The document discusses the Brunauer-Emmett-Teller (BET) surface area analysis method. It provides background on BET analysis, describing how it was developed in 1938 and is based on measuring nitrogen gas adsorbed on a solid surface. The document outlines the BET equation and process, explaining that BET analysis involves measuring the amount of nitrogen gas adsorbed and desorbed by a material at liquid nitrogen temperature to determine surface area and pore size distribution. The document notes limitations of BET analysis and discusses its applications in studying catalysts, polymers, and other materials.

1. Brunauer-Emmett-Teller(BET) Surface
area and Pore size distribution
Presented by
SHIV SHANKAR
Research scholar
IIT(ISM) DHANBAD,
INDIA

2. Contents
Introduction
Historical background
Porosity
measurement methods
Adsorption
Adsorption isotherm
Langmuir's theory
BET Theorem
BET Method Limitations
Applications
Discussion and conclusion
2

3. INTRODUCTIONS
• Measuring surface area, volume and distribution of pores,
has numerous applications in the study of catalysts, active
carbon, pharmaceutical materials, ceramics, polymers,
paints, coatings and nanotubes.
• Therefore, different methods for measuring surface area
and porosity have been considered, which can be referred
to microscopic methods and adsorption methods.
• If a solid is impenetrable and has a completely stable
shape, its total surface area can be estimated to be
approximately measurable.
• But in the case of porous structures, there are difficulties
in determining porosity and the overall surface area.
• One of the most important methods for accurately
measuring the total area of porous samples is the BET
method, which is based on the adsorption of certain
molecular species in the gas state on their surface.
5

4. Historical background
Named after Stephen Brunauer, P.H. Emmet and
Edward Teller
Developed in 1938
They were working on ammonia catalysts
First method to measure the specific surface of
finely divided and porous solids
6

5. Porosity
Concept
Size
Type
Shape
measurement

6. • Porosity or void fraction is a
measure of the void (i.e.
"empty") spaces in a material,
and is a fraction of the
volume of voids over the total
volume.
• Porous materials are also
referred to as materials with a
porosity of between 0 and 1.
concept
6

7. size
type Pore width／nm
Micropores <2
Mesoprores 2～50
Macropores 50<
7

8. type
8

9. shape
9

10. measurement
In determining the porosity, three special surface parameters, porosity specific porosity and
porosity are defined as follows:
𝑚 𝑎 𝑠𝑠
Specific surface= 𝑡 𝑜𝑡 𝑎𝑙𝑎𝑟𝑒𝑎 m 2 /g
Porosity percentage =
𝑡 𝑜𝑡 𝑎𝑙𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑎𝑣𝑖𝑡𝑖𝑒𝑠
10
𝑡 𝑜𝑡 𝑎𝑙𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒𝑜𝑏𝑗𝑒𝑐𝑡
×100

11. measurement methods
 Image-based SEM
TEM
 Dispersion
 Mercury Porosimetry
 Absorption Freundlich
Langmuir
Temkin
 BET Theorem

12. Adsorption
12

13. Adsorption Isotherms
13
Type-I Microporous solids (Langmuir
Isotherm)
Type-II Multilayer adsorption on non-
porous / macroporous solids
Type-III Adsorption on non-porous /
macroporous solids with weak
adsorption
Type-IV Adsorption on meso porous
solids with hysteresis loop
Type-V Same as IV type with weak
adsorbate-adsorbent interaction
Type-VI Stepped adsorption isotherm,
on different faces of solid and/or strong
nteraction with surface

14. Types of hysteresis according to cavity geometry
14

15. The Langmuir theory by Irvin Langmuir in 1916 is expressed in connection
with the adsorptionof monolayer gas molecules on a solid surface, which is
known by its own name.
This theory is derived from the physical adsorption law of the gas molecule on
the solid surface, with the following assumptions taken into account:
1. The surface of the solid body is a completely homogeneous surface, that
is,all places have the same priority for adsorption.
2. Any place does not absorb more than one molecule; in such a
situation, a single layer of molecules will be adsorbed onto the
solid surface.
3. The gas molecules adsorbed in the vapor phase have an ideal behavior, that
is, there isno interaction between the gas molecules with the adsorbent
surface.
15

16. 𝑝
𝑛 𝑎
=
1
𝑛 𝑚
𝑎
∗ 𝑏
+
𝑝
𝑛 𝑚
𝑎
Langmuir Equation
p= pressure
na= amount of gas adsorbed, mol/g
na
m = mono layer capacity of sample, mol/g
b = Langmuir constant

17. The BET Theorem
• The BET system operates on the basis of measuring the
amount of nitrogen gas adsorbed and depleted by the
material at a constant liquid nitrogen temperature (77 K).
• After the cell contains the specimen in the liquid nitrogen
reservoir, with the gradual increase in nitrogen gas
pressure at each stage, the amount of gas adsorbed by the
material is calculated.
• Then, with the gradual reduction of the gas pressure, the
amount of material depletion is measured, and finally, the
graph of the volume of nitrogen gas adsorbed and
desorbed by the substance is drawn on the basis of relative
pressure at a constant temperature.
• The BET diagram, also called the Adsorption / Desorption
Isotherm, is a linear graph for extracting the effective
surface of the material17

