Determination of the pore connectivity and pore size distribution and pore spatial distribution of porous chromatographic particles from nitrogen sorption measurements and pore network modelling theory

The pore connectivity, pore size distribution and pore spatial distribution of the porous structure of native and silanized silica particles were determined by matching the experimental nitrogen sorption data with the theoretical results obtained from pore network model simulations. The agreement between theory and experiment is found to be good. The results clearly indicate that the deposition of the silane layer to the pore surfaces of the native silica particles produces a silanized silica particle with a mean pore diameter and pore connectivity smaller than that of the native silica particle. Furthermore, the evaluation of the pore diffusivity of ribonuclease under unretained conditions shows that the lower values of the pore connectivity found in the samples of silanized silica particles, when compared with the values of the pore connectivity obtained for the native silica particles, increase the diffusional mass transfer resistance within the porous structure of the silanized silica particles.     

A method for the determination of accessible surface area,pore volume,pore size and its volume distribution for homogeneous pores of different shapes

We develop a novel method to determine the accessible pore volume, the accessible pore size and its distribution for pores having homogeneous surfaces but taking an arbitrary shape. The accessible pore volume is essentially the volume space that is accessible to the centre of an adsorbate molecule, while the accessible pore size is defined by the largest sphere that can be accommodated in the accessible space. The size of this sphere depends on the point in the accessible volume that we select. The accessible pore size is therefore, a local variable and this means that even a geometrically simple pore can possess many sizes. Each local accessible pore size is associated with a local accessible pore volume and the relationship between this pore volume and pore size is called the accessible pore size distribution. In this paper, we illustrate this methodology with a number of model pores ranging from simple to complex geometry and present the analytical accessible pore size distribution.     

Characteristic heats of adsorption for slit pore and defected pore models

The characteristics of the heat of adsorption from a slit pore model of carbon are presented. This is shown to have a few key features that are always present, regardless of the pore size distribution used, as long as there is a reasonable range of pore sizes considered. The adsorption in a slit pore model is compared against the adsorption for a defected pore model. The isotherms of the defected pore model are qualitatively different from those of the slit pore and similar to those of amorphous carbon models presented in the literature. The heat of adsorption of the defected pore model is qualitatively different from the slit pore model, and its behavior falls between those of the slit pore model and the amorphous carbon models in the literature.     

Evolution of pore size distribution and average pore size of porous ceramic membranes during modification by counter-diffusion chemical vapor deposition

The modification of porous ceramic membranes by counter-diffusion chemical vapor deposition (CVD) is studied theoretically and experimentally. Numerical simulations of the evolution of the membrane permeance, average pore size and pore size distribution as a function of extent of modification are presented and compared with experimetal data. It is found that the change of the average pore size of the membranes after modification strongly depends on the initial pore size distribution of the membrane, CVD reaction kinetics and characterization method. Experimental data suggest that CVD of zirconia (and yttria) inside porous ceramic membranes by reaction of zirconium (and yttrium) chlorides with steam/air at elevated temperatures proceeds by quasi-zero reaction kinetics with respect to the oxidant, typical of non-stoichiometric supply of the reactants from opposite sides of the membrane. Under such conditions, CVD modification may result in a modest increase of the average pore size of coarse-pore ceramic membranes as suggested by numerical calculations and experimental data.     

Nanoporous metals with controlled multimodal pore size distribution

A simple two-step dealloying strategy is described to make free-standing metal membranes with hierarchical porous architecture. This structure has a bimodal pore size distribution composed of large porosity channels and small porosity channel walls, where each pore size can be tailored independently of the others. A new gas-phase electroless plating technique was also developed here that could be used to uniformly fill porous structures with pore size as small as 10 nm.     

Comparison between different presentations of pore size distribution in porous materials

The different presentations of the pore size distribution derived from the gas adsorption method and the mercury porosimetry are connected with some problems. This concerns especially the use of the logarithmically differential pore volume distribution. The incorrect application of this distribution to bimodal pore systems involves the danger of an apparent overemphasizing of larger pores. This effect may also occur using the incremental pore size distribution in case the experimental point spacing considerably increases towards the larger pore radii. The pore volume density distribution defined as the linear derivative of the cumulative pore volume curve with respect to the pore radius has been found the most convenient form among the various kinds of pore volume distribution presentations. It has been shown that the direct comparison between this distribution and the logarithmically differential pore volume distribution is not allowed. Nevertheless, there is a clear connection between these definitions for the pore size distribution so that they are completely equivalent.     

