CE70009 - Product Characterisation Flashcards
How do monochromatic and polychromatic and polarized light differ?
Mono - one wavelength
Poly - multiple wavelengths
Polarised - waves all in one direction
What’s collimated light?
When light rays are parallel to each other
What’s coherent light?
When there is no interference between waves
List key parts of transmission microscope:
Ocular / eyepiece
Objective lens
Stage
Condenser lens
Condenser diaphragm
Focusing knobs
How is numerical aperture, NA, calculated?
NA = nsinØ
n = refractive index of medium in which lens is working, = 1.0 for air, 1.33 for water, and up to 1.56 for oils
How does resolution, light transmission, working distance, and depth of field vary with numerical aperture, NA?
Resolution increases with NA
Light transmission decreases with NA
Working distance decreases with NA
Depth of field decreases with NA
What is bright and dark field illumination?
Bright field microscopes usually have halogen lamp or LED light sources. This type of microscope tends to have low contrast owning to the biological samples transmitting most of the light. Staining if often required to combat this problem, which comes with the disadvantage that live imaging is difficult due to staining killing the cells.
Dark field microscopy is generally preferred therefore over light field. With a dark field microscope a special aperture is used to focus incident light meaning the background stays dark. The light does not pass directly through the sample being studied. Instead light is reflected off the specimen, making it appear to be emitting light. Brightfield microscopy shows clear magnification while the dark field image shows minute details.
Bright field – sample is dark while background is bright
Dark field: sample is bright while background is dark. Light is shone from top and we look at the light that is reflected back. Hollow cone of light with great obliquity. no transmission: reflection or scattering
What’s confocal microscopy?
An optical imaging technique for increasing optical resolution and contrast of a micrograph by means of using a spatial pinhole to block out-of-focus light in image formation.
Confocal microscopy offers several advantages over conventional optical microscopy, including shallow depth of field, elimination of out-of-focus glare, and the ability to collect serial optical sections from thick specimens. In the biomedical sciences, a major application of confocal microscopy involves imaging either fixed or living cells and tissues that have usually been labelled with one or more fluorescent probes.
When fluorescent specimens are imaged using a conventional widefield optical microscope, secondary fluorescence emitted by the specimen that appears away from the region of interest often interferes with the resolution of those features that are in focus. This situation is especially problematic for specimens having a thickness greater than about 2 micrometers. The confocal imaging approach provides a marginal improvement in both axial and lateral resolution, but it is the ability of the instrument to exclude from the image the “out-of focus” flare that occurs in thick fluorescently labelled specimens, which has caused the recent explosion in popularity of the technique.
In confocal microscopy a pinhole is used in the focal plane both at illumination and at detection.
In this way out of focus emitted light is effectively rejected by the detection pinhole and an increased resolution is obtained .
How does a TEM (transmission electron microscope) work?
• Gun emits electrons
• Electric field accelerates
• Magnetic (and electric) field control path of electrons
• Electron wavelength @ 200KeV = 2x10-12 m
• Resolution normally achievable @ 200KeV = 2 x 10-10 m = 2Å
• High Vacuum
The sample will appear dark. Shadowing technique.
Very thin sample required
How is the wavelength of electrons determined?
By accelerating voltage (V) on the filament from which they were emitted.
Wavelength = 0.1*(150/V)^0.5
Very high voltages (~100kV) required.
Why is high vacuum needed in TEM?
For transmission electron microscopy, vacuum needed as the mean free path of electrons is very short in air.
High vacuum of 10^-5 mbar aimed for.
Also
- tungsten filaments burn out in air
- columns must be kept dust free
The vacuum is achieved via pumps
What is SEM (scanning electron microscopy) used for?
• Topography and morphology
• Chemistry
• Crystallography
• Orientation of grains
• In-situ experiments:
– Reactions with atmosphere
– Effects of temperature
In brief: we shoot high-energy electrons and analyze the outcoming electrons/x-rays
• A SEM typically has orders of magnitude better depth of focus than a optical microscope making SEM suitable for studying rough surfaces
• The higher magnification, the lower depth of focus
What are issues with SEM?
Needs to be conducted in vacuum.
Samples need to be dry.
If electrons get absorbed by the sample, the surface becomes negative and repels further electrons. So, the sample should be coated with a conductor e.g. gold.
What is STM?
How does it work?
Scanning tunnelling microscopy
A scanning tunnelling microscope (STM) is an instrument for imaging surfaces at the atomic level.
The STM is based on the concept of quantum tunnelling. When a conducting tip is brought very near to the surface to be examined,
a voltage difference applied between the two can allow electrons to tunnel through the vacuum between them. The resulting tunnelling current is a function of tip position, applied voltage, Information is acquired by monitoring the current as the tip’s position scans across the surface, and is usually displayed in image form.
STM can be a challenging technique, as it requires extremely clean and stable surfaces, sharp tips, excellent vibration control, and sophisticated electronics.
STM requires a conducting material to tunnel.
What is AFM?
How does it work?
Atomic force microscopy
AFM consists of scanning a sample with a probe mounted on a cantilever and determining the surface topography from the deflection of laser light on the probe with a position sensitive detector.
The tip (or the sample) is positioned using an extremely precise piezo-electric unit, reaching Å resolution (in x,y,z).
The probe-sample interactions, which flex the cantilever, are repulsive at short distances. The tip can either be in permanent contact with the sample – contact mode –, or oscillating at its resonance frequency (~100 kHz), tapping briefly the sample – tapping mode.
Further, a feedback mechanism keeps the oscillating amplitude constant.
What are issues with AFM (atomic force microscopy)?
As the sharp point moves along the surface of the sample, if the sample is soft, the point may cause the sample surface to deform.
AFM may then detect what is under the surface instead of the surface itself.
What are 3 common types of scattering techniques to identify particle size?
Light scattering
X-ray scattering
Neutron scattering
What are the issues with scattering?
You can’t identify the structure inherently from the scatter / crystal pattern. Estimates and guesses must be made.
What are the 4 outcomes of shining a light on a substance?
Reflection
Transmission (passing through)
Absorption
Scattering
What is the key law of reflection?
Angle of incidence = angle of reflectiom
What is snells law?
Snells law calculates n, the refractive index
Sin (i) / Sin (r) = n
Where I and r are angle if incidence and refraction
What does the Beer-Lambert law for absorption show?
The Beer-Lambert Law (also called Beer’s Law) is a relationship between the attenuation of light through a substance and the properties of that substance.
A = ƐlC
A - absorbance
Ɛ - molar absorptivity
l - length of light path
c - concentration
What is constructive and destructive interference?
Constructive - waves in phase amplify each each other
Destructive - waves out of phase cancel each other out
What is the condition for constructive interference?
n * λ= 2 d sin (Ø /2)
Bragg equation
Where:
λ - wavelength
d - spacing between crystal lattice planes
What is reciprocal space?
Reciprocal space (also called k-space) provides a way to visualize the results of the Fourier transform of a spatial function.
It’s a mathematical space that represents spatial frequencies rather than physical positions.
In scattering, what is q?
q is the distance of the scattered light,
q = 4piSinø / lambda
Where ø is the angle made by scattering, lambda is the light wavelength
Also,
q = |ks| - |ki|
Where:
ks - scattered beam wave vector
ki - incident beam wave vector
What is the intensity of coherently, elastically scattered radiation dependant on?
I(q) = N(delta*density * V)^2 * P(q)S(q)
N = molecules/unit volume
V = molecular volume
P(q) = form factor / particle shape
S(q) = structure factor / inter-particle correlation distances
Delta mean density = density (r)- density s = the scattering density difference between the scattering particle and solvent
What do form factor, P, and structure factor, S, represent?
P - particle shape
S - inter-particle correlation distances
Scattering measures both S+P in ‘reciprocal’ space
What is the relationship between q and d?
small q ~ large d [large q ~ small d]
small lambda ~ large q ~ small d
Where:
q - the magnitude of the scattering vector
d - particle diameter
lambda - wavelength
To summarize:
A larger q often corresponds to smaller structural features or finer details within the sample.
Smaller wavelengths (λ) typically lead to larger q values in scattering experiments, enabling the investigation of smaller structural elements.
What is Rayleigh scattering?
Rayleigh scattering is the elastic scattering of light by molecules and particles much smaller than the wavelength of the incident light.
Rayleigh scattering intensity has a very strong dependence on the size of the particles (it is proportional the sixth power of their diameter). It is inversely proportional to the fourth power of the wavelength of light, which means that the shorter wavelength in visible white light (violet and blue) are scattered stronger than the longer wavelengths toward the red end of the visible spectrum.
This type of scattering is therefore responsible for the blue colour of the sky during the day and the orange colours during
sunrise and sunset.
What are the limits to Rayleigh scattering?
Rayleigh scattering only works for particles less than lambda/10, so microemulsions, nanoparticles and polymers can be sized in this way, note though the very strong dependence on d, so experiments are seriously effected by very small amounts of dust.
What is low angle scattering?
Small-angle scattering (SAS) is a technique based on deflection of collimated radiation away from the straight trajectory after it interacts with structures much larger than the wavelength of the radiation.
The deflection is small (0.1-10°) hence the name small-angle.
For particles larger than the wavelength of light, the light scatters from the edge of the particle at an angle which is dependent on the size of the particle.
Larger particles scatter light at relatively smaller angles than light scattered from smaller particles. From observing the intensity of light scattered at different angles, we can determine the relative amounts of different size particles.
As the particles get close to or smaller than the wavelength of light, more of the light intensity is scattered to higher angles and back-scattered.
What is the most suitable method to determine particle size from light scattering measurements?
Fraunhofer diffraction is the simplest method of determining particle size from light scattering measurements. It applies to particles larger than approximately one micron.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer condition) from the object (in the far-field region), and also when it is viewed at the focal plane of an imaging lens.
What scattering technique do we use for particles in solution between 1 micron and 50 nm?
Dynamic light scattering
What is dynamic light scattering?
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. (Useful for particles between 50 nm and 1 um)
When in solution, macromolecules are buffeted by the solvent molecules. This leads to a random motion of the molecules called Brownian motion.
As light scatters from the moving macromolecules, this motion imparts a randomness to the phase of the scattered light, such that when the scattered light from two or more particles is added together, there will be a changing destructive or constructive interference. This leads to time-dependent fluctuations in the intensity of the scattered light.
In a QELS (Dynamic Light Scattering) measurement, the time-dependent fluctuations in the scattered light are measured by a fast photon counter. The fluctuations are directly related to the rate of diffusion of the molecule through the solvent. Therefore, the fluctuations can be analyzed to determine a hydrodynamic radius for the sample
The smaller the particles, the faster the fluctuations.
(QELS = Quasi Elastic Light Scattering aka photon correlation spectroscopy)
What is PCS?
Photon correlation spectroscopy
How is gamma related to the magnitude of scattering vector, q?
Γ can be converted to the diffusion constant D for the particle via the relation:
D=Γ/q^2
Where:
Γ - decay rate
q - magnitude of scattering vector
D - diffusion constant
What is q in scattering measurement techniques?
The magnitude of the scattering vector
What are problems with light scattering?
• Only works for single particle scattering, multiple scattering much harder to analyse, thus only works for very dilute suspensions.
• Apart from DLS only relatively large particles can be studied, no information about the nature of particles or their structure can be obtained.
• To go smaller or to investigate smaller features we need to use light of shorter wavelength, such as X-rays or neutrons
How does refractive index effect how we see objects?
Seeing objects requires a difference in refractive index between the object and its surroundings
n (air) ~ 1
n (water) ~ 1.33
n (glass) ~ 1.50
n (toluene) ~ 1.49
Glass beads:
• nearly disappear in toluene
• best visible in air.
