Gas adsorption in active carbons and the slit-pore model 1 : pure gas adsorption

We describe procedures based on the polydisperse independent ideal slit-pore model, Monte Carlo simulation and density functional theory (a 'slab-DFT') for predicting gas adsorption and adsorption heats in active carbons.A novel feature of this work is the calibration of gas-surface interactions to a high surface area carbon, rather than to a low surface area carbon as in all previous work. Our models are used to predict the adsorption of carbon dioxide, methane, nitrogen, and hydrogen up to 50 bar in several active carbons at a range of near-ambient temperatures based on an analysis of a single 293 K carbon dioxide adsorption isotherm. The results demonstrate that these models are useful for relatively simple gases at near-critical or supercritical temperatures

Simulating fluid-solid equilibrium with the Gibbs ensemble

The Gibbs ensemble is employed to simulate fluid-solid equilibrium for a shifted-force Lennard-Jones system. This is achieved by generating an accurate canonical Helmholtz free-energy model of the (defect-free) solid phase. This free-energy model is easily generated, with accuracy limited only by finite-size effects, by a single isothermal-isobaric simulation at a pressure not too far from coexistence for which the chemical potential is known. We choose to illustrate this method at the known triple-point because the chemical potential is easily calculated from the coexisting gas. Alternatively, our methods can be used to locate fluid-solid coexistence and the triple-point of pure systems if the chemical potential of the solid phase can be efficiently calculated at a pressure not too far from the actual coexistence pressure. Efficient calculation of the chemical potential of solids would also enable the Gibbs ensemble simulation of bulk solid-solid equilibrium and the grand-canonical ensemble simulation of bulk solids

Gas adsorption in active carbons and the slit-pore model 2 : mixture adsorption prediction with DFT and IAST

We use a fast density functional theory (a 'slab-DFT') and the polydisperse independent ideal slit-pore model to predict gas mixture adsorption in active carbons. The DFT is parametrized by fitting to pure gas isotherms generated by Monte Carlo simulation of adsorption in model graphitic slit-pores. Accurate gas molecular models are used in our Monte Carlo simulations with gas-surface interactions calibrated to a high surface area carbon, rather than a low surface area carbon as in all previous work of this type, as described in part 1 of this work (Sweatman, M. B.; Quirke, N. J. Phys. Chem. B 2005, 109, 10381). We predict the adsorption of binary mixtures of carbon dioxide, methane, and nitrogen on two active carbons up to about 30 bar at near-ambient temperatures. We compare two sets of results; one set obtained using only the pure carbon dioxide adsorption isotherm as input to our pore characterization process, and the other obtained using both pure gas isotherms as input. We also compare these results with ideal adsorbed solution theory (IAST). We find that our methods are at least as accurate as IAST for these relatively simple gas mixtures and have the advantage of much greater versatility. We expect similar results for other active carbons and further performance gains for less ideal mixtures

Analysis of free energy functional density expansion theories

Density expansion theories are often used, within the density functional formalism, to approximate the Helmholtz free-energy functional of simple classical fluids. An overview of the theoretical framework of density expansion theories is presented. Several density functional theories that employ truncated density expansions are then analysed with attention focused on their thermodynamic properties. It is found that, of these theories, only the commonly used mean-field theory satisfies the Gibbs adsorption equation; the inconsistencies within the other theories arise from truncation of the density expansion without appropriate modification of the expansion coefficients. Other repercussions of truncating the density expansion are discussed

Weighted density functional theory for simple fluids: supercritical adsorption of a Lennard-Jones fluid in an ideal slit pore

The adsorption of a Lennard-Jones fluid in an ideal slit pore is studied using weighted density functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. Rosenfeld's accurate fundamental measure functional is employed for the repulsive functional while another weighted density functional method is employed for the attractive functional. This other method requires an accurate equation of state for the bulk fluid and an accurate pair-direct correlation function for a uniform fluid, determined analytically or numerically. The results for this theory are compared against mean-field density functional theory and grand canonical ensemble simulation results, modeling the adsorption of ethane in a graphite slit. The results indicate that the weighted density functional method applied to the attractive functional can offer a significant increase in accuracy over the mean-field theory

Weighted density-functional theory for simple fluids; prewetting of a Lennard-Jones fluid

