Capillary condensation and evaporation in alumina nanopores with controlled modulations

Pore Size Distribution Analysis Using Developing Hysteresis of Nitrogen in the Cylindrical Pores of Silica

A new method of mesopore size analysis was developed for the cylindrical pores of silica using a developing hysteresis of nitrogen measured at liquid nitrogen temperature. The method is based on the semimacroscopic approach of a modified Bonnet-Wolf model that deals with the grand potential of a vapor bubble in the cylindrical pore. It is capable of assessing correctly the pore structures of mesoporous materials with cylindrical pores using the narrow hysteresis loop of the developing hysteresis. When the mesoporous materials possess cylindrical pores of minor imperfections, two pore size distributions (PSDs) from the adsorption and desorption branches overlap. On the other hand, for cylindrical pores with an enhanced amplitude of pore corrugations and/or constrictions, PSD from the desorption branch is shifted to smaller pore sizes compared to the one from the adsorption branch, and at the same time, both the PSDs evaluated are shifted to lower pore sizes compared to the actual ones. The actual PSD can be assessed from the reversible isotherm measured at a hysteresis critical temperature. In principle, the present method may enable the determination of the PSDs from the adsorption hysteresis measured at any given temperature for mesoporous materials with cylindrical pores.

Revisiting the Nature of Adsorption and Desorption Branches: Temperature Dependence of Adsorption Hysteresis in Ordered Mesoporous Silica

To gain a deeper understanding as to the nature of the adsorption hysteresis due to capillary condensation of nitrogen in ordered mesoporous silicas, we calculated the temperature dependences of the activated condensation, equilibrium transition, and activated desorption pressures for nitrogen in spherical and cylindrical silica pores with several different pore sizes on the basis of semimacroscopic continuum models. The results clearly indicate that the models capture the exact nature of capillary condensation and evaporation phenomena of a fluid in cagelike and cylindrical mesopores. The temperature dependences of the adsorption hysteresis of nitrogen measured confirm previous theoretical predictions for cylindrical pores: for the ordered mesoporous silicas with cylindrical mesopores at least greater than ∼7 nm in diameter, the capillary condensation takes place via a nucleation process followed by a growth process of a bridging meniscus at pressures higher than the equilibrium transition, while the capillary evaporation takes place via a receding meniscus from pore ends at the equilibrium. For SBA-15 and MCM-41 with smaller mesopore sizes, on the other hand, the capillary condensation takes place close to the equilibrium transition pressures, while the capillary evaporation takes place at pressures lower than the equilibrium, owing to single pore blocking due to corrugation of the cylindrical pores. We discuss the effect of curvature on surface tension in capillary condensation, as well as the relation between a change in the mechanisms of adsorption and desorption and the pore corrugation in the cylindrical pores.

Current Regulation and Property Study of Porous Anodic Alumina Films with a Periodic Pore Structure

Porous anodic alumina (PAA) films with periodically modulated pore diameters are prepared by cyclic anodization of Al in a 0.6 M H₃PO₄ solution at room temperature. Studies have demonstrated that the oscillating current signals have an important effect on the structures of PAA films. Scanning electron microscopy (SEM) images of the PAA film show that when the positive triangle wave current signal is applied, with the increase in the maximum current value, PAA gradually exhibits a symmetrically modulated pore diameter structure, and part of the pores generates slub-like branches. When the maximum current value is 60 mA, the effect of modulation on the pore diameter is the most obvious and the UV reflectance spectrum shows the lowest reflectivity. A sawtooth wave current signal will cause the generation of a V-shaped structure at the junction of adjacent oxide layers. This work provides important guidance for regulating the structure of PAA by changing the current signal.

How Solutes Modify the Thermodynamics and Dynamics of Filling and Emptying in Extreme Ink-Bottle Pores

