On the existence of a hysteresis loop in open and closed end pores

We have studied the adsorption of argon at 87 K in slit pores of finite length with a smooth graphitic potential, open at both ends or closed at one end. Simulations were carried out using conventional GCMC (grand canonical Monte Carlo) or kMC (kinetic Monte Carlo) in the canonical ensemble with extremely long Markov chain, of at least 2 × 10⁸ configurations; selected simulations with much longer Markov chains do not show any change in the results. When the pore width is in the micropore range (0.65 nm), type I isotherms are obtained for both pore models and for both simulation methods. However, wider pores (1, 2 and 3 nm in width) all exhibit hysteresis loops in the GCMC simulations, while in the canonical ensemble simulations, the isotherms pass through a sigmoid van der Waals type loop in the transition region. This loop locates the true equilibrium transition. For the pores with one closed end, this transition is close to, or coincides with, the adsorption branch of the GCMC hysteresis loop, but for the open-ended pores, it is more closely associated with the desorption branch. In a separate study of adsorption hysteresis in an infinitely long slit pore, using both simulation techniques, the van der Waals loop follows the adsorption branch of the GCMC isotherm to the transition, then reverts to a long vertical section that falls midway between the two hysteresis branches and finally moves to the desorption transition close to the evaporation pressure. An examination of molecular distributions inside the pores reveals two coexisting phases in the canonical simulations, whereas in the grand canonical simulations, the molecules are uniformly distributed along the length of the pores.     

Computer modeling and analysis of heterogeneous structures of microporous carbonaceous materials

The aim of this work was to study the problems connected with computer modeling and analysis of heterogeneous structures of microporous carbonaceous materials. The research was focused on the numerical properties of original mathematical models for heterogeneous multilayer adsorption on microporous carbonaceous materials presented in our earlier papers and their applicability to examination of real microporous materials. These models are aimed at drawing information on pore structure and capacity on the basis of adsorption isotherms of small molecule adsorbates. They easily fit typical adsorption data in wide relative pressure ranges. In the theory presented, adsorption of small nearly spherical molecules in irregular pores of molecular size has been considered and side adsorbate–adsorbate interactions are neglected. The molecules mentioned are located in pores by forming aggregates, the size of which is limited by the geometry of the pores. The set of adsorbate molecules, which were adsorbed mainly due to adhesive interactions with the adsorbent matter, is treated as the first layer adsorption. Joining further molecules is viewed as the second, third,... layer adsorption. The main idea of the approach to modeling microporous structure presented, consists of introducing of realistic relationships between geometrical properties of pores and adsorption energy. Special attention was focused on the analysis of the influence of the number of model parameters on identification reliability and evaluation errors of porous structure parameters. This paper gives more information on properties of the identification technique presented in our earlier papers. The five-parameter and six-parameter identification reliability is analyzed in more detail, for different values of the system parameters. In this context, the efficiency of simultaneous examination of two isotherms is also studied.     

Pressure effects in confined nanophases

In this article, we review how pressure effects in pores affect both the physics of the confined fluid and the properties of the host porous material. Molecular simulations in which high-pressure effects were observed are first discussed; we will see how the strong dependence on bulk phase pressure of the freezing temperature of a fluid confined in nanopores can be explained by important variations of the pressure within the pore. We then discuss recent works in which direct calculations of the pressure tensor of fluids confined in pores provide evidence for large pressure enhancements. Finally, practical applications of these pressure effects in which gas adsorption in microporous solids (pore size < 2 nm) was found to enhance their mechanical properties by increasing the elastic modulus by a factor 4 are discussed.     

Differences in the adsorption and diffusion behaviour of water and non-polar gases in nanoporous carbon: role of cooperative effects of pore confinement and hydrogen bonding

We investigate the effect of pore confinement and molecular geometry on the adsorption and self-diffusion of H₂O, CO₂, Ar, CH₄, C₃H₆, SF₆ and C₅H₁₂, in a realistic model of nanoporous silicon carbide derived carbon (SiC-DC), constructed using hybrid reverse Monte Carlo simulation. Adsorption isotherms, adsorbate–adsorbate and adsorbate–adsorbent contributions to the isosteric heat of adsorption are determined to study the effect of pore confinement, microporosity and molecular geometry on adsorption of these gases. We describe the cooperative effect of pore confinement and hydrogen bonding on the formation of water clusters and anomalous adsorption behaviour of water compared with non-polar gases. We find that, in contrast to literature results based on the slit-pore model, pore-filling does not occur below the saturation pressure in hydrophobic amorphous carbon materials such as SiC-DC and activated carbon fibre. We also compare self-diffusivities and activation energy barriers of water and non-polar gases in the microporous structure of SiC-DC to identify underlying correlations with molecular properties. We demonstrate that the self-diffusivity of water deviates considerably from the correlation between diffusivity and molecular kinetic diameter observed for non-polar gases. This is attributed to the reduced diffusivity of water, and its relatively large energy barrier at high loadings despite its small kinetic diameter, which is due to the blocking effect of water clusters at pore entries.     