18. BET Equation
Pa = Particulate gas pressure adsorbed in equilibrium at 77.4 kPa inPascal
P0=Particulate pressure of gas adsorbed in Pascal
V= volume of gas adsorbed under standard conditions (T = 273.15K, P = 1.013 ×105) in milliliters
Vm = volume of gas adsorbed in standard mode for producing a single Layer on thesample
surface in ml
C = Fixed amount which depends on the enthalpy of adsorbed gas on thepowder sample
E1=Heat of adsorption of 1st layer, EL=Heat of adsorption of 2nd or higher layer.
E1-EL=Heat of liquefaction or vaporization.
18
𝑝 𝑎
𝑉 𝑝0 − 𝑝 𝑎
=
1
𝑉𝑚 𝐶
+
𝐶 − 1
𝐶𝑉𝑚
𝑝 𝑎
𝑝0

19. the width from the origin of the graph
the gradient of the BET
The following equation can be used to obtain the Vm in a
simpler way called the single-point method, but decreases
slightly
If the relative pressure is 0.3, the result obtained from the
single-point method and the multi-point method will be in
good agreement

20. Total Surface area:
SA =
𝑉 𝑚 𝑁
𝑀
Acs
Specific Surface area:
SSA =
𝑆𝐴
𝑊
N = Avogadro’s number
M = Molecular Weight of adsorbate
Acs=Adsorbate cross sectional area

21. Cooling under
vacuum up to 77K
Weighed
sample
Solid Sample
N2
Controlled
increments
Calculation of gas
required to form mono
layer
Quantity of
adsorbed gas
calculated
Pressure is
allowed to
equilibrate
Defines isotherm at
each Pressure &
temperature
Gasallowedto
condenseinpores
Determination of pore
structure
Pressure is increased
to saturation
Incremental reduction in
gas pressure
Evaluation of adsorption and
desorption
Apparatus

22. Pore size Distribution
There are two methods for measuring the distribution of pore volumes
named as:
• Mercury-Penetration method
• Nitrogen-Desorption method

23. Mercury-Penetration method
Given by Ritter and Drake,
𝑎= radius of cylindrical pore
Nitrogen-Desorption method
𝜋𝑎2
𝑝 = −2𝜋𝑎𝜎 cos 𝜃
𝑎 =
−2𝜎 cos 𝜃
p
𝑎 =
2vg
Sg

24. Helium-Mercury method
The volume of helium displaced by a sample of catalyst is measured, then the
helium is removed and the volume of mercury that is displaced is measured and
the difference in these volumes gives the pore volume of catalyst sample.
Porosity is calculated by the given formula:
𝜀 𝑝 =
𝑚 𝑝 𝑣 𝑔
𝑚 𝑝 𝑣 𝑔+𝑚 𝑝
1
𝜌 𝑠
=
𝑣 𝑔
𝑣 𝑔+
1
𝜌 𝑠
= 𝜌 𝑝 𝑣𝑔 𝜌 𝑝 = 𝜌𝑠(1 − 𝜀 𝑝)

25. BET Method Limitations
25
• The BET method is an estimated method, and it is critically criticized for assuming that
adsorption in the n layer occurs when the n-1 layer is completely filled.
• Therefore, in order to overcome this problem, it is necessary to correct the constant C
according to some experimental parameters.
• Of course, doing so will not change the surface area of the calculated level, because when the
P / P0 ratio is in the range of 0.3 to 0.05, in most cases, multi-layer adsorption does not occur.
When the relative pressure P / P0 is between 0.3 and 0.05, adsorption data is well suited to the
BET equation, and at this time, it is usually possible to accurately measure the surface area.
But when the P / P0 value is above the above limit, complexities arise from adsorption at more
than one layer or from compaction.
• When the P / P0 ratio is less than the upper limit, in most cases, the amount of adsorption is so
low that it can not be measuredaccurately
• In porous materials, only the holes in the passage allow gas to pass. But the BETmethod
measures the level of cavities in the path and closedcavities.
• If the sample contains significant cavity values, the BET method measures the amount of
surface that does not actually pass through some of the gas. So the measurement error in
this method is high.

26. Advantages of The BET method
26
• Among the methods used to determine porosity and surface area,
adsorption- based methods, especially the BET method, have the ability
to measure porosity a magnitude of 0.4 to 50 nm, as well as the ease of
measurement and its low cost to take advantage of it.
• This method also allows the type, size, and form of porosity
contained in the material to be adsorbed from the type of isotherm.

27. Applications

28. Discussion and conclusion
Among the methods used to determine porosity and surface
area, adsorption methods, especially the BET method, have the
ability to measure porosity at a magnitude of 0.4 to 50 nm, and
also the ease of measurement and its low cost are considered as
benefits. It turns out. It also allows the type of porosity found in
the material to be derived from the type of adsorption isotherm.
Limitations of this method include time- consuming, low
accuracy of this method for low levels and the need for powder
samples

29. Resources and references
 http://edu.nano.ir/paper/301
 Measurement of active surface and pore
volume in nanomaterials/SelectedArticles
of the Nanotechnology Monthly
 Characterization of Nanostructures/
SVERRE MYHRA • JOHN C. RIVIÈREK12508ISBN

30. THANKS!
31