We investigate the filling and emptying of extreme ink-bottle porous media-micrometer-scale pores connected by nanometer-scale pores-when changing the pressure of the external vapor, in a case where the pore liquid contains solutes. These phenomena are relevant in diverse contexts, such as the weathering of building materials and artwork, aerosol formation in the atmosphere, and the hydration of soils and plants. Using model systems made of vein-shaped microcavities interconnected by a mesoporous matrix, we show experimentally that the presence of a nonvolatile solute shifts the condensation and evaporation transitions and in a way that is consistent with a modified Kelvin-Laplace equation that takes into account the osmotic pressure of the solution. Emptying occurs far below saturation, when the Kelvin stress, mediated by the large curvature of the liquid-vapor interfaces in the nanopores, is negative enough to induce spontaneous bubble nucleation in the microveins. Filling, on the other hand, occurs close to equilibrium (i.e., at saturation, p_sat for pure water and p_s < p_sat for a solution), driven by the weak capillary pressure of the liquid-vapor interface in the microveins. Interestingly, solutes allow the system to reach situations where the vapor is supersaturated with respect to the solution ( p_s < p < p_sat). We show that in that latter situation, a condensation layer covers the outer surface of the porous system, preventing the generation of Kelvin stresses but inducing osmotic stresses and flows that are vapor pressure-dependent. The timescales and dynamics reflect these different driving forces: emptying proceeds through discrete, stochastic nucleation events with very fast, unsteady bubble growth associated with a poroelastic relaxation process, while filling occurs collectively in all veins of the sample through a slower steady-state process driven by a combination of osmosis and capillarity. The dynamics can however be rendered symmetrical between filling and emptying if bubbles pre-exist during emptying, a case that we explore using cycling of the vapor pressure around equilibrium.

Adsorption on alumina nanopores with conical shape

Adsorption on porous solids depends on the morphology of the pores, the cylindrical one being the most studied in the literature. In this work, we present the first experimental investigation of adsorption and evaporation on conical nanopores produced by anodization of aluminium oxide. The pores are about 50 μm long, with the wide ends having a diameter of ∼79 nm and the narrow ones of ∼30 nm. Three different pores configurations are considered: open at both ends, open only at the narrow end and open only at the wide end. Despite the very small value of the conical angle α, estimated to be ∼0.06°, just barely above α = 0° corresponding to a cylindrical pore, the adsorption isotherms look strikingly different from those measured on cylindrical pores of similar size. First of all, the hysteresis loops of the conical pores with two open ends and with open wide ends practically coincide. Furthermore, they are narrower and the adsorption and evaporation branches are broader than those of the cylindrical pores with similar size. Finally, conical pores with open narrow ends exhibit a large hysteresis indicative of pore blocking. To unravel the mechanisms underlying adsorption and evaporation in such conical pores, we also report complementary results obtained using on-lattice grand canonical Monte Carlo simulations.

Scanning of Adsorption Hysteresis In Situ with Small Angle X-Ray Scattering

Everett's theorem-6 of the domain theory was examined by conducting adsorption in situ with small angle x-ray scattering (SAXS) supplemented by the contrast matching technique. The study focuses on the spectrum differences of a point to which the system arrives from different scanning paths. It is noted that according to this theorem at a common point the system has similar macroscopic properties. Furthermore it was examined the memory string of the system. We concluded that opposite to theorem-6: a) at a common point the system can reach in a finite (not an infinite) number of ways, b) a correction for the thickness of the adsorbed film prior to capillary condensation is necessary, and c) the scattering curves although at high-Q values coincide, at low-Q values are different indicating different microscopic states. That is, at a common point the system holds different metastable states sustained by hysteresis effects. These metastable states are the ones which highlight the way of a system back to a return point memory (RPM). Entering the hysteresis loop from different RPMs different histories are implanted to the paths toward the common point. Although in general the memory points refer to relaxation phenomena, they also constitute a characteristic feature of capillary condensation. Analogies of the no-passing rule and the adiabaticity assumption in the frame of adsorption hysteresis are discussed.

Adsorption on ordered and disordered duplex layers of porous anodic alumina

We have carried out systematic experiments and numerical simulations of the adsorption on porous anodic aluminum oxide (AAO) duplex layers presenting either an ordered or a disordered interconnecting interface between the large (cavity) and small (constriction) sections of the structured pores. Selective blocking of the pore openings resulted in three different pore topologies: open structured pores, funnel pores, and ink-bottle pores. In the case of the structured pores having an ordered interface, the adsorption isotherms present a rich phenomenology characterized by the presence of two steps in the condensation branch and the opening of one (two) hysteresis loops during evaporation for the ink-bottle (open and funnel) pores. The isotherms can be obtained by summing the isotherms measured on uniform pores having the dimensions of the constrictions or of the cavities. The numerical analysis of the three different pore topologies indicates that the shape of the junction between the two pore sections is only important for the adsorption branch. In particular, a conic junction which resembles that of the AAO pores represents the experimental isotherms for the open and funnel pores better, but the shape of the junction in the ink bottle pores does not matter. The isotherms for the duplex layers with a disordered interface display the same general features found for the ordered duplex layers. In both cases, the adsorption branches coincide and have two steps which are shifted to lower relative pressures compared to those for the ordered duplex. Furthermore, the desorption branches comprise hysteresis loops much wider than those of the ordered duplex layers. Overall, this study highlights the important role played by morphologies where there are interconnections between large and small pores.

