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.     

Water diffusion in nanoporous glass: an NMR study at different hydration levels

By pulsed field gradient nuclear magnetic resonance measurements, we investigated the translational diffusion of water confined in the 200 A diameter pores of a sol-gel silica glass. The experiments, performed as a function of the hydration level, showed an enhancement of the self-diffusion coefficient when the water content corresponds to one or fewer monolayers. An explanation for this occurrence has been given in terms of a two-phase process involving a fast molecular exchange between the liquid and the vapor phase. Moreover, in partially filled pores, the surface water diffusion coefficient was measured, and was 4 times lower than the diffusion of liquid confined water in saturated spaces.     

NMR cryoporometry with octamethylcyclotetrasiloxane as a probe liquid. Accessing large pores

Octamethylcyclotetrasiloxane is presented and investigated as probe liquid for NMR cryoporometry or DSC-based thermoporometry. This compound which may imbibe into both hydrophilic and hydrophobic pores is shown to exhibit a melting point depression that is larger than that for other cryoporometric probe materials such as cyclohexane. The transverse relaxation time differs by more than three orders of magnitude between the solid and liquid states, separated by a sharp phase transition. Hence, as demonstrated in controlled pore glasses, octamethylcyclotetrasiloxane can provide pore size distributions for materials with pore sizes up to the micrometer range.     

Effect of a porous medium on the phase transitions and mobility of cyclohexane molecules

The effect of a porous medium on the phase transitions and molecular mobility of cyclohexane at a liquid content corresponding to a monolayer is studied by pulsed NMR. The times of longitudinal T ₁ and transverse T ₂ magnetic relaxation of protons of cyclohexane introduced into granulated porous glasses of the Vycor type with average pore diameters of 4, 11, and 32 nm are measured in the temperature range of 128–293 K. In spite of a relatively low liquid content, two phase transitions are observed for all porous glass samples at temperatures lower than those inherent in pure cyclohexane. At low temperatures, nonfreezing cyclohexane volumes with characteristic times of T ₂ ～ 100–200 μs and relative populations of 5–10% remain preserved due to the presence of a small number of micropores commensurable with molecular sizes. The appearance of an additional component with T ₂ ～ 200 μs upon temperature elevation to 148 K attests to thawing out of some cyclohexane volumes, which begins long before the crystal-plastic crystal phase transition. The nonexponential character of the transverse magnetization decay of cyclohexane above the temperature of the plastic crystal-liquid phase transition in the porous glass with a pore diameter of 4 nm suggests the existence of barriers for rapid molecular exchange. The obtained experimental results are indicative of the cluster mechanism of cyclohexane adsorption in the studied porous glasses.     

Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci

The thermodynamic properties of liquids trapped in microscopic pores are described in theory by the Kelvin equation, which relates the equilibrium meniscus curvature to the relative vapor pressure. We report here two series of experiments designed to test the validity of the Kelvin equation by direct measurement of the mean radius of curvature of the surface of cyclohexane condensed between crossed mica cylinders. In one series of experiments, the relative vapor pressure of the volatile cyclohexane was controlled by mixing it with a relatively involatile solute (n-dodecane or n-hexadecane). We found that the mean radius of curvature rapidly reached that predicted by the Kelvin equation at each relative vapor pressure of the volatile liquid, but that there was also a slow, but continuous, accumulation of the “involatile” solute at the point of condensation as the system approached true equilibrium. Such accumulation of very low vapor pressure materials may be one factor responsible for the discordant results reported by earlier workers. We find that the process of impurity buildup is complex, and suggest that studies of real porous systems may be affected by accumulation of “involatile” impurities through the vapor phase and by surface diffusion. The other series of experiments was designed to eliminate the impurity problem by maintaining the vapor pressure by temperature control of the pure liquid. The results from this series of experiments were not time dependent, and no evidence of contamination was found. The measured radii were within ±6% of those predicted by the Kelvin equation, for radii in the range 4–20 nm. We conclude that the thermodynamic basis of the Kelvin equation is valid in principle for menisci with radii as low as 4 nm.     

Does water condense in carbon pores?