Restricted diffusion of molecules in porous affinity chromatography adsorbents.

A restricted diffusion model is constructed and solved in order to study the permeability of large adsorbate molecules in the pores of affinity chromatography media, when the adsorbate molecules are adsorbed onto immobilized ligands. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size distribution, pore connectivity of the adsorbent, molecular size of adsorbate and ligand, and the fractional saturation of adsorption sites (ligands), are considered. Affinity adsorbents with dilute and high ligand concentrations are examined, and the permeability of the adsorbate in porous networks of connectivity nT is studied by means of effective medium approximation (EMA) numerical solutions. As expected, the permeability of the adsorbate decreases as the size of the adsorbate and/or ligand molecule increases. The permeability also decreases when the fractional saturation of the ligands increases, as well as when the pore connectivity of the network decreases. The dependence of the permeability on the pore connectivity tends to be less marked in adsorbents with concentrated ligand than in porous media with dilute ligand concentration. The conditions are also presented for which the percolation threshold is attained in a number of different systems. The restricted diffusion model and results of this work may be of importance in studies involving the modeling, prediction of the dynamic behavior, design, and control of affinity chromatography (biospecific adsorption) systems employing porous adsorbents. The theoretical results may also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix, so that the adsorbate of interest can be efficiently separated from a given solution. Furthermore, with appropriate modifications this restricted diffusion model may be used in studies involving the immobilization of ligands or enzymes in porous solids.     

Combined Diffusive and Viscous Transport of Methane in a Carbon Slit Pore

Abstract

The transport of mass through porous materials can occur by essentially two different mechanisms: (1) diffusion and (2) viscous flow. The former occurs when there is a gradient in chemical potential of the pore fluid, while the latter occurs in the presence of a pressure gradient. In general, fluid transport occurs by both of these mechanisms and their respective contributions to the total intra-pore flux are approximately additive. Experimentally, there is no unambiguous way of determining the individual contributions to the total flux of these two modes of transport. Fortunately, molecular simulations does provide a solution.

We present a novel simulation method in which the separate contributions to the total flux are determined. The method involves the use of two non-equilibrium molecular dynamics techniques: dual control volume grand canonical molecular dynamics (DCV GCMD) and an algorithm for simulating planar Poiseuille flow. We apply this technique to study the combined (viscous and diffusive) transport of methane through single slit-shaped graphite pores of width 2.5, 5.0 and 10.0 methane diameters. We find that the viscous contribution to the total intrapore flux through each of these pores is 10%, 15% and 34%, respectively.     

Adsorption behaviors of hydrogen sulphide on Au(110) nanoslit array surfaces using molecular dynamics simulations

The adsorption behaviour of gas molecules on detector surfaces has a profound influence on the sensitivity of the detector. For this reason, this study used molecular dynamics simulation to explore the dynamic adsorption behaviour of hydrogen sulphide (H₂S) molecules on various types of Au surfaces, including a planar Au(1?1?0) structure and three types of slit array structures. The influence of system temperature, adsorbate concentration and the slit width of nanoarrays on diffusivity, average adsorption energy and static adsorption amount were systematically examined. Simulation results indicate that the self-diffusivity of the adsorbate molecules increases with temperature but decreases with adsorbate concentration. At low concentrations (~3 mol/L), each type of Au(1?1?0) surface structure shows good capacity to adsorb all H₂S molecules. With increasing concentration at 6.5 mol/L, the high concentration leads to adsorption saturation and many free H₂S molecules in the planar Au(1?1?0) structure. Moreover, desorption also begins to appear on the planar structures at a temperature of 300 K (at 6.5 mol/L). The simulation results indicate that the columnar array structures with a slit width ≥5.76 Å allow molecules to swiftly spread into the slits and provide more stable adsorption sites (i.e. with a higher adsorption energy), which can effectively address the issues of high-temperature desorption and adsorption saturation. Particularly at low temperatures (≤100 K), slit structures presented a level of static adsorption of H₂S that was 30% to 35 higher than that of planar structures.     

