Adsorption, structure and dynamics of benzene in ordered and disordered porous carbons

Molecular simulations are used to study the adsorption, structure, and dynamics of benzene at 298 K in atomistic models of ordered and disordered nanoporous carbons. The ordered porous carbon is a regular slit pore made up of graphene sheets. The disordered porous carbon is a structural model that reproduces the morphological (pore shape) and topological (pore connectivity) disorder of saccharose-based porous carbons. As expected for pores of a regular geometry, the filling occurs at well-defined pressures which are an increasing function of the pore width H. In contrast, in qualitative agreement with experimental data for activated carbon fibers, the filling of the disordered carbon is continuous and spans over a large pressure range. The structure and dynamics of benzene in the disordered carbon also strongly depart from that for the slit pore geometry. While benzene in the slit graphite nanopores exhibits significant layering, benzene in the disordered porous carbon exhibits a liquid-like structure very close to its bulk counterpart. Both the ordering and self-diffusivity of benzene in the graphite nanopores depend in a complex manner on the pore width. The dynamics is either slower or faster than its bulk counterpart; our data show that the self-diffusivity decreases as the number of confined layers n divided by the pore width H increases (except for very small pore sizes for which benzene crystallizes and is necessarily slower than the liquid phase). The dynamics of benzene in the disordered porous carbon is isotropic and is much slower than that for the graphite slit nanopores (even with the smallest slit nanopore considered in this work). The results above show that the adsorption, structure, and dynamics of benzene confined in disordered porous carbons cannot be described in simple terms using an ideal model such as the slit pore geometry.     

A grand canonical Monte Carlo study of capillary condensation in mesoporous media: effect of the pore morphology and topology

We study by means of Grand Canonical Monte Carlo simulations the condensation and evaporation of argon at 77 K in nanoporous silica media of different morphology or topology. For each porous material, our results are compared with data obtained for regular cylindrical pores. We show that both the filling and emptying mechanisms are significantly affected by the presence of a constriction. The simulation data for a constricted pore closed at one end reproduces the asymmetrical shape of the hysteresis loop that is observed for many real disordered porous materials. The adsorption process is a quasicontinuous mechanism that corresponds to the filling of the different parts of the porous material, cavity, and constriction. In contrast, the desorption branch for this pore closed at one end is brutal because the evaporation of Ar atoms confined in the largest cavity is triggered by the evaporation of the fluid confined in the constriction (which isolates the cavity from the gas reservoir). This evaporation process conforms to the classical picture of "pore blocking effect" proposed by Everett many years ago. We also simulate Ar adsorption in a disordered porous medium, which mimics a Vycor mesoporous silica glass. The adsorption isotherm for this disordered porous material having both topological and morphological defects presents the same features as that for the constricted pore (quasicontinuous adsorption and steep desorption process). However, the larger degree of disorder of the Vycor surface enhances these main characteristics. Finally, we show that the effect of the disorder, topological and/or morphological, leads to a significant lowering of the capillary condensation pressure compared to that for regular cylindrical nanopores. Also, our results suggest that confined fluids isolated from the bulk reservoir evaporate at a pressure driven by the smallest size of the pore.     

Swelling behavior of the filling-type membrane

A model that can express the swelling of the filling-type membrane was developed by modifying a model that was developed for a crystalline polymer. The filling-type membrane is composed of two different polymers. One is porous substrate and another is a polymer that filled pores of the substrate. The filling technique can effectively suppress polymer swelling due to the substrate matrix. The model needs two parameters: one is a unit ratio of tie segments in the substrate to the filling polymer, f, which can express a mechanical strength of the substrate, and another is the Flory interaction parameter, χ, between the filling polymer and a solvent that expresses a mixing energy. A porous high-density polyethylene film was used as a porous substrate, and plasma-graft filling polymerization technique could make the filling-type membrane. Methylacrylate was used as a grafting monomer that filled the pores of substrate. A swelling behavior of the filling-type membrane and pure poly(methylacrylate) were measured by the vapor sorption method at different solvent activities. The model was in good agreement with experimental results for the filling-type membrane. Using the model, swelling of the filling-type polymer was compared with a crosslinked polymer, which can be expressed by Flory and Rehner model. The comparison showed that the filling technique is a good way to suppress polymer swelling, and a high crosslinking density is needed to obtain the same level of swelling suppression effect the filling type membrane showed. © 1997 John Wiley & Sons, Inc.     

