Surface Chemistry of Materials 1 2 3 4

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Surface Chemistry of Materials 1. 2. 3. 4. 5. 6. 7. 8. Introduction to

Surface Chemistry of Materials 1. 2. 3. 4. 5. 6. 7. 8. Introduction to Surfaces Why are surfaces different from the bulk? Why we need a vacuum (no Hoover jokes, please) Methods for probing surfaces Adsorption of gases Adsorption isotherm Surface Area Adsorption from solution

Surfaces L[m] 1 macroscopic regime 10 -3 mesoscopic regime 10 -6 10 -9 microscopic

Surfaces L[m] 1 macroscopic regime 10 -3 mesoscopic regime 10 -6 10 -9 microscopic regime 10 -12 10 -9 10 -6 10 -3 1 t[s]

Surface Science methods AB+C=>AC+B Experimental surface science Computational surface science Construction of models

Surface Science methods AB+C=>AC+B Experimental surface science Computational surface science Construction of models

Atoms at a surface are low-coordinate relative to the bulk Surface atom, 5 bonds

Atoms at a surface are low-coordinate relative to the bulk Surface atom, 5 bonds to nearest neighbors vacuum Surface Bulk atom, 6 bonds to nearest neighbors

Unused surface bonds can interact, causing change in surface structure Surface dimerization

Unused surface bonds can interact, causing change in surface structure Surface dimerization

Reconstruction of Si(100) A. Unreconstructed Si(100)(1 x 1) surface. The Si atoms of the

Reconstruction of Si(100) A. Unreconstructed Si(100)(1 x 1) surface. The Si atoms of the topmost layer are highlighted in orange; these atoms are bonded to only two other Si atoms, both of which are in the second layer (shaded grey). B. Reconstructed Si(100)(2 x 1) surface. The Si atoms of the topmost layer form a covalent bond with an adjacent surface atom are thus drawn together as pairs; they are said to form "dimers". 6

Redistribution of Charge near surface sets up the Surface Dipole + + + -

Redistribution of Charge near surface sets up the Surface Dipole + + + - - + + Bulk 7

Charge distribution at Surfaces electrons spill out from the surface

Charge distribution at Surfaces electrons spill out from the surface

Surface relaxations at metal surfaces Smoluchowski smoothing at metal surfaces, Finnis and Heine, J.

Surface relaxations at metal surfaces Smoluchowski smoothing at metal surfaces, Finnis and Heine, J. Phys. Chem. B 105, L 37 (1973) The charge density will be redistributed at the surface such the charge is moved from the regions directly above the atom cores to the regions between the atoms. The atoms in the surface layer experience a charge imbalance. This give rise to an inward electrostatic force which leads to a compression of the separation between the surface layers.

Bulk

Bulk

Surfaces A I The surface break the 3 D-periodicity of the bulk crystal Total

Surfaces A I The surface break the 3 D-periodicity of the bulk crystal Total energy of the system: GI+II=GI+GII+DGsurface II

Surface energy A I Gibbs free energy: II S G(T, p) = E-TS +

Surface energy A I Gibbs free energy: II S G(T, p) = E-TS + p. V= j. Njmj where the chemical potential is defined Surface energy g = Energy cost to create a surfaces g= 1 (GI+II(T, p)A Solids (low T): S N m ]) i i i G(T, p) ~ G(0, 0) ~ Etot g= 1 (Esurf -Ebulk) A

Work function is the extra energy needed to promote an electron from the HOMO

Work function is the extra energy needed to promote an electron from the HOMO (Fermi level) into the vacuum different for different surfaces e. g~ 4. 3 e. V, W ~ 5. 3 e. V, Pt EVacuum E Work Function EFermi

Work function surface dipole d Work function F + d - Potential difference Df=f

Work function surface dipole d Work function F + d - Potential difference Df=f ( )-f (- )=4 d

Work function F Chemical potential of the electrons m=E(N+1)-E(N)=EF Work function F=f ( )-m

Work function F Chemical potential of the electrons m=E(N+1)-E(N)=EF Work function F=f ( )-m = Df-m Potential difference Df=f ( )-f (- )=4 d Lang and Kohn, PRB 1, 4555(1970)

quiz • Describe Surface atoms, its bonding and surface charge? • Describe Surface Gipps

quiz • Describe Surface atoms, its bonding and surface charge? • Describe Surface Gipps energy? • What is surface work function? • Where is the vacuum level fits? • Where is the Frmi level fits? • How surface atom overcome low coordination? • Complete figure 1 ? ? E ? ? ? EFermi

Surface Analysis UHV, XPS, TEM

Surface Analysis UHV, XPS, TEM

UHV Technology Experimental surface science only possible in UHV. Reason: The surface composition should

UHV Technology Experimental surface science only possible in UHV. Reason: The surface composition should remain unchanged (clean) during the experiment. From kinetic gas theory it follows: Impingement rate: Mean free path: Molecular density: Monolayer formation time: Some important numbers: Pressure (Torr) n (cm-3) I (cm-2 s-1) 760 2 x 1019 3 x 1023 700 Å 3 ns 1 3 x 1016 4 x 1020 50 μm 2μs 10 -3 3 x 1013 4 x 1017 5 cm 2 ms 10 -6 3 x 1010 4 x 1014 50 m 2 s 10 -10 3 x 106 4 x 1010 500 km 10 hours

