Title: ETH_Sem6 / ACIV / Section1

Q: Types of solids oxides (3)
A: - Ionic: CN of M > valency of M, eg MgO, TiO_2, Al2O3
- Covalent: CN = valency, eg SiO_2
- Molecular: CN < valency, eg CrO_3

Octahedra and tetrahedra building interconnection types

\(\mu_1\)-hydroxile groups types (3)

Q: Three categories of solid materials in terms of electronics
A: - Insulators: wide band gap > 3 eV
- Semi-conductors: narrow BG < 3 eV
- Conductors: overlap of conduction and valence band (this is the case for metals)

Q: Classification grain size
A: Name | Grain size | Surface area
Divided State | < 10 \(\mu m\) | < 1 m^2/g
Colloidal State | < 1 \(\mu m\) | 1 - 100 m^2/g
Nanomaterial | < 10 nm | > 100 m^2/g

Q: Classification Porosity
A: - Macropores > 50 nm
- Mesopores 2 nm < 50 nm
- Micropores < 2 nm

Q: N_2 adsorption curves types and material classification
A: Type I: microporous material
Type II: non-porous or macroporous mat.
Type IV: mesoporous mat., typically with
hysteresis
Type III&V: rare, related to low \(\ce{N2}\)/surface
interaction
Type VI: rare, successive layer adsorptions

Q: Langmuir adsorption model
A: Assume that an adsorbate behaves as an ideal gas at isothermal conditions -> Adsorption and desorption are treated as a reversible chemical reaction:
\[A_g + S \rightleftharpoons A_{ad}\]This yields the Langmuir adsorption formula for the fractional occupancy of adsorption sites (\(V_m\) is the volume of a monolayer of adsorbed gas)
\[\Theta_A = \frac{V}{V_m} = \frac{K_{eq}^A p_A}{1+K_{eq}^A p_A}\]In a plot from Wikipedia this looks like

Q: Assumptions of the Langmuir adsorbtion model (5)
A: 1. The surface containing the adsorbing sites is a perfectly flat plane with no corrugations.
2. The adsorbing gas adsorbs into an immobile state.
3. All sites are energetically equivalent.
4. Only monolayer coverage.
5. No interactions between adsorbate molecules on adjacent sites.

Q: BET theory (5 Hypotheses + Evaluation)
A: BET: Brunauer-Emmett-Teller
Extension of Langmuir Theory, considering multilayer adsorption with the following hypotheses:
- gas molecules physically adsorb on a solid in layers infinitely;
- gas molecules only interact with adjacent layers; and
- the Langmuir theory can be applied to each layer.
- the enthalpy of adsorption for the first layer is constant and greater than for the second (and higher).
- the enthalpy of adsorption for the second (and higher) layers is the same as the enthalpy of liquefaction.
This yields the BET equation for the coverage
\[\Theta = \frac{n_{ads}}{n_m} = \frac{c p}{(1-p/p_0)(p_0+p(c-1))}\]with \(c = \exp\left(\frac{E_1 - E_L}{RT}\right)\), the BET constant, \(E_1\) the adsorption energy of the first layer and \(E_L\) the adsorption energy of any subsequent layer, \(p_0\) the vapor pressure and \(n_m\) the monolayer adsorption equivalent. For analysis the equation is usually rearranged to
\[\frac{p/p_0}{n_{ads}(1-p/p_0)} = \frac{1}{n_m c} + \frac{c-1}{n_m c}\frac{p}{p_0}\]This gives a linear relationship
within \(0.05 < p/p_0 < 0.35\) and from the intercept/slope, \(n_m\) and from there, using the adsorption cross section \(\sigma_m\), the surface area \[\frac{A}{m} = \frac{n_m}{m} \sigma_m N_A\]is obtained.

Q: Approximate pore size, adsorption type and porosity
A: Ca. 10 nm pore size
Type IV
Mesoporous

Q: Approximate pore size, adsorption type and porosity
A: Pore size ca. 5 nm
Type IV
Mesoporous

Q: Which material has the smaller pores?
A: Have a look at the relative pressure at which capillary condensation (and thus the second inset) occurs and take into account the absence/presence of a hysteresis. The smaller the pores, the smaller is the relative pressure at which capillary condensation occurs and a hysteresis is more likely for larger pores. Thus material 2 has smaller pores than material 1.

