Assessed workshop questions for

CHM6201
Polymer Characterization and Analysis. Part B

Please, return your answers via email to [email protected]
before 9am on 16th December 2020. Insert in the email subject a phrase
"Workshop answers" followed by your name.


1. A sample of polystyrene foam has been analysed by small-angle X-ray scattering. It
has been determined that Porod’s constant of this system is 9.8 × 10-4 cm-1 Å-4.
Calculate the specific surface area of the polymer, assuming that the mass density of
polystyrene is 1.05 g/cm3 and scattering length density of air occupying the foam
pores is 0.0 cm-1. Express your answer in m-1 units. Considering that the interfaces
between polymer and air are sharp, draw a schematic Porod plot for the studied
material, include scaling for the y-axis.
[6 marks]

2. Prove that 02 sinq k  , where q is the modulus of the scattering vector, k0 is the
modulus of the wave vector and  is the half of the scattering angle. Use a schematic
drawing if required.
[4 marks]
3. Guinier approximation can be used to measure the radius of gyration of objects
from their scattering pattern. Explain the meaning of the term radius of gyration.
[2 marks]
4. Answer both parts of this question. SAXS measurements of 1vol% dispersion of low-
dispersity worm-like micelles formed by self-assembled block copolymers in water
suggest that their contour length is about 100 nm and the cross-section diameter is 7
nm.
(i) Given that the scattering length density of the copolymer molecules is 10.2 × 1010
cm-2 calculate differential scattering cross-section per unit sample volume at q = 0
nm-1, where q is length of scattering vector. Express your answer in cm-1 units.
[4 marks]
(ii) How would the differential scattering cross-section per unit sample volume change
at q = 0 nm-1 if the worm-like micelle diameter increases by a factor of three, while the
particle volume concentration in the dispersion remains unchanged at 1 vol%?
[4 marks]
5. The theory describing scattering of electromagnetic radiation considers three cases:
the Rayleigh-Gans-Debye approximation, general Mie theory and Fraunhofer
approximation (diffraction). Which of these cases should be used for analysing static
light scattering of a dispersion of spherical polymer particles in water if their diameter
is about 10 microns, wavelength of light used for the measurements is 628 nm and the
refractive indexes of water and the polymer are 1.33 and 1.60, respectively? Justify
your answer.
[4 marks]




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