Any radiation can be used in the same way as light to “see”. The requirement is a difference between the way the radiation interacts with the atoms and molecules in the object and its surroundings, i.e. CONTRAST.
Explain the fundamentals of neutrons:
• Neutrons have zero charge and negligible electric dipole and therefore interact with matter via nuclear forces (to do with nucleus of atom)
• Nuclear forces are very short range (a few fermis, where 1 fermi = 10-15 m) and the sizes of nuclei are typically 100,000 smaller than the distances between them.
• Neutrons can therefore travel long distances in material without being scattered or absorbed, i.e. they are and highly penetrating (to depths of 0.1-0.01 m).
• Example: attenuation of low energy neutrons by Al is ~1%/mm compared to >99%/mm for x-rays
• They have amplitude and phase
• They can be scattered elastically or inelastically
What happens in elastic scattering?
Elastic scattering changes direction but not the magnitude of the wave vector.
Inelastic scattering changes both direction and magnitude of the neutron wave vector.
It is the elastic, coherent scattering of neutrons that gives rise to small-angle scattering
How is the scattering cross section of an atom found?
The scattering cross section of an atom, σ (sigma)
σ = 4πb^2
Where b is the scattering length of the nucleus and measures the strength of the neutron-nucleus interaction.
..as if b were the radius of the nucleus as seen by the neutron.
How is scattering length of a nucleus, b, found?
• For some nuclei, b depends upon the energy of the incident neutrons because compound nuclei with energies close to those of excited nuclear states are formed during the scattering process.
• This resonance phenomenon gives rise to imaginary components of b. The real part of b gives rise to scattering, the imaginary part to absorption.
• b has to be determined experimentally for each nucleus and cannot be calculated reliably from fundamental constants.
How do isotopes affect neutron scattering lengths?
Neutron scattering lengths for isotopes of the same element can have very different neutron scattering properties.
This is NOT the case for light scattering.
How is scattering length density found?
The average scattering length density rho for a particle is simply the sum of the scattering lengths (b)/unit volume
What is contrast (or solvent) matching?
Matching the scattering density of a molecule with the solvent.
This facilitates the study of one component by rendering the other as “invisible”
What’s DLS?
Dynamic light scattering
What particle sizes is light microscopy suitable for?
Around 100 nm. Visible light range.
What particle size is electron microscopy suitable for?
Around 0.1 nm. Atomic level.
Why is Fourier transformation required?
The Fourier transform is central in scattering. In scattering, an incident wave travels through a sample. All of the entities in the sample act as scattering sources, giving rise to secondary waves that interfere with one another.
The transform inverts the units of the input variable. For instance, when the input stream represents time, the Fourier space will represent frequency (1/time).
What is numerical aperture?
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.
Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective.
What is resolution?
In microscopy, the term “resolution” is used to describe the ability of a microscope to distinguish details of a specimen or sample.
In other words, the minimum distance between 2 distinct points of a specimen where they can still be seen by the observer or microscope camera as separate entities.
Compare AFM and STM (atomic force and scanning tunnelling microscopy)
AFM:
- Works in liquid and gas conditions
- The AFM works on the interaction forces between the tip and the sample surface.
- AFM can image both conductive and non- conductive samples.
- Sub-nanometer resolution in all modes
STM:
- Only works in high vacuum
- STM is a sort of microscopy that scans the surface of a sample using a conductive tip.
- Only images conductive samples.
- Atomic resolution
AFM has a higher topographic contrast, direct height measurement, and superior surface characteristics than STM.
AFM can offer data on a sample’s physical and mechanical properties, such as height, roughness, and elasticity. STM can provide data on a sample’s electronic properties, such as conductivity and electronic structure.
How do displays in real space and reciprocal space vary?
Real space is where the substance’s atoms actually are. Reciprocal space shows the diffraction pattern from the atoms, which may not change in accordance with changes in real space.
E.g. if atoms get closer together, the constructive pattern of the diffracted waves get further apart.
How is hydrodynamic radius (effective radius of an ion in a solution measured by assuming that it is a body moving through the solution and resisted by the solution’s viscosity) calculated?
rh = kT/6πηD
Where:
k is Boltzmann’s constant
T is the temperature in K
η is the solvent viscosity.
rh is hydro’ radius
D is diffusion constant
What does contrast refer to in microscopy?
The difference in scattering length density between particles and solvent
What is spectroscopy?
The study of matter using electromagnetic radiation.
What is Planck’s equation?
What does it show?
E = hv = hc/λ = hcv*
Where E is the energy of a particle of light (photon), v is its frequency, and h is Planck’s constant.
c is speed of light and λ is wavelength.
The wave number is represented by the Greek letter nu (ν) with a tilde over it. Here, it is written as v*
What’s vibrational spectroscopy?
A method of measuring molecular vibrations
What conditions are necessary for exchanges (emission and absorption) to occur between light and matter?
The energy of absorbed radiation must exactly match that of a transition in an atom or molecule.
If the frequency of absorbed radiation exactly matches the frequency of vibration of a functional group in a molecule, the emitted wave is reduced in amplitude. This is due to IR absorption.
What happens when IR is absorbed by a chemical bond?
The bond will experience a jump / increase in energy (in eV).
The amplitude of the vibrations of the chemical bonds will increase. Amplitude of vibration changes, not frequency.
Note - if the bond was not vibrating in the first place, there would be no interaction between the bond and the IR waves.
Define IR spectrum:
A representation of what electromagnetic radiation is absorbed or emitted by a sample
What are the regions of the IR spectrum?
Near IR (near to visible): 14000 - 4000 /cm Overtones and harmonics
Mid IR: 4000 - 400 /cm Molecular vibrations
Far IR: 400 - 10 /cm Rotations / low energy vibrations
How is the energy of a harmonic oscillator calculated? (Simple solution to Schrodinger wave equation)
E = (v+0.5)hv’
v’ = (1/2π)*(k/m)^0.5
Where:
E - energy of the state corresponding to integer v
v - quantum number (integer)
ν’ - frequency
h - planck constant
k - spring/force constant
m - mass
In equation 2, v may be replaced by v* (wave number), becoming (1/2πc)*(k/m)^0.5.
Mass may be replaced by mu. ((mu = (m1m2)/(m1+m2))
What is the vibrational selection rule / rule for quantum number jumps?
For harmonic oscillators, Δv = +/- 1
Jump in only 1 neighbouring energy level can be made at once.
What is μ in spectroscopy?
μ = m1*m2/(m1+m2)
Where μ is the reduced mass if both ends of a diatomic molecule are moving. m are the molecule masses.
How do energy levels for the anharmonic vibrations of real molecules differ to those of harmonic vibrations?
For anharmonic vibrations, as energy increases, the ‘jump’ between energy levels decreases.
Whereas, the jump for harmonic vibrations remains the same. The harmonic model is suitable for real molecules, especially at lower energy levels.
The bonds in actual molecules are not obeying Hook’s law exactly.
The force needed to compress a bond by a definite distance is larger
than the force required to stretch this bond, thus potential is anharmonic.
Define IR active:
Able to absorb IR radiation
Define fundamental transition:
Transition from ground state to first excited state (0 -> 1)
Define anharmonic motion:
Oscillatory motion in which the restoring force is not proportional to the displacement
Define the selection rule for IR activity:
The motion corresponding to a normal mode should be accompanied by a change of dipole moment
∂μ / ∂r ≠ 0
The selection rule for infrared (IR) activity in molecular spectroscopy is a set of guidelines that determine whether a vibrational mode of a molecule will interact with infrared radiation and produce an IR absorption or not.
Here are the key points of the selection rule for IR activity:
- A change in the molecular dipole moment is required. In other words, the molecule must oscillate or vibrate in such a way that the distribution of charge within the molecule changes.
- Symmetry consideration: the vibrational mode must also have the appropriate symmetry properties to interact with IR radiation. Symmetry is a fundamental concept in molecular spectroscopy, and only certain vibrational modes with specific symmetries will be IR active.
- The mode must be associated with a net change in the molecular dipole moment: In a molecule, there may be multiple vibrational modes, but not all of them will be IR active. Only those modes that result in a net change in the molecule’s dipole moment will be IR active.
- The intensity of the IR absorption is directly proportional to the magnitude of the change in the molecular dipole moment during the vibrational transition. Larger changes in dipole moment result in more intense IR absorption bands.
Define normal mode:
A characteristic vibrational pattern of a molecule or group of atoms.
Each normal mode has a discrete vibrational frequency
In general, a non-linear molecule with N atoms has 3N – 6 normal modes of vibration, but a linear molecule has 3N – 5 modes, because rotation about the molecular axis cannot be observed.
A diatomic molecule has one normal mode of vibration, since it can only stretch or compress the single bond.
How can diatomic molecules move?
By rotation, vibration, and translation
A molecule with N atoms has 3N ‘degrees of freedom’
What is the dipole moment?
How do you calculate dipole moment, μ?
It is a measure of the asymmetry of charge distribution on the two atoms (for diatomic molecules)
μ = q * r
Where q is charge and r is distance (bond length)
∂μ / ∂r ≠ 0 during molecular vibration
Why is CO2 a greenhouse gas? (Consider IR)
CO2 molecules can vibrate in ways that simpler nitrogen and oxygen molecules cannot, which allows CO2 molecules to capture the IR photons.
CO2 has 3N-5 (3*3-5 = 4) vibrations as it is a linear molecule - symmetric, antisymmetric, and 2 bending modes.
How many vibration modes do linear and non-linear molecules have?
Linear: 3N - 5
Non-linear: 3N-6
Where N is the number of atoms
What’s a degenerate vibration?
A degenerate vibration refers to a situation where two or more vibrational modes of a molecule have the same vibrational frequency.
These degenerate vibrational modes have identical vibrational frequencies and are often associated with the same symmetry properties.
Degeneracy in molecular vibrations can occur when the symmetry of a molecule allows for multiple vibrational modes with the same energy.
For example, consider a diatomic molecule like oxygen (O2). It has two atoms, and when it vibrates, it can do so in different ways. In the case of O2, there are two vibrational modes associated with stretching the O-O bond. These two modes have the same vibrational frequency, and they are said to be degenerate. This degeneracy is a result of the symmetry of the molecule.
How is absorbance calculated using the Beer-Lambert law?
A = εcl
Where:
ε - molar absorptivity (or absorption or extinction coefficient)
c - concentration
l - length (or thickness or pathlength)
The absorption of a species is proportional to its concentration
A = ln (I0/I) = (ac)c(ab)*b
Where:
I0 - incident intensity
I - emitted intensity
c - concentration
b - path length (l)
ab and ac are constants of proportion ?*
What are the the IR sampling methods? (3)
Transmission (liquid films between transparent salt plates)
Reflection (specular or diffuse. Used for surface coatings, powdered, and textured samples. Surface sensitive)
Attenuated total reflection (ATR) (small penetration depth. Ideal for strongly absorbing samples. Surface sensitive) [Regarding ATR, dp refers to penetration depth of IR beam in the sample - typically 0.2 - 3 um].
What is dp, when looking at IR spectroscopy?
Penetration depth (of IR into the material)
[Equation to calculate is within notes]
How does FT-IR work?
Source of Infrared Radiation:
FT-IR spectroscopy begins with an IR radiation source, typically a thermal source like a heated filament or a globar. This source emits a broad spectrum of IR radiation that covers a range of frequencies.
Sample Interaction:
The IR radiation is directed onto the sample being analyzed. The sample may be in various forms, such as a solid, liquid, or gas. Molecules in the sample interact with the incident IR radiation.
