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Chemical Engineering

Porosimetry of a Silica Alumina Powder


Source: Kerry M. Dooley and Michael G. Benton, Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA

Surface area and pore size distribution are attributes used by adsorbent and catalyst manufacturers and users to ensure quality control and to determine when products are at the end of their useful lives. The surface area of a porous solid is directly related to its adsorption capacity or catalytic activity. The pore size distribution of an adsorbent or catalyst is controlled such that pores are large enough to easily admit molecules of interest, but small enough to provide a high surface area per mass.

Surface area and pore size distribution can be measured by the technique of isothermal nitrogen adsorption/desorption. In this experiment, a nitrogen porosimeter will be used to measure the surface area and pore size distribution of a silica/alumina powder.


Surface areas of micro- (<2 nm pores) and mesoporous (2 - 50 nm pores) solids can be as large as several hundred m2/g. Accurate measurement requires an equation relating surface area to volume adsorbed (Vads) and pressure at constant temperature (the isotherm). One then regresses the isotherm equation to determine the fit parameters. The normal method of reporting the surface area is to divide the sample area in m2 by the solid mass in grams to yield what is often called the specific surface area, A.

All adsorption isotherms can be divided into five classes (Figure 1).1 For physical adsorption, only types II or IV are relevant; the rest describe bonding isotherms ("chemical adsorption"). Type I is Langmuir, and types III and V are "swelling" isotherms often found with polymeric adsorbents. Points Vads = Vm in types II and IV represent (approximately) the location of an adsorbed monolayer. The remainder of the curve represents multilayer adsorption and then capillary condensation.

Figure 1
Figure 1. Brunauer's classification of adsorption isotherms.

The three isotherm equations most frequently used are those due to Langmuir; Freundlich; and Brunauer, Emmett, and Teller (BET). Only the BET equation can relate Vm and the adsorption energy parameters of a vapor to amount adsorbed.

An adsorbate is a compound in a gas or liquid phase that attaches to the surface of the solid adsorbent being investigated. Physical adsorption depends upon weak intermolecular forces only. The ΔH of such adsorption is <3 times the heat of vaporization. It is only important at low temperatures near and below the adsorbate's saturation temperature. The N2 adsorption/desorption used in the porosimeter takes place at the normal boiling point of liquid N2 (77 K). The process is rapid and reversible. A monolayer is a single layer of molecules completely covering the pore surfaces of a porous material.

The interior of a porosimeter contains two chambers with one sensitive pressure transducer, a flow controller to chamber 1, and a vacuum pump. Chamber 1 contains the transducer and is held at room temperature. Chamber 2 contains the sample and sits in a liquid N2 bath. To operate a nitrogen porosimeter, first both chambers are evacuated. Then a small amount of nitrogen is added into Chamber 1. The amount of gas admitted (ΔN1) can be calculated from V1, the pressure transducer, and the ideal gas law.

Equation 4  (1)

where ΔP1 is the increase in pressure read by the transducer. Once the valve between the two chambers, ~5 min elapses during which adsorption occur in chamber 2 and the system eventually comes to equilibrium. The adsorption onto the surface removes N2 from the gas phase, lowering the pressure read by the transducer. The amount adsorbed during this step is:

Equation 5  (2)

Steps (2 - 3) are repeated until a pressure near the saturation P0 is reached. This procedure constitutes the "adsorption branch" of the cycle. For desorption, the process is reversed. More is involved in this process than is presented here (e.g., the sample volume must also be accounted for, the temperature of the liquid N2 bath must be known precisely, and a non-ideality correction is usually applied). For each cycle of steps (2 - 3) one datum of amount adsorbed (usually expressed as gas volume Vads, again using the ideal gas law) vs. pressure (expressed as P/P0) is collected. All data collected at a fixed temperature is called an adsorption isotherm (when P2 is increased successively) or a desorption isotherm (when P2 is lowered).