Penetration into three-dimensional complex porous structures

The short-term uptake of a fluid by porous media is important in a number of processes, such as in coating and printing operations. We present a new model to predict short-term absorption into real pore geometries taking into account fluid properties, surface forces, and the complex pore geometry. Two assumptions are made to reduce the complexity of the situation: (1) the flow resistance between pores can be estimated from pore geometry or air permeability measurements, and (2) the volume of fluid in the constrictions between pores is small. Pores can be connected in any manner and can be in any arrangement. The absorption rates predicted by the model are compared to experimental values obtained with coating layers of plastic, kaolin, and calcium carbonate pigments. These coatings are characterized in terms of void fraction, pore size, contact angle, and permeability. The comparison is good for water and inks when the air permeability of the porous layer is used to determine the average resistance to flow in the sample. These resistance values are close to the values obtained from pore geometries estimated from particle packing simulations.     

A dynamic wicking technique for determining the effective pore radius of pregelatinized starch sheets

A dynamic wicking technique is employed for the first time for the determination of the effective mean pore radius of a thin-layer porous food: drum dried pregelatinized starch sheets. The technique consists of measuring the penetration rate of various n-alkanes in the porous matrix of the starch sheets and using this data to calculate the effective pore radius via the Washburn equation. Pore sizes in the order of a few nanometers have been determined in the starch sheets depending on the drum dryer’s operating variables (drum rotation speed, steam pressure and starch feed concentration). The conditions for the application of the technique in porous foods are discussed as compared to the conditions for single capillaries and inorganic porous material measured in other studies.     

Electrochemistry of capillary systems with narrow pores. II. Electroosmosis

Manegold and Solf have reported systematic deviations of the electroosmotic properties of collodion membranes with narrow pores from predictions based on the Helmholtz–Smoluchowski model. To interpret the electroosmotic data quantitatively it is necessary to replace the assumption of the Helmholtz–Smoluchowski model that the thickness of the electric double layer is small compared with the pore radius by a new assumption. We have assumed that the counter ions are distributed homogeneously in the pore fluid. In Part I of this series of contributions, equations have been given describing the electroosmotic properties of a membrane with narrow pores based on the new assumption. These equations are derived here in detail and are applied to an analysis of the experimental data given by Manegold and Solf.     

Electrochemistry of capillary systems with narrow pores. II. Electroosmosis

Manegold and Solf have reported systematic deviations of the electroosmotic properties of collodion membranes with narrow pores from predictions based on the Helmholtz–Smoluchowski model. To interpret the electroosmotic data quantitatively it is necessary to replace the assumption of the Helmholtz–Smoluchowski model that the thickness of the electric double layer is small compared with the pore radius by a new assumption. We have assumed that the counter ions are distributed homogeneously in the pore fluid. In Part I of this series of contributions, equations have been given describing the electroosmotic properties of a membrane with narrow pores based on the new assumption. These equations are derived here in detail and are applied to an analysis of the experimental data given by Manegold and Solf.     

Construction by molecular dynamics modeling and simulations of the porous structures formed by dextran polymer chains attached on the surface of the pores of a base matrix: characterization of porous structures

