Simulation studies of sorption in model cylindrical micropores

Unraveling the influence of surface functionalities on gas Physisorption: A comprehensive study on SBA-15 nanoporous material from Monte Carlo simulation for improved Textural-Energetic characterization

In this study, we conducted experimental and Monte Carlo simulation studies in the grand canonical ensemble (GCMC) to investigate the role of molecular orientation and surface heterogeneity on the adsorption of N2 at 77 K. Our research focused on a series of ordered nanoporous materials (SBA-15) with varying degrees of oxygen functionalities. Specifically, we examined the effects of surface heterogeneity on the calculation of pore size distribution (PSD) and the Brunauer-Emmett-Teller (BET) area of porous materials. To provide a comprehensive perspective, we compared our results with three levels of surface oxidation, including a pristine case without any surface oxidation. The results from both our experimental and simulation data reveal the importance of chemical heterogeneity in determining equilibrium properties such as molecular packing within the pores, differential enthalpies of adsorption, and N2 orientation distribution. Our findings suggest that accurate characterization of surface heterogeneity is crucial for understanding gas adsorption in nanoporous materials and for developing better models for predicting their performance in various applications. Moreover, our simulations revealed substantial changes in the molecular orientation of adsorbate particles with increasing surface heterogeneity. This insight provides valuable information about the behavior of molecules within the nanoporous materials, further enhancing our understanding of the complex adsorption processes in these systems.

Heat of adsorption, adsorption stress, and optimal storage of methane in slit and cylindrical carbon pores predicted by classical density functional theory

Temperature, pressure and pore-size dependences of the heat of adsorption, adsorption stress, and adsorption capacity of methane in simple models of slit and cylindrical carbon pores are studied using classical density functional theory (CDFT) and grand-canonical Monte-Carlo (MC) simulation. Studied properties depend nontrivially on the bulk pressure and the size of the pores. Heat of adsorption increases with loading, but only for sufficiently narrow pores. While the increase is advantageous for gas storage applications, it is less significant for cylindrical pores than for slits. Adsorption stress and the average adsorbed fluid density show oscillatory dependence on the pore size and increase with bulk pressure. Slit pores exhibit larger amplitude of oscillations of the normal adsorption stress with pore size increase than cylindrical pores. However, the increase of the magnitude of the adsorption stress with bulk pressure increase is more significant for cylindrical than for slit pores. Adsorption stress appears to be negative for a wide range of pore sizes and external conditions. The pore size dependence of the average delivered density of the gas is analyzed and the optimal pore sizes for storage applications are estimated. The optimal width of slit pore appears to be almost independent of storage pressure at room temperature and pressures above 10 bar. Similarly to the case of slit pores, the optimal radius of cylindrical pores does not exhibit much dependence on the storage pressure above 15 bar. Both optimal width and optimal radii of slit and cylindrical pores increase as the temperature decreases. A comparison of the results of CDFT theory and MC simulations reveals subtle but important differences in the underlying fluid models employed by the approaches. The differences in the high-pressure behaviour between the hard-sphere 2-Yukawa and Lennard-Jones models of methane, employed by the CDFT and MC approaches, respectively, result in an overestimation of the heat of adsorption by the CDFT theory at higher loadings. However, both adsorption stress and adsorption capacity appear to be much less sensitive to the differences between the models and demonstrate excellent agreement between the theory and the computer experiment.

Cooperative CO2 adsorption promotes high CO2 adsorption density over wide optimal nanopore range

Separation of CO2 based on adsorption, absorption, and membrane techniques is a crucial technology necessary to address current global warming issues. Porous media are essential for all these approaches and understanding the nature of the porous structure is important for achieving highly efficient CO2 adsorption. Porous carbon is considered to be a suitable porous media for investigating the fundamental mechanisms of CO2 adsorption, because of its simple morphology and its availability in a wide range of well-defined pore sizes. In this study, we investigated the dependence of CO2 adsorption on pore structures such as pore size, volume, and specific surface area. We also studied slit-shaped and cylindrical pore morphologies based on activated carbon fibers of 0.6–1.7 nm and carbon nanotubes of 1–5 nm, respectively, with relatively uniform structures. Porous media with larger specific surface areas gave higher CO2 adsorption densities than those of media having larger pore volumes. Narrower pores gave higher adsorption densities because of deep adsorption potential wells. However, at a higher pressure CO2 adsorption densities increased again in nanopores including micropores and small mesopores. The optimal pore size ranges of CO2 adsorption in the slit-shaped and cylindrical carbon pores were 0.4–1.2 and 1.0–2.0 nm, respectively, although a high adsorption density was only expected for the narrow carbon nanopores from adsorption potentials. The wider nanopore ranges than expected nanopore ranges are reasonable when considering intermolecular interactions in addition to CO2–carbon pore interactions. Therefore, cooperative adsorption among CO2 in relatively narrow nanopores can allow for high density and high capacity adsorption.

