Pore Size Distribution Of Membranes Research Articles

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.

Pore Size Distributions of Polysulfonic UF Membranes and Protein Adsorption

Abstract To compare actual and effective porous structure in operative conditions of ultrafiltration membranes, flux, retention, and the amount of adsorbed protein have been measured for 0.1% w/w aqueous solutions of several proteins [lysozyme, pepsin, bovine serum albumin (BSA), lipase, and γ-globulin] with molecular weights from 14.6 to 150 kD tangentially filtered through two asymmetric polysulfone membranes, E-100 and E-500. From retention and flux experiments, the dependency of mass transfer coefficients on molecular volume has been analyzed. Results imply that protein molecules behave as being slightly uncoiled, especially when filtered through the smallest pore size membrane. By using a simple sieving model, retention data allow pore size distributions to be obtained. The data are modified by taking into account adsorption and volume hindrance effects in operational conditions.

Pore size distribution determination from liquid permeation through microporous membranes

Knowledge of the pore size distribution of a microfiltration or ultrafiltration membrane is necessary in order to accurately predict membrane performance in any given application. The liquid permeation technique presented in this paper has been used to obtain data for determining pore size distribution for nearly sixty years. However, the mathematical technique presented in this paper to interpret the experimental data has not been used since its conception in the early nineteen-thirties. This paper examines the merits of this mathematical technique which, when coupled with modern computing capabilities and precise data acquisition, can be used to effectively determine accurate, continuous pore size distributions of hydrophobic membranes.

Effect of pore size distribution of ultrafiltration membranes on virus rejection in crossflow conditions

The ultrafiltration process is successfully used in wastewater reuse systems. It will also be used widely in drinking water supplies. In wastewater reuse and for safer drinking water supplies the potential for virus rejection by membrane processes is advantageous. Rejection of viruses was examined experimentally by using coliphage Qβ as a tracer. Several types of ultrafiltration membranes with molecular weight cutoff size of 20,000-40,000 were tested. All of these membranes leaked phages to some extent, contrary to the expectation from nominal cutoff size. Penetration of virus through ultrafiltration membranes was theoretically examined by taking pore size distribution of the membranes into account. Modified pore theory and a log-normal pore size distribution model gave an unsatisfactory explanation of the results. The presence of abnormally large pores which are not included in the main distribution was indicated.

Critical Factors in the Determination of the Pore Size Distribution of Ultrafiltration Membrances Using the Liquid Displacement Method

The pore size distribution of ultrafiltration membranes can be determined using the liquid displacement method developed by Munari and coworkers. However, when this technique is employed, several phenomena have to be taken into consideration in order to avoid erroneous results. In this paper three phenomena are discussed. 1) During the measurement the liquid flow is increased stepwise, resulting in pressure instabilities at the membrane surface. 2) The membrane permeability may be dependent on the pressure and has to be determined at several pressures. 3) Successive measurements of the same module show large differences between the first run and following runs. Traces of glycerol, incomplete pore filling, or long-term swelling are thought to be responsible for erroneous results in the first run.

Use of the log-normal probability density function to analyze membrane pore size distributions: functional forms and discrepancies

The log-normal probability density function has been used extensively in the characterization of membrane pore size distributions and in the theoretical analysis of the effect of these distributions on membrane transport. There has, however, been considerable discrepancy regarding the proper functional form for this probability distribution as well as the proper interpretation of the parameters used to define the distribution. This short communication examines the different forms that have been presented in the literature for the log-normal distribution, properly interprets the parameters that appear in these functions, and provides the appropriate equations required to transform between these different distributions and properly evaluate the appropriate statistical parameters.

Porosimetric Characterization of Inorganic Membranes

Abstract This paper deals with the evaluation of pore size and pore size distribution of inorganic membranes by liquid-liquid displacement porometry. Carbon and ceramic membranes were tested with a fully automatic porometer, and different results were obtained depending on the type of membrane. Membranes were also examined with the aid of a scanning electron microscope. The results of porosimetric measurements are discussed in conjunction with those of microscopic observations.

Sieve mechanism of microfiltration

A mathematical model for dead-end microfiltration (MF) of dilute suspensions is suggested. The model is based on a sieve mechanism and takes into account the probability of membrane pore blocking during MF of dilute colloid suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and particle size probability distribution functions is deduced. According to the suggested model a similarity property is deduced, which allows one to predict the flux though the MF membrane as a function of time for any pressure and dilute concentration based on one experiment at a single pressure and concentration. The model enables one to calculate all the necessary physico-chemical parameters that are relevant for the determination of the dependency of flux on time. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solve analytically and the derived equation is in good agreement with the measurements on four different track-etched membranes. A condition is found for which the MF membrane trans forms into an ultrafiltration membrane. A simple approximate solution of the IDE is deduced and that approximate solution as well as the similarity property of MF processes is in good agreement with the measurements on a commercial teflon MF membrane.