Using grand canonical Monte Carlo (GCMC) simulations of molecular models, we investigate the nature of water adsorption and desorption in slit pores with graphitelike surfaces. Special emphasis is placed on the question of whether water exhibits capillary condensation (i.e., condensation when the external pressure is below the bulk vapor pressure). Three models of water have been considered. These are the SPC and SPC/E models and a model where the hydrogen bonding is described by tetrahedrally coordinated square-well association sites. The water-carbon interaction was described by the Steele 10-4-3 potential. In addition to determining adsorption/desorption isotherms, we also locate the states where vapor-liquid equilibrium occurs for both the bulk and confined states of the models. We find that for wider pores (widths >1 nm), condensation does not occur in the GCMC simulations until the pressure is higher than the bulk vapor pressure, P0. This is consistent with a physical picture where a lack of hydrogen bonding with the graphite surface destabilizes dense water phases relative to the bulk. For narrow pores where the slit width is comparable to the molecular diameter, strong dispersion interactions with both carbon surfaces can stabilize dense water phases relative to the bulk so that pore condensation can occur for P < P0 in some cases. For the narrowest pores studied--a pore width of 0.6 nm--pore condensation is again shifted to P > P0. The phase-equilibrium calculations indicate vapor-liquid coexistence in the slit pores for P < P0 for all but the narrowest pores. We discuss the implications of our results for interpreting water adsorption/desorption isotherms in porous carbons.     

Gas-Generating Porous Electrodes: The Nature of the Low-Polarizability Portion in the Polarization Curves

The phenomenon of a low-polarizability portion (LPP) is discussed in the paper. The phenomenon is responsible for the possible rapid increase in the current in polarization curves (PC) for the gas generation in gas-generating porous electrodes (GGPE). A fresh viewpoint on the nature of LPP is propounded. The inflection in PC, which follows the linear Tafel portion, owes its inception to the emergence, in the electrode pores, of a network of gas pores that are freed of electrolyte and are connected with each other. The effective diffusion coefficient for gas molecules in gas pores filled with water vapor is larger than the effective diffusion coefficient for the same gas molecules in liquid pores filled with an electrolyte solution by several orders of magnitude. The emergence of a gas phase in a GGPE leads to a rapid increase in the effective diffusion coefficient. This circumstance in turn is capable of rapidly intensifying processes of the formation and removal of gas, which leads to a considerable increase in the overall current. A method for obtaining an approximate solution of the problem (the notion on ideal porous electrode) is suggested. A system of equations is derived, which can sufficiently accurately, qualitatively and quantitatively describe the character of variations in a polarization curve in the initial part of a low-polarizability portion. Theoretical and experimental polarization curves for the chlorine evolution on a dimensionally stable anode are compared quantitatively.     

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.     

Confinement effect on the adsorption from a binary liquid system near liquid/liquid phase separation

The preferential adsorption of one component of a binary system at the inner surfaces of mesoporous silica glasses was studied in a wide composition range at temperatures close to liquid/liquid phase separation. Confinement effects on the adsorption were investigated by using three controlled-pore glass (CPG-10) materials of different mean pore size (10 to 50 nm). For the experimental system (2-butoxyethanol+water), which exhibits an upper miscibility gap, strong preferential adsorption of water occurs, as the coexistence curve is approached at bulk compositions, at which water is the minority component. In this strong adsorption regime the area-related surface excess amount of adsorbed water decreases with decreasing pore width, while the shift in the volume-related mean composition of the pore liquid shows an opposite trend, i.e., greatest deviation from bulk composition occurring in the most narrow pores. A simple mean-field lattice model of a liquid mixture confined by parallel walls is adopted to rationalize these experimental findings. This model reproduces the main findings of the confinement effect on the adsorption near liquid/liquid phase separation.     

Nucleation in hydrophobic cylindrical pores: a lattice model

We consider the nucleation process associated with capillary condensation of a vapor in a hydrophobic cylindrical pore (capillary evaporation). The liquid-vapor transition is described within the framework of a simple lattice model. The phase properties are characterized both at the mean-field level and with Monte Carlo simulations. The nucleation process for the liquid to vapor transition is then specifically considered. Using umbrella sampling techniques, we show that nucleation occurs through the condensation of an asymmetric vapor bubble at the pore surface. Even for highly confined systems, good agreement is found with macroscopic considerations based on classical nucleation theory. The results are discussed in the context of recent experimental work on the extrusion of water in hydrophobic pores.     

