Advanced Characterization methods
- Administration (syllabus, grading , etc.)
Syllabus:
Overview of course
Error analysis
Spectroscopy
Underlying physics – characterization of energy transitions in materials
Optical (absorption and emission, Raman, time dependent)
XPS,
NMR, EPR
Electrochemical
Scattering/diffraction
Fundamental idea – structure determination through scatter of radiation or particles
Optical
X-ray, neutron, electron
Fractionation
Separation of complex mixture according to specific quantity, followed by detection
Mass spec
Chromatography
Imaging
Optical (transmission, fluorescence, confocal, TP)
Electron microscopy (SEM, TEM, STM)
AFM & variations
Direct
Direct measurement of quantity
Electrical
Magnetic
Thermal
Date / Topic / Assignment10/20 / Intro, error analysis
10/21 / Lab – fluorescence spectroscopy / Lab notebook
10/22 / Optical spectroscopy
10/24 / Optical spectroscopy / Choose presentation topic
10/27 / Surface spectroscopy (XPS)
10/28 / Lab – XPS
10/29 / NMR
10/31 / EPR, EC, etc. / 1st homework
11/03 / Intro to scattering/diffraction, XRD
11/04 / Lab – EC detection
11/05 / XRD, E-diffraction, neutron
11/07 / Intro to imaging, optical / 1st lab due
11/10 / Electron microscopy
11/11 / Lab-DLS
11/12 / Scanning probe microscopy / 2nd homework
11/14 / Fractionation – MS
11/17 / Mid-term exam
11/18 / Lab – SEM
11/19 / Chromatography
11/21 / Chromatography, cont.
11/24 / Direct measurements – electrical
11/25 / Lab – AFM
11/26 / Magnetic, thermal / 3rd homework
11/28 / Thanksgiving holiday
12/01 / Elemental analysis
12/02 / No lab – oral presentations
12/03 / On-line vs. lab-based / 2nd lab due
12/05
Grading
Labs – 6 labs, notebooks should be kept, two lab reports, will not know beforehand which ones. One report technical, the other less technical. 20%
Three homeworks 15%
One mid term exam 15%
One topic for presentation – three types of presentation (15-30 second, 2-3 minute, 10-15 minute) 15 %
Final 20%
Integrative experience 15%
2. Overview of course
More of a survey course – not in much depth about specific techniques, but will cover a lot of ground
However, will still explore underlying physics of general classes of technique (spectroscopy, scattering) as well as specific examples in some detail
Techniques will be described in terms of:
What exactly is being measured?
What is the underlying physics of the method?
How is the raw data analyzed, what is the end result (after analysis)?
What are the assumptions being made in both the measurement and analysis?
What sample preparation is needed?
What are the (dis)advantages compared to other techniques?
What are the limitations?
Characterization methods may be for determination of:
Composition
Structure
Process
Specific properties (thermal, electrical, etc.)
Can subdivide the course accordingly, but from the underlying physics, this doesn’t make mush sense (and often hard to separate, many techniques cover more than one)
The course will be divided according to some underlying principle of the method, in particular, we’ll cover the following
1. Spectroscopy – dispersion, energy resonant processes, e.g. optical absorption & fluorescence, NMR, ESR, XPS, SIMS, Auger, DSC, rheology.
2. Scattering and diffraction – interaction of radiation with material, not energy dispersion, but relating output to some structure or composition, X-ray, light scattering, electron, neutron diffraction.
3. Fractionation – Subdivide the sample according to some physical property, e.g., mass spec, GC, GPC, HPLC, electrophoresis.
4. Imaging – Create visual representation of some property – optical microscopy, TEM, SEM ,scanning probe.
5. Specific properties & other – electrical, mechanical, BET.
6. Process – measurement of something that changes with some reaction of system, generally more empirical.
For the specific properties, the analysis is straightforward. For example, in a measurement of electrical conductivity the current response to an applied voltage is measured. The assumptions and analysis may need to consider the relation between the actual response we measure (needle deflection) to the underlying quantity.