Why do we need a vacuum? O 2 hydrocarbons H 2 O CO 2

Why do we need a vacuum? O 2 hydrocarbons H 2 O CO 2 ØAtoms at the surface directly interact with gases in the environment ØRxns occur at the surface that don’t occur in the bulk ØWe need to control this

Typical Atom Surface Density: ~ 1015 atoms/cm 2 Flux of atoms of mass M

Typical Atom Surface Density: ~ 1015 atoms/cm 2 Flux of atoms of mass M to this surface from the gas phase (F) is given by (at gas temperature T) : F (atoms/cm 2 -sec) = 3. 51 x 1022 P(Torr) x [M(g/mole) T]-1/2 (Somorjai) Note: At P = 3 x 10 -5 Torr, M = 28 gr/mole; T = 300 K F ~ 1015 atoms/cm 2 -sec. Thus, assuming a “sticking coefficient” of 1, the surface is covered by a fresh monolayer every second under a mild vacuum

q. Sticking Coefficient = probability/collision that an atom coming from the vacuum and colliding

q. Sticking Coefficient = probability/collision that an atom coming from the vacuum and colliding with the surface will stick! q. Sticking coefficients are often small (e. g. , N 2 on Au) but can approach 1 for , e. g. , N 2 on clean W. q. We need to keep surface contaminant concentrations low over the course of an experiment (~ 1 hour, say). Therefore, pressures ~ 10 -9 or lower are required. q. This is known as ultra-high vacuum (UHV). Important: in measuring surface concentrations of adsorbed atoms, it is NOT pressure, but Pressure x Time [Exposure] that is important. 1 Langmuir = 10 -6 Torr-sec is the standard unit of exposure

Ultra-High-Vacuum (UHV) Technology Material: Take only low outgassing and temperature stable materials! Stainless steel

Ultra-High-Vacuum (UHV) Technology Material: Take only low outgassing and temperature stable materials! Stainless steel (304), copper, aluminum, refractory metals (Ta, W, Mo) μ-metal, glass, ceramics, teflon, viton, capton Do not take: plastics, rubber, zinc plated steel, brass, glue, Pumping systems: Rotary pumps Cryosorption pumps Ion pumps Turbomolecular pumps Pressure gauges: Thermocouple and Pirani Ion gauge (Bayard-Alpert)

X-Ray Photoelectron Spectroscopy (XPS) In XPS core levels are excited, the spectrum reflects the

X-Ray Photoelectron Spectroscopy (XPS) In XPS core levels are excited, the spectrum reflects the energy levels of the atom. Therefore elemental characterization is possible. In addition to the photoelectrons there is a number of additional features in the spectrum, like continuous background, Auger peaks, plasmon losses. Furthermore, the cross section for excitation may be different for individual levels. Valence band electrons are only weakly excited. Qualitative evaluation of XPS spectra involves the comparison of spectra in the XPS-atlas. Quantitative evaluation can be done similarly to that described for AES. In general this method is more accurate for XPS, because less electrons are involve. Ni

High resolution XPS can yield a number of additional information: In particular the fine

High resolution XPS can yield a number of additional information: In particular the fine structure of the core levels, i. e. spin-orbit coupling can easily be seen. This splitting increases with binding energy. Furthermore, slight changes in the binding energies due to different chemical environment can be measured (typically 1 – 10 e. V): Chemical shift. Different oxidation states will have different chemical shifts. The ability to investigate chemical composition is the reason for the name: ESCA The atomic environment on the surface normally differs from that in the bulk. Therefore, bulk and surface features are observed simultaneously. The surface sensitivity can be enhanced by grazing incidence light, and/or increasing the detection angle.

Transmission Electron Microscopy (TEM) The principle is the same as for optical microscopy, but

Transmission Electron Microscopy (TEM) The principle is the same as for optical microscopy, but using electron lenses. Due to the small de Broglie wavelength of high energetic electrons (100 ke. V Δ ≈2Å) the resolution is much higher. Due to the limited penetration depth the samples should be very thin: about 100 - 1000Å. In classical TEM metals were deposited on alkali halides, covered by a thin film of carbon and then the alkali halide substrate was removed by dissolving in water. In this way nucleation, growth and coalescence of metal islands can be studied. Furthermore, the surface structure of alkali halides can be studied by this step decoration method. Na. Cl cleavage surface decorated with Au Another method to obtain thin samples is by mechanical cutting, electrochemical etching and ion milling. Cross section of hetero-structures with atomic resolution can be studied. Si/Tb. Si 2/Si double heterostructure

Figure 1 quiz 1. 2. 3. 4. 5. 6. 7. What is UHV, why

Figure 1 quiz 1. 2. 3. 4. 5. 6. 7. What is UHV, why it is used for surface? What is XPS, principle and application? How is XPS different from XRD? What is TEM, how it is helpful for surface? What is in the figure 1 related to? What is in the figure 2 related to? What is in the figure 3 related to? Figure 3 Turbomolecular pumps Figure 2

