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.

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.

Modeling of adsorption in finite cylindrical pores by means of density functional theory

Adsorption of argon at its boiling point infinite cylindrical pores is considered by means of the non-local density functional theory (NLDFT) with a reference to MCM-41 silica. The NLDFT was adjusted to amorphous solids, which allowed us to quantitatively describe argon adsorption isotherm on nonporous reference silica in the entire bulk pressure range. In contrast to the conventional NLDFT technique, application of the model to cylindrical pores does not show any layering before the phase transition in conformity with experimental data. The finite pore is modeled as a cylindrical cavity bounded from its mouth by an infinite flat surface perpendicular to the pore axis. The adsorption of argon in pores of 4 and 5 nm diameters is analyzed in canonical and grand canonical ensembles using a two-dimensional version of NLDFT, which accounts for the radial and longitudinal fluid density distributions. The simulation results did not show any unusual features associated with accounting for the outer surface and support the conclusions obtained from the classical analysis of capillary condensation and evaporation. That is, the spontaneous condensation occurs at the vapor-like spinodal point, which is the upper limit of mechanical stability of the liquid-like film wetting the pore wall, while the evaporation occurs via a mechanism of receding of the semispherical meniscus from the pore mouth and the complete evaporation of the core occurs at the equilibrium transition pressure. Visualization of the pore filling and empting in the form of contour lines is presented.

Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).

Controlled growth of anodic aluminium oxide films with hexagonal array of nanometer-sized pores filled with textured copper nanowires

Anodic aluminium oxide (AAO) films exhibiting a homogeneous morphology of parallel pores perpendicular to the surface were prepared in a two-step anodization process and filled with copper by electrochemical deposition. The optimum growth conditions for the formation of freestanding AAO films with hexagonal compact array of cylindrical pores were studied by field emission scanning electron microscopy and small angle X-ray scattering. The results show well-defined periodic structures with uniform pores size distribution for films with pore diameters between 40 and 70 nm prepared using different voltages and temperatures during the second anodization step. X-ray photoelectron spectroscopy and X-ray diffraction analysis of AAO films filled with copper show the formation of nanowires with high structural order, exhibiting a preferential crystalline orientation along the (2 2 0) axis and only small fraction of copper oxides. The best results for textured Cu nanowires were obtained at a reduction potential of -300 mV. (C) 2009 Elsevier Ltd. All rights reserved.

On the specific filtration mechanism of a mesoporous silica membrane, prepared with non-connecting parallel pores

We report the singular filtration properties of an ultrafiltration membrane made with mesoporous silica that exhibits cylindrical pores aligned mostly normal to the support. This membrane supported on tubular commercial macroporous alumina supports was prepared by the interfacial growth mechanism between stable silica-surfactant hybrid micelles made of the association of silica oligomers with polyethyleneoxide-based (PEO) surfactants and sodium fluoride, a well-known silica condensation catalyst [Boissière et al., An ultrafiltration membrane made with mesoporous MSU-X silica, Chem. Mater. 15 (2003) 460-463]. It appears that the combined effect of the silica nature of the membrane, whose surface charge can be easily adjusted by changing the pH and the non-connected cylindrical shape of the pores provides a new behavior in the retention properties, as proved by the filtration of polyoxyethylene polymers (PEO) with different molecular weights. Depending on the filtration conditions, a rejection rate of 80% and a steep cut-off at 2000 Da can be obtained or, on the reverse, polymers three times bigger than the pore diameter can diffuse through the membrane. This new filtration mechanism, which opens up new modes of separation modes, is explained in the light of both topology of the porous network and pH-dependent interactions between PEO polymers and silica porous media. © 2004 Elsevier B.V. All rights reserved.

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.

Equilibrium adsorption in cylindrical mesopores: A modified Broekhoff and de boer theory versus density functional theory

This paper presents a thermodynamic analysis of capillary condensation phenomena in cylindrical pores. Here, we modified the Broekhoff and de Boer (BdB) model for cylindrical pores accounting for the effect of the pore radius on the potential exerted by the pore walls. The new approach incorporates the recently published standard nitrogen and argon adsorption isotherm on nonporous silica LiChrospher Si-1000. The developed model is tested against the nonlocal density functional theory (NLDFT), and the criterion for this comparison is the condensation/evaporation pressure versus the pore diameter. The quantitative agreement between the NLDFT and the refined version of the BdB theory is ascertained for pores larger than 2 nm. The modified BdB theory was applied to the experimental adsorption branch of adsorption isotherms of a number of MCM-41 samples to determine their pore size distributions (PSDs). It was found that the PSDs determined with the new BdB approach coincide with those determined with the NLDFT (also using the experimental adsorption branch). As opposed to the NLDFT, the modified BdB theory is very simple in its utilization and therefore can be used as a convenient tool to obtain PSDs of all mesoporous solids from the analysis of the adsorption branch of adsorption isotherms of any subcritical fluids.