Comparison between different presentations of pore size distribution in porous materials

The different presentations of the pore size distribution derived from the gas adsorption method and the mercury porosimetry are connected with some problems. This concerns especially the use of the logarithmically differential pore volume distribution. The incorrect application of this distribution to bimodal pore systems involves the danger of an apparent overemphasizing of larger pores. This effect may also occur using the incremental pore size distribution in case the experimental point spacing considerably increases towards the larger pore radii. The pore volume density distribution defined as the linear derivative of the cumulative pore volume curve with respect to the pore radius has been found the most convenient form among the various kinds of pore volume distribution presentations. It has been shown that the direct comparison between this distribution and the logarithmically differential pore volume distribution is not allowed. Nevertheless, there is a clear connection between these definitions for the pore size distribution so that they are completely equivalent. Received: 15 May 1998 / Revised: 8 October 1998 / Accepted: 10 October 1998     

Pore spanning lipid bilayers on mesoporous silica having varying pore size

Synthetic lipid bilayers have similar properties as cell membranes and have been shown to be of great use in the development of novel biomimicry devices. In this study, lipid bilayer formation on mesoporous silica of varying pore size, 2, 4, and 6 nm, has been investigated using quartz crystal microbalance with dissipation monitoring (QCM-D), fluorescent recovery after photo bleaching (FRAP), and atomic force microscopy (AFM). The results show that pore-spanning lipid bilayers were successfully formed regardless of pore size. However, the mechanism of the bilayer formation was dependent on the pore size, and lower surface coverages of adsorbed lipid vesicles were required on the surface having the smallest pores. A similar trend was observed for the lateral diffusion coefficient (D) of fluorescently labeled lipid molecules in the membrane, which was lowest on the surface having the smallest pores and increased with the pore size. All of the pore size dependent observations are suggested to be due to the hydrophilicity of the surface, which decreases with increased pore size.     

Shrinkage and pore structure in preparation of carbon aerogels

To aim at thermal insulator applications, the shrinkage and the pore structure of resorcinol–formaldehyde (RF) aerogels and carbon aerogels were investigated during the supercritical drying and the carbonization process. The water (W) molar ratio has small effects on the surface area or the particle size, but has significant effects on the density of the aerogel. Higher W/R ratio leads to lower density and larger pore size, and leads to less shrinkage during the carbonization process. The molar ratio of catalyst sodium carbonate (C) has significant effects on the shrinkage, pore size, and particle size of the aerogel. Lower R/C ratio leads to smaller particle size and smaller pore size, and thus induces more shrinkage both in the supercritical drying and in the carbonization, the obtained CA is much denser. The R/C ratio should be higher than 300 to prevent excessive shrinkage. In order to synthesize carbon aerogels combining with small shrinkage, low density (less than 0.1 g/cm³), and small pore size (less than 150 nm) for thermal insulators, the preferred W/R ratio is between 90 and 100, and the preferred R/C ratio is between 300 and 600.     

Kinetics of protein adsorption by nanoporous carbons with different pore size

Kinetics of bovine serum albumin and ovalbumin adsorption by nanoporous carbons with different main pore sizes (1.6, 5, 7.8 and 28 nm) was studied. Experimental kinetics curves were well described by multi-exponential equation with different number of exponents (from 1 to 4). Protein adsorption kinetics showed significant dependence on pore size of carbonaceous adsorbent. Correlation between pore size distribution and amount of protein adsorbed revealed threshold pore size 7.3 nm for BSA and 6.8 nm for OVA, which are close to hydrodynamic diameter of protein molecules. The fastest and the highest adsorption of proteins were observed in carbons having developed porosity with pore sizes larger than 15 nm.     