Significant increases in the separation of bioactive molecules by using ion-exchange chromatography are realized by utilizing porous adsorbent particles in which the affinity group/ligand is linked to the base matrix of the porous particle via a polymeric extender. To study and understand the behavior of such systems, the M3B model is modified and used in molecular dynamics (MD) simulation studies to construct porous dextran layers on the surface of a base matrix, where the dextran polymer chains and the surface are covered by water. Two different porous polymer layers having 25 and 40 monomers per main polymer chain of dextran, respectively, are constructed, and their three-dimensional (3D) porous structures are characterized with respect to porosity, pore size distribution, and number of conducting pathways along the direction of net transport. It is found that the more desirable practical implications with respect to structural properties exhibited by the porous polymer layer having 40 monomers per main polymer chain, are mainly due to the higher flexibility of the polymer chains of this system, especially in the upper region of the porous structure. The characterization and analysis of the porous structures have suggested a useful definition for the physical meaning and implications of the pore connectivity of a real porous medium that is significantly different than the artificial physical meaning associated with the pore connectivity parameter employed in pore network models and whose physical limitations are discussed; furthermore, the methodology developed for the characterization of the three-dimensional structures of real porous media could be used to analyze the experimental data obtained from high-resolution noninvasive three-dimensional methods like high-resolution optical microscopy. The MD modeling and simulations methodology presented here could be used, considering that the type and size of affinity group/ligand as well as the size of the biomolecule to be adsorbed onto the affinity group/ligand are known, to construct different porous dextran layers by varying the length of the polymeric chain of dextran, the number of attachment points to the base matrix, the degree of side branching, and the number of main polymeric chains immobilized per unit surface area of base matrix. After the characterization of the porous structures of the different porous dextran layers is performed, then only a few promising structures would be selected for studying the immobilization of adsorption sites on the pore surfaces and the subsequent adsorption of the bioactive molecules onto the immobilized affinity groups/ligands.     

Nanoporous surface wetting behavior: the line tension influence

The aim of this work is to develop a physical model to describe the evolution of the apparent contact angle for four different liquids on nanotextured alumina surfaces with different pore radius. The nanoporous alumina templates were fabricated by anodization of Al foil in a 0.3 M oxalic acid solution. Scanning electron microscopy was used to characterize the morphology of the surfaces. The templates are approximately 400 nm in thickness and consist of a well-ordered hexagonal array of uniform radius pores spaced 105 nm apart with pore radii from 12 to 42 nm. The wettability of nanoporous alumina templates was investigated using contact-angle measurements. We measured the contact angles using four liquids: water, ethylene glycol, aniline, and a mixture of ethylene glycol and aniline. We developed a new theoretical model for the contact angle on nanoporous surfaces as a function of the pore radius. This model is based on energy considerations and involves liquid penetration into the nanopores driven by the capillarity (Laplace's law). Because the air is compressed inside the pores, this model also includes the effect of the line tension. This is important because the three-phase line length is greatly enhanced in our nanoporous structures. For example: for a millimeter-sized droplet, the three-phase line around the perimeter of the droplet is a few millimeters long, whereas the total three-phase line within the pores can reach several tens of meters. Using our model, the line-tension value for our nanopore samples is positive and ranges from 4 to 13 × 10(-9) N, which falls within the wide interval from 10(-11) to 10(-5) N quoted in the literature. Nanoporous surfaces may allow the effect of line tension to be visible for micro- to macrodroplets.     

Pseudocritical or hysteresis temperature versus pore size for simple fluids confined in cylindrical nanopores

The adsorption/desorption isotherms measured in nanoporous materials generally present a hysteresis. The hysteresis shrinks upon increasing the temperature (for a given pore size) or decreasing the pore size (for a given temperature), until it finally disappears at the so-called hysteresis (or pseudocritical) temperature T(h) or hysteresis (or pseudocritical) pore size R(h), not to be confused with a true critical point. In this paper, a Monte Carlo approach allowed calculating the surface free energy of confined fluid along the adsorption/desorption isotherms for various cylindrical pore sizes and temperatures. A simple phenomenological model then allowed exploiting these results to determine the relation between T(h) and R(h). The prediction is compared to various literature models and experimental data, showing agreement within uncertainties. On the other hand, the simulations cannot be used directly to predict T(h) and R(h) since they significantly overestimate the hysteresis width. The model predicts a nonlinear relation between the reduced hysteresis temperature and the inverse pore radius.     