The BET isotherm follows two assumptions. The first assumption is that each molecule in the first adsorbed layer (the monolayer) provides only one site for the second and subsequent (multi-)layers. Adsorption initially takes place layer by layer. The second assumption is that the heat of adsorption, ΔH1, applies to the first monolayer, whereas the heat of liquefaction of the vapor, ΔHL, applies to adsorption in layers 2, 3 etc. Brunauer et al. simplified the estimation of Vm and the energy parameters to the following isotherm equation:2

Equation 6(3)

Equation 7(4)

where P0 is the saturation pressure at a given temperature, T. This expression represents a type II or IV isotherm in the range 0.05 < P/P0 < 0.35. There is a progression from multilayer adsorption (P/P0 to ~0.3-0.35) to capillary condensation (higher P/P0) in which the smaller pores become completely filled. This occurs because the fugacity (vapor pressure) in a small pore is reduced, in accordance with the Kelvin equation (Equation 5), by the surface tension (σ).1

Equation 8(5)

The left-hand side gives the P/P0 at which capillary condensation takes place in a cylindrical pore with adsorbate contact angle θ and pore diameter D. The capillary effect is significant only in pores <~200 nm in diameter. Pores larger than this are uncommon in most commercial porous adsorbents and catalysts.


1. Starting the porosimeter

  1. Start the porosimeter and allow it to stabilize.
  2. Weigh the plastic tube holder, sample tube, glass insert, and plastic valve that screws into the top of the tube.
  3. Then load the sample in the tube and re-weigh. When loading, try to get at least 20 m2 of total surface area in the tube. Look up a typical surface area range for the type of solid you are using. However, never use less than 50 mg of sample.
  4. Using the software for the porosimeter, initialize a new sample by clicking 'File' followed by 'New Sample' and select the appropriate method. Enter both weights (apparatus and apparatus + sample) into the program and rename the sample.
  5. Load the sample and O-ring into the degas port and adjust the degas conditions as needed. The following program should be followed: the sample should first be heated and evacuated to 12 μm of Hg at a low temperature (90 °C) during the 'Evacuation Phase'. Then, ramp to the desired final temperature (usually 300 °C for inorganic materials and carbons) and hold for the desired time (the "Heating Phase").
  6. Load the sample tube and O-ring into the sample port. Push upwards on the tube slightly before turning the nut to engage the pin that opens the plastic valve can engage. Make sure to hold the tube vertically.
  7. Place a heating mantle under the bulb holding the sample tube, and support the heating mantle with a lab jack. Do not wiggle the bulb - hold the mantle firmly.
  8. Show the degas schematic by clicking under "Degas" and selecting "Show degas schematic". Select "Unit 1", then "Start Degas." Click "Browse" to select your sample file(s), then "Start". The degas phase removes all traces of water and CO2 from the sample before the adsorption experiment. N2 cannot displace both water and CO2! Once the desired pressure and temperature have been reached, degas steps can be skipped.
  9. When the degas phase reaches the "cool down" step, lower the heating mantle and let the sample tube cool to room temperature.
  10. Backfill the sample with helium. If the pressure does not approach 800 mm Hg, then the sample tube may have popped out of the fitting. If necessary, hold in place with your hands.
  11. Once degassing is complete, weigh the sample and apparatus and edit the mass in the sample file.

2. Porosimetry measurement

  1. Fill the porosimeter's Dewar flask with liquid N2.
  2. Put the plastic jacket on the sample tube, and load the sample and O-ring in the port above the Dewar flask. Attach the plastic insulating cover on the Dewar near the sample port.
  3. Click 'Unit 1', then 'Sample Analysis'. Browse for the degassed sample file, then click 'Start' to begin taking measurements.
  4. Ensure the initial evacuation completes successfully. If that fails, try re-setting the tube in the port (check the O-ring and re-tighten the nut). Measurements will be collected automatically over several hours. Results can be downloaded into an Excel spreadsheet.

