BET Theory Explained

Surface area is an important physical property that influences the reactivity, dissolution, catalysis, and separation of materials. The surface area often must be carefully engineered and measured to optimize specific functions. In this Webinar, our applications lab will explain with real-world examples:

- Physical adsorption technique - BET theory
- Sample preparation – the start of a good measurement
- Calculating specific surface area from gas adsorption on solid surfaces
- Troubleshooting – what happens when things go wrong?

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BET Theory and how its used to
calculate surface area
HORIBA Scientific
Particle Analysis
Carl Lundstedt
June 25, 2019

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BET Theory seeks to explain the physical
adsorption of gas molecules onto solid surfaces

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Particles of similar size can vary drastically in
surface area

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Physical adsorption occurs due to Van der Waals forces
when at low temperatures and without chemical reactions
Adsorbate
Adsorbent

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BET Theory extends the Langmuir theory from
monolayer adsorption to multilayer adsorption

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We use the BET equation to determine the
monolayer absorbed gas volume ( v
m)
1
????????????[(????????????
0/????????????)–1]
=
????????????−1
????????????
????????????????????????
????????????
????????????
0
+
1
????????????
????????????????????????
????????????= adsorbed gas quantity
????????????
0= saturation pressure of adsorbate
????????????= equilibrium pressure of adsorbate
????????????= BET constant = exp
????????????1−????????????????????????
????????????????????????
????????????
1= heat of adsorption for the first layer
????????????
????????????= heat of vaporization

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BET equation can be plotted to determine monolayer
adsorbed gas quantity and the BET constant
1
????????????[(????????????
0/????????????)–1]
=
????????????−1
????????????
????????????????????????
????????????
????????????
0
+
1
????????????
????????????????????????
????????????=????????????????????????+????????????
1
????????????[(????????????
0/????????????)–1]
????????????
????????????
0
1
????????????
????????????????????????
????????????−1
????????????
????????????????????????

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Take numerical values for slope and intercept to
solve for v
mand c
????????????????????????????????????????????????????????????=
????????????−1
????????????
????????????????????????
intercept=
1
????????????
????????????????????????
????????????
????????????=
1
????????????????????????????????????????????????????????????+????????????????????????????????????????????????????????????????????????????????????????????????????????????
????????????=1+
????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????????????????

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From the monolayer absorbed gas volume ( v
m),
we can determine total and specific surface area
????????????
????????????=
????????????
????????????????????????????????????
????????????
????????????
????????????= total surface area of sample material
????????????
????????????= monolayer absorbed gas volume
????????????= Avogadro’s number = 6.02 x 10
23
molecules/mol
????????????= cross- sectional area of adsorbed gas molecule
????????????= molar volume of adsorbed gas????????????
????????????????????????????????????=
????????????????????????
????????????
[=] m
2
/g
????????????
????????????????????????????????????= specific surface area
????????????= mass of sample

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Can only assume linear relationship for adsorption
isotherms in the range of 0.05 < ????????????/????????????
0< 0.30

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Pore width can make a big difference on shape of
isotherm
2 nm 50 nm
Micropores Mesopores Macropores
Zeolite,
Activated
carbon,
Metal organic
framework
Mesoporous silica,
Activated carbon
Sintered metals
and ceramics

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Usually apply BET theory to Type 2 and Type 4
isotherms, apply to Type 1 with caution
Microporous
(C > 150)
Macroporous/
non-porous
(C > 80)
Mesoporous
(C > 80) (C < 2)
(C < 2)
Step-wise
multilayer

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Have to insert sample into cell and degas sample to
remove excess moisture on surface

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BET measurement includes calibration of 1 cm
3
of
nitrogen, adsorption, and desorption

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Large surface area samples will adsorb and desorb
more nitrogen

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BET multipoint measurement example
3
rd
point2
nd
point1
st
point

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Plot at least 3 points to obtain multi-point plot, solve
for BET constant (c) and V
m(monolayer volume)
BET constant = 145.84
Surface area = 11.36 m
2
/g

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