Modeling and analysis of elution stage of biospecific adsorption in finite bath

A model is developed and used to predict the dynamic behavior of the elution stage of biospecific adsorption (affinity chromatography) in a finite bath. Both nonselective and selective elution of monovalent adsorbates is considered. The model expressions account for film and pore diffusion resistances for the adsorbate(s) and the eluent, and various rate expressions for the desorption of the adsorbate from the adsorbate-ligand complex are constructed and studied. The results indicate that the duration of the elution stage depends significantly on the Sherwood number of the adsorbate and the rate of the interaction step between the ligand and the adsorbate relative to the diffusion of the adsorbate in the pore during elution. In nonselective elution, when the value of the effective pore diffusivity of the eluent is significantly larger than that of the adsorbate, the results suggest that it would be advantageous to use an initial eluent concentration in the finite bath that is only slightly higher than the critical eluent concentration in order to minimize the risk of product and ligand damage. In selective elution the amount of adsorbate recovered in the elution stage is greatly influenced by the initial concentration of the eluent and the equilibrium dissociation constants of the adsorbate-ligand and adsorbate-eluent complexes.     

Properties of microfiltration membranes: flux loss during constant pressure permeation of bovine serum albumin

An experimental study of permeation of dilute BSA solutions (filtration) at microfiltration membranes has been carried out. Most measurements were made with capillary pore aluminum oxide membranes, with some comparative measurements with tortuous and capillary pore polymeric membranes. In all cases, a continuous and substantial decrease in the rate of permeation with time was observed. This decrease in permeation with time was observed. This decrease in permeation rate was due neither to concentration polarization nor to protein adsorption alone. However, it could be quantified using the standard blocking filtration law, which describes a decrease in pore volume due to deposition of protein on the walls of the pore. The maximum calculated thickness of the deposited layers was 55nm on the walls of 200-nm diameter pores. This phenomenon is quite different to adsorption of protein at such surfaces, this latter giving only sub-monolayer or monolayer protein coverage under the conditions studied.     

N-octane diffusivity enhancement via carbon dioxide in silica slit-shaped nanopores – a molecular dynamics simulation

Equilibrium molecular dynamics simulations were conducted to study the competitive adsorption and diffusion of mixtures containing n-octane and carbon dioxide confined in slit-shaped silica pores of width 1.9 nm. Atomic density profiles substantiate strong interactions between CO₂ molecules and the protonated pore walls. Non-monotonic change in n-octane self-diffusion coefficients as a function of CO₂ loading was observed. CO₂ preferential adsorption to the pore surface is likely to attenuate the surface adsorption of n-octane, lower the activation energy for n-octane diffusivity, and consequently enhance n-octane mobility at low CO₂ loading. This observation was confirmed by conducting test simulations for pure n-octane confined in narrower pores. At high CO₂ loading, n-octane diffusivity is hindered by molecular crowding. Thus, n-octane diffusivity displays a maximum. In contrast, within the concentration range considered here, the self-diffusion coefficient predicted for CO₂ exhibits a monotonic increase with loading, which is attributed to a combination of effects including the saturation of the adsorption capacity of the silica surface. Test simulations suggest that the results are strongly dependent on the pore morphology, and in particular on the presence of edges that can preferentially adsorb CO₂ molecules and therefore affect the distribution of these molecules equally on the pore surface, which appears to be required to provide the effective enhancement of n-octane diffusivity.     

Mechanism of methane adsorption on groove space in organic matter surface

Organic matter plays an important role in methane adsorption in shale. Pore surface of organic matter is usually rough and uneven, which results in a large amount of groove space on the pore surface. Thus, the influence of groove space on the adsorption capacity of methane in shale cannot be neglected. Nanoscale pore structures of the organic-rich shale in the Longmaxi Formation were investigated by low-pressure nitrogen gas adsorption as a basis for constructing models. We simplified the internal groove space into triangular prisms with different angles. The grand canonical Monte Carlo simulation and molecular dynamics simulation were used to analyse the methane molecule adsorption behaviour in pores. The results showed that the pore morphology of organic-rich shale in the Longmaxi Formation was mainly slit-shaped pores. The excess adsorption isotherms showed good agreement between experiment and simulation, indicating that the model is suitable and reliable. Methane molecules can enter into the groove space with an opening size of 0.738 nm, while they fail to enter into groove spaces with an opening size less than 0.492 nm. This understanding has important significance for the study of the adsorption characteristics of organic pores which have undergone multiple evolutions in geological history.     