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 charge effect on the hindrance factors for diffusion and convection of a solute in pores II

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Electrical charge effect on osmotic flow through pores

An electrostatic model for osmotic flow through circular cylindrical pores is developed to describe the reflection coefficient for the membrane transport in the presence of surface charges on the pore wall and the solute. For a spherical solute placed at an arbitrary radial position in the pore, the electrical potential was computed by a spectral element method applied to the Poisson-Boltzmann equation together with the condition of electrical neutrality. The interaction energy between the surface charges was used to estimate the osmotic reflection coefficient. The proposed model predicts that even for a small Debye length compared to the pore radius, the repulsive electrostatic interaction between the surface charges could significantly increase the osmotic flow through the pore.

Electrodeposition of Ag-Ni-Fe Nanowires

Present work provides an electrodeposition based methodology for synthesizing Ag-Ni-Fe nanowires. Nanowire morphology was achieved by using an anodic alumina membrane having cylindrical pores of similar to 200 nm diameter. Compositional analysis at a single nanowire level revealed a fairly uniform distribution of component elements in the nanowire volume. Structural characterization strongly indicated toward a presence of randomly oriented, non-equilibrium, nano-crystalline phase volume inside the nanowires. Magnetic characterization revealed a soft magnetic character for the as-synthesized Ag-Ni-Fe nanowires. (C) 2014 The Electrochemical Society. All rights reserved.

Synthesis and characterization of Ag-Co-Ni nanowires

This work provides an electrodeposition-based methodology for synthesizing multicomponent nanowires containing Ag, Co and Ni atoms. Nanowire morphology was obtained by using an anodic alumina membrane with cylindrical pores of similar to 200-nm diameter. Structural, compositional and magnetic characterization revealed that the as-synthesized nanowires adopted a core-shell microstructure. The core (axial region) contained pure Ag phase volumes with a plate-like morphology oriented perpendicular to the nanowire axis. The shell (peripheral region) contained pure Ag nanoparticles along with superparamagnetic Co and Ni rich clusters.

Preparation of Microporous Membranes by Swift Heavy Ion Irradiation and Impedance Characterization

Polypropylene (PP) microporous membranes were successfully prepared by swift heavy ion irradiation and track-etching. Polypropylene foils were irradiated with Au-197 ions of kinetic energy 11.4 MeV.u(-1) (total energy of 2245.8 MeV) and fluence 1x10(8) ions.cm(-2) at normal incidence. The damaged regions produced by the gold ions along the trajectories were etched in H2SO4 and K2Cr2O7 solutions leading to the formation of cylindrical pores in the membranes. The pore diameters of the PP microporous membranes increased from 380 to 1610 nm as the etching time increased from 5 to 30 min. The surface and cross-section morphologies of the porous membranes were characterized by scanning electron microscopy (SEM). The micropores in the membranes were found to be cylindrical in shape, homogeneous in distribution, and equal in size. Some mathematical relations of the porosity of the PP microporous membranes were established by analytic derivation. The microporous membranes were used in lithium-ion batteries to measure their properties as separators. The electrical conductivity of the porous membrane immersed in liquid electrolyte was found to be comparable to that of commercial separators by electrochemical impedance spectroscopy (EIS). The results showed that the porosity and electrical conductivity were dependent on the ion fluence and etching time. By adjusting these two factors, microporous membranes with good porosity and electrical conductivity were made that met the requirements for commercial use.

AFM study of the self-assembly behavior of hexa-armed star polymers with a discotic triphenylene core

The size-armed polystyrenes and poly-(methyl methacrylate)s with a triphenylene core showed different self-assembling patterns, isolated cylinders for polySt on mico and highly ordered cylindrical pores for polyMMA on a silicon water. With a decrease of polymer concentration in tetrahydrofuran (HHF), the size and height of cylinders decreased for polySt, but fur polyMMA, the size and depth of the cylindrical pores increased. Slow evaporation of the solvent and a low molecular weight favored the formation of regular patterns.