expands on , allowing for on solid surfaces. It's crucial for determining and in porous materials, especially those with or .
The , derived from , helps calculate . This is vital for characterizing materials used in catalysis, adsorption, and energy storage, where high surface area often means better performance.
BET Theory for Multilayer Adsorption
Principles and Assumptions
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Core electron binding energies of adsorbates on Cu(111) from first-principles calculations ... View original
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Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase ... View original
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Core electron binding energies of adsorbates on Cu(111) from first-principles calculations ... View original
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Top images from around the web for Principles and Assumptions
Core electron binding energies of adsorbates on Cu(111) from first-principles calculations ... View original
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Water adsorption and O-defect formation on Fe 2 O 3 (0001) surfaces - Physical Chemistry ... View original
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Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase ... View original
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Core electron binding energies of adsorbates on Cu(111) from first-principles calculations ... View original
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Water adsorption and O-defect formation on Fe 2 O 3 (0001) surfaces - Physical Chemistry ... View original
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BET theory extends the Langmuir adsorption model to multilayer adsorption
Allows for the determination of surface area and pore size distribution of porous materials
Assumes gas molecules can adsorb onto a solid surface in an infinite number of layers
No interaction between each adsorption layer
First adsorbed layer has a equal to the heat of condensation of the
Subsequent layers have a heat of adsorption equal to the heat of liquefaction
Introduces the concept of a of the adsorbed film
Ratio of the amount of adsorbate in each layer to the amount required to form a monolayer
Applicability and Adsorption Isotherms
BET theory is most applicable to Type II and Type IV
Exhibit multilayer adsorption and capillary condensation in mesopores (pores with diameters between 2 and 50 nm)
Type II isotherms are characteristic of non-porous or macroporous materials (pores with diameters greater than 50 nm)
Show unrestricted monolayer-multilayer adsorption
Type IV isotherms are characteristic of mesoporous materials
Exhibit a hysteresis loop associated with capillary condensation in mesopores
BET Equation Derivation and Limitations
Derivation of the BET Equation
Derived by considering the equilibrium between the rates of condensation and evaporation for each adsorption layer
BET equation can be linearized to obtain vm and c from the slope and intercept of a BET plot
Plot of 1/[v((P0/P)−1)] versus P/P0
Assumptions and Limitations
Assumes the surface is energetically homogeneous
No lateral interactions between adsorbed molecules
BET equation is valid only for a limited range of relative pressures
Typically between 0.05 and 0.35, where multilayer adsorption is dominant
May not accurately describe adsorption in microporous materials (pores with diameters less than 2 nm)
Pore filling rather than layer-by-layer adsorption occurs in micropores
Surface Area Determination Using BET
Specific Surface Area Calculation
Specific surface area of a porous material can be calculated from the monolayer volume vm obtained from the BET equation
Surface area is given by: SBET=(vm∗NA∗σ)/(V∗m)
NA: Avogadro's number
σ: cross-sectional area of the adsorbate molecule
V: molar volume of the gas
m: mass of the sample
Nitrogen is the most commonly used adsorbate for BET surface area measurements
Typical cross-sectional area of 0.162 nm2 per molecule at 77 K
Experimental Procedure
BET method requires the measurement of an adsorption isotherm
Typically using a volumetric or gravimetric technique
Obtains the volume of gas adsorbed at different relative pressures
Sample is degassed to remove adsorbed contaminants
Cooled to liquid nitrogen temperature (77 K) for
Adsorption isotherm is measured by incrementally dosing the sample with nitrogen gas
Measuring the equilibrium pressure after each dose
Importance of Specific Surface Area
Specific surface area is an essential characteristic of porous materials
Influences their performance in various applications (catalysis, adsorption, and energy storage)
High specific surface area materials (activated carbons, zeolites, and metal-organic frameworks) are desirable for adsorption and catalysis
Provide more sites for adsorption and reaction
Specific surface area can be used to compare the effectiveness of different porous materials
Optimize their synthesis and processing conditions
BET Isotherm Analysis and Surface Area Calculation
Adsorption Isotherm Interpretation
BET adsorption isotherm plots the volume of gas adsorbed (v) against the (P/P0) at a constant temperature
Shape of the isotherm provides information about the pore structure and adsorption behavior of the material
Type II isotherms indicate non-porous or macroporous materials
Type IV isotherms indicate mesoporous materials with capillary condensation
Linear region of the BET plot (typically between relative pressures of 0.05 and 0.35) is used to determine the monolayer volume vm and the BET constant c
Slope and intercept of the linear fit are used to calculate vm and c
Surface Area Calculation from Experimental Data
Specific surface area is calculated from vm using the appropriate values for the adsorbate cross-sectional area and molar volume
Example calculation for nitrogen adsorption at 77 K:
BET constant c is related to the heat of adsorption
Provides information about the strength of the adsorbate-adsorbent interactions
Higher values of c indicate stronger interactions and a more energetically homogeneous surface
Deviations from linearity in the BET plot at low or high relative pressures may indicate the presence of micropores or mesopores, respectively
Alternative analysis methods (Langmuir, Dubinin-Radushkevich, or Barrett-Joyner-Halenda) may be required for accurate characterization of these materials
Pore size distribution can be obtained from the adsorption isotherm using methods such as the Barrett-Joyner-Halenda (BJH) analysis
Based on the Kelvin equation and the assumption of cylindrical pores