What is on the surface? Adsorption of gas

What is on the surface? Adsorption of gas

DEFINITIONS Adsorption: The uptake of gaseous or liquid components of mixtures from external and/or

DEFINITIONS Adsorption: The uptake of gaseous or liquid components of mixtures from external and/or internal surface of porous solids. Adsorbate: Substance in the adsorbed state. Adsorptive: Adsorbable substance in the fluid phase. Adsorbent: Solid material on which adsorption occurs. Absorption: When the species of the adsorbate travel between the atoms, ions or the molecules of the adsorbent. Desorption: The process of removal of an adsorbed substance from the surface on which it is absorbed

Adsorption PHASE I ‘PHASE’ 2 Absorption (“partitioning”) PHASE I PHASE 2 Henry’s Law

Adsorption PHASE I ‘PHASE’ 2 Absorption (“partitioning”) PHASE I PHASE 2 Henry’s Law

Causes of Adsorption • Dislike of Water Phase – ‘Hydrophobicity’ • Attraction to the

Causes of Adsorption • Dislike of Water Phase – ‘Hydrophobicity’ • Attraction to the Sorbent Surface • van der Waals forces: physical attraction • electrostatic forces (surface charge interaction) • chemical forces (e. g. , - and hydrogen bonding)

Adsorption Phenomenon The surface of a solid shows a strong affinity for molecules that

Adsorption Phenomenon The surface of a solid shows a strong affinity for molecules that come into contact with it. Certain solid materials concentrate specific substances from a solution onto their surfaces. Adsorption Phenomenon Physical adsorption (physisorption): Physical attractive forces (van der Waals forces) e. g. Carbon ads, Activated alumina Chemical adsorption (chemisorption): the adsorbed molecules are held to the surface by covalent forces. (little application in ww treatment)

Adsorption of gas

Adsorption of gas

Energy Adsorption Activation barrier Ediss Eads z Physisorption well Chemisorption well

Energy Adsorption Activation barrier Ediss Eads z Physisorption well Chemisorption well

Thermodynamics for adsorption a ma Host Definition of adsorbate energy: Eads=DG=G[host+ads]-{G[host]+Na ma} where G(T,

Thermodynamics for adsorption a ma Host Definition of adsorbate energy: Eads=DG=G[host+ads]-{G[host]+Na ma} where G(T, p)= E-TS + p. V=F+p. V Ftrans, Frot, p. V negligible for solids, but not in the gas phase The adsorbates vibrate at the surface: Fvib(T, w)=Evib (T, w)-TSvib (T, w) This gives the adsorption energy Eads={E[host+defect]+Fvib(T, w)}-{E[host]+Na ma}

Thermodynamics for adsorption Convert the energy values of the chemical potential into T and

Thermodynamics for adsorption Convert the energy values of the chemical potential into T and p-dependence of the gas phase reservoir mi(T, pi)=m. DFT+DG(T, p 0)+ k. T ln(pi /p 0) Interpolate DG(T, p 0) from tables. Reuter and Scheffler, PRB 65, 035406 (2002). Eads(T, p)={E[host+defect]+Fvib(T)}-{E[host]+ma(T, pa)} The adsorbate concentration can be estimated in the dilute limit C=N exp(-Eads/k. T) where N is the number of adsorbtion sites

Physisorption metal r’ - + z The electrostatic energy: Taylor expand in terms of

Physisorption metal r’ - + z The electrostatic energy: Taylor expand in terms of 1/z: z r + -

van der Waals interaction Cohesive energy for graphite as function of a- and c-lattice

van der Waals interaction Cohesive energy for graphite as function of a- and c-lattice parameters. Calculated with GGA XCfunctional Rydberg et al. , Surf. Sci. 532, 606 (2003).

Physisorption of O 2 on graphite h=3. 4 Å DFT-GGA: Eads=0. 04 e. V/O

Physisorption of O 2 on graphite h=3. 4 Å DFT-GGA: Eads=0. 04 e. V/O 2 TPD-experiment: Eads=0. 12 e. V/O 2 Ulbricht et al. , PRB 66, 075404 (2002)

Chemisorption A gas molecular bond to surface molecule or atom or ion including charge

Chemisorption A gas molecular bond to surface molecule or atom or ion including charge transfer

Adsorption sites T B B H H T Close packed (111)-surface Bridge site Hollow

Adsorption sites T B B H H T Close packed (111)-surface Bridge site Hollow FCC-site F F Top site Hollow HCP-site

Weak chemisorption limit If the interaction between the substrate and the adsorbate is weak,

Weak chemisorption limit If the interaction between the substrate and the adsorbate is weak, i. e. V ak is small compared to the bandwidth of the substrate band. Ex for a sp-band. D is then independent of energy which means that L =0. The projected density of states for the adsorbate atom is then a Lorentzian with a width D, centered around ea e |a> sp-band D

Strong. When chemisorption limit the adsorbate interacts with a narrow d-band, then the e

Strong. When chemisorption limit the adsorbate interacts with a narrow d-band, then the e can be k approximated by center value ec such that the denominator in the Green’s function becomes: Solving this equation gives two roots corresponding to bonding and anti bonding levels of the absorbate system. e |a> d-band

Charge transfer Gurney suggested that the atomic levels of a adsorbate atom would broaden

Charge transfer Gurney suggested that the atomic levels of a adsorbate atom would broaden and that there would be a charge transfer between the substrate and the adsorbate atom. Gurney, Phys Rev. 47, 479 (1933) a) Charge would be donated to the substrate if the atom has low ionization energy and b) charge would be attracted from the substrate if the atom has a high ionization energy.

