Adsorption of argon and nitrogen in cylindrical pores of MCM-41 materials: application of density functional theory

Adsorption of argon and nitrogen at their respective boiling points in cylindrical pores of MCM-41 type silica-like adsorbents is studied by means of a non-local density functional theory (NLDFT), which is modified to deal with amorphous solids. By matching the theoretical results of the pore filling pressure versus pore diameter against the experimental data, we arrive at a conclusion that the adsorption branch (rather than desorption) corresponds to the true thermodynamic equilibrium. If this is accepted, we derive the optimal values for the solid–fluid molecular parameters for the system amorphous silica–Ar and amorphous silica–N2, and at the same time we could derive reliably the specific surface area of non-porous and mesoporous silica-like adsorbents, without a recourse to the BET method. This method is then logically extended to describe the local adsorption isotherms of argon and nitrogen in silica-like pores, which are then used as the bases (kernel) to determine the pore size distribution. We test this with a number of adsorption isotherms on the MCM-41 samples, and the results are quite realistic and in excellent agreement with the XRD results, justifying the approach adopted in this paper.

Effects of potential models in the vapor-liquid equilibria and adsorption of simple gases on graphitized thermal carbon black

In this paper, we investigate the effects of various potential models in the description of vapor–liquid equilibria (VLE) and adsorption of simple gases on highly graphitized thermal carbon black. It is found that some potential models proposed in the literature are not suitable for the description of VLE (saturated gas and liquid densities and the vapor pressure with temperature). Simple gases, such as neon, argon, krypton, xenon, nitrogen, and methane are studied in this paper. To describe the isotherms on graphitized thermal carbon black correctly, the surface mediation damping factor introduced in our recent publication should be used to calculate correctly the fluid–fluid interaction energy between particles close to the surface. It is found that the damping constant for the noble gases family is linearly dependent on the polarizability, suggesting that the electric field of the graphite surface has a direct induction effect on the induced dipole of these molecules. As a result of this polarization by the graphite surface, the fluid–fluid interaction energy is reduced whenever two particles are near the surface. In the case of methane, we found that the damping constant is less than that of a noble gas having the similar polarizability, while in the case of nitrogen the damping factor is much greater and this could most likely be due to the quadrupolar nature of nitrogen.

Modeling nitrogen adsorption in spherical pores of siliceous materials by density functional theory

Adsorption of nitrogen in spherical pores of FDU-1 silica at 77 K is considered by means of a nonlocal density functional theory (NLDFT) accounting for a disordered structure of pore walls. Pore size distribution analysis of various FDU-1 samples subject to different temperatures of calcination revealed three distinct groups of pores. The principal group of pores is identified as ordered spherical mesopores connected with each other by smaller interconnecting pores and irregular micropores present in the mesopore walls. To account for the entrances (connecting pores) into spherical mesopores, a concept of solid mass distribution with respect to the apparent density was introduced. It is shown that the introduction of the aforementioned distribution was sufficient to quantitatively describe experimental adsorption isotherms over the entire range of relative pressures spanning six decades.

Effects of surface heterogeneity on the adsorption of nitrogen on graphitized thermal carbon black

In this paper, we study the surface heterogeneity and the surface mediation on the intermolecular potential energy for nitrogen adsorption on graphitized thermal carbon black (GTCB). The surface heterogeneity is modeled as the random distribution of effective carbonyl functional groups on the graphite surface. The molecular parameters and the discrete charges of this carbonyl group are taken from Jorgensen, et al. (J. Am. Chem. Soc., (1984) 106, 6638) while those for nitrogen (dispersive parameters and discrete charges) are taken from Murthy et al. (Mol. Phys., (1983) 50, 531) in our Grand Canonical Monte Carlo (GCMC) simulation. The solid surface mediation in the reduction of intermolecular potential energy between two fluid molecules was taken from a recent work by Do et al. (Langmuir, (2004) 20, 7623). Our simulation results accounting for the surface heterogeneity and surface mediation on intermolecular potential energy were compared with the experimental data of nitrogen at 77 and 90 K. The solid-fluid dispersive parameters are determined from the Lorentz-Berthelot (LB) rule. The fraction of the graphite surface covered with carbonyl functional groups was then derived from the consideration of the Henry constant, and for the data of Kruk et al. (Langmuir, (1999) 15, 1435) we have found that 1% of their GTCB surface is covered with effective carbonyl functional groups. The damping constant, due to surface mediation, was determined from the consideration of the portion of the adsorption isotherm where the first layer is being completed, and it was found to take a value of 0.0075. With these parameters, we have found that the GCMC simulation results describe the data over the complete range of pressure substantially better than any other MC models in the literature. The implication of this work is demonstrated with local adsorption isotherms of 10 and 20 A slit pores. One was obtained without allowance for surface mediation, while the other correctly accounts for these factors. The two local isotherms differ substantially, and the implication is that if we used incorrect local isotherms (i.e. without the surface mediation) the pore size distribution would be incorrectly derived.