Saturation-dependent nuclear magnetic resonance relaxation of fluids confined inside porous media with micrometer-sized pores

In the present study, we investigate the relationship between the relaxation rate and the filling factor in partially saturated porous media. The filling fluids are polar (water, acetone) and nonpolar (cyclohexane, hexane). The porous sample is a silica glass (Vitrapor#5) with the nominal mean pore size of d = 1 μm ( ± 0.6 μm). All nuclear magnetic resonance relaxation experiments are performed at 20 °C using a NMR instrument operable at 20 MHz proton resonance frequency. The experimental results are compared with a two-phase exchange model providing us information on the strength of surface relaxation and fluid distribution inside pores. These results will affect the NMR estimations about fluid content of porous media.     

Molecular exchange dynamics in partially filled microscale and nanoscale pores of silica glasses studied by field-cycling nuclear magnetic resonance relaxometry

Nuclear magnetic spin-lattice relaxation experiments have been performed in partially filled porous glasses with wetting and nonwetting fluids. The frequency dependence of the spin-lattice relaxation rate in Vycor (4 nm pores) and VitraPOR #5 (1 microm pores) silica glasses was studied as a function of the filling degree with the aid of field-cycling NMR relaxometry. The species of primary interest were water ("polar") and cyclohexane ("nonpolar"). Spin-lattice relaxation was examined in the frequency range from 1 kHz to 400 MHz with the aid of a field-cycling NMR relaxometer and an ordinary 400 MHz NMR spectrometer. Three different mobility states of the fluid molecules are distinguished: The adsorbed state at the pore walls, the bulklike liquid phase, and the vapor phase. The adsorbate spin-lattice relaxation rate is dominated by the "reorientation mediated by translational displacements" (RMTD) mechanism taking place at the adsorbate/matrix interface at frequencies low enough to neglect rotational diffusion of the molecules. The experimental data are analyzed in terms of molecular exchange between the different mobility states. Judged from the dependence of the spin-lattice relaxation rates on the filling degree, limits for slow and fast exchange (relative to the RMTD time scale) can be distinguished and identified. It is concluded that water always shows the features of slow exchange irrespective of the investigated pore sizes and filling degrees. This is in contrast to cyclohexane which is subject to slow exchange in micrometer pores, whereas fast exchange occurs in nanoscopic pores. The latter case implies that the vapor phase contributes to molecular dynamics in this case at low filling degrees while it is negligible otherwise.     

Characterization of pore structure in a nanoporous low-dielectric-constant thin film by neutron porosimetry and X-ray porosimetry

A small-angle neutron scattering (SANS) porosimetry technique is presented for characterization of pore structure in nanoporous thin films. The technique is applied to characterize a spin-on organosilicate low dielectric constant (low-k) material with a random pore structure. Porosimetry experiments are conducted using a "contrast match" solvent (a mixture of toluene-d8 and toluene-h8) having the same neutron scattering length density as that of the nanoporous film matrix. The film is exposed to contrast match toluene vapor in a carrier gas (air), and pores fill with liquid by capillary condensation. The partial pressure of the solvent vapor is increased stepwise from 0 (pure air) to P0 (saturated solvent vapor) and then decreased stepwise to 0 (pure air). As the solvent partial pressure increases, pores fill with liquid solvent progressively from smallest to largest. SANS measurements quantify the average size of the empty pores (those not filled with contrast match solvent). Analogous porosimetry experiments using specular X-ray reflectivity (SXR) quantify the volume fraction of solvent adsorbed at each step. Combining SXR and SANS data yields information about the pore size distribution and illustrates the size dependence of the filling process. For comparison, the pore size distribution is also calculated by application of the classical Kelvin equation to the SXR data.     

