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     

Cation control of pore and channel size in cage-based metal-organic porous materials

Porous materials resembling zeolites that are composed of organic and inorganic building units were synthesized and characterized. Control of pore and channel size was achieved by using different-sized cations. The metal-assembled, anionic cage molecule, Co(4)1(2)(8-), with a hydrophobic cavity and four carboxylate rich arms, was used as a structural unit for the formation of materials with pores and channels. When assembled into a solid material with dications (Mg(2+), Ca(2+), Sr(2+), and Ba(2+)), Co(4)1(2)(8-) arranges into sheets of cages linked together by cations. The series of materials based on Co(4)1(2)(8-) and containing alkaline earth cations was characterized using X-ray crystallography. The magnesium material packs with cages close together, has small channels, and has cation-carboxylate linkages in three dimensions. The calcium material has cages packed with voids between them and has 5 x 10 A channels and 10 x 21 A pores. The strontium and barium materials also pack with voids between the cages and similarly to each other. They have 11 x 13 A and 11 x 11 A channels and 10 x 27 A and 9 x 27 A pores, respectively. Each of these materials has many (20-50) solvent water molecules associated with each cage. The associated water can be removed from and adsorbed by the materials. The heat of water binding has been measured to be -52 kJ/mol (Mg(4)Co(4)1(2)); -47 kJ/mol (Ca(4)Co(4)1(2)); -48 kJ/mol (Sr(4)Co(4)1(2)); -49 kJ/mol (Ba(4)Co(4)1(2)).     

Modified liquid displacement method for determination of pore size distribution in porous membranes

A new method called constant pressure liquid displacement method (CPLM) was developed and tested to measure the pore size distribution of porous membranes. The permeability, defined as a ratio of the flow rate to the pressure applied, used to be assumed constant either for a conventional liquid displacement method or for a bubble point method, leading to the erroneous interpretation of the pore size distribution. However, it was possible to eliminate such an assumption by measuring the flow rates experimentally at a standard low pressure through the pores penetrated with a permeating liquid according to the proposed method. The pore size distribution for a hydrophobic PVDF membrane was successfully measured by the CPLM and compared with those measured by two different methods such as the conventional liquid displacement method and the mercury intrusion method.     

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.     

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.     

Characterization of pore size distribution in porous silicon by NMR cryoporosimetry and adsorption methods

The results of studying the pore size distribution of mesoporous silicon by NMR cryoporosimetry are described. These data are compared with the results obtained by adsorption methods.     

High resolution heat flow DSC: Application to study of phase transitions,and pore size distribution in saturated porous materials

Suitable container design permits very high temperature and differential temperature resolution in DSC even when relatively large (? 0.14 cm³) samples are used; and thus energy signals associated with phase change occurring over large temperature intervals may be analysed in differential elements. An original and powerful high resolution low temperature DSC technique (the authorsψ plot”) for studying and comparing pore size distributions (PSD) in water saturated samples (for pores having Kelvin radii between 1,2 and about 500 nm) is given, together with an application which shows that the PSD in a water saturated organic ion exchanger could be obtained from analysis of three Gaussian distributions which precisely generate a curve which is an excellent empirical fit to the recorded low temperature exotherm obtained by freezing pure water within the sample.     

Inorganic salt hydrates as cryoporometric probe materials to obtain pore size distribution

The depression of the melting temperature of Zn(NO3)2.6H2O was used to obtain the pore size distributions in controlled pore glasses. Measured by 1H NMR, the average value of the temperature depression DeltaT and the known average pore size yield K=DeltaT.d approximately 116 K.nm as the material-dependent factor for Zn(NO3)2.6H2O in the Gibbs-Thompson equation. The melting temperature is close to room temperature. Hence, this salt hydrate and some related other ones are better materials than water (K approximately 50 K.nm) for cryoporometric studies of systems with hydrophilic pores. The data also provide 46 mN/m for the solid-liquid surface tension of this salt hydrate.     