Filter-extruded liposomes revisited: a study into size distributions and morphologies in relation to lipid-composition and process parameters

Filter-extrusion is a widely used technique for down-sizing of phospholipid vesicles. In order to gain a detailed insight into size and size distributions of filter-extruded vesicles composed of egg phosphatidyl-choline (with varying fractions of cholesterol) – in relation to extrusion-parameters (pore-size, number of filter passages, and flow-rate), flow field-flow fractionation in conjunction with multi-angle laser light scattering (AF4-MALLS, Wyatt Technology Corp., Santa Barbara, CA) was employed. Liposome size-distributions determined by AF4-MALLS were compared with those of dynamic light scattering and correlated with cryo-transmission electron microscopy and ³¹P-NMR-analysis of lamellarity. Both the mean size of liposome and the width of size distribution were found to decrease with sequential extrusion through smaller pore size filters, starting at a size range of ≈70–415?nm upon repeated extrusion through 400?nm pore-filters, eventually ending with a size range from ≈30 to 85?nm upon extrusion through 30?nm pore size filters. While for small pores sizes (50?nm), increased flow rates resulted in smaller vesicles, no significant influence of flow rate on mean vesicle size was seen with larger pores. Cholesterol at increasing mol fractions up to 0.45 yielded bigger vesicles (at identical process conditions). For a cholesterol mol fraction of 0.5 in combination with small filter pore size, a bimodal size distribution was seen indicating cholesterol micro-crystallites. Finally, a protocol is suggested to prepare large (～?300?nm) liposomes with rather narrow size distribution, based on the filter extrusion at defined flow-rates in combination with freeze-/thaw-cycling and bench-top centrifugation.     

Computer Simulation of Isothermal Mass Transport in Graphite Slit Pores

Abstract

Results are presented from a simulation study of the mass transport of oxygen and nitrogen through graphite slit pores. The work is motivated by an attempt to understand the molecular origins of the kinetic selectivity displayed when air is separated into its major components using pressure swing adsorption. A combination of non-equilibrium molecular dynamics (NEMD), equilibrium molecular dynamics (EMD) and grand canonical Monte Carlo methods has been employed in our study to extract the maximum information. Transport diffusivities, self-diffusivities, permeabilities and Darken thermodynamic factors have been calculated as a function of pore width and temperature for pure component oxygen and nitrogen. In addition, new EMD simulation data for an 80:20 mixture of nitrogen and oxygen is reported, including a direct calculation of the Stefan-Maxwell coefficients. The results are discussed in terms of the oxygen selectivity and the possible mechanisms, which increase or decrease this quantity.

We find that the pore width behaviour of the diffusion coefficients consists of three distinct regimes: a regime at larger pore widths in which single component diffusion coefficients are largely independent of pore width, an optimum pore width at which both diffusivities increase substantially but the slit pore is selective towards nitrogen, and a regime at very low pore widths at which the diffusivities decrease sharply, but the slits are selective towards oxygen. The mechanism behind each of these regimes is discussed in terms of “entropic” effects and potential barrier heights.

We have also found that permeability selectivity is substantially reduced in a mixture of the two gases with a composition similar to that of air. Cross diffusion coefficients in the mixture have been calculated and shown to be non-negligible.     

Molecular Simulations of Phase Transitions in Pores

Abstract

Methods for simulating phase transitions in narrow pores are reviewed, and the advantages and disadvantages of different techniques are discussed. Examples are given of applications to vapor-liquid, liquid-liquid, melting and freezing, solid-solid and layering transitions. While there has been a considerable body of simulation work on vapor-liquid, wetting and layering transitions for simple fluids and pore geometries, much remains to be done on more complex geometries and network effects, on heterogeneous surfaces, and on liquid-liquid, melting and solid-solid transitions in pores.     

Modelling Gas Adsorption in Slit-Pores Using Monte Carlo Simulation

Abstract

We discuss the use of Monte Carlo simulation to model the equilibrium adsorption of gases in slit pores. Databases of adsorption isotherms have been calculated for nitrogen, carbon-monoxide, methane and carbon-dioxide for a range of pressures, pore widths and temperatures. We discuss the implications of these results for materials characterisation procedures based on gas adsorption data.     

