BET theory seeks to explain the physical adsorption of gas molecules onto solid surfaces and extends the Langmuir theory of monolayer adsorption to multilayer adsorption. The BET equation is used to determine the monolayer absorbed gas volume from which the total and specific surface area of a material can be calculated. A multipoint BET analysis involves measuring adsorption and desorption of nitrogen gas over a sample at different equilibrium pressures and plotting the data to determine the BET constant and monolayer volume.

1. © 2018 HORIBA, Ltd. All rights reserved. 1© 2018 HORIBA, Ltd. All rights reserved. 1
BET Theory and how its used to
calculate surface area
HORIBA Scientific
Particle Analysis
Carl Lundstedt
June 25, 2019

2. © 2018 HORIBA, Ltd. All rights reserved. 2
BET Theory seeks to explain the physical
adsorption of gas molecules onto solid surfaces

3. © 2018 HORIBA, Ltd. All rights reserved. 3
Particles of similar size can vary drastically in
surface area

4. © 2018 HORIBA, Ltd. All rights reserved. 4
Physical adsorption occurs due to Van der Waals forces
when at low temperatures and without chemical reactions
Adsorbate
Adsorbent

5. © 2018 HORIBA, Ltd. All rights reserved. 5
BET Theory extends the Langmuir theory from
monolayer adsorption to multilayer adsorption

6. © 2018 HORIBA, Ltd. All rights reserved. 6
We use the BET equation to determine the
monolayer absorbed gas volume (vm)
1
𝑣𝑣[(𝑝𝑝0/𝑝𝑝) – 1]
=
𝑐𝑐 − 1
𝑣𝑣𝑚𝑚 𝑐𝑐
𝑝𝑝
𝑝𝑝0
+
1
𝑣𝑣𝑚𝑚 𝑐𝑐
𝑣𝑣 = adsorbed gas quantity
𝑝𝑝0 = saturation pressure of adsorbate
𝑝𝑝 = equilibrium pressure of adsorbate
𝑐𝑐 = BET constant = exp
𝐸𝐸1−𝐸𝐸𝐿𝐿
𝑅𝑅𝑅𝑅
𝐸𝐸1 = heat of adsorption for the first layer
𝐸𝐸𝐿𝐿 = heat of vaporization

7. © 2018 HORIBA, Ltd. All rights reserved. 7
BET equation can be plotted to determine monolayer
adsorbed gas quantity and the BET constant
1
𝑣𝑣[(𝑝𝑝0/𝑝𝑝) – 1]
=
𝑐𝑐 − 1
𝑣𝑣𝑚𝑚 𝑐𝑐
𝑝𝑝
𝑝𝑝0
+
1
𝑣𝑣𝑚𝑚 𝑐𝑐
𝑦𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏
1
𝑣𝑣[(𝑝𝑝0/𝑝𝑝) – 1]
𝑝𝑝
𝑝𝑝0
1
𝑣𝑣𝑚𝑚 𝑐𝑐
𝑐𝑐 − 1
𝑣𝑣𝑚𝑚 𝑐𝑐

8. © 2018 HORIBA, Ltd. All rights reserved. 8
Take numerical values for slope and intercept to
solve for vm and c
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
𝑐𝑐 − 1
𝑣𝑣𝑚𝑚 𝑐𝑐
intercept =
1
𝑣𝑣 𝑚𝑚 𝑐𝑐
𝑣𝑣𝑚𝑚 =
1
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
𝑐𝑐 = 1 +
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

9. © 2018 HORIBA, Ltd. All rights reserved. 9
From the monolayer absorbed gas volume (vm),
we can determine total and specific surface area
𝑆𝑆𝑡𝑡 =
𝑣𝑣𝑚𝑚 𝑁𝑁𝑁𝑁
𝑉𝑉
𝑆𝑆𝑡𝑡 = total surface area of sample material
𝑣𝑣𝑚𝑚= monolayer absorbed gas volume
𝑁𝑁 = Avogadro’s number = 6.02 x 1023 molecules/mol
𝑠𝑠 = cross-sectional area of adsorbed gas molecule
𝑉𝑉 = molar volume of adsorbed gas
𝑆𝑆𝐵𝐵𝐵𝐵𝐵𝐵 =
𝑆𝑆𝑡𝑡
𝑎𝑎
[=] m2/g
𝑆𝑆𝐵𝐵𝐵𝐵𝐵𝐵 = specific surface area
𝑎𝑎 = mass of sample

10. © 2018 HORIBA, Ltd. All rights reserved. 10
Can only assume linear relationship for adsorption
isotherms in the range of 0.05 < 𝑝𝑝/𝑝𝑝0 < 0.30

11. © 2018 HORIBA, Ltd. All rights reserved. 11
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

12. © 2018 HORIBA, Ltd. All rights reserved. 12
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

13. © 2018 HORIBA, Ltd. All rights reserved. 13
Have to insert sample into cell and degas sample to
remove excess moisture on surface

14. © 2018 HORIBA, Ltd. All rights reserved. 14
BET measurement includes calibration of 1 cm3 of
nitrogen, adsorption, and desorption

15. © 2018 HORIBA, Ltd. All rights reserved. 15
Large surface area samples will adsorb and desorb
more nitrogen

16. © 2018 HORIBA, Ltd. All rights reserved. 16
BET multipoint measurement example
3rd point2nd point1st point

17. © 2018 HORIBA, Ltd. All rights reserved. 17
Plot at least 3 points to obtain multi-point plot, solve
for BET constant (c) and Vm (monolayer volume)
BET constant = 145.84
Surface area = 11.36 m2/g

18. © 2018 HORIBA, Ltd. All rights reserved. 18© 2018 HORIBA, Ltd. All rights reserved. 18

19. © 2018 HORIBA, Ltd. All rights reserved.
19