Adsorption of surfactants onto acrylic ester resins with different pore size distribution

In this study, a series of acrylic ester resins with different pore size distribution were prepared successfully by varying the type and the amount of pore-forming agents. In order to inves-tigate the adsorption behavior and mechanism of surfactants on acrylic ester resins, three kinds of surfactants were utilized as adsorbates that were sodium 6-dodecyl benzenesulfonate (6-NaDBS), sodium 1-dodecyl benzene sulfonate (1-NaDBS) and sodium 1-dodecyl sulfonate, respectively. It was observed that the surface area was available in a particular pore size and an appropriate pore size of resins appeared to be more important for the adsorption of surfactants. As compared to commercial acrylic ester resins XAD-7 and HP2MG, 50# and 38# resins exhibited more excellent adsorption properties toward 1-NaDBS and 6-NaDBS. The experimental equilibrium data were fitted to the Langmuir, and double-Langmuir models. Two models provided very good fittings for all resins over the temperature range studied. The investigation indicated that electrostatic attraction and hydrogen bond between resins and surfactants were the main forces and had an obvious effect on adsorption proc-ess.     

Evaluation of methods for determining the pore size distribution and pore-network connectivity of porous carbons

The pore size distribution (PSD) and the pore-network connectivity of a porous material determine its properties in applications such as gas storage, adsorptive separations, and catalysis. Methods for the characterization of the pore structure of porous carbons are widely used, but the relationship between the structural parameters measured and the real structure of the material is not yet clear. We have evaluated two widely used and powerful characterization methods based on adsorption measurements by applying the methods to a model carbon which captures the essential characteristics of real carbons but (unlike a real material) has a structure that is completely known. We used three species (CH4, CF4, and SF6) as adsorptives and analyzed the results using an intersecting capillaries model (ICM) which was modeled using a combination of Monte Carlo simulation and percolation theory to obtain the PSD and the pore-network connectivity. There was broad agreement between the PSDs measured using the ICM and the geometric PSD of the model carbon, as well as some systematic differences which are interpreted in terms of the pore structure of the carbon. The measured PSD and connectivity are shown to be able to predict adsorption in the model carbon, supporting the use of the ICM to characterize real porous carbons.     

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.     

Nondestructive technique for the characterization of the pore size distribution of soft porous constructs for tissue engineering

Polymer scaffolds tailored for tissue engineering applications possessing the desired pore structure require reproducible fabrication techniques. Nondestructive, quantitative methods for pore characterization are required to determine the pore size and its distribution. In this study, a promising alternative to traditional pore size characterization techniques is presented. We introduce a quantitative, nondestructive and inexpensive method to determine the pore size distribution of large soft porous solids based on the on the displacement of a liquid, that spreads without limits though a porous medium, by nitrogen. The capillary pressure is measured and related to the pore sizes as well as the pore size distribution of the narrowest bottlenecks of the largest interconnected pores in a porous medium. The measured pore diameters correspond to the narrowest bottleneck of the largest pores connecting the bottom with the top surface of a given porous solid. The applicability and reproducibility of the breakthrough technique is demonstrated on two polyurethane foams, manufactured using the thermally induced phase separation (TIPS) process, with almost identical overall porosity (60-70%) but very different pore morphology. By selecting different quenching temperatures to induce polymer phase separation, the pore structure could be regulated while maintaining the overall porosity. Depending on the quenching temperature, the foams exhibited either longitudinally oriented tubular macropores interconnected with micropores or independent macropores connected to adjacent pores via openings in the pore walls. The pore size and its distribution obtained by the breakthrough test were in excellent agreement to conventional characterization techniques, such as scanning electron microscopy combined with image analysis, BET technique, and mercury intrusion porosimetry. This technique is suitable for the characterization of the micro- and macropore structure of soft porous solids intended for tissue engineering applications. The method is sensitive for the smallest bottlenecks of the largest continuous pores throughout the scaffold that contributes to fluid flow.     

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.     