ADSORPTION Summary Chemisorption physisorption Temperature range over which adsorption occurs Virtually unlimited ; however,

ADSORPTION Summary Chemisorption physisorption Temperature range over which adsorption occurs Virtually unlimited ; however, a given molecule may be effectively adsorbed only over a small range Near or below the condensation point of the gas ( e. g. CO 2 < 200 K ) A dsorption enthalpy Wide range, related to the chemical bond strength typically 40 – 800 k. J/mol Related to factors like molecular mass and polarity but typically 5 – 40 k. J/mol ( i. e. ~ heat of liquefaction ) Nature of adsorption Often dissociative and may be irreversible Nondissociative and reversible Saturation uptake Limited to one monlayer Multilayer uptake is possible Kinetics of adsorption Very variable; often is an activated process Fast, because it is a nonactivated process

Figure 1 1. What is adsorption, desorption, adsorbate, absorption, adsorbent? 2. What cause adsorption

Figure 1 1. What is adsorption, desorption, adsorbate, absorption, adsorbent? 2. What cause adsorption to occur? 3. What forces makes physical adsorption? 4. What is chemical adsorption? 5. What difference between physical and chemical adsorption? 6. What is weak adsorption? 7. What is strong adsorption? 8. What is charge transfer? 9. Complete gaps in figure 1? Energy quiz ? ? ? ? ? Ediss z ? ? ? well Eads ? ? ? well

Adsorption Isotherm

Adsorption Isotherm

Adsorptive Equilibration in a Porous Adsorbent Pore Early Later Laminar Boundary Layer GAC Particle

Adsorptive Equilibration in a Porous Adsorbent Pore Early Later Laminar Boundary Layer GAC Particle Adsorbed Molecule Diffusing Molecule Equilibrium

ADSORPTION ISOTHERMS Adsorption isotherm is the equation that relates the amount of a substance

ADSORPTION ISOTHERMS Adsorption isotherm is the equation that relates the amount of a substance attached to a surface to its concentration in the gas phase or in solution, at a fixed temperature. v. The process of Adsorption is usually studied through graphs know as adsorption isotherm. It is the graph between the amounts of adsorbate (x) adsorbed on the surface of adsorbent (m) and pressure at constant temperature. Different adsorption isotherms have been Freundlich, Langmuir and BET theory. v. In the process of adsorption, adsorbate gets adsorbed on adsorbent.

According to Le-Chatelier principle, the direction of equilibrium would shift in that direction where

According to Le-Chatelier principle, the direction of equilibrium would shift in that direction where the stress can be relieved. In case of application of excess of pressure to the equilibrium system, the equilibrium will shift in the direction where the number of molecules decreases. Since number of molecules decreases in forward direction, with the increases in pressure, forward direction of equilibrium will be favored. Basic Adsorption Isotherm From the graph, we can predict that after saturation pressure Ps, adsorption does not occur anymore. This can be explained by the fact that there are limited numbers of vacancies on the surface of the adsorbent. At high pressure a stage is reached when all the sites are occupied and further increase in pressure does not cause any difference in adsorption process. At high pressure, Adsorption is independent of pressure.

Langmuir Isotherm In 1916 Langmuir proposed another Adsorption Isotherm known as Langmuir Adsorption isotherm.

Langmuir Isotherm In 1916 Langmuir proposed another Adsorption Isotherm known as Langmuir Adsorption isotherm. This isotherm was based on different assumptions one of which is that dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules. Assumptions of Langmuir Isotherm Langmuir proposed his theory by making following assumptions. 1. Fixed number of vacant or adsorption sites are available on the surface of solid. 2. All the vacant sites are of equal size and shape on the surface of adsorbent. 3. Each site can hold maximum of one gaseous molecule and a constant amount of heat energy is released during this process. 4. Dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules.

Langmuir Isotherm Where A (g) is unadsorbed gaseous molecule, B(s) is unoccupied metal surface

Langmuir Isotherm Where A (g) is unadsorbed gaseous molecule, B(s) is unoccupied metal surface and AB is Adsorbed gaseous molecule. 5. Adsorption is monolayer or unilayer. Derivations of the Langmuir Adsorption Equation Calculation of Equilibrium Constant Langmuir proposed that dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules. Using the equilibrium equation, equilibrium constant can be calculated.

Derivations of the Langmuir Adsorption Equation Where Ka represents equilibrium constant forward reaction and

Derivations of the Langmuir Adsorption Equation Where Ka represents equilibrium constant forward reaction and Kd represents equilibrium constant for backward direction. According to Kinetic theory, Rate of forward reaction = Ka [A] [B] Rate of backward reaction = Kd [AB] At equilibrium, Rate of forward reaction is equal to Rate of backward reaction This equation represents the equilibrium constant for distribution of adsorbate between the surface and the gas phase.

