BET surface area

Published by Andy Connelly 13th March 2017. Last updated 10th May 2017 by Andy Connelly

Introduction

Measuring surface area and porosity of powders is difficult. There are few techniques available and none of those are straightforward. The choice for surface area measurement generally comes down to a technique known as BET. Porosity is the easier measurement as you can use: mercury porosimetry, helium porosimetry, density methods, or BET [1,2]. The measurement of porosity and surface area by BET is a relatively simple measurement to carry out; however, the mathematics and physics behind BET is a little more complicated and so understanding the result can be difficult.

BET measures surface area based on gas adsorption [3]. More specifically, it allows “determination of the overall specific external and internal surface area of disperse (e.g. nano-powders) or porous solids by measuring the amount of physically adsorbed gas according to the Brunauer, Emmett and Teller (BET) method”.[4]

DISCLAIMER: I am not an expert in surface area measurement. The content of this blog is what I have discovered through my efforts to understand the subject. I have done my best to make the information here in as accurate as possible. If you spot any errors or admissions, or have any comments, please let me know.

How it works

BET is the initials of the three people who developed the mathematics required for the measurement to work. Brunauer, Emmett, and Teller found a way to calculate the specific surface area of a sample including the pore size distribution from gas adsorption. The volume of gas (usually nitrogen) adsorbed to the surface of the particles is measured at the boiling point of nitrogen (-196°C). At this temperature the nitrogen gas is below the critical temperature and so condenses on the surface of the particles. It is assumed that the gas condenses onto the surface in a monolayer and so, because you know the size of the gas atom/molecule, the amount of adsorbed (condensed) gas is correlated to the total surface area of the particles including pores at the surface (inaccessible pores are not detected). It is this correlation calculation, volume absorbed to surface area, that BET theory gives you.

Adsorption

Adsorption is the adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface. There are generally accepted to be six adsorption isotherms (Figure 1). The BET method is applicable only to adsorption isotherms of type II (disperse, nonporous or macroporous solids) and type IV (mesoporous solids, pore diameter between 2 nm and 50 nm).  The BET method cannot reliably be applied to solids which absorb (as opposed to adsorb) the measuring gas.

As the gas (adsorbative) is pumped into the sample tube the gas covers the external and the accessible internal pore surfaces of a solid. In BET theory it covers the sample with a monolayer of adsorbate (please see reference [5] for a more detailed description). At higher P/P0 the coverage will be more complex.

The amount of gas used in creating the monolayer can be calculated from the adsorption isotherm using the BET equation (see below). Any gas may be used, provided it is physically adsorbed by weak bonds at the surface of the solid (van der Waals forces), and can be desorbed by a decrease in pressure at the same temperature.

IUPAC classification of adsorption isotherms
Figure 1 — IUPAC classification of adsorption isotherms (typical BET range is indicated in Types II and IV by the shaded areas) (after [3]) na=quantity of absorbed gas, p/p0 is the relative pressure

BET equation

The BET equation can be used to calculate the surface area of a sample. Other equations are available to calculate surface area from gas adsorbtion (see Table 1); however, BET is the most popular. The derivation for this equation can be found elsewhere (e.g. [4]) here it is sufficient to show that the measured inputs to this equation are:

  • the equilibrium (p) and the saturation (p0) pressure of adsorbates at the temperature of adsorption.
  • The adsorbed gas quantity (na) (for example, in volume units)
BET_eqn
BET equation [7]

The calculated quantities are:

  • the nm is the monolayer capacity
  • the BET constant, C.

nm_BET_eqn
Finding nm [7]
C_BET_eqn
Finding C [7]
To calculate these values the BET equation is plotted as an adsorption isotherm typically at a relative pressure (P/P0) between 0.05-0.35. In this range BET theory suggests it should form a straight line (see Figure 2). The value nm can then be found from the gradient and from that the surface area can be calculated using the molecular cross-sectional area.

stotal_BET_eqn
Total surface area [7]
Where N is Avogadro’s number, s the adsorption cross section of the adsorbing species, and V the molar volume of the adsorbate gas. The exact form of this equation will vary depending on the units being used (see references [6] and [7] for alternative treatments).