Three-dimensional pore structure of chromatographic adsorbents from electron tomography

The pore structure of chromatographic adsorbents directly influences macromolecular partitioning and transport in chromatography. Quantitative structural characterization of chromatographic media has generally been performed in terms of the mean pore size or, at best, the pore size distribution (PSD), but more detailed information on, e.g., connectivity has been lacking. We have applied electron tomography, a 3D TEM technique that views a sample from multiple perspectives and allows reconstruction of the volumetric structure, to capture the internal details of microporous chromatographic media with nanometer-scale resolution. Visualization of reconstructions of three adsorbents, Toyopearl SP-650 C, SP-550 C, and CM Sepharose FF, provides thorough and direct information on the geometry and the interconnectivity of the pore network. The structures are qualitatively consistent with in situ AFM images, and quantitative data for the porosities and PSDs from the analysis of tomographic data agree reasonably well with inverse size-exclusion chromatography results. For a more straightforward representation of the networking and size features of the disordered pore space, a 3D thinning algorithm was used to derive pore skeletons and consequently quantitative data on distributions of local path lengths, widths, tortuosities, and connectivities. Such enriched structural information can be instrumental in more discriminate structural evaluation and construction of engineered pore models for the study of solute intraparticle transport.     

Easy synthesis of iron doped ordered mesoporous carbon with tunable pore sizes

Precise control of the pore sizes for porous carbon materials is of importance to study the confinement effect of metal particles because the pore size in nanosize range will decide the physical and chemical properties of the metal nanoparticles.In this paper,we report a new approach for the synthesis of iron doped ordered mesoporous carbon materials with adjustable pore size using Fe-SBA-15 as hard template and boric acid as the pore expanding reagent.The pore size can be precisely adjusted by a step of 0.4 nm in the range of 3-6 nm.The carbonization temperature can be lowered to 773 K due to the catalytic role of the doped iron.The present approach is suitable for facile synthesis of metal imbedded porous carbon materials with tunable pore sizes.     

Highly aminated mesoporous silica nanoparticles with cubic pore structure

Mesoporous silica with cubic symmetry has attracted interest from researchers for some time. Here, we present the room temperature synthesis of mesoporous silica nanoparticles possessing cubic Pm3?n symmetry with very high molar ratios (>50%) of 3-aminopropyl triethoxysilane. The synthesis is robust allowing, for example, co-condensation of organic dyes without loss of structure. By means of pore expander molecules, the pore size can be enlarged from 2.7 to 5 nm, while particle size decreases. Adding pore expander and co-condensing fluorescent dyes in the same synthesis reduces average particle size further down to 100 nm. After PEGylation, such fluorescent aminated mesoporous silica nanoparticles are spontaneously taken up by cells as demonstrated by fluorescence microscopy.     

Quantitative information on pore size distribution from the tangents of comparison plots

The comparison plot obtained from the nitrogen adsorption data has a similar shape to that of the curve of accumulating pore volume of a solid. The intrinsic nature of this relation is discussed. It is known that the derivatives of the accumulating pore volume with respect to the pore size are the pore size distribution (PSD) of the solid. Thus, the tangent curve of the comparison plot can display, at least qualitatively, the PSD of a solid, over a wide range of pore sizes (from approximately 1 to 50 nm) because the comparison plot is applicable to both micropores and mesopores. Quantitative pore structure information can be derived from the comparison plots by establishing a relationship between the t value and the pore size from the samples with uniform pore structure and known pore sizes, such as MCM-41 and alumina pillared clay samples. A calculation procedure to derive quantitative PSD from the comparison plots is suggested, giving reasonable results. This study proposes concise and reliable methods based on the comparison plots to derive information on pore structure in porous solids.     

Determination of pore size distribution in hollow fibre membranes

Isopropanol displacement under nitrogen pressure was used for the determination of pore size distribution in microfiltration polypropylene hollow fibres. Applying various assumptions about gas transport process two completely different characteristics of pore sizes were obtained. To verify these results an analysis of SEM images of the investigated membrane was conducted concerning its porous structure (pore diameters, surface occupied by pores). According to the SEM analysis the mean coverage of membrane surface by pore entrances should be about 20% of total area. For the distribution which accounted for pore evacuation according to Young–Laplace equation with contact angle θ=67° surprisingly dense coverage amounting to over 70% of total surface (by calculated total pore number over 10¹³ per m²) was predicted. Results for the distribution which accounted for gas bubble formation at the membrane surface (equivalent to θ=0°) fit into the expected range of pore numbers and membrane coverages (about 10¹¹ per m² and about 10%, respectively). It is concluded that the mechanism of bubble formation, determined by an actual pressure, liquid surface tension and pore size, is the crucial process while the value of contact angle θ does not play any role in the determination of pore size distribution.     

