Pore Size Distribution of Track Etched Membranes

Track-etched membranes are thin, polymeric materials with a well-defined pore structure created by irradiation with particles or ions of known size, or by chemical etching. These processes allow membrane pore sizes and density to be carefully controlled.

Track-etched membranes are believed to possess cylindrical pores, with diameters matching the size of the particle used to create the pore channels, which are almost structurally identical to the ideal models on which every pore size and permeability calculation is founded.

Although the pore size distributions of track-etched membranes are notable for their sharpness, there is still a degree of deviation in their sizes. In the ion/particle bombardment process, the particle beam can overlap and aggregates of particles can form during the etching process, resulting in larger pore sizes in both processes.

Capillary flow porometry (CFP) is commonly utilized to characterize porous media, and it is a perfect method to characterize the quality and consistency of track-etched membranes. The principle of the measurement is the impregnation of a porous sample with a wetting liquid and the displacement of the liquid out of the pores by using gas at increasing pressure (Figure 1).

Displacement of liquid out of the pores in CPF.

Figure 1. Displacement of liquid out of the pores in CPF.

Pores in materials can be grouped into three main groups depending on the path type of the pore (Figure 2):

  • Closed pores. These are pores with an entirely enclosed pore path.
  • Blind pores. Here, the pore path begins at one surface and ends inside the material.
  • Through pores. In through pores, the pore path connects one surface of the material with another surface.

Different pore types.

Figure 2. Different pore types.

Neither closed pores nor blind pores contribute to the flow through the material, and a CFP system can only measure through pores.

The two variables being measured in CFP are the differential gas pressure applied and the gas flow rate through the sample. The pore size is calculated by the Young-Laplace equation, as seen in Equation 1:

P = 4*γ*cos θ/D (1)

where (P) is the pressure required to displace the wetting liquid from the pore, (γ) is the surface tension of the liquid, (θ) is the contact angle and (D) is the diameter of the pore. In smaller pore sizes, higher pressures are needed to displace the wetting liquid from the pores.

However, CFP does succumb to certain limitations when considering the measurement of pore sizes in the submicron and nanometer range. This is because the maximum pressure achievable by CFP commercial devices (35 bars or 500 psi) is not high enough to displace the wetting liquid out of very small pores below 15 nm diameter.

Additionally, pressures higher than 35 bars are believed to significantly deform or damage the materials being tested. As a result, high differential pressures across membranes, which are often delicate in nature, are not suitable as a method of characterization. Fortunately, alternative methods have been finalized, which offer much lower rates of distortion along with more realistic measurement conditions.

Liquid Liquid Displacement Porometry (LLDP) is the perfect alternative to CFP for the characterization of micro- and nanopores. Like CFP, LLDP requires porous samples to be imbued with a wetting liquid. However, unlike CFP, displacing the wetting liquid is carried out by using a second liquid, often called “displacement liquid”, at increasing pressure (Figure 3).

Displacementof liquid out of the pores in LLDP.

Figure 3. Displacementof liquid out of the pores in LLDP.

As in CFP, differential pressure using the Young-Laplace equation is used to calculate pore size. But, because the interfacial tension between two liquids is much lower than the surface tension at the interface gas-liquid (almost by an order of magnitude), LLDP measures smaller pores than CFP without requiring high pressures.

LLDP is also ideal for full characterization of hollow fibers at low pressures. In CFP, hollow fibers often burst or collapse because of mechanical damage incurred from applied high pressures.

Scanning Electron Microscopy (SEM) is an image-analysis based characterization technique that stems from the interaction of a focused beam of high-energy electrons with the surface of a material. When this kind of electron beam makes contact with the sample, the electrons decelerate and originate a beam of secondary electrons, which generates an SEM image.

This offers information on the structure and morphology of the sample. In the present work, CFP, LLDP and SEM were used to characterize commercial polycarbonate, track etched membranes.

Materials and Methods

1. Samples

Hydrophilic polycarbonate tracked-etched membranes, manufactured by IT4IP (Belgium).
Lot: M/160909/R/1
Thickness: 25 μm
Pore size quoted by the manufacturer: 50 nm

2. Capillary Flow Porometers: POROLUX™ 500 and POROLUX™ 1000

The sample is impregnated with an inert and nontoxic wetting liquid and an inert gas such as nitrogen is used to displace the liquid out of the porous network in a process called a wet run. The “wet curve” shows the gas flow through the sample measured against the applied pressure, which is inversely proportional to the size of the pore.