BET plot
Figure 2: BET plot

The BET constant (C) is also calculated from the intercept and gradient and is related to the energy of adsorption in the first adsorbed layer. Consequently the value of C is an indication of the magnitude of the adsorbent/adsorbate interactions. C is normally between 100 – 200, if it is lower than around 20 there is significant adsorbent/adsorbate and the BET method is invalid. Greater than 200 and the sample may contain significant porosity.

The specific surface area is then calculated using the mass of sample.

SBET_BET_surface area

Other measurements available

It is not just BET surface area that can be measured using this method. Table 1 shows a selection of other measurements that can be made.

BET_methods
Table 1: Various measurements available on BET instruments.

The simplest (and would guess most common) measurements that are available for BET are:

  • BET surface area: as described above. Surface area calculated using the BET equation.
  • Total Pore Volume: This is the simplest measurement of porosity the BET allows. The calculation is the result of Lord Kelvin’s observations of capillaries.

Practical aspects

What actually happens

The process of BET measurement is shown in Figure 3. As all data are measured relative to P0 this value must also be calculated. P0 is the saturation pressure of adsorbate at the temperature of adsorption. It can either be measured initially for an empty tube or it can be measured at the same time as the measurement described below is occurring in a third tube (not shown in Figure 3).

The following describe the main steps in the process of BET measurement:

  1. Degas: Prior to the determination of an adsorption isotherm over the BET region the sample must be degassed, while avoiding irreversible changes to the surface. This is generally done either using a vacuum system or by flushing the sample with a gas (e.g. N2) often at elevated temperature. The temperature used depends on the stability of the sample. A temperature of 110°C is quoted [8] for nitrogen isotherms where the sample is stable to this temperature. Once cool the sample must be reweighed to take into account any mass loss during degassing.
  2. Evacuate: The sample and reference tubes are evacuated. The reference tube will be treated in the same way as the sample tube throughout the measurement.
  3. Volume: At this stage most BET methodologies will carry out a dead-volume measurement using an inert gas such as He. This result is used to correct the quantity of adsorbate adsorbed. It is important that the sample and reference tube have similar dead volumes. A glass rod or glass beads are often used to reduce dead volume and to give the two tubes similar dead volumes.
  4. Evacuate: The dead-volume gas is then removed by vacuum.
  5. Adsorption: The adsorbate gas is admitted to the two tubes either in doses or as a slow continuous flow. Adsorption of the gas on to the sample occurs, and the pressure in the confined volume continues to fall until the adsorbate and the adsorptive are in equilibrium. The amount of adsorbate at the equilibrium pressure is the difference between the amount of gas admitted and the amount of adsorptive remaining in the gas phase. To calculate this the pressure, temperatures, and (dead) volume of the system is required. The reference tube pressure is also used as a reference. This step gives the adsorption isotherm over a selected range of P/P0.
  6. Desorption: For the calculation of certain quantities (see Table 1) a desorption step is also required where a vacuum is applied in the reverse of Step 5. This will give the “desoption isotherm”

Normally, the determination of specific surface area requires at least 3 measurements of adsorbed gas quantity (na) each at different values of P/P0. However, under certain circumstances it may be acceptable to determine the specific surface area of a powder from a single value of na measured at a single value of P/P0 such as 0.300. These single point measurements should only be made on well characterised systems where multipoint analyses show linearity.

measuring surface area with BET.
Figure 3: Measuring surface area with BET.

Sample Considerations and Preparations

A general guideline is that you will need 0.5-2g – more sample for larger particle size:

  • For surface area 5 m2/g you need 2-3 g
  • For surface area 10 m2/g you need 2-3 g
  • For surface area 30 m2/g you need 0.5-1 g
  • For surface are 60 m2/g you need 0.25-0.5 g

It is a non-destructive technique and so you can get your sample back! The number of samples you can run will depend on the instrument. Some instruments allow multiple samples to be analysed at the same time, others can only analyse one. A standard BET surface area analysis may take around 45mins.

