Self-diffusion of methane in single-walled carbon nanotubes at sub- and supercritical conditions

The diffusivities of methane in single-walled carbon nanotubes (SWNTs) are investigated at various temperatures and pressures using classical molecular dynamics (MD) simulations complemented with grand canonical Monte Carlo (GCMC) simulations. The carbon atoms at the nanotubes are structured according to the (m, m) armchair arrangement and the interactions between each methane molecule and all atoms of the confining surface are explicitly considered. It is found that the parallel self-diffusion coefficient of methane in an infinitely long, defect-free SWNT decreases dramatically as the temperature falls, especially at subcritical temperatures and high loading of gas molecules when the adsorbed gas forms a solidlike structure. With the increase in pressure, the diffusion coefficient first declines rapidly and then exhibits a nonmonotonic behavior due to the layering transitions of the adsorbed gas molecules as seen in the equilibrium density profiles. At a subcritical temperature, the diffusion of methane in a fully loaded SWNT follows a solidlike behavior, and the value of the diffusion coefficient varies drastically with the nanotube diameter. At a supercritical temperature, however, the diffusion coefficient at high pressure reaches a plateau, with the limiting value essentially independent of the nanotube size. For SWNTs with the radius larger than approximately 2 nm, capillary condensation occurs when the temperature is sufficiently low, following the layer-by-layer adsorption of gas molecules on the nanotube surface. For SWNTs with a diameter less than about 2 nm, no condensation is observed because the system becomes essentially one-dimensional.     

Fluid in a closed narrow slit

The behavior of a fluid inside a closed narrow slit between solid walls is examined on the basis of the density functional theory. It is shown that the constraint of constant number of molecules leads to interesting effects which are absent when the slit is open and in contact with a reservoir. If the slit walls are identical, the density profiles at low temperatures or at high average densities rhoav of the fluid molecules in the slit have a sharp maximum in the middle of the slit, the value of the density at maximum being comparable to that of a liquid. The density of fluid at the walls is in this case comparable to the density of a vapor phase. At high temperatures or at low rhoav the fluid density in the middle of the slit is of the same order of magnitude as at the walls. For nonidentical walls the density maximum is shifted towards the wall with a stronger wall-fluid interaction. The transition between the two types (with and without the sharp maximum) of density profiles with the change of temperature in the slit occurs in a narrow range of temperatures, this range being larger for narrower slits. The pressures which the fluid exerts on the walls as well as the forces per unit area arising due to stresses in the sidewalls of the system can decrease with increasing rhoav. Such a behavior is not possible for homogeneous systems and can be explained by analyzing the fluid density at the walls when rhoav increases. The normal and transversal components of the pressure tensor were calculated as functions of the distance from the wall using the equation of hydrostatic equilibrium and direct calculation of the forces between molecules, respectively. The normal component decreases with increasing distance near the wall in contrast to the normal component near the liquid-vapor interface reported previously in the literature. The behavior of the transverse component does not depend on the fluid-solid interaction and is comparable to that for a liquid-vapor interface.     

Temperature dependence of local density augmentation for acetophenone N,N,N',N'-tetramethylbenzidine exciplex in supercritical water

Local density augmentation around exciplex between acetophenone and N,N,N',N'-tetramethylbenzidine in supercritical water was measured by observing the peak shift of transient absorption spectrum at temperatures from 380 to 410 degrees C and at pressures from 6 to 37 MPa. Large local density augmentation was observed at lower solvent densities. Local density augmentation was evaluated by the excess density, which was defined as the difference between local density and bulk density, and the density enhancement factor, which was defined by the ratio of the local density to the bulk density. The number of solvating molecules was estimated with a Langmuir adsorption model. The excess density was found to exhibit a maximum at approximately 0.15 g cm(-3), which decreased with increasing temperature. The density enhancement factor was found to decrease with increasing temperature; however, its value was much greater than unity at 410 degrees C, which provides evidence that exciplex-water interactions still exist at these conditions. The temperature dependence of local density augmentation around the exciplex in supercritical water was comparable with that in supercritical carbon dioxide, which suggests that the ratios of the solute-solvent and solvent-solvent interactions are comparable between these two systems.     

