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# The BET method for measurement of surface area.

The BET method uses a measurement of the physisorption of a gas to derive a value of “surface area” for a sample.

The gas molecules can pass between particles and into all pores, cracks, and surface roughness, so that the measurement probes the full microscopic surface area of the sample.

Most often, the sample in the form of powder or granules, and the result is stated as a Specific Surface Area, in units of area per unit mass. It may also be given as area per unit of volume, or as the absolute area for an object.

## A short description of the BET method

The BET method uses:

## The BET measurement

BET analysis requires measurement of an “Adsorption isotherm”.

Because the BET model uses the relative pressure of the adsorptive, it is necessary that the gas be condensible at the adsorption temperature - in other words, the «gas» is really a vapour.

A typical measurement involves :

1. putting a known amount of sample into a sample cell or container.
2. outgassing or other treatment of the sample, to remove impurities, moisture.
3. increasing the pressure of the gas, while measuring the amount adsorbed on the surface of the sample. For the best precision, this is done at a number of discrete pressures, and with a wait for equilibrium and measurement of the amount adsorbed at each point.
4. often, the saturation vapour pressure, $$P_0$$ is measured at the same time, or it may be calculated from knowledge of the temperature.

BET is most widely performed using adsorption of Nitrogen gas at 77 K, the boiling point of liquid nitrogen, but other species and temperatures are used.

• Argon at 87 K (liquid Argon temperature)
• Krypton at 77 K
• Carbon dioxide, CO2 at 0 °C
• Water at 20 °C using DVS instruments, such as the IGAsorp and the SPS.

For BET, the adsorption isotherm is measured as a graph of “amount adsorbed”, $$n_{adsorbed}$$ versus “Relative Pressure”, $$P/P_0$$, where $$P$$ is the pressure of the adsorbtive, and $$P_0$$ is its saturated vapour pressure at the fixed experimental temperature.

Instruments like the BELSORP mini X BET analyser, and the BELSORP MAX II sorption analyser, can easily measure the adsorption isotherm of gases such as Nitrogen, Argon, Krypton, often at cryogenic temperatures.

For applications where the surface areas of the samples vary, but the substance remains unchanged, there is a the possibility of using only a single point on the BET isotherm. This simple measurement is very rapidly performed by the mono-point BELSORP-MR1

Adsorption of Water and other volatile substances is often performed by Dynamic Vapour Sorption instruments, such as the IGAsorp from Hiden Isochema, and the multisample SPS from ProUmid.

## The BET model

The BET model, named for its creators (Brunauer, Emmett, and Teller ), describes how an increasing pressure of gas causes the progressive formation of :

• a first layer of molecules, which interact directly with the surface, followed by
• subsequent layers which behave as if they were condensing pure liquid on top of the first layer.

The model has two parameters :

• $$n_m$$, the monolayer coverage: the number of atoms in a single filled layer
• $$C$$ , the C constant, which is interpreted as describing relative strength of the interaction between the surface and the first layer, compared with the following layers.

Depending on the value of C, the first layer may be almost complete before the next layers begin to form so that there is a sharp knee, or the monolayer may not form until high values of $$P/P_0$$, giving a Type III type of isotherm.

## The BET fit

A simple treatment of the data gives the BET plot: if the BET model is valid, then the plot is linear, and the slope and intercept are used to calculate the amount of vapour in a “monolayer”. Using a known value for the amount of surface area occupied by each molecule in the monoloayer, the surface area of the sample is obtained.

Mercer Instruments specialises in the supply and support of scientific instruments for measurements of sorption, and characterisation of pore size and surface area.
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