The gas flow against the applied pressure through the dry sample is also measured in a process called a dry run. The “half-dry curve” is generated by dividing the flow values of the dry curve by two. It is also plotted against the applied pressure in the same graphic. From the wet curve, the dry curve and the “half-dry curve” data, information on the porous network can be built up, as seen in Figure 4.

Measuring curves and resulting parameters in CFP (d = dry curve, w = wet curve, d/2 = half-dry curve, FBP = largest pore, MFP = mean flow pore, calculated at the pressure where the wet and the half-dry curves meet and it is the pore size at which 50 % of the total gas flow can be accounted). The minimum pore size is calculated at the pressure at which the wet and the dry curve meet (from this point onwards the flow will be the same because all the pores have been emptied).

Figure 4. Measuring curves and resulting parameters in CFP (d = dry curve, w = wet curve, d/2 = half-dry curve, FBP = largest pore, MFP = mean flow pore, calculated at the pressure where the wet and the half-dry curves meet and it is the pore size at which 50 % of the total gas flow can be accounted). The minimum pore size is calculated at the pressure at which the wet and the dry curve meet (from this point onwards the flow will be the same because all the pores have been emptied).

Capillary flow porometry makes use of two measurement methods, detailed below.

  • The pressure scan method (POROLUX™ 500): The pressure increases continuously at a constant rate and measurements of the gas flow through the sample are taken. This method is fast and very reproducible, and it is recommended for quality control (Figure 5).
  • Pressure/step stability method (POROLUX™ 1000): The user-defined stability algorithms for both pressure and flow need to be met before data points are taken. This means the porometer detects when a pore empties at a certain pressure and does not accept a data point until all pores with the same diameter, but with different length and tortuosity, have been emptied in full. This is confirmed by measuring a stable gas flow before increasing the pressure to the next value. This method is more accurate and recommended for research and development applications (Figure 6).

Pressure scan.

Figure 5. Pressure scan.

Pressure step/stability.

Figure 6. Pressure step/stability.

The ASTM F-316-03 standard defines the calculation of the FBP (the maximum pore size) at the pressure at which the first continuous gas bubbles are detected. Different criteria are available because ASTM doesn’t give a unique definition of the minimum flow through the sample, explained below.

  • Calculated FBP: the FBP is calculated by using the pressure needed to realize a particular minimum flow. This method poses the risk of missing the actual first pore opening because of the arbitrary selection of a certain flow value as higher pressures are sometimes needed to reach the selected flow. The pressure scan method only uses this calculated FBP method.
  • Measured FBP: a linear rate of pressure is attained by establishing a steady flow rate into the instrument, for instance flow in, with no flow out will yield a steady increase in pressure. At the precise time of first pore opening (called the bubble point), this linear rate of pressure increase changes because the flow in is now faced with some flow out. The FBP is defined at the particular pressure where a certain deviation in the linear rate of pressure increase is detected.

3. Liquid Liquid Displacement Porometer POROLIQ™ 1000

Experimental method

Firstly, the sample is imbued with a wetting liquid and put in the sample holder, which has been specifically designed to eradicate any possible sources of air bubbles and prevent subsequent disruptions in flow values. Then, the sample holder is filled with a displacement liquid.

The pressure is gradually increased and the flow rate of the displacement liquid against the applied pressure is recorded, a process called the “LLDP curve.” Before the wetting liquid is displaced, all the through pores are “blocked,” and consequently, the flow rate through the pores is zero. Once an appropriate pressure level has been reached capable of displacing the wetting liquid from the largest pores, the “First Flow Point” is detected.

The POROLIQ™ 1000 is based on the step/stability method: it identifies the opening of pores at specific pressures and does not record a data point until all the pores with the same diameter at the same pressure are fully open. Depending on factors like tortuosity, interconnectivity, and length, pores of equal diameter may open at different rates. Due to this fact, it’s vital to determine the stability of both pressure and flow by complex control algorithms in order to achieve the best possible levels of accuracy.

The measurement proceeds with increasing pressures until the wetting liquid is entirely expelled from every pore. This point is confirmed by a linear dependence of flow of the displacement liquid on pressure.

Once the LLDP curve has been recorded, the flow rate of the displacement liquid alone is measured against the applied pressure on the sample. This is called a permeability or PERM curve.

4. SEM

SEM images were generated with a Phenom Bench-top SEM G2 Pro from Phenom World in the Netherlands. The magnification and the acceleration voltage used for each image are shown in the image itself.