Microporous silicon and biosensor development: structural analysis, electrical characterisation and biocapacity evaluation

An investigation of the fabrication of microporous silicon (MPS) layers as a material for the development of an electrolyte insulator semiconductor (EIS) capacitance sensor has been performed. The goal was to create a high surface area substrate for the immobilisation of biorecognition elements. Structural analysis of MPS layers as a function of key etch parameters, namely implant type (p or n), implant dose, hydrofluoric acid (HF) etch concentration and current density has been performed using scanning electron microscopy (SEM). It was possible to image porous layers with average pore diameter as low as 4 nm. n-type silicon samples had larger pore networks than p-type samples and reducing the silicon resistivity led to a reduction in the pores per microm2. It was found that increasing the HF etch concentration reduced the average pore diameter and increased the pores per microm2. Increasing the current density at which the etch was performed has the same effect. Understanding the effect of these parameters allows the MPS layer to be tuned to match specifications for optimum biocapacity. Different MPS layers were electrically characterised using capacitance-voltage and capacitance-frequency sweeps, in order to determine the effect of porosity on increases in surface area. The measured capacitance increased with increasing pores per microm2. p-type silicon with a boron implant in the back of the wafer, which had been etched in 25% HF in ethanol at a current density of 75 mA/cm2 yielded the highest capacitance signal per unit area. The effect of porosity and pore size on the biocapacity of the samples was also determined. For avidin immobilisation, with pores sizes above 5 nm, as the porosity increased the biocapacity increased. MPS fabricated in p-type silicon with a front and back implant etched in 25% HF at a current density of 25 mA/cm2 was used for the capacitance detection of synthetic oligonucleotides.     

On gap junction structure

We have studied the stain distribution within rat liver gap junctions for specimens prepared by thin sectioning and negative staining. Pools of stain molecules exist in two specific locations with respect to the distinctive morphological units (connexons) of the junction. One pool of stain surrounds the connexons and is restricted to the extracellular space in the gap between the adjacent plasma membranes. The other pool of stain is located along in the central axis of each connexon, measures 1-2 nm in diameter and 4-5 nm in length, and is restricted to the gap region. On rare occasions, barely discernible linear densities seem to extend from this latter pool of stain and traverse the entire width of the junction. The data indicate the existence of a hydrophilic cavity along the central axis of te connexon which, in most instances, is restricted to the gap region. However, the precise depth to which this cavity may further extend along the connexon axis is still uncertain.     

Ion transport through membrane-spanning nanopores studied by molecular dynamics simulations and continuum electrostatics calculations

Narrow hydrophobic regions are a common feature of biological channels, with possible roles in ion-channel gating. We study the principles that govern ion transport through narrow hydrophobic membrane pores by molecular dynamics simulation of model membranes formed of hexagonally packed carbon nanotubes. We focus on the factors that determine the energetics of ion translocation through such nonpolar nanopores and compare the resulting free-energy barriers for pores with different diameters corresponding to the gating regions in closed and open forms of potassium channels. Our model system also allows us to compare the results from molecular dynamics simulations directly to continuum electrostatics calculations. Both simulations and continuum calculations show that subnanometer wide pores pose a huge free-energy barrier for ions, but a small increase in the pore diameter to approximately 1 nm nearly eliminates that barrier. We also find that in those wider channels the ion mobility is comparable to that in the bulk phase. By calculating local electrostatic potentials, we show that the long range Coulomb interactions of ions are strongly screened in the wide water-filled channels. Whereas continuum calculations capture the overall energetics reasonably well, the local water structure, which is not accounted for in this model, leads to interesting effects such as the preference of hydrated ions to move along the pore wall rather than through the center of the pore.     

Ultrastructure of electrical synapses between nociceptive and anterior pagoda neurons in the CNS of the leech (Whitmania pigra)

We have used electron microscopy to measure quantitatively the morphology of electrical synapses in a circuit that has been proposed to account for the positional discrimination of the leech. Injection of a presynaptic nociceptive sensory neuron and the postsynaptic anterior pagoda neuron with HRP showed gap junctions in the neuropil. After double labeling, La³⁺-treated ganglia revealed labeled gap junctions from 2.0 to 3.5 nm wide. Between the labeled axon terminals, there were innexons with diameters of 8 to 10 nm. The innexon's central pore diameter was 2 nm, and the mean of the center-to-center distance between two innexons was 30 nm. Except for the gap junction areas of nociceptive sensory neuron axon terminals, the other ultrastructural parameters measured by freeze fracture were similar to those of samples labeled with HRP and filled with La³⁺. These data suggested that the gap width, innexon diameter, and its central pore do not on their own account for the mechanism of positional discrimination, which may depend rather on the differences in distribution and number of gap junctions. Electronic Publication