For others, we are using some raw data to infer other characteristics, which is likely to require both more analysis as well as assumptions about the underlying physics. For example, X-ray diffraction itself might be interesting but the main purpose is to reveal underlying crystal structure.
3. Spectroscopy (spectrometry) – material response vs. input energy
Materials have some energy response determined by composition and structure – the location and strength of these will be unique to the particular sample. Spectroscopy deals with looking at this dependence by applying some energy to a system and looking at the response as a function of this energy.
A. Optical – input is in the form of EM radiation, change in the energy is a change in the photon energy, i.e., the frequency or wavelength (not the irradiance).
Absorption
UV-VIS
IR, FTIR
Emission
Fluorescence
Interaction
Raman
Variations
Nonlinear
Time dependent
Combinations
Background
Interactions of EM radiation with matter
Photons can be absorbed and emitted, but also interact non-resonantly (scatter – all optical interaction with matter can be described in terms of scattering).
Semiclassically, the optical electric field of the radiation interacts with the charges in the material. For now, we consider the interaction with the electrons, although this can easily be generalized. Interaction with the electrons is the main one for optical properties in the ultraviolet and visible. Macroscopically and to first order, the complex polarization vector is the key quantity. Usually, the electric dipole approximation is invoked, which says that the important interaction between material and radiation is simply the interaction of a dipole with the field. The term in the Hamiltonian is
This is often much weaker than other effects and can be calculated with perturbation theory. The term that comes out of this is the matrix element of r, which is proportional to the transition dipole moment
Note that this is not the (permanent) dipole moment of the ground state – this is a dipole moment of the transition itself. On the macro scale, this is the difference between a permanent and induced polarization.
How is this connected to absorption?
We can wave our hands and use the following argument. The applied (optical) electric field induces a dipole. The energy of the dipole will be proportional to the square of the polarization and so the square of the dipole moment. So energy remove from the beam (& given to the dipole) is proportional to the square of the dipole moment as defined above. The irradiance of the incident beam is the energy per cross sectional area per time, so the absorption (change in this energy per unit cross section) will also be proportional to the square of the dipole moment.
The propagation of EM radiation through material can be characterized by the complex refractive index. The real part is the “usual” refractive index that relates to the speed of light in the material. The complex part is related to the absorption. The infinitesimal change in irradiance is
This equation tells us that the relative change will be proportional to a constant () and the infinitesimal distance the beam travels. Solving it gives
(Beer’s law)
Where L is the distance traveled through the medium.
Often we want an absorption per unit concentration of the absorbing species. Also, logs to base 10 are more practical for applications. The molar extinction coefficient is defined as
where C is the concentration, usually molar (short aside on molar concentrations if needed). The corresponding equation for the irradiance is
{Note – be careful about the use of and , since they are defined by different people different ways. Chemists usually use to be absorption coefficient divided by the concentration, and occasionally is used with the natural log instead of the base 10 log.}
The exponent is the Absorbance, or Optical Density of the sample, and is a unitless quantity.
As we’ll see later, most transitions are not narrow lines, but rather broad peaks. A typical absorption peak in the visible looks like (OHP)
in other words, the absorption coefficient is some function of frequency or wavelength. An integrated absorption coefficient can be defined as
where is the frequency. A unitless quantity called the oscillator strength can be defined as
where me is the electron mass, c is the speed of light, 0 is the free space permittivity, L is the path length and e is the electron charge. Finally, one can show that the relation to the dipole moment defined earlier is
for a transition between states n and m.
The transition dipole moment leads to selection rules for optical transitions. If the symmetry of the initial and final states are the same, the transition dipole moment will be zero, and so there will be no interaction with the field. This results in a so-called forbidden transition – in more intuitive terms, transitions are forbidden when charge distribution of ground and excited states does not change symmetry
A forbidden transition will have orders of magnitude weaker absorption than an allowed one.
Why weak and not completely gone?