The prewetting of a Lennard-Jones fluid is studied using weighted density-functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. An accurate functional for hard spheres is used for the repulsive functional and a weighted density-functional method is used for the attractive part. The results for this theory are compared against mean-field density-functional theory, the theory of Velasco and Tarazona [E. Velasco and P. Tarazona, J. Chem. Phys. 91, 7916 (1989)] and grand canonical ensemble simulation results. The results demonstrate that the weighted density functional for attractive forces may offer a significant increase in accuracy over the other theories. The density-functional and simulation results also indicate that a previous estimate of the wetting temperature for a model of the interaction of argon with solid carbon dioxide, obtained from simulations [J. E. Finn and P. A. Monson, Phys. Rev. A, 39, 6402 (1989)], is incorrect. The weighted density-functional method indicates that triple-point prewetting is observed for this model potential

Modelling gas adsorption in amorphous nanoporous materials

This section is about modelling gas adsorption in amorphous nanoporous materials. It is held in the Handbook of theoretical and computational nanotechnology

Analysis of gas adsorption in Kureha active carbon based on the slit-pore model and Monte-Carlo simulations

We analyse the adsorption of carbon dioxide and several light alkenes and alkanes on Kureha active carbon at a range of temperatures. We find generally good agreement between the alkene and alkane isotherms at moderate to high pressure, but find that at the lowest relative pressures for each gas there are significant discrepancies that seem to be correlated with the strength of gas-surface interactions. This pattern is similar to that observed in our previous work on the adsorption of light alkenes and alkanes on active carbon, except the errors here are much smaller. One possible explanation for this error is poor diffusion in the experiments at the lowest relative pressures, leading to measurements of non-equilibrium states. We suggest that this poor diffusion might be caused by potential barriers (i.e. it is activated diffusion) in the narrowest pores. We also find that our analysis of the adsorption of carbon dioxide at 273 K is inconsistent with all the alkene and alkane data. We suggest this discrepancy arises because our model of gas-surface interactions does not take contributions from polar surface sites into account. Although this study is specific to Kureha active carbon, we expect that our conclusions are relevant to other studies of gas adsorption on active carbon; they highlight the need for great care when taking measurements at low pressures, and motivate improvements in molecular models for gas adsorption in active carbons

Predicting the adsorption of gas mixtures: adsorbed solution theory versus classical density functional theory

Accurate prediction of the adsorption properties of fluid mixtures in equilibrium with surfaces and/or nanoporous structures is of considerable scientific and practical importance. Often, while the pure fluid adsorption isotherms are known for each component, those for the mixture are not. Using data from Monte Carlo simulations of model mixtures (including hydrogen and carbon dioxide) adsorbed in graphitic slit pores, for a range of pressures to 1000 bar, we compare theories for mixed adsorption which require pure fluid isotherm data as input. In particular, we develop and evaluate methods based on adsorbed solution theory (AST) and classical density functional theory (DFT). We find that a novel approximate DFT-based model is generally more accurate than AST methods in predicting the adsorption isotherms of mixtures of simple gases

Characterization of porous materials by gas adsorption: comparison of nitrogen at 77 K and carbon dioxide at 298 K for activated carbon

Amorphous materials are usually characterized using nitrogen adsorption isotherms at 77 K taken at pressures up to 1 bar to obtain pore size distributions. Activated carbons are amorphous microporous graphitic materials containing pores which can range from nanometers to microns in width and which can, in principle, be tailored to adsorb specific molecules or classes of molecule by changing the method of preparation (the activation process). For the physical chemist, they pose the challenge of understanding how gases adsorb in graphitic nanopores, that is, in restricted geometries, and of using that understanding to improve their characterization. In this paper, we compare pore size distributions of an ultrahigh surface area activated carbon (AX21) determined from nitrogen adsorption measurements up to 0.6 bar at 77 K with those determined from carbon dioxide adsorption measurements up to 20 bar at 298 K. Our analysis employs grand canonical and Gibbs ensemble Monte Carlo simulations together with accurate site−site interaction models of the adsorbates. We find that the calculated pore size distributions for each adsorbate are quite different, and the adsorption of one gas can be estimated from the adsorption of the other gas to within an error of 25% at the highest pressures only. At lower pressures, we speculate that large errors are due to the behavior of nitrogen in carbon micropores in which diffusion is severely limited. To substantiate this speculation, we have calculated the self-diffusion coefficient for nitrogen at 77 K and carbon dioxide at 298 K in carbon slit pores using equilibrium molecular dynamics. The results suggest that nitrogen is diffusionally limited, and possibly frozen, in such pores whereas carbon dioxide remains mobile. We conclude that room-temperature carbon dioxide adsorption isotherms up to the saturation pressure could provide a more accurate characterization of carbon microstructure than nitrogen isotherms at 77 K up to 1 bar