Porosimetry is a technique to measure the surface areas and pore sizes of porous solids. It is commonly used in materials science. For instance, in ceramic manufacture, the surface of both precursor powders and finished pieces exert a strong influence on physical properties. Porosimetry is also useful in chemical engineering. Supported heterogeneous catalysts require large surface area-to-volume ratios to optimize reaction speeds. And adsorbent materials need large surface areas to perform separations. This video illustrates the principles of porosimetry, demonstrates a procedure for surface area and pore size measurements, and discusses related applications.

Adsorption is the process by which fluid molecules adhere and concentrate on the surface of a solid. One type of adsorption, known as physisorption, begins with a gas molecule, the adsorbate, contacting the solid surface, the adsorbent. The valence electrons of the gas atoms delocalize into the orbitals of the solid atoms, creating a weak intermolecular interaction. As more gas molecules physisorb to the surface, they form layers. The adsorbate cannot penetrate the solid, but it can deposit in the micropores, mesopores and capillaries, which greatly increase the surface area available for adsorption. Physisorbtion is an equilibrium phenomenon that increases with pressure and reverses into desorption as pressure decreases. A graph of adsorption as a function of pressure at constant temperature is known as an Adsorption Isotherm. Gasses are best described using the BET Isotherm. It relates the adsorbed gaseous volume to the volume of a gaseous monolayer and a function of the energy released through adsorption. At low pressures, the BET model assumes gas molecules form sequential monolayers on the solid surface. However, above 1/3 the critical pressure, the adsorbate condenses and is better modeled by the Kelvin Equation. Now that we've seen how adsorption works, let's see how it is applied in a porosimeter.

A porosimeter is an analytical device capable of highly automated surface area and pore size measurements. It consists of two chambers connected by a valve. The first chamber contains a flow-controlled gas inlet and a pressure transducer. The second holds the sample of adsorbent and is cooled by liquid nitrogen. Both chambers connect to a vacuum pump. Initially, the chambers are evacuated and the connecting valve closed. Nitrogen gas passes through an inlet and into the first chamber. The molar quantity of nitrogen is determined from the pressure measurement. Next, the valve between the two chambers is opened, and the nitrogen molecules begin adsorbing on the solid. The pressure correspondingly decreases until equilibrium is reached, and the molar adsorption is calculated. Then more nitrogen gas is added to the first chamber, and the cycle repeats. The molar adsorption measurements are then plotted to generate Adsorption Isotherms. To calculate the desorption isotherm, the vacuum pump is used to partially evacuate the chamber, effectively reversing the process. Those are the principles. Now let's examine the operating procedure in the lab.

In this experiment, the surface area and pore size distribution of a silica alumina powder will be measured using a nitrogen porosimeter. Begin by starting the porosimeter and allowing it to stabilize. The sample holder consists of four components. A sample tube. A tube holder. A glass insert. And a plastic valve. Weigh the assembly. Then load the sample into the tube. Use at least 50 milligrams of sample and enough to provide at least 20 square meters of surface area. Seal the sample and weigh it again. Using the control software, initialize a new sample and select a method. Enter the empty and loaded sample holder weights. Apply an O-ring to the sample tube and load the sample into the degas port. The degas steps are needed because nitrogen cannot adsorb on a surface that has already adsorbed water or carbon dioxide. Set the degas vacuum and temperature set points to typical values for inorganic materials, such as a vacuum of 12 microtorr with temperature ramping from 90 degrees Celsius to the desired final temperature. Place a heating mantle under the bulb holding the sample tube and support the heating mantle with a lab jack. Enter the degas schematic. Click unit one. Start degas. Select the sample file and begin. When the degas procedure reaches its cool-down phase, lower the heating mantle holding the sample tube in place, if necessary, and allow the sample tube to cool to room temperature. The degas concludes with the sample tube being back-filled with helium. Weigh the sample tube after degassing is complete. Enter the mass data into the sample file. Using cryogenic safety equipment, fill the porosimeter's Dewar with liquid nitrogen, and attach the plastic insulating cover. Keeping the tube vertical, load the sample tube and O-ring into the sample port until the plastic valve engages. Click unit one, sample analysis. Browse for the sample file for the degassed sample and click start. Ensure the initial evacuation completes successfully. The unit may then be left unattended until measurements are complete.