Absorption of IR Radiation:
When the IR radiation interacts with the sample, molecules absorb energy at specific frequencies corresponding to their vibrational and rotational modes. Different chemical bonds (e.g., C-H, O-H, C=O) have characteristic vibrational frequencies, and these are what FT-IR spectroscopy detects.
Detector:
The transmitted light, which has not been absorbed by the sample, reaches a detector. The detector records the intensity of the transmitted IR radiation as a function of frequency.
Interferometer:
The key innovation in FT-IR spectroscopy is the interferometer. Instead of measuring the intensity of IR radiation at each frequency one by one, FT-IR uses an interferometer to obtain an interferogram, which contains information about all frequencies simultaneously.
Fourier Transformation:
The interferogram is then subjected to a mathematical technique called Fourier transformation. This transformation converts the data from the time domain (as a function of time) into the frequency domain (as a function of frequency).
Spectrum Generation:
The Fourier-transformed data results in an IR spectrum, which is a graph of intensity (absorbance) versus frequency (in wavenumbers, typically measured in cm⁻¹). Peaks in the spectrum represent the frequencies at which the sample absorbed IR radiation.
Data Analysis:
The obtained IR spectrum is analyzed to identify the functional groups and chemical bonds present in the sample. Each peak corresponds to a specific vibrational or rotational mode of the molecules in the sample.
Guided inquiry Q1: Do you know any spectroscopic technique?
Visible light/UV
IR
Near-IR
X-ray (crystallography or absorption spec)
Neutron
Raman scattering
Mass spec
Fluorescence
Mössbauer (gamma-ray spec)
EPR spectroscopy, also known as electron spin resonance
(They can be categorised into types: absorption, emission, fluorescence, nuclear magnetic resonance, scattering)
Guided inquiry Q2: What is on the x-axis of an IR spectrum?
Typically, wavenumber ( /cm) is along the x-axis of a spectrum.
The y-axis is typically a measure of transmittance.
For a UV/visible light spectrum, x and y axis may be wavelength and absorbance respectively.
Guided inquiry Q3: Describe the IR spectrum of CO2
x-axis: wavenumber (/cm)
y-axis: transmittance (%)
CO2 is a linear molecule therefore has 4 vibrational modes (3*number of molecules - 5).
However, not all of these vibrations absorb IR. The symmetrical stretch of CO2 is inactive in the IR because this
vibration produces no change in the dipole moment of the molecule. In order to be IR active, a vibration must cause a change in the dipole moment of the molecule.
Only two IR bands (2350 and 666 cm–1) are seen for carbon dioxide, instead of four corresponding to the four fundamental vibrations.
Carbon dioxide is an example of why one does not always see as many bands as implied by our simple calculation.
In the case of CO2, two bands are degenerate, and one vibration does not cause a change in dipole moment.
Other reasons why fewer than the theoretical number of IR bands are seen include:
1) An absorption is not in the 4000–400 cm–1 range.
2) An absorption is too weak to be observed.
3) Absorptions are too close to each other to be resolved on the instrument.
4) Weak bands which are overtones or combinations of fundamental vibrations are observed.
Which of the following molecules display an IR spectrum?
HCl, CO2, C6H6, SF6, N2, O3
HCl (the stretch of bond introduces a difference in the dipole moment of the molecule)
CO2 (bands made by the doubly degenerate bend and asymmetric stretch)
C6H6 (Arenes have absorption bands in the 650-900 cm−1 region due to bending of the C–H bond out of the plane of the ring. Arenes also possess a characteristic absorption at about 3030-3100 cm−1 as a result of the aromatic C–H stretch. Two bands (1500 and 1660 cm−1) caused by C=C in plane vibrations are the most useful for characterization as they are intense)
SF6 (has 2 stretching modes and 4 bending bonds)
O3 (Symmetric Stretch (ν1) - stretching of both O-O bonds while the central oxygen remains stationary. It is the strongest IR absorption band in the ozone spectrum, typically occurring around 1,100 cm⁻¹. Asymmetric Stretch (ν3) - the two O-O bonds stretch in opposite directions while the central oxygen atom remains stationary. This is another strong IR absorption band, typically occurring around 1,250 cm⁻¹. Bend (ν2) - involves the bending of the O-O-O angle. The bend mode is typically observed at around 700 cm⁻¹.
(N2 is a symmetrical molecule so there is no change in dipole moment as it vibrates.
Which of the following molecules display a Raman spectrum?
HCl, CO2, C6H6, SF6, N2, O3
HCl (contains polarizable bonds)
C6H6
CO2 (it has polar covalent bonds that have significant polarizability)
SF6 (polar molecule with polar S-F bonds)
N2
O3 (significant polarizability)
N2 and C6H6 can also produce Raman spectra, but they are generally weaker due to their nonpolar characteristics.
How would you proceed to determine the amount of oleic acid in water?
Sketch curves if needed and indicate the procedure step by step.
Transmission or ATR infrared spectroscopy could be used for this.
First a calibration curve could be made that would take advantage of the Beer Lambert law. The calibration involves the preparation of standards of known concentration. If properly done, a linear trend is found.
Second, this curve could then be used to determine the amount of oleic acid in the aqueous sample. It should be noted that the absorbance measured for the sample should be within the range of absorbance measured for the standards.
Determining the amount of oleic acid in water using spectroscopy typically involves measuring the absorbance of light at specific wavelengths, as oleic acid has characteristic absorption peaks in the UV-Visible spectrum. Here’s a step-by-step procedure for this analysis:
Materials and Equipment:
Oleic acid sample
Deionized or distilled water
Spectrophotometer
Quartz cuvettes or sample cells
UV-Visible spectrophotometer
Appropriate solvent (e.g., ethanol) for preparing oleic acid solutions
Chemical balance
Pipettes and pipette tips
Clean glassware and lab supplies
Procedure:
Prepare Oleic Acid Solutions:
a. Weigh an appropriate amount of oleic acid using a chemical balance to make a stock solution (typically in milligrams or grams).
b. Dissolve the oleic acid in a suitable solvent (e.g., ethanol) to make a concentrated stock solution.
Dilute the Stock Solution:
a. Prepare a series of dilute oleic acid solutions by taking specific volumes of the stock solution and diluting them with deionized or distilled water. The concentrations of these solutions should cover the expected range of oleic acid concentrations.
Blank Solution:
a. Prepare a blank solution by using the same solvent (e.g., ethanol) and deionized or distilled water. This blank solution will be used as a reference to account for the solvent’s absorption.
Instrument Setup:
a. Turn on the UV-Visible spectrophotometer and allow it to warm up according to the manufacturer’s instructions.
b. Set the spectrophotometer to the appropriate wavelength range for oleic acid analysis, typically in the UV-Visible range.
c. Use a quartz cuvette or sample cell that is compatible with the spectrophotometer.
Calibration:
a. Measure the absorbance of the blank solution at the selected wavelength(s). This establishes a baseline for the solvent.
b. Measure the absorbance of each of the dilute oleic acid solutions at the same wavelength(s).
Create a Calibration Curve:
a. Plot the concentration of oleic acid (x-axis) against the absorbance values (y-axis) for the standards.
b. Use this calibration curve to determine the concentration of oleic acid in the samples.
Sample Measurement:
a. Prepare a sample solution by diluting the unknown oleic acid in water.
b. Measure the absorbance of the sample solution at the same wavelength(s) used for the standards.
Calculate Oleic Acid Concentration:
a. Use the calibration curve to determine the concentration of oleic acid in the sample based on its absorbance.
Data Analysis:
a. Record the results, and if necessary, repeat the measurements for the sample to ensure accuracy and precision.
b. Calculate the concentration of oleic acid in the sample based on the calibration curve.
Reporting:
a. Report the concentration of oleic acid in the sample, including the units used (e.g., mg/L or g/L).
https://www.sciencedirect.com/science/article/pii/S0022286019302509
Cocoa butter exhibits several polymorphs. Which technique(s)
could you use to identify the phase(s) in a sample?
Raman spectroscopy - Raman spectroscopy is a non-destructive technique that can provide information about the molecular vibrations and crystal structures of materials. Different polymorphs exhibit distinct Raman spectra due to variations in their crystal lattice structures. By comparing the Raman spectra of the sample with reference spectra of known cocoa butter polymorphs, you can identify the phases present.
X-ray Diffraction (XRD) - XRD can provide detailed information about the arrangement of atoms or molecules in a sample. By analyzing the XRD pattern of cocoa butter, you can determine which polymorph(s) are present in the sample.
The above two are the most important techniques. The below could also be used.
Differential Scanning Calorimetry (DSC) - DSC is commonly used to analyze the thermal behavior of materials, including phase transitions. Different polymorphs of cocoa butter have distinct melting points and enthalpies of fusion. By performing a DSC analysis, you can identify the phase transitions and infer the presence of specific polymorphs.
Polarized Light Microscopy (PLM) - PLM is a microscopy technique that involves the use of polarized light to observe the birefringence patterns of crystalline materials. Different cocoa butter polymorphs exhibit characteristic birefringence patterns under polarized light. By comparing the observed patterns with reference images of known polymorphs, you can identify the phases.
Infrared Spectroscopy (IR) - Infrared spectroscopy can provide information about the functional groups and molecular vibrations in a sample. Different cocoa butter polymorphs may exhibit variations in their IR spectra. By comparing the IR spectra of the sample with reference spectra of known polymorphs, you can gain insights into the phases present.
Microscopy Techniques (Optical and Electron Microscopy) - Microscopy techniques, including optical and electron microscopy, can be used to visually examine the crystalline structure of cocoa butter. Differences in crystal morphology, size, and arrangement can help identify specific polymorphs.
Solid-State NMR Spectroscopy - Solid-state nuclear magnetic resonance (NMR) spectroscopy is a technique that can provide information about the local structure and interactions within a solid sample. It can be used to investigate the differences in the molecular environment of cocoa butter polymorphs.
What is polymorphism?
Polymorphism is the ability of a specific chemical composition to crystallize in more than one form. This generally occurs as a response to changes in temperature or pressure or both. The different structures of such a chemical substance are called polymorphic forms, or polymorphs.
A solid material with at least 2 different molecular arrangements that gives distinct crystal species.
What is ATR?
Attenuated total reflection.
ATR uses a property of total internal reflection resulting in an evanescent wave. A beam of infrared light is passed through the ATR crystal in such a way that it reflects at least once off the internal surface in contact with the sample. This reflection forms the evanescent wave which extends into the sample. The penetration depth into the sample is typically between 0.5 and 2 micrometres.
Attenuated total reflection (ATR) is a sampling technique used in conjunction with infrared spectroscopy which enables samples to be examined directly in the solid or liquid state without further preparation.
How is dipole moment induced by electric field calculated?
μ = αE
The polarizability, a, represents the ability of an applied electric field
E to induce a dipole moment μ in atom or molecule. Polarizabilities
of atoms are isotropic, whereas polarizabilities of molecules may
vary with positions of atoms in the molecule, depending on
molecule’s symmetry.
What is Stokes shift?
The term Stokes shift is used in Raman spectroscopy where it describes whether the Raman scattered radiation is at lower energy (Stokes shifted) or higher energy (anti-Stokes shifted) than the Rayleigh scattered radiation.
When radiation is scattered from a molecule the majority of photons scatter elastically with no change in the vibrational energy of molecule during the scattering process (Rayleigh scattering).
In Stokes Raman scattering the molecule gains a quantum of vibrational energy from the photon during the scattering process and the Stokes radiation, therefore, has a longer wavelength than the incident radiation (less energy)
In anti-Stokes Raman scattering the reverse occurs, with the molecule losing a quantum of vibrational energy during the scattering process and the anti-Stokes radiation, therefore, has a shorter wavelength than the incident (more energy)
Raman peaks are characterised by their wavenumber shift away from the incident radiation, with Stokes peaks having a positive wavenumber shift and anti-Stokes shifts being negative.