A new method to determine pore size and its volume distribution of porous solids having known atomistic configuration

A simple method, based on Monte Carlo integration, is presented to derive pore size and its volume distribution for porous solids having known configuration of solid atoms. Because pores do not have any particular shape, it is important that we define the pore size in an unambiguous manner and the volume associated with each pore size. The void volume that we adopt is the one that is accessible to the center of mass of the probe particle. We test this new method with porous solids having well defined pores such as graphitic slit pores and carbon nanotubes, and then apply it to obtain the pore volume distribution of complex solids such as disordered solids, rectangular pores, defected graphitic pores, metal organic framework and zeolite.     

Tailoring pore size and pore size distribution of kidney dialysis hollow fiber membranes via dual-bath coagulation approach

Polyethersulfone (PES) hollow fiber membranes for kidney dialysis application were prepared by the dry-jet wet-spinning method. A dual-coagulation bath technology was first time employed for fabricating the kidney dialysis membranes with a tight inner skin and loose outer supporting layer structure. A weak coagulant isopropanol (IPA) was served as the first external coagulation bath, while water as the second bath. Experiments demonstrate their advantages of better controlling both inner and outer skin morphology. The as-spun fibers have a higher mean effective pore size (μ_p), pure water permeation flux (PWP) and molecular weight cut-off (MWCO) with an increase in N-methyl-2-pyrrolidone (NMP) percentage in bore fluid (i.e., internal coagulant). After being treated in 8000 ppm NaOCl solution for 1 day, fibers show larger pore sizes and porosity in both inner and outer surfaces, and thinner inner and outer layers than their as-spun counterparts. Among them, the bleached fibers spun with 50 wt.% NMP in bore fluid have the MWCO (43 kDa) and PWP (40 × 10⁻⁵ L m⁻² Pa⁻¹ h⁻¹) suitable for kidney dialysis application. Based on SEM observations and solute rejection performance, the further heat treated fibers in an aqueous solution is found to be an effective way to fine tune membranes morphology and MWCO for kidney dialysis application. The solute rejection performance data of the hollow fiber membranes spun with 55 wt.% NMP in bore fluid after heat treated at 90 °C in water for 2 h were found to be very appropriate for the kidney dialysis application.     

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.     

Error introduced into determination of pore size distribution by size exclusion chromatography

Simultaneous use of large standard molecules and small particles of the product examined gives rise to errors in pore size determination by size exclusion chromatography. This error is calculated for packings of spherical particles, thus making corrections possible.     

Comparison of heterogeneous pore models QSDFT and 2D-NLDFT and computer programs ASiQwin and SAIEUS for calculation of pore size distribution

The pore size distributions (PSD) of selected carbons were calculated from their nitrogen adsorption isotherms using both the QSDFT model implemented in ASiQwin version 3.0 software (Quantachrome Instruments) and 2D-NLDFT model implemented in SAIEUS software (Micromeritics). The results showed that both the QSDFT and the 2D-NLDFT methods give similar PSDs despite the different methods for accounting for the heterogeneity of the carbon adsorbent. The characteristic features of the methods and software were discussed and possible improvements were proposed.     

Analysis of pore size distribution by 2H NMR

The pore size distributions of four controlled pore glasses with mean diameters ranging from ca. 7.9 to 23.9 nm were analysed by measuring the (2)H NMR signals from the liquid fraction of confined benzene-d(6) and cyclohexane-d(12) as a function of temperature, in steps of ca. 0.1-1 K. The liquid and solid components of the adsorbates were distinguished, on the basis of the spin-spin relaxation time T(2), by employing a spin-echo sequence. The experimental intensity curves of the non-frozen liquids are well represented by a sum of two error functions. The observed melting point depressions are well represented by the simplified Gibbs-Thompson equation DeltaT = k(p)/R where R is the pore radius and k(p) is a characteristic property of the adsorbate. The k(p) value mainly affects the position of the pore size distribution curve, i.e., the mean pore radius, while the slope of the intensity curve determines the width of the distribution curve. In practice, the NMR method can only be used to determine pore sizes with reasonable accuracy in the mesoporous range unless liquids undergoing larger melting point depressions than the ones investigated so far can be found.