1) Mark-Houwink equation-based question:

Explain the Mark-Houwink relationship and its significance in calculating the molecular weight of a polymer.
When does the Flory equation be similar to the Mark-Houwink equation?

2) Use the datasets of polyvinyl alcohol (in water) and polystyrene (in cyclohexane) provided in the tables below and:

Calculate molecular weight, A2, and radius of gyration of both polymers by preparing Zimm plots.
Compare the obtained data for both systems and elaborate on whether the values obtained are reasonable or not.
What is the importance of the extrapolation of data to small angles and zero concentrations?

We know that:

We will use 600 nm as the wavelength of the incident light (l or l0) for this problem.
Assume dn/dc (specific refractive increment) as 0.10 mL/g and 0.20 mL/g for PVA and polystyrene solutions, respectively.
The Refractive index for the solvent (water): is 1.4898, and for cyclohexane is 1.4678
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 ‘50’ in this question.
R(q) or DR = Rayleigh’s ratio; this, as we discussed, is required to obtain the absolute scattered light intensity from the relative scattered light intensity. That is, the absolute scattered light intensity is directly related to the molar mass of the polymer.
q – scattering angle
P(q) – form factor (angular dependence) – this incorporates the effects of chain size and conformation on the angular dependence of scattered light intensity

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