Q: Approximate the surface area, using \(\sigma_m(N_2) = 0.162 \, \mathrm{nm^2}\) and that the intercept is at about \(i \approx 2 \, \mathrm{g/mol}\)
A: The slope is about \(s \approx 280 \, \mathrm{g/mol}\). Using \(n_m = \frac{1}{s + i} \approx 3.5 \, \mathrm{mmol/g}\) for the amount N_2 molecules required to cover a monolayer, we can get the surface area as\[A = n_m \sigma_m N_A \approx 342 \, \mathrm{m^2/g}\]

Q: What property of a material can be investigated using BJH theory?
A: The pore size distribution

Q: For which types of materials may BJH theory be applied?
A: BJH theory is limited to mesoporous and small-pore macroporous materials, but the Kelvin equation is not valid for micropores.

Q: BJH plot, what can you extract from this, in which category would you place the material?
A: The maximum of the pore size distribution is at \(d_P = 7.1 \, \mathrm{nm}\), and the pore size distribution is relatively narrow. The material is thus categorized as mesoporous.

Q: What other technique would you use to confirm what you observe with BJH? What are the limitations?
A: Another technique to investigate the pore size and pore size distribution of a porous material is Transmission Electron Microscopy (TEM). The limitation of this method is that the pores need to be relatively ordered and the material has to be stable and homogeneous to be fully resolved in the resulting TEM picture.

Q: What information on a material can one obtain using X-ray diffraction? What physical property is observed? What are the limitations?
A: The interference pattern when X-ray light interacts with a crystal is observed and the resulting angle-dependent intensities are related to the electron density and thus the structure of the material. The method is limited to crystalline materials with adequately sized crystals.
For powders, powder XRD gives some less detailed information.

Q: What information on a material can one obtain using X-ray absorption spectroscopy? What physical property is observed? What are the limitations?
A: Typically a sharp increase in absorption at the wavelength that corresponds to the excitation of core electrons into the LUMO. Pre-edge features (XANES) can reveal info on the coordination geometry and oxidation state of the metal. Post-edge (EXAFS) can reveal info on interatomic distances, coordination numbers and ligand types. Limitation is that a Synchrotron is required.

Q: What information on a material can one obtain using NMR Spectroscopy? What physical property is observed? What are their limitations?
A: The chemical shielding of nuclear spins is related to the local electronic environment. Since the energetic splitting is small, the sensitivity tends to be low. For inorganic materials, small gyromagnetic ratios, peak broadening due to quadrupolar interactions, as well as heterogeneity of sites reduces the sensitivity further.
The sensitivity can be significantly increased by DNP, where magnetization is transferred from exogenous polarized radicals to the surface of the investigated material. Also probe molecules (e.g. pyridine) can be used.

Q: What information on a material can one obtain using IR spectroscopy? What physical property is observed? What are their limitations?
A: The absorption of IR can be related to specific vibrational modes of the material and is particularly efficient to monitor vibrations with large dipolar moments (eg OH groups). When combined with the usage of probe molecules, IR spectroscopy can be used to investigate the (lewis) acidity of surface sites.
It is limited to molecules with a dipole moment (eg CO_2 symmetric stretch would not work).

Q: What information on a material can one obtain using scanning electron microscopy? What physical property is observed?
A: The surface of a material is scanned with a focused electron beam and either secondary or backscattered electrons are recorded. Typically provides an image of the surface topology as a 2D projection.

Q: What information on a material can one obtain using atomic force microscopy? What physical property is observed?
A: The surface is scanned with a sharp tip and the attraction/repulsion between the tip and the surface provides an image of the surface topology.

Q: What information on a material can one obtain using scanning tunneling microscopy? What physical property is observed? What are the limitations?
A: The tunneling current between a surface and a tip hovering above it is measured, providing a highly resolved image that corresponds to the local density of states of the surface (comparable to the HOMO/LUMO in molecules). STM is limited to conductive materials.

