T Plot Adsorption

Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid (the absorbate) is dissolved by or permeates a liquid or solid (the absorbent), respectively.

• T Plot Adsorption Definition
• T-plot Adsorption
• T Plot Adsorption Analysis
• T Plot Adsorption Isotherm
• T Plot Adsorption Method

A plot of 1 / x / m versus 1 / c should generate a straight line. Since the adsorption process is an equilibrium process it is desirable to investigate the thermodynamic parameters. Adsorption of nitrogen and other gases by char-coal, including an extensive series of measure-ments over a wide range of temperature by Ida Homfray 3. Langmuir's monumental work on monolayer adsorption 4 resulted in renewed interest in the interpretation of adsorption data. According to the Langmuir model (now called ‘ideal localised. Adsorption decreases with increase in temperature. More surface area more is the rate of adsorption. Adsorption also depends on concentration of solute in a solution. Adsorption also depends on nature of adsorbate and nature of adsorbent. Freundlich explains the adsorption from solution phase using concentration of the solution instead of pressure. A typical plot of ln k/ T vs. 1/T (Eyring equation plot) In general, the ¦G. values are positive at all temperatures suggesting that adsorption reactions require some energy from an external source to convert reactants into products. A negative value of ¦H. suggests that the adsorption phenomenon is exothermic while a.

Brunauer–Emmett–Teller (BET) theory aims to explain the physical adsorption of gasmolecules on a solidsurface and serves as the basis for an important analysis technique for the measurement of the specific surface area of materials. The observations are very often referred to as physical adsorption or physisorption. In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published the first article about the BET theory in the Journal of the American Chemical Society.^[1] The BET theory applies to systems of multilayer adsorption and usually utilizes probing gases that do not chemically react with material surfaces as adsorbates to quantify specific surface area. Nitrogen is the most commonly employed gaseous adsorbate used for surface probing by BET methods. For this reason, standard BET analysis is most often conducted at the boiling temperature of N₂ (77 K). Further probing adsorbates are also utilized, albeit with lower frequency, allowing the measurement of surface area at different temperatures and measurement scales. These have included argon, carbon dioxide, and water. Specific surface area is a scale-dependent property, with no single true value of specific surface area definable, and thus quantities of specific surface area determined through BET theory may depend on the adsorbate molecule utilized and its adsorption cross section.^[2]

Concept[edit]

The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses:

1. gas molecules physically adsorb on a solid in layers infinitely;
2. gas molecules only interact with adjacent layers; and
3. the Langmuir theory can be applied to each layer.
4. the enthalpy of adsorption for the first layer is constant and greater than the second (and higher).
5. the enthalpy of adsorption for the second (and higher) layers is the same as the enthalpy of liquefaction.

The resulting BET equation is

1v[(p0/p)−1]=c−1vmc(pp0)+1vmc,(1){displaystyle {frac {1}{vleft[left({p_{0}}/{p}right)-1right]}}={frac {c-1}{v_{mathrm {m} }c}}left({frac {p}{p_{0}}}right)+{frac {1}{v_{m}c}},qquad (1)}

T Plot Adsorption Definition

where p{displaystyle p} and p0{displaystyle p_{0}} are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, v{displaystyle v} is the adsorbed gas quantity (for example, in volume units), and vm{displaystyle v_{mathrm {m} }} is the monolayer adsorbed gas quantity. c{displaystyle c} is the BET constant,

c=exp⁡(E1−ELRT),(2){displaystyle c=exp left({frac {E_{1}-E_{mathrm {L} }}{RT}}right),qquad (2)}

where E1{displaystyle E_{1}} is the heat of adsorption for the first layer, and EL{displaystyle E_{mathrm {L} }} is that for the second and higher layers and is equal to the heat of liquefaction or heat of vaporization.

Equation (1) is an adsorption isotherm and can be plotted as a straight line with 1/v[(p0/p)−1]{displaystyle 1/{v[({p_{0}}/{p})-1]}} on the y-axis and φ=p/p0{displaystyle varphi ={p}/{p_{0}}} on the x-axis according to experimental results. This plot is called a BET plot. The linear relationship of this equation is maintained only in the range of 0.05<p/p0<0.35{displaystyle 0.05<{p}/{p_{0}}<0.35}. The value of the slope A{displaystyle A} and the y-intercept I{displaystyle I} of the line are used to calculate the monolayer adsorbed gas quantity vm{displaystyle v_{mathrm {m} }} and the BET constant c{displaystyle c}. The following equations can be used:

vm=1A+I(3){displaystyle v_{m}={frac {1}{A+I}}qquad (3)}

c=1+AI.(4){displaystyle c=1+{frac {A}{I}}.qquad (4)}

The BET method is widely used in materials science for the calculation of surface areas of solids by physical adsorption of gas molecules. The total surface area Stotal{displaystyle S_{mathrm {total} }} and the specific surface areaSBET{displaystyle S_{mathrm {BET} }} are given by