Influence of the pore size of reversed phase materials on peptide purification processes

The influence of the pore size of a chromatographic reversed phase material on the adsorption equilibria and diffusion of two industrially relevant peptides (i.e. a small synthetic peptide and insulin) has been studied using seven different reversed phase HPLC materials having pore sizes ranging from 90 Å to 300 Å. The stationary phase pore size distribution was obtained by inverse size exclusion measurement (iSEC). The effect of the pore size on the mass transfer properties of the materials was evaluated from Van Deemter experiments. It has been shown that the lumped mass transfer coefficient increases linearly with the average pore size. The Henry coefficient and the impurity selectivity were determined in diluted conditions. The saturation capacity of the main peptides was determined in overloaded conditions using the inverse method (i.e. peak fitting). It was shown that the adsorption equilibria of the peptides on the seven materials is well described by a surface-specific adsorption isotherm. Based on this a lumped kinetic model has been developed to model the elution profile of the two peptides in overloaded conditions and to simulate the purification of the peptide from its crude mixture. It has been found that the separation of insulin from its main impurity (i.e. desamido-insulin) was not affected by the pore size. On the other hand, in the case of the synthetic peptide, it was found that the adsorption of the most significant impurity decreases with the pore size. This decrease is probably due to an increase in silanol activity with decreasing pore size.     

Synthesis and characterization of pore size-tunable magnetic mesoporous silica nanoparticles

Magnetic mesoporous silica nanoparticles (M-MSNs) are emerging as one of the most appealing candidates for theranostic carriers. Herein, a simple synthesis method of M-MSNs with a single Fe(3)O(4) nanocrystal core and a mesoporous shell with radially aligned pores was elaborated using tetraethyl orthosilicate (TEOS) as silica source, cationic surfactant CTAB as template, and 1,3,5-triisopropylbenzene (TMB)/decane as pore swelling agents. Due to the special localization of TMB during the synthesis process, the pore size was increased with added TMB amount within a limited range, while further employment of TMB lead to severe particle coalescence and not well-developed pore structure. On the other hand, when a proper amount of decane was jointly incorporated with limited amounts of TMB, effective pore expansion of M-MSNs similar to that of analogous mesoporous silica nanoparticles was realized. The resultant M-MSN materials possessed smaller particle size (about 40-70 nm in diameter), tunable pore sizes (3.8-6.1 nm), high surface areas (700-1100 m(2)/g), and large pore volumes (0.44-1.54 cm(3)/g). We also demonstrate their high potential in conventional DNA loading. Maximum loading capacity of salmon sperm DNA (375 mg/g) was obtained by the use of the M-MSN sample with the largest pore size of 6.1 nm.     

Modelling of the pore size distribution of ultrafiltration membranes

A dilute aqueous solution of polydisperse neutral dextrans was used to determine the sieving properties (flux and rejection) of porous polyacrylonitrile membranes. Gel ermeation chromatography was used to measure the solute mole and concentration in the permeate. From these data, rejection coefficients were calculated as a function of solute molecular size. A mathematical model was then developed to relate the flux and solute rejection to pore size distribution and the total number of pores, based upon the assumption that solute rejection was the result of purely geometric considerations. As a first approximation, a solute molecule was considered either too large to enter a membrane pore, or if it entered, its concentration in the permeate from that pore, as well as the solvent flux through the pore, were not affected. This model also considered the effects of steric hindrance and hydrodynamic lag on the convection of solute through a membrane. The shape and sharpness of pore size distributions were found to be useful in comparisons of ultrafiltration membranes.     

Low-temperature adsorption of hydrogen on nanoporous aluminophosphates: effect of pore size

Several nanoporous aluminophosphates (AlPOs) have been used to analyze the effect of pore diameter on the hydrogen adsorption characteristics. The heat of adsorption and adsorption capacity per unit micropore volume increase with decreasing pore size. AlPOs with smaller micropores favorably adsorb hydrogen at relatively low pressures. This work demonstrates that small pore size and large micropore volume are beneficial for high hydrogen uptake.