Q: Overview of the acidic and basic species that may occur at the surface of a metal oxide.
A: Pink: Metals with low coordination numbers may act as Lewis acids
Blue: Hydroxyl groups and adsorbed water can induce Brønsted acidity
Green: Nucleophilic oxygens are Brønsted bases

Q: Techniques to characterise acids and bases present on a metal surface (5)
A: 1. Calorimetry (Coupled with spectroscopy)
2. Thermal Programmed Desorption (TPD): one gradually increases the temperature of the surface and observes which species (typically probe molecules such as ammonia NH_3) are released at each temperature increment. The higher the temperature, the stronger the Lewis acid to which the species had coordinated.
3. Bellamy-Hollow-Williams Method: correlates the IR-shift of the hydroxyl groups of the metal oxide surface MO-H (\(\Delta \nu_{\mathrm{MO-H}}\)) upon adsorption of probe molecules such as ethylene, CO or pyridine with what is observed for the surface silanols in silica SiO-H as a reference.
4. Catalytic reactions
5. Probe Molecules combined with IR or NMR spectroscopy

Q: Schematic depiction of the Stern layer
A: Consists of chemisorbed water and a few subsequent physisorbed water layers
IEP: Isoelectric point -> no movement of colloids in electric field

Q: IR frequency O-H: (a) before adsorption, and at (b) 0.1, (c) 0.2, (d) 0.3, (e)1.0 mbar of CO.
Does CO interact with all three types of hydroxyl groups?
Explain the formation of the peaks at \(3660 \, \mathrm{cm^{-1}}\) and \(3280 \, \mathrm{cm^{-1}}\).
A: CO does not interact with all three types of O-H groups, the red part at \(3567 \, \mathrm{cm^{-1}}\) remains unchanged. Upon increasing \(p_{\mathrm{CO}}\), the green band disappears and a new band appears at \(3280 \, \mathrm{cm^{-1}}\). The blue band is shifted to \(3660\, \mathrm{cm^{-1}}\). The red-shift indicates that the O-H bond is weakened upon CO adsorption.

Q: IR frequency C-O stretching: (a) before adsorption, and at (b) 0.1, (c) 0.2, (d) 0.3, (e) 1.0, (f) 5.0 mbar of CO
Describe the FTIR spectrum of free CO in terms of frequency and intensity. What property of the CO band can be altered via physisorption and chemisorption respectively?
A: The IR band of free CO is at \(\approx 2143\, \mathrm{cm^{−1}}\) and has low intensity owing to the weak dipole moment of the molecule. The polarity of CO is weak because the singly occupied sp and p_z orbitals on each atom form a \(\sigma\) and \(\pi\) bond respectively. This leaves the carbon p_y orbital empty and the oxygen p_y orbital doubly occupied, allowing for a second dative \(\pi\) bond, which leads to a \(\mathrm{C}^- - \mathrm{O}^+\) polarization, that is almost exactly balanced out by the opposite polarization from electronegativity.
Physisorption, which is not accompanied with electron density transfer from or to the surface, will not affect the CO bond strength and hence the vibration frequency as well. However they display higher dipole moments, resulting in increased intensity.
Chemisorption will alter the bond strength depending on the \(\pi\) backdonation (red-shift, if not blue-shift).

Q: Draw the MO diagram of CO. What is special about the HOMO of this molecule?
A: The HOMO of CO is rather localized on carbon than on oxygen, as it has some antibonding character. This is why if there is sigma donation from CO (and not pi backdonation), then the bond contracts and is blue-shifted in the IR.

