Chapter 32 – STRUCTURE FACTORS FOR PARTICULATE SYSTEMS

Download Presentation

Chapter 32 – STRUCTURE FACTORS FOR PARTICULATE SYSTEMS

Loading in 2 Seconds...

- 70 Views
- Uploaded on
- Presentation posted in: General

Chapter 32 – STRUCTURE FACTORS FOR PARTICULATE SYSTEMS

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Chapter 32 – STRUCTURE FACTORS FOR

PARTICULATE SYSTEMS

32:1. THE ORNSTEIN-ZERNIKE EQUATION

32:2. THE PERCUS-YEVICK APPROXIMATION

32:3. THE MEAN SPHERICAL APPROXIMATION

h(r)

c(r)

Hard Sphere

Screened Coulomb

U(r)

Square Well

r

32:1. THE ORNSTEIN-ZERNIKE EQUATION

The OZ equation:

Take Fourier transform:

Inter-particle structure factor:

Interaction potentials:

Hard Sphere

U(r)

r

32:2. THE PERCUS-YEVICK APPROXIMATION

PY closure relation:

Hard-sphere interaction potential:

PY solution of the OZ equation:

.

Parameters:

Result:

RESULT

Inter-particle structure factor:

Scattering cross section:

FORM FACTOR P(Q) AND STRUCTURE FACTOR SI(Q)

Screened Coulomb

U(r)

r

32:3. 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

RESULT

Inter-particle structure factor:

Scattering cross section:

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.