Development of equations for differential and integral enthalpy change of adsorption for simulation studies

We present equations to calculate the differential and integral enthalpy changes of adsorption for their use in Monte Carlo simulation. Adsorption of a system of N molecules, subject to an external potential energy, is viewed as one of transferring these molecules from a reference gas phase (state 1) to the adsorption system (state 2) at the same temperature and equilibrium pressure (same chemical potential). The excess amount adsorbed is the difference between N and the hypothetical amount of gas occupying the accessible volume of the system at the same density as the reference gas. The enthalpy change is a state function, which is defined as the difference between the enthalpies of state 2 and state 1, and the isosteric heat is defined as the negative of the derivative of this enthalpy change with respect to the excess amount of adsorption. It is suitable to determine how the system behaves for a differential increment in the excess phase adsorbed under subcritical conditions. For supercritical conditions, use of the integral enthalpy of adsorption per particle is recommended since the isosteric heat becomes infinite at the maximum excess concentration. With these unambiguous definitions we derive equations which are applicable for a general case of adsorption and demonstrate how they can be used in a Monte Carlo simulation. We apply the new equations to argon adsorption at various temperatures on a graphite surface to illustrate the need to use the correct equation to describe isosteric heat of adsorption.     

Hydrogen confinement in carbon nanopores: extreme densification at ambient temperature

In-situ small-angle neutron scattering studies of H(2) confined in small pores of polyfurfuryl alcohol-derived activated carbon at room temperature have provided for the first time its phase behavior in equilibrium with external H(2) at pressures up to 200 bar. The data were used to evaluate the density of the adsorbed fluid, which appears to be a function of both pore size and pressure and is comparable to the density of liquid H(2) in narrow nanopores at ～200 bar. The surface-molecule interactions responsible for densification of H(2) within the pores create internal pressures that exceed the external gas pressure by a factor of up to ～50, confirming the benefits of adsorptive storage over compressive storage. These results can be used to guide the development of new carbon adsorbents tailored for maximum H(2) storage capacities at near-ambient temperatures.     

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.     

Solubilities of caffeine and theophylline in supercritical ammonia

The solubilities of caffeine and theophylline in supercritical ammonia at 140°C have been determined. Both compounds exhibited substantial solubility in the ammonia, with caffeine showing the greatest increase in solubility near the critical pressure where density increases most rapidly. However, theophylline showed an appreciable solubility at pressures substantially below the critical pressure. Possible chemical reactions of supercritical ammonia with these solutes at this temperature were found to be unimportant in the present study. The role of supercritical ammonia as a solvent for polar organic molecules is discussed.     

Computer simulation investigation of the water-benzene interface in a broad range of thermodynamic States from ambient to supercritical conditions

The dependence of the properties of the water-benzene system on the thermodynamic conditions in a broad range of temperatures and pressures has been investigated by computer simulation methods. For this purpose, Monte Carlo simulations have been performed at 23 different thermodynamic states, ranging from ambient to supercritical conditions. The density profiles of the water and benzene molecules have been determined at each of the thermodynamic states investigated. Information on the dependence of the mutual solubility of the two components in each other as well as of the width of the interface on the temperature and pressure has been extracted from these profiles. The width of the interface has been found to increase with increasing temperature up to a certain point, where it diverges. The temperature of this divergence corresponds to the mixing of the two phases. The determination of the critical mixing temperature at various pressures allowed us to estimate the upper critical curve, separating the two-phase and one-phase liquid systems, of the phase diagram of the simulated water-benzene system. In analyzing the preferential orientation of the interfacial molecules relative to the interface, it has been found that the main orientational preference of the benzene molecules is to lie parallel with the plane of the interface, and the water molecules penetrated deepest into the benzene phase prefer to stay perpendicular to the interface, pointing by one of their O-H bonds almost straight toward the benzene phase, whereas the waters located at the aqueous side of the interface are preferentially aligned parallel with the interfacial plane. Although the strength of the observed orientational preferences decreases rapidly with increasing temperature, the preferred orientations themselves are found to be independent of the thermodynamic conditions. Remains of the orientational preferences of the molecules are found to be present up to temperatures as high as 650 K. The analysis of the relative orientation of the neighboring water-benzene pairs has revealed that the radius of the first hydration shell of the benzene molecules is independent of the thermodynamic conditions, even if the system consists of one single phase. It has been found that the nearest water neighbors of the benzene molecules are preferentially located above and below the benzene ring, whereas more distant water neighbors, belonging still to the first hydration shell, prefer to stay within the plane of the benzene molecule. In the two-phase systems the dipole vector of the nearest waters has been found to be preferentially perpendicular to the vector pointing from the center of the benzene molecule to the water O atom.     