Stotal=(vmNs)V,(5){displaystyle S_{mathrm {total} }={frac {left(v_{mathrm {m} }Nsright)}{V}},qquad (5)}

SBET=Stotala,(6){displaystyle S_{mathrm {BET} }={frac {S_{mathrm {total} }}{a}},qquad (6)}

where vm{displaystyle v_{mathrm {m} }} is in units of volume which are also the units of the monolayer volume of the adsorbate gas,N{displaystyle N} is the Avogadro number, s{displaystyle s} the adsorption cross section of the adsorbing species, V{displaystyle V} the molar volume of the adsorbate gas, and a{displaystyle a} the mass of the solid sample or adsorbent.

Derivation[edit]

The BET theory can be derived similarly to the Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before an upper layer formation starts. Furthermore, the authors made five assumptions:^[3]

1. Adsorptions occur only on well-defined sites of the sample surface (one per molecule)
2. The only molecular interaction considered is the following one: a molecule can act as a single adsorption site for a molecule of the upper layer.
3. The uppermost molecule layer is in equilibrium with the gas phase, i.e. similar molecule adsorption and desorption rates.
4. The desorption is a kinetically-limited process, i.e. a heat of adsorption must be provided:
   • these phenomena are homogeneous, i.e. same heat of adsorption for a given molecule layer.
   • it is E₁ for the first layer, i.e. the heat of adsorption at the solid sample surface
   • the other layers are assumed similar and can be represented as condensed species, i.e. liquid state. Hence, the heat of adsorption is E_L is equal to the heat of liquefaction.
5. At the saturation pressure, the molecule layer number tends to infinity (i.e. equivalent to the sample being surrounded by a liquid phase)

Consider a given amount of solid sample in a controlled atmosphere. Let θ_i be the fractional coverage of the sample surface covered by a number i of successive molecule layers. Let us assume that the adsorption rate R_ads,i-1 for molecules on a layer (i-1) (i.e. formation of a layer i) is proportional to both its fractional surface θ_i-1 and to the pressure P, and that the desorption rate R_des,i on a layer i is also proportional to its fractional surface θ_i:

Rads,i−1=kiPΘi−1{displaystyle R_{mathrm {ads} ,i-1}=k_{i}PTheta _{i-1}}

Rdes,i=k−iΘi,{displaystyle R_{mathrm {des} ,i}=k_{-i}Theta _{i},}

where k_i and k_−i are the kinetic constants (depending on the temperature) for the adsorption on the layer (i−1) and desorption on layer i, respectively. For the adsorptions, these constant are assumed similar whatever the surface.Assuming an Arrhenius law for desorption, the related constants can be expressed as

ki=exp⁡(−Ei/RT),{displaystyle k_{i}=exp(-E_{i}/RT),}

where E_i is the heat of adsorption, equal to E₁ at the sample surface and to E_L otherwise.

T Plot Adsorption Definition

where p{displaystyle p} and p0{displaystyle p_{0}} are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, v{displaystyle v} is the adsorbed gas quantity (for example, in volume units), and vm{displaystyle v_{mathrm {m} }} is the monolayer adsorbed gas quantity. c{displaystyle c} is the BET constant,

c=exp⁡(E1−ELRT),(2){displaystyle c=exp left({frac {E_{1}-E_{mathrm {L} }}{RT}}right),qquad (2)}

where E1{displaystyle E_{1}} is the heat of adsorption for the first layer, and EL{displaystyle E_{mathrm {L} }} is that for the second and higher layers and is equal to the heat of liquefaction or heat of vaporization.

Equation (1) is an adsorption isotherm and can be plotted as a straight line with 1/v[(p0/p)−1]{displaystyle 1/{v[({p_{0}}/{p})-1]}} on the y-axis and φ=p/p0{displaystyle varphi ={p}/{p_{0}}} on the x-axis according to experimental results. This plot is called a BET plot. The linear relationship of this equation is maintained only in the range of 0.05<p/p0<0.35{displaystyle 0.05<{p}/{p_{0}}<0.35}. The value of the slope A{displaystyle A} and the y-intercept I{displaystyle I} of the line are used to calculate the monolayer adsorbed gas quantity vm{displaystyle v_{mathrm {m} }} and the BET constant c{displaystyle c}. The following equations can be used:

vm=1A+I(3){displaystyle v_{m}={frac {1}{A+I}}qquad (3)}

c=1+AI.(4){displaystyle c=1+{frac {A}{I}}.qquad (4)}

The BET method is widely used in materials science for the calculation of surface areas of solids by physical adsorption of gas molecules. The total surface area Stotal{displaystyle S_{mathrm {total} }} and the specific surface areaSBET{displaystyle S_{mathrm {BET} }} are given by