Pore size distribution of unsupported SnO2 membranes prepared by sol-gel process

Unsupported SnO2 membranes were prepared by sol-gel process and characterized by N2 adsorption-desorption isotherms and X-ray diffraction. Results show that the texture of dried samples does not change appreciably with the concentration of electrolyte. All of the pore size range used in ultrafiltration process was screened using sintering temperature between 300 and 700°C.

Determination of the pore size distribution of membranes by gel permeation chromatography

AbstractPolyacrylonitrile membranes with different separation ranges are prepared and characterized by gel permeation chromatography. The determination of the pore size distribution of the ultrafiltration flat membrane (upper ultrafiltration range) and of the microfiltration hollow fiber membrane (lower microfiltration range) is affected by different measuring procedures. A comparison of the parameters of separation performance is obtained by making use of aqueous poly(ethylene glycol) (PEG) mixtures with broad molecular weight distribution, or the application of single PEG test substances is performed. The obtained results are discussed in connection with the separation range of membranes and the molecular weight of test solutions.

A new approach to the evaluation of the effects of protein adsorption onto a polysulfone membrane

A simple but suitable interpretation of fouling due to protein adsorption onto ultrafiltration membranes, is to attribute it to a modification of the morphological structure of the membranes, namely a decrease in pore size, and to an increase in toe hydrodynamic friction between solute molecules carried by the solvent flow and the pore walls. Evidence is obtained by evaluating the pore size and pore size distribution of a clean polysulfone membrane and of the same membrane adsorbed with bovine serum albumin solutions of different concentrations. The parameters (mean pore radius and standard deviation) of the normal pore size distribution are calculated by a method based on a pore flow model as described in a previous work [J. Membrane Sci., 61 (1991) 49]. Once those parameters are obtained, their correctness is evaluated, using a predictive model including the parameters. The values of ultrafiltration fluxes and rejections calculated by this theoretical predictive model are compared with the experimental data obtained for the ultrafiltration of dextran solutions. A good agreement is verified, thus validating the theory of prevailing pore adsorption, the characterization method and the predictive transport model.

Diagnosis of membrane fouling using a rotating annular filter. 2. Dilute particle suspensions of known particle size

In a continuing study of membrane fouling, we report on the behavior of dilute particle suspensions in a rotating annular filter with a nominal 0.45 μm surface modified polysulfone microfiltration membrane. Particle size (25.7, 11.9, and 2.02 μm), particle type (styrene/divinylbenzene and styrene/polyvinyltoluene), transmembrane pressure (10–100 kPa) and rotational speed (0, 1000, 2000, 3000 and 4000 rpm) were varied. The mean flux-transmembrane pressure data are analyzed using a recent narrow-gap solution to the Navier-Stokes equations for azimuthal flow in an annulus with Darcy's law for flow through a porous wall on the inner rotating cyclinder [Belfort et al., J. Membrane Sci., 77 (1993) 1]. By accounting for centrifugal pressure, the data for all rotational speeds can be plotted with one universal correlation for each feed type. From these data, we suggest that particle intrusion into the pores of the membrane causing pore constriction and plugging is the dominant form of fouling for the systems studied here. Particle intrusion depends on membrane pore size distribution, density difference between the particles and the carrying fluid, particle size, and rotational speed. Also, intruded particles reduce volumetric flow through the blocked pores thus increasing the resistance to flow and reducing the mean permeation flux. Using a corrected version of the Meireles et al. [J. Membrane Sci., 56 (1991) 13] approach, changes in the mean membrane pore size distribution resulting from this intrusion are predicted. By minimizing the sum of the squares of the errors between calculated and measured flux-pressure slopes for two suspensions containing different particle diameters, we obtained best fit values for the mean radius r * and the variance σ 2 of the log-normal pore size distribution.

Membranes as fractals: Implication and consequences

The fractal nature of synthetic membranes suggests a new approach to implement pore size distributions in membrane characterization. The fractal definition of membrane morphology implies that the pore size distribution of a synthetic membrane can be described by a set of three parameters such as the minimum and maximum pore radius and the fractal dimension D. The effect of such a pore size distribution on solute sieving curves has been determined parametrically for the permeation of dilute aqueous solutions of polyethylene glycols through ultrafiltration membranes. These results have been compared to sieving curves obtained from the normal and log-normal pore size distributions which represent the conventional approach in defining the porosity of synthetic membranes.

EFFECT OF POLYVINYLPYRROLIDONE ADDITIVE ON THE PORE SIZE AND THE PORE SIZE DISTRIBUTION OF POLYETHERSULFONE (VICTREX) MEMBRANES

Investigations were made on the effect of the presence of polyvinylpyrrolidone (PVP) additive in the casting solution on the performance of polyethersulfone (PES) ultrafiltration membranes in the range of PVP/PEs weight ratio below 0.5. It was further attempted to investigate the effect of PVP additive on the size of PES polymer in the casting solution and the pore size and the pore size distribution of PES membranes. It was found that the presence of PVP additive decreases both the polymer size and the membrane pore size. Discussions were made on the mechanism of the formation of the pore based on the correlation between the polymer size and the pore size.

