Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 20

V

O ′

k s

r M ′

θ

q

O

M

k i

De nition of the scattering parameters in a light scattering experiment: scattering wave vector q , Figure 2.1

scattering angle θ , scattering volume V.

Usually the wavelength of the incident beam is changed very little by the scattering
process, so

jk i j jk s j:

The scattering wave vector is determined by

q ¼ k s k i : ð 2 : 1 Þ

In light scattering,

2k i sin 2 ¼

4 π

λ i

sin 2 : q ¼ ð 2 : 2 Þ

In X-ray scattering, the scattering vector is generally de ned by s =( k s - k u )/(2 π ), so that

2
λ i

s ¼ sin θ;

or

q
2

s ¼

π :

ð 2 : 3 Þ

The path difference of a point O 0 is speci

ed by the vector r against the origin O. Then the

phase lag is

¼ : ð 2 : 4 Þ

rq

For X-rays the amplitude of the waves scattered by scattering volume dV is

e i2 π s r dV

dA ðsÞ¼ A e ρðrÞ ; ð 2 : 5 Þ