Adsorption in alumina pores open at one and at both ends

We have studied adsorption in regular, self-ordered alumina pores open at both ends or only at one end. The straight, non-connected pores have diameters ranging from 22 to 83 nm, with a relative dispersion below 1% in the pore size. Adsorption isotherms measured in open pores with a torsional microbalance show pronounced hysteresis loops characterized by nearly vertical and parallel adsorption and desorption branches. Blocking one end of the pores with glue has a strong influence on adsorption, as expected from classical macroscopic arguments. However, the experimental measurements show an unexpectedly rich phenomenology dependent on the pore size. For large pores (Dp ≥ 67 nm), the isotherms for closed end pores present much narrower hysteresis loops whose adsorption and desorption boundaries envelop the desorption branches of the isotherms for the corresponding open pores of the same size. The loop for small closed end pores (Dp = 22 nm) is slightly wider than that for open pores while the adsorption branches coincide. For large pores, in contrast, the desorption branches of pores with the same Dp overlap regardless of the pore opening. These observations are in agreement with our grand canonical Monte Carlo (GCMC) simulations for a cylindrical pore model with constrictions, suggesting that the alumina pores could be modeled using a constricted pore model whose adsorption isotherm depends on the ratio of the constriction size to the pore size (Dc/Dp).

Drying by cavitation and poroelastic relaxations in porous media with macroscopic pores connected by nanoscale throats

We investigate the drying dynamics of porous media with two pore diameters separated by several orders of magnitude. Nanometer-sized pores at the edge of our samples prevent air entry, while drying proceeds by heterogeneous nucleation of vapor bubbles--cavitation--in the liquid in micrometer-sized voids within the sample. We show that the dynamics of cavitation and drying are set by the interplay of the deterministic poroelastic mass transport in the porous medium and the stochastic nucleation process. Spatiotemporal patterns emerge in this unusual reaction-diffusion system, with temporal oscillations in the drying rate and variable roughness of the drying front.

Effects of carbon coating and pore corrugation on capillary condensation of nitrogen in SBA-15 mesoporous silica

To examine the origin of an ink-bottle-like structure in SBA-15 formed by carbon coating and the effects of pore corrugation on capillary condensation and evaporation of a vapor in the cylindrical pores, we measured the adsorption isotherms of nitrogen at 77 K on 10 kinds of SBA-15 samples before and after a carbon coating process by the exposure to acetylene at 1073 K, as well as desorption scanning curves and subloops on the untreated samples. These SBA-15 samples were synthesized under the different conditions of initial SiO2/P123 ratio and hydrothermal treatment. SBA-15 with relatively large microporosity tends to form easily constrictions inside the main channels by the carbon coating. This strongly suggests that the rough pore walls of SBA-15 may induce the incomplete wetting of carbon layers on the pore walls to form the constrictions inside the cylindrical pores. A comparison of two subloops implies that the pores of SBA-15 synthesized with a SiO2/P123 ratio of 75 consist of an assembly of connecting domains of different diameters; that is, the pores are highly corrugated. For SBA-15 synthesized with a SiO2/P123 ratio of 60, the amplitude of the pore corrugation is significantly decreased by the prolonged hydrothermal treatment at 373 K. On the other hand, for SBA-15 synthesized with a SiO2/P123 ratio of 45, the amplitude of the corrugation is negligibly small, although the cylindrical pores are interconnected through narrow necks with each other. It is found that the smaller the amplitude of the pore corrugation, the smaller the width of the hysteresis loop.

On the irreversibility of the adsorption isotherm in a closed-end pore

We present a simulation study of argon adsorption in a closed-end mesopore of uniform diameter in order to investigate the occurrence of hysteresis and propose two principal reasons for its existence: the variation in the shape and radius of curvature of the meniscus and the change in the packing of adsorbate during adsorption and desorption. This interpretation differs from classical theories that neglect both of these factors, and therefore find that adsorption-desorption in a closed-end pore is reversible. A detailed simulation study of the effects of temperature on the microscopic behavior of the adsorbate supports the interpretation proposed here.

