Chapter 32

1
Chapter 32 STRUCTURE FACTORS FOR PARTICULATE
SYSTEMS
321. THE ORNSTEIN-ZERNIKE EQUATION
322. THE PERCUS-YEVICK APPROXIMATION
323. THE MEAN SPHERICAL APPROXIMATION
2
321. THE ORNSTEIN-ZERNIKE EQUATION
The OZ equation
Take Fourier transform
Inter-particle structure factor
Interaction potentials
3
322. THE PERCUS-YEVICK APPROXIMATION
PY closure relation
Hard-sphere interaction potential
PY solution of the OZ equation
.
Parameters
Result
4
RESULT
Inter-particle structure factor
Scattering cross section
5
FORM FACTOR P(Q) AND STRUCTURE FACTOR SI(Q)
6
323. THE MEAN SPHERICAL APPROXIMATION
Screened Coulomb interaction potential
MSA closure relation

MSA solution of the OZ equation
Take Fourier transform to obtain tedious result
not reproduced here
7
RESULT
Inter-particle structure factor
Scattering cross section
8
COMMENTS
-- The OZ equation along with one of the closure
relations (the PY or the MSA for charged
systems) is used to calculate the structure
factor for scattering particles. -- Structure
factors are needed to mode the cross section for
concentrated systems.