Thermodynamic Resistance to Matter Flow at The Interface of a Porous Membrane

Nanoporous materials are important in industrial separation, but their application is subject to strong interfacial barriers to the entry and transport of fluids. At certain conditions the fluid inside and outside the nanoporous material can be viewed as a two-phase system, with an interface between them, which poses an excess resistance to matter flow. We show that there exist two kinds of phenomena which influence the interfacial resistance: hydrodynamic effects and thermodynamic effects, which are independent of each other. Here, we investigate the role of the thermodynamic effects in carbon nanotubes (CNTs) and slit pores and compare the associated thermodynmic resistance with that due to hydrodynamic effects traditionally modeled by the established Sampson expression. Using CH4 and CO2 as model fluids, we show that the thermodynamic resistance is especially important for moderate to high pressures, at which the fluid within the CNT or slit pore is in the condensed state. Further, we show that at such pressures the thermodynamic resistance becomes comparable with the internal resistance to fluid transport at length scales typical of membranes used in fuel cells, and of importance in membrane-based separation, and nanofluidics in general.

Capillary condensation of adsorbates in porous materials

Hysteresis in capillary condensation is important for the fundamental study and application of porous materials, and yet experiments on porous materials are sometimes difficult to interpret because of the many interactions and complex solid structures involved in the condensation and evaporation processes. Here we make an overview of the significant progress in understanding capillary condensation and hysteresis phenomena in mesopores that have followed from experiment and simulation applied to highly ordered mesoporous materials such as MCM-41 and SBA-15 over the last few decades.

Studies of capillary phase transitions of methane in metal-organic frameworks by gauge cell Monte Carlo simulation

Capillary phase transitions of CH(4) confined in a series of metal-organic frameworks (MOFs) were investigated in this work using gauge cell Monte Carlo simulations. The results show that capillary phase transitions can occur in MOFs, and the effects of temperature, pore size, and adsorption energy are very significant. Furthermore, this work shows the confinement can induce a shift in critical point for fluids confined in MOFs, leading to a decrease in critical temperature and an increase in critical density. The critical point shift is more obvious for MOFs with small pore size and large adsorption energy.

Appropriate volumes for adsorption isotherm studies: The absolute void volume, accessible pore volume and enclosing particle volume

In adsorption studies the choice of an appropriate void volume in the calculation of the adsorption isotherm is very crucial. It is often taken to be the apparent volume as determined by the helium expansion experiments. Unfortunately this method has difficulties especially when dealing with microporous solids, in which adsorption of helium might become significant at ambient temperatures. The amount adsorbed is traditionally obtained as the excess amount and the term "excess" refers to the excess over the amount occupying the apparent volume that has the same density as the bulk gas density. This could give rise to the maximum in the plot of excess amount versus pressure under supercritical conditions, and in some cases giving negative excess. Such behavior is difficult to analyze because the excess amount is not amenable to any classical thermodynamic treatments. In this paper we will present a method to determine the absolute void volume, and in that sense this volume is independent of temperature and adsorbate. The volume that is accessible to the centers of gas molecules is also investigated, and it is called the accessible volume. This volume depends on the choice of adsorbate, and it is appropriate to use this volume to calculate the pore density because we can assess how dense the adsorbed phase is. In the quest to determine the "absolute" adsorption isotherm so that a thermodynamics analysis can be applied, it is necessary to introduce the concept of "enclosing" volume, which is essentially the volume that encloses all solid particles, including all void spaces in them. The amount adsorbed is defined by the number of molecules residing in this volume. Having these volumes, we can derive the geometrical accessible void volume inside the particle and the solid volume, from which the particle and solid densities can be calculated.

Distribution of carbon nanotube sizes from adsorption measurements and computer simulation

The method for the evaluation of the distribution of carbon nanotube sizes from the static adsorption measurements and computer simulation of nitrogen at 77 K is developed. We obtain the condensation/evaporation pressure as a function of pore size of a cylindrical carbon tube using Gauge Cell Monte Carlo Simulation (Gauge Cell MC). To obtain the analytical form of the relationships mentioned above we use Derjaguin-Broekhoff-deBoer theory. Finally, the pore size distribution (PSD) of the single-walled carbon nanohorns (SWNHs) is determined from a single nitrogen adsorption isotherm measured at 77 K. We neglect the conical part of an isolated SWNH tube and assume a structureless wall of a carbon nanotube. We find that the distribution of SWNH sizes is broad (internal pore radii varied in the range 1.0-3.6 nm with the maximum at 1.3 nm). Our method can be used for the determination of the pore size distribution of the other tubular carbon materials, like, for example, multiwalled or double-walled carbon nanotubes. Besides the applicable aspect of the current work the deep insight into the problem of capillary condensation/evaporation in confined carbon cylindrical geometry is presented. As a result, the critical pore radius in structureless single-walled carbon tubes is determined as being equal to three nitrogen collision diameters. Below that size the adsorption-desorption isotherm is reversible (i.e., supercritical in nature). We show that the classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena is a powerful method that can be applied for the determination of the distribution of nanotube sizes.

Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations

Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size is the highest, whereas an increase of the pore size and the density of hydrogen volumetric energy causes the polymer swelling up to a value slightly below the one computed from the bulk phase. Quantum confinement-inducing polymer shrinking is of great importance for realizing the potential of quantum molecular sieves.