- have neglected other parts of wave function (nuclear) – remove symmetry – e.g. spin-orbit coupling allowing triplet state excitation
- have used the dipole approximation – higher order terms may allow transition, but are weaker
In semiconductor and insulating crystals, the picture is similar. If the bottom of the conduction band and the top of the valence band are at different values of k, optical absorption or emission can only occur with the absorption or emission of a phonon, in a so-called indirect transition. This can be much weaker, in particular for emission.
Einstein A, B coefficients (detailed derivation will come next semester)
The rate of stimulated emission will be proportional to the input irradiance. The coefficient of proportionality is called the Einstein B-coefficient. The rate of spontaneous emission is constant for an excited state and is referred to the Einstein A-coefficient. These two are not independent, one can use energy conservation to find that
Fate of excited states (OHP)
1. Luminescence
2. Inter- and Intra-molecular transfer
3. Quenching
4. Ionization
5. Isomerization
6. Dissociation
7. Direct reaction or charge transfer
We’ll talk more about these when we come to fluorescence emission spectroscopy.
Absorption spectroscopy
UV-VIS-NIR – UV radiation technically runs from about 10 nm (~100 eV) to about 390 nm (~3.2 eV), but most absorption spectroscopy is done in the lower end of energy, in the wavelength range 180 to 390 nm. Visible is defined as between 390 and 780 nm. Infrared is separated into three regions: NIR (780 nm to 3.0 microns) MIR (3.6-6.0 microns) FIR (6 to 15 microns). Sometimes an additional region called the extreme IR is defined (15 to 1 mm) but recently this has received more attention as the so-called THz region.
UV-VIS are usually grouped together because they involve transitions in the outer shell electrons. Not only are these important for identifying materials (composition) but are much more sensitive to surrounding changes such as bonding (structure). Infrared spectroscopy usually involves transitions between vibrational states, with energies corresponding to wavelength ranges from 800 nm to several microns.
UV-VIS – broad, often featureless, so not useful for identification of composition. More likely to be used for process control or as basic property – where something absorbs. Visual aspect of application, e.g., paper, colorants. Photometric titration.
Time scales (excited state lifetimes) – 10-11 to 10-8 sec
Causes of nonzero peak widths:
1. Intrinsic (lifetime, natural) broadening (uncertainty principle – in excited state for finite time, so the specification of it cannot be arbitrarily precise).
2. Vibrational and rotational sublevels
3. Doppler broadening – Doppler shifts due to motion of scatterers, direction and speed are distributions, so shifts have cumulative effect of broadening
4. Interactions with surroundings
Pressure (collisional) broadening – collisions with other scatterers induce shifts in frequency
Interactions with solvent – similar to pressure
Most of this discussion has been relevant to atomic and molecular spectra. Similar effects are also present in bulk materials such as semiconductors. In this case, it is often difficult to measure transmission spectra, so reflection spectra can be taken instead. These will probe the surface of the sample.
In ATR = Attenuated Total Reflection spectroscopy, the sample is in contact with a prism. Light is incident on the sample through the prism, where it is reflected at the prism/sample interface. At this interface, the light penetrates into the sample, even for total reflection. At absorbing wavelengths, this removes energy from the beam, which is measured in the output (reflected) beam spectrum.
Practical application
Spectrometers (spectrophotometers) – dispersive (moving, diode array), FT
Broadband sources, usually cw
Deuterium – UV
Tungsten – Vis
Xe – both
heater (blackbody) – IR
Detectors
PMTs
Photodiodes (arrays)
For UV-VIS, two calibrations are usually required – dark and reference. The dark removes the baseline signal from ambient light, detector noise or electronic offset, and the reference determines the I0 term in Beer’s law. This includes the spectral input of the source, any absorption by the cuvette and solvent, and the spectral response of the detector.
FT spectrometers
Instead of dispersive (either many detectors or moving grating, prism) all light from a broadband source is used. In absorption spectrometers, this is sent through an interferometer (usually Michelson). Changing the length of one of the interferometers arms modulates the output and creates a Fourier transform of the input light.