Dextran transport through asymmetric ultrafiltration membranes: Comparison with hydrodynamic models

Although dextran sieving is often used to evaluate the pore size characteristics of the ultrafiltration membranes, there is still considerable disagreement regarding the proper interpretation of these sieving measurements. We obtained experimental data for the transport of polydisperse dextrans through asymmetric polyethersulfone membranes of differing molecular weight cut-off in a stirred ultrafiltration device. Gel permeation chromatography is used to evaluate the actual sieving coefficient as a function of dextran molecular weight from data for the bulk and filtrate concentrations, with the bulk mass transport effects evaluated using a stagnant film model. There is no evidence of any dextran deformation even at fluxes as high as 10−4 m/sec. The flux dependence of the actual sieving coefficients is in good agreement with membrane transport theory, allowing the evaluation of both the hindered diffusivities and asymptotic sieving coefficients as a function of dextran molecular weight. The results are shown to be in good agreement with available hydrodynamic models for spherical solutes in cylindrical pores with the effective solute to pore size ratio evaluated using a partitioning model which implicitly accounts for the membrane pore size distribution.

The nucleation of organic additives in membrane casting solution (I) (the theory and direct evidence)

In order to effectively control the pore size and pore size distribution of membranes, the nucleation of an organic additive, triphenylphosphine (ATP) in concentrated polymer solutions has been studied theoretically by statistical thermodynamics and experimentally by scanning electron microscopy (SEM) and nuclear magnetic resonance (NMR). A theory to predict the nucleation of an additive in a polymeric membrane casting solution has been developed based on a lattice model. Both thermodynamically stable and dynamically stable nucleation of an additive in a membrane casting solution was predicted to be possible, which was supported by the experimental results. In order to use the nucleation of organic additives in a concentrated polymer solution for the fabrication of membranes, a double phase inversion method (DPIM) was developed.

Diffusive and convective protein transport through asymmetric membranes

AbstractExperimental data are obtained for bovine serum albumin transport through asymmetric polyethersulfone ultrafiltration membranes of differing molecular weight cutoff in a stirred ultrafiltration device. The actual membrane sieving coefficient is determined from filtrate concentration measurements using a stagnant film model to account for bulk mass transport effects. These sieving coefficients are then used to evaluate the relative contributions of diffusive and convective transport to the overall protein flux. The results are in good agreement with available hydrodynamic models for the hindrance factors for convective and diffusive transport of spherical solutes through well‐defined pores, with the effective solute to pore size ratio evaluated from a partitioning model that explicitly accounts for the ellipsoidal shape of the protein and the membrane pore size distribution. The implications of these results to the analysis of experimental data for membrane sieving and to the design of effective protein fractionation devices are also discussed.

溶質阻止率を用いた限外ろ過膜の細孔構造の解析：細孔構造におよぼす操作条件の影響

An improved method is presented for describing the apparent intrinsic pore properties (mean pore size and pore size distribution) of ultrafiltration membrane from solute rejection curves. To obtain the apparent intrinsic pore properties, firstly the mean pore diameter is determined from the solute rejection curve by correcting the steric and hydrodynamic hindrance effect of pores on molecules, and secondly the effects of operating conditions (pressure, feed concentration and recirculation velocity) on the pore properties are examined by ultrafiltration of seven solutes using SEPA-PS-0 membrane and are eliminated by extrapolating to “zero” operating conditions.The pore property parameters (μ, Dp and θ) obtained from the solute rejection curve are affected by two factors: 1) the plugging of membrane pores by the solute and 2) the deformation of solute due to the variation of pressure and feed concentration. But the recirculation velocity does not affect the pore property parameters. the mean pore diameter is about 60 A and the pore diameter distribution range is from 30 A to 103 A for SEPA-PS-0 membrane at the “zero” operating condition state.

Influence of casting solution concentration on structure and performance of cellulose acetate membranes

On the basis of separation curves, the pore size and pore size distribution of cellulose acetate ultrafiltration membranes are determined. Quantitative conclusions are drawn as to the influence of casting solution concentration on membrane structure and performance. The polymer concentration in the casting solution was varied between 17.5 and 21% wt.

Prediction of rejection coefficients in ultrafiltration

The rejection coefficient for the ultrafiltration of monodisperse solutes (polystyrene in cyclohexane at theta temperature) was calculated from average pore size and pore size distribution of mineral membranes, assuming a sieve mechanism for membrane crossflow and negligible adsorption. In the case of high adsorption, conditions of saturation of the membrane were reached, and the average pore size was corrected by applying Poiseuilles's law to solvent flow. Experimental results agreed well with the rejection coefficients thus calculated.