If we excite with a laser at 532 nm, where should the Stokes vibrational oxygen Raman peak appear?
Stoke shift / line: v0 - vs
Calculate the oxygen Raman wavelength: according to the Raman shift is 1556 cm-1
With an excitation wavelength at 532 nm the oxygen Stokes line will appear at 1/532 nm – 1556 cm-1
= 18797 cm-1– 1556 cm-1= 17241 cm-1 = 580 nm
How does Raman microscopy work?
Laser Excitation: A monochromatic laser source, typically in the visible or near-infrared range, is directed onto the sample. The laser light is focused on the sample, creating a small, intense beam at the point of interest. This focused laser beam serves as the excitation source.
Raman Scattering: When the laser light interacts with the sample, a small fraction of the incident photons undergoes inelastic scattering, known as Raman scattering. In this process, the energy of the photons is either increased (Stokes scattering) or decreased (anti-Stokes scattering) by an amount corresponding to the energy levels of molecular vibrations and rotations in the sample.
Raman Shift: The energy difference between the incident laser light and the scattered light is called the Raman shift. It is measured in wavenumbers (cm⁻¹) or nanometers (nm) and is characteristic of the vibrational and rotational modes of specific chemical bonds within the molecules in the sample. By analyzing the Raman shifts, you can obtain information about the chemical composition and molecular structure of the sample.
Spectrograph: The Raman-scattered light is collected and directed into a spectrograph. The spectrograph disperses the collected light into its constituent wavelengths, creating a Raman spectrum. This spectrum represents the intensity of the scattered light at different Raman shifts.
Detection: The Raman spectrum is detected by a sensitive detector, such as a charged-coupled device (CCD) or a photomultiplier tube (PMT). The detector records the intensity of the Raman signals across the entire spectrum.
Data Analysis: The Raman spectrum provides valuable information about the molecular vibrations and chemical bonds present in the sample. By analyzing the peaks and patterns in the spectrum, researchers can identify the chemical compounds present, understand their molecular structures, and even quantify their concentrations.
Raman microscopy offers several advantages, including the ability to perform non-destructive and label-free chemical analysis of a wide range of materials, including solids, liquids, and gases. It can be used in various fields, such as materials science, biology, chemistry, and pharmaceuticals, for characterizing and studying a wide range of samples at the microscopic level.
What’s a microtome?
An instrument for cutting extremely thin sections of material for examination under a microscope.
What is Raman band normalisation for?
For quantitative analysis Raman band normalisation is required in order to correct spectra for changes in focus, alignment, laser intensity, and signal attenuation, etc.
Therefore, to compare the two different bands from depth profiles it is necessary to account for possible laser power fluctuations, which was accomplished using band area normalisation.
Example for PET:
In order for the 1096 cm-1 band (crystalline PET) to be assessed it is
necessary to normalise its intensity with respect to a band that is unaffected by crystallinity.
The band at 795 cm-1 was selected for normalization as it is known to be insensitive to conformation or crystallinity.
Band normalisation is performed by dividing the area of the the 1096 cm-1 band by the area of the band at 795 cm-1
What is SERS?
Surface-enhanced Raman spectroscopy or surface-enhanced Raman scattering (SERS) is a surface-sensitive technique that enhances Raman scattering by molecules adsorbed on rough metal surfaces or by nanostructures.
What’s a surface plasmon?
A collective oscillation of surface conduction electrons in materials
with a negative real and small positive imaginary dielectric constant
What is TERS?
Tip-enhanced Raman spectroscopy (TERS) is a variant of surface-enhanced Raman spectroscopy (SERS).
TERS uses a metallic-coated tip—typically on a scanning probe / atomic force microscope—to enhance the Raman signal from molecules within a few nanometres of the tip. You can determine the spectrum originating from molecules solely in the small volume close to the tip.
This is done by comparing the spectrum from the surface with and without the tip present. This gives a much higher spatial resolution than normal Raman scattering (nanometre-scale, rather than about 0.2 µm).
How can particle surface area be enhanced?
Grinding / milling (size reduction)
Synthesis process (change in morphology/texture)
Activation / partial decomposition / lyophilisation (creation of pores)
How can particle surface area be decreased?
Melting
Sintering
Ostwald ripening (the process of disappearance of small particles or droplets by dissolution and deposition on the larger particles or droplets)
List particle pore types:
Closed
Passing
Dead end / blind
Interparticle
Interconnected
List potential particle pore shapes:
Cylindrical
Slit
Wedge/conical
Spherical / ink bottle
What is the size of micropores, mesopores, and macropores?
Micro: < 2nm (e.g. activated carbon, zeolites)
Meso: 2-50 nm (activated carbon, zeolites, silica)
Macro: > 50 nm (sintered metals, ion-exchanger resin, ceramic)
List key techniques for surface area / porosity determination of porous samples:
Gas adsorption (for pores below 50nm)
Mercury porosimetry (pores above 3.5 nm)
Helium pycnometer overall density (and thus porosity)
What’s an isotherm?
A plot of the amount of vapour/gas adsorbed by a sample as a function of pressure
What’s adsorption?
Phsyicochemical process by which an atom or molecule attaches itself onto the surface of a solid state material
What’s hysteresis?
Difference in adsorption vs desorption parts of an isotherm
What’s an adsorbate and adsorbent?
Adsorbate - gas or vapour species which adsorbs on a surface
Adsorbent - solid substrate on which molecule adsorbs
What is referred to by ‘cross-sectional area of molecule’?
The area occupied by a molecule when adsorbed on a surface
What are the main adsorption processes?
Physical adsorption
Chemisorption
Condensation processes e.g. pore filling
What are the properties of physical adsorption processes?
Non-activated
Non-selective
Rapid
Multilayer
No re-distribution of e- density
Describe the steps of gas adsorption isotherm formation:
Initially, micropores are filled. Having walls on either side of the gas molecules means there are stronger forces for adsorption.
Then monolayers (knee) form on the surface, followed by multilayers.
Finally is capillary condensation.
What is the Langmuir isotherm model?
The Langmuir isotherm is a model that describes the adsorption of a gas onto a solid surface.
The model assumes a monolayer adsorption process, meaning that molecules adsorb onto the surface one layer at a time. The Langmuir isotherm is commonly used in the study of physical adsorption, such as in the adsorption of gases on solid surfaces.
q= 1+K⋅P / K⋅P
q is the amount of gas adsorbed per unit mass of the adsorbent (adsorption capacity),
P is the pressure of the gas,
K is the Langmuir constant, which is related to the energy of adsorption.
Langmuir isotherm assumptions:
Monolayer adsorption only
One type of adsorption site
Each site can accommodate only one molecule
Negligible interactions between neighbouring adsorbates
What are the assumptions of a BET isotherm?
Multilayer adsorption
Adsorption sites are energetically equivalent
The BET (Brunauer-Emmett-Teller) isotherm is a widely used model for the adsorption of gases on solid surfaces, particularly on porous materials such as activated carbon. The BET isotherm is an extension of the Langmuir isotherm, which assumes monolayer adsorption. In contrast, the BET isotherm considers the formation of multilayer adsorption on the surface of the material.
How does liquid surface impact vapour pressure?
Convex surfaces (drops) have higher vapour pressures than flat surfaces, which are higher than concave surfaces (filled pores).
Only noticeable for nm scale droplets and filled pores.
Differences are due to the number of molecules in the liquid.
What does a Helium Pycnometer do?
It works out the pore volume or % porosity.
A Helium Pycnometer is an instrument used to measure the volume and, subsequently, the density of a material. It operates on the principle of gas displacement, specifically using helium as the displacing gas. The technique is commonly employed for determining the true volume and density of solid materials, particularly those that may have irregular shapes or porosity.
Principle of Operation:
The sample is placed in a chamber within the pycnometer.
Helium gas is introduced into the chamber at a known pressure.
Gas Displacement:
The helium gas displaces the air and penetrates the pores or voids in the sample. As helium fills the voids, it replaces the air within the material.
Volume Measurement:
The volume of helium displaced is precisely measured.
By knowing the volume of the chamber and the volume of helium introduced, the volume of the sample (including its pores) can be calculated.
Density Calculation:
The density of the material is calculated by dividing the mass of the sample by its volume.
Accuracy and Precision:
Helium is used because it has a very small molecular size and is non-reactive, making it suitable for penetrating small pores and accurately measuring the volume.
Applications:
Helium Pycnometry is commonly used for determining the density of materials such as powders, ceramics, metals, polymers, and other porous materials.
It is particularly useful in research and industry where precise knowledge of material density is important for quality control, material characterization, or research purposes.
When is mercury porosimetry / mercury intrusion used?
To examine porosity - instead of using a gas, mercury is employed to determine porosity.
Used for meso/macroporous solids (3.5 nm - 500 um)
Limitations:
- it measures the largest entrances towards a pore, not the actual inner size.
- can only use sample once
- requires mercury
- limited to cylindrical pore geometry
What has more energy - IR or Raman spectroscopy?
In terms of the energy of the photons involved, infrared (IR) spectroscopy typically involves photons of lower energy compared to Raman spectroscopy.
In IR spectroscopy, photons in the infrared region of the electromagnetic spectrum are absorbed by molecules, causing vibrational transitions. These photons have energies that correspond to the molecular vibrations being probed, usually in the range of about 2 to 15 micrometers wavelength.
Raman spectroscopy involves the inelastic scattering of photons by molecular vibrations. The incident photons undergo a change in energy upon interacting with the molecule, resulting in either higher or lower energy photons being scattered. The energy differences involved in Raman scattering are typically higher than those in IR spectroscopy.
So, while both techniques involve the interaction of light with molecular vibrations, Raman spectroscopy tends to involve higher-energy interactions than infrared spectroscopy.
What sectors is FT-IR applicable to?
Forensics
Materials
Colloid science
Pharmaceuticals
Studying drug tablet formation and dissolution
Studying oil fouling
Purification of antibodies
What are the common IR microscopy sampling techniques?
Transmission (light passes through sample) - sample thickness 10-20 um
Reflectance (sample thickness N/A)
Absorption/reflectance (sample thickness 5 - 10 um)
Micro ATR (Attenuated total reflection) - sample thickness N/A
What’s an airy disk?
The central bright circular region of the pattern produced by light diffracted when passing through a circular aperture.
Define spatial resolution:
Spatial resolution refers to the scale or size of the smallest unit of an image capable of distinguishing objects, or a measure of the smallest angular or linear distance to identify adjacent objects in an image.
Spatial resolution is defined as the ability to distinguish two neighbouring structures as separated.
How is spatial resolution, r, calculated?
r = 1.22λ / (2NA)
Where λ is wavelength and NA is numerical aperture
What’s chromatic aberration?
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colours to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light.
In microscopes, chromatic aberration arises due to the dispersion of light passing through the lens elements. This dispersion causes different colours (wavelengths) of light to be refracted by different amounts, resulting in the inability of the lens to bring all colours into focus simultaneously at the same point. As a result, the image formed may suffer from colour blurring or distortion, especially at the edges of the specimen being observed.
To mitigate chromatic aberration, microscope designers use various techniques:
- Using a pseudo hemisphere on top of the sample to stop light refraction.
- Apochromatic Lenses: These are specially designed lenses that reduce chromatic aberration by bringing three primary colors (red, green, and blue) to a common focus.
- Achromatic Lenses: These lenses are corrected to bring two wavelengths (usually red and blue) into focus at the same point, reducing but not entirely eliminating chromatic aberration.
