Polystyrene exhibits co-solvency with acetone and alkanes at room temperature However to find the correct composition: Material Science Assignment, NTU, Singapore

• Polystyrene exhibits co-solvency with acetone and alkanes at room temperature. However, to find the correct composition, assume that we have used acetone: hexane solvent mixtures as 20:80, 50:50, and 80:20. An osmotic pressure technique was employed on these systems at room temperature (298K) and the data obtained was given below. The solvent (mixture) density varies as 0.666 g/cm3, 0.7057 g/cm3 and 0.8062 g/cm3 and for 20:80, 50:50, and 80:20 mixtures.

Concentration versus osmotic pressure data for polystyrene with different
ratios of solvent mixture

1. Determine the molecular weight of the polymer and the second virial coefficient (A2) in each mixture of solvents. Assume that A3 and subsequent coefficients are negligible.
2. Based on the obtained data, which solvent mixture is a good solvent for
   polystyrene? Explain.
3. Looking at the molecular weights, A2 values, and osmotic data, are the obtained results reasonable? Justify your choice with proper reasoning.
4. Are these ideal or non-ideal solutions? Explain.

Use the dataset of polystyrene provided in the table below and:

• Calculate molecular weight, A2, and radius of gyration of the polymer by preparing a Zimm plot.
• Explain the obtained data.
• What is the importance of extrapolation of data to small angles and zero
  concentrations?

We will use a 660 nm wavelength light (l or l0) for this problem.
dn/dc = 0.10 mL/g
Rayleigh ratio for the solvent used: 1.207 x 10-3
/m
Refractive index for the solvent: 1.4898.
K – optical constant (depends on the refractive index, no, of the pure solvent)
c or c2 – polymer concentration
k (used in the plot) – arbitrary mathematical constant added to provide spacing between
curves (no physical meaning). For consistency, let us take it as ‘75’ in this question.
R(q) or DR = Rayleigh’s ratio
q – scattering angle