Derivation Langmuir Equation which depicts a relationship between the number of active sites of

Derivation Langmuir Equation which depicts a relationship between the number of active sites of the surface undergoing adsorption (i. e. extent of adsorption) and pressure. To derive Langmuir Equation and new parameter ‘ θ ’ is introduced. Let θ the number of sites of the surface which are covered with gaseous molecules. Therefore, the fraction of surface which are unoccupied by gaseous molecules will be (1 – θ). Now, Rate of forward direction depends upon two factors: Number of sited available on the surface of adsorbent, (1 – θ) and Pressure, P. Therefore rate of forward reaction is directly proportional to both mentioned factors. Similarly, Rate of backward reaction or Rate of Desorption depends upon number of sites occupied by the gaseous molecules on the surface of adsorbent.

Derivation At equilibrium, rate of adsorption is equal to rate of desorption. Ka P

Derivation At equilibrium, rate of adsorption is equal to rate of desorption. Ka P (1 – θ) = Kd θ We can solve the above equation to write it in terms of θ. Ka. P – Ka. P θ = Kd θ Ka. P = Ka. P θ + Kd θ Ka. P = (Kd + Ka. P) θ Divide numerator and denominator on RHS by Kd, we get

Derivation Now put in earlier equation we get Or And Langmuir Adsorption Equation This

Derivation Now put in earlier equation we get Or And Langmuir Adsorption Equation This is known as Langmuir Adsorption Equation. Or

1 Surface well covered 1 - θ ≈ θ a Change [A] to P

1 Surface well covered 1 - θ ≈ θ a Change [A] to P in gas phase 1 K [A] 1+ K [A] Surface sparsely covered θ = Kc [A] θ = [A] Slope = 1/K 1/θ 1 b 1 = 1+ θ 1 K [A] 1/ [ A ] Fig. 4 (a) Schematic plots of θ (fraction of surface covered) against[A]for a system obeying the Langmuir adsorption isotherm, without dissociation. (b) Reciprocal Langmuir plots.

Alternate form of Langmuir Adsorption Equation Langmuir adsorption equation can be written in an

Alternate form of Langmuir Adsorption Equation Langmuir adsorption equation can be written in an alternate form in terms of volume of gas adsorbed. Let V be volume of gas adsorbed under given sets of conditions of temperature and pressure and Vmono be the adsorbed volume of gas at high pressure conditions so as to cover the surface with a unilayer of gaseous molecules. Substituting the value of θ in Langmuir equation We get Or in terms of pressure P we get

EXAMPLE A surface is half-covered by a gas when the pressure of 1 bar

EXAMPLE A surface is half-covered by a gas when the pressure of 1 bar is applied. The simple Langmuir isotherm is applied; a. What is K/bar-1? b. What pressures give 75% c. What coverage is given by pressures of 0. 1 bar, 0. 5 bar, 100 bar? a v/vm = KP / 1 + KP 0. 5 = K /1 + K 0. 5 (1+K) = K 0. 5 + 0. 5 K = K 0. 5 = K- 0. 5 K 0. 5 = 0. 5 K K = 1 bar-1

b 0. 75 = 1 x P/ 1 + 1 x P 0. 75

b 0. 75 = 1 x P/ 1 + 1 x P 0. 75 + 0. 75 P = P 0. 75 = 0. 25 P P = 0. 75/0. 25 = 3 bar c For 0. 1 bar, v/vm = KP/1+KP = 1 x 0. 1/1+(1 x 0. 1) = 0. 1/1. 1= 0. 909 to percent (x 100) = 0. 909 x 100 = 90. 9%

Alternate form of Langmuir Adsorption Equation in alternate form Thus, if we plot a

Alternate form of Langmuir Adsorption Equation in alternate form Thus, if we plot a graph between P/V, P, we will obtain a straight line with P/V Slope = 1/Vmono } 1/KVmono P

Limitations of Langmuir Adsorption Equation The adsorbed gas has to behave ideally in the

Limitations of Langmuir Adsorption Equation The adsorbed gas has to behave ideally in the vapor phase. This condition can be fulfilled at low pressure conditions only. Thus Langmuir Equation is valid under low pressure only. Langmuir Equation assumes that adsorption is monolayer. But, monolayer formation is possible only under low pressure condition. Under high pressure condition the assumption breaks down as gas molecules attract more and more molecules towards each other. BET theory proposed by Brunauer, Emmett and Teller explained more realistic multilayer adsorption process. Another assumption was that all the sites on the solid surface are equal in size and shape and have equal affinity for adsorbate molecules i. e. the surface of solid if homogeneous. But we all know that in real solid surfaces are heterogeneous. Langmuir Equation assumed that molecules do not interact with each other. This is impossible as weak force of attraction exists even between molecules of same type. The adsorbed molecules has to be localized i. e. decrease in randomness is zero (ΔS = 0). This is not possible because on adsorption liquefaction of gases taking place, which results into decrease in randomness but the value is not zero. From above facts we can conclude that, Langmuir equation is valid under low pressure conditions.