- Fluorite or ED (Extra-low Dispersion) Glass: Using materials with low dispersion properties helps in minimizing chromatic aberration.
- Adding Corrective Elements: Combining different lens elements and using multiple lenses in a system can compensate for chromatic aberration to improve image quality.
What are advantages of micro ATR FT-IR imaging?
Fast imaging with good spatial resolution
No staining or labelling needed
Can monitor many samples / high throughput
What’s resolution of macro and micro ATR?
Macro: 300 um
Micro: < 4 um
Properties of macro ATR FT-IR imaging:
No / minimal sample prep
No averaging through thick sample
All absorbance bands on scale
Aqueous samples can be studied
Properties of diamond can be used
What is thermal analysis?
A group of techniques in which a physical property is measured as a function of temperature, while the sample is subjected to a controlled temperature programme (heating, cooling, or isothermal)
Examples of properties of interest:
Specific heat
Thermal expansion
Weight
Flow stress
Viscosity
Phase change
Give examples of thermal analysis techniques:
Differential Scanning Calorimetry (DSC) - Heat Flow during Transitions
Thermogravimetric Analysis (TGA) - Weight Loss
Dynamic Mechanical Analysis (DMA) - Viscoelastic Properties
Thermomechanical Analysis (TMA) - Thermal Expansion Coefficient
Differential Thermal Analysis (DTA) - Heat of Transition
Temperature Programmed Desorption (TPD) - Evolved gases, binding energy
What is the principle of thermogravimetric analysis (TGA)?
Mass of a sample is measured as a function of temp or time.
The sample is typically heated at a constant heating rate or held at a constant temperature.
What’s TGA?
Thermogravimetric analysis
What can cause a sample mass change during TGA as a sample is heated?
Weight change can be due to:
- Gas or vapour desorption/adsorption (evaporation of moisture)
- Hydrate or solvent formation or decomposition
- Phase transition (vaporization, sublimation)
- Oxidative or thermal decomposition
- Oxidation reactions (in air or O2 atm)
- Reduction reactions (H2 atm)
What should be considered when carrying out TGA?
The gas phase flow around sample must be controlled:
- Air
- Nitrogen
The amount of sample needed is generally small: < 100mg
Temperature range: usually room temperature to 1000 oC
Mass sensitivity/resolution:
- 10 mg (semi-microbalance)
- 1 mg (micro-balance)
- 0.1 mg (ultra-microbalances)
Change in gas density with temperature: buoyancy effect
Sample preparation:
- Sample should be representative of the product
- Mass should be adequate for the instrument
- Sample should not be contaminated
- Sample size, morphology
Crucibles or pans made in quartz, glass, alumina, platinum
Sample Atmosphere:
- Protective purge gas for the furnace and microbalance
- Inert or reactive gas (N2, He, Ar, air, CO2, O2, H2 in Ar)
Change of physical properties of the sample during measurement (e.g. volume)
Motion of sample pan- noise in mass measurement
Microbalance stability with time- drift in mass baseline
Heating rate and time for sample to be heated by furnace
What is TGA used for?
Characterization of products:
Thermal stability, decomposition temperature
Purity
Composition, moisture content, solvent content
Polymorph identification
Examination of properties:
Adsorption/desorption processes
Vaporization processes
Reaction’ kinetics, stoichiometry
Influence of reactive gases
What is a plasticiser?
A plasticizer is a low-volatility liquid or solid substance that’s added to a raw polymer like a type of plastic or rubber to improve its flexibility, make it easier to shape and mould, and reduce friction on its surface.
A plasticiser is any material whose presence causes a reduction in the Tg. We might crudely consider it as a type of molecular lubricant.
Water similarly will plasticise many materials.
Water will increase the free volume and depress the Tg.
How does heating rate affect TGA results?
Higher heating rate:
- maximum mass loss occurs at a higher temp.
- mass loss occurs over a broader temperature range
Remark: onset temperature (the point on the TGA curve where a deflection is first observed from the established baseline prior to the thermal event) is more useful than peak temperature
List key temperature ranges for TGA:
< 150C: Evaporation of volatiles, solvents, and monomers.
Removal of moisture
150 - 450C: Removal of crystallisation water.
Decomposition of organics
450 - 900: Carbon combustion.
Why use TGA with evolved gas analysis?
To analyse the exhaust gas produced. TGA can only identify changes in mass with time and temperature - it does not identify individual components.
FT-IR may also be used.
What is DVS?
Dynamic vapour sorption
Describe water vapour pressure behaviour:
At 20C water has a vapour pressure 17.53 Torr which is the equivalent to 0.02338Bar or 2300 Pa.
If for a specific system that the water vapour pressure present was measured at 8.76 Torr, then the relative humidity would be 50%RH with aw of 0.50.
If we sealed this vessel and increased the temperature to 50C, then real vapour pressure would still be 8.76 Torr. However, now the saturated vapour pressure at 50C for water is 92.51 Torr. The RH is now 9.45%!
Let us decrease the temperature to 5C, for which the saturated vapour pressure of water is 6.54 Torr. Now our actual vapour pressure is greater than the maximum allowed- condensation will occur.
What’s a polymorph?
A crystalline solid that exhibits two or more unit cell constructions.
Very common for new drug substances to have between 3 and 8 polymorphs
Common Examples:
- Carbon (graphite, diamond, fullerene’s)
- Sulfur (monoclinic, Rhombic, Orthorhombic, Triclinic)
- Calcium Carbonate (calcite, aragonite, vaterite)
What is DVS / dynamic vapour sorption?
Dynamic vapor sorption (DVS) is a gravimetric technique that measures how quickly and how much of a solvent is absorbed by a sample such as a dry powder absorbing water.
It does this by varying the vapor concentration surrounding the sample and measuring the change in mass which this produces.
The technique is mostly used for water vapor, but is suitable for a wide range of organic solvents.
It is a much slower process than TGA.
What properties can DVS measure?
(Dynamic vapour sorption)
Sorption Isotherms
BET Surface Area
Pore Size Distribution
Glass Transition Humidity
Diffusion Coefficient
Permeability of Thin Film
Water Capacity
Stability Mapping
Amorphous Content
What is glass transition temperature, Tg?
Glass-transition temperature (Tg) is the temperature at which molecular mobility begins to take place, below which molecular mobility is frozen and the elastomer becomes rigid and glassy.
What does DSC stand for?
Differential scanning calorimetry
What is DSC / Differential scanning calorimetry?
DSC measures the energy changes occurring as a sample is heated, cooled or held isothermally, together with the temperature at which these changes are observed.
Differential scanning calorimetry (DSC) is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature.
In fact, DSC measures heat flow as a function of T
A reference “sample” must be used
The energy changes can be due to:
* Phase transition -melting, glass, crystalline phase
* Ferromagnetic–diamagnetic transition
Purge gases are used to control the sample environment, and purge volatile from the system and prevent contamination
Temperature range: -180 oC to 750 oC (cooler for sub-ambient temperature)
Mass of sample: 1 to 20 mg
No reaction can take place in a DSC (check decomposition temperature using TGA before)
What occurs in power compensated DSC?
The sample and a reference are placed in separate furnaces.
Aim: maintain both at the same T, even during a thermal event in the sample.
The difference in power supplied to the two furnaces so that ΔT=0 is measured
High resolution / high sensitivity research studies.
What happens in heat flux DSC?
The sample and reference are both within the same furnace and connected by a low-resistance heat-flow path.
Aim: apply the same temperature profile to both sample and reference ports and one measures the difference in heat flow difference between the two
More widespread
What influences DSC / differential scanning calorimetry reuslts?
Purge gas
- check thermal conductivity of purge gas
- N2 for RT and above but He if low T (N2 condenses at low T), Ar for T > 600 oC
Pans
- closed/unclosed
- sample should not react with pan
- aluminium if T < 600 oC
Scan rate
Sample
- should be representative of the product
- mass should be adequate for the instrument (avoid any pressure build up)
- morphology: good contact with pan (disk
What is curing?
Toughening/hardening of a polymer material via cross-linking, triggered by electron beams, heat or chemical additives.
Why is thermal history considered regarding DSC?
The effect of previous heating/cooling treatments (i.e. thermal history) can impact the DSC trace of a sample
As a result, the second heating DSC trace should be considered to analyse the sample itself.
What does a large well-defined endotherm suggest regarding DSC results?
Pure crystal melting
Solvate/hydrate loss
Stress relaxation
What does a shallow broad endotherm suggest regarding DSC results?
Moisture/residual solvent loss
Sublimation
Range of MWs melting
What does a large well-defined exotherm suggest regarding DSC results?
Crystallization in/from liquid state
Degradation of unstable material
Crystal structure rearrangement
What does a shallow broad exotherm suggest regarding DSC results?
Cure reaction
Oxidation
How would one sketch the IR spectrum of CO2?
First consider the possible vibrational motions of CO2.
There are 4 modes (calculated by 3N-5). These are:
- symmetric stretching (1340cm-1)
- antisymmetric stretching (2349 cm-1)
- out-of-plane bending (667 cm-1)
- in-plane bending (667 cm-1)
Since the latter two are degenerate, we would expect 3 bands for the IR spectrum. However, the symmetric band is not IR active (no change in dipole moment) so only 2 bands are observed: bending and antisymmetric stretching.
What are the key interactions between particles?
Van der Waals
Electrical double layer
Steric
What are steric effects?
Steric effects arise from the spatial arrangement of atoms. When atoms come close together there is generally a rise in the energy of the molecule.
Steric effects are nonbonding interactions that influence the shape (conformation) and reactivity of ions and molecules. Steric effects complement electronic effects, which dictate the shape and reactivity of molecules.
Steric repulsive forces between overlapping electron clouds result in structured groupings of molecules stabilized by the way that opposites attract and like charges repel.
What happens when polymers adsorb to a surface?
When polymers adsorb to a
surface they generally do not
lay flat on the surface, but
extend away from the surface
as well. The polymer segments
thus exist as a series of tails,
loops and trains as shown
below.
This means that when
polymers are adsorbed onto
particle surfaces, they may
interfere with each other before
van der Waals forces play a
significant role and aggregate
the particles.
What are Hookean solids?
These are materials throughout which there is a continuous structure that can be deformed on the application of a force, but which will return to its pre-deformed state once that force is
removed.
A Hookean solid is characterised by a modulus. The modulus tells us how much the material will deform on the application of a unit force.
Hookean materials are materials that exhibit linear elasticity, meaning that their deformation is directly proportional to the force applied to them. This relationship is described by Hooke’s law.
What are Newtonian fluids?
A Newtonian fluid is one whose viscosity is not affected by shear rate: all else being equal, flow speeds or shear rates do not change the viscosity.
These are generally simple fluids made up of small molecules such as simple solvents and solutions. A Newtonian fluid will flow under the application of a force, and cannot regain its pre-deformed state when that force is
removed.
A Newtonian fluid is characterised by a
viscosity. The viscosity tells us how fast the fluid will flow under the application of a unit force.
What do formulations consist of?
Formulations are made up of more than one component.
They often consist of a liquid phase that may contain solid particles, liquid droplets, polymer molecules or surfactants.
When complex formulations are put together they rarely exhibit simple Newtonian or Hookean behaviour.
Their flow and deformation characteristics are a complex
mixture of elastic (solid-like) and viscous (liquid-like) properties.
The terms viscous and elastic are used over and again when describing rheological properties of materials.
They are used synonymously with the terms solid-like and liquid-like.
What do viscous and elastic terms refer to?
Viscous - liquids
Elastic - solids
What do formulations consist of?
Formulations are made up of more than one component.