Stotal=(vmNs)V,(5){displaystyle S_{mathrm {total} }={frac {left(v_{mathrm {m} }Nsright)}{V}},qquad (5)}

SBET=Stotala,(6){displaystyle S_{mathrm {BET} }={frac {S_{mathrm {total} }}{a}},qquad (6)}

where vm{displaystyle v_{mathrm {m} }} is in units of volume which are also the units of the monolayer volume of the adsorbate gas,N{displaystyle N} is the Avogadro number, s{displaystyle s} the adsorption cross section of the adsorbing species, V{displaystyle V} the molar volume of the adsorbate gas, and a{displaystyle a} the mass of the solid sample or adsorbent.

Derivation[edit]

The BET theory can be derived similarly to the Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before an upper layer formation starts. Furthermore, the authors made five assumptions:^[3]

1. Adsorptions occur only on well-defined sites of the sample surface (one per molecule)
2. The only molecular interaction considered is the following one: a molecule can act as a single adsorption site for a molecule of the upper layer.
3. The uppermost molecule layer is in equilibrium with the gas phase, i.e. similar molecule adsorption and desorption rates.
4. The desorption is a kinetically-limited process, i.e. a heat of adsorption must be provided:
   • these phenomena are homogeneous, i.e. same heat of adsorption for a given molecule layer.
   • it is E₁ for the first layer, i.e. the heat of adsorption at the solid sample surface
   • the other layers are assumed similar and can be represented as condensed species, i.e. liquid state. Hence, the heat of adsorption is E_L is equal to the heat of liquefaction.
5. At the saturation pressure, the molecule layer number tends to infinity (i.e. equivalent to the sample being surrounded by a liquid phase)

Consider a given amount of solid sample in a controlled atmosphere. Let θ_i be the fractional coverage of the sample surface covered by a number i of successive molecule layers. Let us assume that the adsorption rate R_ads,i-1 for molecules on a layer (i-1) (i.e. formation of a layer i) is proportional to both its fractional surface θ_i-1 and to the pressure P, and that the desorption rate R_des,i on a layer i is also proportional to its fractional surface θ_i:

Rads,i−1=kiPΘi−1{displaystyle R_{mathrm {ads} ,i-1}=k_{i}PTheta _{i-1}}

Rdes,i=k−iΘi,{displaystyle R_{mathrm {des} ,i}=k_{-i}Theta _{i},}

where k_i and k_−i are the kinetic constants (depending on the temperature) for the adsorption on the layer (i−1) and desorption on layer i, respectively. For the adsorptions, these constant are assumed similar whatever the surface.Assuming an Arrhenius law for desorption, the related constants can be expressed as

ki=exp⁡(−Ei/RT),{displaystyle k_{i}=exp(-E_{i}/RT),}

where E_i is the heat of adsorption, equal to E₁ at the sample surface and to E_L otherwise.

Finding the linear BET range[edit]

It is still not clear on how to find the linear range of the BET plot for microporous materials in a way that reduces any subjectivity in the assessment of the monolayer capacity. Rouquerol et al.^[4] suggested a procedure that is based on two criteria:

• C must be positive implying that any negative intercept on the BET plot indicates that one is outside the valid range of the BET equation.
• Application of the BET equation must be limited to the range where the term V(1-P/P₀) continuously increases with P/P₀.

These corrections are an attempt to salvage the BET theory which is restricted to type II isotherm. Even with this type, use of the data is restricted to 0.5 to 3.5 of P/P0{displaystyle P/P_{0}}, routinely discarding 70% of the data. Even this restriction has to be modified depending upon conditions. The problems with the BET theory are multiple and reviewed by Sing.^[5] A serious problem is that there is no relationship between the BET and the calorimetric measurements in experiments. It violates the Gibbs' phase rules. It is extremely unlikely that it measure correctly the surface area, formerly great advantage of the theory. It is based upon chemical equilibrium, which assumes localized chemical bond (this approach has been abandoned by the modern theories. See ^[6] chapter 4, χ/ESW and Chapter 7, DFT or better NLDFT) in total contradiction to what is known about physical adsorption, which is based upon non-local intermolecular attractions. Two extreme problems is that in certain cases BET leads to anomalies and the C constant can be negative, implying an imaginary energy.

