Chapter 32 – STRUCTURE FACTORS FOR
This presentation is the property of its rightful owner.
Sponsored Links
1 / 8

Chapter 32 – STRUCTURE FACTORS FOR PARTICULATE SYSTEMS PowerPoint PPT Presentation


  • 58 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Chapter 32 – STRUCTURE FACTORS FOR PARTICULATE SYSTEMS

An Image/Link below is provided (as is) to download presentation

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 - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 32 structure factors for particulate systems

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


Chapter 32 structure factors for particulate systems

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:


Chapter 32 structure factors for particulate systems

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:


Chapter 32 structure factors for particulate systems

RESULT

Inter-particle structure factor:

Scattering cross section:


Chapter 32 structure factors for particulate systems

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


Chapter 32 structure factors for particulate systems

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


Chapter 32 structure factors for particulate systems

RESULT

Inter-particle structure factor:

Scattering cross section:


Chapter 32 structure factors for particulate systems

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.


  • Login