GCMC-surface area of carbonaceous materials with N-2 and Ar adsorption as an alternative to the classical BET method

In this paper we apply a new method for the determination of surface area of carbonaceous materials, using the local surface excess isotherms obtained from the Grand Canonical Monte Carlo simulation and a concept of area distribution in terms of energy well-depth of solid–fluid interaction. The range of this well-depth considered in our GCMC simulation is from 10 to 100 K, which is wide enough to cover all carbon surfaces that we dealt with (for comparison, the well-depth for perfect graphite surface is about 58 K). Having the set of local surface excess isotherms and the differential area distribution, the overall adsorption isotherm can be obtained in an integral form. Thus, given the experimental data of nitrogen or argon adsorption on a carbon material, the differential area distribution can be obtained from the inversion process, using the regularization method. The total surface area is then obtained as the area of this distribution. We test this approach with a number of data in the literature, and compare our GCMC-surface area with that obtained from the classical BET method. In general, we find that the difference between these two surface areas is about 10%, indicating the need to reliably determine the surface area with a very consistent method. We, therefore, suggest the approach of this paper as an alternative to the BET method because of the long-recognized unrealistic assumptions used in the BET theory. Beside the surface area obtained by this method, it also provides information about the differential area distribution versus the well-depth. This information could be used as a microscopic finger-print of the carbon surface. It is expected that samples prepared from different precursors and different activation conditions will have distinct finger-prints. We illustrate this with Cabot BP120, 280 and 460 samples, and the differential area distributions obtained from the adsorption of argon at 77 K and nitrogen also at 77 K have exactly the same patterns, suggesting the characteristics of this carbon.

Cost-effectiveness of cognitive-behavioural therapy and drug interventions for major depression

Objective: Antidepressant drugs and cognitive-behavioural therapy (CBT) are effective treatment options for depression and are recommended by clinical practice guidelines. As part of the Assessing Cost-effectiveness - Mental Health project we evaluate the available evidence on costs and benefits of CBT and drugs in the episodic and maintenance treatment of major depression. Method: The cost-effectiveness is modelled from a health-care perspective as the cost per disability-adjusted life year. Interventions are targeted at people with major depression who currently seek care but receive non-evidence based treatment. Uncertainty in model inputs is tested using Monte Carlo simulation methods. Results: All interventions for major depression examined have a favourable incremental cost-effectiveness ratio under Australian health service conditions. Bibliotherapy, group CBT, individual CBT by a psychologist on a public salary and tricyclic antidepressants (TCAs) are very cost-effective treatment options falling below $A10 000 per disability-adjusted life year (DALY) even when taking the upper limit of the uncertainty interval into account. Maintenance treatment with selective serotonin re-uptake inhibitors (SSRIs) is the most expensive option (ranging from $A17 000 to $A20 000 per DALY) but still well below $A50 000, which is considered the affordable threshold. Conclusions: A range of cost-effective interventions for episodes of major depression exists and is currently underutilized. Maintenance treatment strategies are required to significantly reduce the burden of depression, but the cost of long-term drug treatment for the large number of depressed people is high if SSRIs are the drug of choice. Key policy issues with regard to expanded provision of CBT concern the availability of suitably trained providers and the funding mechanisms for therapy in primary care.

Modeling of adsorption and nucleation in infinite cylindrical pores by two-dimensional density functional theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.