In this demonstration, nitrogen was adsorbed and desorbed on a silica alumina adsorbent. The isotherms demonstrate hysteresis. This suggests either the formation of a meniscus late in the adsorption cycle that reduces the surface area available for desorption, or different meniscus geometries for the adsorption and desorption cycles. In the low pressure region where the BET Isotherm applies, the molar adsorption as a function of pressure is multiplied by the average area occupied by a single nitrogen molecule to obtain surface area. Regressing these data, according to the BET equation, yields the surface area of the sample. Differential analysis using the cylindrical form of the Kelvin Equation, yields the pore size distribution and suggests the pore geometry is indeed cylindrical.

Porosimetry is routinely used in material science and specialty chemical manufacture. Carbon aerogel foams are highly porous, three-dimensional carbon networks, suitable for catalyst supports and super capacitors. Research is proceeding into new manufacturing techniques, such as sol gel synthesis, which allow high control over surface area. Porosimetry is a necessary part of quality control for the resulting materials. Naturally occurring sub-surface carbonate rocks exhibit surface porosity and adsorb carbon dioxide. However, the adsorption process is affected by the presence of high-pressure fluid in several phases. Porosimetry is used to measure surface area, while x-ray tomography is used to non-invasively study the adsorption process. These studies are needed for the development of carbon capture and storage technologies.

You've just watched Jove's Introduction to Porosimetry. You should now be familiar with the adsorption process, a procedure for measuring surface area, and some applications. As always, thanks for watching.


In the capillary condensation region, the isotherm generally shows hysteresis so that the apparent equilibrium pressures observed in adsorption and desorption experiments are different (Figure 2). The desorption branch is always at lower fugacity and pressure. The hysteresis begins at P/P0 = ~0.6, where capillary condensation begins to dominate the adsorption process, although the pore size distribution algorithm uses the entire isotherm. The calculated total pore volume, using the ideal gas law and the molar volume of liquid N2, is 0.63 cm3/g.

Figure 2
Figure 2. Volume adsorbed (gas phase basis) vs. relative pressure (the isotherm) for N2 adsorption on silica-alumina S/N 3001.

Two explanations for this effect have been proposed.1 During adsorption, multilayers build up on pore walls, but a complete meniscus is not formed until saturation is reached. Therefore, the surface area for adsorption (the wall surfaces) exceeds that of desorption (meniscus only) in the capillary condensation region. The adsorption branch of the isotherm is therefore governed by a multilayer isotherm analogous to the BET equation, but desorption in the capillary condensation region is governed by the Kelvin equation (Equation 5). The differences in the branches could also arise from a difference in the shape of the meniscus. During adsorption the pore fills radially and a cylindrical meniscus is formed. During desorption, the meniscus is hemispherical and the Kelvin equation applies. By either argument, only the desorption isotherm should be used to calculate the pore size distribution in the hysteresis region, although neither argument is entirely correct. Disagreements from theory arise from deviations in the shape of the pores from simple cylindrical geometry and from the fact that transmission electron microscopy and other techniques suggest that BOTH explanations are partly correct. In particular, the physics of adsorption dictates that there must be some adsorbed material in the pores, clinging to the walls even below the Kelvin Pv/P0 = P/P0. The space occupied by this multilayer adsorbed material must be corrected for in the Kelvin pore size calculation - this is called a "t-plot correction" in the literature. Various theoretical equations can be used to calculate this adsorbed layer thickness (= t), as a function of P/P0. For our system, the Halsey-Faas correction to obtain t is used automatically in the machine software, and the pore size distribution for both branches computed automatically.

The BET equation yields a straight line when plotted linearly (see Equation 3), to give Vm and c from the slope and intercept. The specific surface area, A, is found assuming the average area occupied by one molecule of adsorbate (am) is known (for N2, 0.1620 nm2):1

Equation 9 (6)

where Vm [=] cm3/g, A [=] m2/g, and L = Avogadro's number.