Q: How is the Point of Zero Charge (PZC) defined?
A: pH where the net charge (sum, not individual) of the surface vanishes

Q: How can the PZC be determined experimentally?
A: By potentiometric (pH) titrations of material colloids in an electrolyte solution:
1. An electrolyte solution of a given concentration is titrated twice, once without material colloids, once with material colloids. The measured pH is plotted via the used volume of acid (or base). The surface of the colloids can adsorb protons at pH values below the PZC (results in higher pH) and release protons above the PZC (results in lower pH), therefore the volume that is needed to reach a given pH depends on the presence of the colloids.
2. At any pH, the amount of protons adsorbed/released by the surface can be calculated from the difference in volume required to reach a certain pH with and without colloids in the solution. Assuming no ions other than protons in the solution that can penetrate the Stern layer, the surface charge is obtained from equation\[\sigma_0 = \frac{\Delta V c F}{A m}\]where \(\Delta V\) is the difference in the volume of acid (or base) to reach a certain pH between the blank titration and the suspension of colloids, \(c\) is the concentration of the added acid (or base), \(F\) is the Faraday constant, \(A\) is the specific surface area, and \(m\) is the mass of colloids in suspension.
3. The PZC is the pH at which the density of charge \(\sigma_0 = 0\) and the volume of acid (or base) required in the titration is independent of the presence of colloids. In principle, the PZC could therefore already be determined by comparison of the titration curves with and without colloids at a single electrolyte concentration. To increase the accuracy of the determination of the PZC, this procedure is repeated at different electrolyte concentrations. For each electrolyte concentration, a titration with and without colloids is performed and the resulting function of \(\sigma_0\) is plotted against the pH. The PZC is the point at which all these curves cross.

Q: What is the effect of the ionic strength of the suspension (electrolyte concentration) on the PZC?
A: The ionic strength should not have any effect on the PZC as it influences the amount of positively and negatively charged surfaces species equally. However, the ionic strength can influence the net surface charge of the material, when the pH is larger or smaller than the PZC:

Q: What is the Stern Layer, how does it affect the behavior of charges on the surface of a particle?
What is the difference between the PZC and the isoelectric point (IEP)?
A: The Stern Layer is a shell of multiple structured layers of water that surround a particle. The rigidity of this layer prevents large, soft ions from reaching the surface of the particle (protons are very hard and can get through). This has the effect that one observes a different PZC for the surface of the particle and for the surface of the Stern Layer. The latter pH is called the isoelectronic point (IEP). The IEP is measured by electrophoresis and defined as the pH where the electrokinetic potential of the colloids is 0. At this point, the colloids do not move in the electric field since the electromotive force on them is zero.

Q: The point of zero charge of titania generally lies in the range from 3.5 to 6.5, depending on the preparation method. At which pH would you operate to deposit platinum on the titania surface using hexachloroplatinic acid (\(\ce{H2[PtCl6]}\))? Which pH would you use for tetraamine platinum(II) chloride (\(\ce{[Pt(NH3)4]Cl2}\))?
A: The surface of the particles in the solution is positively charged at a pH below the PZC, and negatively charged at a pH above the PZC. Thus, at a pH below the PZC, the surface attracts anions and at a pH above the PZC, it attracts cations. Platinum deposition on \(\ce{TiO2}\) should hence be done at \(pH < 3.5\) for \(\ce{[PtCl6]^{2−}}\) and at \(pH > 6.5\) for \(\ce{[Pt(NH3)4]^{2+}}\).

Q: The PZC of maple sawdust (4.72±0.06), wood ash (9.50±0.07), and brown algae (6.06±0.11) were determined. Which of these materials would you study to treat water contaminated with \(\ce{Hg^{2+}}\)?
A: To adsorb positively charged metal cations, the material should have a net negative surface charge at neutral pH. Thus the PZC should be <7. Out of the three materials, maple sawdust has the lowest PZC and is thus the most promising material for this application.