A tutorial on the cross-entropy method

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning. combinatorial optimization

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

The adsorption of water in finite carbon pores

Grand canonical Monte Carlo simulations were applied to the adsorption of SPCE model water in finite graphitic pores with different configurations of carbonyl functional groups on only one surface and several pore sizes. It was found that almost all finite pores studied exhibit capillary condensation behaviour preceded by adsorption around the functional groups. Desorption showed the reverse transitions from a filled to a near empty pore resulting in a clear hysteresis loop in all pores except for some of the configurations of the 1.0nm pore. Carbonyl configurations had a strong effect on the filling pressure of all pores except, in some cases, in 1.0nm pores. A decrease in carbonyl neighbour density would result in a higher filling pressure. The emptying pressure was negligibly affected by the configuration of functional groups. Both the filling and emptying pressures increased with increasing pore size but the effect on the emptying pressure was much less. At pressures lower than the pore filling pressure, the adsorption of water was shown to have an extremely strong dependence on the neighbour density with adsorption changing from Type IV to Type III to linear as the neighbour density decreased. The isosteric heat was also calculated for these configurations to reveal its strong dependence on the neighbour density. These results were compared with literature experimental results for water and carbon black and found to qualitatively agree.

Does colonization asymmetry matter in metapopulations?

Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.

Nanoscale tubular vessels for storage of methane at ambient temperatures

Novel carbon nanostructures can serve as effective storage media for methane, a source of clean energy for the future. We have used Grand Canonical Monte Carlo Simulation for the modeling of methane storage at 293 K and pressures up to 80 MPa in idealized bundles of (10,10) armchair-type single-walled carbon nanotubes and wormlike carbon pores. We have found that these carbon nanomaterials can be treated as the world's smallest high-capacity methane storage vessels. Our simulation results indicate that such novel carbon nanostructures can reach a high volumetric energy storage, exceeding the US FreedomCAR Partnership target of 2010 (5.4 MJ dm(-3)), at low to moderate pressures ranging from 1 to 7 MPa at 293 K. On the contrary, in the absence of these nanomaterials, methane needs to be compressed to approximately 13 MPa at 293 K to achieve the same target. The light carbon membranes composed of bundles of single-walled carbon nanotubes or wormlike pores efficiently physisorb methane at low to moderate pressures at 293 K, which we believe should be particularly important for automobiles and stationary devices. However, above 15-20 MPa at 293 K, all investigated samples of novel carbon nanomaterials are not as effective when compared with compression alone since the stored volumetric energy and power saturate at values below those of the bulk, compressed fluid.

Optimization of slitlike carbon nanopores for storage of hythane fuel at ambient temperatures

Carbons with slitlike pores can serve as effective host materials for storage of hythane fuel, a bridge between the petrol combustion and hydrogen fuel cells. We have used grand canonical Monte Carlo simulation for the modeling of the hydrogen and methane mixture storage at 293 K and pressure of methane and hydrogen mixture up to 2 MPa. We have found that these pores serve as efficient vessels for the storage of hythane fuel near ambient temperatures and low pressures. We find that, for carbons having optimized slitlike pores of size H congruent to 7 angstrom ( pore width that can accommodate one adsorbed methane layer), and bulk hydrogen mole fraction >= 0.9, the volumetric stored energy exceeds the 2010 target of 5.4 MJ dm(-3) established by the U. S. FreedomCAR Partnership. At the same condition, the content of hydrogen in slitlike carbon pores is congruent to 7% by energy. Thus, we have obtained the composition corresponding to hythane fuel in carbon nanospaces with greatly enhanced volumetric energy in comparison to the traditional compression method. We proposed the simple system with added extra container filled with pure free/adsorbed methane for adjusting the composition of the desorbed mixture as needed during delivery. Our simulation results indicate that light slit pore carbon nanomaterials with optimized parameters are suitable filling vessels for storage of hythane fuel. The proposed simple system consisting of main vessel with physisorbed hythane fuel, and an extra container filled with pure free/adsorbed methane will be particularly suitable for combustion of hythane fuel in buses and passenger cars near ambient temperatures and low pressures.

The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.