They often consist of a liquid phase that may contain solid particles, liquid droplets, polymer molecules or
surfactants.
When complex formulations are put together they rarely exhibit simple Newtonian or Hookean behaviour.
Their flow and deformation characteristics are a complex mixture of elastic (solid-like) and viscous (liquid-like) properties.
The terms viscous and elastic are used over and again when describing rheological properties of materials.
They are used synonymously with the terms solid-like and liquid-like.
What’s a dilatant fluid?
A dilatant / shear thickening fluid is a non-Newtonian fluid where the shear viscosity increases with applied shear stress.
What is viscoelasticity?
Materials that exhibit behaviour somewhere between viscous and elastic are termed viscoelastic.
This term encompasses a whole spectrum of behaviours associated with interactions between formulation components.
What are the 3 main types of deformation flow, regarding rheology?
The rheological behaviour of materials is not only related to the structure of the materials, it is also very sensitive to the deformation experienced.
These can be broken down into three
types:
Shear flow
Extensional flow
Complex flow
Describe shear flow:
Consider two infinite, parallel plates separated by a distance h. One plate, say the top one, translates with a constant velocity u0 in its own plane.
For Newtonian fluids the velocity gradient across the gap is constant, this velocity gradient is the shear rate.
In a shearing flow, adjacent layers of fluid move parallel to each other with different speeds.
Describe extensional flow:
In extension deformation, material is caused to stretch. The deformation is in the direction of flow.
Extensional fluid flow occurs when a fluid undergoes stretching or elongation, causing its particles to move away from each other. This flow pattern often results in thinning and attenuation of the fluid, creating regions of decreased density.
It’s common in scenarios like liquid jets, polymer processing, or certain geological formations where forces elongate the fluid, leading to the redistribution of particles and changes in flow characteristics.
What is complex fluid flow?
Complex fluid flow refers to the behavior of fluids that exhibit intricate and non-linear responses to external forces. These fluids possess characteristics that go beyond the simple behavior of Newtonian fluids, often displaying viscoelasticity, non-Newtonian behavior, multiphase interactions, or complex rheological properties.
Shear and extensional flow may be present.
Complex fluids can be found in systems such as multiphase flows, colloidal dispersions, and polymeric liquids. These systems are known to exhibit such rheological flow behaviors as shear thinning, yield-pseudoplasticity, shear-thickening, and viscoelasticity.
What is shear stress?
Shear stress, is the force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stres, given the symbol 𝜏.
Shear stress may occur in solids or liquids; in the latter it is related to fluid viscosity.
𝜏 = F/A
What is strain?
Strain, given the symbol ε and γ, is a relative deformation.
In a shear deformation it is defined as the distance moved in the direction of the deformation, divided by the height of the unit that was deformed
In an extensional deformation the strain is simply the length of the unit before deformation divided by the length after deformation.
ε = dl/l = tan a
Where l is distance and a is the angle by which the fluid has sheared.
What is shear rate or strain rate?
This is the rate by which the strain is varying and is given by the rate at which the fluid is moving in relation to the walls of the container, divided by the gap between the walls of the container.
It has units of 1/sec and is given the symbol ɣ’
What is viscosity?
When a fluid is forced to flow by an applied stress, 𝜏, the viscosity of the fluid, η, determines the shear rate, ɣ’ (or ε and γ)
η = 𝜏/ɣ’
On removal of the applied stress, the strain generated does not return to zero. Flow has occurred; the viscosity is the resistance to flow.
A Newtonian fluid has a constant viscosity and any applied shear stress and has units of Pa s.
What is elasticity?
A material’s ability to return to its original shape after being subjected to deformation, like stretching or compression. When a force is applied to a material, it deforms, and in an elastic material, once the force is removed, the material regains its initial form.
This behavior is governed by the material’s elastic modulus, which determines the extent of deformation for a given stress and the material’s ability to recover its original shape once the stress is removed.
When a solid element is placed under a shear stress, it experiences a shear strain. The magnitude of this strain is determined by the modulus of the material, G, which has units of Pa.
The application of a shear stress to a perfect solid results in an instantaneous deformation or strain, which persists as long as the stress is applied.
On removal of the stress, the system undergoes an instantaneous recovery to a state of zero strain, no flow has occurred.
What is a rheometer?
What are the 2 main ways they can work?
A rheometer is a scientific instrument used to measure the flow and deformation characteristics of materials, especially fluids and soft solids, under various conditions.
It applies controlled stress or controlled strain to a sample and measures the resulting response.
In a controlled strain instrument, the material is subjected to a forced deformation. This deformation or strain results in a stress being transmitted through the material, which can be measured by some means.
In a controlled stress instrument, the material is subjected to a controlled stress by control of the torque and the resultant deformation is recorded.
What occurs in large strain, steady shear measurements?
Measurements that involve the continuous shearing of a sample in one direction lead to large strain deformations.
These types of measurements give information on the flow properties of materials and can give information on
the processability of formulations.
These measurements are termed viscometric or steady state viscosity measurements.
Other information about the structure and dynamics of the formulation can be inferred from the data, however
more detailed structural information is gained from small strain oscillatory measurements.
What’s a viscometry test?
A viscometry test is designed to measure the viscosity of a material as a function of either the applied stress or shear rate.
At each stress we need to look for an equilibrium value for the viscosity. In this equilibrium region the slope of the strain against time curve is linear giving a constant shear rate. The steady state viscosity is then the applied stress divided by the equilibrium shear rate.
The apparent viscosity can then be plotted as a function of the applied shear stress or the measured shear rate to obtain a flow curve.
What’s the equation for the power law?
What type of fluid can it be used for?
Peusoplastics
𝜏 = kɣ^n
η = kɣ^(n-1)
K is the consistency index, indicating the fluid’s resistance to flow under shear stress.
n is the flow behavior index, characterizing how the fluid viscosity changes with shear rate.
η is apparent viscosity
ɣ is shear rate
What are K and n in the power law equation for modelling pseudoplastics?
K is the consistency index, indicating the fluid’s resistance to flow under shear stress.
n is the flow behaviour index, characterizing how the fluid viscosity changes with shear rate.
What is the equation for modelling bingham plastics?
𝜏 = 𝜏B + ηpɣ’
Where 𝜏B is the yield stress and ηp is the plastic viscosity.
η = 𝜏B / ɣ’ + ηp
What is the equation for modelling Herschel Bulkley flow?
𝜏 = 𝜏HB + kɣ^(n)
Where 𝜏HB is yield stress, K is the consistency index, and n is the flow behaviour index.
The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a complicated, non-linear way (essentially a combination of the Bingham and Power Law models).
What is thixotropy?
‘Thixotropy’ is shear thinning property; when an alloy is sheared it thins, but when it is allowed to stand it thickens again.
Thixotropy is the tendency of a material to recover structure lost during shear, either after the cessation of shear, or as the shear stress or shear rate is reduced.
One of the ways in which thixotropy is observed experimentally is in the difference between the viscosity (or stress) measured as the stress is increased (up sweep) with the viscosity (or stress) recorded as the stress is then reduced (down sweep).
How do thixotropy and elasticity differ?
Thixotropy: It refers to a property where certain materials exhibit a time-dependent decrease in viscosity or apparent thickness under continuous shear stress. These materials become less viscous or flow more easily over time when subjected to constant stress. Once the stress is removed, they gradually regain their original viscosity or thickness.
Elasticity: This property involves a material’s ability to deform under stress and return to its original shape once the stress is removed. Elastic materials store energy temporarily when deformed and release it upon relaxation, displaying a reversible deformation.
While both thixotropy and elasticity involve material response to external forces, thixotropy specifically relates to changes in viscosity or flow behaviour over time under constant stress, whereas elasticity pertains to the reversible deformation and recovery of a material under stress.
What is a key consideration when analysing thixotropy?
The important thing we need to understand about thixotropy is the rate at which the material recovers its structure and the difference between the structure before and after shear.
This is usually the case in real applications, where the material structure has been broken down and is then required to structure when there is no further stress being applied.
The best way to do this is to apply a constant shear rate to the material for a set time and then monitor the structure recovery after shear, using a non-invasive low strain oscillation measurement.
What is creep?
Creep refers to the gradual deformation of a material under the influence of a constant or sustained load or stress over an extended period.
When a constant force or stress is applied to a material, especially solid materials like metals, polymers, or geological substances, they may slowly and continuously deform over time, even in the absence of any increase in the applied load.
What happens in a creep experiment?
In a creep experiment, a constant stress is applied for a period of time and the resultant strain is measured during and after the stress has been removed.
The strain response will be very different for different materials.
How can the yield stress of a system be identified?
The yield stress of a dispersion may be determined by doing a series of creep (constant stress) measurements at successive stresses (while leaving an appropriate time for the sample to relax between measurements).
The yield stress is determined by noting the stress where the sample changes from solid-like to liquid-like behaviour.
There are two ways in which this is apparent:
1. The compliance/time plot reaches a constant slope (constant shear rate)
2. The strain is no longer recovered
How is complex shear modulus, G*, found?
G* = max stress / max strain
What is a stress sweep?
An experimental technique used to study the behaviour of materials under varying stress or strain conditions.
In a stress sweep test, a constant frequency or strain amplitude is applied to the material, while the stress (or strain) itself is varied over a range of values.
The material’s response, such as its viscosity, elasticity, or other rheological properties, is then measured at each stress level.
What is the viscosity relationship for non interacting particle spheres?
Einstein relation:
η/ηs = 1 + 2.5 ϕ
Where ϕ is volume fraction and ηs is the viscosity of the continuous phase.
This equation only holds for dilute dispersions with a volume fraction less than 10%.
At concentrations below 20% volume fraction, the Bachelor equation holds well for hard sphere dispersions:
η = 1 + 2.5 ϕ + 6.2 ϕ^2
What equation is used to find the relative viscosity?
The Krieger Dougherty equation
The Krieger-Dougherty equation is used to model the viscosity of a suspension (a mixture of solid particles in a liquid medium). This equation provides an estimation of the viscosity of a suspension based on the volume fraction of the solid particles within the liquid.
η.r = (1 - ϕ/ϕ.max)^(-η*ϕ.max)
ϕ represents the volume fraction of the solid particles in the suspension.
m is an empirical parameter that depends on the characteristics of the particles and the nature of the interaction between the particles and the liquid.
How does volume fraction, ϕ, vary with particle interactions?
For interacting particles, the particles can feel each other at longer range than their physical dimensions due to either electrical double layer interactions or adsorbed polymer.
This increases the “effective” volume fraction of the particles and hence increases the viscosity.
At low volume fractions, the polymer (or double) layers do not interpenetrate and the system is a viscous liquid.
However, as the volume fraction increases the layers overlap and compress to give an effective network throughout the system. At this point the system becomes predominantly elastic with G’ (storage modulus)
dominating G’‘(loss or viscous modulus).
This gives us a method of controlling the rheology of a dispersion simply by changing the particle concentration and the nature of the adsorbed polymer layer.
How can you control rheology?
By controlling the interactions between particles
Using additives
Adding particle thickeners (e.g. clay or find silica)
Adding polymer solutions (e.g. polysaccharides)
Are the following endothermic or exothermic?
Glass transition temperature
Melting
Crystallisation
How would that be seen on a DSC graph?
Glass transition - endothermic
Melting point - endothermic
Crystallization - exothermic
On the graph produced by DSC (temperature - x by heat flow - y), exothermic processes show peaks and endothermic processes show troughs.
How does a confocal microscope work?
Light, often from a laser, passes through a pinhole/small (excitation aperture and is focussed by an objective lens into a small area on the surface of a sample.
As the light hits the sample, only light from the focal plane is collected by an objective lens.