Freundlich Adsorption Equation A Special Case of Langmuir Equation In 1909, Freundlich gave an

Freundlich Adsorption Equation A Special Case of Langmuir Equation In 1909, Freundlich gave an empirical expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as Freundlich Adsorption Isotherm or Freundlich Adsorption equation or simply Freundlich Isotherm. Though Freundlich Isotherm correctly established the relationship of adsorption with pressure at lower values, it failed to predict value of adsorption at higher pressure. Empirical relation used to express the relation between the amount of compound adsorbed and K equation θ=KP 1/n Or Where θ = amount of compound adsorbed, θ=KC 1/n And Ce = equilibrium concentration Linearize form P= equilibrium pressure Log θ = Log K + n Log P Or Log θ = Log K + n Log C

Limitation of Freundlich Adsorption Isotherm Experimentally it was determined that extent of adsorption varies

Limitation of Freundlich Adsorption Isotherm Experimentally it was determined that extent of adsorption varies directly with pressure till saturation pressure Ps is reached. Beyond that point rate of adsorption saturates even after applying higher pressure. Thus Freundlich Adsorption Isotherm failed at higher pressure. Linearize θ=KP 1/n Or θ=KC 1/n Linearize Log θ = Log K + n Log P Or Log θ = Log K + n Log C

Practice The following data were obtained from the measurements of the adsorption of acetic

Practice The following data were obtained from the measurements of the adsorption of acetic acid onto a charcoal surface. Determine the constants in the Freundlich equation. C 0. 018 0. 031 0. 062 0. 126 0. 268 0. 471 0. 882 θ 0. 47 0. 62 0. 80 1. 11 1. 55 2. 04 2. 48

SOLUTION Get the logarithms of the above quantities and tabulate your results as follows:

SOLUTION Get the logarithms of the above quantities and tabulate your results as follows: ln C -4. 02 -3. 47 -2. 78 -2. 07 -1. 32 -0. 75 -0. 13 ln θ -0. 76 -0. 48 -0. 22 0. 104 0. 438 0. 713 0. 908 Ø Draw the relation between ln V and ln C , a straight line obtained, where the slope is equal to 1/n and the intercept equal to ln k. ln θ = ln k + 1/n ln C From the graph 1/n equal to 0. 44 and k = 2. 83 Use the equation, Therefore, θ=KC 1/n θ= 2. 83 c 0. 44

quiz 1. 2. 3. 4. 5. 6. 7. What is adsorption isotherm? What is

quiz 1. 2. 3. 4. 5. 6. 7. What is adsorption isotherm? What is Langmuir Isotherm assumption? What is Langmuir Isotherm limitation? adsorption? What is Freundlich Adsorption limitation? The following data were obtained from the measurements of the adsorption of acetic acid onto a charcoal surface. Determine the constants in the Freundlich equation. C 0. 018 0. 031 0. 062 0. 126 0. 268 0. 471 0. 882 θ 0. 47 0. 62 0. 80 1. 11 1. 55 2. 04 2. 48

BET Isotherm BET Theory founded by Brunauer, Emmett and Teller explained that multilayer formation

BET Isotherm BET Theory founded by Brunauer, Emmett and Teller explained that multilayer formation is the true picture of physical Adsorption. One of the basic assumptions of Langmuir Adsorption Isotherm was that adsorption is monolayer in nature. Langmuir adsorption equation is applicable under the conditions of low pressure. Under these conditions, gaseous molecules would possess high thermal energy and high escape velocity. As a result of this less number of gaseous molecules would be available near the surface of adsorbent. Under the condition of high pressure and low temperature, thermal energy of gaseous molecules decreases and more gaseous molecules would be available per unit surface area. Due to this multilayer adsorption would occur. The multilayer formation was explained by BET Theory.

BET Assumptions 1. Homogeneous surface 2. No lateral interactions between molecules 3. Uppermost layer

BET Assumptions 1. Homogeneous surface 2. No lateral interactions between molecules 3. Uppermost layer is in equilibrium with vapour phase 4. First and Higher layer: Heat adsorption 5. All surface sites have same adsorption energy for Adsorbate 6. Adsorption on the adsorbent occurs in infinite layers 7. The theory can be applied to each layer Langmuir Assumptions 1. Gas molecules behave ideally 2. Only 1 monolayer forms 3. All sites on the surface are equal 4. No adsorbate-adsorbate interaction 5. Adsorbate molecule is immobile another form Where Vmono be the adsorbed volume of gas at high pressure conditions so as to cover the surface with a unilayer of gaseous molecules,

Type of adsorption Type I • The above graph depicts Monolayer adsorption. • This

Type of adsorption Type I • The above graph depicts Monolayer adsorption. • This graph can be easily explained using Langmuir Adsorption Isotherm. • Pores are typically microporus with the exposed surface residing almost exclusively inside the micropores, which once filled with adsorbate, leave little or no external surface for further adsorption.