Results

CFP Results Obtained with Both POROLUX™ Models

Settings used in POROLUX 500:

  • Support: etched metal plate
  • Shape factor: 1
  • Wetting liquid: Porefil™, surface tension 16 dyn/cm
  • FBP criteria: defined as size at flow rate above 10 ml/min flow
  • Slope of pressure increase: 60 s/bar
  • Number of data points: 50.

Settings used in POROLUX™ 1000:

  • Support: etched metal plate
  • Shape factor: 1
  • Wetting liquid: Porefil™, surface tension 16 dyn/cm
  • FBP criteria: defined as size at 30ml/min flow, 30% deviation slope of pressure increase
  • Slope of pressure increase: 20 s/bar
  • Number of data points: 50
  • Stability criteria for pressure: 5%, 0.2 s
  • Stability criteria for flow: 5%, 0.2 s
POROLUX™ 500 POROLUX™ 1000
First Bubble point (nm) 53 ± 2 58 ± 4
Mean flow pore size (nm) 47 ± 3 53 ± 1
Smallest pore size (nm) 38 ± 5 37 ± 5

The confidence interval is defined as three times the standard deviation of 10 individual measurements.

Wet, dry and half dry curve measurements POROLUX™ 500.

Figure 7. Wet, dry and half dry curve measurements POROLUX™ 500.

The flow distribution with respect to the flow is calculated with the gas flow through the sample, as illustrated in Figure 8 below.

Differential flow distribution POROLUX™ 500.

Figure 8. Differential flow distribution POROLUX™ 500.

POROLUX™ 1000 graphics:

Wet, dry and half dry curve measurements POROLUX™ 1000.

Figure 9. Wet, dry and half dry curve measurements POROLUX™ 1000.

Differential flow distribution POROLUX™ 1000.

Figure 10. Differential flow distribution POROLUX™ 1000.

LLDP Results Obtained with POROLIQ™ 1000

  • Support: etched metal plate
  • Shape factor: 1
  • Wetting liquid: Isobutanol, surface tension 2 dyn/cm
  • FBP criteria: defined as size at flow rate above 2 μl/min flow
  • Number of data points: 10
  • Stability criteria for flow: 1%, 90 s
POROLIQ™ 1000
First Bubble point (nm) 85 ± 14
Mean flow pore size (nm) 50 ± 4
Smallest pore size (nm) 36 ± 8

The confidence interval is defined as three times the standard deviation of three individual measurements. The calculation of the First Flow Pore (FFP) size was completed by taking the first data point at which the flow rate is above 2 μl/min.

At the very beginning of an LLDP measurement, there is often some transient movement of the liquid column. With improper detection limits this could provide a false FFP. It has been experimentally verified that the limit of 2 μl/min avoids this scenario and returns reliable, accurate FFP values.

Displacement, permeability and half permeability curves measurements POROLIQ™ 1000.

Figure 11. Displacement, permeability and half permeability curves measurements POROLIQ™ 1000.

Differential flow distribution POROLIQ™ 1000.

Figure 12. Differential flow distribution POROLIQ™ 1000.

Results Obtained from Image Analysis

Pores sizes in the range between 40-60 nm measured manually from SEM image.

Conclusions

The results obtained by CFP, SEM and LLDP are in good agreement within the limits exacted by the use of very different methods with different assumptions and parameters.

The comparison of CFP results generated by the two POROLUX™ models demonstrate slightly larger MFPs obtained with the POROLUX™ 1000. This is because in the step/stability mode, once a stable pressure condition has been reached, the POROLUX™ does not record a data point until the flow through the sample is constant. As a result, if there are pores with different tortuosity and length, they will still be recorded at the same pressure.

Contrary to this, with a pressure scan system in the POROLUX™ 500, there is no waiting time before data points are taken, as seen in situations where pores with the same diameter but different length and tortuosity will sometimes open later and will be recorded at a slightly larger pressure as a result, which is then translated into a smaller pore size.

Results generated by SEM are only based on the size of the pore mouths, whereas CFP and LLDP measure the most constricted part of the pore across the entire pore length, also known as the “pore throat”. Consequently, it is expected that CFP and LLDP pore size distributions show slightly smaller sizes when compared to the values obtained by image analysis.

This information has been sourced, reviewed and adapted from materials provided by Particulate Systems.

For more information on this source, please visit Particulate Systems.

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