Methane adsorption and diffusion in a model nanoporous carbon: an atomistic simulation study

A constricted slit model was introduced to improve, one step further, the performance of the simple slit model in prediction of the adsorption and diffusion behavior of simple molecules in the nanoporous carbons (NPCs). The grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations are performed to study the adsorption and diffusion behavior of methane within the constricted slit models. The models are called slit-1, 2, and 3 with constriction heights 5, 7, and 9 Å respectively. For comparison, we used the slit-0 name for the simple slit without constriction. Adsorption results show that at low pressures, the constriction increases the adsorbed amount irrespective of its height. Slit-2 with a constriction height as a molecular diameter has the greatest heat of adsorption and has highest loading at pressures up to 3,000 kPa. At high pressures, when all pores are filled, the adsorption trend is in line with the pore volumes of slits where slit-0 with higher pore volume is dominant. The density profiles in the models were calculated and examined. The spatial distribution of adsorbed methane molecules was examined by various radial distribution functions calculated by MD. Also, MD simulation results show that the diffusion coefficient of methane decreases in constricted slits. The calculated diffusion coefficients in slit-2 in the direction of the constriction are one order of magnitude smaller than the calculated one in the simple slit model but it is far from the experimental values in the NPCs.     

Monte Carlo simulation of n-alkane adsorption isotherms in carbon slit pores

The single component adsorption of alkanes in carbon slit pores was studied using configurational-biased grand canonical Monte Carlo simulations. Wide ranges of temperature, pressure, alkane chain length, and slit height were studied to evaluate their effects on adsorption. Adsorption isotherms and density and orientation profiles were calculated. The behavior of long alkanes at high temperatures was found to be similar to short alkanes at lower temperatures. This suggests that the isotherms may be related through the Polanyi potential theory.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

Ethane adsorption in slit-shaped micropores: influence of molecule orientation on adsorption capacity

Adsorption of ethane in a slit shaped micropore system has been studied by Monte Carlo molecular simulation by considering this hydrocarbon as a two interacting sites molecule. Ethane adsorption in pore sizes from 0.41 to 1.66 nm was simulated at 303 K. Microscopic characteristics of the adsorbed phase have been studied for pores of different size, comparing two density profiles: the molecule centre of mass profile and the molecular interaction site profile. Averaged angle distribution of molecule positions with respect to the slit plane across the pore width has been also obtained by simulation. These results were related to ethane molecule packing efficiency, which is also related to the adsorption capacity in terms of the adsorbed phase density. Packing efficiency presents an oscillation shape as the result of the adsorbate disorder inside the pore. Pressure influence on the adsorption has been studied by following pore filling by simulation. When pore condensation takes place and for pressures above condensation, fluid-fluid interactions are determinant in molecule disorder observed between the two adsorbed layers.     