Applications[edit]

Cement and concrete[edit]

T-plot Adsorption

The rate of curing of concrete depends on the fineness of the cement and of the components used in its manufacture, which may include fly ash, silica fume and other materials, in addition to the calcinatedlimestone which causes it to harden. Although the Blaine air permeability method is often preferred, due to its simplicity and low cost, the nitrogen BET method is also used.

When hydrated cement hardens, the calcium silicate hydrate (or C-S-H), which is responsible for the hardening reaction, has a large specific surface area because of its high porosity. This porosity is related to a number of important properties of the material, including the strength and permeability, which in turn affect the properties of the resulting concrete. Measurement of the specific surface area using the BET method is useful for comparing different cements. This may be performed using adsorption isotherms measured in different ways, including the adsorption of water vapour at temperatures near ambient, and adsorption of nitrogen at 77 K (the boiling point of liquid nitrogen). Different methods of measuring cement paste surface areas often give very different values, but for a single method the results are still useful for comparing different cements.

Activated carbon[edit]

Activated carbon strongly adsorbs many gases and has an adsorption cross sections{displaystyle s} of 0.162 nm² for nitrogen adsorption at liquid-nitrogen temperature (77 K). BET theory can be applied to estimate the specific surface area of activated carbon from experimental data, demonstrating a large specific surface area, even around 3000 m²/g.^[7] However, this surface area is largely overestimated due to enhanced adsorption in micropores,^[4] and more realistic methods should be used for its estimation, such as the subtracting pore effect (SPE) method.^[8]

Catalysis[edit]

T Plot Adsorption Analysis

In the field of solid catalysis, the surface area of catalysts is an important factor in catalytic activity. inorganic materials such as mesoporous silica and layered clay minerals have high surface areas of several hundred m²/g calculated by the BET method, indicating the possibility of application for efficient catalytic materials.

Specific surface area calculation[edit]

The ISO 9277 standard for calculating the specific surface area of solids is based on the BET method.

See also[edit]

References[edit]

T Plot Adsorption Isotherm

1. ^Brunauer, Stephen; Emmett, P. H.; Teller, Edward (1938). 'Adsorption of Gases in Multimolecular Layers'. Journal of the American Chemical Society. 60 (2): 309–319. Bibcode:1938JAChS..60..309B. doi:10.1021/ja01269a023. ISSN0002-7863.
2. ^Hanaor, D. A. H.; Ghadiri, M.; Chrzanowski, W.; Gan, Y. (2014). 'Scalable Surface Area Characterization by Electrokinetic Analysis of Complex Anion Adsorption'(PDF). Langmuir. 30 (50): 15143–15152. doi:10.1021/la503581e. PMID25495551.
3. ^Sing, Kenneth S.W. (1998). 'Adsorption methods for the characterization of porous materials'. Advances in Colloid and Interface Science. 76–77: 3–11. doi:10.1016/S0001-8686(98)00038-4.
4. ^ ^abRouquerol, J.; Llewellyn, P.; Rouquerol, F. (2007), 'Is the bet equation applicable to microporous adsorbents?', Studies in Surface Science and Catalysis, Elsevier, 160, pp. 49–56, doi:10.1016/s0167-2991(07)80008-5, ISBN9780444520227
5. ^Sing, Kenneth S. W. (2014). Adsorption by Powders and Porous Materials, Principles, Methodology and Applications by F. Rouquerol, J. Rouquerol, K. S. W. Sing. P. Llewellyn and G Maurin, eds., 2nd Edition. Amsterdam.NL: Academic Press/ Elsevier Ltd. pp. 263–267. ISBN978-0-08-097035-6.
6. ^Condon, James (2020). Surface Area and Porosity Determinations by Physisorption, Measurement, Classical Theory and Wuantum Theory, 2nd edition. Amsterdam.NL: Elsevier. pp. Chapters 3, 4 and 5. ISBN978-0-12-818785-2.
7. ^Nakayama, Atsuko; Suzuki, Kazuya; Enoki, Toshiaki; Koga, Kei-ichi; Endo, Morinobu; Shindo, Norifumi (1996). 'Electronic and Magnetic Properties of Activated Carbon Fibers'. Bull. Chem. Soc. Jpn. 69 (2): 333–339. doi:10.1246/bcsj.69.333. ISSN0009-2673. Retrieved 2015-06-26.
8. ^Kaneko, K.; Ishii, C.; Ruike, M.; Kuwabara, H. (1992). 'Origin of superhigh surface area and microcrystalline graphitic structures of activated carbons'. Carbon. 30 (7): 1075–1088. doi:10.1016/0008-6223(92)90139-N. ISSN0008-6223.

T Plot Adsorption Method