The onset of formation of the water liquid phase in pores of carbon adsorbents

A two-stage mechanism of adsorption, including nucleation and condensation, was proposed to describe the formation of the water liquid phase in carbon adsorbents. Adsorption is assumed to occur in cylindrical pores. Nucleation is described by a modified BET model, and condensation is treated by the model of a stretched liquid film on a bent surface. The onset of formation of the liquid phase (OFLP) is determined from the intersection of the adsorption isotherms for these stages. The theoretical value of the relative pressure of OFLP varies over a wide range, decreasing with a decrease in the pore radius and reactiing the relative vapor pressure of 0.178 for the spinodal state of water. The comparison method using isotherms of graphitized carbon black as the reference isotherms was applied for the determination of OFLP of water in real active carbons. This resulted in good agreement between theory and experiment. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 668–671, April, 1999.     

Capillary condensation in mesoporous silica with surface roughness

We construct an atomistic silica pore model mimicking templated mesoporous silica MCM-41, which has molecular-level surface roughness, with the aid of the electron density profile (EDP) of MCM-41 obtained from X-ray diffraction data. Then, we present the GCMC simulations of argon adsorption on our atomistic silica pore models for two different MCM-41 samples at 75, 80, and 87 K, and the results are compared with the experimental adsorption data. We demonstrate that accurate molecular modeling of the pore structure of MCM-41 by using the experimental EDP allows the prediction of experimental capillary evaporation pressures at all investigated temperatures. The experimental desorption branches of the two MCM-41 samples are in good agreement with equilibrium vapor–liquid transition pressures from the simulations, which suggests that the experimental desorption branch for the open-ended cylindrical pores is in thermodynamic equilibrium.     

Characterization of pore structure of a strong anion-exchange membrane adsorbent under different buffer and salt concentration conditions

The quantitative characterization of pore structure of Sartobind Q, a strongly basic membrane anion exchanger that is formed by cross-linked cellulose support and a hydrogel layer on its pore surface, was made combining the results obtained by several experimental techniques: liquid impregnation, batch size-exclusion, inverse size-exclusion chromatography, and permeability. Mercury intrusion and nitrogen sorption porosimetry were carried out for a dry cellulose support membrane in order to get additional information for building a model of the bimodal pore structure. The model incorporated the distribution of the total pore volume between transport and gel-layer pores and the partitioning of solutes of different molecular weights was expressed through the cylindrical pore model for the transport pores and random plane model for the gel layer. The effect of composition of liquid phase on the pore structure was investigated in redistilled water, phosphate and Tris–HCl buffers containing up to 1 M NaCl. Evident differences in the bimodal pore structure were observed here when both the specific volume and size of the hydrogel layer pores significantly decreased with the ionic strength of liquid phase.     

Diffusion and phase equilibria of binary fluids in mesopores

The formation of adsorption hysteresis in mesoporous material with random pore structure may be interrelated with different distributions of the fluid density attained along different paths of the system preparation. To access microscopic details of these distributions, in addition to the main sorptive liquid, distribution of which along the pore space of Vycor porous glass was of interest, a small amount of a probe liquid with a substantially lower vapor pressure has been added. Molecular diffusivities of both liquids then have been traced using pulsed field gradient NMR. Due to different vapor pressures, the two molecular species explore different spaces occupied by the capillary-condensed (accessible for both species) and gaseous (accessible only for the molecules of the main sorptive) phases. Comparative analysis of the diffusion properties obtained at different states along the adsorption isotherm revealed further insight into peculiarities of the fluid distribution and mass transfer of binary fluids in pores.     