The collected light passes through a second pinhole (emission pinhole), allowing only in-focus light to reach a detector.
A confocal microscope uses point illumination and a pinhole in an optically conjugate plane in front of the detector to eliminate out-of-focus signal.
As only light produced by fluorescence very close to the focal plane can be detected, the image’s optical resolution, particularly in the sample depth direction, is much better than that of wide-field microscopes.
However, as much of the light from sample fluorescence is blocked at the pinhole, this increased resolution is at the cost of decreased signal intensity – so long exposures are often required.
To offset this drop in signal after the pinhole, the light intensity is detected by a sensitive detector, usually a photomultiplier tube (PMT) or avalanche photodiode, transforming the light signal into an electrical one.
What is dynamic light scattering?
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution.
A monochromatic light source, usually a laser, is shot through a polarizer and into a sample. The scattered light then goes through a second polarizer where it is collected by a photomultiplier and the resulting image is projected onto a screen. This is known as a speckle pattern.
All of the molecules in the solution are being hit with the light and all of the molecules diffract the light in all directions. The diffracted light from all of the molecules can either interfere constructively (light regions) or destructively (dark regions).
This process is repeated at short time intervals and the resulting set of speckle patterns is analyzed by an autocorrelator that compares the intensity of light at each spot over time.
When light hits small particles, the light scatters in all directions (Rayleigh scattering) as long as the particles are small compared to the wavelength (below 250 nm). Even if the light source is a laser, and thus is monochromatic and coherent, the scattering intensity fluctuates over time.
This fluctuation is due to small particles in suspension undergoing Brownian motion, and so the distance between the scatterers in the solution is constantly changing with time.
This scattered light then undergoes either constructive or destructive interference by the surrounding particles, and within this intensity fluctuation, information is contained about the time scale of movement of the scatterers. Sample preparation either by filtration or centrifugation is critical to remove dust and artifacts from the solution.
What’s SPM?
Scanning/surface probe microscopy
These include: atomic force (AFM), scanning tunnelling (STM), and AFM IR microscopy
What’s the Gaussian lens equation?
1/f = 1/s1 + 1/s2
This equation provides the fundamental relation between the focal length of the lens and the size of the optical system.
Where:
f - focal length
s1 - object distance
s2 - image distance
What’s the purpose of a condenser in microscopy?
Illuminate the object at the point on which objectives are focused
Provide uniform illumination
Supply light cone sufficiently large
for objective
Enhance resolution
Numerical aperture adjustment
What’s the Mie scattering theory?
A generalized solution that describes the scattering of an electromagnetic wave by a homogeneous spherical medium having a refractive index different from that of the medium through which the wave is traversing.
- Particle size < wavelength / 10 => Rayleigh’s scattering
- wavelength/10 < Particle size < wavelength => Mie scattering
- Particle size > wavelength => Optical scattering
What is QELS / PCS?
In Dynamic Light Scattering, also called quasi elastic light scattering QELS, or photon correlation spectroscopy, PCS the time-dependent fluctuations in the scattered light are measured by a fast photon counter.
The fluctuations are directly related to the rate of diffusion of the particle through the solvent.
Therefore, the fluctuations can be analysed to determine a hydrodynamic radius for the particle.
From this we can calculate the second order autocorrelation coefficient:
g^2 = B + β*e^(-2Γτ)
Where:
B - baseline of the correlation function at infinite delay
β - correlation function amplitude at zero delay
Γ - decay rate
τ - time (passed)
How do you calculate the second order autocorrelation coefficient for PCS (photon correlation spectroscopy / dynamic light scattering / QELS)?
g^2 = B + β*e^(-2Γτ)
Where:
B - baseline of the correlation function at infinite delay
β - correlation function amplitude at zero delay
Γ - decay rate
τ - time (passed)
How is the magnitude of scattering vector, q, calculated?
q = (4* pi* n0 *sin(θ/2))/λ
Where:
n0 - solvent refractive index
λ - wavelength of incident light
θ - scattering angle
What’s the Stokes-Einstein equation?
What’s it used for?
Calculating hydrodynamic radius:
r.h = (kT) / (6piηD)
Where:
k- Boltzmann’s constant
T - temperature in K
η - solvent viscosity
D - Diffusion constant
What rule is considered for Raman spectroscopy?
∂a / ∂r ≠ 0
Where:
a is polarizability of a molecule
- At a small mutual distance between electrons and nuclei (compact molecule, tightly bound), an external electric field has a weaker influence on the molecule due to stronger interactions within the molecule (and vice versa).
- As the mutual distance between electrons and nuclei changes through molecular vibrations, the molecule’s polarizability (α) and induced dipole moment can be altered.
How is the ratio of the number of particles or molecules in an excited state (Ns) to the total number of particles or molecules (N0 ) in a system expressed?
Ns/N0 = e^(-dE/kT)
Where:
Ns - # particles in excited state
N0 - total # particles
dE - energy change
k - Boltzmann constant
T - temperature
How do you know if a molecule can be detected via Raman spectroscopy?
Presence of Polarizability:
Raman spectroscopy detects the vibrational modes of molecules, so molecules with a change in polarizability during vibration are detectable. For example, molecules with polarizable bonds or functional groups that induce a change in dipole moment during vibration are suitable for Raman spectroscopy.
Raman-Active Vibrations:
Molecules must possess Raman-active vibrational modes. Not all vibrational modes are detectable by Raman spectroscopy. The molecule should have modes that cause a change in polarizability, resulting in observable Raman scattering.
Scattering Efficiency:
The intensity of Raman scattering depends on the efficiency of interaction between the incident light and the molecule. Some molecules might have weak Raman signals due to low scattering efficiency, while others exhibit strong Raman signals.
Fluorescence Interference:
Molecules prone to strong fluorescence might hinder Raman signal detection. If the fluorescence signal overlaps with the Raman scattering region, it could mask or interfere with the Raman signal.
For a molecule to exhibit a Raman effect, there must be a change in its electric dipole-electric dipole polarizability with respect to the vibrational coordinate corresponding to the rovibronic state. The intensity of the Raman scattering is proportional to this polarizability change.
Transitions which have large Raman intensities often have weak IR intensities and vice versa. If a bond is strongly polarized, a small change in its length such as that which occurs during a vibration has only a small resultant effect on polarization. Vibrations involving polar bonds (e.g. C-O , N-O , O-H) are therefore, comparatively weak Raman scatterers. Such polarized bonds, however, carry their electrical charges during the vibrational motion, (unless neutralized by symmetry factors), and this results in a larger net dipole moment change during the vibration, producing a strong IR absorption band.
What’s a polarizability ellipsoid?
A graphical representation used to describe the anisotropic polarizability of a molecule or a crystal.
The lengths of the ellipsoid’s axes and their orientations convey information about the magnitude and directionality of polarizability along different axes within the molecule or crystal structure.
How is average pore size, r, calculated for cylindrical and slit shaped pores?
r = 2*V.tot / S
Where:
V.tot - total pore volume
S - pore surface area
What does the Kelvin equation show?
For a liquid drop or a filled capillary of radius r, then the vapour pressure po* above that liquid is given by:
ln (po/po) = (2γ*Vm)/(rRT)
Where:
po* - vapour pressure above liquid
po - vapour pressure for a flat liquid surface
γ - surface tension
Vm - molar volume
r - pore size
R - gas constant
T - temperature (K)
How does a BET analyser work?
- A given amount of adsorptive gas is expanded into a vessel containing the adsorbent sample
- Upon expansion the adsorptive gas is partly adsorbed on the surface of the adsorbent, partly remaining as gas phase.
- By a mass balance at equilibrium, the amount of gas being adsorbed can be calculated if the volume which cannot be penetrated by the adsorptive gas is known.
What factors affect drug release?
- Structure of drug and polymer
- Drug and polymer solubility
- Interactions between water, drug and polymer
- Polymer/drug ratio
- Distribution of drug in polymer matrix
ATR-FTIR spectroscopy is a useful tool to study aqueous solutions and drug release.
Combination with the imaging provides a powerful method.
What is heat, Q, considering kinetics and thermodynamics?
Kinetics: heat is a form of energy produced by the motion of atoms and molecules (kinetic theory)
Thermodynamics: heat is related to the internal energy (U) of a system and work done on a system (W) through the First Law of Thermodynamics: U = Q + W,
Where U, Q, and W are internal energy, heat, and work done on a system respectively.
How is enthalpy, H, calculated?
H = U + PV
dH = dQ + VdP = TdS + VdP
How is heat capacity calculated?
Cp(T) = dQ / dT = (dH/dT).P
Heat capacity indicates how much heat is transferred to a system as temperature increases
Regarding thermal analysis techniques, what approach is best for kinetics and thermodynamic studies?
Kinetic: isothermal heat treatment (constant T with time). Study phenomena occurring away from equilibrium temperature.
Thermodynamic: increasing T with time. Study phenomena occurring near equilibrium T, ramp up from below to above equilibrium temp. to trigger transformation.
What are some key parts of a (particle-particle) separation distance vs interaction energy (kT) graph (for the total interaction between particles)?
As separation distance increases, there is a sharp increase in interaction energy from -ve to +ve, starting from point A. This reaches a max, point B, then sharply decreases to point C and plateaus.
A = Primary Minimum (Potential Energy Well):
The primary minimum (A) represents the lowest point in the potential energy curve between two particles.
Particles within this energy well experience an attractive force, indicating a stable equilibrium position with a low potential energy. This suggests that the particles are favourably interacting and may form stable structures or bonds at this distance.
B = Primary Maximum:
The primary maximum (B) is the highest point in the potential energy curve between particles.
At this point, the potential energy reaches its maximum value, indicating a point of instability or repulsion between the particles. This suggests that the particles strongly repel each other at this specific distance.
C = Secondary Minimum:
The secondary minimum (C) refers to a subsequent, smaller potential energy well that appears after the primary maximum.
In this region, particles experience a weaker attraction compared to the primary minimum (A). While the potential energy is higher than at A, it still represents a stable configuration for the particles but with less stability than the primary minimum.
What’s rheology?
The study of the flow and deformation of materials.
What is a modulus?
A constant or coefficient that expresses usually numerically the degree to which a substance or body possesses a property (as elasticity).
A constant factor or ratio.
What is Young’s modulus?
How is it found?
The Young’s modulus (E) is a property of the material that tells us how easily it can stretch and deform and is defined as the ratio of tensile stress (σ) to tensile strain (ε).
It measures the tensile or compressive stiffness when the force is applied lengthwise.
E = σ / ε
A high Young’s modulus value indicates the high stiffness of a material and its resistance to (elastic) deformation under load.
What is the Shear modulus?
How is it found?
The shear modulus, also known as the modulus of rigidity, is a material property that measures the stiffness of a solid material in response to shear stress.
G = τ / γ
G - shear modulus
τ - shear stress
γ - shear strain
A large shear modulus value indicates a solid is highly rigid.
How is Young’s modulus (E) different to the Shear modulus (G)?
They relate to different types of deformation.
Young’s Modulus describes a material’s response to tensile or compressive stress, where the material experiences elongation (tension) or compression along its length.
Shear Modulus measures a material’s response to shear stress, where the material undergoes deformation by sliding layers over each other in a parallel fashion.
When is the cross model (rheology) used?
It is characterised by a shear thinning region linking a low shear limiting viscosity and a high shear limiting viscosity.
η = η∞ + (η0 - η∞)/(1+(k*γ)^m
n0 - zero shear viscosity
η∞ - infinite shear viscosity
K - cross constant
m - shear thinning index
k - consistency index
γ - shear rate
What is the yield stress of a material?
The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.
The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation.
What’s a frequency sweep?
