(199c) A Stand-Alone Evapoporometer for Determining the Pore-Size Distribution of Membranes and Other Porous Media

Evapoporometry (EP) has been advanced as a methodology for determining the pore-size distribution (PSD) of membranes and other porous media such as catalysts, adsorbents, and fuel-cell electrodes. Its development and application have been described in a series of papers [1−7]. The operating principle of EP is based on the Kelvin equation that relates the vapor-pressure depression that occurs in small pores. The vapor-pressure depression of a wetting liquid confined in a small pore increases with decreasing pore diameter. The EP characterization procedure for determining the PSD involves saturating a membrane or other porous media with a volatile wetting liquid and placing it at the bottom of a small test cell. The test cell is designed to ensure that the evaporative mass transfer is controlled by a small hole in its lid. The gas phase in the test cell then will be saturated with respect to the largest pores in the membrane or porous media and supersaturated with respect to all the smaller pores. Hence, evaporation of the volatile liquid will occur progressively from the largest to the smallest pores. By continuously weighing the test cell, the evaporation rate can be determined. The evaporation rate can be related to the vapor pressure at the surface of the membrane or porous media. The pore diameter then can be determined from the Kelvin equation and the mass of the liquid evaporating from the pores can be determined from the gravimetric measurement. The mass-based PSD then can be used to determine the mass-average, flow-average, and molecular weight cutoff pore (MWCO) pore diameters.

The EP technique offers several advantages relative to other techniques for determining the PSD such as liquid-displacement porometry (LDP). EP is based on instantaneous gravimetric measurements that can be done with microgram accuracy. In contrast, LDP requires measuring both the displacement pressure and the volumetric flow rate of the displacing gas or liquid, neither of which can be measured as accurately as mass. The data analysis for EP is straightforward. In contrast, LDP uses the Young-Laplace equation to determine the pore diameter, which is the diameter of the throat of the pore; it then uses this diameter in the Hagen-Poiseuille equation, which in fact should use the average diameter of the pore, to obtain the volume of the pores from the volumetric flow rate of the displacing gas or liquid. Characterization via EP is done at the ambient pressure and temperature. In contrast, LDP requires applying a pressure that can compact porous materials such as polymeric membranes. EP characterization can be done with a broad spectrum of volatile wetting liquids including water, which is particularly advantageous since many membrane applications involve aqueous systems. In contrast, LDP requires using special non-volatile wetting liquids; moreover, the recently advanced liquid-liquid displacement porometry requires finding two non-volatile wetting liquids that do not interact either with each other or with the porous sample being characterized. A particular advantage of EP is that it can be used to characterize the effect of both external and internal pore fouling on the PSD. In contrast, LDP cannot characterize fouled membranes since the required flow of the displacing gas or liquid will remove both the external and internal fouling deposits. EP can determine independently the PSD for just the continuous pores as well the PSD for all the pores. The former is useful for characterizing the PSD of membranes for which only the continuous pores are functional, whereas the latter is useful for characterizing catalysts and adsorbents for which the total surface area of all the pores is needed. EP can also determine the PSD of multi-bore membranes and biofouling layers that is not possible with LDP. Moreover, EP provides a measure of the pore interconnectivity that is not possible with other PSD characterization techniques.

This presentation reports on a substantive improvement in EP characterization. Heretofore, EP characterization required user intervention for the data analysis. A stand-alone evapoporometer has been developed that does not require user intervention after the membrane or porous sample has been placed in the test cell. Moreover, heretofore EP characterization involved using a conventional microbalance for the continuous gravimetric measurement; this was problematic because conventional microbalances are not designed for gravimetric analyses that extend over a longer time. The evapoporometer instrument that has been developed employs a sensitive load cell that obviates the need to use a microbalance. The new evapoporometer incorporates improved software that reduces the error in the data analysis and mitigates the need for user intervention. A schematic and a photograph of this novel stand-alone evapoporometer instrument are shown in Fig. 1. As this figure shows, the laboratory footprint of this novel evapoporometer instrument is considerably smaller than competitive instruments such as liquid-displacement porometers.

An endemic problem with the various techniques for determining the PSD including LDP is that once the pores have been emptied by either displacement or evaporation, a thin layer of adsorbed vapor, which is referred to as the t-layer, remains on the walls of all the pores. Since the t-layer typically has a thickness on the scale of a few nanometers, neglecting it causes an error of less than 5% for pores larger than approximately 100 nm. However, it seriously compromises obtaining the correct mass for smaller pores. The new EP data-analysis protocol corrects the PSD for the t-layer without the need for user intervention.

The histogram in Fig. 2 shows the PSD for three runs for a nominal 30 nm Synder UB70 PVDF membrane plotted as the mass percent of pores as a function of the pore diameter in nanometers. A membrane with a smaller nominal pore diameter was chosen to assess the effect of correcting for the t-layer on the PSD. The evapoporometer determines the mass-based PSD from which the mass-average d_mass, flow-average d_flow, and molecular weight cut-off d_MWCO pore diameters can be determined. The average and standard error for the three remeasurements for the flow-average pore diameter is 35.9 ± 4.7 nm, which agrees within the estimated experiment error with the nominal pore diameter of 30 nm determined by LDP. The correction for the adsorbed t-layer mass, which has been ignored in prior pore-size characterization studies, is significant particularly for smaller pores. For example, the t-layer thickness is 1.1 nm for pores having a diameter of 30 nm; ignoring this t-layer mass results in an error of 14% in determining the total mass in these pores.

References Cited:
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