Investigation of the problems with using gas adsorption to probe catalyst pore structure evolution during coking

A common approach to try to understand the mechanism of coking in heterogeneous catalysts is to monitor the evolution of the pore structure using gas adsorption analysis of discharged pellets. However, the standard methods of analysis of gas adsorption data, to obtain pore-size distributions, make the key assumption of thermodynamically-independent pores. This assumption neglects the possibility of co-operative adsorption phenomena, which will shown to be a critical problem when looking at coking catalysts. In this work the serial adsorption technique has been used to detect and assess the extent of co-operative effects in adsorption within coking catalysts. The reaction of decane over a hydroprocessing catalyst was used as a case study. It has been shown that the conventional analysis method would lead to a flawed picture of the pore structure changes during the coking process. For the case-study considered in this work, it was found that co-operative adsorption effects meant that 26% of the measured adsorption was occurring in pores up to three times larger than the size conventional analysis would presume. The serial adsorption technique was thus shown to provide important additional information on pore structure evolution during coking. A study of the kinetics of adsorption has been used to infer information about the general spatial location of the coking process within a pellet.

Optofluidic characterization of nanoporous membranes

An optofluidic method that accurately identifies the internal geometry of nanochannel arrays is presented. It is based on the dynamics of capillary-driven fluid imbibition, which is followed by laser interferometry. Conical nanochannel arrays in anodized alumina are investigated, which present an asymmetry of the filling times measured from different sides of the membrane. It is demonstrated by theory and experiments that the capillary filling asymmetry only depends on the ratio H of the inlet to outlet pore radii and that the ratio of filling times vary closely as H(7/3). Besides, the capillary filling of conical channels exhibits striking results in comparison to the corresponding cylindrical channels. Apart from these novel results in nanoscale fluid dynamics, the whole method discussed here serves as a characterization technique for nanoporous membranes.

Controlling the role of nanopore morphology in capillary condensation

The effect of pore morphology on capillary condensation and evaporation in nanoporous silicon is studied experimentally. A variety of cooperative and local effects are observed in tailored nanopores with well-defined regions by directly probing gas adsorption in each region using optical interferometry. All observations are ascribed to the ability of the nanopore region to access the gas reservoir directly and the nucleation of liquid bridges at local heterogeneities within the nanopore region. These assumptions, consistent with recent simulations, can be extended to any real nanoporous system.

Adsorption, capillary bridge formation, and cavitation in SBA-15 corrugated mesopores: a Derjaguin-Broekhoff-de Boer analysis

A Derjaguin-Broekhoff-de Boer analysis of adsorption and desorption in SBA-15 mesoporous silica is presented, using realistic geometrical models that account for the pore corrugation in these materials. The model parameters are derived from independent electron tomography and small-angle scattering characterization. A geometrical characteristic of the pore that is found to be important for adsorption is the corrugation length, l(C), which describes the longitudinal size of the geometrical defects along a given pore. Capillary bridges are possible only for large values of l(C). The results are explained in terms of two spinodal and two equilibrium pressures, characterizing the wide and the narrow sections of the pores. Simplified analytical expressions are obtained, which provide necessary conditions for bridge formation and for cavitation in terms of the radii of the narrow and wide sections of the pores, as well as of l(C). Quite generally, the results show that the deviation of the pore shape from that of ideal cylinders is key to understanding adsorption and desorption in corrugated mesopores, notably in SBA-15.

Stability intervals of metastable states in hysteretic systems

Hysteresis in disordered systems originates in a plethora of metastable states. Previous works focused on their distribution inside the hysteresis. In contrast, an analysis of their range of metastability is proposed. This model, designed to catch the main features of fluid adsorption in porous materials, shows strong evidence that, in the thermodynamic limit, despite that metastable states of finite range can be found, they are exponentially dominated by those infinitely localized states.