Q: Density of charges on a surface
A: \[\sigma_0 = \frac{F}{A}(\ce{[M-OH2+]}-\ce{[M-O-]})\]Typical values are in the range of \(\pm 100-200 \, \mathrm{\mu C\, m^{-2}}\)

Q: BJH Theory
A: BJH: Barrett, Joyner, Halenda
- used to determine the pore size distribution of a material
- the vapour pressure inside a pore depends on the radius of the pore -> relation is given for cylindrical pores by the Kelvin equation
- the smaller the pore the lower the condensation pressure
- pressure is lowered stepwise
- in each step the radius for the pores that undergo capillary evaporation can be calculated using the Kelvin equation
- volume that is desorbed in that step can therefore be correlated to the number of pores with that specific radius
Problem: there are two distinct mechanisms of adsorption
- Capillary condesation in the pores (aforementioned)
- physical multilayer adsorption on the pore walls
- if the pressure is lowered-> measured amount of released volume also includes contributions from the reduction of the thickness of the physically adsorbed layer -> need to introduce a correction term in the Kelvin equation
- BJH model has the same limitations for high and low pressure as BET therory

Q: Kelvin equation
A: \(\ln \left( \frac{p}{p_0} \right )= \frac{2\gamma V_l}{r_kRT}\)
\(V_l: \) molar volume
\(\gamma: \) surface tension
\(r_k\): pore radius

Q: Photoelectric effect
A: - X-Ray photon interacts wih a tightly bound orbital electron (K,L,M shells) and transfers all of its energy to this electron
- the photon "dissapears" and  a photoelectron is ejected from one of the shells of the atom
- kinetic energy of the ejected photon is equal to the photon energy minus the binding energy of the electron: \(E_{kin} =h\nu-E_b\)
- The resulting excited state is not stable and decays either via the emission of characteristic X-rays (fluorescence) or emission of an Auger electron

Q: Mössbauer spectroscopy
A: - uses \(\gamma\)-rays to probe a material
- Gives Information about: structural environment, oxidation state and coordination number of a metal
- Disadvantages: limited to a small number of elements (e.g. Fe,Sn)

Q: XPS (X-ray photoelectron spectroscopy)
A: - analyzes the kinetic energy of the emitted photoelectron \(E_{kin}\)
- element and oxidation state specific
- gives composition of matter
- core binding energies \(E_{bin}\) depend on the element as well as the short-ranged chemical environment of the atom -> results in a chemical shift of the kinetic energies of the photon electrons
- surface sensitive technique -> electrons travel only a few nanometers in solids -> depth that is probed depends on the material
- depth profiles can be obtained by varying the incident photon energy with a tunable X-ray source -> e.g at synchrotron or by varying the detection angle

Braggs law

Q: Debeye-Scherrer equation
A: - estimates the size of crystalline domains \(\tau\) in a sample from its XRD pattern
k: shape factor
\(\lambda:\) X-ray wavelength
\(\theta:\) diffraction angle of the peak
Limitations:
- particles are assumed to be spherical and crystalline: fails for small radii -> degree of crystallinity and regularity of shape tend to be harder to control
- neglects polydispersity of size distribution by assuming the FWHM arieses from the mean size (i.e larger and smaller grains counterbalance each other)

Q: XAS spectrum parts
A: XANES:
- near-edge spectroscopy at x-ray energies before and at the adsorption edge
- gives info about: coordination geometry, oxidation state of the metal
EXAFS:
- x-ray energies above the adsorption edge
- here: ejected photoelectrons carry significant kinetic energy
- shows typically oscillations -> result from interference phenomena between the outgoing photoelectron wave and components of backscattered waves from neighboring atoms in the material
- gives info about: interatomic distances, coordination number, ligand types

Q: AFM
A: - Atomic force microscopy
- based on the mechanical interaction between the surface of the specimen and a sharp tip
- attraction and repulsion between tip and surface gives an image of the surface topology with atomic resolution
tip is connected to a cantilever, whose vertical displacements are measured with a laser beam and an optical detector
- the lateral resolution depends on the sharpness of the tip -> should be as sharp as possible
Static mode:
- tip is either in contact with the surface or close above
- rendering a stable distance between tip and specimen that is required for high resolution rather difficult
Dynamic mode:
- cantilever oscillates with its resonance frequency
- the tip-specimen interaction changes the amplitude, phase or frequency of the oscillation
- allows higher resolution than static mode
Increase in resolution by a factor of 2 or 3 by binding CO to atom on tip via coordination chemistry (works like a needle)