Questions from class - Lecture 4

Question 1

What is the definition of the scattering vector?

Answer 1

The scattering vector is the difference between the incident wavevector and the scattered wavevector:

q = k_i - k_s.

For elastic scattering:

q = 4πn/lambda * sin (theta/2)

Question 2

What is the form factor of a chain with a certain radius of gyration?

Answer 2

P(q) = 1/N^2 * ∑∑ sin(qR_ij)/qR_ij.

For small scattering angles qR_ij = qR_g, and a Taylor expansion can be used:

P(q) = 1 - 1/3q^2 + …

Question 3

What is the Guinier approximation?

Answer 3

P(q) ≈ exp[-1/3 * q^2]

for qR_g < 1

Question 4

Which regimes does a scattering curve of a single polymer feature?

Answer 4

Intermolecular regime, Guinier regime and the fractal regime.