Problem solving with BET

There is a problem with you BET measurement if:

  • A straight line is not obtained –this is generally taken as a correlation coefficient worse than 0.999.
  • If there is a negative intercept.
    • If C is above 200 – this may be indicative of the presence of micropores.
    • If C is below 100 – this may indicate strong adsorbent-adsorbate interactions
  • In the context of physisorption, it is expedient to classify pores according to their sizes [5]:
    • pores with widths exceeding about 50 nm (0.05 pm) are called macropores;
    • pores of widths between 2 nm and 50 nm are called mesopores;
    • pores with widths not exceeding about 2 nm are called micropores.

Solutions to BET problems

  • Very small sample surface area: Nitrogen at its boiling point (about 77,3 K) is usually the most suitable adsorptive. If the sensitivity of the instrument when using nitrogen is insufficient for low specific surface areas of about 1 m2g-1 or lower, the application of krypton adsorption at liquid nitrogen temperature for the specific surface area analysis is recommended. This in part is due to the low p0 (lower saturation vapour pressure) for krypton which helps reduce the dead-space correction as the gas is more likely to condense of the sample surface. Alternatively, glass filler rods (or glass spheres) can also be used with nitrogen gas (see below) (see [4] for more a more detailed treatment).
  • Very small amount of sample available: this leaves you with large amount a “dead-space”. This issue can either be address using krypton (as above) or using glass filler rods (and spheres) to reduce the dead-space.
  • Difficulty achieving a straight line: This may be due to several issues. You may not have the enough sample for the surface area (see above). Alternatively, your sample may have high porosity which may be causing problems with the measurements. Another common problem is insufficient degassing (of gas or water) of sample. This may result in degassing during the measurement and problems with your results. The other possibility is that the sample does not produce a linear adsorption isotherm over the standard BET range (P/P0 = 0.05-0.3). This will be sample dependent, see [8] for more details. For some samples you need to expand/shrink the P/P0 range. You may need to go as low as P/P0=0.01. As long as you are consistent in the change over all your samples it is an acceptable adaptation of the method.

Reporting BET data

It is strongly recommended that in reporting a BET value the following factors are reported as a minimum (after [5]):

  • Make and model of equipment used
  • Pretreatment and outgassing conditions.
  • Mass of outgassed sample
  • Adsorptive (e.g. nitrogen or krypton).
  • BET plot (showing region of p/p°)
  • BET data:
    • Specific surface area (m2g-1)
    • BET constant (C) value
    • Correlation coefficient and uncertainty value based on this
    • Adsorptive, temperature (K)
  • Methodological uncertainty data – based on repeated measurements of one representative sample

Summary

The practical measurement of BET is relatively simple. However, understanding the data and ensuring the data you produce is reliable is not straight forward. It is important that you understand the measurement you have made. Hopefully what I have written above will help this.

Further reading:

  • Introduction to Powder Surface Area, S Lowell, 1979
  • S. Lowell, J.E. Shields, M.A. Thomas, M. Thommes, Characterization of Porous Solids and Powders : Surface Area, Pore Size and Density , Kluwer Academic Publisher, Dordrecht, 2004, Springer 2006.
  • Peter Klobes, Klaus Meyer and Ronald G. Munro, Porosity and Specific
  • E.S.PALIK, Specific Surface Area measurements on Ceramic Powders, Powder Technology. 18 (1977) 45-48

    References

    [1] http://homepages.see.leeds.ac.uk/~earpwjg/PG_EN/CD%20Contents/Formation%20Evaluation%20English/Chapter%205.PDF (March 2017)

    [2] https://en.wikipedia.org/wiki/Specific_surface_area (March 2017)

    [3] Adsorption of Gases in Multimolecular Layers, Brunauer, Emmett, Teller, Feb 1938, vol. 60, 309.l

    [4] Determination of the specific surface area of solids by gas adsorption — BET method, Second edition, BS ISO 9277:2010

    [5] REPORTING PHYSISORPTION DATA FOR GAS/SOLID SYSTEMS with Special Reference to the Determination of Surface Area and Porosity (Recommendations 1984)

    [6] Genini VII Operators Manual (V2.00), Micromeritics, 239-42828-01 (2012)

    [7] en.wikipedia.org/wiki/BET_theory (August 2015)

    [8] Adsorption, Surface Area, and Porosity, S.J. Gregg and K.S.W. Sing, Academic Press (1967)

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