(see handout)
In an FTIR, this is used to modulate the input broadband IR source. The output in the FT of the source, with the displacement of the arm being the FT variable. This is sent through the material, and the output is FT’ed to give the transmitted light, and then the spectrum is determined.
IR absorption
The energy of photons in the IR region corresponds mostly to transitions between vibrational and rotational states in materials. The optical absorption bands for these transitions are much narrower than typical ones in UV-VIS spectroscopy, and so are much more useful for identification of the constituents of a sample.
The basic physics underlying these bands is easily understood at a simple level using the mass and spring model. The response of a system of masses attached by springs will depend on the excitation (initial conditions), the masses and the spring constants. In this case, the masses are the atoms and the springs the bonds, so the IR spectrum will uniquely determine the constituents and bonds between them, i.e., the molecules in the sample. Since calculation from first principles is difficult/time consuming, most analysis is empirical – bands of known compounds or functional groups have been measured and categorized in the literature.
(OHPs– energy levels, typical IR spectra)
Solid samples: powder samples are usually pressed in KBr pellets – these give very IR transparent samples with little scattering.
Liquids: Cells are usually very narrow, since IR absorption coefficients are generally high. Sodium chloride is a typical material for the cell windows, since it has good transparency in the IR.
Most current IR absorption spectrometers are of the FT type.
(Handout)
There are many advantages to FT-type spectrometers, the main one being that all the light transmitted through the sample is measured by the detector.
Raman Spectroscopy
IR spectra have similar selection rules as for optical spectroscopy – this means that many bands can not be measured with usual IR absorption. Raman spectroscopy (scattering) offers a way around this - since the interactions involve more than one photon, the selection rules are different than in standard absorption spectroscopy. Raman spectroscopy also has the useful advantage of much fewer problems due to water than IR spectroscopy (water gives a large broad signal conventional IR spectroscopy, which can hide other lines of interest).
The Raman effect is a parametric effect in which a photon is “absorbed” and re-emitted, with the energy difference being taken up by or released from a vibrational state of the material. When the final state has higher energy than the initial, the results are the so-called Stokes lines, when the final state has lower energy, they are the anti-Stokes lines. The Stokes lines arise from the final state being a higher vibrational state of the ground state manifold, the anti-Stokes line occurs when the initial state is one of these and the final state a lower energy vibrational level or the ground state. Since these rely on a finite population in these vibrational levels, they are generally much weaker and also temperature dependent.
X-ray absorption. The absorption of higher energy photons, in the X-ray region, usually causes transitions involving inner shell electrons, which are less affected by environment. This can give elemental information, rather than molecular. These electrons are generally ejected from the atom. (OHP of typical spectrum).
Appearance of X-ray absorption – now kinetic energy of electrons released plays a role – the edges are sharp with tails as more KE is given to the electrons.
The absorption can be measured in the usual way, or by monitoring the resulting fluorescence.
The measurement of the emitted electrons constitutes XPS – more on this later.
Photoluminescence
There are a number of possible fates of the excited state atom or molecule in terms of how it loses its energy, usually decaying back to the ground state. We can broadly divide these into two groups of transitions: radiative and non-radiative, depending on whether or not a photon is emitted in the process. (OHP)
The emission of photons in the UV-VIS range is referred to generally as luminescence. When the excitation is by a photon, the process is called photoluminescence (general term) or fluorescence/phosphorescence, depending on the state the emission comes from (and the time scale of the decay). Other processes can excite the material which then emits photons, for example chemical processes (chemiluminescence) biological (bioluminescence), electron injection (electroluminescence), etc.
The spin multiplicity of a state, defined as 2S+1, can yield information on the probability of a radiative transition. The usual stable (lowest energy) state is one where the electron spins are paired, S=0 and the multiplicity 2S+1=1 – this is termed the singlet state. When two electrons are unpaired, S=1, 2S+1=3 and the state is called a triplet state. The ordering of the state in energy is often added as a subscript, i.e., ground state S0, 1st excited singlet state S1, etc. Triplet states start at T1 being the lowest energy triplet state. The T1 state is lower in energy that S1.