Modeling the Transport of Nanoparticle-Filled Binary Fluids through Micropores

Understanding the transport of multicomponent fluids through porous medium is of great importance for a number of technological applications, ranging from ink jet printing and the production of textiles to enhanced oil recovery. The process of capillary filling is relatively well understood for a single-component fluid; much less attention, however, has been devoted to investigating capillary filling processes that involve multiphase fluids, and especially nanoparticle-filled fluids. Here, we examine the behavior of binary fluids containing nanoparticles that are driven by capillary forces to fill well-defined pores or microchannels. To carry out these studies, we use a hybrid computational approach that combines the lattice Boltzmann model for binary fluids with a Brownian dynamics model for the nanoparticles. This hybrid approach allows us to capture the interactions among the fluids, nanoparticles, and pore walls. We show that the nanoparticles can dynamically alter the interfacial tension between the two fluids and the contact angle at the pore walls; this, in turn, strongly affects the dynamics of the capillary filling. We demonstrate that by tailoring the wetting properties of the nanoparticles, one can effectively control the filling velocities. Our findings provide fundamental insights into the dynamics of this complex multicomponent system, as well as potential guidelines for a number of technological processes that involve capillary filling with nanoparticles in porous media.     

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.     

Restricted diffusion in silica particles measured by pulsed field gradient NMR

The restricted diffusion coefficient of water through porous silica is measured by pulsed field gradient (PFG) NMR as a function of loading in order to develop a model for self-diffusion at full pore filling in sol-gel-made porous silica particles. This model describes the pore or intraparticle diffusion coefficient as a function of particle porosity, tortuosity, and the steric hindrance applied on the molecules by the pore space. The particle morphology is characterized by nitrogen adsorption and an appropriate tortuosity model is chosen in comparison with literature data. To characterize the material, NMR relaxation and diffusion studies at different degrees of pore filling were carried out in relation to the silica/water adsorption isotherm.     

Xenon porometry at room temperature

Xenon porometry is a method in which porous material is immersed in a medium and the properties of the material are studied by means of 129Xe nuclear magnetic resonance (NMR) of xenon gas dissolved in the medium. For instance, the chemical shift of a particular signal (referred to as signal D) arising from xenon inside small pockets formed in the pores during the freezing of the confined medium is highly sensitive to the pore size. In the present study, we show that when naphthalene is used as the medium the pore size distribution of the material can be determined by measuring a single one-dimensional spectrum near room temperature and converting the chemical shift scale of signal D to the pore radius scale by using an experimentally determined correlation. A model has been developed that explains the curious behavior of the chemical shift of signal D as a function of pore radius. The other signals of the spectra measured at different temperatures have also been identified, and the influence of xenon pressure on the spectra has been studied. For comparison, 129Xe NMR spectra of pure xenon gas adsorbed to porous materials have been measured and analyzed.     

Note on nonaqueous electrokinetic transport in charged porous media

A model for electrokinetic transport in charged capillaries is compared with experiments using nonaqueous lithium chloride solutions. The electrokinetic parameters considered are the pore fluid conductivity and the concentration potential. Methanol/water mixtures were the solvent, and track-etched mica membranes with a well-characterized pore structure were the porous medium. The electrolyte concentrations used were such that the Debye lengths of solutions in pores ranged from much smaller to much larger than the radius of pores. The space-charge model is found to be capable of qualitatively describing the trend of the electrokinetic data, but as expected, at higher concentrations the model fails, probably because the assumption that ion—ion interactions are negligible no longer holds. The experimental results show that the pore fluid conductivity depends strongly on the dielectric constant of the solvent, that the absolute value of the pore wall charge tends to decrease with the lowering of the solvent dielectric constant, and that the wall charge tends to increase with the concentration of the chloride ion.     

Diffusion processes in mesoporous adsorbents probed by NMR

In this contribution, we review the results of our experimental studies on diffusion of guest molecules in mesoporous solids using pulsed field gradient (PFG) NMR technique. Having unique potentials to non-invasively probe the microscopic diffusion processes in pores, this method may provide quintessential information on the character of molecular propagation for different pore morphologies and fluid phase state. In particular, different modes of molecular diffusion in partially filled pores may be separately probed and the overall diffusion process could be analyzed taking account of the details of the inter-phase coexistence. In addition to the dynamic properties, some information concerning the distribution of guest molecules within the porous matrix may also be obtained.