A typical BET plot (Figure 3) showing data and regression fit is shown below. The value of R2 (correlation coefficient) and the average relative deviation of the fit are reported. The confidence limits on the slope and intercept from the linear regression can be used to estimate the confidence limit on A, from propagation of error theory. The regressed (predicted) values are: c = 139, Vm = 49.3 cm3/g STP, A = 214 m2/g, R2 = 0.9998, ARD = 0.59%.

Figure 3
Figure 3: BET plot for sample silica-alumina S/N 3001.

A typical pore size distribution for the same sample is shown in Figure 4. For this sample, the average pore D from the distribution was calculated as 8.6 nm, while the cylindrical pore estimate (4 PV/A) was 8.0 nm (PV is pore volume/mass). This is fairly good agreement, suggesting that these pores are roughly cylindrical. Using both the adsorption and desorption dV/dD the average pore diameter can be determined from the properties of a probability distribution. Note that (dV/dD) x (dD) is the probability of adsorbed volume, expressed as a gas phase volume, at D. The desorption average, D, is always smaller than the adsorption average, as predicted by Equation 5. This is because, as shown in Figure 2, its fugacities (Pv, Pv = P) at a given Vads are smaller.

Figure 4
Figure 4. Calculated pore-size distribution of the data in Figure 2, desorption branch.

Applications and Summary

The method of measurement and calculation presented here is the gold standard in porosimetry. The mercury porosimetry technique is an alternative, but its high pressures and possibility of exposure to mercury are disadvantages. Better pressure transducers, vacuum pumps, and software have greatly extended the utility of N2 porosimetry, and the method gives all 3 key adsorbent or catalyst morphological measurements (A, pore volume, pore size distribution) in one experiment. It also provides information on pore shape.

Commercial catalysts and adsorbents are often manufactured to tight pore size specifications. The fastest way to determine if the correct morphology is present is to measure the pore size distribution. For example, uneven temperature control in the calcining (heat treatment) step during manufacture can greatly alter the distribution. For many catalysts, lifetimes are greatly shortened if larger pores are not present, even if the surface area is still high, because these large pores often serve as gateways for the removal of oligomeric carbon residues ("coke") that otherwise would poison many active sites.

For cylindrical pores the average pore diameter, D, should also equal 4PV/A (PV is pore volume/mass). The software reports the cylindrical estimates for both adsorption and desorption branches, and the magnitude of their differences from the average diameters calculated from the distributions themselves gives an idea of the porous material's deviation from perfectly cylindrical pores. Some solids have pores that are slit-like, with a critical short dimension (h) analogous to the diameter of 2 PV/A for very long and wide slit pores. Find both the adsorption and desorption estimates of the average, and then determine if the porous solid is more slit-like, comparing the different branch estimates to more exact values generated from the probability distributions. If both cylindrical and slit estimates are significantly in error, what could this mean? Similar calculations could be done to test for other pore shapes.

Porosimeters can be easily adapted to measure surface areas as small as 0.01 m2/g (e.g., in concretes, although Kr or Xe are used instead of N2) and pore sizes less than 1 nm (e.g., in zeolites, although Ar is used and special procedures necessary). While it is true that zeolites are important catalysts and commercial adsorbents, their primary use is in detergents, where they can bind almost all the grime removed from laundry.

Additionally, it is also important to know the morphological properties of tableting materials, such as excipients (lubricants) and binders, to control the pill tableting process and the dissolution and degradation of outer shells to ensure controlled release of the active pharma ingredient in vivo.


  1. Gregg and K.S.W. Sing, Adsorption, Surface Area, & Porosity, 2nd Ed., Academic, 1982 , and D. Ruthven, Principles of Adsorption and Adsorption Processes, Wiley, New York, 1984.
  2. J. Amer. Chem. Soc., 60, 309-319 (1938).
Porosimetry of a Silica Alumina Powder
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