adsorption data at 77 K (dotted and dashed dotted lines

2.2.2 Open Loop Hysteresis. For long, hysteresis in porous materials has been of much interest to adsorption scientists. In general, experimentally observed hysteresis phenomena can be grouped into two classes. The first class of hysteresis, or closed loop hysteresis, involves adsorbate condensation in mesoporous materials, while the other class of hysteresis, or open loop hysteresis, is normally observed in ultra-microporous carbons such as coals and molecular sieve carbons. In particular, closed loop hysteresis shows irreversible adsorption only in the vicinity of the condensation region, but is reversible outside this region. Such irreversibility is related to the high activation energy of adsorbate droplet growth resulting from the confinement. In contrast, open loop hysteresis shows the occurrence of irreversible adsorption down to the lowest experimental pressure. From Figure 2a, it can be seen that the crossing time of N2 and Ar at low temperatures (77K<100 K) from cage A to cage B, or adsorption time (4s<τads<5hrs), is within the experimental adsorption time scale, while their crossing time from cage B to cage A, or desorption time (588s<τdes<134 days), is far beyond the experimental time scale. This suggests that the open loop hysteresis is related to the high activation energy arising from constriction of the pore mouth. For further clarification, it is evident from Table 1 that the crossing time of carbon dioxide at 273 K between cages A and B is very short, leading its instantaneous equilibrium under practical adsorption experimental conditions, i.e. no open loop hysteresis is expected to be observed. This prediction is consistent with experimental observation of adsorption hysteresis of N2 at 77 K in Takeda 3 Å, but not for CO2 at 273 K in the same carbon, as shown in Figures 5(a, b).

2.2.3 Gaseous Mixture Selectivity. An intriguing feature of carbonaceous adsorbents is their excellent capability for mixture separation. For instance, molecular sieve carbon (MSC) has long been industrially utilised as an adsorbent in the pressure swing adsorption (PSA) technique due to its extremely high gas selectivity. However, for a typical example of a CO2/CH4 mixture under supercritical condition theoretical adsorption modelling of the mixture using a slit-pore model showed at best only small value of selectivity (<4.5) regardless of pore size, while extremely high selectivity of this mixture in molecular sieve carbons is experimentally shown. The latter is very consistent with extremely high crossing time of CH4 at ambient temperature in comparison with that of CO2, as shown in Table 1. Consequently, it is clearly evident that extremely high adsorption selectivity in disordered porous carbons cannot be achieved based on difference in adsorption affinity of individual species in the mixture, unless the size of the pore mouth is reduced to the molecular dimension at which activated diffusion occurs.

2.2.4 Gasification. High surface area and pore volume is essentially created in the activation stage of preparation of carbonaceous porous materials, whereby a small amount of carbon atoms is removed by partial oxidation. In this activation stage, it is interesting to observe that majority of the surface area of activated carbon is initially created with removal of small carbon fraction (< 5%), as shown in Figure 6. Accordingly, the opening of new pores must occur in this initial stage of the activation process. However, if these new pores are formed from etching of carbon planes, such small carbon fraction removed cannot account for the dramatically increased surface area unless a significant increase in pore accessibility of the existing pore structure occurs as a result of the opening of pore mouths. The latter mechanism would appear reasonable considering that the pore mouth normally contains highly reactive defects. Consequently, the pore mouth will be enlarged as the reactive defects are removed, leading to significant increase in pore accessibility. This is further supported by the results in Figure 7, showing a steep increase in helium density of coke during gasification as a consequence of increase in helium accessibility early in the gasification process.

3 CONCLUSION

We have presented here an overview of our studies on pore accessibility in nanoporous carbons, covering both the semi-empirical approach (percolation model) and the atomic level approach using transition state theory. Furthermore, the impact of pore accessibility on adsorption in porous carbons is also presented. In particular, our review concentrates on explanation of the anomalous adsorption behaviour of adsorbate fluids in porous carbons such as open loop hysteresis, increase in adsorbed quantity with increasing temperature, extremely high selectivity, and significantly increased surface area encountered at the early stage of the process of activation of carbons. Such atomistic modelling provides a realistic picture of the adsorption process in porous carbons, which will ultimately facilitate the design of carbons with optimal structure for gas mixture separation and storage.

CHARACTERIZATION MEASUREMENTS OF COMMON REFERENCE NANOPOROUS MATERIALS BY GAS ADSORPTION (ROUND ROBIN TESTS)

J. Silvestre-Albero, A. Sepúlveda-Escribano, F. Rodríguez-Reinoso, V. Kouvelos, G. Pilatos, N. K. Kanellopoulos, M. Krutyeva, F. Grinberg, J. Kaerger, A. I. Spjelkavik, M. Stöcker, A. Ferreira, S. Brouwer, F. Kapteijn, J. Weitkamp, S. D. Sklari, V. T. Zaspalis, D. J. Jones, L. C. de Menorval, M. Lindheimer, P. Caffarelli, E. Borsella, A. A. G. Tomlinson, M. J. G. Linders, J. L. Tempelman, E. A. Bal

1 INTRODUCTION

The correct characterization of the textural characteristics of porous solids is of paramount importance in order to understand their behaviour in a certain application. Traditionally, textural characterization as been performed using adsorption of probe molecules (Ar, N2, CO2, etc.); among them, N2 adsorption at low temperature (77 K) is the most widely applied. N2 adsorption covers the relative pressure (P/Po) range from 10-6 to 1 and provides information about the whole microporosity (up to 2 nm). Unfortunately, the low adsorption temperature becomes detrimental for samples exhibiting kinetic restrictions due to the limited accessibility of the N2 molecule to the narrow microporosity. This limitation can be overcome using CO2 adsorption at a higher temperature (273 K). CO2 adsorption covers a shorter relative pressure range (from 10-6 to 0.03) and it is very helpful to complement N2 in the characterization of the narrow microporosity (up to 0.7 nm).

As described above, the correct characterization of the porous structure is a major drawback in research fields related to the preparation, characterization and application of porous materials. However, the reliability of the experimental results in adsorption measurements is highly affected by several factors. There are errors associated with the characteristics of the experimental equipment (pressure-transducer precision), the calibration of the equipment, the experience of the operator (e.g. time left to ensure that the equilibrium has been reached), the correct application of the mathematical models (eg. Brunauer-Emmett-Teller (BET), Dubinin-Radushkevich (DR), etc.) and so on. With this in mind, this manuscript reports the results of a Round Robin adsorption test performed under the auspicious of the European Network of Excellence INSIDEPORES (In-SItu study and DEvelopment of processes involving nano-PORous Solids). The Round Robin is aimed to compare the textural properties of 4 reference samples (Takeda 4A, Takeda 5A, Spherical Carbon and silicalite H-ZSM5 Si/Al=400) obtained from the N2 adsorption isotherms at 77 K and the CO2 adsorption isotherms at 273 K (adsorption measurements on H-ZSM5 are not included due to the limited space available). This comparison will allow to identify and to emphasize possible weaknesses in the different steps involved in the characterization process. The Round Robin tests involved 10 groups from different countries all of them core members of the INSIDEPORES network of Excellence.