Reliable measurement of near-critical adsorption by gravimetric method

A gravimetric apparatus is used to measure the excess adsorption at high pressure. The equipment consists of a Rubotherm magnetic suspension balance, which allows to measure also the density of the fluid. In order to obtain the excess adsorbed amount, the measured weight has to be corrected with a buoyancy term, for which the density of the adsorbing fluid has to be known at each experimental conditions. Therefore the homogeneity of density in the high-pressure cell plays a fundamental role in determining the accuracy of the measured excess adsorbed amounts. This paper is intended to show the impact of the actual approach to thermostating the unit on the density distribution of the adsorbing fluid inside the high-pressure cell. Namely, by changing the inlet position of the heating fluid, large differences in the measured excess adsorption are produced. The closer to the critical point of the fluid, the stronger are these differences. An optimum configuration for our measuring device has been found and it has been used to study the adsorption of carbon dioxide (CO₂) on Filtrasorb 400 activated carbon at supercritical and near-critical conditions.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Determination of Kamlet-Taft solvent parameters pi* of high pressure and supercritical water by the UV-Vis absorption spectral shift of 4-nitroanisole

Kamlet-Taft solvent parameters, pi*, of high pressure and supercritical water were determined from 16-420 degrees C based on solvatochromic measurements of 4-nitroanisole. For the measurements, an optical cell that could be used at high temperatures and pressures was developed with the specification of minimal dead space. The low dead space cell allowed us to measure the absorption spectra of 4-nitroanisole at high temperature conditions before appreciable decomposition occurred. The behavior of pi* in terms of water density (pi* = 1.77rho- 0.71) was found to be linear, except in the near critical region, in which deviations were observed that could be attributed to local density augmentation. Excess density, which was defined as the difference between local density and bulk density, showed a maximum near the critical density of water. The frequencies of UV-Vis spectra of 4-(dimethylamino)benzonitrile and N,N-dimethyl-4-nitroaniline were correlated with pi* based on a linear solvation energy relationship (LSER) theory. Local density augmentation around 4-nitroanisole and that around 4-(dimethylamino)benzonitrile were similar but the augmentation observed around N,N-dimethyl-4-nitroaniline was larger.     

Direct measurements of pore fluid density by vibrating tube densimetry

The densities of pore-confined fluids were measured for the first time by means of vibrating tube densimetry (VTD). A custom-built high-pressure, high-temperature vibrating tube densimeter was used to measure the densities of propane at subcritical and supercritical temperatures (between 35 and 97 °C) and carbon dioxide at supercritical temperatures (between 32 and 50 °C) saturating hydrophobic silica aerogel (0.2 g/cm(3), 90% porosity) synthesized inside Hastelloy U-tubes. Additionally, supercritical isotherms of excess adsorption for CO(2) and the same porous solid were measured gravimetrically using a precise magnetically coupled microbalance. Pore fluid densities and total adsorption isotherms increased monotonically with increasing density of the bulk fluid, in contrast to excess adsorption isotherms, which reached a maximum and then decreased toward zero or negative values above the critical density of the bulk fluid. The isotherms of confined fluid density and excess adsorption obtained by VTD contain additional information. For instance, the maxima of excess adsorption occur below the critical density of the bulk fluid at the beginning of the plateau region in the total adsorption, marking the end of the transition of pore fluid to a denser, liquidlike pore phase. Compression of the confined fluid significantly beyond the density of the bulk fluid at the same temperature was observed even at subcritical temperatures. The effect of pore confinement on the liquid-vapor critical temperature of propane was less than ~1.7 K. The results for propane and carbon dioxide showed similarity in the sense of the principle of corresponding states. Good quantitative agreement was obtained between excess adsorption isotherms determined from VTD total adsorption results and those measured gravimetrically at the same temperature, confirming the validity of the vibrating tube measurements. Thus, it is demonstrated that vibrating tube densimetry is a novel experimental approach capable of providing directly the average density of pore-confined fluids, and hence complementary to the conventional gravimetric or volumetric/piezometric adsorption techniques, which yield the excess adsorption (the Gibbsian surface excess).     

Liquids confined in wedge shaped pores: nonuniform pressure induced by pore geometry

Lennard-Jones liquids confined in wedge shaped nanopores are investigated using molecular dynamics computer simulations. We show that small deviations from the parallel slit geometry result in nonuniform pressures and density profiles along the pore. In conditions of high confinement and thermodynamic states close to the triple point, wedge shaped pores can induce the formation of solid phases in specific regions within the nanopore.