Surface self-diffusion of organic molecules adsorbed in porous silicon

The pulsed field gradient nuclear magnetic resonance method has been employed to probe self-diffusion of organic guest molecules adsorbed in porous silicon with a 3.6 nm pore size. The molecular self-diffusion coefficient and intrapore adsorption were simultaneously measured as a function of the external vapor pressure. The latter was varied in a broad range to provide pore loading from less than monolayer surface coverage to full pore saturation. The measured diffusivities are found to be well-correlated with the adsorption isotherms. At low molecular concentrations in the pores, corresponding to surface coverages of less than one monolayer, the self-diffusion coefficient strongly increases with increasing concentration. This observation is attributed to the occurrence of activated diffusion on a heterogeneous surface. Additional experiments in a broad temperature range and using binary mixtures confirm this hypothesis.     

Short timescale inkjet ink component diffusion: an active part of the absorption mechanism into inkjet coatings

The structures of inkjet coatings commonly contain a high concentration of fine diameter pores together with a large pore volume capacity. To clarify the interactive role of the porous structure and the coincidentally occurring swelling of binder during inkjet ink vehicle imbibition, coating structures were studied in respect to their absorption behaviour for polar and non-polar liquid. The absorption measurement was performed using compressed pigment tablets, based on a range of pigment types and surface charge polarity, containing either polyvinyl alcohol (PVOH) or styrene acrylic latex (SA) as the binder, by recording the liquid uptake with a microbalance. The results indicate that, at the beginning of liquid uptake, at times less than 2 s, the small pores play the dominant role with respect to the inkjet ink vehicle imbibition. Simultaneously, water molecules diffuse into and within the hydrophilic PVOH binder causing binder swelling, which diminishes the number of active small pores and reduces the diameter of remaining pores, thus slowing the capillary flow as a function of time. The SA latex does not absorb the vehicle, and therefore the dominating phenomenon is then capillary absorption. However, the diffusion coefficient of the water vapour across separately prepared PVOH and SA latex films seems to be quite similar. In the PVOH, the polar liquid diffuses into the polymer network, whereas in the SA latex the hydrophobic nature prevents the diffusion into the polymer matrix and there exists surface diffusion. At longer timescale, permeation flow into the porous coating dominates as the resistive term controlling the capillary driven liquid imbibition rate.     

Water in extremely narrow planar pores with crystalline walls. 2. Thermodynamics

The free energy, entropy, and work of water vapor adsorption in planar pores with widths of 0.62 and 1.25 nm located in a silver iodide crystal parallel to its basal face have been computed at the molecular level. In contrast to adsorption on a free surface, the adsorption in the pores proceeds in three stages, i.e., the formation of molecular films on the walls, coalescence of the films, and densification of the fluid in the pore volume. At the second stage, the equilibrium between the fluid in the pore and the vapor over the pore at temperatures corresponding to normal conditions is thermodynamically unstable and accompanied by the development of a free energy barrier and the existence of metastable states. As temperature is elevated, the instability is gradually evened out; however, its signs remain preserved even at the boiling temperature of water. Extremely narrow pores with widths smaller than 1 nm are always filled with water under conditions of even a rather dry natural atmosphere. The filling of pores several nanometers wide in strongly unsaturated water vapors overcomes the free-energy barrier; however, the fluid that has filled the pore remains stable with respect to evaporation in vapors with densities lower than the density of saturated vapor by several orders of magnitude. The existence of the free-energy barrier and metastable states in nanosized breaks in crystals creates conditions for hysteresis of adsorption-desorption cycles.     

Diffusion of cyclohexane in native and surface-modified mesoporous glasses

Diffusion of cyclohexane in mesoporous silica materials with different degrees of surface silanization has been probed by means of pulsed field gradient nuclear magnetic resonance. The self-diffusion coefficients have been measured at various pore fillings from about 10% of one monolayer coverage to complete pore saturation by the capillary-condensed phase. It is found that the surface modification, namely grafting of dimethyloctadecylmethoxysilane molecules to the silica surface, reduces diffusivities of guest molecules as compared to the native sample. The contribution of the Knudsen molecular diffusion to the measured diffusivity has been assessed using the model of fast molecular exchange between the adsorbed phase on the pore walls and the molecules in the gaseous phase in the pore interior. The diffusivity data were correlated with the degree of the surface modification, with the latter being probed by measuring ¹H and ¹³C spectra using magic angle spinning (MAS) solid state NMR, nitrogen adsorption and thermogravimetry.