Type of adsorption Type II • • Type II Adsorption Isotherm shows large deviation

Type of adsorption Type II • • Type II Adsorption Isotherm shows large deviation from Langmuir model of adsorption. The intermediate flat region in the isotherm corresponds to monolayer formation. In BET equation, value of C has to be very large in comparison to 1. Most frequently found when adsorption occurs on nonporous powders or powders with diameters exceeding micropores. Inflection point occurs near the completion of the first adsorbed monolayer • ∆Hodes> ∆Hovap

Type of adsorption Type III • • • Type III Adsorption Isotherm also shows

Type of adsorption Type III • • • Type III Adsorption Isotherm also shows large deviation from Langmuir model. In BET equation value if C <<< 1 Type III Adsorption Isotherm obtained. This isotherm explains the formation of multilayer. There is no flattish portion in the curve which indicates that monolayer formation is missing. Characterised by heats of adsorption less than the adsorbate heat of liquification, adsorption proceeds as the adsorbate interaction with an adsorbed layer is greater than the interaction with the adsorbent surface.

Type of adsorption Type IV • At lower pressure region of graph is quite

Type of adsorption Type IV • At lower pressure region of graph is quite similar to Type II. This explains formation of monolayer followed by multilayer. • The saturation level reaches at a pressure below the saturation vapor pressure. This can be explained on the basis of a possibility of gases getting condensed in the tiny capillary pores of adsorbent at pressure below the saturation pressure (PS) of the gas. • Occur on porous adsorbents with pores in the range of 1. 5 – 100 nm. At higher pressures the slope shows increased uptake of adsorbate as pores become filled, inflection point typically occurs near completion of the first monolayer

Type of adsorption Type V • • Explanation of Type V graph is similar

Type of adsorption Type V • • Explanation of Type V graph is similar to Type IV. Example of Type V Adsorption Isotherm is adsorption of Water (vapors) at 1000 C on charcoal. Type IV and V shows phenomenon of capillary condensation of gas. Are observed where there is small adsorbate-absorbent interaction potentials (similar to type III), and are also associated with pores in the 1. 5 – 100 nm range

quiz 1. What is BET isotherm? 2. Compare between Langmuir Isotherm and BET assumption?

quiz 1. What is BET isotherm? 2. Compare between Langmuir Isotherm and BET assumption? 3. What is BET type I ? Apply to all 4. What is they type of BET curve in the figure? Apply to all

Surface Area Why? ? Surface area directly correlates with desired properties. • • Reactivity

Surface Area Why? ? Surface area directly correlates with desired properties. • • Reactivity Dissolution Catalysis Separation

Surface area • Surface area: Best described as the external surface area of a

Surface area • Surface area: Best described as the external surface area of a solid object including surface attributable to pores. Gas adsorption provides a distinct advantage as many classical models for particle measurement and characterisation fail to consider porosity

BET application • (BET), most common method used to describe specific surface area: The

BET application • (BET), most common method used to describe specific surface area: The BET equation – W= weight of gas adsorbed P/P 0 =relative pressure Wm = weight of adsorbate as monolayer C = BET constant

BET equation requires a linear plot of 1/[W(P/P 0)-1] against P/P 0 • Slope

BET equation requires a linear plot of 1/[W(P/P 0)-1] against P/P 0 • Slope (s) Intercept (i) • Wm (weight of monolayer)

 • Total Surface area (St) can then be derived N = Avagadro’s number

• Total Surface area (St) can then be derived N = Avagadro’s number (6. 023 x 1023) M = Molecular weight of Adsorbate Acs = Adsorbate cross sectional area (16. 2Å2 for Nitrogen) • Specific Surface Area (S) is then determined by total Surface area by sample weight

 • Single point BET: Involves determining specific surface area using a single value

• Single point BET: Involves determining specific surface area using a single value on the isotherm • Multipoint BET: Minimum of three data points.

Multipoint BET Plot: Relative Pressure P/Po Summary: 1. 10536 e-01 1. 53021 e-01 1.

Multipoint BET Plot: Relative Pressure P/Po Summary: 1. 10536 e-01 1. 53021 e-01 1. 99422 e-01 2. 48028 e-01 2. 97227 e-01 Volume@STP 1 / [ W((Po/P) - 1) ] cc/g 7. 5355 8. 1192 8. 7403 9. 4102 10. 1099 1. 3195 e+01 1. 7804 e+01 2. 2803 e+01 2. 8045 e+01 3. 3472 e+01 BET summary Slope = 108. 451, Intercept = 1. 195 e+00, Correlation coefficient, r = 0. 99999 C constant= 91. 759 Surface Area = 31. 762 m²/g

C Constant • Relative error between single and multipoint BET, (typically measured at P/P

C Constant • Relative error between single and multipoint BET, (typically measured at P/P 0 of 0. 3)

Porosity Typical Pore Structure

Porosity Typical Pore Structure

IUPAC classification on pores - Macroporous (>50 nm) - Mesoporus (2 -50 nm) -

IUPAC classification on pores - Macroporous (>50 nm) - Mesoporus (2 -50 nm) - Microporus (<2 nm)