In rheology, a frequency sweep is an experimental technique used to study the viscoelastic properties of materials as a function of the applied frequency.
It’s a fundamental test conducted on viscoelastic materials to understand how their mechanical properties, such as elasticity and viscosity, vary with changes in the frequency of applied stress or strain.
The frequency sweep can tell us about the time scales of stress relaxation in a material.
By probing the structure as a function of frequency in the linear viscoelastic region (i.e. below the critical strain) we can determine the balance between elastic and viscous processes at different timescales.
What are the storage and loss moduli?
The storage modulus (G’) and loss modulus (G’’) are rheological parameters used to characterize the viscoelastic behavior of materials.
G’ represents the energy stored and later recovered by a material when subjected to deformation. It reflects the material’s elasticity or stiffness.
G’’ represents the energy dissipated as heat when a material undergoes deformation. It reflects the material’s viscosity or ability to flow.
What interparticle forces are considered when looking at the rheology of dispersions?
Predominantly attractive and repulsive
Attractive:
- van der Waals attractive force
- polymeric depletion flocculation forces
- polymeric bridging flocculation
Repulsive:
– electrostatic repulsion between similarly charged particles
– steric interactions between adsorbed polymer layers The balance between all of these forces determines the overall stability of a system.
Define Elastic (Storage) Modulus
A measure of how much energy must be put into the sample in order to distort it.
Define plastic viscosity
The plastic viscosity is the slope of the shear stress, shear rate curve for stresses higher than the yield value. Strictly this applies to a Bingham fluid, but generally it’s the slope of the linear portion of this curve.
μp is the plastic viscosity, denoting the material’s resistance to flow once the yield stress is exceeded.
How would you measure Yield Stress?
Creep experiments.
Applied shear rate is increased. Shear stress at which the strain significantly increases would be the yield stress.
(Can also be done by measuring the shear stress as a function of shear rate - when this stress causes the fluid to flow this would be the yield value).
How would you measure Elastic (storage) modulus?
Elastic modulus is best measured by an oscillatory shear experiment when an oscillatory strain is applied, and the stress is measured (or vice versa).
The elastic modulus is then calculated by:
G’=τ/γ cos δ
Where τ is max stress, γ is max strain, and δ is the phase shift of the strain to the stress (or vice versa).
Both the yield stress and the elastic modulus have the same units, Pa, but measure different aspects of the material, explain exactly what each parameter represents.
The yield stress is the stress required to irreversibly destroy any structure in the sample.
The elastic modulus is the stress required to elastically deform the structure i.e reversibly.
What is the difference between static light scattering and dynamic light scattering?
SLS measures the intensity of scattered light at a fixed angle (usually 90 degrees) without considering changes over time. It assesses the distribution of particle sizes or molecular masses in a sample.
From this using the Fraunhofer equation the particle size can be determined over the range 1 um-1mm or thereabouts.
DLS monitors the fluctuations in scattered light intensity over time due to Brownian motion of particles in the solution. It measures the temporal fluctuations in scattering intensity caused by particles moving within the detection volume.
From data, the diffusion coefficient and hence hydrodynamic particle size can be determined. In order to be valid Brownian motion must be significant and sedimentation minimal so works from about 5 nm to 5 micron
How does static (low angle) light scattering differ from x-ray scattering and neutron scattering in terms of the range of interactions and structure that can be probed by each?
The principles are the same but the structures which can be determined depend on wavelength of the radiation, thus light can look at structures larger than light wavelength i.e 500 nm and upward.
Neutrons ( and x-rays) much smaller, fractions of nm and upwards typically up to 10-100 nm depending on the angle, the smaller than angle the larger the object which can be studied.
What technique would you choose to use to determine the particle size of the following? Briefly explain your choice.
(i) Latex particles which are to be used in a paint (approx. 200nm in
radius)
(ii) Fog Droplets in air (approx. 200µm in radius)
(iii) Yeast in a bioreactor (approx. 2500 nm in diameter)
(iv) Gold nanoparticles which are adsorbed onto an alumina support.
(i) Dynamic light scattering, its simple quick cheap and easy.
DLS is suitable for nanoparticles in the sub-micron range, like latex particles. It provides size distribution and average size measurements. SAXS is also effective for nanoscale particles and offers information on particle sizes, shapes, and structures.
(ii) Static light scattering, pretty much the only choice really, size range is suitable
(iii) Pretty much anything actually, either light scattering technique SEM or even optical microscopy would be OK
(iv) SEM or TEM, would pick up the gold on the alumina OK, Light scattering no as it would only measure the larger alumina support
Sketch the N2 sorption isotherm at 77 K of this activated carbon.
Label important features on the isotherm and indicate what they
represent.
x-axis = relative pressure (P/P0)
y axis = amount adsorbed (moles, mmol/g)
Hysteresis due to differences in adsorption and desorption.
Bottom line is adsorption, top line is desorption.
The isotherm should display a type I/IV isotherm shape including:
- knee indicating completion of monolayer coverage/micropore filling
- slope for multilayer filling
- hysteresis indicative of mesoporous nature.
How is the moles of gas adsorbed, n.ads, calculated?
n.ads = V.tot / Vm
Where:
V.tot - total pore volume
Vm - molar volume (of liquid N2 at 77 K = 34.65 cm3/mol)
n.ads = PV/(RT)
Where:
P - standard pressure (10^5 Pa)
V - volume of N2 adsorbed at P/P0 = 0.97
R - gas constant
T - standard temp (298K)
How is total pore volume calculated?
V.tot = P.sV.adsV.m / (R*T.s)
Where:
P.s - standard pressure (10^5 Pa)
V.ads - volume of N2 adsorbed at P/P0 = 0.97
V.m molar volume of liquid N2 at 77 K (34.65 cm3/mol)
R: gas constant
T: temperature
OR
V.tot = n*Vm
n - volume adsorbed (mmol/g)
V.m molar volume of liquid N2 at 77 K (34.65 cm3/mol)
What are RBMs?
Radial breathing modes (RBMs) are vibrations that happen in tiny structures like carbon nanotubes.
Imagine these tiny tubes made of carbon atoms, like rolled-up sheets of graphene.
When these tubes vibrate, they do so in a way that looks like they’re expanding and contracting radially, like the way your chest expands and contracts when you breathe.
This expansion and contraction are what we call radial breathing modes.
Compare upright vs inverted TERS:
Inverted:
* Imaging with ca.10 nm spatial resolution
* Higher Raman collection efficiency
* Transparent or very thin samples only
Upright:
* Imaging with 20-50 nm spatial resolution
* More difficult to obtain optimal polarisation
* Suitable for opaque and thick samples
Which spectroscopic technique would you use to differentiate single-walled carbon nanotubes of different diameters?
Explain why
TERS – tip-enhanced Raman spectroscopy: a novel technique that combines the high spatial resolution of atomic force microscopy (AFM) with the chemical information of
Raman spectroscopy.
This breaks the diffraction limit associated with confocal Raman microscopy.
Metal-tip covered with nano-particles gold (or silver) that produce
surface-enhanced effect at the edge of the tip
Therefore, the signal measured will be localised significantly better than the focus of laser beam in Raman microscopy, achieving spatial resolution on the order of nm, suitable for differentiation of carbon nanotubes (SWCNT).
Can use upright illumination (for non-transparent
samples) and inverted illumination (for transparent samples).
Differentiation of different carbon nanotubes by obtaining TERS spectra from the small area of dispersed nanotubes, where different Raman signals from bundles of carbon nanotubes of different diameters provide the opportunity to differentiate their locations within the mixture.
This is possible because wavenumber of the corresponding radial breathing modes (RBM) are
directly related to the diameters of SWCNT -plotting distribution of intensity of RBM would allow to obtain image showing distribution of SWCNT of a particular diameter.
How would you measure the distribution of substances during tablet dissolution using FTIR spectroscopic imaging?
FTIR spectrometer and infrared array detector used to measure thousands
of spectra simultaneously from different locations within the sample.
The main approach to study tablet dissolution is macro ATR-FTIR imaging. t
ATR accessories include an inverted prism accommodated in a large sample compartment (or macro chamber) of a spectrometer.
The main reason for the choice of ATR is because water strongly absorbs IR radiation, whilst the ATR probes layer of only a few
um thick
The inverted prism crystals are made of ZnSe, diamond, Si, or Ge.
Areas from ca. 1 mm2 to a few cm2 studied.
This approach is suitable for studies of dynamic systems (e.g. dissolving tablet) to detect concertation profiles of drug, polymer and water within interfacial areas of tablet/aqueous medium.
How does DSC scan rate influence results?
The scan rate refers to the rate at which the temperature of the sample is changed (C / min)
Faster scan rate: greater sensitivity because flow increases
Slower scan rate: better resolution because of thermal gradients
How does the spatial resolution of micro ATR-FTIR compare to FTIR?
Micro-ATR-FTIR imaging offers greatly improved spatial resolution compared to more conventional transmission FTIR spectroscopic imaging.
Micro ATR-FTIR imaging uses a microscope with a Ge crystal objective to increase the numerical aperture and spatial resolution.
This results in micro ATR-FTIR providing higher spatial resolution (2-3 um), but images are of a small area (50 x 50 um2)
Spatial resolution is defined by the Rayleigh criterion, r=1.22λ/2NA where NA is numerical aperture of the system (NA=n sinθ).
r is the minimal distance required to have a contrast of 26.4 % between 2 objects nearby.
When imaging in micro ATR-FTIR mode, IR light approaches the sample through a high refractive index material which provides an opportunity to increase its NA, improving spatial resolution. (Ge enhances SR by 4 times)
It is possible to increase spatial resolution in transmission using an objective with a high NA, but also using a solid immersion lens.
Describe (with the aid of a diagram if helpful) two experiments that can be used to
assess the thixotropy of a complex fluid:
- Shear rate sweep experiment – this involves applying a range of shear rates to the fluid and measuring the resulting changes in viscosity over time.
- Time sweep experiment – a constant shear rate is applied to the fluid and changes with viscosity over time are measured.
- Oscillatory rheology experiment – the fluid is subjected to oscillatory shear stress, and the changes in viscosity and storage (elastic) and loss (viscous) moduli are measured over time. Analyse the phase angle, which looks at the relationship between elastic and viscous responses. Thixotropic fluids will exhibit a crossover frequency between G’ and G”, corresponding to the transition from solid-like to fluid-like behaviour. G’ starts > G”, then should cross, and G” would be > G’
- Creep and recovery experiment – constant stress (creep) applied to fluid for defined period, followed by removal of the stress (recovery) and a measurement of the fluid’s ability to return to its original state
Compare chemisorption vs physisorption:
Physisorption:
* Weak, long range bonding
* VdW interactions
* Not surface specific
* Enthalpy adsorption: 5-50 kJ/mol
* Non-activated. Increasing temperature always reduces surface coverage
* No reaction
* Multilayer adsorption
Chemisorption:
* Strong, short range bonding
* Surface specific
* Enthalpy adsorption: 50-500 kJ/mol
* Activation energy (often) - increasing temperature can favour adsorption
* Surface reaction
* Monolayer adsorption
Explain the working principle of an infrared focal plane array detector:
It is used to image and detect electromagnetic waves (9-14um).
An array of photosensitive elements is arranged on the focal plane array detector. Infrared rays emitted from infinity are imaged on these photosensitive elements of the focal plane array through the optical system.
The detector converts the light signal into an electrical signal and performs integral amplification, sampling, output buffer and multiplexing system, and is finally sent to the monitoring system to form an image.
What is the equation for depth of penetration in microscopy?
dp = λ / (2π (n1^2*sin^2 θ - n2^2)^0.5)