Cavitation in metastable fluids confined to linear mesopores

We study the adsorption process of nitrogen (at 77.4 and 51.3 K) and argon (at 60 K) in porous silicon duplex layers, Si/A/B and Si/B/A, where the pores of A are on average narrower than the pores of B. We compare the experimental isotherms to that calculated from elemental isotherms measured in layers A and B supported by or detached from the silicon substrate. This allows us to confirm our previous studies which show that the relaxation of the substrate constraint modifies the adsorption strains and leads to a decrease of the adsorbed amount before condensation and consequently increases the condensation pressure. In the so-called ink-bottle Si/B/A configuration, layer B empties while layer A remains filled which proves that layer B empties via cavitation. The vapor pressure at which cavitation occurs in layer B in Si/B/A configuration is close to the pressure at which the same layer empties when it is in direct contact with the gas reservoir (Si/A/B configuration) which indicates that layer B contains all the ingredients necessary for cavitation to occur. The absolute value of the liquid pressure at which cavitation occurs is much lower than the value predicted by the theory of homogeneous nucleation. Nucleation of gas bubbles thus takes place on the surface of the pore walls. This is the crucial point of the paper. A receding meniscus with a contact angle lower than π/2 inside a pore and a gas bubble with a contact angle higher than π/2 are thus mutually exclusive. A receding meniscus cannot enter a pore. This has nothing to do with a pore-blocking effect; this is related to the physical parameters which define the contact angle inside the pores, that is, the surface energies at the solid-liquid, solid-vapor, and liquid-vapor interfaces. For argon at 60 K in the Si/B/A duplex layer, cavitation in layer B activates the emptying of a fraction of pores of layer A which constitutes a direct observation of metastable states.

Numerical characterization of the density of metastable states within the hysteresis loop in disordered systems

An improved approach is proposed to analyze the density of metastable states within any hysteresis loop, such as those observed in magnetic materials or for adsorption in porous materials. Except for a few analytically tractable models, most calculations have to be performed numerically on finite systems. The main points to be addressed thus concern the average over various material samples (the so-called realizations of the disorder), and the finite size analysis to estimate the thermodynamic limit. As an improvement of previously existing methods, it is proposed to introduce the Fourier transform of the density of metastable states (characteristic function). Its logarithm is shown to be additive and can straightforwardly be averaged over disorder. This procedure leads to a new definition of the complexity in finite size, giving the usual quenched complexity in the thermodynamic limit, while being better suited to performing finite size analysis. The calculations are illustrated on a molecular simulation based model for a simple fluid adsorbed in heterogeneous siliceous tubular pores mimicking mesoporous materials like MCM-41 or porous silicon. This approach is expected to be of general interest for hysteresis phenomena, including magnetic materials.

NMR studies of cooperative effects in adsorption

The conversion of gas adsorption isotherms into pore size distributions generally relies upon the assumption of thermodynamically independent pores. Hence, pore-pore cooperative adsorption effects, which might result in a significantly skewed pore size distribution, are neglected. In this work, cooperative adsorption effects in water adsorption on a real, amorphous, mesoporous silica material have been studied using magnetic resonance imaging (MRI) and pulsed-gradient stimulated-echo (PGSE) NMR techniques. Evidence for advanced adsorption can be seen directly using relaxation time weighted MRI. The number and spatial distributions of pixels containing pores of different sizes filled with condensate have been analyzed. The spatial distribution of filled pores has been found to be highly nonrandom. Pixels containing the largest pores present in the material have been observed to fill in conjunction with pixels containing much smaller pores. PGSE NMR has confirmed the spatially extensive nature of the adsorbed ganglia. Thus, long-range (≥40 μm) cooperative adsorption effects, between larger pores associated with smaller pores, occur within mesoporous materials. The NMR findings have also suggested particular types of pore filling mechanisms occur within the porous solid studied.

Highly ordered porous alumina with tailor-made pore structures fabricated by pulse anodization

A new anodization method for the preparation of nanoporous anodic aluminum oxide (AAO) with pattern-addressed pore structure was developed. The approach is based on pulse anodization of aluminum employing a series of potential waves that consist of two or more different pulses with designated periods and amplitudes, and provides unique tailoring capability of the internal pore structure of anodic alumina. Pores of the resulting AAOs exhibit a high degree of directional coherency along the pore axes without branching, and thus are suitable for fabricating novel nanowires or nanotubes, whose diameter modulation patterns are predefined by the internal pore geometry of AAO. It is found from microscopic analysis on pulse anodized AAOs that the effective electric field strength at the pore base is a key controlling parameter, governing not only the size of pores, but also the detailed geometry of the barrier oxide layer.