Capillary condensation in cylindrical nanopores

Using grand canonical Monte Carlo simulations, we have explored the phenomenon of capillary condensation (CC) of Ar at the triple temperature inside infinitely long, cylindrical pores. Pores of radius R = 1 nm, 1.7 nm, and 2.5 nm have been investigated using a gas-surface interaction potential parametrized by the well depth D of the gas on a planar surface made of the same material as that comprising the porous host. For strongly attractive situations--i.e., large D--one or more (depending on R) Ar layers adsorb successively before liquid fills the pore. For very small values of D, in contrast, negligible adsorption occurs at any pressure P below saturated vapor pressure P0; above saturation, there eventually occurs a threshold value of P at which the coverage jumps from empty to full, nearly discontinuously. Hysteresis is found to occur in the simulation data whenever abrupt CC occurs--i.e., for R > or = 1.7 nm--and for small D when R = 1 nm. Then, the pore-emptying branch of the adsorption isotherm exhibits larger coverage than the pore-filling branch, as is known from many experiments and simulation studies. The relation between CC and wetting on planar surfaces is discussed in terms of a threshold value of D, which is about one-half of the value found for the wetting threshold on a planar surface. This finding is consistent with a simple thermodynamic model of the wetting transition developed previously.

Quasi One-Dimensional Nanopores in Single-Wall Carbon Nanohorn Colloids Using Grand Canonical Monte Carlo Simulation Aided Adsorption Technique

The average interstitial nanopore structure of single-wall carbon nanohorn (SWNH) assemblies was determined using X-ray diffraction and grand canonical Monte Carlo (GCMC) simulation aided N(2) adsorption at 77 K. The interstitial nanopores of SWNH assemblies can be regarded as quasi one-dimensional pores due to the partial orientation of the SWNH particles; the average pore width of the interstitial pores is 0.6 nm. Good agreement between the GCMC simulation of a structural model with one-dimensional interstitial nanopores and an experimental adsorption isotherm below P/P(0) = 10(-4) is evidence of the quasi one-dimensionality of the interstitial nanopores. A snapshot from the GCMC simulation showed one-dimensional growth of adsorbed N(2) molecules.

Adsorption hysteresis in nanopores

Capillary condensation hysteresis in nanopores is studied by Monte Carlo simulations and the nonlocal density functional theory. Comparing the theoretical results with the experimental data on low temperature sorption of nitrogen and argon in cylindrical channels of mesoporous siliceous molecular sieves of MCM-41 type, we have revealed four qualitatively different sorption regimes depending on the temperature and pore size. As the pore size increases at a given temperature, or as the temperature decreases at a given pore size, the following regimes are consequently observed: volume filling without phase separation, reversible stepwise capillary condensation, irreversible capillary condensation with developing hysteresis, and capillary condensation with developed hysteresis. We show that, in the regime of developed hysteresis (pores wider than 5 nm in the case of nitrogen sorption at 77 K), condensation occurs spontaneously at the vaporlike spinodal while desorption takes place at the equilibrium. A quantitative agreement is found between the modeling results and the experimental hysteresis loops formed by the adsorption-desorption isotherms. The results obtained provide a better understanding of the general behavior of confined fluids and the specifics of sorption and phase transitions in nanomaterials.

Statistical geometry of cavities in a metastable confined fluid

The statistical geometry of cavities in a confined Lennard-Jones (LJ) fluid is investigated with the focus on metastable states in the vicinity of the stability limit of the liquidlike state. For a given configuration of molecules, a cavity is defined as a connected region where there is sufficient space to accommodate an additional molecule. By means of grand canonical Monte Carlo simulations, we generated a series of equilibrium stable and metastable states along the adsorption-desorption isotherm of the LJ fluid in a slit-shaped pore of ten molecular diameters in width. The geometrical parameters of the cavity distributions were studied by Voronoi-Delaunay tessellation. We show that the cavity size distribution in liquidlike states, characterized by different densities, can be approximated by a universal log-normal distribution function. The mean void volume increases as the chemical potential &mgr; and, correspondingly, the density decreases. The surface-to-volume relation for individual cavities fulfills the three-dimensional scaling S(cav)=gV(2/3)(cav) with the cavity shape factor g=8.32-9.55. The self-similarity of cavities is observed over six orders of magnitude of the cavity volumes. In the very vicinity of the stability limit, &mgr;-->&mgr;(sl), large cavities are formed. These large cavities are ramified with a fractal-like surface-to-volume relation, S(cav) approximately V(cav). Better statistics are needed to check if these ramified cavities are similar to fragments of a spanning percolation cluster. At the limit of stability, the cavity volume fluctuations are found to diverge as (<V(2)(cav)>-<V(cav)>(2)) approximately [(&mgr;-&mgr;(sl))/kT](-gamma(c)) with the exponent gamma(c) approximately 0.93. This exponent can be referred to as the cavity pseudocritical exponent, in analogy with the other pseudocritical exponents characterizing the divergence of thermodynamic quantities at the spinodal point.