Porosity Pore Volume – Total pore volume is derived from the amount of vapour

Porosity Pore Volume – Total pore volume is derived from the amount of vapour adsorbed at a relative temperature close to unity (assuming pores are filled with liquid adsorbate). Vads = volume of gas adsorbed Vliq = volume of liquid N 2 in pores Vm = molar vol. of liquid adsorbate (N 2=34. 7 cm 3/mol) Pa = ambient pressure T = ambient temperature

Adsorption/Desorption Isotherm

Adsorption/Desorption Isotherm

�Pore Volume Data Total pore volume for pores with Radius less than 15. 93

�Pore Volume Data Total pore volume for pores with Radius less than 15. 93 Å at P/Po = 0. 395090 5. 787 e-01 cc/g BJH method cumulative adsorption pore volume 2. 103 e+00 cc/g BJH method cumulative desorption pore volume 2. 192 e+00 cc/g DH method cumulative adsorption pore volume 2. 054 e+00 cc/g DH method cumulative desorption pore volume 2. 146 e+00 cc/g HK method cumulative pore volume 4. 257 e-01 cc/g SF method cumulative pore volume 4. 358 e-01 cc/g NLDFT method cumulative pore volume 1. 904 e+00 cc/g �Pore Size Data Average pore Radius 3. 505 e+01 Å BJH method adsorption pore Radius (Mode Dv(r)) 1. 698 e+01 Å BJH method desorption pore Radius (Mode Dv(r)) 1. 710 e+01 Å DH method adsorption pore Radius (Mode Dv(r)) 1. 698 e+01 Å DH method desorption pore Radius (Mode Dv(r)) 1. 710 e+01 Å HK method pore Radius (Mode) 1. 838 e+00 Å SF method pore Radius (Mode) 2. 261 e+00 Å NLDFT pore Radius (Mode) 2. 376 e+01 Å

Nova Quantachrome 4200 e

Nova Quantachrome 4200 e

quiz 1. Why is surface area measurement important? 2. How surface area being measured?

quiz 1. Why is surface area measurement important? 2. How surface area being measured? 3. Describe porosity and its IUPAC type?

Adsorption from solutions • Liquid behaves similar to gas in adsorption • Pervious isotherm

Adsorption from solutions • Liquid behaves similar to gas in adsorption • Pervious isotherm will be applied with solution like gas • P will be changed to concentration

Langmuir Isotherm Primarily for gases and based on the following assumptions 1. The energy

Langmuir Isotherm Primarily for gases and based on the following assumptions 1. The energy of adsorption is constant and independent of the extent of surface coverage 2. The adsorption is on localized sites and there is no interaction between the adsorbed molecules 3. The maximum adsorption possible is that of a complete monolayer X = mole of solute adsorbed per gram of adsorbent C = equilibrium conc. of solute in solution Xm = Number of moles adsorbed/g of adsorbent to give a complete monolayer b = constant related to the energy of adsorption

Freundlich Isotherm Empirical relation used to express the relation between the amount of compound

Freundlich Isotherm Empirical relation used to express the relation between the amount of compound sorbed and Keq Where x/m = amount of compound sorbed And Ce = equilibrium concentration The use of this relation to evaluate experimental data is essentially “curve fitting” and has no mechanistic base. 1. K provides an index of the extent of sorption and is often listed w/o units 2. n = indicates whether the relation between x/m and Ce is linear (n=1) or concave down (n<1) or concave up (n>1) – and when n = 1, K equals the distribution coefficient

L-curve isotherm • Solute has a relatively high affinity for the sorbent surface at

L-curve isotherm • Solute has a relatively high affinity for the sorbent surface at low surface coverage - Affinity sorbate-sorbent decreases with increasing coverage Isotherm types that are commonly observed in environmental sciences q q S-curve isotherm • Affinity of sorbent for sorbate is q less than of solution at low solute concentration. • As the concentration of solute increases and exceeds the retention capacity of the solution, sorption peaks up. H-curve isotherm • Very high affinity sorbatesorbent. • Probability of inner sphere complexes formation Ce Ce C-curve isotherm • Characteristics of nonionic and hydrophobic compounds • Constant partitioning

SORPTION KINETICS Batch Studies Column Studies • Distribution defined by sorption - not desorption

SORPTION KINETICS Batch Studies Column Studies • Distribution defined by sorption - not desorption • Common 24 -hr equilibration batch experiments • Rapid removal from solution: >99% in 2 to 3 hrs • True equilibrium usually not attained • Movement of pollutant monitored as a function of sorbent type (e. g. soil), column dimensions, flow rates, and ionic strength. Water used as eluent • Principles of chromatography can be used • Data used to analyze sorption kinetics by 2 -site Freundlich relation and where • S = amount sorbed at respective site (f=fraction of S 1 and 1 -f=fraction S 2) • C= concentration in solution • k= rate constant • K and n are Freundlich parameters from batch experiments and K 1=Kf and K 2=K(1 -f)

quiz 1. What is Langmuir Isotherm for liquid? 2. What is Freundlich Isotherm for

quiz 1. What is Langmuir Isotherm for liquid? 2. What is Freundlich Isotherm for liquid? 3. Describe the figure? Apply to all q