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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. h(r). c(r). Hard Sphere. Screened Coulomb. U(r). Square Well. r. 32:1. THE ORNSTEIN-ZERNIKE EQUATION.

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Chapter 32 – STRUCTURE FACTORS FOR PARTICULATE SYSTEMS

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  1. 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

  2. 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:

  3. 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:

  4. RESULT Inter-particle structure factor: Scattering cross section:

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

  6. 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

  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.

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